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Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations
Journal Pre-proofs Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations Esther J. Ocola, Jaan Laane PII: DOI: Reference:
S0301-0104(19)31153-X https://doi.org/10.1016/j.chemphys.2019.110647 CHEMPH 110647
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Chemical Physics
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Please cite this article as: E.J. Ocola, J. Laane, Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations, Chemical Physics (2019), doi: https://doi.org/10.1016/j.chemphys.2019.110647
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Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations Esther J. Ocola and Jaan Laane* Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255
Abstract With the aid of ab initio calculations, the one-dimensional representations of the ringpuckering vibrations of several four-membered ring molecules have been refined. These onedimensional models include contributions from MH2 (M= C, Si, Ge) rocking motions and utilize the computed parameter ω which reflects the relative amounts of ring angle bendings. This model leads to much more accurate determinations of the coordinate dependent kinetic energy expressions 𝑔44(x) which in turn allow much more accurate calculations of the ring-puckering potential energy functions (PEFs) based on experimental data. The resulting experimental PEFs agree remarkably well with the theoretical functions determined from ab initio calculations. For each molecule spectroscopic data were fit very well utilizing the refined kinetic energy functions and two term PEFs. They were fit even better using three term PEFs including x6 terms. The PEFs, barrier heights, and energy minima are presented for each of these molecules and their isotopic species.
Keywords: Potential energy functions; ring puckering vibration; ab initio calculations; refined kinetic energy expressions; four membered rings; far infrared and Raman spectra. * Corresponding author email: LAANE@ CHEM.TAMU.EDU, phone: 979-220-5341 1
1. Introduction We and others have been studying the vibrational potential energy functions of largeamplitude ring-puckering vibrations of four-membered rings and larger molecules for more than half a century [1-13]. For selective molecules, such as those studied in the present work, where the ring-puckering vibrations are of low-frequency, they can be examined independently from the other 3N-7 vibrations based on the separation of high and low frequencies [14,15]. As first pointed out by Bell [10] in 1945, this vibration is of special quantum mechanical interest in that the potential energy function (PEF) for the motion should be governed by a quartic term rather than the usual quadratic one such as that for the harmonic oscillator. As shown by Laane [11], the form of the one-dimensional potential energy function should actually be 𝑉 = 𝑎𝑥4 +𝑏𝑥2
(1)
where 𝑥 is the ring-puckering coordinate as defined in Fig. 1 for silacylobutane (SiCB). The distance between the two ring diagonals is taken to be 2𝑥. Two opposite ring atoms move up a distance 𝑥 from the planar ring structure and two atoms move down a distance 𝑥. Whether the energy minimum for a four-membered ring corresponds to a planar structure where 𝑥 = 0 or to a puckered one depends on the angle strain and torsional forces within the molecule. As shown in detail by Laane [11], if the angle strain in each molecule originates from a quadratic dependence on the interior ring angle deviations from ideality (𝑉~∆ϕ2), both the 𝑎 and 𝑏 coefficients in Eq. (1) would be positive. However, torsional forces such as -CH2-CH2- interactions generally result in negative contributions to 𝑏. Hence, silacyclobutane, which has both -CH2-CH2- and -SiH2-CH2interactions contributing to a negative 𝑏 value, is non-planar with a barrier to planarity of 442 cm-1 as reported in the original far-infrared study [12].
2
Many of the earlier studies which we carried out utilized reduced coordinates, which do not require knowledge of the reduced mass, to fit the experimental data with a reduced potential energy function (PEF). The most common form of the reduced PEF is 𝑉 = 𝐴(𝑍4 ―𝐵𝑍2)
(2)
Fig. 1. Definition of the ring-puckering angle (𝜃), the SiH2 rocking angle (𝛽) and the ringpuckering coordinate (𝑥) for SiCB. The angle 𝛽 is defined as the angle between the bisectors of the CSiC an HSiH angles. All values shown are the results from CCSD/cc-pVTZ computations. where Z is a reduced (dimensionless) coordinate and where the coefficients 𝐴 and 𝐵 can be related to 𝑎, 𝑏 in Eq. (1) if the reduced mass µ is known. Similarly, 𝑥 and 𝑍 can be related for known values of µ. In 1970 Laane [13] provided numerical tables for solutions to the energy levels from Eq. (2) for a large range of 𝐵 values, and these were widely used by many laboratories. One problem with solutions to Eq. (2) is that the ring-puckering energy minima are given in terms of 𝑍 and not in dimensioned units. Hence, the actual puckering minima could not be determined. Another problem with Eq. (2) is that it implies that the reduced mass is fixed, whereas, as is now well known, it varies considerably as a function of the puckering coordinate. To overcome these problems numerical methods for calculating the reduced mass as a function of coordinate were first utilized by Malloy [16] and then fully described by the Laane group [17,18]. This allowed the reciprocal reduced mass functions g44(𝑥) to be calculated with a dependence on the puckering 3
coordinate 𝑥. (Subcripts 1 to 3 on g were reserved for the molecular rotations). The quantum mechanical problem then has the form ∂ ―ћ2 ∂ (𝑥) g 44 ∂𝑥 2 ∂𝑥
(3)
+𝑉(𝑥) = 𝐸𝛹
where 𝑉 is given in Eq. (2) or as shown below including a 𝑥6 term. 𝑉 = 𝑎𝑥4 +𝑏𝑥2 + 𝑐𝑥6.
(4)
In order to correctly calculate the coordinate dependence of g44(𝑥), as pointed out by Gwinn and co-workers [19], it is necessary to know the relative amounts of bending at the interior angles of the four-membered rings. The Gwinn group defined
ω=
(11 ―+ ρρ)
(5)
where 𝜌 for silacyclobutane in Fig. 1 would be 𝜌=
(
)
∆𝑟𝐶𝛽 ― 𝑆𝑖 ∆𝑟𝐶𝛼 ― 𝐶𝛼 𝑟°𝐶𝛽 ― 𝑆𝑖 / 𝑟°𝐶𝛼 ― 𝐶𝛼
(6)
where the 𝑟° are the lengths of the diagonals in the planar molecule, and where the ∆𝑟 are changes in the diagonal distances upon puckering. Thus 𝜌 = 1 and ω = 0 when all of the ring angles decrease equally during ring-puckering. This is the case for cyclobutane. For silacyclobutane, since the CSiC angle bending force constant is less than the CCSi force constant, 𝜌 will be less than 1.0 and ω will be positive. Until recently the correct value of ω could only be roughly approximated. With the advent of reliable ab initio computations, however, we are now able to calculate the 𝜌 values quite accurately and thus get reliable values for ω. These will be utilized for our computations in this work. Another problem with obtaining reliable g44(𝑥) expansions has been the approximation that the ring-puckering vibration is entirely one-dimensional. In previous studies [20] we showed 4
that the SiH2 rocking in 1,3-disilacyclobutane (13Si2CB) is strongly coupled to the puckering motion and we defined a rocking parameter 𝑅 for the amount of rocking that was proportional to the puckering coordinate 𝑥. This parameter 𝑅 is defined as 𝑅 = 𝛽/𝑥
(7)
where 𝛽 in radians is the magnitude of the MH2 (M=C,Si, Ge) rocking and 𝑥 is the puckering coordinate in Å. Similarly, Egawa [21] has defined the same type of parameter for the amount of CH2 rocking
coupled to the puckering of cyclobutane. For cases such as these we are now able to use ab initio calculations to predict quite accurately the amount of MH2 (M = C, Si or Ge) rocking occurring during the puckering vibrations. It should be emphasized that molecules such as cyclobutane (CB) and silacyclobutane (SiCB) each have thirty vibrations and trimethylene oxide (TMO) has twenty four vibrations. Fortunately, most vibrations other than the ring-puckering are of small amplitude so their very small contributions to the overall potential energy surface can quite safely be neglected. We have incorporated the moderate-amplitude MH2 rocking motions into the vibrational model and this has helped considerably in refining the PEFs. We feel that inclusion of additional motions in our model would be of little value. In the present paper we will calculate the structures and conformational energies of the four-membered ring molecules shown below as a function of the puckering coordinate 𝑥. For each 𝑥 value we then determine the relative amounts of angle bending within the ring as well as the amount of CH2 and/or SiH2 and/or GeH2 rocking. This provides us with values for ω and the rocking parameters 𝑅 that we can use to give us much more accurate computations of g44(𝑥) for each molecule. Our expectation is that while the frequency fits with the experimental data may only be somewhat improved, but we will have much more accurate representations of how the
5
potential energy varies with the dimensioned coordinate 𝑥. This will also provide us with much more accurate values for 𝑥 and the puckering dihedral angles that correspond to the energy minima (𝑥𝑚𝑖𝑛). It should be emphasized that the objective of this study is aimed at utilizing ab initio calculations to more accurately refine the model of the one-dimensional ring-puckering vibration and therefore produce much more accurate kinetic energy functions. These in turn result in improved and more meaningful one-dimensional potential energy functions. Although we have used a fairly high level of theory for the computations and this has resulted in theoretical PEFs which agree quite well with the experimental ones, we have not strived to carry out even higher level calculations which could improve the PEFs even more. Such calculations would have taken huge amounts of computing time for each of the molecules we have studied. Moreover, the CCSD/cc-pVTZ computations that we have carried out are more than adequate for refining the vibrational models for the puckering vibration.
2. Calculations 2.1. Structure calculations The geometrical structures of each of these molecules were calculated using CCSD/ccpVTZ and MP2/cc-pVTZ ab initio computations. In the present paper we will primarily discuss the results from the CCSD/cc-pVTZ calculations. The Gaussian 09 program [22] was used for the computations, and the Semichem AMPAC/AGUI program [23] was used to visualize the structures. The calculated geometrical structures of the molecules are shown in Fig. 2 and Fig. 3. 6
supplementary Table S1 compares the experimental geometrical parameters to those from our computations for the puckered and the planar conformations. On the whole, there is a very good agreement. Fig. S1 in the supplementary material presents the calculated geometrical structures of the molecules in their planar conformations. These were also needed for the kinetic energy calculations. Higher level ab initio calculations would be warranted for the molecules with heavier atoms such as Se and Ge. However, we felt that the CCSD/cc-pVTZ computations would nonetheless yield useful estimates for the and values and thus produce better kinetic energy functions. As can be seen in later discussion, the agreement between the experimental PEF and that from theory is poorer for TMSe.
Fig. 2. Calculated structural parameters of CB and related molecules in their minimum energy conformations (puckered) from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å).
7
Fig. 3. Ring-puckering angles of the energetic minimum, 𝜃𝑚𝑖𝑛 from CCSD/cc-pVTZ computations. 2.2. Kinetic energy calculations The Laane RDMS4 program [17,18] based on vector and numerical methods was used to calculate the coordinate dependent kinetic energy functions for the ring-puckering of each of the four-membered ring molecules. The geometrical parameters for the computed planar structures of these molecules provided the input for the program. As discussed above, the ab initio calculations allowed us to calculate for each molecule the 𝜌 and 𝜔 values, which are related to the relative amounts of angle bending, and also the 𝑅 values reflecting the amounts of MH2 or MD2 rocking. (M=C, Si, or Ge). Table 1 presents the calculated 𝜌, 𝜔, 𝑥𝑚𝑖𝑛, 𝛽 and 𝑅 values for each molecule. The expressions for 𝑔44(𝑥) for each molecule are given in Table S2. Fig. 4 shows how 𝑔44(𝑥) varies with the ring-puckering coordinate, 𝑥, for these molecules. As can be seen, in all cases 𝑔44 (𝑥) is largest for the planar structure at x = 0 but decreases as the reduced mass increases as the molecule puckers. As we observed from our calculations on 13Si2CB the reduced mass and 𝑔44(x) 8
values vary a great deal depending on the rocking parameters 𝑅. Hence, the excellent agreement between experimental and theoretical PEFs (to be shown below) resulted from very accurate representations of the vibrational model. It might be noted that in Fig. 4 the similarity in the CB, SiCB, and GeCB 𝑔44(𝑥) functions is coincidental and arises from the fact that 𝑅(MH2) is larger for M=C than for M=Si or Ge. Higher mass values for M produce higher reduced masses but higher reduced 𝑅 values have the same effect. 2.3. Potential energy calculations The one-dimensional quantum mechanical problem is given in Eq. (3). The DA1OPTN Meinander-Laane potential energy program [24] was used to calculate the potential energy functions, energy levels, energy level spacings and ring-puckering barriers for each of the molecules. The constants 𝑎 and 𝑏 in Eq. (1) or 𝑎, 𝑏 and 𝑐 in Eq. (4) were adjusted to give the best least square fit with the experimental data for each molecule. These experimentally fit PEFs were compared to those generated from the 𝑉(𝑥) vs. 𝑥 computations from ab initio calculations. The latter will be referred to as theoretical PEFs.
2.4. Wavefunctions calculations The Hermite polynomial coefficients of the wavefunctions for the potential energy functions were calculated using our DA1OPTN Meinander-Laane potential energy program [24]. The wavefunctions were calculated using MAPLE 2015.1 computing environment [25].
9
Fig. 4. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion. Table 1 Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters. CBa
Calculated constants 𝜌 1.000 𝜔 0.000 Angles, degrees 𝛽𝑚𝑖𝑛(MH2)c,d 5.6° 𝛽𝑚𝑖𝑛(α-CH2) 5.6° 𝛽𝑚𝑖𝑛(β-MH2) 5.6° Rocking parameters, rad/Å 𝑅(MH2)e 0.69 𝑅(α-CH2) -0.69 𝑅(β-MH2) 0.69
TMOb
TMS
TMSe
SiCB
GeCB
13Si2CB
13Ge2CB
CBONE
0.731
0.611
0.635
0.919
0.813
0.612
0.677
1.247
0.155
0.242
0.223
0.042
0.103
0.241
0.193
-0.110
---
---
---
5.5°
4.0°
3.7°
1.3°
---
1.6°
2.8°
3.2°
6.5°
6.2°
6.0°
1.8°
4.9°
3.8°
4.7°
4.8°
4.7°
4.0°
4.9°
1.3°
2.9°
---
---
---
0.59
0.45
0.50
0.49
---
0.29
-0.36
-0.37
-0.70
-0.69
-0.81
-0.69
-1.22
0.66
0.62
0.57
0.50
0.55
0.50
0.49
0.71
a The
calculated values are from CCSD/cc-pVTZ computations. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO. This molecule has a calculated α-CH2 twist angle of about 6° at the minimum energy and 7° at 𝑥 = 0.100 Å. c𝛽 For TMO the value at 𝑥 = 0.100 Å was 𝑚𝑖𝑛 is the value at 𝑥𝑚𝑖𝑛 for all molecules except for TMO. used. d M = C, Si or Ge. e𝑅=𝛽 𝑚𝑖𝑛/𝑥𝑚𝑖𝑛 for all molecules except for TMO. For TMO the value of 𝑅 = (𝛽𝑥 = 0.1 Å)/0.1 was used. b
10
3. Results and discussion For each molecule we will summarize what has been done previously, and then we will present the refined results from our new calculations. Our calculations show only minor changes for cyclobutane since 𝜔 is clearly zero. Moreover, Egawa et al [21] have also previously considered interactions with CH2 rocking in their calculations. However, our refined 𝑔44(𝑥) terms will yield significant improvement for the other molecules, especially for those with SiH2 or GeH2 rocking vibrations.
3.1. Cyclobutane Miller and Capwell [26] first reported the observation of four Raman bands for cyclobutane (CB) and six for cyclobutane-d8 (CB-d8) in 1971. From this data they calculated barriers to planarity of 518 cm-1 for CB, and 508 cm-1 for CB-d8. Stone and Mills [27] in 1970 reported combination band data for a CH2 deformation mode and calculated a barrier of 503 cm-1 for CB. Malloy and Lafferty [16] reworked the data from both groups utilizing coordinate dependent kinetic energy expressions and calculated barriers of 515 cm-1 for CB and 501 cm-1 for CB-d8. Egawa and co-workers [21] in 1987 examined both electron diffraction results and infrared combination band data of CB. They also estimated the extent of the CH2 rocking during the puckering vibration. Their calculated barrier to inversion was 510 cm-1 based on a PEF that included a 𝑐𝑥6 term (Eq. 4). For CB 𝜌 = 1 and 𝜔 = 0 since all of the interior ring angles are equivalent. In our present study we find from the ab initio calculations that 𝑅 = 0.69 rad/Å which reflects a CH2 rocking angle (𝛽𝑚𝑖𝑛) of 5.6° when CB is at its energy minimum with a puckering angle of 29.5°. Egawa and co-workers19 also included rocking in their reduced mass calculation but did not have the computational tools that we have now. They therefore made a best guess
11
estimation for the amount of rocking. Their model predicted 6.2° of CH2 rocking at the energy minima. Using our 𝜔 and 𝑅 parameters we determined the kinetic energy functions for CB and CB-d8 and these are given in Table S2. For clarity we also show g44 (𝑥) for CB below: g44 (𝑥) = 7.032 × 10 ―3 ― 9.515 × 10 ―3𝑥2 +1.238 × 10 ―2𝑥4 ―1.728 × 10 ―1𝑥6.
(8)
Utilizing this and adjusting the 𝑎 and 𝑏 constants in Eq. (1) to obtain the best fit with the experimental data gave us 𝑉𝐶𝐵 (cm-1) = 1.317 × 106𝑥4 ― 5.187 × 104𝑥2 .
(9)
This PEF has an inversion barrier of 511 cm-1, 𝑥𝑚𝑖𝑛= ±0.140 and 𝜃𝑚𝑖𝑛 = ±29.2°. Repeating the calculation including a 𝑐𝑥6 term provided a somewhat better fit with 𝑉𝐶𝐵 (cm-1) = 1.123 × 106𝑥4 ―4.909 × 104𝑥2 + 2.842 × 106𝑥6.
(10)
This has an inversion barrier of 510 cm-1 while 𝑥𝑚𝑖𝑛= ±0.142 and 𝜃𝑚𝑖𝑛 = ±29.6°. It should be noted that the 𝑥6 term is primarily used for refining the shape of the PEF as the range of relevant 𝑥 values are much smaller than unity, resulting in the value of 𝑥6 being very small. The potential energy parameters for Eqs. (1) and (4) were also determined for CB-d8 and CB-d1 using the published infrared combination bands and Raman data [21,26-28]. These are shown in Tables 2 and 3 which also summarize all the relevant parameters for all of the molecules included in the present study. As can be seen, the barriers and energy minima are very similar for CB-d8 and CB-d1 as compared to CB. For each of the cyclobutane isotopic species the frequency fit is quite good using just Eq. (1), but the addition of the 𝑐𝑥6 term produces better fits. For each calculation we have determined the average square deviation (ASD) to assess the quality of the fit. These values, which are listed in Table 4, are determined by squaring the deviation Δ for each transition and then taking the sum and dividing by the number of transition frequencies considered. 12
Table 5 presents the observed transition frequencies for CB and its isotopic species and these are compared to our calculations from the present work. Fig. 5(a) shows the experimentally fit PEF with Eq. (4) and the theoretical ring-puckering PEF for CB. The experimentally observed infrared transitions are also shown in the figure. Fig. 5(b) shows the calculated wavefunctions for the lower energy levels.
Fig. 6 compares the calculated PEFs for the isotopic species of CB from
the experimental data. They are remarkably similar confirming that our refined kinetic energy functions are working as expected. Fig. S2 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for CB and its deuterated species CB-d8 and CB-d1.
13
Table 2 Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Molecule
Barrier cm-1
𝑥𝑚𝑖𝑛
𝜃𝑚𝑖𝑛
𝜔
𝑅(MH2)
𝑅(α-CH2)
𝑅(β-MH2)
104
511
±0.140
±29.2°
0.000
0.69
-0.69
0.69
1.319 × 106
-5.205 × 104
513
±0.140
±29.2°
0.000
0.69
-0.69
0.69
236.1
1.293 × 106
-5.100 × 104
503
±0.140
±29.2°
0.000
0.69
-0.69
0.69
110.4
1.043 ×
106
-9.006 ×
103
19
±0.066
±14.1°
0.155
---
-0.29
0.66
105
-7.768 ×
103
15
±0.062
±13.4°
0.155
---
-0.29
0.66
µ0, u
𝑎, cm-1/Å4
CB
142.2
1.317 ×
106
CB-d1
152.9
CB-d8 TMO
𝑏 cm-1/Å2 -5.187 ×
TMO-αd2
126.7
9.981 ×
TMO-βd2
124.1
1.026 × 106
-8.021 × 103
16
±0.063
±13.4°
0.155
---
-0.29
0.66
TMO-α,α'd4
147.6
9.695 × 105
-7.164 × 103
13
±0.061
±13.1°
0.155
---
-0.29
0.66
162.7
9.840 ×
105
-6.998 ×
103
12
±0.060
±12.8°
0.155
---
-0.29
0.66
105
-2.776 ×
104
273
±0.140
±26.8°
0.242
---
-0.36
0.62
TMO-d6 TMS
121.5
7.068 ×
TMS-αd2
137.3
6.866 × 105
-2.703 × 104
266
±0.140
±26.9°
0.242
---
-0.36
0.62
TMS-βd2
146.4
7.161 × 105
-2.778 × 104
269
±0.139
±26.7°
0.242
---
-0.36
0.62
157.8
6.730 ×
105
-2.634 ×
104
258
±0.140
±26.8°
0.242
---
-0.36
0.62
105
-2.702 ×
104
264
±0.140
±26.7°
0.242
---
-0.36
0.62
TMS-α,α'd4 TMS-d6
185.4
6.928 ×
TMSe
119.6
5.877 × 105
-2.977 × 104
377
±0.159
±29.9°
0.223
---
-0.37
0.57
SiCB
142.4
6.223 × 105
-3.308 × 104
440
±0.163
±31.8°
0.042
0.59
-0.7
0.50
149.1
5.980 ×
105
-3.237 ×
104
438
±0.165
±32.1°
0.042
0.59
-0.7
0.50
105
-3.201 ×
104
439
±0.166
±32.3°
0.042
0.59
-0.7
0.50
SiCB-d1 SiCB-d2
155.1
5.839 ×
13Si2CB
161.6
3.189 × 105
-1.057 × 104
88
±0.129
±22.2°
0.241
0.5
-0.81
0.50
13Si2CB-d3
196.4
3.151 × 105
-1.043 × 104
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
207.4
3.172 ×
105
-1.044 ×
104
86
±0.128
±22.1°
0.241
0.5
-0.81
0.50
105
-1.044 ×
104
409
±0.156
±30.1°
0.103
0.45
-0.69
0.55
13Si2CB-d4 GeCBb
142.5
3.172 ×
13Ge2CBb
173.2
6.101 × 105
-3.158 × 102
1
±0.047
±7.8°
0.193
0.49
-0.69
0.49
CBONE
207.9
6.501 × 105
-2.252 × 103
2
±0.042
±4.4°
-0.110
---
-1.22
0.71
276.4
105
103
2
±0.042
±4.5°
-0.110
---
-1.22
0.71
CBONE-α,α'd4
7.129 ×
-2.560 ×
aµ
0, ω and the 𝑅 values were determined using the computed CCSD/cc-pVTZ structure. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO.
14
Table 3 Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐𝑥6. Molecule
Barrier cm-1
𝑥𝑚𝑖𝑛
𝜃𝑚𝑖𝑛
𝜔
106
510
±0.142
±29.6°
0.000
-5.176 × 104
3.694 × 105
514
±0.141
±29.4°
1.145 × 106
-4.900 × 104
2.324 × 106
504
±0.142
9.191 ×
105
-7.492 ×
103
2.381 ×
106
15
105
-7.162 ×
103
1.143 ×
106
µ0, u
𝑎, cm-1/Å4
CB
142.2
1.123 ×
106
CB-d1
152.9
1.297 × 106
CB-d8
236.1 110.4
TMO
𝑏 cm-1/Å2 -4.909 ×
104
c cm-1/Å6 2.842 ×
𝑅(α-CH2)
𝑅(β-MH2)
0.69
-0.69
0.69
0.000
0.69
-0.69
0.69
±29.6°
0.000
0.69
-0.69
0.69
±0.063
±13.6°
0.155
---
-0.29
0.66
14
±0.061
±13.2°
0.155
---
-0.29
0.66
𝑅(MH2)
TMO-αd2
126.7
9.405 ×
TMO-βd2
124.1
9.715 × 105
-7.478 × 103
1.143 × 106
14
±0.062
±13.3°
0.155
---
-0.29
0.66
TMO-α,α'd4
147.6
9.159 × 105
-6.618 × 103
1.104 × 106
12
±0.060
±12.9°
0.155
---
-0.29
0.66
162.7
9.315 ×
105
-6.492 ×
103
1.130 ×
106
11
±0.059
±12.6°
0.155
---
-0.29
0.66
105
-2.741 ×
104
3.366 ×
105
273
±0.141
±26.9°
0.242
---
-0.36
0.62
TMO-d6 TMS
121.5
6.824 ×
TMS-αd2
137.3
6.828 × 105
-2.697 × 104
5.454 × 104
266
±0.140
±26.9°
0.242
---
-0.36
0.62
TMS-βd2
146.4
6.723 × 105
-2.718 × 104
5.771 × 105
270
±0.140
±26.9°
0.242
---
-0.36
0.62
157.8
6.741 ×
105
-2.635 ×
104
-1.942 ×
104
258
±0.140
±26.8°
0.242
---
-0.36
0.62
105
-2.643 ×
104
6.292 ×
105
264
±0.141
±26.9°
0.242
---
-0.36
0.62
TMS-α,α'd4 TMS-d6
185.4
6.495 ×
TMSe
119.6
4.992 × 105
-2.816 × 104
9.559 × 105
378
±0.162
±30.4°
0.223
---
-0.37
0.57
SiCB
142.4
6.117 × 105
-3.288 × 104
1.081 × 105
440
±0.163
±31.9°
0.042
0.59
-0.7
0.50
149.1
5.980 ×
105
-3.237 ×
104
8.000 ×
102
438
±0.165
±32.1°
0.042
0.59
-0.7
0.50
105
-3.247 ×
104
-2.999 ×
105
438
±0.165
±32.2°
0.042
0.59
-0.7
0.50
SiCB-d1 SiCB-d2
155.1
6.096 ×
13Si2CB
161.6
3.033 × 105
-1.036 × 104
1.853 × 105
87
±0.130
±22.3°
0.241
0.5
-0.81
0.50
13Si2CB-d3
196.4
3.118 × 105
-1.040 × 104
4.595 × 104
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
207.4
3.079 ×
105
-1.033 ×
104
1.202 ×
105
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
105
-3.235 ×
104
-4.200 ×
105
409
±0.156
±30.1°
0.103
0.45
-0.69
0.55
0.193
0.49
-0.69
0.49
13Si2CB-d4 GeCBb
142.5
6.521 ×
13Ge2CBb
173.2
1.925 × 105
-8.426 × 102
2.651 × 104
1
±0.047
±7.8°
CBONE
207.9
6.820 × 105
-2.570 × 103
-7.307 × 105
2
±0.043
±4.6°
-0.110
---
-1.22
0.71
276.4
105
103
106
0
±0.000
±0.0°
-0.110
---
-1.22
0.71
CBONE-α,α'd4
4.112 ×
1.356 ×
6.392 ×
aµ
0, ω and the 𝑅 values were determined using the computed CCSD/cc-pVTZ structure. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO.
15
Table 4 Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4). ASD (cm-2) Molecule
CB CB-d8 CB-d1c TMO TMO-αd2 TMO-βd2 TMO-α,α’d4 TMO-d6 TMS TMS-αd2 TMS-βd2 TMS-α,α’d4 TMS-d6 TMSe SiCB SiCB-d1 SiCB-d2 13Si2CB 13Si2CB-d3 13Si2CB-d4 CBONE CBONE-d4
𝑉(𝑥4,𝑥2)a
𝑉(𝑥6,𝑥4,𝑥2)b
0.91 0.36 --0.50 0.15 0.13 0.08 0.06 0.34 0.13 0.06 0.07 0.09 0.38 0.44 0.58 1.24 0.10 0.01 0.09 1.23 0.36
0.02 0.11 --0.00 0.01 0.01 0.01 0.01 0.28 0.13 0.00 0.06 0.07 0.37 0.43 0.58 1.18 0.01 0.01 0.07 1.04 0.27
a
Using Eq. (1).
b
Using Eq. (4). The ASD values are based on infrared data except for CB-d1 for which Raman data were used.
c
.
16
Table 5 Observed and Calculated Ring-Puckering Transitions (cm-1) for CB, CB-d8 and CB-d1. CB Transition Cb. Bandsa
CB-d8
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
1–3
198.6
198.6
0.0
198.9
-0.3
209.7
-11.1
---
157.5
---
158.2
---
167.4
---
2–4
---
157.7
---
157.1
---
177.1
---
141.3
140.8
0.5
141.0
0.3
153.0
-11.7
3–5
176.1
176.7
-0.6
175.8
0.3
187.3
-11.2
141.9
142.5
-0.6
142.6
-0.7
153.5
-11.6
4–6
117.4
118.9
-1.5
117.4
0.0
124.5
-7.1
105.8
106.2
-0.4
105.8
0.0
126.5
-20.7
5–7
174.8
176.1
-1.3
174.8
0.0
178.1
-3.3
128.2
128.5
-0.3
128.0
0.2
137.8
-9.6
6–8
174.9
175.7
-0.8
175.1
-0.2
162.1
12.8
92.7
94.1
-1.4
93.3
-0.6
92.4
0.3
7–9
204.1
204.6
-0.5
204.1
0.0
200.6
3.5
132.9
133.4
-0.5
132.8
0.1
133.9
-1.0
8 – 10
220.1
220.2
-0.1
220.2
-0.1
215.1
5.0
137.9
138.0
-0.1
137.6
0.3
126.8
11.1
9 – 11
236.0
235.6
0.4
236.0
0.0
232.0
4.0
154.0
154.3
-0.3
154.2
-0.2
150.9
3.1
10 – 12
250.1
249.0
1.1
250.0
0.1
245.9
4.2
165.0
164.8
0.2
164.9
0.1
161.0
4.0
11 – 13
263.0
261.4
1.6
262.9
0.1
258.7
4.3
175.2
174.7
0.5
175.0
0.2
172.2
3.0
12 – 14
---
272.9
---
274.9
---
270.4
---
184.5
183.7
0.8
184.2
0.3
181.6
2.9
13 – 15
---
283.6
---
286.1
---
281.4
---
192.4
192.0
0.4
192.7
-0.3
190.3
2.1
4 – 5f
17.8
19.8
-2.0
19.4
-1.6
10.5
7.3
---
1.7
---
1.6
---
0.5
6–7f
---
77.0
---
76.8
---
64.2
---
23.2
24.1
-0.9
23.8
-0.6
11.8
11.4
0–2
---
197.8
---
198.2
---
209.3
---
---
157.5
---
158.1
---
167.4
---
199.4
198.2
1.2
198.6
0.8
209.5
-10.1
157.1
157.5
-0.4
158.2
-1.1
167.4
-10.3
1–3
---
198.6
---
198.9
---
209.7
---
---
157.5
---
158.2
---
167.4
---
2–4
159.3
157.7
1.6
157.1
2.2
177.1
-17.8
---
140.8
---
141.0
---
153.0
---
---
167.2
---
166.4
---
182.2
---
141.3
141.6
-0.3
141.8
-0.5
153.3
-12.0
3–5
177.1
176.7
0.4
175.8
1.3
187.3
-10.2
---
142.5
---
142.6
---
153.5
---
4–6
119.2
118.9
0.3
117.4
1.8
124.5
-5.3
105.0
106.2
-1.2
105.8
-0.8
126.5
-21.5
5–7
177.1
176.1
1.0
174.8
2.3
178.1
-1.0
128.2
128.5
-0.3
128.0
0.2
137.8
-9.6
Ramane
17
---
Table 5. Continued. CB Transition
Ramane
CB-d8
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
6–8
---
175.7
---
175.1
---
162.1
---
92.0
94.1
-2.1
93.3
-1.3
92.4
-0.4
7–9
---
204.6
---
204.1
---
200.6
---
132.9
133.4
-0.5
132.8
0.1
133.9
-1.0
CB-d1 Transition
Experimental. fit Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
3–4
156.0
156.9
-0.9
157.0
-1.0
174.5
-18.5
0–2
---
192.5
---
192.7
---
203.1
---
192.5
192.8
-0.3
192.9
-0.4
203.2
-10.7
1–3
---
193.0
---
193.2
---
203.3
---
2–4
159.0
157.5
1.5
157.5
1.5
174.7
-15.7
3–5
170.0
171.6
-1.6
171.6
-1.6
182.0
-12.0
4–6
113.5
113.6
-0.1
113.5
0.0
122.7
-9.2
5–7
166.5
167.5
-1.0
167.4
-0.9
170.5
-4.0
6–8
162.0
161.9
0.1
161.9
0.1
148.3
13.7
7–9
---
192.7
---
192.8
---
189.1
---
8 – 10
208.0
207.4
0.6
207.5
0.5
202.1
5.9
2–5
174.0
172.2
1.8
172.2
1.8
182.2
-8.2
Ramang
a Ref.
[21] from combination bands analysis.
Using Eq. (1). Eq. (4). d From CCSD/cc-pVTZ computations. b
c Using e Ref.
[26].
f Deduced, g Ref.
Ref. [26].
[38].
18
Fig. 5. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for CB. The observed transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.142 Å and 𝜃𝑚𝑖𝑛= ±29.6°.
Fig. 6. Experimental PEFs for CB isotopic species based on Eq. (4).
19
3.2. Trimethylene oxide, trimethylene sulfide, and trimethylene selenide The first molecule for which the ring-puckering far-infrared spectra were recorded was trimethylene oxide (TMO) and results were reported both by the R. C. Lord [29] group at MIT and the Strauss group at Berkeley [30]. Far-infrared spectra of TMO, TMO-αd2, TMO-βd2, TMO-α, α'd4 and TMO-d6 were later reported by Wieser, Danyluk and Kydd [31] in 1972 and Raman spectra by Kiefer, Bernetein, Wieser and Danyluk [32,33]. In 1973 Jokisaari and Kauppinen published high resolution far-infrared spectra of TMO [34]. The ultra-high resolution ringpuckering spectrum of TMO was reported by G. Moruzzi, M. Kunzmann, B. P. Winnewisser and M. Winnewiser in 2003 [35]. Microwave spectra with detailed theoretical analyses were published by the Gwinn [36-39] group at Berkeley. These included the definition of 𝜌 and 𝜔, but these parameters could only be roughly estimated at that time. Hence, the resulting kinetic energy expressions were only estimates. In our present work for TMO we determined the values of 𝜌 and of 𝜔 for TMO from the computed CCSD/cc-pVTZ and MP2/cc-pVTZ puckered and planar structures. The configuration at the energetic minimum for TMO from the CCSD/cc-pVTZ calculation came out to be almost planar with 𝑥𝑚𝑖𝑛 = ±0.004 at 𝜃𝑚𝑖𝑛 = 0.2°, whereas the calculated MP2/cc-pVTZ structure has a 𝑥𝑚𝑖𝑛 = ±0.069 at 𝜃𝑚𝑖𝑛 = 14.8°. Because the CCSD structure was nearly planar, we calculated the 𝜌, 𝜔, 𝛽 and 𝑅 values at 𝑥 = 0.100 Å and 𝜃 = 21.4° rather than at the energy minimum. This resulted in the 𝜌, 𝜔, 𝛽 and 𝑅 values shown in Table 1 and these are compared to those from the MP2/cc-pVTZ calculations in Table S3. Table S4 shows the kinetic energy expressions for all of the isotopic species from both types of calculations, and these are compared graphically in Fig. S3. Table 6 presents the observed transition frequencies for TMO and its isotopic derivatives and these are compared to our calculated values from the CCSD/cc-pVTZ calculations. 20
Table S5 in
the supplementary material presents the observed transition frequencies for TMO and its isotopic derivatives and these are compared to our calculated values from the MP2/cc-pVTZ calculations. As can be seen, the frequency fit for reach molecule for both cases is very good using Eq. (1) and is nearly perfect using Eq. (4). Comparison of Tables 6 (CCSD calculation) and S5 (MP2) shows that the MP2-cc-pVTZ calculations for this molecule yield a somewhat better agreement with the experimental data. The parameters of the PEFs equations from the CCSD computations are given in Tables 2 and 3 and are compared to those from the MP2/ccpVTZ computations in Tables S6 and S7. Table S8 shows the calculated ASDs using both computations, where the ones from the MP2/ccpVTZ computations are slightly better for TMO. As seen in Table 7, the CCSD/cc-pVTZ calculations in most cases give better agreement with the experimental data, but TMO is an exception. Fig. 7(a) shows the experimentally fit and theoretical ring-puckering PEFs for TMO using the kinetic energy functions defined by the CCSD/cc-pVTZ computations. Fig. 7(b) shows the calculated wavefunctions for the lower energy levels of TMO from these calculations. Fig. S4(a) in the supplementary material compares the experimentally fit and theoretical ring-puckering PEFs for TMO where the kinetic energy parameters were based on MP2/cc-pVTZ computations. These can be seen to be virtually identical.
Fig. S4(b) shows the calculated
wavefunctions for the lower energy levels of TMO from these calculations. Figs. 8 and S5 show that the experimental PEFs for all the isotopic species are almost identical. Calculations by the Wieser group [31] to fit their data previously assumed fixed reduced masses and carried out their calculations in reduced coordinates using the Laane tables [13]. Their frequency fits were reasonably good but the lack of a reliable 𝑔44(𝑥) expression did not allow them to obtain good 𝑉 (𝑥) vs 𝑥 PEFs. The calculated inversion barriers in our present work range from 12 to 19 cm-1
21
using Eq. (1) and from 11 to 15 cm-1 using Eq. (4). The lowest vibrational level at about 26 cm-1 for TMO lies above the barrier so this large amplitude puckering vibration in this state is not restricted to a puckered structure even though the energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063 Å with a 𝜃𝑚𝑖𝑛 = ±13.6° derived from the experimental fit applying the CCSD parameters, and at 𝑥𝑚𝑖𝑛 = ±0.062 Å with a 𝜃𝑚𝑖𝑛 = ±13.4° derived from the experimental fit applying the MP2 parameters. Our ab initio computations also show that the α-CH2’s twist about 6° at 𝑥𝑚𝑖𝑛. Fig. S6 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the MP2/cc-pVTZ calculations for TMO and its deuterated species. TMO has also been investigated theoretically using the Hougen-Bunker-Johns Model [40] by Foltynowicz and co-workers [41,42] and also by Szalay and co-workers [43]. Satisfactory agreement between experimental and theoretical transition frequencies was achieved.
22
Table 6 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs. TMO Transition
TMO-αd2
Experimental. fit 4
,𝑥2)b
∆
FIRa
Observed
0–1
52.92
51.53
1.39
1–2
89.56
90.37
2–3
104.44
3–4
𝑉(𝑥
4
𝑉(𝑥 ,𝑥
Experimental fit
2
,𝑥6)c
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
∆
Theoreticald
∆
Observed
53.10
-0.18
79.58
-26.66
48.7
48.2
0.5
48.7
0.0
72.8
-24.1
-0.81
89.46
0.10
104.01
-14.45
81.7
82.1
-0.4
81.7
0.0
95.1
-13.4
104.89
-0.45
104.45
-0.01
118.79
-14.35
95.1
95.5
-0.4
95.1
0.0
108.6
-13.5
117.95
118.45
-0.50
117.92
0.03
130.67
-12.72
107.2
107.6
-0.4
107.2
0.0
119.5
-12.3
4–5
128.89
129.36
-0.47
128.95
-0.06
140.70
-11.81
117.0
117.4
-0.4
117.1
-0.1
128.6
-11.6
5–6
138.42
138.73
-0.31
138.51
-0.09
149.49
-11.07
125.5
125.8
-0.3
125.6
-0.1
136.7
-11.2
6–7
146.94
146.99
-0.05
147.01
-0.07
157.36
-10.42
133.0
133.2
-0.2
133.2
-0.2
143.9
-10.9
7–8
154.65
154.40
0.25
154.70
-0.05
164.53
-9.88
139.9
139.9
0.0
140.0
-0.1
150.4
-10.5
8–9
161.73
161.14
0.59
161.75
-0.02
171.13
-9.40
146.3
146.0
0.3
146.2
0.1
156.5
-10.2
9 – 10
168.25
167.35
0.90
168.28
-0.03
177.27
-9.02
152.0
151.6
0.4
151.9
0.1
162.1
-10.1
10 – 11
174.45
173.10
1.35
174.37
0.08
183.02
-8.57
157.4
156.8
0.6
157.3
0.1
167.4
-10.0
0–2
142.58
141.89
0.69
142.55
0.03
183.58
-41.00
---
130.3
---
130.3
---
167.8
---
0–3
247.04
246.78
0.26
247.00
0.04
302.38
-55.34
---
225.8
---
225.5
---
276.4
---
0–4
364.95
365.24
-0.29
364.92
0.03
433.05
-68.10
---
333.4
---
332.7
---
395.9
---
0–5
493.86
494.59
-0.73
493.86
0.00
573.75
-79.89
---
450.8
---
449.8
---
524.5
---
0–2
143.1
141.9
1.2
142.6
0.5
183.6
-40.5
130.7
130.3
0.4
130.3
0.4
167.8
-37.1
1–3
194.3
195.3
-1.0
193.9
0.4
222.8
-28.5
176.4
177.6
-1.2
176.8
-0.4
203.6
-27.2
2–4
222.7
223.3
-0.6
222.4
0.3
249.5
-26.8
201.8
203.1
-1.3
202.4
-0.6
228.0
-26.2
3–5
247.5
247.8
-0.3
246.9
0.6
271.4
-23.9
224.0
225.0
-1.0
224.3
-0.3
248.1
-24.1
4–6
267.7
268.1
-0.4
267.5
0.2
290.2
-22.5
242.2
243.2
-1.0
242.7
-0.5
265.3
-23.1
5–7
286.1
285.7
0.4
285.5
0.6
306.8
-20.7
258.2
259.1
-0.9
258.8
-0.6
280.6
-22.4
6–8
302.1
301.4
0.7
301.7
0.4
321.9
-19.8
272.9
273.2
-0.3
273.1
-0.2
294.3
-21.4
7–9
317.0
315.5
1.5
316.4
0.6
335.7
-18.7
285.4
285.9
-0.5
286.1
-0.7
306.9
-21.5
Ramane
23
Table 6 Continued. TMO Transition
Ramane
TMO-αd2
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
4
𝑉(𝑥 ,𝑥
∆
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
8 – 10
~331
328.5
---
330.0
---
348.4
---
~299
297.6
---
298.1
---
318.6
---
9 – 11
~344
340.4
---
342.7
---
360.3
---
---
308.4
---
309.2
---
329.5
---
TMO-βd2 Transition FIRa
TMO-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–1
49.6
49.2
0.4
49.5
0.1
73.8
-24.2
43.7
43.4
0.3
43.8
-0.1
65.9
-22.2
1–2
83.5
84.0
-0.5
83.5
0.0
96.4
-12.9
73.4
73.6
-0.2
73.2
0.2
85.9
-12.5
2–3
97.2
97.6
-0.4
97.3
-0.1
110.1
-12.9
85.3
85.6
-0.3
85.3
0.0
98.1
-12.8
3–4
109.6
110.0
-0.4
109.7
-0.1
121.1
-11.5
96.1
96.4
-0.3
96.1
0.0
107.9
-11.8
4–5
119.7
120.0
-0.3
119.8
-0.1
130.4
-10.7
104.9
105.2
-0.3
104.9
0.0
116.2
-11.3
5–6
128.5
128.7
-0.2
128.6
-0.1
138.6
-10.1
112.6
112.7
-0.1
112.6
0.0
123.5
-10.9
6–7
136.3
136.3
0.0
136.3
0.0
145.9
-9.6
119.2
119.4
-0.2
119.3
-0.1
130.0
-10.8
7–8
143.4
143.2
0.2
143.3
0.1
152.6
-9.2
125.3
125.4
-0.1
125.4
-0.1
135.9
-10.6
8–9
149.7
149.4
0.3
149.7
0.0
158.7
-9.0
130.9
130.9
0.0
131.0
-0.1
141.4
-10.5
9 – 10
155.7
155.1
0.6
155.6
0.1
164.4
-8.7
136.4
135.9
0.5
136.2
0.2
146.5
-10.1
10 – 11
---
160.5
---
161.1
---
169.8
---
141.0
140.6
0.4
141.0
0.0
151.3
-10.3
0–2
133.3
133.1
0.2
133.0
0.3
170.1
-36.8
117.5
117.0
0.5
117.0
0.5
151.8
-34.3
1–3
180.8
181.6
-0.8
180.8
0.0
206.4
-25.6
158.8
159.2
-0.4
158.5
0.3
184.1
-25.3
2–4
207.2
207.6
-0.4
207.0
0.2
231.2
-24.0
181.4
182.0
-0.6
181.4
0.0
206.1
-24.7
3–5
229.6
230.1
-0.5
229.5
0.1
251.5
-21.9
201.0
201.6
-0.6
201.1
-0.1
224.2
-23.2
4–6
248.0
248.7
-0.7
248.4
-0.4
269.0
-21.0
217.3
217.9
-0.6
217.5
-0.2
239.7
-22.4
5–7
265.3
265.0
0.3
264.9
0.4
284.5
-19.2
231.7
232.2
-0.5
231.9
-0.2
253.5
-21.8
6–8
280.3
279.5
0.8
279.6
0.7
298.5
-18.2
244.7
244.8
-0.1
244.8
-0.1
265.9
-21.2
Ramane
24
Table 6 Continued. TMO-βd2 Transition
Ramane
TMO-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
~293
292.6
---
293.0
---
311.3
---
~256
256.3
---
256.4
---
277.3
---
8 – 10
~304
304.5
---
305.2
---
323.1
---
~267
266.8
---
267.2
---
287.9
---
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMO-d6 Transition FIRa
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
0–1
41.2
40.9
0.3
41.2
0.0
61.8
-20.6
1–2
69.2
69.4
-0.2
69.0
0.2
80.7
-11.5
2–3
80.5
80.7
-0.2
80.5
0.0
92.1
-11.6
3–4
90.7
91.0
-0.3
90.7
0.0
101.3
-10.6
4–5
99.1
99.3
-0.2
99.1
0.0
109.1
-10.0
5–6
106.2
106.4
-0.2
106.3
-0.1
115.9
-9.7
6–7
112.7
112.8
-0.1
112.7
0.0
122.1
-9.4
7–8
118.3
118.4
-0.1
118.5
-0.2
127.6
-9.3
8–9
123.7
123.6
0.1
123.8
-0.1
132.8
-9.1
9 – 10
128.7
128.4
0.3
128.7
0.0
137.6
-8.9
10 – 11
133.3
132.8
0.5
133.2
0.1
142.1
-8.8
0–2
~109
110.3
---
110.3
---
142.5
---
1–3
149.9
150.1
-0.2
149.5
0.4
172.8
-22.9
2–4
171.7
171.7
0.0
171.2
0.5
193.4
-21.7
3–5
190.1
190.3
-0.2
189.8
0.3
210.4
-20.3
4–6
205.6
205.7
-0.1
205.3
0.3
225.0
-19.4
5–7
219.1
219.2
-0.1
219.0
0.1
238.0
-18.9
6–8
231.5
231.2
0.3
231.2
0.3
249.7
-18.2
Ramane
25
Table 6 Continued. TMO-d6 Transition
Ramane
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
242.7
242.1
0.6
242.2
0.5
260.4
-17.7
8 – 10
~253
252.0
---
252.4
---
270.4
---
a FIR
data for TMO from Ref. [35]. FIR data TMO deuterated analogs from Ref. [31]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Raman data for TMO from Ref. [32]. Raman data for TMO deuterated analogs from Ref. [33]. b
26
Table 7 Comparison of experimental barriers, and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛 values with those from theoretical calculations. Experimental fit Theoretical 𝑉(𝑥6,𝑥4,𝑥2)a CCSD/cc-pVTZ MP2/cc-pVTZ -1 -1 -1 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Barrier, cm 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Barrier, cm 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Molecule Barrier, cm CB 510 ±0.142 ±29.6° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° CB-d8 504 ±0.142 ±29.6° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° CB-d1b 514 ±0.141 ±29.4° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° TMO 15 ±0.062 ±13.4° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-αd2 13 ±0.061 ±13.2° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-βd2 14 ±0.061 ±13.0° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-α,α’d4 12 ±0.059 ±12.6° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-d6 11 ±0.058 ±12.4° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMS 273 ±0.141 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-αd2 266 ±0.140 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-βd2 270 ±0.140 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-α,α’d4 258 ±0.140 ±26.8 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-d6 264 0.141 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMSe 378 ±0.162 ±30.4° 339 ± 0.148 ± 27.8° 512 ± 0.164 30.9° SiCB 440 ±0.163 ±31.9° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° SiCB-d1 438 ±0.165 ±32.1° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° SiCB-d2 438 ±0.165 ±32.2° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° 13Si2CB 87 ±0.130 ±22.3° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° 13Si2CB-d3 86 ±0.129 ±22.2° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° 13Si2CB-d4 86 ±0.129 ±22.2° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° GeCB ------409 ± 0.156 ± 30.1° 567 ± 0.169 32.6° 13Ge2CB ------1 ± 0.047 ± 7.8° 24 ± 0.104 17.1° CBONE 2 ±0.043 ±4.6° 36 ± 0.073 ± 15.5° 114 ± 0.097 20.8° CBONE-α,α’d4 0 ±0.000 ±0.0° 36 ± 0.073 ± 15.5° 114 ± 0.097 20.8° a Using Eq. (4). 27
Fig. 7. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using CCSD/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063Å and 𝜃𝑚𝑖𝑛= ±13.6°.
Fig. 8. Experimental PEFs for TMO isotopic species based on Eq. (4) from CCSD/cc-pVTZ computations.
28
The far-infrared spectra of TMS were first reported in 1966 by the Strauss group [44]. In 1974 Wieser, Duckett and Kydd reported the far-infrared spectra of TMS, TMS-αd2, TMS-βd2, TMS-α, α'd4 and TMS-d6 [45]. The Raman spectra for TMS were reported by Durig, Shing, Carreira and Li [46] and the Raman spectra of the deuterated analogs were reported by Wieser and Kydd [47]. The microwave spectrum, vibration-rotation interaction, and potential function for the ring-puckering vibration of TMS were studied by the Gwinn group [19]. Table S2 in the supplementary material shows the kinetic energy terms and Tables 2 and 3 show the and potential energy parameters calculated in the present work for TMS and its isotopic species.
Table 8 presents the experimentally observed transitions for these molecules and
compares them to our calculated values. The barriers can be seen to range from 258 to 273 cm-1 for the isotopic species, and these are similar to previously reported barriers [19,44-47]. Our present fit of the experimental data yields energy minima at 𝑥𝑚𝑖𝑛 = ± 0.141 Å and the CCSD/ccpVTZ ab initio calculation gives ± 0.133.Å. Fig. 9(a) shows the experimentally fit and theoretical ring-puckering PEFs for TMS. Fig. 9(b) shows the calculated wavefunctions for the lower energy levels of TMS. Fig. 10 shows that the experimentally fit PEFs for all the isotopic species are again almost identical. Fig. S7 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for TMS and its deuterated species.
29
Table 8 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMS and deuterated analogs. TMS Transition
TMS-αd2
Experimental. fit
Experimental fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
0–1
0.2746e
0.2871
-0.0125
0.2789
-0.0043
0.5930
-0.3184
1–2
138.7
138.8
-0.1
138.8
-0.1
129.5
2–3
---
12.5
---
12.3
---
3–4
86.0
86.0
0.0
85.8
4–5
62.7
62.8
-0.1
5–6
84.3
84.4
6–7
91.3
7–8
∆
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
0.181
---
0.180
---
0.364
---
9.2
131.9
132.0
-0.1
132.0
-0.1
126.0
5.9
19.5
---
---
8.9
---
8.8
---
14.1
---
0.2
81.9
4.1
82.7
82.3
0.4
82.3
0.4
78.3
4.4
62.6
0.1
71.3
-8.6
---
53.3
---
53.3
---
61.9
---
-0.1
84.3
0.0
88.1
-3.8
76.4
76.3
0.1
76.2
0.2
80.1
-3.7
91.6
-0.3
91.6
-0.3
95.9
-4.6
82.2
82.3
-0.1
82.3
-0.1
87.0
-4.8
99.7
99.8
-0.1
99.8
-0.1
103.7
-4.0
90.0
90.0
0.0
90.0
0.0
94.4
-4.4
8–9
107.8
106.6
1.2
106.7
1.1
110.4
-2.6
95.7
96.4
-0.7
96.4
-0.7
100.7
-5.0
9 – 10
114.2
112.8
1.4
112.9
1.3
116.5
-2.3
101.9
102.1
-0.2
102.1
-0.2
106.5
-4.6
10 – 11
118.3
118.5
-0.2
118.7
-0.4
122.1
-3.8
107.5
107.3
0.2
107.4
0.1
111.7
-4.2
11 – 12
123.9
123.7
0.2
124.0
-0.1
127.3
-3.4
112.9
112.2
0.7
112.2
0.7
116.5
-3.6
12 – 13
128.4
128.6
-0.2
128.9
-0.5
132.1
-3.7
---
116.7
---
116.7
---
121.0
---
13 – 14
---
133.1
---
133.6
---
136.6
---
---
120.9
---
121.0
---
125.2
---
0–3
151.3
151.6
-0.3
151.5
-0.2
149.5
1.8
140.6
141.0
-0.4
141.0
-0.4
140.5
0.1
2–5
160.2
161.2
-1.0
160.8
-0.6
172.6
-12.4
144.6
144.4
0.2
144.4
0.2
154.3
-9.7
0–2
139.1
139.1
0.0
139.1
0.0
130.0
9.1
131.7
132.2
-0.5
132.2
-0.5
126.4
5.3
1–3
151.0
151.3
-0.3
151.2
-0.2
148.9
2.1
140.6
140.8
-0.2
140.8
-0.2
140.1
0.5
2–4
99.5
98.4
1.1
98.1
1.4
101.4
-1.9
91.5
91.1
0.4
91.1
0.4
92.4
-0.9
3–5
147.0
148.7
-1.7
148.4
-1.4
153.1
-6.1
135.3
135.6
-0.3
135.5
-0.2
140.2
-4.9
4–6
147.0
147.2
-0.2
146.9
0.1
159.4
-12.4
129.2
129.6
-0.4
129.5
-0.3
142.0
-12.8
5–7
175.0
176.0
-1.0
175.9
-0.9
184.1
-9.1
158.3
158.5
-0.2
158.5
-0.2
167.1
-8.8
6–8
191.5
191.4
0.1
191.3
0.2
199.7
-8.2
172.1
172.3
-0.2
172.3
-0.2
181.5
-9.4
Ramanf
30
Table 8 Continued. TMS Transition
Ramanf
TMS-αd2
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
208.4
206.4
2.0
206.4
2.0
214.2
-5.8
186.0
186.4
-0.4
186.4
-0.4
195.2
-9.2
8 – 10
---
219.4
---
219.6
---
227.0
---
197.5
198.5
-1.0
198.5
-1.0
207.2
-9.7
9 – 11
---
231.3
---
231.6
---
238.7
---
209.3
209.5
-0.2
209.5
-0.2
218.1
-8.8
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMS-βd2 Transition
TMS-α,α'd4
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
0–1
---
0.139
1–2
131.8
2–3
Experimental. Fit
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥4,𝑥2)b
---
0.129
---
0.282
---
---
0.109
---
0.109
---
0.201
---
131.6
0.2
131.7
0.1
124.2
7.6
124.1
124.2
-0.1
124.1
0.0
121.7
2.4
---
7.4
---
7.1
---
11.9
---
---
6.0
---
6.0
---
9.3
---
3–4
82.4
82.6
-0.2
82.5
-0.1
77.0
5.4
---
78.8
---
78.8
---
75.7
---
4–5
---
49.5
---
49.0
---
57.5
---
---
44.0
---
44.1
---
51.6
---
5–6
73.6
73.9
-0.3
73.6
0.0
76.4
-2.8
68.6
68.4
0.2
68.4
0.2
71.8
-3.2
6–7
79.1
79.4
-0.3
79.1
0.0
83.0
-3.9
72.9
73.1
-0.2
73.1
-0.2
77.6
-4.7
7–8
87.1
87.2
-0.1
87.0
0.1
90.3
-3.2
80.2
80.5
-0.3
80.5
-0.3
84.7
-4.5
8–9
93.3
93.5
-0.2
93.4
-0.1
96.4
-3.1
86.0
86.3
-0.3
86.3
-0.3
90.6
-4.6
9 – 10
99.0
99.2
-0.2
99.1
-0.1
101.9
-2.9
91.3
91.6
-0.3
91.5
-0.2
95.9
-4.6
10 – 11
104.4
104.3
0.1
104.4
0.0
107.0
-2.6
96.2
96.4
-0.2
96.3
-0.1
100.7
-4.5
11 – 12
109.3
109.1
0.2
109.3
0.0
111.7
-2.4
101.3
100.8
0.5
100.8
0.5
105.2
-3.9
12 – 13
113.8
113.6
0.2
113.8
0.0
116.1
-2.3
---
104.9
---
104.9
---
109.3
---
13 – 14
118.2
117.7
0.5
118.1
0.1
120.2
-2.0
---
108.8
---
108.7
---
113.2
---
0–3
138.9
139.1
-0.2
138.9
0.0
136.4
2.5
130.3
130.3
0.0
130.3
0.0
131.2
-0.9
2–5
---
139.6
---
138.6
---
146.3
---
129.2
128.9
0.3
128.9
0.3
136.5
-7.3
∆
31
∆
Table 8 Continued. TMS-βd2 Transition
Ramanf
TMS-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–2
134.6
131.7
2.9
131.8
2.8
124.5
10.1
126.9
124.3
2.6
124.2
2.7
121.9
5.0
1–3
139.2
138.9
0.3
138.8
0.4
136.1
3.1
130.5
130.2
0.3
130.2
0.3
131.0
-0.5
2–4
90.3
90.0
0.3
89.6
0.7
88.8
1.5
86.4
84.8
1.6
84.8
1.6
84.9
1.5
3–5
131.6
132.2
-0.6
131.5
0.1
134.4
-2.8
123.6
122.9
0.7
122.9
0.7
127.2
-3.6
4–6
122.4
123.5
-1.1
122.6
-0.2
133.9
-11.5
112.4
112.4
0.0
112.4
0.0
123.4
-11.0
5–7
152.8
153.4
-0.6
152.7
0.1
159.4
-6.6
141.5
141.5
0.0
141.4
0.1
149.4
-7.9
6–8
166.1
166.7
-0.6
166.2
-0.1
173.2
-7.1
153.1
153.5
-0.4
153.5
-0.4
162.3
-9.2
7–9
180.2
180.7
-0.5
180.4
-0.2
186.6
-6.4
166.4
166.8
-0.4
166.7
-0.3
175.3
-8.9
8 – 10
192.4
192.6
-0.2
192.5
-0.1
198.3
-5.9
177.4
177.8
-0.4
177.8
-0.4
186.4
-9.0
9 – 11
---
203.5
---
203.5
---
209.0
---
186.5
187.9
-1.4
187.9
-1.4
196.6
-10.1
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMS-d6 Transition
Experimental. fit 4
,𝑥2)b
FIRa
Observed
0–1
---
0.046
---
0.043
---
0.097
---
1–2
120.0
119.9
0.1
120.0
0.0
116.4
3.6
2–3
---
3.1
---
3.0
---
5.4
---
3–4
---
80.2
---
80.0
---
74.1
---
4–5
---
32.6
---
32.4
---
40.6
---
5–6
61.7
61.7
0.0
61.5
0.2
63.8
-2.1
6–7
63.9
63.9
0.0
63.8
0.1
68.0
-4.1
7–8
71.6
71.6
0.0
71.6
0.0
75.0
-3.4
8–9
77.0
77.0
0.0
77.1
-0.1
80.4
-3.4
9 – 10
81.7
82.0
-0.3
82.2
-0.5
85.4
-3.7
10 – 11
86.5
86.6
-0.1
86.8
-0.3
89.9
-3.4
11 – 12
91.5
90.7
0.8
91.0
0.5
94.0
-2.5
𝑉(𝑥
∆
32
Table 8 Continued. TMS-d6 Transition
Experimental. fit 4
,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
123.1
---
121.9
---
115.9
-0.3
115.5
0.1
120.2
-4.6
119.0
120.0
-1.0
120.1
-1.1
116.5
2.5
1–3
120.2
123.1
-2.9
123.1
-2.9
121.8
-1.6
2–4
83.0
83.3
-0.3
83.1
-0.1
79.5
3.5
3–5
112.7
112.8
-0.1
112.5
0.2
114.7
-2.0
4–6
95.6
94.4
1.2
94.0
1.6
104.4
-8.8
5–7
125.8
125.6
0.2
125.3
0.5
131.8
-6.0
6–8
135.6
135.5
0.1
135.4
0.2
143.0
-7.4
7–9
148.5
148.7
-0.2
148.7
-0.2
155.4
-6.9
8 – 10
158.5
159.1
-0.6
159.3
-0.8
165.8
-7.3
9 – 11
167.8
168.6
-0.8
169.0
-1.2
175.2
-7.4
10 – 12
177.0
177.3
-0.3
177.8
-0.8
183.9
-6.9
FIRa
Observed
0–3
---
123.1
2–5
115.6
0–2
𝑉(𝑥
∆
Ramanf
FIR data of TMS and the deuterated analogs from Ref. [45]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Derived from microwave measurements. f Raman data for TMS from Ref. [46]. Raman data for TMS deuterated analogs from Ref. [47]. a
b
33
Fig. 9. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMS. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.141 Å and 𝜃𝑚𝑖𝑛 = ±26.9°.
Fig. 10. Experimental PEFs for TMS isotopic species based on Eq. (4).
The far-infrared spectra of TMSe were reported in 1969 by Harvey, Durig and Morrissey [48]. The kinetic energy terms for this molecule are given in Table S2 and the potential energy 34
parameters are given in Tables 2 and 3. Table 4 compares the observed and calculated frequencies. The frequency fit using Eq. (1) is good while that with Eq. (4) is even better. The experimental barrier is 378 cm-1 whereas the CCSD/cc-pVTZ computation gives 339 cm-1. Fig. 11(a) shows that the experimental and theoretical ring-puckering PEFs for TMSe are in reasonably good agreement. Fig. 11(b) shows the calculated wavefunctions for the lower energy levels for TMSe. Fig. S8 compares the two experimental PEFs using Eqs. (1) and (4) with those from the CCSD/ccpVTZ calculations.
Fig. 11. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMSe. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.162 Å and 𝜃𝑚𝑖𝑛= ±30.4°.
35
Table 9 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMSe. TMSe Transition FIRa
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–1
---
0.023
---
0.019
---
0.076
---
1–2
158.0
159.0
-1.0
159.2
-1.2
155.6
2.4
2–3
1.7
1.8
-0.1
1.7
0.0
4.7
-3.0
3–4
116.5e
115.9
0.6
115.6
0.9
103.4
13.1
4–5
28.3e
28.8
-0.5
28.0
0.3
44.8
-16.5
5–6
78.7e
78.7
0.0
77.8
0.9
81.3
-2.6
6–7
74.1e
74.3
-0.2
73.7
0.4
84.5
-10.4
7–8
86.5
86.7
-0.2
86.3
0.2
94.2
-7.7
8–9
93.0
93.3
-0.3
93.1
-0.1
101.1
-8.1
9 – 10
99.5
99.8
-0.3
99.8
-0.3
107.5
-8.0
10 – 11
105.0
105.5
-0.5
105.7
-0.7
113.2
-8.2
11 – 12
111.5
110.7
0.8
111.2
0.3
118.4
-6.9
12 – 13
116.5
115.6
0.9
116.2
0.3
123.3
-6.8
13 – 14
120.5
120.1
0.4
121.0
-0.5
127.8
-7.3
14 – 15
125.6f
124.3
1.3
125.4
0.2
132.1
-6.5
15 – 16
129.5?f
128.3
---
129.7
---
136.1
---
0–3
160.2
160.9
-0.7
160.9
-0.7
160.4
-0.2
2–5
146.2
146.5
-0.3
145.2
1.0
152.9
-6.7
4–7
179.5?
181.8
---
179.5
---
210.6
---
Far-infrared data from Ref. [48]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e From the average of combination and differential bands. f From differential bands. a
b
3.3. Silacyclobutane, 1,3-disilacyclobutane, germacyclobutane and 1,3-digermacyclobutane Silacyclobutane (SiCB) was first synthesized by Laane [49] in 1967. The far-infrared study of SiCB and silacyclobutane-1,1-d2 (SiCB-d2) was later reported in 1968 by Laane and Lord [12]. A sample was sent to Pringle who performed the microwave study [50]. The Laane group also 36
reported the Raman spectra [51]. The initial computations assumed a fixed reduced mass and there was no attempt to take into account the interaction with SiH2 and CH2 rocking motions. In 1982 the Laane group reported the far-infrared spectra of 1-silacyclobutane-d1 (SiCB-d1) [52]. In the present study from the ab initio computations on SiCB we determine 𝜌 = 0.919 and 𝜔 = 0.042 reflecting easier angle bending at the silicon atom than at the carbon atoms. For MH2 rocking we found 𝑅(SiH2) = 0.59 rad/Å, 𝑅(??-CH2) = -0.70 rad/Å, and 𝑅(β-CH2) = 0.50 rad/Å. This results in the kinetic energy expressions for SiCB, SiCB-d1 and SiCB-d2 which are given in Table S2. The calculated PEF parameters to fit the experimental data are given in Tables 2 and 3. Fig. 12(a) shows the experimentally fit and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. Fig. 12(b) shows the calculated wavefunctions for the lower energy levels. Fig. 13 compares the experimental PEFs for SiCB and to those of its deuterated analogs, and these can be seen to be almost identical. The observed and calculated frequencies are shown in Table 10. As is the case for all of these molecules, the frequency fit is very good using Eq. (1) and even better using Eq. (4).
The
experimental barrier is 440 cm-1 whereas the CCSD/cc-pVTZ computation gives 472 cm-1. Fig. S9 compares the two experimental PEFs from Eqs. (1) and (4) for each isotopic species with those from the CCSD/cc-pVTZ calculations.
37
Fig. 12. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.163 Å and 𝜃𝑚𝑖𝑛= ±31.9°.
Fig. 13. Experimental PEFs for SiCB isotopic species based on Eq. (4).
38
Table 10 Observed and Calculated Ring-Puckering Transitions (cm-1) for SiCB and deuterated analogs. SiCB Transition
Experimental. fit
FIRa
Observed
0–1
(0.003)e
4
∆
0.003
0.000
𝑉(𝑥
,𝑥2)b
158.96
1–2 0–3
SiCB-d1
157.78
159.25
4
𝑉(𝑥 ,𝑥
Experimental fit 2
,𝑥6)c
0.003 159.24
,𝑥2)b
∆
Theoreticald
∆
Observed
0.000
0.001
0.002
---
0.002
153.3
154.3
158.96 -1.32
𝑉(𝑥
4
162.88 -1.32
163.04
-5.18
154.5
∆
---
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
0.002
---
0.001
154.3 -1.1
154.5
∆
---
159.7 -1.1
159.8
0–2
158.96
158.96
162.88
154.3
154.3
159.7
1–3
159.24
159.23
163.04
154.5
154.5
159.8
-6.5
2–3
0.26
0.28
-0.02
0.28
-0.02
0.16
0.10
---
0.2
---
0.2
---
0.1
---
3–4
133.45
133.14
0.16
133.11
0.20
140.25
-6.88
133.0
131.4
1.5
131.4
1.5
138.8
-5.9
133.43
2–4 2–5
141.80
142.26
133.39 -0.32
141.98
3–5
142.16
140.41 -0.23
146.18
141.89
146.02
131.6 -4.30
138.2
138.2
131.6 0.1
138.0
138.2
139.0 0.1
138.0
143.5
-5.3
143.4
4–5
---
8.83
---
8.78
---
5.77
5–6
85.37
85.07
0.30
84.99
0.38
92.91
-7.54
84.3
85.4
-1.1
85.4
85.4
93.8
-9.5
6–7
49.85
50.65
-0.80
50.56
-0.71
43.55
6.30
44.6
44.6
0.0
44.6
44.6
39.0
5.6
7–8
74.70
74.82
-0.12
74.73
-0.03
74.44
0.26
71.3
71.3
0.0
71.3
71.3
72.2
-0.9
8–9
79.22
78.96
0.26
78.90
0.32
76.62
2.60
75.9
74.3
1.6
74.3
74.3
73.2
2.7
9 – 10
86.20
86.18
0.02
86.13
0.07
84.72
1.48
81.3
81.7
-0.4
81.7
81.7
81.6
-0.3
10 – 11
92.10
91.73
0.37
91.70
0.40
90.32
1.78
---
87.0
---
87.0
---
87.0
---
11 – 12
98.50
96.86 101.54
.64 -0.52
96.85 101.55
1.65 -0.53
95.56 100.30
2.94 0.72
-----
92.0 96.5
-----
92.0 96.5
-----
92.2 96.8
-----
12 – 13
101.02
105.80
0.56
105.91
0.45
104.69
1.67
---
100.7
---
100.7
---
101.1
---
13 – 14
106.36
109.94
0.52
109.99
0.47
108.78
1.68
---
104.6
---
104.6
---
105.1
---
14 – 15
110.46
113.76
-0.53
113.84
-0.61
112.62
0.61
---
108.3
---
108.3
---
108.9
---
15 – 16
113.23
117.38
-0.30
117.47
-0.39
116.25
0.83
---
111.8
---
111.8
---
112.4
---
16 – 17
117.08
85.07
0.30
84.99
0.38
92.91
-7.54
---
87.0
---
87.0
---
87.0
---
4–6
94.41
93.90
0.51
93.77
0.64
98.68
-4.27
92.2
92.1
0.1
92.1
0.1
98.4
-6.2
5–7
135.79
135.72
0.07
135.55
0.24
136.46
-0.67
130.3
130.1
0.2
130.1
0.2
132.8
-2.5
39
6.2f
6.6
-0.4
6.6
6.6
4.6
1.6
Table 10 Continued. SiCB Transition
SiCB-d1
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
4–6
94.41
125.47
5–7
135.79
6–8
Experimental. Fit
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
Observed
𝑉(𝑥4,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
-1.30
125.29
-1.12
118.00
6.17
92.2
92.1
0.1
92.1
0.1
98.4
-6.2
153.78
0.03
153.64
0.17
151.07
2.74
130.3
130.1
0.2
130.1
0.2
132.8
-2.5
124.17
165.14
-0.46
165.03
-0.35
161.35
3.33
115.8
115.9
-0.1
115.9
-0.1
111.2
4.6
7–9
153.81
177.91
-0.80
177.84
-0.73
175.05
2.06
144.9
145.6
-0.7
145.6
-0.7
145.4
-0.5
8 – 10
164.68
188.59
1.62
188.55
1.66
185.88
4.33
156.0
156.0
0.0
156.0
0.0
154.7
1.3
9 – 11
177.11
198.39
0.82
198.40
0.81
195.86
3.35
---
168.7
---
168.7
---
168.6
---
10 – – 13 12 11
190.21 199.21
207.42 125.47
-0.18 -1.30
207.46 125.29
-0.22 -1.12
204.99 118.00
2.25 6.17
180.4? ---
188.5
-----
188.5
-----
189.0
---
12 – 14
207.24
153.78
0.03
153.64
0.17
151.07
2.74
---
197.2
---
197.3
---
197.9
---
1–4
291.7
292.39
-0.7
292.4
-0.7
303.29
-11.6
---
285.8
---
285.8
---
298.6
---
3–6
~227
227.05
---
226.88
---
238.92
---
---
223.4
---
223.4
---
237.2
---
4–7
144.56
144.55
0.01
144.33
0.23
142.33
2.23
---
136.7
---
136.7
---
137.4
---
5–8
210.68
210.54
0.14
210.28
0.40
210.90
-0.22
---
201.3
---
201.3
---
205.1
---
7 – 10
239.64
239.96
-0.32
239.77
-0.13
235.79
3.85
---
227.2
---
227.2
---
315.1
---
8 – 11
256.7
256.9
-0.2
256.7
0.0
251.7
5.0
---
243.0
---
243.0
---
326.4
---
0–2
157.9
159.0
-1.1
159.0
-1.1
162.9
-5.0
---
154.3
---
154.3
---
159.7
---
1–3
157.9
159.2
-1.3
156.2
1.7
163.0
-5.1
---
154.5
---
154.5
---
159.8
---
2–4
133.4
133.4
0.0
133.4
0.0
140.4
-7.0
---
131.6
---
131.5
---
139.0
---
3–5
142.1
142.0
0.1
141.9
0.2
146.0
-3.9
---
138.0
---
138.0
---
143.4
---
4–6
94.7
93.9
0.8
93.8
0.9
98.7
-4.0
---
92.1
---
92.1
---
98.4
---
5–7
136.2
135.7
0.5
135.5
0.7
136.5
-0.3
---
130.1
---
130.1
---
132.8
---
6–8
125.5
125.5
0.0
125.3
0.2
118.0
7.5
---
115.9
---
115.9
---
111.2
---
7–9
154.4
153.8
0.6
153.6
0.8
151.1
3.3
---
145.6
---
145.6
---
145.4
---
8 – 10
165.2
165.1
0.1
165.0
0.2
161.3
3.9
---
156.0
---
156.0
---
154.7
---
9 – 11
177.0
177.9
-0.9
177.8
-0.8
175.0
2.0
---
168.7
---
168.7
---
168.6
---
∆
∆
∆
Ramang
40
Table 10 Continued. SiCB-d2 Transition
Experimental. fit 4
,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
0.001
---
0.001
---
151.0
-1.3
150.7
-1.0
157.0
-7.3
---
0.1
---
0.1
---
0.1
---
3–4
130.6
130.2
0.4
130.1
0.5
137.5
-6.9
4–5
5.0
5.1
-0.1
5.2
-0.2
3.7
1.3
5–6
86.0
86.4
-0.4
86.6
-0.6
94.7
-8.7
6–7
40.5?
39.6
---
39.7
---
35.3
---
7–8
68.1
68.7
-0.6
68.8
-0.7
70.5
-2.4
8–9
73.0
70.6
2.4
70.6
2.4
70.3
2.7
9 – 10
79.5
78.2
1.3
78.1
1.4
79.0
0.5
10 – 11
84.7
83.4
1.3
83.3
1.4
84.3
0.4
3–5
135.6
135.3
0.3
135.2
0.4
141.2
-5.6
4–6
90.5?
91.5
---
91.7
---
98.4
---
5–7
125.6
126.1
-0.5
126.2
-0.6
130.0
-4.4
6–8
107.2
108.4
-1.2
108.5
-1.3
105.8
1.4
7–9
138.2
139.4
-1.2
139.4
-1.2
140.8
-2.6
8 – 10
~148
148.9
---
148.7
---
149.2
---
9 – 11
160.3
161.7
-1.4
161.4
-1.1
163.3
-3.0
10 – 12
---
171.8
---
171.4
---
173.7
---
11 – 13
180.4?
181.1
---
180.6
---
183.3
---
2–5
135.5
135.4
0.1
135.4
0.1
141.3
-5.8
4–7
132.8
131.2
1.6
131.4
1.4
133.7
-0.9
5–8
195.6
194.8
0.8
195.1
0.5
200.5
-4.9
6–9
176.8?
179.0
---
179.0
---
176.1
---
0–2
149.9
150.4
-0.5
150.7
-0.8
157.0
-7.1
1–3
149.9
150.5
-0.6
150.9
-1.0
157.1
-7.2
2–4
129.0
129.8
-0.8
130.2
-1.2
137.6
-8.6
3–5
135.4
134.7
0.7
135.2
0.2
141.2
-5.8
4–6
93.0
91.2
1.8
91.7
1.3
98.4
-5.4
5–7
---
125.5
---
126.2
---
130.0
---
6–8
107.9
107.7
0.2
108.5
-0.6
105.8
2.1
7–9
142.4
138.6
3.8
139.4
3.0
140.8
1.6
8 – 10
157.0
148.0
9.0
148.7
8.3
149.2
7.8
FIRa
Observed
0–1
---
0.001
1–2
149.7
2–3
𝑉(𝑥
∆
Ramang
a
FIR data for SiCB from Ref. [12]. FIR data for SiCB-d1 and SiCB-d2 from Ref. [52]. 41
Using Eq. (1). Eq. (4). d From CCSD/cc-pVTZ computations. e Approximate value from microwave work, Ref. [50]. f Calculated from observed transitions 3 – 4 and 3 – 5. g Raman data for SiCB and SiCB-d from Ref. [51]. 2
b
c Using
1,3-Disilacyclobutane (13Si2CB) and its 1,1,3,3-d4 (13Si2CB-d4) derivative were first synthesized by Irwin and Laane and its far-infrared and Raman spectra were published in the same paper in 1977 [20]. Later in 1980 the Laane group studied the combination band spectra for the 1,3-disilacyclobutane-1,1,3-d3 derivative (13Si2CB-d3) [53]. The molecules were reported to be puckered with barriers to inversion of 87 cm-1, 86 cm-1 and 87 cm-1, respectively. This work along with a force constant investigation showed that the ring-puckering and SiH2 in-phase rocking motions were strongly coupled [20]. In our present work we find 𝜔 = 0.241 reflecting the fact that CSiC angles in the ring are considerably easier to bend than SiCSi angles. We also find that there is substantial SiH2 rocking and some CH2 rocking occurring during the puckering vibration as 𝑅 (SiH2) = 0.50 rad/Å and 𝑅(α-CH2) = -0.81 rad/Å. The kinetic energy and potential energy parameters for 13Si2CB, 13Si2CB-d3 and 13Si2CBd4 are given in Tables S2 and Tables 2 and 3. Fig. 14(a) shows the experimentally fit and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. Fig. 14(b) shows the calculated wavefunctions for the lower energy levels. Fig. 15 shows that the experimental PEFs for 13Si2CB and its deuterated analogs are almost identical. The observed and calculated frequencies are shown in Table 11. The calculated inversion barriers from experimental data are 86-87 cm-1.
The ab initio calculation predicts a
value of 89 cm-1. Fig. S10 shows the comparison of the experimental PEFs using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for 13Si2CB and its deuterated species. 42
Fig. 14. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. The 0 – 1 transition value is from the experimental fit. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.130 Å and 𝜃𝑚𝑖𝑛= ±22.3°.
Fig. 15. Experimental PEFs for 13Si2CB isotopic species based on Eq. (4). 43
Table 11 Observed and Calculated Ring-Puckering Transitions (cm-1) for 13Si2CB, 13Si2CB-d3 and 13Si2CB-d4. 13Si2CB Transition
13Si2CB-d3
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
0–1
---
2.954
---
2.873
1–2
56.0
56.1
-0.1
2–3
~31.6
31.2
3–4
49.5
4–5
Experimental fit
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
---
1.819
---
1.805
3.8
52.8
52.8
0.0
29.4
---
---
24.2
-0.1
46.9
2.6
43.3
54.7
-0.2
52.2
2.3
-0.1
60.9
0.1
58.4
66.2
-0.2
66.0
0.0
70.6
70.7
-0.1
70.6
8–9
74.7
74.7
0.0
9 – 10
78.5
78.4
10 – 11
82.0
11 – 12
Theoreticald
∆
Theoreticald
∆
---
2.612
---
---
1.547
---
55.9
0.1
52.2
52.8
0.0
49.7
3.1
---
30.9
---
---
24.2
---
22.6
---
49.9
-0.4
49.6
43.3
0.0
43.3
0.0
40.7
2.6
54.5
54.9
-0.4
46.9
47.0
-0.1
47.0
-0.1
44.7
2.2
5–6
61.0
61.1
2.6
52.8
52.8
0.0
52.8
0.0
50.4
2.4
6–7
66.0
63.6
2.4
57.2
57.3
-0.1
57.3
-0.1
55.0
2.2
7–8
0.0
68.3
2.3
61.5
61.3
0.2
61.3
0.2
59.2
2.3
74.7
0.0
72.5
2.2
65.1
65.0
0.1
65.0
0.1
63.0
2.1
0.1
78.4
0.1
76.5
2.0
68.1
68.3
-0.2
68.3
-0.2
66.5
1.6
81.8
0.2
81.9
0.1
80.2
1.8
71.4
71.3
0.1
71.4
0.0
69.8
1.6
85.3
85.0
0.3
85.2
0.1
83.6
1.7
---
74.2
---
74.2
---
72.9
---
12 – 13
88.2
88.0
0.2
88.2
0.0
86.9
1.3
---
76.8
---
76.9
---
75.8
---
13 – 14
91.2
90.8
0.4
91.1
0.1
90.0
1.2
---
79.4
---
79.4
---
78.6
---
14 – 15
93.9
93.5
0.4
93.8
0.1
93.0
0.9
---
81.7
---
81.8
---
81.2
---
0–3
89.6
90.3
-0.7
89.7
-0.1
84.2
5.4
---
78.9
---
78.8
-----
73.9
---
Ramane
89.6
90.3
-0.7
0–2
---
59.1
---
58.8
---
54.8
---
---
54.6
---
54.6
---
51.3
---
1–3
86
87.3
-1.3
86.8
-0.8
81.6
4.4
---
77.1
---
77.0
---
72.4
---
2–4
~80
81.1
---
80.5
---
76.3
---
---
67.6
---
67.5
---
63.3
---
3–5
105
104.9
0.1
104.3
0.7
99.1
5.9
---
90.3
---
90.3
---
85.3
---
4–6
116
116.1
-0.1
115.6
0.4
110.6
5.4
---
99.8
---
99.8
---
95.1
---
5–7
127
127.3
-0.3
126.9
0.1
122.0
5.0
---
110.1
---
110.1
---
105.4
---
6–8
137
136.8
0.2
136.6
0.4
131.9
5.1
---
118.6
---
118.6
---
114.2
---
∆
44
Observed
∆
Table 11 Continued. 13Si2CB Transition
Ramane
13Si2CB-d3
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
146
145.4
0.6
145.2
0.8
140.8
5.2
---
126.3
---
126.3
---
122.2
---
8 – 10
153
153.1
-0.1
153.1
-0.1
149.0
4.0
---
133.2
---
133.3
---
129.5
---
9 – 11
161
160.3
0.7
160.3
0.7
156.7
4.3
---
139.6
---
139.7
---
136.3
---
10 – 12
~168
166.9
---
167.1
---
163.8
---
---
145.5
---
145.6
---
142.7
---
11 – 13
173
173.0
0.0
173.4
-0.4
170.5
2.5
---
151.0
---
151.2
---
148.7
---
12 – 14
~180
178.8
---
179.3
---
176.9
---
---
156.2
---
156.4
---
154.4
---
13 – 15
187
184.3
2.7
184.9
2.1
183.0
4.0
---
161.1
---
161.3
---
159.8
---
13Si2CB-d4 Transition
Experimental. fit 4
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
1.602
---
1.562
---
1.321
---
1–2
52.0
52.0
0.0
52.0
0.0
49.1
2.9
2–3
---
22.7
---
22.5
---
20.9
---
3–4
41.8
41.8
0.0
41.7
0.1
39.1
2.7
4–5
45.1
45.1
0.0
45.0
0.1
42.7
2.4
5–6
50.7
50.8
-0.1
50.7
0.0
48.3
2.4
6–7
55.0
55.2
-0.2
55.1
-0.1
52.8
2.2
7–8
59.1
59.1
0.0
59.1
0.0
56.8
2.3
8–9
62.5
62.6
-0.1
62.6
-0.1
60.5
2.0
9 – 10
65.8
65.9
-0.1
65.9
-0.1
63.9
1.9
10 – 11
68.7
68.8
-0.1
68.9
-0.2
67.1
1.6
11 – 12
71.4
71.6
-0.2
71.7
-0.3
70.1
1.3
12 – 13
75.2
74.2
1.0
74.3
0.9
72.9
2.3
13 – 14
~77
76.6
---
76.8
---
75.6
---
FIRa
Observed
0–1
𝑉(𝑥
,𝑥2)b
45
Table 11 Continued. 13Si2CB-d4 Transition
Experimental. fit 4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
FIRa
Observed
14 – 15
79.0
79.0
0.0
79.1
-0.1
78.1
0.9
15 – 16
81.2
81.1
0.1
81.4
-0.2
80.6
0.6
0–3
76.0
76.3
-0.3
76.0
0.0
71.3
4.7
𝑉(𝑥
FIR data for 13Si2CB and 13Si2CB-d4 from Ref. [20]. FIR data for 13Si2CB-d3 from Ref. [53]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Raman data for 13Si CB from Ref. [20]. 2 a
b
46
There are no experimental ring-puckering spectra for GeCB nor for 13Ge2CB. Nevertheless, we calculated their kinetic energy expressions and these are shown in Table S2. The calculated PEFs parameters based on the ab initio calculations are shown in Tables 2 and 3. Fig. 16(a) shows the theoretical ring-puckering PEFs and energy levels for GeCB. The barrier is calculated to be 409 cm-1. The predicted infrared transition frequencies are also shown in the figure. Fig. 16(b) shows the calculated wavefunctions for the lower energy levels of GeCB. Fig. 17(a) shows the theoretical ringpuckering PEFs and energy levels for 13Ge2CB. The predicted infrared transitions are also shown in the figure. As can be seen, the molecule is essentially planar with a calculated barrier of 1 cm-1, and this results from the small magnitude of the -GeH2-CH2- torsional interactions. Fig. 17(b) shows the calculated wavefunctions for the lower energy levels of 13Ge2CB.
47
Fig. 16. (a) Theoretical ring-puckering PEFs for GeCB. The predicted infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.156Å and 𝜃𝑚𝑖𝑛= ±30.1°.
Fig. 17. (a) Theoretical ring-puckering PEFs for 13Ge2CB. The predicted infrared transitions are also shown in the figure. The predicted 0 – 1 transition is 29.6 cm-1. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.047Å and 𝜃𝑚𝑖𝑛= ±7.8°.
48
3.4. Cyclobutanone Borgers and Strauss [44] reported the far-infrared spectra of cyclobutanone (CBONE) in 1966 and determined a ring-puckering PEF with a barrier of 5 cm-1. In the same year Durig and Lord [54] published the far-infrared spectra for CBONE and its deuterated analog cyclobutanoned4 (CBONE-α,α'd4). They predicted a very low barrier for the ring-puckering of CBONE [54] but did not report a value. Fig. 18(a) shows the experimental and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. Fig. 18(b) shows the calculated wavefunctions for the lower energy levels.
Fig. 19 shows the calculated
PEFs from experimental fits for CBONE and its deuterated analog. The barrier to planarity is 2 cm-1 whereas the theoretical calculation predicts 36 cm-1. The observed and calculated frequencies are shown in Table 12. The kinetic energy terms for CBONE and CBONE-d4 are given in Table S2 and the potential energy parameters are given in Tables 2 and 3. Fig. S11 shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for CBONE and its deuterated species CBONE-α,α'd4.
49
Fig. 18. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.043 Å and 𝜃𝑚𝑖𝑛= ±4.6°.
Fig. 19. Experimental PEFs for CBONE isotopic species based on Eq. (4).
50
Table 12 Observed and Calculated Ring-Puckering Transitions (cm-1) for CBONE and CBONE- α,α'd4. CBONE- α,α'd4
CBONE Transition
Experimental. fit 4
,𝑥2)b
∆
Experimental fit ∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
31.6
---
36.6
---
23.2
---
47.1
46.8
0.3
47.1
0.0
56.7
-9.6
1.6
54.2
54.3
-0.1
54.3
-0.1
63.4
-9.2
73.6
-1.4
60.6
60.5
0.1
60.2
0.4
73.6
-13.0
0.2
81.2
-3.8
65.6
65.7
-0.1
65.4
0.2
81.2
-15.6
82.3
-0.8
87.8
-6.3
69.8
70.2
-0.4
70.0
-0.2
87.8
-18.0
-1.65
85.20
0.05
93.6
-8.3
73.2
74.10
-0.9
74.20
-1.0
93.6
-20.4
91.1
---
1.5
---
98.7
---
78.9
77.7
1.2
78.1
0.8
98.7
-19.8
157.5
0.4
157.6
0.3
143.3
14.6
---
132.7
138.1
---
143.3
---
FIRa
Observed
0–1
36.5
38.1
-1.6
1–2
56.8
55.4
2–3
65.0
3–4
𝑉(𝑥
4
𝑉(𝑥 ,𝑥
2
,𝑥6)c
∆
Theoreticald
∆
37.9
-1.4
23.2
13.3
~30
1.4
55.5
1.3
56.7
0.1
64.1
0.9
64.2
0.8
63.4
72.2
71.3
0.9
71.3
0.9
4–5
77.4
77.2
0.2
77.2
5–6
81.5
82.4
-0.9
6–7
85.25
86.90
7– 8
---
0–3
157.9
FIR data for CBONE from Ref. [44]. FIR data for CBONE-α,α'd4 from Ref. [54]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. a
b
51
Observed
𝑉(𝑥
4
,𝑥2)b
---
∆
3.5. Comparison of CCSD and MP2 results Comparisons of the calculated ring-puckering barriers and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛values obtained from the experimental fits using Eq. (4) with those from the theoretical CCSD/cc-pVTZ and MP2/cc-pVTZ calculations are shown in Table 7. Overall, the CCSD computations lead to better predictions for the ring-puckering barriers and 𝜃𝑚𝑖𝑛. This table shows that the CCSD/cc-pVTZ calculations predicted the barriers to planarity for the ring-puckering with errors ranging from 2 to 14%, and the 𝜃𝑚𝑖𝑛 values with errors with a ranging from zero to 9% for all the molecules except TMO and CBONE, both of which are essentially planar with tiny barriers. The errors from the MP2/cc-pVTZ calculations ranged from of 35 to 86% for the barriers and from 1 to 16% for the 𝜃𝑚𝑖𝑛 values for the molecules other than TMO and CBONE. For TMO, which has an experimental barrier of 15 cm-1 and 𝜃𝑚𝑖𝑛 equal to 13.4°, the MP2 calculation did better at prediction. For TMO the CCSD calculation predicted a basically planar molecule while the MP2 calculation predicted a barrier of 21 cm-1 and a 𝜃𝑚𝑖𝑛 equal to 14.8°. For CBONE, both methods predicted somewhat higher barriers than the experimental value of 2 cm-1.
52
Fig. 20. Experimental PEFs for the ring-puckering of four-membered ring molecules based on Eq. (4).
4. Conclusion As discussed above, the far-infrared, Raman and/or combination band spectra of these fourmembered ring molecules have previously been published. In addition, one-dimensional potential energy functions utilizing either Eq. (1) in dimensional form or Eq. (2) in reduced (dimensionless) form have been reported. Typically, fairly good frequency fits and reasonable calculations of potential energy barriers were achieved. The major flaw in these calculations has been the inability to determine to what degree other low-frequency vibrational motions couple with the simple onedimensional puckering model. In an investigation of 1,3-disilacyclobutane and its d4 species18 we found that by empirically adjusting the extent of coupling between a SiH2 rocking mode and the ring puckering we could utilize the same PEF for both isotopic species. Our present work more accurately models how MH2 (M = C, Si, or Ge) rocking motions couple with the puckering. In
53
addition, these computations have allowed us to much better calculate the values of 𝜔, which describes the relative angle bendings within these four-membered rings. The net result is that we have achieved much more reliable kinetic energy expansions 𝑔44(𝑥). These in turn have allowed us to attain much improved PEFs and to accurately establish their energy minima and energy barriers. We have also found that these refined PEFs agree remarkably well with those generated directly from the CCSD/cc-pVTZ ab initio calculations. Previous work on these molecules which did not utilize reliable rocking parameters 𝑅 resulted in incorrect reduced mass calculations and poor agreement between experimental and ab initio results. For each molecule we calculated the optimized PEF using both Eq. (1) and Eq. (4). Fig. 20 compares these based on Eq. (4). As we have shown before11 the potential energy parameter 𝑎 arises mostly from angle strain while 𝑏 arises from torsional forces. The coefficient 𝑐 in Eq. (4) primarily has the effect of slightly refining the shape of the PEF. Table 4 shows that the magnitude of the improvement from adding the 𝑥6 term is fairly small. As can be seen, in Tables 2 and 3 the magnitude of the angle strain coefficient 𝑎 goes in the order CB > TMO > TMS > SiCB > TMSe > 13Si2CB which is in the order expected. CCC angles are stiffer than CSC, CSeC, or CSiC angles, for example. The negative magnitudes of the coefficient 𝑏 reflect the fact that -CH2-CH2interaction are stronger than the -SiH2-CH2- torsional interactions. Cyclobutane has four of the former while TMO and TMS have only two and thus correspondingly lower 𝑏 values. SiCB has two -CH2-CH2 and two -CH2-SiH2- interactions while 13Si2CB has two of the latter.
Acknowledgements The authors wish to thank the Welch Foundation (Grant A-0396) for financial support. Computations were carried out on the Texas A&M University Department of Chemistry Medusa
54
computer system funded by the National Science Foundation, Grant No. CHE-0541587. The Laboratory for Molecular Simulation provided the Semichem AMPAC/AGUI software.
Appendix A. Supplementary material Supplementary material associated with this article can be found online at https://doi.org/..... References [1] J. Laane, E. J. Ocola, H. J. Chun, in Frontiers and Advances in Molecular Spectroscopy, edited by J. Laane (Elsevier: Amsterdam, 2017), p. 101. [2] J. Laane, in Frontiers of Molecular Spectroscopy, edited by J. Laane (Elsevier: Amsterdam,2009), p.63. [3] J. Laane, J. Phys. Chem. A, 104, 7715 (2000). [4] J. Laane, in Structures and Conformations of Non-Rigid Molecules, edited by J. Laane, M. Dakkouri, B. van der Veken, and H. Oberhammer (Kluwer Publishing: Amsterdam, 1993), p. 65. [5] J. Laane, Int. Rev. in Phys. Chem. 18, 301 (1999). [6] J. Laane, Annu. Rev. Phys. Chem. 45, 179 (1994). [7] J. Laane, J. Pure and Appl. Chem. 59, 1307 (1987). [8] L.A. Carreira, R. C. Lord, and T. B. Malloy Jr. Top. Curr. Chem. 82, 1 (1979). [9] J. Laane, Quart. Rev. 25, 533 (1971). [10] R. P. Bell, Proc. R. Soc. London, A183, 328 (1945). [11] J. Laane, J. Phys. Chem. 95, 9246 (1991). [12] J. Laane, R. C. Lord, J. Chem. Phys. 48, 1508 (1968). 55
[13] J. Laane, Appl. Spectrosc. 24, 73 (1970). [14] E. B. Wilson, Jr., J. Chem. Phys. 7, 1047 (1939). [15] E. B. Wilson, Jr., J. Chem. Phys. 9, 76 (1941). [16] T. B. Malloy, Jr., T. J. Lafferty, J. Mol. Spec. 54, 20 (1975). [17] J. Laane, M. A. Harthcock, P. M. Killough, L. E. Bauman, and J. M. Cooke, J. Mol. Spec. 91, 286 (1982). [18] M. A. Harthcock and J. Laane, J. Mol. Spec. 91, 300 (1982). [19] D. O. Harris, H. W. Harrington, A. C. Luntz, and W. D. Gwinn, J. Chem. Phys. 44, 3467 (1966). [20] R. M. Irwin, J. M. Cooke and J. Laane, J. Am. Chem. Soc. 99, 3273 (1977). [21] T. Egawa, T. Fukuyama, S. Yamamoto, F. Takabayashi, H. Kambara, T. Ueda, and K. Kuchitsu, J. Chem. Phys. 86, 6018 (1987). [22] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, et al. Gaussian 09, Revision A.02, Gaussian, Inc: Wallingford, CT (2009). [23] AGUI, Semichem, Inc: Shawnee, KS, www.semichem.com. [24] N. Meinander, J. Laane, J. Mol. Struct. 569, 1 (2001). [25] Maple 2015, Waterloo Maple Inc: Waterloo, ON, Canada, www.maplesoft.com. [26] F. A. Miller and R. J. Capwell, Spectrochim. Acta 27A. 947 (1971). [27] J. M. R. Stone and I. M. Mills, Mol. Phys. 18, 631 (1970). [28] C. Rafilipomanana, D. Cavagnat, R. Cavagnat, J. C. Lassegues, and C. Biran, J. Mol. Struct. 127. 283 (1985). [29] A. Danti, W. J. Lafferty, and R. C. Lord, J. Chem. Phys. 33, 294 (1960).
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[30] S. I. Chan, T. R. Borgers, J. W. Russell, H. L. Strauss, and W. D. Gwinn, J. Chem. Phys. 44, 1103 (1966). [31] H. Wieser, M. Danyluk, and R. A. Kydd, J. Mol. Spectrosc. 43, 382 (1972). [32] W. Kiefer, H. J. Berstein M. Danyluk and H. Wieser, Chem. Phys. Lett. 12, 605 (1972). [33] W. Kiefer, H. J. Berstein H. Wieser, and M. Danyluk, J. Mol. Spectrosc. 43, 393 (1972). [34] J. Jokisaari and J. Kaupinen, J. Chem. Phys. 59, 2260 (1973). [35] G. Mozzurri, M. Kunzmann, B. P. Winnewisser, and M. Winnewisser. J. Mol. Spectrosc. 219, 152 (2003). [36] J. Fernández, R. J. Myers, and W. D. Gwinn, J. Chem. Phys. 23, 758 (1955). [37] S. I. Chan, J. Zinn, J. Fernández, and W. D. Gwinn, J. Chem. Phys. 33, 1643 (1960). [38] S. I. Chan, J. Zinn, and W. D. Gwinn, W. D. J. Chem. Phys. 33, 295 (1960). [39] S. I. Chan, J. Zinn, and W. D. Gwinn, J. Chem. Phys. 34, 1319 (1961). [40] J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spectrosc. 34, 136 (1970). [41] I. Foltynowicz, J. Konarski, and Marek Kręglewski, J. Mol. Spectrosc. 87, 29 (1981). [42] I. Foltynowicz, J. Mol. Spectrosc. 96, 239 (1982). [43] V. Szalay, G. Bánhegyi, and G. Fogarasi, J. Mol. Spectrosc. 126, 1 (1987). [44] T. R. Borgers and H. L. Strauss, J. Chem. Phys. 45, 947 (1966). [45] H. Wieser, J. A. Duckett, and R. A. Kydd, J. Mol. Spectrosc. 51, 115 (1974). [46] J. R. Durig, A. C. Shing, L. A. Carreira, and Y. S. Li, J. Chem. Phys. 57, 4398 (1972). [47] H. Wieser and R. A. Kydd, J. Raman Spectrosc. 4, 401-407 (1976). [48] A. B. Harvey, J. R. Durig, and A. C. Morrisey, J. Chem. Phys. 50, 4949 (1969). [49] J. Laane, J. Am. Chem. Soc. 89, 1144 (1967). [50] W. C. Pringle, Jr., J. Chem. Phys. 54, 4979 (1971).
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[51] J. D. Lewis, T. H. Chao, and J. Laane, 62, 1932 (1975). [52] M. A. Harthcock, J. M. Cooke, J. Laane, J. Phys. Chem. 86, 4335 (1982). [53] P. W. Jagodzinski, R. M. Irwin, J. M. Cooke, and J. Laane, J. Mol. Spec. 84, 139 (1980). [54] J. R. Durig, J. R. and R. C. Lord, J. Chem. Phys. 45, 61 (1966).
Captions for tables In the Main Body: Table 1. Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters. Table 2. Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Table 3. Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐𝑥6. Table 4. Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4). Table 5. Observed and Calculated Ring-Puckering Transitions (cm-1) for CB, CB-d8 and CB-d1. Table 6. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs. Table 7. Comparison of experimental barriers, and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛 values with those from theoretical calculations. Table 8. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMS and deuterated analogs. Table 9. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMSe. Table 10. Observed and Calculated Ring-Puckering Transitions (cm-1) for SiCB and deuterated analogs. Table 11. Observed and Calculated Ring-Puckering Transitions (cm-1) for 13Si2CB, 13Si2CB-d3 and 13Si2CB-d4. Table 12. Observed and Calculated Ring-Puckering Transitions (cm-1) for CBONE and CBONEα,α'd4. 58
In the supplementary material: Table S1. Comparison of the Experimental Geometrical Parameters of CB and Related Molecules to those from our Computations for the Puckered and the Planar Configurations. Table S2. Coefficients of the Kinetic Energy Functions for CB and Related Molecules. 𝑔44(𝑥) = 𝑎𝑥0 +𝑏𝑥 + 𝑐𝑥2 +𝑑𝑥3 + 𝑒𝑥4 +𝑓𝑥5 +𝑔𝑥6. Table S3. Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters for TMO. Table S4. Coefficients of the Kinetic Energy Functions for TMO and deuterated analogs. 𝑔44(𝑥) = 𝑎𝑥0 +𝑏𝑥 + 𝑐𝑥2 +𝑑𝑥3 + 𝑒𝑥4 +𝑓𝑥5 +𝑔𝑥6. Table S5. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs from MP2/cc-pVTZ computations. Table S6. Ring-Puckering Parameters for TMO and deuterated analogs using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Table S7. Ring-Puckering Parameters for TMO and deuterated analogs using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐 𝑥6. Table S8. Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4) for TMO. Captions for figures In the main body: Fig. 1. Definition of the ring-puckering angle (𝜃), the SiH2 rocking angle (𝛽) and the ringpuckering coordinate (𝑥) for SiCB. The angle 𝛽 is defined as the angle between the bisectors of the CSiC an HSiH angles. All values shown are the results from CCSD/cc-pVTZ computations. Fig. 2. Calculated structural parameters of CB and related molecules in their minimum energy conformations (puckered) from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å). Fig. 3. Ring-puckering angles of the energetic minimum, ϴ𝑚𝑖𝑛 from CCSD/cc-pVTZ computations. Fig. 4. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion.
59
Fig. 5. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for CB. The observed transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.142 Å and 𝜃𝑚𝑖𝑛= ±29.6°. Fig. 6. Experimental PEFs for CB isotopic species based on Eq. (4). Fig. 7. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using CCSD/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063Å and 𝜃𝑚𝑖𝑛= ±13.6°. Fig. 8. Experimental PEFs for TMO isotopic species based on Eq. (4) from CCSD/cc-pVTZ computations. Fig. 9. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMS. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.141 Å and 𝜃𝑚𝑖𝑛= ±26.9°. Fig. 10. Experimental PEFs for TMS isotopic species based on Eq. (4). Fig. 11. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMSe. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.162 Å and 𝜃𝑚𝑖𝑛= ±30.4°. Fig. 12. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.163 Å and 𝜃𝑚𝑖𝑛= ±31.9°. Fig. 13. Experimental PEFs for SiCB isotopic species based on Eq. (4). Fig. 14. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. The 0 – 1 transition value is from the experimental fit. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.130 Å and 𝜃𝑚𝑖𝑛= ±22.3°. Fig. 15. Experimental PEFs for 13Si2CB isotopic species based on Eq. (4). Fig. 16. (a) Theoretical ring-puckering PEFs for GeCB. The predicted infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.156Å and 𝜃𝑚𝑖𝑛= ±30.1°.
60
Fig. 17. (a) Theoretical ring-puckering PEFs for 13Ge2CB. The predicted infrared transitions are also shown in the figure. The predicted 0 – 1 transition is 29.6 cm-1. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.047Å and 𝜃𝑚𝑖𝑛= ±7.8°. Fig. 18. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.043 Å and 𝜃𝑚𝑖𝑛= ±4.6°. Fig. 19. Experimental PEFs for CBONE isotopic species based on Eq. (4). Fig. 20. Experimental PEFs for the ring-puckering of four-membered ring molecules based on Eq. (4). In the supplementary material: Fig. S1 Calculated structural parameters of CB and related molecules in their planar conformations from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å). Fig. S2. Experimentally fit and theoretical ring-puckering PEFs for (a) CB, (b) CB-d8 and (c) CB-d1 from CCSD/cc-pVTZ computations. Fig. S3. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion of TMO. Fig. S4. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using MP2/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.062Å and 𝜃𝑚𝑖𝑛= ±13.4°. Fig. S5. Experimental PEFs for TMO isotopic species based on Eq. (4) using the 𝜌, 𝜔, 𝛽 and 𝑅 parameters for TMO defined by MP2/cc-pVTZ computations. Fig. S6. Experimentally fit and theoretical ring-puckering PEFs for (a) TMO, (b) TMO-αd2, (c) TMO-βd2, (d) TMO-α,α'd4, (e) TMO-d6. from MP2/cc-pVTZ computations. Fig. S7. Experimentally fit and theoretical ring-puckering PEFs for (a) TMS, (b) TMS-αd2, (c) TMS-βd2, (d) TMS-α,α’d4 and (e) TMS-d6 from CCSD/cc-pVTZ computations. Fig. S8. Experimentally fit and theoretical ring-puckering PEFs for TMSe from CCSD/cc-pVTZ computations. Fig. S9. Experimentally fit and theoretical ring-puckering PEFs for (a) SiCB, (b) SiCB-d1 and (c) SiCB-d2 from CCSD/cc-pVTZ computations. 61
Fig. S10. Experimentally fit and theoretical ring-puckering PEFs for (a) 13Si2CB, (b) 13Si2CBd3 and (c) 13Si2CB-d4 from CCSD/cc-pVTZ computations. Fig. S11. Experimentally fit and theoretical ring-puckering PEFs for (a) CBONE and (b) CBONEα,α’d4 from CCSD/cc-pVTZ computations. Graphical Abstract
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S0301-0104(19)31153-X https://doi.org/10.1016/j.chemphys.2019.110647 CHEMPH 110647
To appear in:
Chemical Physics
Received Date: Revised Date: Accepted Date:
26 September 2019 21 November 2019 27 November 2019
Please cite this article as: E.J. Ocola, J. Laane, Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations, Chemical Physics (2019), doi: https://doi.org/10.1016/j.chemphys.2019.110647
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© 2019 Published by Elsevier B.V.
Ring-puckering potential energy functions for cyclobutane and related molecules based on refined kinetic energy expansions and theoretical calculations Esther J. Ocola and Jaan Laane* Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255
Abstract With the aid of ab initio calculations, the one-dimensional representations of the ringpuckering vibrations of several four-membered ring molecules have been refined. These onedimensional models include contributions from MH2 (M= C, Si, Ge) rocking motions and utilize the computed parameter ω which reflects the relative amounts of ring angle bendings. This model leads to much more accurate determinations of the coordinate dependent kinetic energy expressions 𝑔44(x) which in turn allow much more accurate calculations of the ring-puckering potential energy functions (PEFs) based on experimental data. The resulting experimental PEFs agree remarkably well with the theoretical functions determined from ab initio calculations. For each molecule spectroscopic data were fit very well utilizing the refined kinetic energy functions and two term PEFs. They were fit even better using three term PEFs including x6 terms. The PEFs, barrier heights, and energy minima are presented for each of these molecules and their isotopic species.
Keywords: Potential energy functions; ring puckering vibration; ab initio calculations; refined kinetic energy expressions; four membered rings; far infrared and Raman spectra. * Corresponding author email: LAANE@ CHEM.TAMU.EDU, phone: 979-220-5341 1
1. Introduction We and others have been studying the vibrational potential energy functions of largeamplitude ring-puckering vibrations of four-membered rings and larger molecules for more than half a century [1-13]. For selective molecules, such as those studied in the present work, where the ring-puckering vibrations are of low-frequency, they can be examined independently from the other 3N-7 vibrations based on the separation of high and low frequencies [14,15]. As first pointed out by Bell [10] in 1945, this vibration is of special quantum mechanical interest in that the potential energy function (PEF) for the motion should be governed by a quartic term rather than the usual quadratic one such as that for the harmonic oscillator. As shown by Laane [11], the form of the one-dimensional potential energy function should actually be 𝑉 = 𝑎𝑥4 +𝑏𝑥2
(1)
where 𝑥 is the ring-puckering coordinate as defined in Fig. 1 for silacylobutane (SiCB). The distance between the two ring diagonals is taken to be 2𝑥. Two opposite ring atoms move up a distance 𝑥 from the planar ring structure and two atoms move down a distance 𝑥. Whether the energy minimum for a four-membered ring corresponds to a planar structure where 𝑥 = 0 or to a puckered one depends on the angle strain and torsional forces within the molecule. As shown in detail by Laane [11], if the angle strain in each molecule originates from a quadratic dependence on the interior ring angle deviations from ideality (𝑉~∆ϕ2), both the 𝑎 and 𝑏 coefficients in Eq. (1) would be positive. However, torsional forces such as -CH2-CH2- interactions generally result in negative contributions to 𝑏. Hence, silacyclobutane, which has both -CH2-CH2- and -SiH2-CH2interactions contributing to a negative 𝑏 value, is non-planar with a barrier to planarity of 442 cm-1 as reported in the original far-infrared study [12].
2
Many of the earlier studies which we carried out utilized reduced coordinates, which do not require knowledge of the reduced mass, to fit the experimental data with a reduced potential energy function (PEF). The most common form of the reduced PEF is 𝑉 = 𝐴(𝑍4 ―𝐵𝑍2)
(2)
Fig. 1. Definition of the ring-puckering angle (𝜃), the SiH2 rocking angle (𝛽) and the ringpuckering coordinate (𝑥) for SiCB. The angle 𝛽 is defined as the angle between the bisectors of the CSiC an HSiH angles. All values shown are the results from CCSD/cc-pVTZ computations. where Z is a reduced (dimensionless) coordinate and where the coefficients 𝐴 and 𝐵 can be related to 𝑎, 𝑏 in Eq. (1) if the reduced mass µ is known. Similarly, 𝑥 and 𝑍 can be related for known values of µ. In 1970 Laane [13] provided numerical tables for solutions to the energy levels from Eq. (2) for a large range of 𝐵 values, and these were widely used by many laboratories. One problem with solutions to Eq. (2) is that the ring-puckering energy minima are given in terms of 𝑍 and not in dimensioned units. Hence, the actual puckering minima could not be determined. Another problem with Eq. (2) is that it implies that the reduced mass is fixed, whereas, as is now well known, it varies considerably as a function of the puckering coordinate. To overcome these problems numerical methods for calculating the reduced mass as a function of coordinate were first utilized by Malloy [16] and then fully described by the Laane group [17,18]. This allowed the reciprocal reduced mass functions g44(𝑥) to be calculated with a dependence on the puckering 3
coordinate 𝑥. (Subcripts 1 to 3 on g were reserved for the molecular rotations). The quantum mechanical problem then has the form ∂ ―ћ2 ∂ (𝑥) g 44 ∂𝑥 2 ∂𝑥
(3)
+𝑉(𝑥) = 𝐸𝛹
where 𝑉 is given in Eq. (2) or as shown below including a 𝑥6 term. 𝑉 = 𝑎𝑥4 +𝑏𝑥2 + 𝑐𝑥6.
(4)
In order to correctly calculate the coordinate dependence of g44(𝑥), as pointed out by Gwinn and co-workers [19], it is necessary to know the relative amounts of bending at the interior angles of the four-membered rings. The Gwinn group defined
ω=
(11 ―+ ρρ)
(5)
where 𝜌 for silacyclobutane in Fig. 1 would be 𝜌=
(
)
∆𝑟𝐶𝛽 ― 𝑆𝑖 ∆𝑟𝐶𝛼 ― 𝐶𝛼 𝑟°𝐶𝛽 ― 𝑆𝑖 / 𝑟°𝐶𝛼 ― 𝐶𝛼
(6)
where the 𝑟° are the lengths of the diagonals in the planar molecule, and where the ∆𝑟 are changes in the diagonal distances upon puckering. Thus 𝜌 = 1 and ω = 0 when all of the ring angles decrease equally during ring-puckering. This is the case for cyclobutane. For silacyclobutane, since the CSiC angle bending force constant is less than the CCSi force constant, 𝜌 will be less than 1.0 and ω will be positive. Until recently the correct value of ω could only be roughly approximated. With the advent of reliable ab initio computations, however, we are now able to calculate the 𝜌 values quite accurately and thus get reliable values for ω. These will be utilized for our computations in this work. Another problem with obtaining reliable g44(𝑥) expansions has been the approximation that the ring-puckering vibration is entirely one-dimensional. In previous studies [20] we showed 4
that the SiH2 rocking in 1,3-disilacyclobutane (13Si2CB) is strongly coupled to the puckering motion and we defined a rocking parameter 𝑅 for the amount of rocking that was proportional to the puckering coordinate 𝑥. This parameter 𝑅 is defined as 𝑅 = 𝛽/𝑥
(7)
where 𝛽 in radians is the magnitude of the MH2 (M=C,Si, Ge) rocking and 𝑥 is the puckering coordinate in Å. Similarly, Egawa [21] has defined the same type of parameter for the amount of CH2 rocking
coupled to the puckering of cyclobutane. For cases such as these we are now able to use ab initio calculations to predict quite accurately the amount of MH2 (M = C, Si or Ge) rocking occurring during the puckering vibrations. It should be emphasized that molecules such as cyclobutane (CB) and silacyclobutane (SiCB) each have thirty vibrations and trimethylene oxide (TMO) has twenty four vibrations. Fortunately, most vibrations other than the ring-puckering are of small amplitude so their very small contributions to the overall potential energy surface can quite safely be neglected. We have incorporated the moderate-amplitude MH2 rocking motions into the vibrational model and this has helped considerably in refining the PEFs. We feel that inclusion of additional motions in our model would be of little value. In the present paper we will calculate the structures and conformational energies of the four-membered ring molecules shown below as a function of the puckering coordinate 𝑥. For each 𝑥 value we then determine the relative amounts of angle bending within the ring as well as the amount of CH2 and/or SiH2 and/or GeH2 rocking. This provides us with values for ω and the rocking parameters 𝑅 that we can use to give us much more accurate computations of g44(𝑥) for each molecule. Our expectation is that while the frequency fits with the experimental data may only be somewhat improved, but we will have much more accurate representations of how the
5
potential energy varies with the dimensioned coordinate 𝑥. This will also provide us with much more accurate values for 𝑥 and the puckering dihedral angles that correspond to the energy minima (𝑥𝑚𝑖𝑛). It should be emphasized that the objective of this study is aimed at utilizing ab initio calculations to more accurately refine the model of the one-dimensional ring-puckering vibration and therefore produce much more accurate kinetic energy functions. These in turn result in improved and more meaningful one-dimensional potential energy functions. Although we have used a fairly high level of theory for the computations and this has resulted in theoretical PEFs which agree quite well with the experimental ones, we have not strived to carry out even higher level calculations which could improve the PEFs even more. Such calculations would have taken huge amounts of computing time for each of the molecules we have studied. Moreover, the CCSD/cc-pVTZ computations that we have carried out are more than adequate for refining the vibrational models for the puckering vibration.
2. Calculations 2.1. Structure calculations The geometrical structures of each of these molecules were calculated using CCSD/ccpVTZ and MP2/cc-pVTZ ab initio computations. In the present paper we will primarily discuss the results from the CCSD/cc-pVTZ calculations. The Gaussian 09 program [22] was used for the computations, and the Semichem AMPAC/AGUI program [23] was used to visualize the structures. The calculated geometrical structures of the molecules are shown in Fig. 2 and Fig. 3. 6
supplementary Table S1 compares the experimental geometrical parameters to those from our computations for the puckered and the planar conformations. On the whole, there is a very good agreement. Fig. S1 in the supplementary material presents the calculated geometrical structures of the molecules in their planar conformations. These were also needed for the kinetic energy calculations. Higher level ab initio calculations would be warranted for the molecules with heavier atoms such as Se and Ge. However, we felt that the CCSD/cc-pVTZ computations would nonetheless yield useful estimates for the and values and thus produce better kinetic energy functions. As can be seen in later discussion, the agreement between the experimental PEF and that from theory is poorer for TMSe.
Fig. 2. Calculated structural parameters of CB and related molecules in their minimum energy conformations (puckered) from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å).
7
Fig. 3. Ring-puckering angles of the energetic minimum, 𝜃𝑚𝑖𝑛 from CCSD/cc-pVTZ computations. 2.2. Kinetic energy calculations The Laane RDMS4 program [17,18] based on vector and numerical methods was used to calculate the coordinate dependent kinetic energy functions for the ring-puckering of each of the four-membered ring molecules. The geometrical parameters for the computed planar structures of these molecules provided the input for the program. As discussed above, the ab initio calculations allowed us to calculate for each molecule the 𝜌 and 𝜔 values, which are related to the relative amounts of angle bending, and also the 𝑅 values reflecting the amounts of MH2 or MD2 rocking. (M=C, Si, or Ge). Table 1 presents the calculated 𝜌, 𝜔, 𝑥𝑚𝑖𝑛, 𝛽 and 𝑅 values for each molecule. The expressions for 𝑔44(𝑥) for each molecule are given in Table S2. Fig. 4 shows how 𝑔44(𝑥) varies with the ring-puckering coordinate, 𝑥, for these molecules. As can be seen, in all cases 𝑔44 (𝑥) is largest for the planar structure at x = 0 but decreases as the reduced mass increases as the molecule puckers. As we observed from our calculations on 13Si2CB the reduced mass and 𝑔44(x) 8
values vary a great deal depending on the rocking parameters 𝑅. Hence, the excellent agreement between experimental and theoretical PEFs (to be shown below) resulted from very accurate representations of the vibrational model. It might be noted that in Fig. 4 the similarity in the CB, SiCB, and GeCB 𝑔44(𝑥) functions is coincidental and arises from the fact that 𝑅(MH2) is larger for M=C than for M=Si or Ge. Higher mass values for M produce higher reduced masses but higher reduced 𝑅 values have the same effect. 2.3. Potential energy calculations The one-dimensional quantum mechanical problem is given in Eq. (3). The DA1OPTN Meinander-Laane potential energy program [24] was used to calculate the potential energy functions, energy levels, energy level spacings and ring-puckering barriers for each of the molecules. The constants 𝑎 and 𝑏 in Eq. (1) or 𝑎, 𝑏 and 𝑐 in Eq. (4) were adjusted to give the best least square fit with the experimental data for each molecule. These experimentally fit PEFs were compared to those generated from the 𝑉(𝑥) vs. 𝑥 computations from ab initio calculations. The latter will be referred to as theoretical PEFs.
2.4. Wavefunctions calculations The Hermite polynomial coefficients of the wavefunctions for the potential energy functions were calculated using our DA1OPTN Meinander-Laane potential energy program [24]. The wavefunctions were calculated using MAPLE 2015.1 computing environment [25].
9
Fig. 4. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion. Table 1 Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters. CBa
Calculated constants 𝜌 1.000 𝜔 0.000 Angles, degrees 𝛽𝑚𝑖𝑛(MH2)c,d 5.6° 𝛽𝑚𝑖𝑛(α-CH2) 5.6° 𝛽𝑚𝑖𝑛(β-MH2) 5.6° Rocking parameters, rad/Å 𝑅(MH2)e 0.69 𝑅(α-CH2) -0.69 𝑅(β-MH2) 0.69
TMOb
TMS
TMSe
SiCB
GeCB
13Si2CB
13Ge2CB
CBONE
0.731
0.611
0.635
0.919
0.813
0.612
0.677
1.247
0.155
0.242
0.223
0.042
0.103
0.241
0.193
-0.110
---
---
---
5.5°
4.0°
3.7°
1.3°
---
1.6°
2.8°
3.2°
6.5°
6.2°
6.0°
1.8°
4.9°
3.8°
4.7°
4.8°
4.7°
4.0°
4.9°
1.3°
2.9°
---
---
---
0.59
0.45
0.50
0.49
---
0.29
-0.36
-0.37
-0.70
-0.69
-0.81
-0.69
-1.22
0.66
0.62
0.57
0.50
0.55
0.50
0.49
0.71
a The
calculated values are from CCSD/cc-pVTZ computations. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO. This molecule has a calculated α-CH2 twist angle of about 6° at the minimum energy and 7° at 𝑥 = 0.100 Å. c𝛽 For TMO the value at 𝑥 = 0.100 Å was 𝑚𝑖𝑛 is the value at 𝑥𝑚𝑖𝑛 for all molecules except for TMO. used. d M = C, Si or Ge. e𝑅=𝛽 𝑚𝑖𝑛/𝑥𝑚𝑖𝑛 for all molecules except for TMO. For TMO the value of 𝑅 = (𝛽𝑥 = 0.1 Å)/0.1 was used. b
10
3. Results and discussion For each molecule we will summarize what has been done previously, and then we will present the refined results from our new calculations. Our calculations show only minor changes for cyclobutane since 𝜔 is clearly zero. Moreover, Egawa et al [21] have also previously considered interactions with CH2 rocking in their calculations. However, our refined 𝑔44(𝑥) terms will yield significant improvement for the other molecules, especially for those with SiH2 or GeH2 rocking vibrations.
3.1. Cyclobutane Miller and Capwell [26] first reported the observation of four Raman bands for cyclobutane (CB) and six for cyclobutane-d8 (CB-d8) in 1971. From this data they calculated barriers to planarity of 518 cm-1 for CB, and 508 cm-1 for CB-d8. Stone and Mills [27] in 1970 reported combination band data for a CH2 deformation mode and calculated a barrier of 503 cm-1 for CB. Malloy and Lafferty [16] reworked the data from both groups utilizing coordinate dependent kinetic energy expressions and calculated barriers of 515 cm-1 for CB and 501 cm-1 for CB-d8. Egawa and co-workers [21] in 1987 examined both electron diffraction results and infrared combination band data of CB. They also estimated the extent of the CH2 rocking during the puckering vibration. Their calculated barrier to inversion was 510 cm-1 based on a PEF that included a 𝑐𝑥6 term (Eq. 4). For CB 𝜌 = 1 and 𝜔 = 0 since all of the interior ring angles are equivalent. In our present study we find from the ab initio calculations that 𝑅 = 0.69 rad/Å which reflects a CH2 rocking angle (𝛽𝑚𝑖𝑛) of 5.6° when CB is at its energy minimum with a puckering angle of 29.5°. Egawa and co-workers19 also included rocking in their reduced mass calculation but did not have the computational tools that we have now. They therefore made a best guess
11
estimation for the amount of rocking. Their model predicted 6.2° of CH2 rocking at the energy minima. Using our 𝜔 and 𝑅 parameters we determined the kinetic energy functions for CB and CB-d8 and these are given in Table S2. For clarity we also show g44 (𝑥) for CB below: g44 (𝑥) = 7.032 × 10 ―3 ― 9.515 × 10 ―3𝑥2 +1.238 × 10 ―2𝑥4 ―1.728 × 10 ―1𝑥6.
(8)
Utilizing this and adjusting the 𝑎 and 𝑏 constants in Eq. (1) to obtain the best fit with the experimental data gave us 𝑉𝐶𝐵 (cm-1) = 1.317 × 106𝑥4 ― 5.187 × 104𝑥2 .
(9)
This PEF has an inversion barrier of 511 cm-1, 𝑥𝑚𝑖𝑛= ±0.140 and 𝜃𝑚𝑖𝑛 = ±29.2°. Repeating the calculation including a 𝑐𝑥6 term provided a somewhat better fit with 𝑉𝐶𝐵 (cm-1) = 1.123 × 106𝑥4 ―4.909 × 104𝑥2 + 2.842 × 106𝑥6.
(10)
This has an inversion barrier of 510 cm-1 while 𝑥𝑚𝑖𝑛= ±0.142 and 𝜃𝑚𝑖𝑛 = ±29.6°. It should be noted that the 𝑥6 term is primarily used for refining the shape of the PEF as the range of relevant 𝑥 values are much smaller than unity, resulting in the value of 𝑥6 being very small. The potential energy parameters for Eqs. (1) and (4) were also determined for CB-d8 and CB-d1 using the published infrared combination bands and Raman data [21,26-28]. These are shown in Tables 2 and 3 which also summarize all the relevant parameters for all of the molecules included in the present study. As can be seen, the barriers and energy minima are very similar for CB-d8 and CB-d1 as compared to CB. For each of the cyclobutane isotopic species the frequency fit is quite good using just Eq. (1), but the addition of the 𝑐𝑥6 term produces better fits. For each calculation we have determined the average square deviation (ASD) to assess the quality of the fit. These values, which are listed in Table 4, are determined by squaring the deviation Δ for each transition and then taking the sum and dividing by the number of transition frequencies considered. 12
Table 5 presents the observed transition frequencies for CB and its isotopic species and these are compared to our calculations from the present work. Fig. 5(a) shows the experimentally fit PEF with Eq. (4) and the theoretical ring-puckering PEF for CB. The experimentally observed infrared transitions are also shown in the figure. Fig. 5(b) shows the calculated wavefunctions for the lower energy levels.
Fig. 6 compares the calculated PEFs for the isotopic species of CB from
the experimental data. They are remarkably similar confirming that our refined kinetic energy functions are working as expected. Fig. S2 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for CB and its deuterated species CB-d8 and CB-d1.
13
Table 2 Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Molecule
Barrier cm-1
𝑥𝑚𝑖𝑛
𝜃𝑚𝑖𝑛
𝜔
𝑅(MH2)
𝑅(α-CH2)
𝑅(β-MH2)
104
511
±0.140
±29.2°
0.000
0.69
-0.69
0.69
1.319 × 106
-5.205 × 104
513
±0.140
±29.2°
0.000
0.69
-0.69
0.69
236.1
1.293 × 106
-5.100 × 104
503
±0.140
±29.2°
0.000
0.69
-0.69
0.69
110.4
1.043 ×
106
-9.006 ×
103
19
±0.066
±14.1°
0.155
---
-0.29
0.66
105
-7.768 ×
103
15
±0.062
±13.4°
0.155
---
-0.29
0.66
µ0, u
𝑎, cm-1/Å4
CB
142.2
1.317 ×
106
CB-d1
152.9
CB-d8 TMO
𝑏 cm-1/Å2 -5.187 ×
TMO-αd2
126.7
9.981 ×
TMO-βd2
124.1
1.026 × 106
-8.021 × 103
16
±0.063
±13.4°
0.155
---
-0.29
0.66
TMO-α,α'd4
147.6
9.695 × 105
-7.164 × 103
13
±0.061
±13.1°
0.155
---
-0.29
0.66
162.7
9.840 ×
105
-6.998 ×
103
12
±0.060
±12.8°
0.155
---
-0.29
0.66
105
-2.776 ×
104
273
±0.140
±26.8°
0.242
---
-0.36
0.62
TMO-d6 TMS
121.5
7.068 ×
TMS-αd2
137.3
6.866 × 105
-2.703 × 104
266
±0.140
±26.9°
0.242
---
-0.36
0.62
TMS-βd2
146.4
7.161 × 105
-2.778 × 104
269
±0.139
±26.7°
0.242
---
-0.36
0.62
157.8
6.730 ×
105
-2.634 ×
104
258
±0.140
±26.8°
0.242
---
-0.36
0.62
105
-2.702 ×
104
264
±0.140
±26.7°
0.242
---
-0.36
0.62
TMS-α,α'd4 TMS-d6
185.4
6.928 ×
TMSe
119.6
5.877 × 105
-2.977 × 104
377
±0.159
±29.9°
0.223
---
-0.37
0.57
SiCB
142.4
6.223 × 105
-3.308 × 104
440
±0.163
±31.8°
0.042
0.59
-0.7
0.50
149.1
5.980 ×
105
-3.237 ×
104
438
±0.165
±32.1°
0.042
0.59
-0.7
0.50
105
-3.201 ×
104
439
±0.166
±32.3°
0.042
0.59
-0.7
0.50
SiCB-d1 SiCB-d2
155.1
5.839 ×
13Si2CB
161.6
3.189 × 105
-1.057 × 104
88
±0.129
±22.2°
0.241
0.5
-0.81
0.50
13Si2CB-d3
196.4
3.151 × 105
-1.043 × 104
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
207.4
3.172 ×
105
-1.044 ×
104
86
±0.128
±22.1°
0.241
0.5
-0.81
0.50
105
-1.044 ×
104
409
±0.156
±30.1°
0.103
0.45
-0.69
0.55
13Si2CB-d4 GeCBb
142.5
3.172 ×
13Ge2CBb
173.2
6.101 × 105
-3.158 × 102
1
±0.047
±7.8°
0.193
0.49
-0.69
0.49
CBONE
207.9
6.501 × 105
-2.252 × 103
2
±0.042
±4.4°
-0.110
---
-1.22
0.71
276.4
105
103
2
±0.042
±4.5°
-0.110
---
-1.22
0.71
CBONE-α,α'd4
7.129 ×
-2.560 ×
aµ
0, ω and the 𝑅 values were determined using the computed CCSD/cc-pVTZ structure. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO.
14
Table 3 Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐𝑥6. Molecule
Barrier cm-1
𝑥𝑚𝑖𝑛
𝜃𝑚𝑖𝑛
𝜔
106
510
±0.142
±29.6°
0.000
-5.176 × 104
3.694 × 105
514
±0.141
±29.4°
1.145 × 106
-4.900 × 104
2.324 × 106
504
±0.142
9.191 ×
105
-7.492 ×
103
2.381 ×
106
15
105
-7.162 ×
103
1.143 ×
106
µ0, u
𝑎, cm-1/Å4
CB
142.2
1.123 ×
106
CB-d1
152.9
1.297 × 106
CB-d8
236.1 110.4
TMO
𝑏 cm-1/Å2 -4.909 ×
104
c cm-1/Å6 2.842 ×
𝑅(α-CH2)
𝑅(β-MH2)
0.69
-0.69
0.69
0.000
0.69
-0.69
0.69
±29.6°
0.000
0.69
-0.69
0.69
±0.063
±13.6°
0.155
---
-0.29
0.66
14
±0.061
±13.2°
0.155
---
-0.29
0.66
𝑅(MH2)
TMO-αd2
126.7
9.405 ×
TMO-βd2
124.1
9.715 × 105
-7.478 × 103
1.143 × 106
14
±0.062
±13.3°
0.155
---
-0.29
0.66
TMO-α,α'd4
147.6
9.159 × 105
-6.618 × 103
1.104 × 106
12
±0.060
±12.9°
0.155
---
-0.29
0.66
162.7
9.315 ×
105
-6.492 ×
103
1.130 ×
106
11
±0.059
±12.6°
0.155
---
-0.29
0.66
105
-2.741 ×
104
3.366 ×
105
273
±0.141
±26.9°
0.242
---
-0.36
0.62
TMO-d6 TMS
121.5
6.824 ×
TMS-αd2
137.3
6.828 × 105
-2.697 × 104
5.454 × 104
266
±0.140
±26.9°
0.242
---
-0.36
0.62
TMS-βd2
146.4
6.723 × 105
-2.718 × 104
5.771 × 105
270
±0.140
±26.9°
0.242
---
-0.36
0.62
157.8
6.741 ×
105
-2.635 ×
104
-1.942 ×
104
258
±0.140
±26.8°
0.242
---
-0.36
0.62
105
-2.643 ×
104
6.292 ×
105
264
±0.141
±26.9°
0.242
---
-0.36
0.62
TMS-α,α'd4 TMS-d6
185.4
6.495 ×
TMSe
119.6
4.992 × 105
-2.816 × 104
9.559 × 105
378
±0.162
±30.4°
0.223
---
-0.37
0.57
SiCB
142.4
6.117 × 105
-3.288 × 104
1.081 × 105
440
±0.163
±31.9°
0.042
0.59
-0.7
0.50
149.1
5.980 ×
105
-3.237 ×
104
8.000 ×
102
438
±0.165
±32.1°
0.042
0.59
-0.7
0.50
105
-3.247 ×
104
-2.999 ×
105
438
±0.165
±32.2°
0.042
0.59
-0.7
0.50
SiCB-d1 SiCB-d2
155.1
6.096 ×
13Si2CB
161.6
3.033 × 105
-1.036 × 104
1.853 × 105
87
±0.130
±22.3°
0.241
0.5
-0.81
0.50
13Si2CB-d3
196.4
3.118 × 105
-1.040 × 104
4.595 × 104
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
207.4
3.079 ×
105
-1.033 ×
104
1.202 ×
105
86
±0.129
±22.2°
0.241
0.5
-0.81
0.50
105
-3.235 ×
104
-4.200 ×
105
409
±0.156
±30.1°
0.103
0.45
-0.69
0.55
0.193
0.49
-0.69
0.49
13Si2CB-d4 GeCBb
142.5
6.521 ×
13Ge2CBb
173.2
1.925 × 105
-8.426 × 102
2.651 × 104
1
±0.047
±7.8°
CBONE
207.9
6.820 × 105
-2.570 × 103
-7.307 × 105
2
±0.043
±4.6°
-0.110
---
-1.22
0.71
276.4
105
103
106
0
±0.000
±0.0°
-0.110
---
-1.22
0.71
CBONE-α,α'd4
4.112 ×
1.356 ×
6.392 ×
aµ
0, ω and the 𝑅 values were determined using the computed CCSD/cc-pVTZ structure. The puckered configuration at 𝑥 = 0.100 Å was used to calculate the values for TMO.
15
Table 4 Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4). ASD (cm-2) Molecule
CB CB-d8 CB-d1c TMO TMO-αd2 TMO-βd2 TMO-α,α’d4 TMO-d6 TMS TMS-αd2 TMS-βd2 TMS-α,α’d4 TMS-d6 TMSe SiCB SiCB-d1 SiCB-d2 13Si2CB 13Si2CB-d3 13Si2CB-d4 CBONE CBONE-d4
𝑉(𝑥4,𝑥2)a
𝑉(𝑥6,𝑥4,𝑥2)b
0.91 0.36 --0.50 0.15 0.13 0.08 0.06 0.34 0.13 0.06 0.07 0.09 0.38 0.44 0.58 1.24 0.10 0.01 0.09 1.23 0.36
0.02 0.11 --0.00 0.01 0.01 0.01 0.01 0.28 0.13 0.00 0.06 0.07 0.37 0.43 0.58 1.18 0.01 0.01 0.07 1.04 0.27
a
Using Eq. (1).
b
Using Eq. (4). The ASD values are based on infrared data except for CB-d1 for which Raman data were used.
c
.
16
Table 5 Observed and Calculated Ring-Puckering Transitions (cm-1) for CB, CB-d8 and CB-d1. CB Transition Cb. Bandsa
CB-d8
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
1–3
198.6
198.6
0.0
198.9
-0.3
209.7
-11.1
---
157.5
---
158.2
---
167.4
---
2–4
---
157.7
---
157.1
---
177.1
---
141.3
140.8
0.5
141.0
0.3
153.0
-11.7
3–5
176.1
176.7
-0.6
175.8
0.3
187.3
-11.2
141.9
142.5
-0.6
142.6
-0.7
153.5
-11.6
4–6
117.4
118.9
-1.5
117.4
0.0
124.5
-7.1
105.8
106.2
-0.4
105.8
0.0
126.5
-20.7
5–7
174.8
176.1
-1.3
174.8
0.0
178.1
-3.3
128.2
128.5
-0.3
128.0
0.2
137.8
-9.6
6–8
174.9
175.7
-0.8
175.1
-0.2
162.1
12.8
92.7
94.1
-1.4
93.3
-0.6
92.4
0.3
7–9
204.1
204.6
-0.5
204.1
0.0
200.6
3.5
132.9
133.4
-0.5
132.8
0.1
133.9
-1.0
8 – 10
220.1
220.2
-0.1
220.2
-0.1
215.1
5.0
137.9
138.0
-0.1
137.6
0.3
126.8
11.1
9 – 11
236.0
235.6
0.4
236.0
0.0
232.0
4.0
154.0
154.3
-0.3
154.2
-0.2
150.9
3.1
10 – 12
250.1
249.0
1.1
250.0
0.1
245.9
4.2
165.0
164.8
0.2
164.9
0.1
161.0
4.0
11 – 13
263.0
261.4
1.6
262.9
0.1
258.7
4.3
175.2
174.7
0.5
175.0
0.2
172.2
3.0
12 – 14
---
272.9
---
274.9
---
270.4
---
184.5
183.7
0.8
184.2
0.3
181.6
2.9
13 – 15
---
283.6
---
286.1
---
281.4
---
192.4
192.0
0.4
192.7
-0.3
190.3
2.1
4 – 5f
17.8
19.8
-2.0
19.4
-1.6
10.5
7.3
---
1.7
---
1.6
---
0.5
6–7f
---
77.0
---
76.8
---
64.2
---
23.2
24.1
-0.9
23.8
-0.6
11.8
11.4
0–2
---
197.8
---
198.2
---
209.3
---
---
157.5
---
158.1
---
167.4
---
199.4
198.2
1.2
198.6
0.8
209.5
-10.1
157.1
157.5
-0.4
158.2
-1.1
167.4
-10.3
1–3
---
198.6
---
198.9
---
209.7
---
---
157.5
---
158.2
---
167.4
---
2–4
159.3
157.7
1.6
157.1
2.2
177.1
-17.8
---
140.8
---
141.0
---
153.0
---
---
167.2
---
166.4
---
182.2
---
141.3
141.6
-0.3
141.8
-0.5
153.3
-12.0
3–5
177.1
176.7
0.4
175.8
1.3
187.3
-10.2
---
142.5
---
142.6
---
153.5
---
4–6
119.2
118.9
0.3
117.4
1.8
124.5
-5.3
105.0
106.2
-1.2
105.8
-0.8
126.5
-21.5
5–7
177.1
176.1
1.0
174.8
2.3
178.1
-1.0
128.2
128.5
-0.3
128.0
0.2
137.8
-9.6
Ramane
17
---
Table 5. Continued. CB Transition
Ramane
CB-d8
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
6–8
---
175.7
---
175.1
---
162.1
---
92.0
94.1
-2.1
93.3
-1.3
92.4
-0.4
7–9
---
204.6
---
204.1
---
200.6
---
132.9
133.4
-0.5
132.8
0.1
133.9
-1.0
CB-d1 Transition
Experimental. fit Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
3–4
156.0
156.9
-0.9
157.0
-1.0
174.5
-18.5
0–2
---
192.5
---
192.7
---
203.1
---
192.5
192.8
-0.3
192.9
-0.4
203.2
-10.7
1–3
---
193.0
---
193.2
---
203.3
---
2–4
159.0
157.5
1.5
157.5
1.5
174.7
-15.7
3–5
170.0
171.6
-1.6
171.6
-1.6
182.0
-12.0
4–6
113.5
113.6
-0.1
113.5
0.0
122.7
-9.2
5–7
166.5
167.5
-1.0
167.4
-0.9
170.5
-4.0
6–8
162.0
161.9
0.1
161.9
0.1
148.3
13.7
7–9
---
192.7
---
192.8
---
189.1
---
8 – 10
208.0
207.4
0.6
207.5
0.5
202.1
5.9
2–5
174.0
172.2
1.8
172.2
1.8
182.2
-8.2
Ramang
a Ref.
[21] from combination bands analysis.
Using Eq. (1). Eq. (4). d From CCSD/cc-pVTZ computations. b
c Using e Ref.
[26].
f Deduced, g Ref.
Ref. [26].
[38].
18
Fig. 5. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for CB. The observed transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.142 Å and 𝜃𝑚𝑖𝑛= ±29.6°.
Fig. 6. Experimental PEFs for CB isotopic species based on Eq. (4).
19
3.2. Trimethylene oxide, trimethylene sulfide, and trimethylene selenide The first molecule for which the ring-puckering far-infrared spectra were recorded was trimethylene oxide (TMO) and results were reported both by the R. C. Lord [29] group at MIT and the Strauss group at Berkeley [30]. Far-infrared spectra of TMO, TMO-αd2, TMO-βd2, TMO-α, α'd4 and TMO-d6 were later reported by Wieser, Danyluk and Kydd [31] in 1972 and Raman spectra by Kiefer, Bernetein, Wieser and Danyluk [32,33]. In 1973 Jokisaari and Kauppinen published high resolution far-infrared spectra of TMO [34]. The ultra-high resolution ringpuckering spectrum of TMO was reported by G. Moruzzi, M. Kunzmann, B. P. Winnewisser and M. Winnewiser in 2003 [35]. Microwave spectra with detailed theoretical analyses were published by the Gwinn [36-39] group at Berkeley. These included the definition of 𝜌 and 𝜔, but these parameters could only be roughly estimated at that time. Hence, the resulting kinetic energy expressions were only estimates. In our present work for TMO we determined the values of 𝜌 and of 𝜔 for TMO from the computed CCSD/cc-pVTZ and MP2/cc-pVTZ puckered and planar structures. The configuration at the energetic minimum for TMO from the CCSD/cc-pVTZ calculation came out to be almost planar with 𝑥𝑚𝑖𝑛 = ±0.004 at 𝜃𝑚𝑖𝑛 = 0.2°, whereas the calculated MP2/cc-pVTZ structure has a 𝑥𝑚𝑖𝑛 = ±0.069 at 𝜃𝑚𝑖𝑛 = 14.8°. Because the CCSD structure was nearly planar, we calculated the 𝜌, 𝜔, 𝛽 and 𝑅 values at 𝑥 = 0.100 Å and 𝜃 = 21.4° rather than at the energy minimum. This resulted in the 𝜌, 𝜔, 𝛽 and 𝑅 values shown in Table 1 and these are compared to those from the MP2/cc-pVTZ calculations in Table S3. Table S4 shows the kinetic energy expressions for all of the isotopic species from both types of calculations, and these are compared graphically in Fig. S3. Table 6 presents the observed transition frequencies for TMO and its isotopic derivatives and these are compared to our calculated values from the CCSD/cc-pVTZ calculations. 20
Table S5 in
the supplementary material presents the observed transition frequencies for TMO and its isotopic derivatives and these are compared to our calculated values from the MP2/cc-pVTZ calculations. As can be seen, the frequency fit for reach molecule for both cases is very good using Eq. (1) and is nearly perfect using Eq. (4). Comparison of Tables 6 (CCSD calculation) and S5 (MP2) shows that the MP2-cc-pVTZ calculations for this molecule yield a somewhat better agreement with the experimental data. The parameters of the PEFs equations from the CCSD computations are given in Tables 2 and 3 and are compared to those from the MP2/ccpVTZ computations in Tables S6 and S7. Table S8 shows the calculated ASDs using both computations, where the ones from the MP2/ccpVTZ computations are slightly better for TMO. As seen in Table 7, the CCSD/cc-pVTZ calculations in most cases give better agreement with the experimental data, but TMO is an exception. Fig. 7(a) shows the experimentally fit and theoretical ring-puckering PEFs for TMO using the kinetic energy functions defined by the CCSD/cc-pVTZ computations. Fig. 7(b) shows the calculated wavefunctions for the lower energy levels of TMO from these calculations. Fig. S4(a) in the supplementary material compares the experimentally fit and theoretical ring-puckering PEFs for TMO where the kinetic energy parameters were based on MP2/cc-pVTZ computations. These can be seen to be virtually identical.
Fig. S4(b) shows the calculated
wavefunctions for the lower energy levels of TMO from these calculations. Figs. 8 and S5 show that the experimental PEFs for all the isotopic species are almost identical. Calculations by the Wieser group [31] to fit their data previously assumed fixed reduced masses and carried out their calculations in reduced coordinates using the Laane tables [13]. Their frequency fits were reasonably good but the lack of a reliable 𝑔44(𝑥) expression did not allow them to obtain good 𝑉 (𝑥) vs 𝑥 PEFs. The calculated inversion barriers in our present work range from 12 to 19 cm-1
21
using Eq. (1) and from 11 to 15 cm-1 using Eq. (4). The lowest vibrational level at about 26 cm-1 for TMO lies above the barrier so this large amplitude puckering vibration in this state is not restricted to a puckered structure even though the energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063 Å with a 𝜃𝑚𝑖𝑛 = ±13.6° derived from the experimental fit applying the CCSD parameters, and at 𝑥𝑚𝑖𝑛 = ±0.062 Å with a 𝜃𝑚𝑖𝑛 = ±13.4° derived from the experimental fit applying the MP2 parameters. Our ab initio computations also show that the α-CH2’s twist about 6° at 𝑥𝑚𝑖𝑛. Fig. S6 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the MP2/cc-pVTZ calculations for TMO and its deuterated species. TMO has also been investigated theoretically using the Hougen-Bunker-Johns Model [40] by Foltynowicz and co-workers [41,42] and also by Szalay and co-workers [43]. Satisfactory agreement between experimental and theoretical transition frequencies was achieved.
22
Table 6 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs. TMO Transition
TMO-αd2
Experimental. fit 4
,𝑥2)b
∆
FIRa
Observed
0–1
52.92
51.53
1.39
1–2
89.56
90.37
2–3
104.44
3–4
𝑉(𝑥
4
𝑉(𝑥 ,𝑥
Experimental fit
2
,𝑥6)c
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
∆
Theoreticald
∆
Observed
53.10
-0.18
79.58
-26.66
48.7
48.2
0.5
48.7
0.0
72.8
-24.1
-0.81
89.46
0.10
104.01
-14.45
81.7
82.1
-0.4
81.7
0.0
95.1
-13.4
104.89
-0.45
104.45
-0.01
118.79
-14.35
95.1
95.5
-0.4
95.1
0.0
108.6
-13.5
117.95
118.45
-0.50
117.92
0.03
130.67
-12.72
107.2
107.6
-0.4
107.2
0.0
119.5
-12.3
4–5
128.89
129.36
-0.47
128.95
-0.06
140.70
-11.81
117.0
117.4
-0.4
117.1
-0.1
128.6
-11.6
5–6
138.42
138.73
-0.31
138.51
-0.09
149.49
-11.07
125.5
125.8
-0.3
125.6
-0.1
136.7
-11.2
6–7
146.94
146.99
-0.05
147.01
-0.07
157.36
-10.42
133.0
133.2
-0.2
133.2
-0.2
143.9
-10.9
7–8
154.65
154.40
0.25
154.70
-0.05
164.53
-9.88
139.9
139.9
0.0
140.0
-0.1
150.4
-10.5
8–9
161.73
161.14
0.59
161.75
-0.02
171.13
-9.40
146.3
146.0
0.3
146.2
0.1
156.5
-10.2
9 – 10
168.25
167.35
0.90
168.28
-0.03
177.27
-9.02
152.0
151.6
0.4
151.9
0.1
162.1
-10.1
10 – 11
174.45
173.10
1.35
174.37
0.08
183.02
-8.57
157.4
156.8
0.6
157.3
0.1
167.4
-10.0
0–2
142.58
141.89
0.69
142.55
0.03
183.58
-41.00
---
130.3
---
130.3
---
167.8
---
0–3
247.04
246.78
0.26
247.00
0.04
302.38
-55.34
---
225.8
---
225.5
---
276.4
---
0–4
364.95
365.24
-0.29
364.92
0.03
433.05
-68.10
---
333.4
---
332.7
---
395.9
---
0–5
493.86
494.59
-0.73
493.86
0.00
573.75
-79.89
---
450.8
---
449.8
---
524.5
---
0–2
143.1
141.9
1.2
142.6
0.5
183.6
-40.5
130.7
130.3
0.4
130.3
0.4
167.8
-37.1
1–3
194.3
195.3
-1.0
193.9
0.4
222.8
-28.5
176.4
177.6
-1.2
176.8
-0.4
203.6
-27.2
2–4
222.7
223.3
-0.6
222.4
0.3
249.5
-26.8
201.8
203.1
-1.3
202.4
-0.6
228.0
-26.2
3–5
247.5
247.8
-0.3
246.9
0.6
271.4
-23.9
224.0
225.0
-1.0
224.3
-0.3
248.1
-24.1
4–6
267.7
268.1
-0.4
267.5
0.2
290.2
-22.5
242.2
243.2
-1.0
242.7
-0.5
265.3
-23.1
5–7
286.1
285.7
0.4
285.5
0.6
306.8
-20.7
258.2
259.1
-0.9
258.8
-0.6
280.6
-22.4
6–8
302.1
301.4
0.7
301.7
0.4
321.9
-19.8
272.9
273.2
-0.3
273.1
-0.2
294.3
-21.4
7–9
317.0
315.5
1.5
316.4
0.6
335.7
-18.7
285.4
285.9
-0.5
286.1
-0.7
306.9
-21.5
Ramane
23
Table 6 Continued. TMO Transition
Ramane
TMO-αd2
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
4
𝑉(𝑥 ,𝑥
∆
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
8 – 10
~331
328.5
---
330.0
---
348.4
---
~299
297.6
---
298.1
---
318.6
---
9 – 11
~344
340.4
---
342.7
---
360.3
---
---
308.4
---
309.2
---
329.5
---
TMO-βd2 Transition FIRa
TMO-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–1
49.6
49.2
0.4
49.5
0.1
73.8
-24.2
43.7
43.4
0.3
43.8
-0.1
65.9
-22.2
1–2
83.5
84.0
-0.5
83.5
0.0
96.4
-12.9
73.4
73.6
-0.2
73.2
0.2
85.9
-12.5
2–3
97.2
97.6
-0.4
97.3
-0.1
110.1
-12.9
85.3
85.6
-0.3
85.3
0.0
98.1
-12.8
3–4
109.6
110.0
-0.4
109.7
-0.1
121.1
-11.5
96.1
96.4
-0.3
96.1
0.0
107.9
-11.8
4–5
119.7
120.0
-0.3
119.8
-0.1
130.4
-10.7
104.9
105.2
-0.3
104.9
0.0
116.2
-11.3
5–6
128.5
128.7
-0.2
128.6
-0.1
138.6
-10.1
112.6
112.7
-0.1
112.6
0.0
123.5
-10.9
6–7
136.3
136.3
0.0
136.3
0.0
145.9
-9.6
119.2
119.4
-0.2
119.3
-0.1
130.0
-10.8
7–8
143.4
143.2
0.2
143.3
0.1
152.6
-9.2
125.3
125.4
-0.1
125.4
-0.1
135.9
-10.6
8–9
149.7
149.4
0.3
149.7
0.0
158.7
-9.0
130.9
130.9
0.0
131.0
-0.1
141.4
-10.5
9 – 10
155.7
155.1
0.6
155.6
0.1
164.4
-8.7
136.4
135.9
0.5
136.2
0.2
146.5
-10.1
10 – 11
---
160.5
---
161.1
---
169.8
---
141.0
140.6
0.4
141.0
0.0
151.3
-10.3
0–2
133.3
133.1
0.2
133.0
0.3
170.1
-36.8
117.5
117.0
0.5
117.0
0.5
151.8
-34.3
1–3
180.8
181.6
-0.8
180.8
0.0
206.4
-25.6
158.8
159.2
-0.4
158.5
0.3
184.1
-25.3
2–4
207.2
207.6
-0.4
207.0
0.2
231.2
-24.0
181.4
182.0
-0.6
181.4
0.0
206.1
-24.7
3–5
229.6
230.1
-0.5
229.5
0.1
251.5
-21.9
201.0
201.6
-0.6
201.1
-0.1
224.2
-23.2
4–6
248.0
248.7
-0.7
248.4
-0.4
269.0
-21.0
217.3
217.9
-0.6
217.5
-0.2
239.7
-22.4
5–7
265.3
265.0
0.3
264.9
0.4
284.5
-19.2
231.7
232.2
-0.5
231.9
-0.2
253.5
-21.8
6–8
280.3
279.5
0.8
279.6
0.7
298.5
-18.2
244.7
244.8
-0.1
244.8
-0.1
265.9
-21.2
Ramane
24
Table 6 Continued. TMO-βd2 Transition
Ramane
TMO-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
~293
292.6
---
293.0
---
311.3
---
~256
256.3
---
256.4
---
277.3
---
8 – 10
~304
304.5
---
305.2
---
323.1
---
~267
266.8
---
267.2
---
287.9
---
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMO-d6 Transition FIRa
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
0–1
41.2
40.9
0.3
41.2
0.0
61.8
-20.6
1–2
69.2
69.4
-0.2
69.0
0.2
80.7
-11.5
2–3
80.5
80.7
-0.2
80.5
0.0
92.1
-11.6
3–4
90.7
91.0
-0.3
90.7
0.0
101.3
-10.6
4–5
99.1
99.3
-0.2
99.1
0.0
109.1
-10.0
5–6
106.2
106.4
-0.2
106.3
-0.1
115.9
-9.7
6–7
112.7
112.8
-0.1
112.7
0.0
122.1
-9.4
7–8
118.3
118.4
-0.1
118.5
-0.2
127.6
-9.3
8–9
123.7
123.6
0.1
123.8
-0.1
132.8
-9.1
9 – 10
128.7
128.4
0.3
128.7
0.0
137.6
-8.9
10 – 11
133.3
132.8
0.5
133.2
0.1
142.1
-8.8
0–2
~109
110.3
---
110.3
---
142.5
---
1–3
149.9
150.1
-0.2
149.5
0.4
172.8
-22.9
2–4
171.7
171.7
0.0
171.2
0.5
193.4
-21.7
3–5
190.1
190.3
-0.2
189.8
0.3
210.4
-20.3
4–6
205.6
205.7
-0.1
205.3
0.3
225.0
-19.4
5–7
219.1
219.2
-0.1
219.0
0.1
238.0
-18.9
6–8
231.5
231.2
0.3
231.2
0.3
249.7
-18.2
Ramane
25
Table 6 Continued. TMO-d6 Transition
Ramane
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
242.7
242.1
0.6
242.2
0.5
260.4
-17.7
8 – 10
~253
252.0
---
252.4
---
270.4
---
a FIR
data for TMO from Ref. [35]. FIR data TMO deuterated analogs from Ref. [31]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Raman data for TMO from Ref. [32]. Raman data for TMO deuterated analogs from Ref. [33]. b
26
Table 7 Comparison of experimental barriers, and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛 values with those from theoretical calculations. Experimental fit Theoretical 𝑉(𝑥6,𝑥4,𝑥2)a CCSD/cc-pVTZ MP2/cc-pVTZ -1 -1 -1 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Barrier, cm 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Barrier, cm 𝑥𝑚𝑖𝑛, Å 𝜃𝑚𝑖𝑛, degrees Molecule Barrier, cm CB 510 ±0.142 ±29.6° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° CB-d8 504 ±0.142 ±29.6° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° CB-d1b 514 ±0.141 ±29.4° 586 ± 0.142 ± 29.5° 821 ± 0.153 31.9° TMO 15 ±0.062 ±13.4° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-αd2 13 ±0.061 ±13.2° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-βd2 14 ±0.061 ±13.0° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-α,α’d4 12 ±0.059 ±12.6° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMO-d6 11 ±0.058 ±12.4° 0 ± 0.001 ± 0.2° 21 ± 0.069 14.8° TMS 273 ±0.141 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-αd2 266 ±0.140 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-βd2 270 ±0.140 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-α,α’d4 258 ±0.140 ±26.8 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMS-d6 264 0.141 ±26.9 243 ± 0.133 ± 25.5° 412 ± 0.152 29.0° TMSe 378 ±0.162 ±30.4° 339 ± 0.148 ± 27.8° 512 ± 0.164 30.9° SiCB 440 ±0.163 ±31.9° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° SiCB-d1 438 ±0.165 ±32.1° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° SiCB-d2 438 ±0.165 ±32.2° 472 ± 0.163 ± 31.7° 654 ± 0.176 34.5° 13Si2CB 87 ±0.130 ±22.3° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° 13Si2CB-d3 86 ±0.129 ±22.2° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° 13Si2CB-d4 86 ±0.129 ±22.2° 89 ± 0.130 ± 22.4° 160 ± 0.150 25.8° GeCB ------409 ± 0.156 ± 30.1° 567 ± 0.169 32.6° 13Ge2CB ------1 ± 0.047 ± 7.8° 24 ± 0.104 17.1° CBONE 2 ±0.043 ±4.6° 36 ± 0.073 ± 15.5° 114 ± 0.097 20.8° CBONE-α,α’d4 0 ±0.000 ±0.0° 36 ± 0.073 ± 15.5° 114 ± 0.097 20.8° a Using Eq. (4). 27
Fig. 7. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using CCSD/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063Å and 𝜃𝑚𝑖𝑛= ±13.6°.
Fig. 8. Experimental PEFs for TMO isotopic species based on Eq. (4) from CCSD/cc-pVTZ computations.
28
The far-infrared spectra of TMS were first reported in 1966 by the Strauss group [44]. In 1974 Wieser, Duckett and Kydd reported the far-infrared spectra of TMS, TMS-αd2, TMS-βd2, TMS-α, α'd4 and TMS-d6 [45]. The Raman spectra for TMS were reported by Durig, Shing, Carreira and Li [46] and the Raman spectra of the deuterated analogs were reported by Wieser and Kydd [47]. The microwave spectrum, vibration-rotation interaction, and potential function for the ring-puckering vibration of TMS were studied by the Gwinn group [19]. Table S2 in the supplementary material shows the kinetic energy terms and Tables 2 and 3 show the and potential energy parameters calculated in the present work for TMS and its isotopic species.
Table 8 presents the experimentally observed transitions for these molecules and
compares them to our calculated values. The barriers can be seen to range from 258 to 273 cm-1 for the isotopic species, and these are similar to previously reported barriers [19,44-47]. Our present fit of the experimental data yields energy minima at 𝑥𝑚𝑖𝑛 = ± 0.141 Å and the CCSD/ccpVTZ ab initio calculation gives ± 0.133.Å. Fig. 9(a) shows the experimentally fit and theoretical ring-puckering PEFs for TMS. Fig. 9(b) shows the calculated wavefunctions for the lower energy levels of TMS. Fig. 10 shows that the experimentally fit PEFs for all the isotopic species are again almost identical. Fig. S7 in the supplementary material shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for TMS and its deuterated species.
29
Table 8 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMS and deuterated analogs. TMS Transition
TMS-αd2
Experimental. fit
Experimental fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
0–1
0.2746e
0.2871
-0.0125
0.2789
-0.0043
0.5930
-0.3184
1–2
138.7
138.8
-0.1
138.8
-0.1
129.5
2–3
---
12.5
---
12.3
---
3–4
86.0
86.0
0.0
85.8
4–5
62.7
62.8
-0.1
5–6
84.3
84.4
6–7
91.3
7–8
∆
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
0.181
---
0.180
---
0.364
---
9.2
131.9
132.0
-0.1
132.0
-0.1
126.0
5.9
19.5
---
---
8.9
---
8.8
---
14.1
---
0.2
81.9
4.1
82.7
82.3
0.4
82.3
0.4
78.3
4.4
62.6
0.1
71.3
-8.6
---
53.3
---
53.3
---
61.9
---
-0.1
84.3
0.0
88.1
-3.8
76.4
76.3
0.1
76.2
0.2
80.1
-3.7
91.6
-0.3
91.6
-0.3
95.9
-4.6
82.2
82.3
-0.1
82.3
-0.1
87.0
-4.8
99.7
99.8
-0.1
99.8
-0.1
103.7
-4.0
90.0
90.0
0.0
90.0
0.0
94.4
-4.4
8–9
107.8
106.6
1.2
106.7
1.1
110.4
-2.6
95.7
96.4
-0.7
96.4
-0.7
100.7
-5.0
9 – 10
114.2
112.8
1.4
112.9
1.3
116.5
-2.3
101.9
102.1
-0.2
102.1
-0.2
106.5
-4.6
10 – 11
118.3
118.5
-0.2
118.7
-0.4
122.1
-3.8
107.5
107.3
0.2
107.4
0.1
111.7
-4.2
11 – 12
123.9
123.7
0.2
124.0
-0.1
127.3
-3.4
112.9
112.2
0.7
112.2
0.7
116.5
-3.6
12 – 13
128.4
128.6
-0.2
128.9
-0.5
132.1
-3.7
---
116.7
---
116.7
---
121.0
---
13 – 14
---
133.1
---
133.6
---
136.6
---
---
120.9
---
121.0
---
125.2
---
0–3
151.3
151.6
-0.3
151.5
-0.2
149.5
1.8
140.6
141.0
-0.4
141.0
-0.4
140.5
0.1
2–5
160.2
161.2
-1.0
160.8
-0.6
172.6
-12.4
144.6
144.4
0.2
144.4
0.2
154.3
-9.7
0–2
139.1
139.1
0.0
139.1
0.0
130.0
9.1
131.7
132.2
-0.5
132.2
-0.5
126.4
5.3
1–3
151.0
151.3
-0.3
151.2
-0.2
148.9
2.1
140.6
140.8
-0.2
140.8
-0.2
140.1
0.5
2–4
99.5
98.4
1.1
98.1
1.4
101.4
-1.9
91.5
91.1
0.4
91.1
0.4
92.4
-0.9
3–5
147.0
148.7
-1.7
148.4
-1.4
153.1
-6.1
135.3
135.6
-0.3
135.5
-0.2
140.2
-4.9
4–6
147.0
147.2
-0.2
146.9
0.1
159.4
-12.4
129.2
129.6
-0.4
129.5
-0.3
142.0
-12.8
5–7
175.0
176.0
-1.0
175.9
-0.9
184.1
-9.1
158.3
158.5
-0.2
158.5
-0.2
167.1
-8.8
6–8
191.5
191.4
0.1
191.3
0.2
199.7
-8.2
172.1
172.3
-0.2
172.3
-0.2
181.5
-9.4
Ramanf
30
Table 8 Continued. TMS Transition
Ramanf
TMS-αd2
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
208.4
206.4
2.0
206.4
2.0
214.2
-5.8
186.0
186.4
-0.4
186.4
-0.4
195.2
-9.2
8 – 10
---
219.4
---
219.6
---
227.0
---
197.5
198.5
-1.0
198.5
-1.0
207.2
-9.7
9 – 11
---
231.3
---
231.6
---
238.7
---
209.3
209.5
-0.2
209.5
-0.2
218.1
-8.8
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMS-βd2 Transition
TMS-α,α'd4
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
0–1
---
0.139
1–2
131.8
2–3
Experimental. Fit
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥4,𝑥2)b
---
0.129
---
0.282
---
---
0.109
---
0.109
---
0.201
---
131.6
0.2
131.7
0.1
124.2
7.6
124.1
124.2
-0.1
124.1
0.0
121.7
2.4
---
7.4
---
7.1
---
11.9
---
---
6.0
---
6.0
---
9.3
---
3–4
82.4
82.6
-0.2
82.5
-0.1
77.0
5.4
---
78.8
---
78.8
---
75.7
---
4–5
---
49.5
---
49.0
---
57.5
---
---
44.0
---
44.1
---
51.6
---
5–6
73.6
73.9
-0.3
73.6
0.0
76.4
-2.8
68.6
68.4
0.2
68.4
0.2
71.8
-3.2
6–7
79.1
79.4
-0.3
79.1
0.0
83.0
-3.9
72.9
73.1
-0.2
73.1
-0.2
77.6
-4.7
7–8
87.1
87.2
-0.1
87.0
0.1
90.3
-3.2
80.2
80.5
-0.3
80.5
-0.3
84.7
-4.5
8–9
93.3
93.5
-0.2
93.4
-0.1
96.4
-3.1
86.0
86.3
-0.3
86.3
-0.3
90.6
-4.6
9 – 10
99.0
99.2
-0.2
99.1
-0.1
101.9
-2.9
91.3
91.6
-0.3
91.5
-0.2
95.9
-4.6
10 – 11
104.4
104.3
0.1
104.4
0.0
107.0
-2.6
96.2
96.4
-0.2
96.3
-0.1
100.7
-4.5
11 – 12
109.3
109.1
0.2
109.3
0.0
111.7
-2.4
101.3
100.8
0.5
100.8
0.5
105.2
-3.9
12 – 13
113.8
113.6
0.2
113.8
0.0
116.1
-2.3
---
104.9
---
104.9
---
109.3
---
13 – 14
118.2
117.7
0.5
118.1
0.1
120.2
-2.0
---
108.8
---
108.7
---
113.2
---
0–3
138.9
139.1
-0.2
138.9
0.0
136.4
2.5
130.3
130.3
0.0
130.3
0.0
131.2
-0.9
2–5
---
139.6
---
138.6
---
146.3
---
129.2
128.9
0.3
128.9
0.3
136.5
-7.3
∆
31
∆
Table 8 Continued. TMS-βd2 Transition
Ramanf
TMS-α,α'd4
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–2
134.6
131.7
2.9
131.8
2.8
124.5
10.1
126.9
124.3
2.6
124.2
2.7
121.9
5.0
1–3
139.2
138.9
0.3
138.8
0.4
136.1
3.1
130.5
130.2
0.3
130.2
0.3
131.0
-0.5
2–4
90.3
90.0
0.3
89.6
0.7
88.8
1.5
86.4
84.8
1.6
84.8
1.6
84.9
1.5
3–5
131.6
132.2
-0.6
131.5
0.1
134.4
-2.8
123.6
122.9
0.7
122.9
0.7
127.2
-3.6
4–6
122.4
123.5
-1.1
122.6
-0.2
133.9
-11.5
112.4
112.4
0.0
112.4
0.0
123.4
-11.0
5–7
152.8
153.4
-0.6
152.7
0.1
159.4
-6.6
141.5
141.5
0.0
141.4
0.1
149.4
-7.9
6–8
166.1
166.7
-0.6
166.2
-0.1
173.2
-7.1
153.1
153.5
-0.4
153.5
-0.4
162.3
-9.2
7–9
180.2
180.7
-0.5
180.4
-0.2
186.6
-6.4
166.4
166.8
-0.4
166.7
-0.3
175.3
-8.9
8 – 10
192.4
192.6
-0.2
192.5
-0.1
198.3
-5.9
177.4
177.8
-0.4
177.8
-0.4
186.4
-9.0
9 – 11
---
203.5
---
203.5
---
209.0
---
186.5
187.9
-1.4
187.9
-1.4
196.6
-10.1
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
TMS-d6 Transition
Experimental. fit 4
,𝑥2)b
FIRa
Observed
0–1
---
0.046
---
0.043
---
0.097
---
1–2
120.0
119.9
0.1
120.0
0.0
116.4
3.6
2–3
---
3.1
---
3.0
---
5.4
---
3–4
---
80.2
---
80.0
---
74.1
---
4–5
---
32.6
---
32.4
---
40.6
---
5–6
61.7
61.7
0.0
61.5
0.2
63.8
-2.1
6–7
63.9
63.9
0.0
63.8
0.1
68.0
-4.1
7–8
71.6
71.6
0.0
71.6
0.0
75.0
-3.4
8–9
77.0
77.0
0.0
77.1
-0.1
80.4
-3.4
9 – 10
81.7
82.0
-0.3
82.2
-0.5
85.4
-3.7
10 – 11
86.5
86.6
-0.1
86.8
-0.3
89.9
-3.4
11 – 12
91.5
90.7
0.8
91.0
0.5
94.0
-2.5
𝑉(𝑥
∆
32
Table 8 Continued. TMS-d6 Transition
Experimental. fit 4
,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
123.1
---
121.9
---
115.9
-0.3
115.5
0.1
120.2
-4.6
119.0
120.0
-1.0
120.1
-1.1
116.5
2.5
1–3
120.2
123.1
-2.9
123.1
-2.9
121.8
-1.6
2–4
83.0
83.3
-0.3
83.1
-0.1
79.5
3.5
3–5
112.7
112.8
-0.1
112.5
0.2
114.7
-2.0
4–6
95.6
94.4
1.2
94.0
1.6
104.4
-8.8
5–7
125.8
125.6
0.2
125.3
0.5
131.8
-6.0
6–8
135.6
135.5
0.1
135.4
0.2
143.0
-7.4
7–9
148.5
148.7
-0.2
148.7
-0.2
155.4
-6.9
8 – 10
158.5
159.1
-0.6
159.3
-0.8
165.8
-7.3
9 – 11
167.8
168.6
-0.8
169.0
-1.2
175.2
-7.4
10 – 12
177.0
177.3
-0.3
177.8
-0.8
183.9
-6.9
FIRa
Observed
0–3
---
123.1
2–5
115.6
0–2
𝑉(𝑥
∆
Ramanf
FIR data of TMS and the deuterated analogs from Ref. [45]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Derived from microwave measurements. f Raman data for TMS from Ref. [46]. Raman data for TMS deuterated analogs from Ref. [47]. a
b
33
Fig. 9. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMS. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.141 Å and 𝜃𝑚𝑖𝑛 = ±26.9°.
Fig. 10. Experimental PEFs for TMS isotopic species based on Eq. (4).
The far-infrared spectra of TMSe were reported in 1969 by Harvey, Durig and Morrissey [48]. The kinetic energy terms for this molecule are given in Table S2 and the potential energy 34
parameters are given in Tables 2 and 3. Table 4 compares the observed and calculated frequencies. The frequency fit using Eq. (1) is good while that with Eq. (4) is even better. The experimental barrier is 378 cm-1 whereas the CCSD/cc-pVTZ computation gives 339 cm-1. Fig. 11(a) shows that the experimental and theoretical ring-puckering PEFs for TMSe are in reasonably good agreement. Fig. 11(b) shows the calculated wavefunctions for the lower energy levels for TMSe. Fig. S8 compares the two experimental PEFs using Eqs. (1) and (4) with those from the CCSD/ccpVTZ calculations.
Fig. 11. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMSe. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.162 Å and 𝜃𝑚𝑖𝑛= ±30.4°.
35
Table 9 Observed and Calculated Ring-Puckering Transitions (cm-1) for TMSe. TMSe Transition FIRa
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
0–1
---
0.023
---
0.019
---
0.076
---
1–2
158.0
159.0
-1.0
159.2
-1.2
155.6
2.4
2–3
1.7
1.8
-0.1
1.7
0.0
4.7
-3.0
3–4
116.5e
115.9
0.6
115.6
0.9
103.4
13.1
4–5
28.3e
28.8
-0.5
28.0
0.3
44.8
-16.5
5–6
78.7e
78.7
0.0
77.8
0.9
81.3
-2.6
6–7
74.1e
74.3
-0.2
73.7
0.4
84.5
-10.4
7–8
86.5
86.7
-0.2
86.3
0.2
94.2
-7.7
8–9
93.0
93.3
-0.3
93.1
-0.1
101.1
-8.1
9 – 10
99.5
99.8
-0.3
99.8
-0.3
107.5
-8.0
10 – 11
105.0
105.5
-0.5
105.7
-0.7
113.2
-8.2
11 – 12
111.5
110.7
0.8
111.2
0.3
118.4
-6.9
12 – 13
116.5
115.6
0.9
116.2
0.3
123.3
-6.8
13 – 14
120.5
120.1
0.4
121.0
-0.5
127.8
-7.3
14 – 15
125.6f
124.3
1.3
125.4
0.2
132.1
-6.5
15 – 16
129.5?f
128.3
---
129.7
---
136.1
---
0–3
160.2
160.9
-0.7
160.9
-0.7
160.4
-0.2
2–5
146.2
146.5
-0.3
145.2
1.0
152.9
-6.7
4–7
179.5?
181.8
---
179.5
---
210.6
---
Far-infrared data from Ref. [48]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e From the average of combination and differential bands. f From differential bands. a
b
3.3. Silacyclobutane, 1,3-disilacyclobutane, germacyclobutane and 1,3-digermacyclobutane Silacyclobutane (SiCB) was first synthesized by Laane [49] in 1967. The far-infrared study of SiCB and silacyclobutane-1,1-d2 (SiCB-d2) was later reported in 1968 by Laane and Lord [12]. A sample was sent to Pringle who performed the microwave study [50]. The Laane group also 36
reported the Raman spectra [51]. The initial computations assumed a fixed reduced mass and there was no attempt to take into account the interaction with SiH2 and CH2 rocking motions. In 1982 the Laane group reported the far-infrared spectra of 1-silacyclobutane-d1 (SiCB-d1) [52]. In the present study from the ab initio computations on SiCB we determine 𝜌 = 0.919 and 𝜔 = 0.042 reflecting easier angle bending at the silicon atom than at the carbon atoms. For MH2 rocking we found 𝑅(SiH2) = 0.59 rad/Å, 𝑅(??-CH2) = -0.70 rad/Å, and 𝑅(β-CH2) = 0.50 rad/Å. This results in the kinetic energy expressions for SiCB, SiCB-d1 and SiCB-d2 which are given in Table S2. The calculated PEF parameters to fit the experimental data are given in Tables 2 and 3. Fig. 12(a) shows the experimentally fit and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. Fig. 12(b) shows the calculated wavefunctions for the lower energy levels. Fig. 13 compares the experimental PEFs for SiCB and to those of its deuterated analogs, and these can be seen to be almost identical. The observed and calculated frequencies are shown in Table 10. As is the case for all of these molecules, the frequency fit is very good using Eq. (1) and even better using Eq. (4).
The
experimental barrier is 440 cm-1 whereas the CCSD/cc-pVTZ computation gives 472 cm-1. Fig. S9 compares the two experimental PEFs from Eqs. (1) and (4) for each isotopic species with those from the CCSD/cc-pVTZ calculations.
37
Fig. 12. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.163 Å and 𝜃𝑚𝑖𝑛= ±31.9°.
Fig. 13. Experimental PEFs for SiCB isotopic species based on Eq. (4).
38
Table 10 Observed and Calculated Ring-Puckering Transitions (cm-1) for SiCB and deuterated analogs. SiCB Transition
Experimental. fit
FIRa
Observed
0–1
(0.003)e
4
∆
0.003
0.000
𝑉(𝑥
,𝑥2)b
158.96
1–2 0–3
SiCB-d1
157.78
159.25
4
𝑉(𝑥 ,𝑥
Experimental fit 2
,𝑥6)c
0.003 159.24
,𝑥2)b
∆
Theoreticald
∆
Observed
0.000
0.001
0.002
---
0.002
153.3
154.3
158.96 -1.32
𝑉(𝑥
4
162.88 -1.32
163.04
-5.18
154.5
∆
---
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
0.002
---
0.001
154.3 -1.1
154.5
∆
---
159.7 -1.1
159.8
0–2
158.96
158.96
162.88
154.3
154.3
159.7
1–3
159.24
159.23
163.04
154.5
154.5
159.8
-6.5
2–3
0.26
0.28
-0.02
0.28
-0.02
0.16
0.10
---
0.2
---
0.2
---
0.1
---
3–4
133.45
133.14
0.16
133.11
0.20
140.25
-6.88
133.0
131.4
1.5
131.4
1.5
138.8
-5.9
133.43
2–4 2–5
141.80
142.26
133.39 -0.32
141.98
3–5
142.16
140.41 -0.23
146.18
141.89
146.02
131.6 -4.30
138.2
138.2
131.6 0.1
138.0
138.2
139.0 0.1
138.0
143.5
-5.3
143.4
4–5
---
8.83
---
8.78
---
5.77
5–6
85.37
85.07
0.30
84.99
0.38
92.91
-7.54
84.3
85.4
-1.1
85.4
85.4
93.8
-9.5
6–7
49.85
50.65
-0.80
50.56
-0.71
43.55
6.30
44.6
44.6
0.0
44.6
44.6
39.0
5.6
7–8
74.70
74.82
-0.12
74.73
-0.03
74.44
0.26
71.3
71.3
0.0
71.3
71.3
72.2
-0.9
8–9
79.22
78.96
0.26
78.90
0.32
76.62
2.60
75.9
74.3
1.6
74.3
74.3
73.2
2.7
9 – 10
86.20
86.18
0.02
86.13
0.07
84.72
1.48
81.3
81.7
-0.4
81.7
81.7
81.6
-0.3
10 – 11
92.10
91.73
0.37
91.70
0.40
90.32
1.78
---
87.0
---
87.0
---
87.0
---
11 – 12
98.50
96.86 101.54
.64 -0.52
96.85 101.55
1.65 -0.53
95.56 100.30
2.94 0.72
-----
92.0 96.5
-----
92.0 96.5
-----
92.2 96.8
-----
12 – 13
101.02
105.80
0.56
105.91
0.45
104.69
1.67
---
100.7
---
100.7
---
101.1
---
13 – 14
106.36
109.94
0.52
109.99
0.47
108.78
1.68
---
104.6
---
104.6
---
105.1
---
14 – 15
110.46
113.76
-0.53
113.84
-0.61
112.62
0.61
---
108.3
---
108.3
---
108.9
---
15 – 16
113.23
117.38
-0.30
117.47
-0.39
116.25
0.83
---
111.8
---
111.8
---
112.4
---
16 – 17
117.08
85.07
0.30
84.99
0.38
92.91
-7.54
---
87.0
---
87.0
---
87.0
---
4–6
94.41
93.90
0.51
93.77
0.64
98.68
-4.27
92.2
92.1
0.1
92.1
0.1
98.4
-6.2
5–7
135.79
135.72
0.07
135.55
0.24
136.46
-0.67
130.3
130.1
0.2
130.1
0.2
132.8
-2.5
39
6.2f
6.6
-0.4
6.6
6.6
4.6
1.6
Table 10 Continued. SiCB Transition
SiCB-d1
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
4–6
94.41
125.47
5–7
135.79
6–8
Experimental. Fit
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
Observed
𝑉(𝑥4,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
-1.30
125.29
-1.12
118.00
6.17
92.2
92.1
0.1
92.1
0.1
98.4
-6.2
153.78
0.03
153.64
0.17
151.07
2.74
130.3
130.1
0.2
130.1
0.2
132.8
-2.5
124.17
165.14
-0.46
165.03
-0.35
161.35
3.33
115.8
115.9
-0.1
115.9
-0.1
111.2
4.6
7–9
153.81
177.91
-0.80
177.84
-0.73
175.05
2.06
144.9
145.6
-0.7
145.6
-0.7
145.4
-0.5
8 – 10
164.68
188.59
1.62
188.55
1.66
185.88
4.33
156.0
156.0
0.0
156.0
0.0
154.7
1.3
9 – 11
177.11
198.39
0.82
198.40
0.81
195.86
3.35
---
168.7
---
168.7
---
168.6
---
10 – – 13 12 11
190.21 199.21
207.42 125.47
-0.18 -1.30
207.46 125.29
-0.22 -1.12
204.99 118.00
2.25 6.17
180.4? ---
188.5
-----
188.5
-----
189.0
---
12 – 14
207.24
153.78
0.03
153.64
0.17
151.07
2.74
---
197.2
---
197.3
---
197.9
---
1–4
291.7
292.39
-0.7
292.4
-0.7
303.29
-11.6
---
285.8
---
285.8
---
298.6
---
3–6
~227
227.05
---
226.88
---
238.92
---
---
223.4
---
223.4
---
237.2
---
4–7
144.56
144.55
0.01
144.33
0.23
142.33
2.23
---
136.7
---
136.7
---
137.4
---
5–8
210.68
210.54
0.14
210.28
0.40
210.90
-0.22
---
201.3
---
201.3
---
205.1
---
7 – 10
239.64
239.96
-0.32
239.77
-0.13
235.79
3.85
---
227.2
---
227.2
---
315.1
---
8 – 11
256.7
256.9
-0.2
256.7
0.0
251.7
5.0
---
243.0
---
243.0
---
326.4
---
0–2
157.9
159.0
-1.1
159.0
-1.1
162.9
-5.0
---
154.3
---
154.3
---
159.7
---
1–3
157.9
159.2
-1.3
156.2
1.7
163.0
-5.1
---
154.5
---
154.5
---
159.8
---
2–4
133.4
133.4
0.0
133.4
0.0
140.4
-7.0
---
131.6
---
131.5
---
139.0
---
3–5
142.1
142.0
0.1
141.9
0.2
146.0
-3.9
---
138.0
---
138.0
---
143.4
---
4–6
94.7
93.9
0.8
93.8
0.9
98.7
-4.0
---
92.1
---
92.1
---
98.4
---
5–7
136.2
135.7
0.5
135.5
0.7
136.5
-0.3
---
130.1
---
130.1
---
132.8
---
6–8
125.5
125.5
0.0
125.3
0.2
118.0
7.5
---
115.9
---
115.9
---
111.2
---
7–9
154.4
153.8
0.6
153.6
0.8
151.1
3.3
---
145.6
---
145.6
---
145.4
---
8 – 10
165.2
165.1
0.1
165.0
0.2
161.3
3.9
---
156.0
---
156.0
---
154.7
---
9 – 11
177.0
177.9
-0.9
177.8
-0.8
175.0
2.0
---
168.7
---
168.7
---
168.6
---
∆
∆
∆
Ramang
40
Table 10 Continued. SiCB-d2 Transition
Experimental. fit 4
,𝑥2)b
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
0.001
---
0.001
---
151.0
-1.3
150.7
-1.0
157.0
-7.3
---
0.1
---
0.1
---
0.1
---
3–4
130.6
130.2
0.4
130.1
0.5
137.5
-6.9
4–5
5.0
5.1
-0.1
5.2
-0.2
3.7
1.3
5–6
86.0
86.4
-0.4
86.6
-0.6
94.7
-8.7
6–7
40.5?
39.6
---
39.7
---
35.3
---
7–8
68.1
68.7
-0.6
68.8
-0.7
70.5
-2.4
8–9
73.0
70.6
2.4
70.6
2.4
70.3
2.7
9 – 10
79.5
78.2
1.3
78.1
1.4
79.0
0.5
10 – 11
84.7
83.4
1.3
83.3
1.4
84.3
0.4
3–5
135.6
135.3
0.3
135.2
0.4
141.2
-5.6
4–6
90.5?
91.5
---
91.7
---
98.4
---
5–7
125.6
126.1
-0.5
126.2
-0.6
130.0
-4.4
6–8
107.2
108.4
-1.2
108.5
-1.3
105.8
1.4
7–9
138.2
139.4
-1.2
139.4
-1.2
140.8
-2.6
8 – 10
~148
148.9
---
148.7
---
149.2
---
9 – 11
160.3
161.7
-1.4
161.4
-1.1
163.3
-3.0
10 – 12
---
171.8
---
171.4
---
173.7
---
11 – 13
180.4?
181.1
---
180.6
---
183.3
---
2–5
135.5
135.4
0.1
135.4
0.1
141.3
-5.8
4–7
132.8
131.2
1.6
131.4
1.4
133.7
-0.9
5–8
195.6
194.8
0.8
195.1
0.5
200.5
-4.9
6–9
176.8?
179.0
---
179.0
---
176.1
---
0–2
149.9
150.4
-0.5
150.7
-0.8
157.0
-7.1
1–3
149.9
150.5
-0.6
150.9
-1.0
157.1
-7.2
2–4
129.0
129.8
-0.8
130.2
-1.2
137.6
-8.6
3–5
135.4
134.7
0.7
135.2
0.2
141.2
-5.8
4–6
93.0
91.2
1.8
91.7
1.3
98.4
-5.4
5–7
---
125.5
---
126.2
---
130.0
---
6–8
107.9
107.7
0.2
108.5
-0.6
105.8
2.1
7–9
142.4
138.6
3.8
139.4
3.0
140.8
1.6
8 – 10
157.0
148.0
9.0
148.7
8.3
149.2
7.8
FIRa
Observed
0–1
---
0.001
1–2
149.7
2–3
𝑉(𝑥
∆
Ramang
a
FIR data for SiCB from Ref. [12]. FIR data for SiCB-d1 and SiCB-d2 from Ref. [52]. 41
Using Eq. (1). Eq. (4). d From CCSD/cc-pVTZ computations. e Approximate value from microwave work, Ref. [50]. f Calculated from observed transitions 3 – 4 and 3 – 5. g Raman data for SiCB and SiCB-d from Ref. [51]. 2
b
c Using
1,3-Disilacyclobutane (13Si2CB) and its 1,1,3,3-d4 (13Si2CB-d4) derivative were first synthesized by Irwin and Laane and its far-infrared and Raman spectra were published in the same paper in 1977 [20]. Later in 1980 the Laane group studied the combination band spectra for the 1,3-disilacyclobutane-1,1,3-d3 derivative (13Si2CB-d3) [53]. The molecules were reported to be puckered with barriers to inversion of 87 cm-1, 86 cm-1 and 87 cm-1, respectively. This work along with a force constant investigation showed that the ring-puckering and SiH2 in-phase rocking motions were strongly coupled [20]. In our present work we find 𝜔 = 0.241 reflecting the fact that CSiC angles in the ring are considerably easier to bend than SiCSi angles. We also find that there is substantial SiH2 rocking and some CH2 rocking occurring during the puckering vibration as 𝑅 (SiH2) = 0.50 rad/Å and 𝑅(α-CH2) = -0.81 rad/Å. The kinetic energy and potential energy parameters for 13Si2CB, 13Si2CB-d3 and 13Si2CBd4 are given in Tables S2 and Tables 2 and 3. Fig. 14(a) shows the experimentally fit and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. Fig. 14(b) shows the calculated wavefunctions for the lower energy levels. Fig. 15 shows that the experimental PEFs for 13Si2CB and its deuterated analogs are almost identical. The observed and calculated frequencies are shown in Table 11. The calculated inversion barriers from experimental data are 86-87 cm-1.
The ab initio calculation predicts a
value of 89 cm-1. Fig. S10 shows the comparison of the experimental PEFs using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for 13Si2CB and its deuterated species. 42
Fig. 14. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. The 0 – 1 transition value is from the experimental fit. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.130 Å and 𝜃𝑚𝑖𝑛= ±22.3°.
Fig. 15. Experimental PEFs for 13Si2CB isotopic species based on Eq. (4). 43
Table 11 Observed and Calculated Ring-Puckering Transitions (cm-1) for 13Si2CB, 13Si2CB-d3 and 13Si2CB-d4. 13Si2CB Transition
13Si2CB-d3
Experimental. fit
FIRa
Observed
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
0–1
---
2.954
---
2.873
1–2
56.0
56.1
-0.1
2–3
~31.6
31.2
3–4
49.5
4–5
Experimental fit
𝑉(𝑥4,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
---
1.819
---
1.805
3.8
52.8
52.8
0.0
29.4
---
---
24.2
-0.1
46.9
2.6
43.3
54.7
-0.2
52.2
2.3
-0.1
60.9
0.1
58.4
66.2
-0.2
66.0
0.0
70.6
70.7
-0.1
70.6
8–9
74.7
74.7
0.0
9 – 10
78.5
78.4
10 – 11
82.0
11 – 12
Theoreticald
∆
Theoreticald
∆
---
2.612
---
---
1.547
---
55.9
0.1
52.2
52.8
0.0
49.7
3.1
---
30.9
---
---
24.2
---
22.6
---
49.9
-0.4
49.6
43.3
0.0
43.3
0.0
40.7
2.6
54.5
54.9
-0.4
46.9
47.0
-0.1
47.0
-0.1
44.7
2.2
5–6
61.0
61.1
2.6
52.8
52.8
0.0
52.8
0.0
50.4
2.4
6–7
66.0
63.6
2.4
57.2
57.3
-0.1
57.3
-0.1
55.0
2.2
7–8
0.0
68.3
2.3
61.5
61.3
0.2
61.3
0.2
59.2
2.3
74.7
0.0
72.5
2.2
65.1
65.0
0.1
65.0
0.1
63.0
2.1
0.1
78.4
0.1
76.5
2.0
68.1
68.3
-0.2
68.3
-0.2
66.5
1.6
81.8
0.2
81.9
0.1
80.2
1.8
71.4
71.3
0.1
71.4
0.0
69.8
1.6
85.3
85.0
0.3
85.2
0.1
83.6
1.7
---
74.2
---
74.2
---
72.9
---
12 – 13
88.2
88.0
0.2
88.2
0.0
86.9
1.3
---
76.8
---
76.9
---
75.8
---
13 – 14
91.2
90.8
0.4
91.1
0.1
90.0
1.2
---
79.4
---
79.4
---
78.6
---
14 – 15
93.9
93.5
0.4
93.8
0.1
93.0
0.9
---
81.7
---
81.8
---
81.2
---
0–3
89.6
90.3
-0.7
89.7
-0.1
84.2
5.4
---
78.9
---
78.8
-----
73.9
---
Ramane
89.6
90.3
-0.7
0–2
---
59.1
---
58.8
---
54.8
---
---
54.6
---
54.6
---
51.3
---
1–3
86
87.3
-1.3
86.8
-0.8
81.6
4.4
---
77.1
---
77.0
---
72.4
---
2–4
~80
81.1
---
80.5
---
76.3
---
---
67.6
---
67.5
---
63.3
---
3–5
105
104.9
0.1
104.3
0.7
99.1
5.9
---
90.3
---
90.3
---
85.3
---
4–6
116
116.1
-0.1
115.6
0.4
110.6
5.4
---
99.8
---
99.8
---
95.1
---
5–7
127
127.3
-0.3
126.9
0.1
122.0
5.0
---
110.1
---
110.1
---
105.4
---
6–8
137
136.8
0.2
136.6
0.4
131.9
5.1
---
118.6
---
118.6
---
114.2
---
∆
44
Observed
∆
Table 11 Continued. 13Si2CB Transition
Ramane
13Si2CB-d3
Experimental. fit Observed
𝑉(𝑥
4
,𝑥2)b
∆
4
𝑉(𝑥 ,𝑥
Experimental. Fit 2
,𝑥6)c
∆
Theoreticald
∆
Observed
𝑉(𝑥
4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
7–9
146
145.4
0.6
145.2
0.8
140.8
5.2
---
126.3
---
126.3
---
122.2
---
8 – 10
153
153.1
-0.1
153.1
-0.1
149.0
4.0
---
133.2
---
133.3
---
129.5
---
9 – 11
161
160.3
0.7
160.3
0.7
156.7
4.3
---
139.6
---
139.7
---
136.3
---
10 – 12
~168
166.9
---
167.1
---
163.8
---
---
145.5
---
145.6
---
142.7
---
11 – 13
173
173.0
0.0
173.4
-0.4
170.5
2.5
---
151.0
---
151.2
---
148.7
---
12 – 14
~180
178.8
---
179.3
---
176.9
---
---
156.2
---
156.4
---
154.4
---
13 – 15
187
184.3
2.7
184.9
2.1
183.0
4.0
---
161.1
---
161.3
---
159.8
---
13Si2CB-d4 Transition
Experimental. fit 4
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
---
1.602
---
1.562
---
1.321
---
1–2
52.0
52.0
0.0
52.0
0.0
49.1
2.9
2–3
---
22.7
---
22.5
---
20.9
---
3–4
41.8
41.8
0.0
41.7
0.1
39.1
2.7
4–5
45.1
45.1
0.0
45.0
0.1
42.7
2.4
5–6
50.7
50.8
-0.1
50.7
0.0
48.3
2.4
6–7
55.0
55.2
-0.2
55.1
-0.1
52.8
2.2
7–8
59.1
59.1
0.0
59.1
0.0
56.8
2.3
8–9
62.5
62.6
-0.1
62.6
-0.1
60.5
2.0
9 – 10
65.8
65.9
-0.1
65.9
-0.1
63.9
1.9
10 – 11
68.7
68.8
-0.1
68.9
-0.2
67.1
1.6
11 – 12
71.4
71.6
-0.2
71.7
-0.3
70.1
1.3
12 – 13
75.2
74.2
1.0
74.3
0.9
72.9
2.3
13 – 14
~77
76.6
---
76.8
---
75.6
---
FIRa
Observed
0–1
𝑉(𝑥
,𝑥2)b
45
Table 11 Continued. 13Si2CB-d4 Transition
Experimental. fit 4
,𝑥2)b
∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
∆
FIRa
Observed
14 – 15
79.0
79.0
0.0
79.1
-0.1
78.1
0.9
15 – 16
81.2
81.1
0.1
81.4
-0.2
80.6
0.6
0–3
76.0
76.3
-0.3
76.0
0.0
71.3
4.7
𝑉(𝑥
FIR data for 13Si2CB and 13Si2CB-d4 from Ref. [20]. FIR data for 13Si2CB-d3 from Ref. [53]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. e Raman data for 13Si CB from Ref. [20]. 2 a
b
46
There are no experimental ring-puckering spectra for GeCB nor for 13Ge2CB. Nevertheless, we calculated their kinetic energy expressions and these are shown in Table S2. The calculated PEFs parameters based on the ab initio calculations are shown in Tables 2 and 3. Fig. 16(a) shows the theoretical ring-puckering PEFs and energy levels for GeCB. The barrier is calculated to be 409 cm-1. The predicted infrared transition frequencies are also shown in the figure. Fig. 16(b) shows the calculated wavefunctions for the lower energy levels of GeCB. Fig. 17(a) shows the theoretical ringpuckering PEFs and energy levels for 13Ge2CB. The predicted infrared transitions are also shown in the figure. As can be seen, the molecule is essentially planar with a calculated barrier of 1 cm-1, and this results from the small magnitude of the -GeH2-CH2- torsional interactions. Fig. 17(b) shows the calculated wavefunctions for the lower energy levels of 13Ge2CB.
47
Fig. 16. (a) Theoretical ring-puckering PEFs for GeCB. The predicted infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.156Å and 𝜃𝑚𝑖𝑛= ±30.1°.
Fig. 17. (a) Theoretical ring-puckering PEFs for 13Ge2CB. The predicted infrared transitions are also shown in the figure. The predicted 0 – 1 transition is 29.6 cm-1. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.047Å and 𝜃𝑚𝑖𝑛= ±7.8°.
48
3.4. Cyclobutanone Borgers and Strauss [44] reported the far-infrared spectra of cyclobutanone (CBONE) in 1966 and determined a ring-puckering PEF with a barrier of 5 cm-1. In the same year Durig and Lord [54] published the far-infrared spectra for CBONE and its deuterated analog cyclobutanoned4 (CBONE-α,α'd4). They predicted a very low barrier for the ring-puckering of CBONE [54] but did not report a value. Fig. 18(a) shows the experimental and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. Fig. 18(b) shows the calculated wavefunctions for the lower energy levels.
Fig. 19 shows the calculated
PEFs from experimental fits for CBONE and its deuterated analog. The barrier to planarity is 2 cm-1 whereas the theoretical calculation predicts 36 cm-1. The observed and calculated frequencies are shown in Table 12. The kinetic energy terms for CBONE and CBONE-d4 are given in Table S2 and the potential energy parameters are given in Tables 2 and 3. Fig. S11 shows the comparison of the PEFs from the experimental fits using Eqs. (1) and (4) with those from the CCSD/cc-pVTZ calculations for CBONE and its deuterated species CBONE-α,α'd4.
49
Fig. 18. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.043 Å and 𝜃𝑚𝑖𝑛= ±4.6°.
Fig. 19. Experimental PEFs for CBONE isotopic species based on Eq. (4).
50
Table 12 Observed and Calculated Ring-Puckering Transitions (cm-1) for CBONE and CBONE- α,α'd4. CBONE- α,α'd4
CBONE Transition
Experimental. fit 4
,𝑥2)b
∆
Experimental fit ∆
𝑉(𝑥4,𝑥2,𝑥6)c
∆
Theoreticald
31.6
---
36.6
---
23.2
---
47.1
46.8
0.3
47.1
0.0
56.7
-9.6
1.6
54.2
54.3
-0.1
54.3
-0.1
63.4
-9.2
73.6
-1.4
60.6
60.5
0.1
60.2
0.4
73.6
-13.0
0.2
81.2
-3.8
65.6
65.7
-0.1
65.4
0.2
81.2
-15.6
82.3
-0.8
87.8
-6.3
69.8
70.2
-0.4
70.0
-0.2
87.8
-18.0
-1.65
85.20
0.05
93.6
-8.3
73.2
74.10
-0.9
74.20
-1.0
93.6
-20.4
91.1
---
1.5
---
98.7
---
78.9
77.7
1.2
78.1
0.8
98.7
-19.8
157.5
0.4
157.6
0.3
143.3
14.6
---
132.7
138.1
---
143.3
---
FIRa
Observed
0–1
36.5
38.1
-1.6
1–2
56.8
55.4
2–3
65.0
3–4
𝑉(𝑥
4
𝑉(𝑥 ,𝑥
2
,𝑥6)c
∆
Theoreticald
∆
37.9
-1.4
23.2
13.3
~30
1.4
55.5
1.3
56.7
0.1
64.1
0.9
64.2
0.8
63.4
72.2
71.3
0.9
71.3
0.9
4–5
77.4
77.2
0.2
77.2
5–6
81.5
82.4
-0.9
6–7
85.25
86.90
7– 8
---
0–3
157.9
FIR data for CBONE from Ref. [44]. FIR data for CBONE-α,α'd4 from Ref. [54]. Using Eq. (1). c Using Eq. (4). d From CCSD/cc-pVTZ computations. a
b
51
Observed
𝑉(𝑥
4
,𝑥2)b
---
∆
3.5. Comparison of CCSD and MP2 results Comparisons of the calculated ring-puckering barriers and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛values obtained from the experimental fits using Eq. (4) with those from the theoretical CCSD/cc-pVTZ and MP2/cc-pVTZ calculations are shown in Table 7. Overall, the CCSD computations lead to better predictions for the ring-puckering barriers and 𝜃𝑚𝑖𝑛. This table shows that the CCSD/cc-pVTZ calculations predicted the barriers to planarity for the ring-puckering with errors ranging from 2 to 14%, and the 𝜃𝑚𝑖𝑛 values with errors with a ranging from zero to 9% for all the molecules except TMO and CBONE, both of which are essentially planar with tiny barriers. The errors from the MP2/cc-pVTZ calculations ranged from of 35 to 86% for the barriers and from 1 to 16% for the 𝜃𝑚𝑖𝑛 values for the molecules other than TMO and CBONE. For TMO, which has an experimental barrier of 15 cm-1 and 𝜃𝑚𝑖𝑛 equal to 13.4°, the MP2 calculation did better at prediction. For TMO the CCSD calculation predicted a basically planar molecule while the MP2 calculation predicted a barrier of 21 cm-1 and a 𝜃𝑚𝑖𝑛 equal to 14.8°. For CBONE, both methods predicted somewhat higher barriers than the experimental value of 2 cm-1.
52
Fig. 20. Experimental PEFs for the ring-puckering of four-membered ring molecules based on Eq. (4).
4. Conclusion As discussed above, the far-infrared, Raman and/or combination band spectra of these fourmembered ring molecules have previously been published. In addition, one-dimensional potential energy functions utilizing either Eq. (1) in dimensional form or Eq. (2) in reduced (dimensionless) form have been reported. Typically, fairly good frequency fits and reasonable calculations of potential energy barriers were achieved. The major flaw in these calculations has been the inability to determine to what degree other low-frequency vibrational motions couple with the simple onedimensional puckering model. In an investigation of 1,3-disilacyclobutane and its d4 species18 we found that by empirically adjusting the extent of coupling between a SiH2 rocking mode and the ring puckering we could utilize the same PEF for both isotopic species. Our present work more accurately models how MH2 (M = C, Si, or Ge) rocking motions couple with the puckering. In
53
addition, these computations have allowed us to much better calculate the values of 𝜔, which describes the relative angle bendings within these four-membered rings. The net result is that we have achieved much more reliable kinetic energy expansions 𝑔44(𝑥). These in turn have allowed us to attain much improved PEFs and to accurately establish their energy minima and energy barriers. We have also found that these refined PEFs agree remarkably well with those generated directly from the CCSD/cc-pVTZ ab initio calculations. Previous work on these molecules which did not utilize reliable rocking parameters 𝑅 resulted in incorrect reduced mass calculations and poor agreement between experimental and ab initio results. For each molecule we calculated the optimized PEF using both Eq. (1) and Eq. (4). Fig. 20 compares these based on Eq. (4). As we have shown before11 the potential energy parameter 𝑎 arises mostly from angle strain while 𝑏 arises from torsional forces. The coefficient 𝑐 in Eq. (4) primarily has the effect of slightly refining the shape of the PEF. Table 4 shows that the magnitude of the improvement from adding the 𝑥6 term is fairly small. As can be seen, in Tables 2 and 3 the magnitude of the angle strain coefficient 𝑎 goes in the order CB > TMO > TMS > SiCB > TMSe > 13Si2CB which is in the order expected. CCC angles are stiffer than CSC, CSeC, or CSiC angles, for example. The negative magnitudes of the coefficient 𝑏 reflect the fact that -CH2-CH2interaction are stronger than the -SiH2-CH2- torsional interactions. Cyclobutane has four of the former while TMO and TMS have only two and thus correspondingly lower 𝑏 values. SiCB has two -CH2-CH2 and two -CH2-SiH2- interactions while 13Si2CB has two of the latter.
Acknowledgements The authors wish to thank the Welch Foundation (Grant A-0396) for financial support. Computations were carried out on the Texas A&M University Department of Chemistry Medusa
54
computer system funded by the National Science Foundation, Grant No. CHE-0541587. The Laboratory for Molecular Simulation provided the Semichem AMPAC/AGUI software.
Appendix A. Supplementary material Supplementary material associated with this article can be found online at https://doi.org/..... References [1] J. Laane, E. J. Ocola, H. J. Chun, in Frontiers and Advances in Molecular Spectroscopy, edited by J. Laane (Elsevier: Amsterdam, 2017), p. 101. [2] J. Laane, in Frontiers of Molecular Spectroscopy, edited by J. Laane (Elsevier: Amsterdam,2009), p.63. [3] J. Laane, J. Phys. Chem. A, 104, 7715 (2000). [4] J. Laane, in Structures and Conformations of Non-Rigid Molecules, edited by J. Laane, M. Dakkouri, B. van der Veken, and H. Oberhammer (Kluwer Publishing: Amsterdam, 1993), p. 65. [5] J. Laane, Int. Rev. in Phys. Chem. 18, 301 (1999). [6] J. Laane, Annu. Rev. Phys. Chem. 45, 179 (1994). [7] J. Laane, J. Pure and Appl. Chem. 59, 1307 (1987). [8] L.A. Carreira, R. C. Lord, and T. B. Malloy Jr. Top. Curr. Chem. 82, 1 (1979). [9] J. Laane, Quart. Rev. 25, 533 (1971). [10] R. P. Bell, Proc. R. Soc. London, A183, 328 (1945). [11] J. Laane, J. Phys. Chem. 95, 9246 (1991). [12] J. Laane, R. C. Lord, J. Chem. Phys. 48, 1508 (1968). 55
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[30] S. I. Chan, T. R. Borgers, J. W. Russell, H. L. Strauss, and W. D. Gwinn, J. Chem. Phys. 44, 1103 (1966). [31] H. Wieser, M. Danyluk, and R. A. Kydd, J. Mol. Spectrosc. 43, 382 (1972). [32] W. Kiefer, H. J. Berstein M. Danyluk and H. Wieser, Chem. Phys. Lett. 12, 605 (1972). [33] W. Kiefer, H. J. Berstein H. Wieser, and M. Danyluk, J. Mol. Spectrosc. 43, 393 (1972). [34] J. Jokisaari and J. Kaupinen, J. Chem. Phys. 59, 2260 (1973). [35] G. Mozzurri, M. Kunzmann, B. P. Winnewisser, and M. Winnewisser. J. Mol. Spectrosc. 219, 152 (2003). [36] J. Fernández, R. J. Myers, and W. D. Gwinn, J. Chem. Phys. 23, 758 (1955). [37] S. I. Chan, J. Zinn, J. Fernández, and W. D. Gwinn, J. Chem. Phys. 33, 1643 (1960). [38] S. I. Chan, J. Zinn, and W. D. Gwinn, W. D. J. Chem. Phys. 33, 295 (1960). [39] S. I. Chan, J. Zinn, and W. D. Gwinn, J. Chem. Phys. 34, 1319 (1961). [40] J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spectrosc. 34, 136 (1970). [41] I. Foltynowicz, J. Konarski, and Marek Kręglewski, J. Mol. Spectrosc. 87, 29 (1981). [42] I. Foltynowicz, J. Mol. Spectrosc. 96, 239 (1982). [43] V. Szalay, G. Bánhegyi, and G. Fogarasi, J. Mol. Spectrosc. 126, 1 (1987). [44] T. R. Borgers and H. L. Strauss, J. Chem. Phys. 45, 947 (1966). [45] H. Wieser, J. A. Duckett, and R. A. Kydd, J. Mol. Spectrosc. 51, 115 (1974). [46] J. R. Durig, A. C. Shing, L. A. Carreira, and Y. S. Li, J. Chem. Phys. 57, 4398 (1972). [47] H. Wieser and R. A. Kydd, J. Raman Spectrosc. 4, 401-407 (1976). [48] A. B. Harvey, J. R. Durig, and A. C. Morrisey, J. Chem. Phys. 50, 4949 (1969). [49] J. Laane, J. Am. Chem. Soc. 89, 1144 (1967). [50] W. C. Pringle, Jr., J. Chem. Phys. 54, 4979 (1971).
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[51] J. D. Lewis, T. H. Chao, and J. Laane, 62, 1932 (1975). [52] M. A. Harthcock, J. M. Cooke, J. Laane, J. Phys. Chem. 86, 4335 (1982). [53] P. W. Jagodzinski, R. M. Irwin, J. M. Cooke, and J. Laane, J. Mol. Spec. 84, 139 (1980). [54] J. R. Durig, J. R. and R. C. Lord, J. Chem. Phys. 45, 61 (1966).
Captions for tables In the Main Body: Table 1. Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters. Table 2. Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Table 3. Ring-Puckering Parametersa for CB and related molecules using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐𝑥6. Table 4. Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4). Table 5. Observed and Calculated Ring-Puckering Transitions (cm-1) for CB, CB-d8 and CB-d1. Table 6. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs. Table 7. Comparison of experimental barriers, and 𝑥𝑚𝑖𝑛 and 𝜃𝑚𝑖𝑛 values with those from theoretical calculations. Table 8. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMS and deuterated analogs. Table 9. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMSe. Table 10. Observed and Calculated Ring-Puckering Transitions (cm-1) for SiCB and deuterated analogs. Table 11. Observed and Calculated Ring-Puckering Transitions (cm-1) for 13Si2CB, 13Si2CB-d3 and 13Si2CB-d4. Table 12. Observed and Calculated Ring-Puckering Transitions (cm-1) for CBONE and CBONEα,α'd4. 58
In the supplementary material: Table S1. Comparison of the Experimental Geometrical Parameters of CB and Related Molecules to those from our Computations for the Puckered and the Planar Configurations. Table S2. Coefficients of the Kinetic Energy Functions for CB and Related Molecules. 𝑔44(𝑥) = 𝑎𝑥0 +𝑏𝑥 + 𝑐𝑥2 +𝑑𝑥3 + 𝑒𝑥4 +𝑓𝑥5 +𝑔𝑥6. Table S3. Calculated values for 𝜌, 𝜔, 𝛽 and 𝑅 parameters for TMO. Table S4. Coefficients of the Kinetic Energy Functions for TMO and deuterated analogs. 𝑔44(𝑥) = 𝑎𝑥0 +𝑏𝑥 + 𝑐𝑥2 +𝑑𝑥3 + 𝑒𝑥4 +𝑓𝑥5 +𝑔𝑥6. Table S5. Observed and Calculated Ring-Puckering Transitions (cm-1) for TMO and deuterated analogs from MP2/cc-pVTZ computations. Table S6. Ring-Puckering Parameters for TMO and deuterated analogs using 𝑉 = 𝑎𝑥4 +𝑏𝑥2. Table S7. Ring-Puckering Parameters for TMO and deuterated analogs using 𝑉 = 𝑎𝑥4 +𝑏𝑥2 +𝑐 𝑥6. Table S8. Comparison of average square deviations (ASD) for the frequency fits using Eqs. (1) and (4) for TMO. Captions for figures In the main body: Fig. 1. Definition of the ring-puckering angle (𝜃), the SiH2 rocking angle (𝛽) and the ringpuckering coordinate (𝑥) for SiCB. The angle 𝛽 is defined as the angle between the bisectors of the CSiC an HSiH angles. All values shown are the results from CCSD/cc-pVTZ computations. Fig. 2. Calculated structural parameters of CB and related molecules in their minimum energy conformations (puckered) from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å). Fig. 3. Ring-puckering angles of the energetic minimum, ϴ𝑚𝑖𝑛 from CCSD/cc-pVTZ computations. Fig. 4. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion.
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Fig. 5. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for CB. The observed transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.142 Å and 𝜃𝑚𝑖𝑛= ±29.6°. Fig. 6. Experimental PEFs for CB isotopic species based on Eq. (4). Fig. 7. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using CCSD/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.063Å and 𝜃𝑚𝑖𝑛= ±13.6°. Fig. 8. Experimental PEFs for TMO isotopic species based on Eq. (4) from CCSD/cc-pVTZ computations. Fig. 9. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMS. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.141 Å and 𝜃𝑚𝑖𝑛= ±26.9°. Fig. 10. Experimental PEFs for TMS isotopic species based on Eq. (4). Fig. 11. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for TMSe. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.162 Å and 𝜃𝑚𝑖𝑛= ±30.4°. Fig. 12. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for SiCB. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.163 Å and 𝜃𝑚𝑖𝑛= ±31.9°. Fig. 13. Experimental PEFs for SiCB isotopic species based on Eq. (4). Fig. 14. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for 13Si2CB. The experimentally observed infrared transitions are also shown in the figure. The 0 – 1 transition value is from the experimental fit. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.130 Å and 𝜃𝑚𝑖𝑛= ±22.3°. Fig. 15. Experimental PEFs for 13Si2CB isotopic species based on Eq. (4). Fig. 16. (a) Theoretical ring-puckering PEFs for GeCB. The predicted infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.156Å and 𝜃𝑚𝑖𝑛= ±30.1°.
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Fig. 17. (a) Theoretical ring-puckering PEFs for 13Ge2CB. The predicted infrared transitions are also shown in the figure. The predicted 0 – 1 transition is 29.6 cm-1. (b) Calculated wavefunctions for the lower energy levels. The calculated energy minima are at 𝑥𝑚𝑖𝑛 = ±0.047Å and 𝜃𝑚𝑖𝑛= ±7.8°. Fig. 18. (a) Experimentally fit with Eq. (4) and theoretical ring-puckering PEFs for CBONE. The experimentally observed infrared transitions are also shown in the figure. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.043 Å and 𝜃𝑚𝑖𝑛= ±4.6°. Fig. 19. Experimental PEFs for CBONE isotopic species based on Eq. (4). Fig. 20. Experimental PEFs for the ring-puckering of four-membered ring molecules based on Eq. (4). In the supplementary material: Fig. S1 Calculated structural parameters of CB and related molecules in their planar conformations from CCSD/cc-pVTZ computations. The bond distances are in Ångströms (Å). Fig. S2. Experimentally fit and theoretical ring-puckering PEFs for (a) CB, (b) CB-d8 and (c) CB-d1 from CCSD/cc-pVTZ computations. Fig. S3. Coordinate dependence of 𝑔44, the reciprocal reduced mass expansion of TMO. Fig. S4. (a) Experimental fit using Eq. (4) compared to the theoretical ring-puckering PEF for TMO using MP2/cc-pVTZ computations. The observed transitions are also shown in the figure. The 0 –1 observed transition is 52.92 cm-1. (b) Calculated wavefunctions for the lower energy levels. The energy minima are at 𝑥𝑚𝑖𝑛 = ±0.062Å and 𝜃𝑚𝑖𝑛= ±13.4°. Fig. S5. Experimental PEFs for TMO isotopic species based on Eq. (4) using the 𝜌, 𝜔, 𝛽 and 𝑅 parameters for TMO defined by MP2/cc-pVTZ computations. Fig. S6. Experimentally fit and theoretical ring-puckering PEFs for (a) TMO, (b) TMO-αd2, (c) TMO-βd2, (d) TMO-α,α'd4, (e) TMO-d6. from MP2/cc-pVTZ computations. Fig. S7. Experimentally fit and theoretical ring-puckering PEFs for (a) TMS, (b) TMS-αd2, (c) TMS-βd2, (d) TMS-α,α’d4 and (e) TMS-d6 from CCSD/cc-pVTZ computations. Fig. S8. Experimentally fit and theoretical ring-puckering PEFs for TMSe from CCSD/cc-pVTZ computations. Fig. S9. Experimentally fit and theoretical ring-puckering PEFs for (a) SiCB, (b) SiCB-d1 and (c) SiCB-d2 from CCSD/cc-pVTZ computations. 61
Fig. S10. Experimentally fit and theoretical ring-puckering PEFs for (a) 13Si2CB, (b) 13Si2CBd3 and (c) 13Si2CB-d4 from CCSD/cc-pVTZ computations. Fig. S11. Experimentally fit and theoretical ring-puckering PEFs for (a) CBONE and (b) CBONEα,α’d4 from CCSD/cc-pVTZ computations. Graphical Abstract
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