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Additional conformer observed in the microwave spectrum of methyl vinyl ketone
Chemical Physics Letters 508 (2011) 10–16
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Additional conformer observed in the microwave spectrum of methyl vinyl ketone David S. Wilcox, Amanda J. Shirar, Owen L. Williams, Brian C. Dian ⇑ Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, IN 47907-2084, USA
a r t i c l e
i n f o
Article history: Received 3 December 2010 In final form 1 April 2011 Available online 3 April 2011
a b s t r a c t A chirped-pulse Fourier transform microwave spectrometer was used to record the rotational spectrum of methyl vinyl ketone (MVK, 3-butene-2-one). Two stable conformations were identified: the previously documented antiperiplanar (ap) conformer and synperiplanar (sp), which is reported for the first time in this microwave study. Methyl torsional analysis resulted in V3 barrier heights of 433.8(1) and 376.6(2) cm1 for ap- and sp-MVK, respectively. Heavy atom isotopic species of both conformers were detected in natural abundance allowing bond lengths and angles of the molecular frames to be calculated through Kraitchman analysis. A comparison with ab initio calculations is included. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The simplest a,b-unsaturated ketone, methyl vinyl ketone (MVK, 3-buten-2-one), is important in atmospheric chemistry as a primary product of isoprene oxidation. Early laboratory studies discovered significant yields of MVK from the reaction of isoprene with the hydroxyl radical [1] or ozone [2]. MVK was later identified in the atmosphere at concentrations strongly correlated with biogenic isoprene [3]. MVK reacts quickly with the hydroxyl radical to generate other carbonyls including methylglyoxal and formaldehyde that contribute to the additional destruction of ozone [4]. Accurately determining the structure of MVK will improve analyses of its chemistry in the atmosphere. The microwave spectrum of MVK was first measured in 1965 by Foster et al. in the region of 7–33 GHz [5]. MVK was identified in the antiperiplanar configuration (ap, Figure 1) and A–E frequency doublets were observed arising from hindered internal rotation of the methyl group. The authors were able to determine a V3 value of 437(7) cm1 for the barrier to internal rotation from this splitting. The microwave spectrum was revisited at higher frequencies (26.4–40 GHz) in 1987 where rotational transitions were determined from the ground and first excited torsional states of apMVK. A slightly smaller V3 value of 424(7) cm1 was reported for internal methyl rotation [6]. No evidence for an additional conformation was reported in either study. Infrared studies, however, have confirmed a second stable conformation, synperiplanar (sp, Figure 1), in the liquid and gas phases [7]. From the measured enthalpies, sp-MVK was found to be 2.36 kJ/mol higher in energy than ap-MVK. Ab initio calculations have predicted similar energies (0.12–2.36 kJ/mol) depending on
⇑ Corresponding author. Fax: +1 765 494 0329. E-mail addresses: [email protected] (D.S. Wilcox), [email protected] (A.J. Shirar), [email protected] (O.L. Williams), [email protected] (B.C. Dian). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.04.001
the level of theory used [7,8]. This small energy difference suggests that the sp conformer could be detected in the MVK rotational spectrum with a chirped-pulse Fourier transform microwave (CPFTMW) spectrometer. Here we present the rotational spectrum of both the ap- and sp-MVK conformers, as well as assignments for the isotopic species (heavy atoms only) in natural abundance.
2. Experimental The CP-FTMW spectrometer has previously been described in detail [9] and will only be summarized here. Methyl vinyl ketone was obtained from Sigma–Aldrich (99% pure) and used without further purification. Approximately 1 mL of sample was introduced into a tank using a freeze–pump-thaw method and balanced to approximately 7 bar with a 30/70% He/Ne mixture. An arbitrary waveform generator with a 10 GS/s sampling rate (Tektronix AWG 7101) produced a 1 ls microwave chirped pulse (1.875– 4.625 GHz). The pulse was then quadrupled (Phase One) and the power increased with a 200 W amplifier (Amplifier Research) to create an 11 GHz bandwidth pulse (7.5–18.5 GHz). This polarizing pulse was then broadcast with a microwave horn into a vacuum chamber with a typical base pressure of 1 106 Torr. The sample was introduced into the chamber with a Series 9 General Valve (2 mm orifice) at a backing pressure of 1 bar resulting in a supersonic expansion that cooled the molecules to an estimated rotational temperature of 4 K. The microwave pulse induced a macroscopic polarization and the resulting free inductive decay was collected with a second microwave horn. The molecular signal passed through a PIN diode limiter (Advanced Control Components) and a switch (single pole single throw, Advanced Technical Materials) before entering a low noise amplifier (+45 dB gain, Miteq). The molecular signal was then mixed with an 18.9 GHz phase locked dielectric resonator oscillator (Microwave Dynamics) and the lower sideband was isolated and digitized at 40 GS/s for
11
D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
X
r ¼1
g¼a;b
qg ¼ kg
Figure 1. The two conformers of methyl vinyl ketone (MVK) designated as antiperiplanar (ap) and synperiplanar (sp).
20 ls with a 12 GHz oscilloscope (Tektronix TDS6124C). In order to signal average, the entire system was synchronized with a 100 MHz phase locked loop (Wenzel Associates) driven by a 10 MHz Rb-disciplined crystal oscillator (Stanford Research Systems) and the timing was controlled with a 20-output Masterclock (Thales Laser). A Kaiser-Bessel digital filter was applied to the time domain signal to suppress side lobes of the rotational transitions in the frequency domain. The Fourier transform of the free induction decay yielded a nominally 11 GHz bandwidth frequency spectrum with 20 kHz resolution. The resolution was interpolated to 5 kHz offline in the spectral fitting program JB95 [10]. A signal-to-noise ratio of 10000:1 on the strongest transition was achieved with 100 000 time domain averages. The ground state microwave spectrum and background spectrum (to remove spurious microwave resonances) were recorded in a combined 15 h.
ð1Þ
where ð2Þ
AA ¼ ARR þ FW 00 q2a ð2Þ
BA ¼ BRR þ FW 00 q2b
ð2Þ
C A ¼ C RR ; and Hcd describes 4th order distortion. In the preceding equation, ð2Þ W 00 is the second order perturbation coefficient of the A-state in the ground torsional level. ARR, etc. are the unperturbed rigid rotor constants in the absence of internal rotation. F and qg (g = a, b) are functions of the methyl rotor inertial moment, I/ ; the direction cosines of the top with respect to the principal axis, kg ; and the principal moments of inertia Ig : 2
F¼
h FR ¼ 2rI/ r
ð3Þ
ð4Þ
I/ : Ig
ð5Þ
^2 ^2 ^2 Heff E ¼ AE P a þ BE P b þ C E P c þ
X
Dg P^g þ Hcd
ð6Þ
g¼a;b
with the operator constants ð2Þ
AE ¼ ARR þ FW 01 q2a BE ¼ BRR þ
ð2Þ FW 01
q2b
ð7Þ
C E ¼ C RR ð1Þ
Dg ¼ FW 01 qg : ð1Þ W 01
ð8Þ
ð2Þ W 01
and are the 1st and 2nd order perturbation coefficients, respectively, for the ground torsional level of the E-state. The A- and E-state perturbation coefficients are tabulated elsewhere [11] as a function of the reduced barrier parameter, s, which is in turn related to V3 by
s¼
^2 ^2 ^2 Heff A ¼ AA P a þ BA P b þ C A P c þ H cd ;
I/ Ig
The (a b) plane of symmetry in both conformers simplifies terms in the Hamiltonians since the c-principal axis is normal to the methyl rotor axis (kc = 0). qc is therefore zero, indicating C RR is unperturbed by internal rotation. The E-state effective Hamiltonian includes linear operators that describe the angular momentum of methyl hydrogen tunneling [14],
3. Results and discussion An effective Hamiltonian describing the torsion-rotation interaction for each A- and E-state symmetry species is implemented in the spectral fitting program JB95 [10]. The fitting parameters in the least squares procedure are based on the perturbative torsion-rotation Hamiltonian. For high V3 barriers to internal rotation, the torsion-rotation cross terms are treated as perturbations. The Hamiltonian is factored through successive Van Vleck transformations into submatrices describing A- and E-internal rotation states separately for each torsional level [11]. In the principal axis frame, this method is straightforward and suitable for molecules in torsional states near the bottom of the potential well with V3 barriers greater than approximately 100 cm1 [12]. Published microwave [5,6] and IR/Raman [13] data have reported V3 barrier heights between 420–437 cm1 for ap-MVK. Furthermore, all recorded lines originated from the ground torsional state (vt = 0 for both symmetry species) under the experimental conditions in this lab. The effective Hamiltonian used to fit the A-states is of the form [14]
k2g
4 V3 : 9 F
ð9Þ
The V3 barrier is thus obtained by determining s from the perturbation coefficients and fixing FR to the appropriate value (I/ is assumed 3.18 lÅ2 from Ref. [11]). Perturbation coefficients, rigid rotor constants, and direction cosines are obtained iteratively from the best-fit parameters of the A- and E-state effective Hamiltonians in a method described by Lavrich et al. [14]. This procedure, generalized for the case of multiple internal rotors, is implemented in a program integrated with the JB95 GUI. An additional torsional analysis was performed with the internal rotor program XIAM [15]. The precision of the V3 barrier becomes harder to determine in the principal axis frame (PAF) as the barrier increases and the torsion-rotation cross terms rapidly decrease to zero. Improved internal rotation parameters such as kg and V3 may be obtained in a number of methods employing Rho-axis frame (RAF) Hamiltonians [12]. A new coordinate axis system is defined in the RAF that is related to the PAF by a rotation of the z-axis parallel to the q vector. The contributions of qx and qy are eliminated from the q vector (qx ¼ qy ¼ 0) in the RAF, permitting the separation of the Hamiltonian into purely torsional and rotational components. In XIAM, the pseudorigid rotor Hamiltonian, HPAF rot ; is expressed in the PAF
^2 ^2 ^2 HPAF rot ¼ AP a þ BP b þ C P c þ H cd :
ð10Þ
Global rotational parameters A, B, C, and Hcd differ from those of Eqs. (1) and (6) in that they simultaneously describe A- and E-state transitions. The torsional Hamiltonian in the RAF contains internal rotation terms that may be directly varied in the fitting procedure:
^ 2 1 ^ HRAF tor ¼ Fðp/ þ qP z Þ þ V 3 ð1 cosð3/ÞÞ: 2
ð11Þ
^/ is the conjugate Here, / is the internal rotation angle and p momentum operator. The final rotational parameters are expressed in the PAF by transforming Eq. (11) back into the PAF and adding the contributions to the rotational constants of Eq. (10) [16].
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D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
The microwave spectrum of methyl vinyl ketone in the region of 6–18.9 GHz is presented in Figure 2. Using the reported rotational constants of Fantoni et al. [6], the A-state lines of ap-MVK were identified in our spectrum and the corresponding E-state transi-
Figure 2. The microwave spectrum of methyl vinyl ketone (MVK). The inset demonstrates the signal-to-noise achieved with the CP-FTMW spectrometer. The dashed line in the inset indicates the average peak height of isotopic species measured in natural abundance for ap-MVK.
tions were fit to the operator constants of Eq. (6) in JB95. Several new lines were included in the fit of the A- and E-states of apMVK, refining the assignments of Foster et al. [5] at higher resolution. Quartic distortion terms were required in both effective Hamiltonians to reduce the root-mean-square error. Improved values of all fitted parameters were obtained by including the previously measured high frequency transitions (19–40 GHz) with their appropriate experimental weights into the analysis. The quantum number assignments from JB95 were used as input for a global analysis in XIAM. The fit parameters from JB95 and XIAM are reported in Tables 1 and 2, respectively [17]. Though no preceding microwave studies have identified a second MVK conformer, experimental IR data has provided evidence for a stable conformation of MVK (synperiplanar of Figure 1) that is 2.36 kJ/mol higher in energy than ap-MVK. Ab initio calculations were performed to estimate conformational energies using the Gaussian suite [18] and are reported in Table 3. Zero-point corrected energies predicted sp-MVK to be the most stable conformer by 0.44 and 0.07 kJ/mol, respectively, at the Hartree–Fock (HF/6311++G(d,p)) and density functional (B3LYP/6-311++G(d,p)) levels of theory in contradiction with experimental results [7]. Secondorder Møller–Plesset perturbation theory (MP2/6-311++G(d,p)) calculations verified the experimental data with ap-MVK as the lower energy conformer by 1.16 kJ/mol. Calculated vibrational mode frequencies of each optimized geometry were positive, indicating that each conformer was a minimum energy structure [17]. Regardless of the computational accuracy, both theory and IR data offer strong evidence that the sp conformer should be observed in the MVK microwave spectrum. After assigning all possible lines to ap-MVK, unassigned doublets up to three orders of magnitude above the noise floor were
Table 1 List of JB95a parameters used to fit the methyl vinyl ketone conformers. ap-MVKb
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) Db (MHz) DI (lÅ2)d
j ne
r (kHz)f s ð1Þ
W 01
d e f g h
A
E
A
E
8941.590(1) 4274.5443(6) 2945.3315(6) 8.1(1) 10–4 4.6(1) 103 5.4(7) 104 2.95(9) 104 2.6(1) 103
8941.525(1) 4274.1989(6) 2945.3364(6) 8.1(2) 104 4.56(9) 103 9.1(6) 104 2.62(9) 104 2.6(1) 103 3.107(1) 7.1(4) 3.17 0.56 29 7.08
8941.597(1) 4274.5458(4) 2945.3346(4) 8.77(8) 104 4.48(3) 103 8.5(4) 104 2.67(3) 104 2.99(5) 103
8941.528(1) 4274.1992(4) 2945.3384(5) 8.22(8) 104 4.57(3) 103 1.03(4) 103 2.53(3) 104 2.67(5) 103 3.109(1) 7.3(2) 3.17 0.56 66 123.94
10240.938(2) 3991.6351(7) 2925.648(1) 7.2(2) 104 2.2(2) 103 1.232(6) 102 1.8(1) 104 3.7(3) 103
10237.429(6) 3991.464(1) 2925.655(1) 9.1(6) 104 2.4(4) 103 4(2) 103 1.7(3) 104 3.3(6) 103 33.570(9) 9.6(9) 3.24 0.71 18 8.00
3.16 0.56 26 5.99
3.16 0.56 85 113.92
35.48702 0.001654
35.32942 0.001693
3.22 0.71 20 5.04 29.86706 0.003859
0.002000
0.002046
0.004661
0.001000
0.001023
0.002330
0.028731 5.453 8941.546(1) 4274.3149(6) 2945.3334(6) 78(1) 435(6)
0.028654 5.453 8941.552(1) 4274.3144(4) 2945.3365(5) 78.5(7) 433(4)
0.054057 5.583 10238.657(4) 3991.507(9) 2925.652(1) 36(5) 375(5)
F (cm1)h ARR (MHz) BRR (MHz) CRR (MHz) hA (°) V3 (cm1)
c
E
ð2Þ
qg
a
sp-MVK
A
ð2Þ
W 00
W 01
b
ap-MVK combinedc
Ref. [10]. Parameters obtained with transitions in our spectral bandwidth (6–18.9 GHz). Includes transitions of Refs. [5] and [6] (6–40 GHz). Inertial defect, DI = Ic Ib Ia. Number of transitions in the fit. Observed minus calculated root-mean-square deviation of the fit. Modulus of the q-vector (unitless). FR fixed to 5.3 cm1.
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D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16 Table 2 List of XIAMa parameters used in the global fit of the methyl vinyl ketone conformers.
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) DI (lÅ2)c
j nd
r (kHz)e s
qf F (cm-1) FR (cm-1) hA (°) hRAM (°)h V3 (cm-1) a b c d e f g h
ap-MVKb
sp-MVK
8941.547(1) 4274.3593(9) 2945.2903(9) 8.3(2) 10–4 4.45(6) 10–3 6.2(9) 10–4 2.47(5) 10–4 2.95(9) 10–3 3.17 0.56 150 101.47 35.35527 0.028736 5.453 5.300g 78.21(2) 66.41 433.8(1)
10238.610(1) 3991.6814(6) 2925.4885(1) 7.3(2) 10–4 1.9(2) 10–3 9.98(7) 10–3 1.8(1) 10–4 3.2(3) 10–3 3.22 0.71 38 5.38 30.31290 0.058276 5.523 5.214(3) 29.71(3) 12.54 376.6(2)
Ref. [15]. Includes transitions of Refs. [5] and [6] (6–40 GHz). Inertial defect, DI = Ic Ib Ia. Number of transitions in the fit. Observed minus calculated root-mean-square deviation of the fit. Modulus of the q-vector (unitless). Fixed. Angle of Rho-axis transformation.
attributed to sp-MVK. Based on the A–E splitting of each doublet, the V3 barrier was expected to be similar but slightly lower than that of ap-MVK. This was anticipated since steric hindrance to internal rotation is increased when the methyl and methylene groups are in close proximity as in the ap conformation. A relaxed potential energy scan (RPES) about the methyl torsional coordinate at the HF level of theory (6-311++G(d,p)) predicted V3 values of 375 and 398 cm1 for sp- and ap-MVK, respectively. DFT (B3LYP/6311++G(d,p)) underestimated the barrier of the known ap conformer by nearly 50% and predicted ap-MVK to be the higher barrier configuration (Table 3). Using the HF results, initial rotational constants for the A- and E-internal rotation species of sp-MVK were generated from Eqs. (2) and (7). The optimized geometry of spMVK was used to predict the unperturbed rigid rotor rotational
constants as well as F and q in a method described by Pitzer [19]. The reduced barrier parameter, s, was determined from F and V3 (Eq. (9)), and perturbation coefficients were estimated from Herschbach’s tables [11]. By simulating the spectrum with the perturbed rotational constants, ambiguity in the relative frequency order of the A–E symmetry doublets was eliminated in the early stages of the fit. The fit parameters of sp-MVK from JB95 and XIAM are also reported in Tables 1 and 2, respectively [17]. The internal rotation analysis in JB95 gave a V3 barrier height of 435(6) cm1 for ap-MVK with our data set, and 433(4) cm1 when high frequency transitions from Refs. [5,6] were included in the fit. The most precise V3 barrier height, 433.8(1) cm1, was obtained with the combined data in XIAM by fixing FR to 5.3 cm1 and floating V3 and the angle between the top axis and a-principal axis, ha. A direct comparison with previously reported results (Table 3) is not straightforward, since the assumptions regarding the reduced moment, F, are different in all three models. The V3 barrier of 424(7) cm1 reported by Fantoni et al. was obtained by fixing the reduced moment, F [6]. In this study, only I/ was fixed, allowing the structural variables of F to be varied in the fit. Similar assumptions were made by Foster et al. who obtained a more directly comparable V3 barrier of 437(7) cm1 with a slightly smaller fixed value of I/ (3.164 lÅ2) [5]. The V3 barrier height of sp-MVK was determined to be 375(5) cm1 in JB95. Including 4th order corrections into the effective Hamiltonians to account for the lower barrier did not improve the precision of V3. It is anticipated that incorporating data from higher J transitions is necessary to reduce the uncertainty with this method. A value of 376.6(2) cm1 was obtained with XIAM by floating the internal rotation parameters FR, ha, and V3. In contrast to ap-MVK, the quality of the fit increased 5-fold by varying FR. The variables FR and V3 are highly correlated, particularly in high barrier cases. It is suspected that due to the lower barrier of spMVK, more information is carried in the FR parameter and thus it was necessary to vary it in the fit. Tables 1–3 summarize internal rotation parameters from this study, calculations, and literature. The high signal-to-noise in the MVK rotational spectrum made it possible to resolve isotopic species in natural abundance, particularly carbon-13 substituted isotopes (1.1% natural abundance). The unperturbed rigid rotor constants of the isotopologues were calculated with the same computational accuracy as the unsubstituted parent species, and rotational constants for the A- and Einternal rotation species were predicted with Eqs. (2) and (7)
Table 3 Comparison of rotational data, dipole moment, and relative energies for experimental, ab initio calculated, and published values for both conformers of methyl vinyl ketone. ap-MVK
sp-MVK
Calculateda b
A (MHz) B (MHz) C (MHz) DI (lÅ2)d V3 (cm1) hA (°) F (cm1) la (D) lb (D) lc (D) DE (kJ/mol) DEZPEf (kJ/mol) a b c d e f
c
HF
DFT
9056.92 4311.38 2974.36 3.11 397.5 80.72 5.53 2.82 2.30 0.00 0 0.44
8934.27 4258.51 2936.50 3.14 258.7 81.63 5.46 2.74 2.07 0.00 0 0.07
Ref. [18]. 6-311++G(d,p) basis set. B3LYP/6-311++G(d,p) basis set. Inertial defect, DI = Ic Ib Ia. l2 (D2). Zero-point corrected energies.
Calculateda
Published b
b
Published c
b
MP2
Ref. [5]
Ref. [6]
HF
DFT
MP2
8912.33 4262.47 2936.26 3.15
8941.45(6) 4274.48(2) 2945.32(2) 3.17 437(7) 75(4) 5.50 6.39(14)e 3.64(16)e
8941.58(1) 4274.494(5) 2945.276(4) 3.16 424(7) 75.46(5) 5.38
10481.39 4012.61 2954.22 3.09 375.2 32.78 5.66 0.60 3.01 0.00 0.04 0
10229.70 3979.18 2916.42 3.12 290.3 32.71 5.59 0.57 2.88 0.00 0.59 0
10141.03 3982.27 2911.12 3.14
83.22 5.42 3.13 2.35 0.00 0 0
32.72 5.56 0.66 3.19 0.00 2.00 1.16
Ref. [7]
2.36
14
D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
Table 4 Isotopic assignments for methyl vinyl ketone. ap-MVK
H313CAC(O)ACH@CH2 13C1
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK(MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) DI (lÅ2)
j n
r (kHz)
H3CA13C(O)ACH@CH2 13C2
H3CAC(O)A13CH@CH2 13C3
H3CAC(O)ACH@13CH2 13C4
H3CAC(18O)ACH@CH2 180
A
E
A
E
A
E
A
E
A
E
8645.609(8) 4255.802(3) 2903.729(2) 6(2) 104 5.4(3) 103 2(2) 103 1.7(4) 104
8645.569(8) 4255.467(3) 2903.731(2) 6(2) 104 5.4(6) 103 4(1) 103 2.4(4) 104
8941.059(4) 4265.567(2) 2941.013(2) 8(1) 104 3.7(4) 103
8878.795(2) 4247.300(2) 2925.623(2) 6(1) 104 6.4(2) 103
8939.992(4) 4137.874(3) 2879.631 (3) 9(2) 104 5.8(3) 103
8939.930(4) 4137.556(3) 2879.627(2) 7(2) 104 5.8(3) 103
8728.645(9) 4129.793(3) 2853.487(3) 3.8(2) 103 2.1(1) 102
N/A N/A N/A
1.8(3) 104
8878.739(6) 4246.962(2) 2925.621(2) 4(2) 104 5.4(2) 103 5(1) 103 2.7(4) 104
1.9(5) 104
3.1(5) 104
3.16 0.53 15 6.671
3.21(8) 3.17 0.53 16 7.277
3.16 0.56 15 3.76
8941.017(7) 4265.219(3) 2941.014(3) 4(2) 104 4.5(7) 103 5(1) 103 3.2(4) 104 1.3(7) 103 3.09(7) 3.17 0.56 16 5.838
3.17 0.56 16 4.927
3.17(5) 3.18 0.56 17 5.968
3.16 0.58 15 8.196
3.01(7) 3.17 0.58 15 6.751
3.16 0.57 10 7.736
10240.006(5) 3985.490(2) 2922.289(2) 2.7(9) 104 4.8(2) 103 5.2(2) 103
10236.587(6) 3985.300(2) 2922.295(2) 5(1) 104 5.2(5) 103 6.0(2) 102
10236.318(5) 3869.542(2) 2859.530(2)
N/A N/A N/A
3.22 0.71 10 4.696
34.11(3) 3.24 0.71 11 4.614
2.1(2) 104 4.0(4) 103
sp-MVK A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) DI (lÅ2)
j n
r (kHz)
10140.193(3) 3899.994(3) 2868.105(2) 4(1) 104 3.8(2) 103 1.12(9) 102 1.6(3) 104
10136.738(3) 3899.832(1) 2868.102(1) 1.0(3)x103 3.3(1) 102 2.0(3) 104
3.22 0.72 12 3.541
33.71(1) 3.24 0.72 13 3.833
10145.439(5) 3970.554(5) 2906.569(3) 5(3) 104 3.6(4) 103 1.0(2) 102 2.2(6) 104
3.22 0.71 12 6.509
assuming the same barrier parameters as the parent conformers. The perturbed rotational constants were then scaled by the difference between the calculated and experimental values of the parent species, increasing the accuracy of the isotopically substituted predictions by 1–2 orders of magnitude. The a- and b-type lines of the 13 C isotopes of ap-MVK were appreciable in intensity (Table 3) resulting in 15–17 line assignments per internal rotor state. Owing to the large signal of the parent species, 10 A-state lines of 18O substituted ap-MVK were also detected. While there were several suspected E-state transitions, a reliable set of parameters was not obtained. The sp-MVK rotational spectrum, in contrast, consists primarily of a b-type transition moment (Table 3). Consequently, the low intensity a-type lines of the sp-MVK 13C isotopologues were difficult to detect; only 10–13 lines were assigned per internal rotor state. We were unable to assign 18O substituted transitions due to the lower signal intensity of the parent species and the relative abundance of this isotope (0.2% natural abundance). The quantum number assignments of the A–E symmetry doublets were confirmed by noting the similar magnitude of doublet splitting with respect to the parent conformer. In general, it was only possible to float combinations of several distortion constants in the fits of the isotopologues. Rotational constants and 4th order distortion terms resulting in the lowest residual error are given in Table 4. With heavy atom substitution data, structural information on the frame of ap-MVK and carbon backbone of sp-MVK was acquired through Kraitchman analysis [20]. Vibrational contributions from the methyl torsion contaminate both A- and E-state effective rotational constants. In order to obtain the most accurate substitution structures (rs), these effects may be removed by calculating the unperturbed rigid rotor constants from Eqs. (2) and (7) in the iterative process of Lavrich et al. [14]. Since the Db cross-terms were not well-determined due to the low J transitions in the fits of the isotopically substituted species, an approximate expression for the rigid rotor constants was used instead [21]:
10142.05(2) 3970.25(3) 2906.58(3) 4.0(6) 103 3.7(7) 102 7(1) 102 2(1) 104 5(1) 102 31.97(5) 3.25 0.71 12 8.815
Aapprox ¼ RR
10239.778(6) 3869.713(4) 2859.546(3) 8(3) 104 4.5(7) 103 9(3) 103
3.22 0.73 11 7.605
1 ðAA þ 2AE Þ: 3
N/A N/A N/A
2.7(1) 102 3.1(5) 104 33.64(4) 3.24 0.73 11 5.494
ð12Þ
A similar relation holds for Bapprox . To account for small differRR ences on the order of 1 kHz between C A and C E , the average was taken to calculate C RR . Eq. (12) is an approximation which neglects denominator corrections accounting for the small differences in the rotational energy levels after Van Vleck transformations. However, a systematic analysis on the equilibrium structure of cismethyl formate (V3 = 372.67 cm1) found that inclusion of denominator corrections induced a negligible effect on the value of the unperturbed rigid rotor constants [21]. The errors of the rs structures in Table 5 are propagated from the rigid rotor constants, although the calculated precision is greater than the zero-point fluctuations of the molecule. Small changes in the pseudoinertial defect (the difference between the equilibrium and effective principal moments estimating the vibration– rotation contribution to rs) upon isotopic substitution lead to systematic errors in the rs coordinates [22]. Corrections with Costain’s method lead to more physically meaningful uncertainties that are comparable with calculated equilibrium structures [23,24]. The adjusted error in Table 5 is given by das /Å = 0.0015/|as|, where as is the Kraitchman coordinate. The larger Costain errors observed in the substitution structures involving the C2 and C4 atoms of both conformers are a consequence of the close proximity of the atoms to the a-principal axis (0.06–0.1 Å) [23]. Costain’s results give errors less than 0.01 Å when coordinates are greater than 0.15 Å from the principal axis; it may be possible to reduce this uncertainty by double-isotopic substitution [25]. Calculated and observed bond lengths and angles generally concurred at all levels of theory in this study with the differences between calculated and experimental values being attributed to the modest basis sets used (Table 5). Without E-state rotational constants for the 18O substituted ap conformer, rigid rotor constants could not be determined. Because of the barrier height, rota-
15
D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16 Table 5 Comparison of the molecular structure according to ab initio predictions and Kraitchmana analysis. ap-MVK Ab initio HF rC1C2 rC2C3 rC3C4 rC2O \C1C2O \C1C2C3 \OC2C3 \C2C3C4 a b c d e f
c
1.512 1.494 1.321 1.191 121.27 119.57 119.16 125.27
sp-MVK b
Ab initiob
Kraitchman DFT
d
1.517 1.489 1.335 1.218 121.20 119.48 119.32 125.40
MP2
c
1.516 1.489 1.345 1.225 121.64 118.92 119.45 124.58
rs
e
1.4774(2) 1.49249(8) 1.33945(4) 1.2411(1) 122.56(2) 121.21(2) 116.23(1) 123.32(1)
Kraitchman
Costain
HFc
DFTd
MP2c
rs e
Costainf
1.48(2) 1.492(8) 1.340(6) 1.24(1) 123(2) 121(2) 116(1) 123(1)
1.510 1.498 1.321 1.190 122.02 116.07 121.91 121.66
1.514 1.497 1.333 1.215 121.92 116.12 121.96 121.81
1.513 1.499 1.343 1.222 122.31 115.80 121.90 121.32
1.5037(1) 1.4751(3) 1.3334(2)
1.504(9) 1.475(9) 1.333(7)
117.94(2)
118(1)
121.96(3)
122(1)
f
Ref. [20]. Ref. [18]. 6-311++G(d,p) basis set. B3LYP/6-311++G(d,p) basis set. Error of substitution structure propagated from rotational constants. Errors corrected with Costain’s method (Refs. [22] and [24]).
tional constants for the A-internal rotation species are expected to be within 0.1% of the rigid rotor values. For these reasons, 18O substituted coordinates were included in the Kraitchman analysis and are in reasonable agreement with theory. One notable disagreement between calculated and experimental values is in the rC1C2 methyl rotor axis bond of ap-MVK. At all levels of theory, the predicted rC1C2 bond length is typical for a carbon–carbon single bond. Within Costain’s error, the experimental bond length is shorter by nearly 2 pm. Ab initio calculations less accurately predicted the V3 barrier associated with the RPES about this bond, suggesting the deviations from experimental values are correlated. It has been suggested that a non-planar species of MVK exists [7], but a RPES conducted about the C2-C3 bond did not reveal any additional minima. Though low in intensity, approximately 550 lines were unassigned in the spectrum with many appearing to be A-E symmetry doublets. We attempted to find vibrationally excited satellite states corresponding to skeletal and methyl torsional motion using the rotational constants of Fantoni et al. [6]. No such lines were found. Efficient vibrational cooling in the supersonic jet diminishes population in these low energy modes and accordingly we do not generally observe vibrational satellites with our spectrometer. From the suspected torsional splitting of the unidentified peaks, dimerization or other clusters with the backing gas in the supersonic jet may account for the remaining lines in the spectrum.
On a final note, the high resolution, high signal-to-noise, and broad bandwidth of the CP-FTMW spectrometer makes it an ideal apparatus for obtaining substitution structures of carbon-based gas phase molecules. By signal averaging, detection of isotopologues in natural abundance requires no additional searching for these transitions in the measurement process, nor does it necessitate the synthesis of additional molecular samples. Though weaker in intensity, the improved predictions for isotopic rotational constants significantly expedite the assignment process of low intensity transitions and hence the additional transitions are efficiently identified in a single broadband spectrum. Acknowledgements The authors would like to thank David Plusquellic for discussions regarding methyl rotor analysis in JB95 and for providing the program that was used to calculate barrier heights, rotor angles, and rigid rotor constants. We are also indebted to Isabelle Kleiner for helpful comments on the topic of internal rotation. This material was supported by the Dr. Henry and Camille Dreyfus Foundation New Faculty Award and Purdue University. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2011.04.001.
4. Conclusion The microwave spectrum of methyl vinyl ketone was measured using a CP-FTMW spectrometer. In addition to the previously observed ap-MVK conformer, a second conformer, sp-MVK, was assigned. A torsional analysis in JB95 gave V3 barriers of 433(4) and 375(5) cm1 for ap- and sp-MVK, respectively, with the former barrier including previously measured high frequency transitions. The internal rotor program XIAM was used to determine more precise barriers of 433.8(1) and 376.6(2) cm1 for ap- and sp-MVK, respectively. The observed differences in precision were found to be a reflection of the models used to interpret the data rather than the resolution of the measurements. The high signal-to-noise of the CP-FTMW spectrometer resolved MVK isotopologues in natural abundance. Kraitchman analysis determined the molecular structure using approximate rigid rotor rotational constants. Ab initio calculations were also completed that resulted in several discrepancies with the experimental data concerning relative energies, barrier heights, and structural parameters, particularly for the ap conformer.
References [1] E.C. Tuazon, R. Atkinson, Int. J. Chem. Kinet. 22 (1990) 1221. [2] R.M. Kamens, M.W. Gery, H.E. Jeffries, M. Jackson, E.I. Cole, Int. J. Chem. Kinet. 14 (1982) 955. [3] D. Pierotti, S.C. Wofsy, D. Jacob, J. Geophys. Res. 95 (1990) 1871. [4] E.C. Tuazon, R. Atkinson, Int. J. Chem. Kinet. 21 (1989) 1141. [5] P.D. Foster, V.M. Rao, R.F. Curl Jr., J. Chem. Phys. 43 (1965) 1064. [6] A.C. Fantoni, W. Caminati, R. Meyer, Chem. Phys. Lett. 133 (1987) 27. [7] A.J. Bowles, W.O. George, W.F. Maddams, J. Chem. Soc. B (1969) 810. [8] J.I. García, J.A. Mayoral, L. Slavatella, X. Assfeld, M.F. Ruiz-López, J. Mol. Struct. 362 (1996) 187. [9] A.J. Shirar, D.S. Wilcox, K.M. Hotopp, G.L. Storck, I. Kleiner, B.C. Dian, J. Phys. Chem. A 114 (2010) 12187. [10] D.F. Plusquellic, R.D. Suenram, B. Maté, J.O. Jensen, A.C. Samuels, J. Chem. Phys. 115 (2001) 3057. [11] D. Herschbach, J. Chem. Phys. 31 (1959) 91. [12] I. Kleiner, J. Mol. Spec. 260 (2010) 1. [13] J.R. Durig, T.S. Little, J. Chem. Phys. 75 (1981) 3660. [14] R. Lavrich, D. Plusquellic, R. Suenram, G. Fraser, A. Walker, M. Tubergen, J. Chem. Phys. 118 (2003) 1253. [15] H. Hartwig, H. Dreizler, Z. Naturforsch 51a (1996) 923. [16] J. Gillies, C. Gillies, J.-U. Grabow, H. Hartwig, E. Block, J. Phys. Chem. 100 (1996) 18708.
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[17] Assigned rotational transitions and calculated vibrational frequencies for apand sp-MVK are given in the Supplemental Information. [18] M.J. Frisch et al., Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004. [19] K.S. Pitzer, J. Chem. Phys. 14 (1946) 239. [20] J. Kraitchman, Am. J. Phys. 21 (1953).
[21] [22] [23] [24] [25]
J. Demaison, L. Margulès, I. Kleiner, A. Császár, J. Mol. Spec. 259 (2010) 70. M. Harmony et al., J. Phys. Chem. Ref. Data 8 (1979) 619. C.C. Costain, J. Chem. Phys. 29 (1958) 864. C.C. Costain, Trans. Am. Crystallogr. Assoc. 2 (1966) 157. K. Wiedenmann, I. Botskor, H. Rudolph, J. Mol. Spec. 113 (1985) 186.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Additional conformer observed in the microwave spectrum of methyl vinyl ketone David S. Wilcox, Amanda J. Shirar, Owen L. Williams, Brian C. Dian ⇑ Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, IN 47907-2084, USA
a r t i c l e
i n f o
Article history: Received 3 December 2010 In final form 1 April 2011 Available online 3 April 2011
a b s t r a c t A chirped-pulse Fourier transform microwave spectrometer was used to record the rotational spectrum of methyl vinyl ketone (MVK, 3-butene-2-one). Two stable conformations were identified: the previously documented antiperiplanar (ap) conformer and synperiplanar (sp), which is reported for the first time in this microwave study. Methyl torsional analysis resulted in V3 barrier heights of 433.8(1) and 376.6(2) cm1 for ap- and sp-MVK, respectively. Heavy atom isotopic species of both conformers were detected in natural abundance allowing bond lengths and angles of the molecular frames to be calculated through Kraitchman analysis. A comparison with ab initio calculations is included. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The simplest a,b-unsaturated ketone, methyl vinyl ketone (MVK, 3-buten-2-one), is important in atmospheric chemistry as a primary product of isoprene oxidation. Early laboratory studies discovered significant yields of MVK from the reaction of isoprene with the hydroxyl radical [1] or ozone [2]. MVK was later identified in the atmosphere at concentrations strongly correlated with biogenic isoprene [3]. MVK reacts quickly with the hydroxyl radical to generate other carbonyls including methylglyoxal and formaldehyde that contribute to the additional destruction of ozone [4]. Accurately determining the structure of MVK will improve analyses of its chemistry in the atmosphere. The microwave spectrum of MVK was first measured in 1965 by Foster et al. in the region of 7–33 GHz [5]. MVK was identified in the antiperiplanar configuration (ap, Figure 1) and A–E frequency doublets were observed arising from hindered internal rotation of the methyl group. The authors were able to determine a V3 value of 437(7) cm1 for the barrier to internal rotation from this splitting. The microwave spectrum was revisited at higher frequencies (26.4–40 GHz) in 1987 where rotational transitions were determined from the ground and first excited torsional states of apMVK. A slightly smaller V3 value of 424(7) cm1 was reported for internal methyl rotation [6]. No evidence for an additional conformation was reported in either study. Infrared studies, however, have confirmed a second stable conformation, synperiplanar (sp, Figure 1), in the liquid and gas phases [7]. From the measured enthalpies, sp-MVK was found to be 2.36 kJ/mol higher in energy than ap-MVK. Ab initio calculations have predicted similar energies (0.12–2.36 kJ/mol) depending on
⇑ Corresponding author. Fax: +1 765 494 0329. E-mail addresses: [email protected] (D.S. Wilcox), [email protected] (A.J. Shirar), [email protected] (O.L. Williams), [email protected] (B.C. Dian). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.04.001
the level of theory used [7,8]. This small energy difference suggests that the sp conformer could be detected in the MVK rotational spectrum with a chirped-pulse Fourier transform microwave (CPFTMW) spectrometer. Here we present the rotational spectrum of both the ap- and sp-MVK conformers, as well as assignments for the isotopic species (heavy atoms only) in natural abundance.
2. Experimental The CP-FTMW spectrometer has previously been described in detail [9] and will only be summarized here. Methyl vinyl ketone was obtained from Sigma–Aldrich (99% pure) and used without further purification. Approximately 1 mL of sample was introduced into a tank using a freeze–pump-thaw method and balanced to approximately 7 bar with a 30/70% He/Ne mixture. An arbitrary waveform generator with a 10 GS/s sampling rate (Tektronix AWG 7101) produced a 1 ls microwave chirped pulse (1.875– 4.625 GHz). The pulse was then quadrupled (Phase One) and the power increased with a 200 W amplifier (Amplifier Research) to create an 11 GHz bandwidth pulse (7.5–18.5 GHz). This polarizing pulse was then broadcast with a microwave horn into a vacuum chamber with a typical base pressure of 1 106 Torr. The sample was introduced into the chamber with a Series 9 General Valve (2 mm orifice) at a backing pressure of 1 bar resulting in a supersonic expansion that cooled the molecules to an estimated rotational temperature of 4 K. The microwave pulse induced a macroscopic polarization and the resulting free inductive decay was collected with a second microwave horn. The molecular signal passed through a PIN diode limiter (Advanced Control Components) and a switch (single pole single throw, Advanced Technical Materials) before entering a low noise amplifier (+45 dB gain, Miteq). The molecular signal was then mixed with an 18.9 GHz phase locked dielectric resonator oscillator (Microwave Dynamics) and the lower sideband was isolated and digitized at 40 GS/s for
11
D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
X
r ¼1
g¼a;b
qg ¼ kg
Figure 1. The two conformers of methyl vinyl ketone (MVK) designated as antiperiplanar (ap) and synperiplanar (sp).
20 ls with a 12 GHz oscilloscope (Tektronix TDS6124C). In order to signal average, the entire system was synchronized with a 100 MHz phase locked loop (Wenzel Associates) driven by a 10 MHz Rb-disciplined crystal oscillator (Stanford Research Systems) and the timing was controlled with a 20-output Masterclock (Thales Laser). A Kaiser-Bessel digital filter was applied to the time domain signal to suppress side lobes of the rotational transitions in the frequency domain. The Fourier transform of the free induction decay yielded a nominally 11 GHz bandwidth frequency spectrum with 20 kHz resolution. The resolution was interpolated to 5 kHz offline in the spectral fitting program JB95 [10]. A signal-to-noise ratio of 10000:1 on the strongest transition was achieved with 100 000 time domain averages. The ground state microwave spectrum and background spectrum (to remove spurious microwave resonances) were recorded in a combined 15 h.
ð1Þ
where ð2Þ
AA ¼ ARR þ FW 00 q2a ð2Þ
BA ¼ BRR þ FW 00 q2b
ð2Þ
C A ¼ C RR ; and Hcd describes 4th order distortion. In the preceding equation, ð2Þ W 00 is the second order perturbation coefficient of the A-state in the ground torsional level. ARR, etc. are the unperturbed rigid rotor constants in the absence of internal rotation. F and qg (g = a, b) are functions of the methyl rotor inertial moment, I/ ; the direction cosines of the top with respect to the principal axis, kg ; and the principal moments of inertia Ig : 2
F¼
h FR ¼ 2rI/ r
ð3Þ
ð4Þ
I/ : Ig
ð5Þ
^2 ^2 ^2 Heff E ¼ AE P a þ BE P b þ C E P c þ
X
Dg P^g þ Hcd
ð6Þ
g¼a;b
with the operator constants ð2Þ
AE ¼ ARR þ FW 01 q2a BE ¼ BRR þ
ð2Þ FW 01
q2b
ð7Þ
C E ¼ C RR ð1Þ
Dg ¼ FW 01 qg : ð1Þ W 01
ð8Þ
ð2Þ W 01
and are the 1st and 2nd order perturbation coefficients, respectively, for the ground torsional level of the E-state. The A- and E-state perturbation coefficients are tabulated elsewhere [11] as a function of the reduced barrier parameter, s, which is in turn related to V3 by
s¼
^2 ^2 ^2 Heff A ¼ AA P a þ BA P b þ C A P c þ H cd ;
I/ Ig
The (a b) plane of symmetry in both conformers simplifies terms in the Hamiltonians since the c-principal axis is normal to the methyl rotor axis (kc = 0). qc is therefore zero, indicating C RR is unperturbed by internal rotation. The E-state effective Hamiltonian includes linear operators that describe the angular momentum of methyl hydrogen tunneling [14],
3. Results and discussion An effective Hamiltonian describing the torsion-rotation interaction for each A- and E-state symmetry species is implemented in the spectral fitting program JB95 [10]. The fitting parameters in the least squares procedure are based on the perturbative torsion-rotation Hamiltonian. For high V3 barriers to internal rotation, the torsion-rotation cross terms are treated as perturbations. The Hamiltonian is factored through successive Van Vleck transformations into submatrices describing A- and E-internal rotation states separately for each torsional level [11]. In the principal axis frame, this method is straightforward and suitable for molecules in torsional states near the bottom of the potential well with V3 barriers greater than approximately 100 cm1 [12]. Published microwave [5,6] and IR/Raman [13] data have reported V3 barrier heights between 420–437 cm1 for ap-MVK. Furthermore, all recorded lines originated from the ground torsional state (vt = 0 for both symmetry species) under the experimental conditions in this lab. The effective Hamiltonian used to fit the A-states is of the form [14]
k2g
4 V3 : 9 F
ð9Þ
The V3 barrier is thus obtained by determining s from the perturbation coefficients and fixing FR to the appropriate value (I/ is assumed 3.18 lÅ2 from Ref. [11]). Perturbation coefficients, rigid rotor constants, and direction cosines are obtained iteratively from the best-fit parameters of the A- and E-state effective Hamiltonians in a method described by Lavrich et al. [14]. This procedure, generalized for the case of multiple internal rotors, is implemented in a program integrated with the JB95 GUI. An additional torsional analysis was performed with the internal rotor program XIAM [15]. The precision of the V3 barrier becomes harder to determine in the principal axis frame (PAF) as the barrier increases and the torsion-rotation cross terms rapidly decrease to zero. Improved internal rotation parameters such as kg and V3 may be obtained in a number of methods employing Rho-axis frame (RAF) Hamiltonians [12]. A new coordinate axis system is defined in the RAF that is related to the PAF by a rotation of the z-axis parallel to the q vector. The contributions of qx and qy are eliminated from the q vector (qx ¼ qy ¼ 0) in the RAF, permitting the separation of the Hamiltonian into purely torsional and rotational components. In XIAM, the pseudorigid rotor Hamiltonian, HPAF rot ; is expressed in the PAF
^2 ^2 ^2 HPAF rot ¼ AP a þ BP b þ C P c þ H cd :
ð10Þ
Global rotational parameters A, B, C, and Hcd differ from those of Eqs. (1) and (6) in that they simultaneously describe A- and E-state transitions. The torsional Hamiltonian in the RAF contains internal rotation terms that may be directly varied in the fitting procedure:
^ 2 1 ^ HRAF tor ¼ Fðp/ þ qP z Þ þ V 3 ð1 cosð3/ÞÞ: 2
ð11Þ
^/ is the conjugate Here, / is the internal rotation angle and p momentum operator. The final rotational parameters are expressed in the PAF by transforming Eq. (11) back into the PAF and adding the contributions to the rotational constants of Eq. (10) [16].
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D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
The microwave spectrum of methyl vinyl ketone in the region of 6–18.9 GHz is presented in Figure 2. Using the reported rotational constants of Fantoni et al. [6], the A-state lines of ap-MVK were identified in our spectrum and the corresponding E-state transi-
Figure 2. The microwave spectrum of methyl vinyl ketone (MVK). The inset demonstrates the signal-to-noise achieved with the CP-FTMW spectrometer. The dashed line in the inset indicates the average peak height of isotopic species measured in natural abundance for ap-MVK.
tions were fit to the operator constants of Eq. (6) in JB95. Several new lines were included in the fit of the A- and E-states of apMVK, refining the assignments of Foster et al. [5] at higher resolution. Quartic distortion terms were required in both effective Hamiltonians to reduce the root-mean-square error. Improved values of all fitted parameters were obtained by including the previously measured high frequency transitions (19–40 GHz) with their appropriate experimental weights into the analysis. The quantum number assignments from JB95 were used as input for a global analysis in XIAM. The fit parameters from JB95 and XIAM are reported in Tables 1 and 2, respectively [17]. Though no preceding microwave studies have identified a second MVK conformer, experimental IR data has provided evidence for a stable conformation of MVK (synperiplanar of Figure 1) that is 2.36 kJ/mol higher in energy than ap-MVK. Ab initio calculations were performed to estimate conformational energies using the Gaussian suite [18] and are reported in Table 3. Zero-point corrected energies predicted sp-MVK to be the most stable conformer by 0.44 and 0.07 kJ/mol, respectively, at the Hartree–Fock (HF/6311++G(d,p)) and density functional (B3LYP/6-311++G(d,p)) levels of theory in contradiction with experimental results [7]. Secondorder Møller–Plesset perturbation theory (MP2/6-311++G(d,p)) calculations verified the experimental data with ap-MVK as the lower energy conformer by 1.16 kJ/mol. Calculated vibrational mode frequencies of each optimized geometry were positive, indicating that each conformer was a minimum energy structure [17]. Regardless of the computational accuracy, both theory and IR data offer strong evidence that the sp conformer should be observed in the MVK microwave spectrum. After assigning all possible lines to ap-MVK, unassigned doublets up to three orders of magnitude above the noise floor were
Table 1 List of JB95a parameters used to fit the methyl vinyl ketone conformers. ap-MVKb
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) Db (MHz) DI (lÅ2)d
j ne
r (kHz)f s ð1Þ
W 01
d e f g h
A
E
A
E
8941.590(1) 4274.5443(6) 2945.3315(6) 8.1(1) 10–4 4.6(1) 103 5.4(7) 104 2.95(9) 104 2.6(1) 103
8941.525(1) 4274.1989(6) 2945.3364(6) 8.1(2) 104 4.56(9) 103 9.1(6) 104 2.62(9) 104 2.6(1) 103 3.107(1) 7.1(4) 3.17 0.56 29 7.08
8941.597(1) 4274.5458(4) 2945.3346(4) 8.77(8) 104 4.48(3) 103 8.5(4) 104 2.67(3) 104 2.99(5) 103
8941.528(1) 4274.1992(4) 2945.3384(5) 8.22(8) 104 4.57(3) 103 1.03(4) 103 2.53(3) 104 2.67(5) 103 3.109(1) 7.3(2) 3.17 0.56 66 123.94
10240.938(2) 3991.6351(7) 2925.648(1) 7.2(2) 104 2.2(2) 103 1.232(6) 102 1.8(1) 104 3.7(3) 103
10237.429(6) 3991.464(1) 2925.655(1) 9.1(6) 104 2.4(4) 103 4(2) 103 1.7(3) 104 3.3(6) 103 33.570(9) 9.6(9) 3.24 0.71 18 8.00
3.16 0.56 26 5.99
3.16 0.56 85 113.92
35.48702 0.001654
35.32942 0.001693
3.22 0.71 20 5.04 29.86706 0.003859
0.002000
0.002046
0.004661
0.001000
0.001023
0.002330
0.028731 5.453 8941.546(1) 4274.3149(6) 2945.3334(6) 78(1) 435(6)
0.028654 5.453 8941.552(1) 4274.3144(4) 2945.3365(5) 78.5(7) 433(4)
0.054057 5.583 10238.657(4) 3991.507(9) 2925.652(1) 36(5) 375(5)
F (cm1)h ARR (MHz) BRR (MHz) CRR (MHz) hA (°) V3 (cm1)
c
E
ð2Þ
qg
a
sp-MVK
A
ð2Þ
W 00
W 01
b
ap-MVK combinedc
Ref. [10]. Parameters obtained with transitions in our spectral bandwidth (6–18.9 GHz). Includes transitions of Refs. [5] and [6] (6–40 GHz). Inertial defect, DI = Ic Ib Ia. Number of transitions in the fit. Observed minus calculated root-mean-square deviation of the fit. Modulus of the q-vector (unitless). FR fixed to 5.3 cm1.
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D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16 Table 2 List of XIAMa parameters used in the global fit of the methyl vinyl ketone conformers.
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) DI (lÅ2)c
j nd
r (kHz)e s
qf F (cm-1) FR (cm-1) hA (°) hRAM (°)h V3 (cm-1) a b c d e f g h
ap-MVKb
sp-MVK
8941.547(1) 4274.3593(9) 2945.2903(9) 8.3(2) 10–4 4.45(6) 10–3 6.2(9) 10–4 2.47(5) 10–4 2.95(9) 10–3 3.17 0.56 150 101.47 35.35527 0.028736 5.453 5.300g 78.21(2) 66.41 433.8(1)
10238.610(1) 3991.6814(6) 2925.4885(1) 7.3(2) 10–4 1.9(2) 10–3 9.98(7) 10–3 1.8(1) 10–4 3.2(3) 10–3 3.22 0.71 38 5.38 30.31290 0.058276 5.523 5.214(3) 29.71(3) 12.54 376.6(2)
Ref. [15]. Includes transitions of Refs. [5] and [6] (6–40 GHz). Inertial defect, DI = Ic Ib Ia. Number of transitions in the fit. Observed minus calculated root-mean-square deviation of the fit. Modulus of the q-vector (unitless). Fixed. Angle of Rho-axis transformation.
attributed to sp-MVK. Based on the A–E splitting of each doublet, the V3 barrier was expected to be similar but slightly lower than that of ap-MVK. This was anticipated since steric hindrance to internal rotation is increased when the methyl and methylene groups are in close proximity as in the ap conformation. A relaxed potential energy scan (RPES) about the methyl torsional coordinate at the HF level of theory (6-311++G(d,p)) predicted V3 values of 375 and 398 cm1 for sp- and ap-MVK, respectively. DFT (B3LYP/6311++G(d,p)) underestimated the barrier of the known ap conformer by nearly 50% and predicted ap-MVK to be the higher barrier configuration (Table 3). Using the HF results, initial rotational constants for the A- and E-internal rotation species of sp-MVK were generated from Eqs. (2) and (7). The optimized geometry of spMVK was used to predict the unperturbed rigid rotor rotational
constants as well as F and q in a method described by Pitzer [19]. The reduced barrier parameter, s, was determined from F and V3 (Eq. (9)), and perturbation coefficients were estimated from Herschbach’s tables [11]. By simulating the spectrum with the perturbed rotational constants, ambiguity in the relative frequency order of the A–E symmetry doublets was eliminated in the early stages of the fit. The fit parameters of sp-MVK from JB95 and XIAM are also reported in Tables 1 and 2, respectively [17]. The internal rotation analysis in JB95 gave a V3 barrier height of 435(6) cm1 for ap-MVK with our data set, and 433(4) cm1 when high frequency transitions from Refs. [5,6] were included in the fit. The most precise V3 barrier height, 433.8(1) cm1, was obtained with the combined data in XIAM by fixing FR to 5.3 cm1 and floating V3 and the angle between the top axis and a-principal axis, ha. A direct comparison with previously reported results (Table 3) is not straightforward, since the assumptions regarding the reduced moment, F, are different in all three models. The V3 barrier of 424(7) cm1 reported by Fantoni et al. was obtained by fixing the reduced moment, F [6]. In this study, only I/ was fixed, allowing the structural variables of F to be varied in the fit. Similar assumptions were made by Foster et al. who obtained a more directly comparable V3 barrier of 437(7) cm1 with a slightly smaller fixed value of I/ (3.164 lÅ2) [5]. The V3 barrier height of sp-MVK was determined to be 375(5) cm1 in JB95. Including 4th order corrections into the effective Hamiltonians to account for the lower barrier did not improve the precision of V3. It is anticipated that incorporating data from higher J transitions is necessary to reduce the uncertainty with this method. A value of 376.6(2) cm1 was obtained with XIAM by floating the internal rotation parameters FR, ha, and V3. In contrast to ap-MVK, the quality of the fit increased 5-fold by varying FR. The variables FR and V3 are highly correlated, particularly in high barrier cases. It is suspected that due to the lower barrier of spMVK, more information is carried in the FR parameter and thus it was necessary to vary it in the fit. Tables 1–3 summarize internal rotation parameters from this study, calculations, and literature. The high signal-to-noise in the MVK rotational spectrum made it possible to resolve isotopic species in natural abundance, particularly carbon-13 substituted isotopes (1.1% natural abundance). The unperturbed rigid rotor constants of the isotopologues were calculated with the same computational accuracy as the unsubstituted parent species, and rotational constants for the A- and Einternal rotation species were predicted with Eqs. (2) and (7)
Table 3 Comparison of rotational data, dipole moment, and relative energies for experimental, ab initio calculated, and published values for both conformers of methyl vinyl ketone. ap-MVK
sp-MVK
Calculateda b
A (MHz) B (MHz) C (MHz) DI (lÅ2)d V3 (cm1) hA (°) F (cm1) la (D) lb (D) lc (D) DE (kJ/mol) DEZPEf (kJ/mol) a b c d e f
c
HF
DFT
9056.92 4311.38 2974.36 3.11 397.5 80.72 5.53 2.82 2.30 0.00 0 0.44
8934.27 4258.51 2936.50 3.14 258.7 81.63 5.46 2.74 2.07 0.00 0 0.07
Ref. [18]. 6-311++G(d,p) basis set. B3LYP/6-311++G(d,p) basis set. Inertial defect, DI = Ic Ib Ia. l2 (D2). Zero-point corrected energies.
Calculateda
Published b
b
Published c
b
MP2
Ref. [5]
Ref. [6]
HF
DFT
MP2
8912.33 4262.47 2936.26 3.15
8941.45(6) 4274.48(2) 2945.32(2) 3.17 437(7) 75(4) 5.50 6.39(14)e 3.64(16)e
8941.58(1) 4274.494(5) 2945.276(4) 3.16 424(7) 75.46(5) 5.38
10481.39 4012.61 2954.22 3.09 375.2 32.78 5.66 0.60 3.01 0.00 0.04 0
10229.70 3979.18 2916.42 3.12 290.3 32.71 5.59 0.57 2.88 0.00 0.59 0
10141.03 3982.27 2911.12 3.14
83.22 5.42 3.13 2.35 0.00 0 0
32.72 5.56 0.66 3.19 0.00 2.00 1.16
Ref. [7]
2.36
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D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16
Table 4 Isotopic assignments for methyl vinyl ketone. ap-MVK
H313CAC(O)ACH@CH2 13C1
A (MHz) B (MHz) C (MHz) DJ (MHz) DJK(MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) DI (lÅ2)
j n
r (kHz)
H3CA13C(O)ACH@CH2 13C2
H3CAC(O)A13CH@CH2 13C3
H3CAC(O)ACH@13CH2 13C4
H3CAC(18O)ACH@CH2 180
A
E
A
E
A
E
A
E
A
E
8645.609(8) 4255.802(3) 2903.729(2) 6(2) 104 5.4(3) 103 2(2) 103 1.7(4) 104
8645.569(8) 4255.467(3) 2903.731(2) 6(2) 104 5.4(6) 103 4(1) 103 2.4(4) 104
8941.059(4) 4265.567(2) 2941.013(2) 8(1) 104 3.7(4) 103
8878.795(2) 4247.300(2) 2925.623(2) 6(1) 104 6.4(2) 103
8939.992(4) 4137.874(3) 2879.631 (3) 9(2) 104 5.8(3) 103
8939.930(4) 4137.556(3) 2879.627(2) 7(2) 104 5.8(3) 103
8728.645(9) 4129.793(3) 2853.487(3) 3.8(2) 103 2.1(1) 102
N/A N/A N/A
1.8(3) 104
8878.739(6) 4246.962(2) 2925.621(2) 4(2) 104 5.4(2) 103 5(1) 103 2.7(4) 104
1.9(5) 104
3.1(5) 104
3.16 0.53 15 6.671
3.21(8) 3.17 0.53 16 7.277
3.16 0.56 15 3.76
8941.017(7) 4265.219(3) 2941.014(3) 4(2) 104 4.5(7) 103 5(1) 103 3.2(4) 104 1.3(7) 103 3.09(7) 3.17 0.56 16 5.838
3.17 0.56 16 4.927
3.17(5) 3.18 0.56 17 5.968
3.16 0.58 15 8.196
3.01(7) 3.17 0.58 15 6.751
3.16 0.57 10 7.736
10240.006(5) 3985.490(2) 2922.289(2) 2.7(9) 104 4.8(2) 103 5.2(2) 103
10236.587(6) 3985.300(2) 2922.295(2) 5(1) 104 5.2(5) 103 6.0(2) 102
10236.318(5) 3869.542(2) 2859.530(2)
N/A N/A N/A
3.22 0.71 10 4.696
34.11(3) 3.24 0.71 11 4.614
2.1(2) 104 4.0(4) 103
sp-MVK A (MHz) B (MHz) C (MHz) DJ (MHz) DJK (MHz) DK (MHz) dJ (MHz) dK (MHz) Da (MHz) DI (lÅ2)
j n
r (kHz)
10140.193(3) 3899.994(3) 2868.105(2) 4(1) 104 3.8(2) 103 1.12(9) 102 1.6(3) 104
10136.738(3) 3899.832(1) 2868.102(1) 1.0(3)x103 3.3(1) 102 2.0(3) 104
3.22 0.72 12 3.541
33.71(1) 3.24 0.72 13 3.833
10145.439(5) 3970.554(5) 2906.569(3) 5(3) 104 3.6(4) 103 1.0(2) 102 2.2(6) 104
3.22 0.71 12 6.509
assuming the same barrier parameters as the parent conformers. The perturbed rotational constants were then scaled by the difference between the calculated and experimental values of the parent species, increasing the accuracy of the isotopically substituted predictions by 1–2 orders of magnitude. The a- and b-type lines of the 13 C isotopes of ap-MVK were appreciable in intensity (Table 3) resulting in 15–17 line assignments per internal rotor state. Owing to the large signal of the parent species, 10 A-state lines of 18O substituted ap-MVK were also detected. While there were several suspected E-state transitions, a reliable set of parameters was not obtained. The sp-MVK rotational spectrum, in contrast, consists primarily of a b-type transition moment (Table 3). Consequently, the low intensity a-type lines of the sp-MVK 13C isotopologues were difficult to detect; only 10–13 lines were assigned per internal rotor state. We were unable to assign 18O substituted transitions due to the lower signal intensity of the parent species and the relative abundance of this isotope (0.2% natural abundance). The quantum number assignments of the A–E symmetry doublets were confirmed by noting the similar magnitude of doublet splitting with respect to the parent conformer. In general, it was only possible to float combinations of several distortion constants in the fits of the isotopologues. Rotational constants and 4th order distortion terms resulting in the lowest residual error are given in Table 4. With heavy atom substitution data, structural information on the frame of ap-MVK and carbon backbone of sp-MVK was acquired through Kraitchman analysis [20]. Vibrational contributions from the methyl torsion contaminate both A- and E-state effective rotational constants. In order to obtain the most accurate substitution structures (rs), these effects may be removed by calculating the unperturbed rigid rotor constants from Eqs. (2) and (7) in the iterative process of Lavrich et al. [14]. Since the Db cross-terms were not well-determined due to the low J transitions in the fits of the isotopically substituted species, an approximate expression for the rigid rotor constants was used instead [21]:
10142.05(2) 3970.25(3) 2906.58(3) 4.0(6) 103 3.7(7) 102 7(1) 102 2(1) 104 5(1) 102 31.97(5) 3.25 0.71 12 8.815
Aapprox ¼ RR
10239.778(6) 3869.713(4) 2859.546(3) 8(3) 104 4.5(7) 103 9(3) 103
3.22 0.73 11 7.605
1 ðAA þ 2AE Þ: 3
N/A N/A N/A
2.7(1) 102 3.1(5) 104 33.64(4) 3.24 0.73 11 5.494
ð12Þ
A similar relation holds for Bapprox . To account for small differRR ences on the order of 1 kHz between C A and C E , the average was taken to calculate C RR . Eq. (12) is an approximation which neglects denominator corrections accounting for the small differences in the rotational energy levels after Van Vleck transformations. However, a systematic analysis on the equilibrium structure of cismethyl formate (V3 = 372.67 cm1) found that inclusion of denominator corrections induced a negligible effect on the value of the unperturbed rigid rotor constants [21]. The errors of the rs structures in Table 5 are propagated from the rigid rotor constants, although the calculated precision is greater than the zero-point fluctuations of the molecule. Small changes in the pseudoinertial defect (the difference between the equilibrium and effective principal moments estimating the vibration– rotation contribution to rs) upon isotopic substitution lead to systematic errors in the rs coordinates [22]. Corrections with Costain’s method lead to more physically meaningful uncertainties that are comparable with calculated equilibrium structures [23,24]. The adjusted error in Table 5 is given by das /Å = 0.0015/|as|, where as is the Kraitchman coordinate. The larger Costain errors observed in the substitution structures involving the C2 and C4 atoms of both conformers are a consequence of the close proximity of the atoms to the a-principal axis (0.06–0.1 Å) [23]. Costain’s results give errors less than 0.01 Å when coordinates are greater than 0.15 Å from the principal axis; it may be possible to reduce this uncertainty by double-isotopic substitution [25]. Calculated and observed bond lengths and angles generally concurred at all levels of theory in this study with the differences between calculated and experimental values being attributed to the modest basis sets used (Table 5). Without E-state rotational constants for the 18O substituted ap conformer, rigid rotor constants could not be determined. Because of the barrier height, rota-
15
D.S. Wilcox et al. / Chemical Physics Letters 508 (2011) 10–16 Table 5 Comparison of the molecular structure according to ab initio predictions and Kraitchmana analysis. ap-MVK Ab initio HF rC1C2 rC2C3 rC3C4 rC2O \C1C2O \C1C2C3 \OC2C3 \C2C3C4 a b c d e f
c
1.512 1.494 1.321 1.191 121.27 119.57 119.16 125.27
sp-MVK b
Ab initiob
Kraitchman DFT
d
1.517 1.489 1.335 1.218 121.20 119.48 119.32 125.40
MP2
c
1.516 1.489 1.345 1.225 121.64 118.92 119.45 124.58
rs
e
1.4774(2) 1.49249(8) 1.33945(4) 1.2411(1) 122.56(2) 121.21(2) 116.23(1) 123.32(1)
Kraitchman
Costain
HFc
DFTd
MP2c
rs e
Costainf
1.48(2) 1.492(8) 1.340(6) 1.24(1) 123(2) 121(2) 116(1) 123(1)
1.510 1.498 1.321 1.190 122.02 116.07 121.91 121.66
1.514 1.497 1.333 1.215 121.92 116.12 121.96 121.81
1.513 1.499 1.343 1.222 122.31 115.80 121.90 121.32
1.5037(1) 1.4751(3) 1.3334(2)
1.504(9) 1.475(9) 1.333(7)
117.94(2)
118(1)
121.96(3)
122(1)
f
Ref. [20]. Ref. [18]. 6-311++G(d,p) basis set. B3LYP/6-311++G(d,p) basis set. Error of substitution structure propagated from rotational constants. Errors corrected with Costain’s method (Refs. [22] and [24]).
tional constants for the A-internal rotation species are expected to be within 0.1% of the rigid rotor values. For these reasons, 18O substituted coordinates were included in the Kraitchman analysis and are in reasonable agreement with theory. One notable disagreement between calculated and experimental values is in the rC1C2 methyl rotor axis bond of ap-MVK. At all levels of theory, the predicted rC1C2 bond length is typical for a carbon–carbon single bond. Within Costain’s error, the experimental bond length is shorter by nearly 2 pm. Ab initio calculations less accurately predicted the V3 barrier associated with the RPES about this bond, suggesting the deviations from experimental values are correlated. It has been suggested that a non-planar species of MVK exists [7], but a RPES conducted about the C2-C3 bond did not reveal any additional minima. Though low in intensity, approximately 550 lines were unassigned in the spectrum with many appearing to be A-E symmetry doublets. We attempted to find vibrationally excited satellite states corresponding to skeletal and methyl torsional motion using the rotational constants of Fantoni et al. [6]. No such lines were found. Efficient vibrational cooling in the supersonic jet diminishes population in these low energy modes and accordingly we do not generally observe vibrational satellites with our spectrometer. From the suspected torsional splitting of the unidentified peaks, dimerization or other clusters with the backing gas in the supersonic jet may account for the remaining lines in the spectrum.
On a final note, the high resolution, high signal-to-noise, and broad bandwidth of the CP-FTMW spectrometer makes it an ideal apparatus for obtaining substitution structures of carbon-based gas phase molecules. By signal averaging, detection of isotopologues in natural abundance requires no additional searching for these transitions in the measurement process, nor does it necessitate the synthesis of additional molecular samples. Though weaker in intensity, the improved predictions for isotopic rotational constants significantly expedite the assignment process of low intensity transitions and hence the additional transitions are efficiently identified in a single broadband spectrum. Acknowledgements The authors would like to thank David Plusquellic for discussions regarding methyl rotor analysis in JB95 and for providing the program that was used to calculate barrier heights, rotor angles, and rigid rotor constants. We are also indebted to Isabelle Kleiner for helpful comments on the topic of internal rotation. This material was supported by the Dr. Henry and Camille Dreyfus Foundation New Faculty Award and Purdue University. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2011.04.001.
4. Conclusion The microwave spectrum of methyl vinyl ketone was measured using a CP-FTMW spectrometer. In addition to the previously observed ap-MVK conformer, a second conformer, sp-MVK, was assigned. A torsional analysis in JB95 gave V3 barriers of 433(4) and 375(5) cm1 for ap- and sp-MVK, respectively, with the former barrier including previously measured high frequency transitions. The internal rotor program XIAM was used to determine more precise barriers of 433.8(1) and 376.6(2) cm1 for ap- and sp-MVK, respectively. The observed differences in precision were found to be a reflection of the models used to interpret the data rather than the resolution of the measurements. The high signal-to-noise of the CP-FTMW spectrometer resolved MVK isotopologues in natural abundance. Kraitchman analysis determined the molecular structure using approximate rigid rotor rotational constants. Ab initio calculations were also completed that resulted in several discrepancies with the experimental data concerning relative energies, barrier heights, and structural parameters, particularly for the ap conformer.
References [1] E.C. Tuazon, R. Atkinson, Int. J. Chem. Kinet. 22 (1990) 1221. [2] R.M. Kamens, M.W. Gery, H.E. Jeffries, M. Jackson, E.I. Cole, Int. J. Chem. Kinet. 14 (1982) 955. [3] D. Pierotti, S.C. Wofsy, D. Jacob, J. Geophys. Res. 95 (1990) 1871. [4] E.C. Tuazon, R. Atkinson, Int. J. Chem. Kinet. 21 (1989) 1141. [5] P.D. Foster, V.M. Rao, R.F. Curl Jr., J. Chem. Phys. 43 (1965) 1064. [6] A.C. Fantoni, W. Caminati, R. Meyer, Chem. Phys. Lett. 133 (1987) 27. [7] A.J. Bowles, W.O. George, W.F. Maddams, J. Chem. Soc. B (1969) 810. [8] J.I. García, J.A. Mayoral, L. Slavatella, X. Assfeld, M.F. Ruiz-López, J. Mol. Struct. 362 (1996) 187. [9] A.J. Shirar, D.S. Wilcox, K.M. Hotopp, G.L. Storck, I. Kleiner, B.C. Dian, J. Phys. Chem. A 114 (2010) 12187. [10] D.F. Plusquellic, R.D. Suenram, B. Maté, J.O. Jensen, A.C. Samuels, J. Chem. Phys. 115 (2001) 3057. [11] D. Herschbach, J. Chem. Phys. 31 (1959) 91. [12] I. Kleiner, J. Mol. Spec. 260 (2010) 1. [13] J.R. Durig, T.S. Little, J. Chem. Phys. 75 (1981) 3660. [14] R. Lavrich, D. Plusquellic, R. Suenram, G. Fraser, A. Walker, M. Tubergen, J. Chem. Phys. 118 (2003) 1253. [15] H. Hartwig, H. Dreizler, Z. Naturforsch 51a (1996) 923. [16] J. Gillies, C. Gillies, J.-U. Grabow, H. Hartwig, E. Block, J. Phys. Chem. 100 (1996) 18708.
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[17] Assigned rotational transitions and calculated vibrational frequencies for apand sp-MVK are given in the Supplemental Information. [18] M.J. Frisch et al., Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004. [19] K.S. Pitzer, J. Chem. Phys. 14 (1946) 239. [20] J. Kraitchman, Am. J. Phys. 21 (1953).
[21] [22] [23] [24] [25]
J. Demaison, L. Margulès, I. Kleiner, A. Császár, J. Mol. Spec. 259 (2010) 70. M. Harmony et al., J. Phys. Chem. Ref. Data 8 (1979) 619. C.C. Costain, J. Chem. Phys. 29 (1958) 864. C.C. Costain, Trans. Am. Crystallogr. Assoc. 2 (1966) 157. K. Wiedenmann, I. Botskor, H. Rudolph, J. Mol. Spec. 113 (1985) 186.