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Gas-phase energy differences between the Z and E rotamers and the rotational barrier heights of methyl formate and trifluromethyl formate: an ab initio study
Chemical Physics Letters 373 (2003) 182–190 www.elsevier.com/locate/cplett
Gas-phase energy differences between the Z and E rotamers and the rotational barrier heights of methyl formate and trifluromethyl formate: an ab initio study Tadafumi Uchimaru
a,b,*
, Seiji Tsuzuki b, Masaaki Sugie a, Akira Sekiya
a
a
b
Research Center for Developing Fluorinated Greenhouse Gas Alternatives, National Institute of Advanced Industrial Science and Technology, Higashi, Tsukuba 305-8565, Japan Research Institute for Computational Sciences, National Institute of Advanced Industrial Science and Technology, Umezono, Tsukuba 305-8568, Japan Received 30 December 2002; in final form 21 March 2003
Abstract Ab initio energy evaluations on the Z and E rotamers, as well as on the rotational transition states connecting them, were carried out for methyl formate and trifluoromethyl formate. The estimates for the energy differences at the basis set limit suggested that the Z/E energy difference and the rotational barrier height are both significantly smaller for trifluoromethyl formate than for methyl formate. Our best estimate for the enthalpy difference at 298 K between the Z and E rotamers for methyl formate is 5.21 kcal/mol, which is slightly larger than the upper edge of uncertainty of previously reported experimental value. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Despite their simple chemical structures of methyl formate [CH3 OC(O)H; MF] and trifluoromethyl formate [CF3 OC(O)H; TFMF], the energy differences between the E and Z rotamers (see Fig. 1), and the barrier heights for interconversion between the rotamers have not been fully elucidated. For MF, detailed IR studies indicated that only the Z rotamer is present in the vicinity of room temperature [1,2]. Correspondingly, no evidence
*
Corresponding author. Fax: +81-29-861-4487. E-mail address: [email protected] (T. Uchimaru).
for the presence of the E rotamer was obtained in early studies of electron diffraction [3] and microwave spectrum [4]. From the IR intensity in the region of the torsional vibrations, Miyazawa [5] concluded that the E rotamer of MF was higher in energy by at least 2.7 kcal/mol than the Z rotamer. In the 1980s, the unstable E rotamer of MF was spectroscopically detected [6–8], and the energy difference between the Z and E rotamers of MF was experimentally derived. Ruschin and Bauer [6] employed a temperature drift technique to conclude that the E rotamer was less stable by 3.85 0.20 kcal/mol than the Z rotamer. Blom and G€ unthard [7] applied thermal molecular beam trapping to study the unstable rotamer in Ar
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00573-6
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Meanwhile, the IR spectrum of TFMF indicated the presence of not only the Z rotamer but also the E rotamer even in the room temperature region (295 2 K) [10]. This observation suggests that the Z and E rotamers of TFMF are much closer in energy than those of MF. Nevertheless, for the energy difference between the Z and E rotamers of TFMF and for the barrier height to their interconversion, no experimental values have been reported. We have carried out systematic energy evaluations for the Z and E rotamers of MF and TFMF and for the rotational transition states connecting the rotamers. In this Letter we will report ab initio estimates for the energy difference at the basis set limit between the rotamers and for the barrier heights to interconversion of the rotamers.
Fig. 1. Structures of the Z and E rotamers of methyl formate (MF; X ¼ H) and trifuoromethyl formate (TFMF; X ¼ F).
matrices to derive a value of 4.75 0.19 kcal/mol for the difference in enthalpy (DH ) between the rotamers. For interconversion of the rotamers of MF, Miyazawa [5] provided an estimate of 13.1 kcal/ mol for the potential energy barrier. Blom and G€ unthard [7] suggested that the barrier height should be 10–15 kcal/mol in the gas phase. The liquid-phase and solution-phase barrier heights have been experimentally derived through ultrasonic relaxation measurements and dynamic NMR analysis [9]. However, to the best of our knowledge, the gas-phase barrier height to Z-to-E and E-to-Z conversion of MF has not yet been experimentally determined.
2. Computational procedure The geometries of the Z and E rotamers and the rotational transition states connecting the rotamers were optimized at the QCISD level with 6-311G(d,p) basis set under frozen-core approximation. Tables 1 and 2 show the optimized
Table 1 QCISD/6-311G(d,p) optimized geometrical parameters for methyl formate (MF)a Coordinate
Z-CH3 OC(O)H c
Cformyl –H Cformyl –O C@O CH3 –O CH3 –Hb CH3 –H0 b H–Cformyl –O O@C–O O–C–O H–CH3 –H0 b H0 –CH3 –H0 b Cfomyl –O–CH3 –Hb O@Cformyl –O–CH3
d
E-CH3 OC(O)H
TS
Calc.
Expt.
Calc.
Calc.
1.099 (1.093) 1.341 (1.337) 1.201 (1.200) 1.436 (1.434) 1.090 (1.085) 1.093 (1.088) 109.0 (109.4) 125.7 (125.7) 114.2 (114.4) 110.6 (110.6) 109.1 (109.1) 60.4 (60.4) 0.0 (0.0)
1.101 0.01 1.334 0.01 1.200 0.01 1.437 0.01 1.086 0.015
1.107 1.349 1.195 1.430 1.090 1.096 113.1 123.0 114.9 109.3 109.8 61.4 180.0
1.104 1.368 1.194 1.428 1.090, 1.096, 1.099
109.18 1 125.52 1 114.47 1 110.40 1.5 – 0.0 5
112.5 124.1 112.4 109.7, 109.2, 109.6 177.4, )63.5, 58.6 91.5
for bond lengths and in degrees for bond angles. Values are given in A The Z and E rotamers both adopt Cs symmetry, while the rotational transition-state (TS) structure does not have any symmetry (C1 symmetry). H and H0 represent the hydrogen atom located on the Cs plane and those located out of the plane, respectively. c QCISD/cc-pVTZ optimized parameters are given in parentheses. d Ref. [4]. a
b
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Table 2 QCISD/6-311G(d,p) optimized geometrical parameters for trifluoromethyl formate (TFMF)a Coordinate
Z-CF3 OC(O)H
E-CF3 OC(O)H
TS
Cformyl –H Cformyl –O C@O CF3 –O CF3 –Fb CF3 –F0 b H–Cformyl –O O@C–O O–C–O F–CF3 –F0b F0 –CF3 –F0 b Cfomyl –O–CF3 –F0b O@Cformyl –O–CF3
1.096 1.381 1.189 1.376 1.323 1.326 107.0 125.9 118.1 108.9 108.9 61.2 0.0
1.098 1.388 1.185 1.363 1.316 1.335 113.3 120.5 116.1 109.2 107.4 60.0 180.0
1.096 1.410 1.184 1.355 1.319, 1.331, 1.341 111.0 122.5 115.8 109.1, 108.9, 107.2 173.9, )65.7, 54.3 91.0
for bond lengths and in degrees for bond angles. Values are given in A The Z and E rotamers both adopt Cs symmetry, while the rotational transition-state (TS) structure does not have any symmetry (C1 symmetry). F and F0 represent the fluorine atom located on the Cs plane and those located out of the plane, respectively. a
b
geometrical parameters of the rotational stationary points for MF and TFMF, respectively. To evaluate the energy of each stationary point, we carried out single-point energy calculations with the series of basis sets developed by Dunning and coworkers [11,12], i.e., the correlation consistent basis sets [cc-pVnZ (n ¼ D, T, Q, 5, 6)], those augmented with diffuse functions [aug-cc-pVnZ (n ¼ D, T, Q)] [13], and the correlation consistent polarized core-valence basis sets (cc-pCVnZ; n ¼ D, T) [14]. For cc-pVDZ–cc-pV5Z basis sets, single-point calculations with electron correlation correction were carried out under frozen-core approximation: up to the CCSD(T) level for the ccpVDZ through cc-pVQZ basis sets and up to the second order Møller-Plesset (MP2) level for the ccpV5Z basis set. For the cc-pV6Z basis set, only Hartree–Fock (HF) level single-point calculations were carried out. To examine the effect of the diffuse functions, we compared the energies calculated using the augcc-pVnZ basis sets (n ¼ D, T, Q) [13] with those obtained from the corresponding calculations using the cc-pVnZ series of basis sets. In addition, to evaluate the contribution of the core-correlation energies on the relative energies of the stationary points, we also considered the energies calculated with the cc-pCVnZ (n ¼ D, T) basis sets [14]: the energies obtained from all electrons (including
core electrons) correlated calculations were compared with the results obtained from the corresponding calculations with only valence electrons correlated (frozen-core approximation). For all the calculations, we employed GA U S S I A N 98 program package [15].
3. Results and discussion For MF and TFMF, the Z and E rotamers both have Cs symmetry, in which all the heavy atoms, except for two fluorine atoms of TFMF, are located on the Cs plane. In the rotational transition state connecting the Z and E rotamers, the CX3 –O bond is nearly perpendicular to the plane of the formyl group: the QCISD/6-311G(d,p) optimized torsional angle of O@Cformyl –O–CX3 is 91.5° and 91.0° for MF and TFMF, respectively (Tables 1 and 2). Among the rotamers of MF and TFMF, experimentally determined geometry has been reported only for the Z rotamer of MF [3,4]. The QCISD/6-311G(d,p) optimized geometrical parameters for the Z rotamers of MF were within the uncertainty of the values derived from microwave experiment [4] (see Table 1). The optimized values of the geometrical parameters remained almost unchanged upon replacing the 6-311G(d, p) basis
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
set with the correlation consistent basis set, ccpVTZ (Table 1). Our results of the geometry optimizations for the Z and E rotamers at the QCISD/6-311G(d,p) level are in reasonable agreement with previously reported ab initio/DFT results for MF [16–21], as well as for TFMF [19,22]. Tables 3 and 4 summarize the results of single-point energy evaluations for MF and TFMF, respectively: the differences in potential energy between the rotational stationary points, the Z and E rotamers and the rotational transition state, are given. For MF, the potential energy differences at the HF level are already converged to 0.01 kcal/mol at cc-pV5Z (Table 3), while for TFMF the HF energy differences do not reach convergence even at cc-pV6Z (Table 4). Thus, we approximated the HF energy differences between the stationary points of TFMF at the complete basis set (CBS) limit via the following asymptotic form (1), which was originally proposed by Feller [23] EðnÞ ¼ ECBS
limit
þ B expðCnÞ:
ð1Þ
This asymptotic expression with assumption of geometric progression has been frequently used to obtain the CBS limit. As compared with the HF energies, the convergence of the energy differences at correlated levels was slower for both MF and TFMF (see Tables 3 and 4). Such slower convergence behavior of correlation energy was also pointed out in recent investigations [24]. To obtain the energy at the complete basis set (CBS) limit, Helgaker et al. [25] have proposed the following expression: E ¼ ECBS
limit
þ bX 3 :
ð2Þ
Cs asz ar et al. [26] have suggested that this asymptotic form may not be strongly operative unless the cc-pVQZ basis set or higher basis sets are employed. Thus, by using the results calculated with cc-pVQZ and cc-pV5Z basis sets, we extrapolated the energy differences to the CBS limits of MP2 the correlation energies at the MP2 level (E1 ) via the asymptotic form of Eq. (2). As can be seen in Tables 3 and 4, convergence of the correlation energies beyond the MP2 level appears to be faster than that at the MP2 level. In
185
their recent investigations on some small molecules, Park and Lee have reported the faster convergence behavior at the CCSD(T) level than at the MP2 level [24]. We estimated the contribution of correlation energy beyond the MP2 level as the differences between the CCSD(T) and MP2 results, d[CCSD(T)], calculated with the cc-pVQZ basis set (DCC ). Moreover, although the differences between the results calculated with the cc-pVnZ basis sets and the corresponding augmented basis sets, aug-ccpVnZ, were rather small (less than 0.1 kcal, Tables 3 and 4), we took the effects of the diffuse functions into account, i.e., the difference between the CCSD(T) results obtained with cc-pVTZ and augcc-pVTZ basis sets (Daug ). Finally, we considered the effect of the core-correlation, whose importance has recently been emphasized for some cases [14,27]. We carried out CCSD(T) calculations using the correlation consistent polarized core-valence basis set, cc-pCVnZ [14]. The results obtained from calculations with all electrons correlated were close to those obtained from frozencore approximation: the differences were less than 0.03 kcal/mol (Tables 3 and 4). Our estimates for the contribution of the core-correlation (DCORE ) are the differences between the energies calculated with all electrons correlated and with frozen-core approximation at the CCSD(T) level in conjunction with the cc-pCVTZ basis set. Our best estimates for the potential energy differences between rotational stationary points are HF MP2 obtained as DE1 þ dE1 þ DCC þ Daug þ DCORE . This expression provides estimates for the potential energy differences between the Z and E rotamers of 5.46 and 1.34 kcal/mol for MF and TFMF, respectively. Our estimates for the potential barrier heights on going from the Z rotamer to the rotational transition state are 13.55 and 7.50 kcal/mol for MF and TFMF (Tables 3 and 4). The change in the calculated values for the potential energy differences between the rotational stationary points result mainly from the changes in the contributions of the HF energies and those of the correlation energies at the MP2 level. With increase of the quality of the basis set employed, the contributions of the HF energies and those of the MP2 correlation energies change in the
186
Table 3 The potential energy differences between the rotational stationary points for methyl formate (MF)a n
cc-pVnZ
aug-cc-pVnZ
E–Z 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
TS-Z 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
TS-E 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
a
d[MP2]
d[CCSD(T)]
D
5.95 5.42 5.32 5.31 5.31 5.31
)0.28 0.00 0.13 0.18
)0.13 )0.15 )0.14
5.54 5.28 5.32
0.24
)0.14
5.41
12.61 12.20 12.14 12.13 12.13 12.13
1.41 1.69 1.79 1.83
)0.48 )0.46 )0.45
13.54 13.44 13.49
1.88
)0.45
13.56
6.67 6.78 6.82 6.82 6.82 6.82
1.69 1.68 1.66 1.65
)0.36 )0.31 )0.31
8.00 8.16 8.17
1.64
)0.31
8.15
D[HF] (128) (276) (504)
5.44 5.33 5.31
cc-pCVnZ d[MP2]
d[CCSD(T)]
0.05 0.12 0.18
)0.17 )0.14
D 5.33 5.32
DCORE
Daug )0.22 0.04
(92) (228)
0.04 (128) (276) (504)
12.26 12.13 12.13
1.62 1.74 1.83
)0.57 )0.47
13.31 13.40
)0.23 )0.03
0.01 (92) (228)
)0.03 (128) (276) (504)
6.82 6.80 6.82
1.57 1.61 1.65
)0.40 )0.33
7.99 8.08
)0.01 )0.08
)0.08
0.01 0.01
0.03 0.03
0.03 (92) (228)
5.46
13.55
0.02 0.02
0.02
8.10
Potential energy differences are given in kcal/mol. The symbol d indicates the increment in the potential energy difference with respect to the preceding level of theory, namely HF ! MP2 ! CCSD(T). The number of basis functions is given in parentheses. b See the text.
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
D[HF]
Table 4 The potential energy differences between the rotational stationary points for trifluoromethyl formate (TFMF)a n
cc-pVnZ
(103) (224) (415) (692) (1071)
TS-Z 2 3 4 5 6 DElimit b
(103) (224) (415) (692) (1071)
TS-E 2 3 4 5 6 DElimit b
(103) (224) (415) (692) (1071)
D[HF]
d[MP2]
d[CCSD(T)]
D
2.06 1.53 1.50 1.49 1.48 1.47
)0.44 )0.35 )0.28 )0.21
)0.01 )0.04 )0.04
1.60 1.13 1.18
)0.13
)0.04
1.29
7.73 7.42 7.41 7.40 7.39 7.39
0.06 0.20 0.25 0.28
)0.17 )0.19 )0.19
7.61 7.43 7.47
0.31
)0.19
7.51
5.66 5.90 5.92 5.91 5.92 5.92
0.50 0.55 0.53 0.49
)0.16 )0.15 )0.15
6.01 6.30 6.30
0.44
)0.15
6.21
(170) (345) (606)
cc-pCVnZ
D[HF]
d[MP2]
d[CCSD(T)]
D
Daug
1.36 1.46 1.48
)0.15 )0.24 )0.21
)0.05 )0.04
1.16 1.18
)0.44 0.05
DCORE (131) (315)
0.05 (170) (345) (606)
7.35 7.40 7.40
0.21 0.23 0.29
)0.27 )0.21
7.28 7.41
)0.33 )0.02
0.00 (131) (315)
)0.02 (170) (345) (606)
5.99 5.94 5.92
0.36 0.46 0.50
)0.22 )0.17
6.13 6.23
0.12 )0.07
)0.07
0.01 0.00
0.02 0.01
0.01 (131) (315)
1.34
7.50
0.01 0.01
0.01
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
E–Z 2 3 4 5 6 DElimit b
aug-cc-pVnZ
6.15
a
Potential energy differences are given in kcal/mol. The symbol d indicates the increment in the potential energy difference with respect to the preceding level of theory, namely HF ! MP2 ! CCSD(T). The number of basis functions is given in parentheses. b See the text.
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Table 5 Energetics of the rotational stationary points of methyl formate (MF) and trifluoromethyl formate (TFMF)a E–Z
TS-Z
TS-E
CH3 CO(O)H (MF) DEe DZPE DH (298 K) DG (298 K)
5.46b (5.28) )0.47 5.21 (5.03) 4.59 (4.41)
13.55b (13.57) )0.81 12.50 (12.52) 12.91 (12.92)
8.10b (8.29) )0.34 7.30 (7.48) 8.33 (8.51)
F3 CO(O)H (TFMF) DEe DZPE DH (298 K) DG (298 K)
1.34b (1.21) )0.18 1.27 (1.14) 0.85 (0.72)
7.50b (7.52) )0.55 6.66 (6.68) 6.96 (6.98)
6.15b (6.31) )0.37 5.39 (5.55) 6.10 (6.26)
a b
The values are given in kcal/mol. The values calculated with CBS-APNO procedure are given in parentheses. See Tables 3 and 4.
opposite direction. As a result, our estimates for the energy differences between the rotational stationary points are rather close to the previously reported ab initio values obtained from MP2/MP3 calculations with a medium size basis set [5,16,22]. 1 To obtain the thermochemical values, we calculated the zero-point energy (ZPE) for each rotational stationary point using scaled HF/6-311G (d,p) harmonic vibrational frequencies (scale factor ¼ 0.9051) [28]. Table 5 lists the calculated values for the differences in enthalpy DH and in free energy DG between the rotational stationary points. It has been confirmed that the CBS-APNO procedure [29,30] provides quite reliable thermochemical values [31]. Thus, the values computed with the CBS-APNO procedure are also given in Table 5. Our estimate for DH between the Z and E rotamers of MF at 298 K is 5.21 kcal/mol. The
1
Wiberg and Laidig obtained the value of 5.59 kcal/mol for Z=E potential energy difference of MF from MP3/6-311+G(d,p) calculations, while Wallington et al. obtained the value of 1.2 kcal/mol for TFMF from MP2/TZ2P calculations. In addition, the MP3/6-311+G(d,p) level calculations of Wiberg and Laidig suggested that the MF rotamer with O@C–O–H torsional angle of 90° was higher by 12.83 kcal/mol in potential energy than the Z rotamer, while the MP2/TZ2P calculations of Wallington et al. suggested that the rotational transition state for TFMF was higher by 7.5 kcal/mol than its Z rotamer. MiyazawaÕs estimate of 13.1 kcal/mol for the potential barrier of MF was derived only from IR measurements. Noteworthy is that his estimate is quite close to the ab initio values.
corresponding CBS-APNO value is 5.03 kcal/mol. Both calculated values are still slightly larger than the upper edge of uncertainty of experimentally derived value of enthalpy difference (DH ) between the Z and E rotamers, 4.75 0.19 kcal/mol, reported by Blom and G€ unthard [7]. 2 For TFMF, DH value between the Z and E rotamers is significantly smaller than for MF: our estimate and the CBS-APNO value for DH at 298 K are 1.27 and 1.14 kcal/mol, respectively (see Table 5). The value of DH on going from the Z rotamer to the rotational transition state is estimated to be 12.50 kcal/mol at 298 K for MF. The corresponding DH estimate for TFMF is 6.66 kcal/mol (see Table 5). Our estimates for DH between the rotational transition states and the Z=E rotamers are again quite close to the corresponding CBSAPNO values (see Table 5). For ordinary esters, such as MF and methyl acetate, one important difference between the Z and E rotamers is found in their dipole moments: the dipole moments of the E rotamers are much larger than those of the Z rotamers. Bond and Schleyer [32] have suggested that the difference in dipole moment between the rotamers should be the primary factor determining the Z preference for
2 Blom and G€ unthard derived DH between the Z and E rotamers of MF from vanÕt Hoff plot in the temperature region from 540 to 885 K. Our calculation results suggest DH of 5.31 kcal/mol in this temperature region.
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Table 6 Calculated values for dipole moment for CH3 OC(O)H (MF) and CF3 OC(O)H (TFMF)a Basis set
Z
E
TS
CH3 OC(O)H (MF) cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z Basis set limitb
1.6187 1.7253 1.7593 1.7740 1.78
3.8189 4.0143 4.1085 4.1548 4.20
2.5594 2.7143 2.7873 2.8212 2.85
CF3 OC(O)H (TFMF) cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z Basis set limitb
1.8742 1.9857 2.0353 2.0502 2.06
1.6243 1.7243 1.7564 1.7757 1.78
1.7982 1.8873 1.9274 1.9441 1.96
a b
The dipole moments calculated using the MP2 densities are given in unit of Debye. See the text.
ordinary esters. They found a direct relationship between the differences in dipole moment of the rotamers and their energy differences. The dipole moments of MF and TFMF calculated using the MP2 densities are given in Table 6. We have derived the values of dipole moments at the basis set limit according to FellerÕs extrapolation procedure [33], i.e., using an expression similar to Eq. (1). For MF, the magnitude of the dipole moment of the E rotamer (4.20 D) is considerably larger than that of the Z rotamer (1.78 D) and that of the rotational transition state (2.85 D) comes between those of the Z and E rotamers. Meanwhile, the difference in dipole moment between the Z and E rotamers is less significant for TFMF (2.06 and 1.78 D, respectively). The magnitude of the dipole moment for the rotational transition state (1.96 D) also comes between those of the Z and E rotamers for TFMF, but conversely to MF, TFMF shows slightly larger dipole moment for the Z rotamer than for the E rotamer. This should be related to the smaller energy difference between the Z and E rotamers, as well as the lower rotational barrier height, for TFMF as compared with those for MF.
4. Concluding remarks We have carried out ab initio energy evaluations on the Z and E rotamers, as well as the ro-
tational transition state connecting them, for methyl formate (MF) and trifluoromethyl formate (TFMF). With systematic increase of the quality of the basis set employed, the contributions of the HF energies and those of the correlation energies at the MP2 level to the potential energy differences between the rotational stationary points were found to change in the opposite direction. The contributions of the electron correlation energies at the MP2 level to the energy differences between the stationary points showed slower convergence than those of the HF energies and those of the electron correlation energies beyond the MP2 level. The addition of diffuse functions to the basis set utilized and the contributions of core-correlation did not significantly alter the estimates for the energy differences at the basis set limit. Our best estimate for the enthalpy difference at 298 K between the Z and E rotamers of MF was 5.21 kcal/mol, which is slightly larger than the upper edge of uncertainty of the experimentally derived value for enthalpy difference of 4.75 0.19 kcal/mol [7]. In accord with the findings of Wallington et al. [22], the estimates for the energy differences at the basis set limit have suggested that the Z/E energy difference, as well as the rotational barrier height, is significantly smaller for TFMF than for MF. This should be related with the fact that the differences in the magnitude of the dipole moments among the rotational stationary points are much smaller for TFMF than for MF.
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Acknowledgements T.U. would like to express his appreciation to Director Dr. Masaaki Yamabe, Director Dr. Kazuo Kitaura, and Deputy Director Dr. Masuhiro Mikami and the members of their group for their help and encouragement.
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[15] M.J. Frisch et al., GA U S S I A N 98, Gaussian, Inc., Pittsburgh, PA, 1998. [16] K.B. Wiberg, K.E. Laidig, J. Am. Chem. Soc. 109 (1987) 5935. [17] D.A. Good, M. Kamboures, R. Santiano, J.S. Francisco, J. Phys. Chem. A 103 (1999) 9230. [18] D.A. Good, J. Hanson, J.S. Francisco, Z. Li, G.-R. Jeong, J. Phys. Chem. A 103 (1999) 10893. [19] D.A. Good, J.S. Francisco, J. Phys. Chem. A 104 (2000) 1171. [20] D.A. Good, J. Hansen, M. Kamoboures, R. Santiono, J.S. Francisco, J. Phys. Chem. A 104 (2000) 1505. [21] D.A. Good, J.S. Francisco, J. Phys. Chem. A 106 (2002) 1733. [22] T.J. Wallington, W.F. Schneider, J. Sehested, M. Bilde, J. Platz, O.J. Nielsen, L.K. Christensen, M.J. Molina, P.W. Wooldridge, J. Phys. Chem. A 101 (1997) 8264. [23] D. Feller, J. Chem. Phys. 96 (1992) 6104. [24] For example S.Y. Park, J.S. Lee, J. Phys. Chem. 116 (2002) 5389. [25] T. Helgaker, W. Klopper, H. Koch, J. Noza, J. Chem. Phys. 106 (1997) 9639. [26] A.G. Csaszar, W.D. Allen, H.F. Schaefer, III, J. Chem. Phys. 108 (1998) 9751. [27] S. Lee, Chem. Phys. Lett. 359 (2002) 440. [28] A.P. Scott, L. Radom, J. Phys. Chem. 100 (1996) 16502. [29] J.A. Montgomery Jr., J.W. Ochterski, G.A. Petersson, J. Chem. Phys. 101 (1994) 5900. [30] J.W. Ochterski, G.A. Petersson, J.A. Montgomery Jr., J. Phys. Chem. 104 (1996) 2598. [31] G.A. Petersson, in: K.K. Irikura, D.J. Frurip (Eds.), Computational Thermochemistry, ACS Symposium Series, Florida, vol. 677, 1996, p. 237. [32] D. Bond, P. von R. Schleyer, J. Org. Chem. 55 (1990) 1003. [33] D. Feller, J. Chem. Phys. 98 (1993) 7059.
Gas-phase energy differences between the Z and E rotamers and the rotational barrier heights of methyl formate and trifluromethyl formate: an ab initio study Tadafumi Uchimaru
a,b,*
, Seiji Tsuzuki b, Masaaki Sugie a, Akira Sekiya
a
a
b
Research Center for Developing Fluorinated Greenhouse Gas Alternatives, National Institute of Advanced Industrial Science and Technology, Higashi, Tsukuba 305-8565, Japan Research Institute for Computational Sciences, National Institute of Advanced Industrial Science and Technology, Umezono, Tsukuba 305-8568, Japan Received 30 December 2002; in final form 21 March 2003
Abstract Ab initio energy evaluations on the Z and E rotamers, as well as on the rotational transition states connecting them, were carried out for methyl formate and trifluoromethyl formate. The estimates for the energy differences at the basis set limit suggested that the Z/E energy difference and the rotational barrier height are both significantly smaller for trifluoromethyl formate than for methyl formate. Our best estimate for the enthalpy difference at 298 K between the Z and E rotamers for methyl formate is 5.21 kcal/mol, which is slightly larger than the upper edge of uncertainty of previously reported experimental value. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Despite their simple chemical structures of methyl formate [CH3 OC(O)H; MF] and trifluoromethyl formate [CF3 OC(O)H; TFMF], the energy differences between the E and Z rotamers (see Fig. 1), and the barrier heights for interconversion between the rotamers have not been fully elucidated. For MF, detailed IR studies indicated that only the Z rotamer is present in the vicinity of room temperature [1,2]. Correspondingly, no evidence
*
Corresponding author. Fax: +81-29-861-4487. E-mail address: [email protected] (T. Uchimaru).
for the presence of the E rotamer was obtained in early studies of electron diffraction [3] and microwave spectrum [4]. From the IR intensity in the region of the torsional vibrations, Miyazawa [5] concluded that the E rotamer of MF was higher in energy by at least 2.7 kcal/mol than the Z rotamer. In the 1980s, the unstable E rotamer of MF was spectroscopically detected [6–8], and the energy difference between the Z and E rotamers of MF was experimentally derived. Ruschin and Bauer [6] employed a temperature drift technique to conclude that the E rotamer was less stable by 3.85 0.20 kcal/mol than the Z rotamer. Blom and G€ unthard [7] applied thermal molecular beam trapping to study the unstable rotamer in Ar
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00573-6
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
183
Meanwhile, the IR spectrum of TFMF indicated the presence of not only the Z rotamer but also the E rotamer even in the room temperature region (295 2 K) [10]. This observation suggests that the Z and E rotamers of TFMF are much closer in energy than those of MF. Nevertheless, for the energy difference between the Z and E rotamers of TFMF and for the barrier height to their interconversion, no experimental values have been reported. We have carried out systematic energy evaluations for the Z and E rotamers of MF and TFMF and for the rotational transition states connecting the rotamers. In this Letter we will report ab initio estimates for the energy difference at the basis set limit between the rotamers and for the barrier heights to interconversion of the rotamers.
Fig. 1. Structures of the Z and E rotamers of methyl formate (MF; X ¼ H) and trifuoromethyl formate (TFMF; X ¼ F).
matrices to derive a value of 4.75 0.19 kcal/mol for the difference in enthalpy (DH ) between the rotamers. For interconversion of the rotamers of MF, Miyazawa [5] provided an estimate of 13.1 kcal/ mol for the potential energy barrier. Blom and G€ unthard [7] suggested that the barrier height should be 10–15 kcal/mol in the gas phase. The liquid-phase and solution-phase barrier heights have been experimentally derived through ultrasonic relaxation measurements and dynamic NMR analysis [9]. However, to the best of our knowledge, the gas-phase barrier height to Z-to-E and E-to-Z conversion of MF has not yet been experimentally determined.
2. Computational procedure The geometries of the Z and E rotamers and the rotational transition states connecting the rotamers were optimized at the QCISD level with 6-311G(d,p) basis set under frozen-core approximation. Tables 1 and 2 show the optimized
Table 1 QCISD/6-311G(d,p) optimized geometrical parameters for methyl formate (MF)a Coordinate
Z-CH3 OC(O)H c
Cformyl –H Cformyl –O C@O CH3 –O CH3 –Hb CH3 –H0 b H–Cformyl –O O@C–O O–C–O H–CH3 –H0 b H0 –CH3 –H0 b Cfomyl –O–CH3 –Hb O@Cformyl –O–CH3
d
E-CH3 OC(O)H
TS
Calc.
Expt.
Calc.
Calc.
1.099 (1.093) 1.341 (1.337) 1.201 (1.200) 1.436 (1.434) 1.090 (1.085) 1.093 (1.088) 109.0 (109.4) 125.7 (125.7) 114.2 (114.4) 110.6 (110.6) 109.1 (109.1) 60.4 (60.4) 0.0 (0.0)
1.101 0.01 1.334 0.01 1.200 0.01 1.437 0.01 1.086 0.015
1.107 1.349 1.195 1.430 1.090 1.096 113.1 123.0 114.9 109.3 109.8 61.4 180.0
1.104 1.368 1.194 1.428 1.090, 1.096, 1.099
109.18 1 125.52 1 114.47 1 110.40 1.5 – 0.0 5
112.5 124.1 112.4 109.7, 109.2, 109.6 177.4, )63.5, 58.6 91.5
for bond lengths and in degrees for bond angles. Values are given in A The Z and E rotamers both adopt Cs symmetry, while the rotational transition-state (TS) structure does not have any symmetry (C1 symmetry). H and H0 represent the hydrogen atom located on the Cs plane and those located out of the plane, respectively. c QCISD/cc-pVTZ optimized parameters are given in parentheses. d Ref. [4]. a
b
184
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
Table 2 QCISD/6-311G(d,p) optimized geometrical parameters for trifluoromethyl formate (TFMF)a Coordinate
Z-CF3 OC(O)H
E-CF3 OC(O)H
TS
Cformyl –H Cformyl –O C@O CF3 –O CF3 –Fb CF3 –F0 b H–Cformyl –O O@C–O O–C–O F–CF3 –F0b F0 –CF3 –F0 b Cfomyl –O–CF3 –F0b O@Cformyl –O–CF3
1.096 1.381 1.189 1.376 1.323 1.326 107.0 125.9 118.1 108.9 108.9 61.2 0.0
1.098 1.388 1.185 1.363 1.316 1.335 113.3 120.5 116.1 109.2 107.4 60.0 180.0
1.096 1.410 1.184 1.355 1.319, 1.331, 1.341 111.0 122.5 115.8 109.1, 108.9, 107.2 173.9, )65.7, 54.3 91.0
for bond lengths and in degrees for bond angles. Values are given in A The Z and E rotamers both adopt Cs symmetry, while the rotational transition-state (TS) structure does not have any symmetry (C1 symmetry). F and F0 represent the fluorine atom located on the Cs plane and those located out of the plane, respectively. a
b
geometrical parameters of the rotational stationary points for MF and TFMF, respectively. To evaluate the energy of each stationary point, we carried out single-point energy calculations with the series of basis sets developed by Dunning and coworkers [11,12], i.e., the correlation consistent basis sets [cc-pVnZ (n ¼ D, T, Q, 5, 6)], those augmented with diffuse functions [aug-cc-pVnZ (n ¼ D, T, Q)] [13], and the correlation consistent polarized core-valence basis sets (cc-pCVnZ; n ¼ D, T) [14]. For cc-pVDZ–cc-pV5Z basis sets, single-point calculations with electron correlation correction were carried out under frozen-core approximation: up to the CCSD(T) level for the ccpVDZ through cc-pVQZ basis sets and up to the second order Møller-Plesset (MP2) level for the ccpV5Z basis set. For the cc-pV6Z basis set, only Hartree–Fock (HF) level single-point calculations were carried out. To examine the effect of the diffuse functions, we compared the energies calculated using the augcc-pVnZ basis sets (n ¼ D, T, Q) [13] with those obtained from the corresponding calculations using the cc-pVnZ series of basis sets. In addition, to evaluate the contribution of the core-correlation energies on the relative energies of the stationary points, we also considered the energies calculated with the cc-pCVnZ (n ¼ D, T) basis sets [14]: the energies obtained from all electrons (including
core electrons) correlated calculations were compared with the results obtained from the corresponding calculations with only valence electrons correlated (frozen-core approximation). For all the calculations, we employed GA U S S I A N 98 program package [15].
3. Results and discussion For MF and TFMF, the Z and E rotamers both have Cs symmetry, in which all the heavy atoms, except for two fluorine atoms of TFMF, are located on the Cs plane. In the rotational transition state connecting the Z and E rotamers, the CX3 –O bond is nearly perpendicular to the plane of the formyl group: the QCISD/6-311G(d,p) optimized torsional angle of O@Cformyl –O–CX3 is 91.5° and 91.0° for MF and TFMF, respectively (Tables 1 and 2). Among the rotamers of MF and TFMF, experimentally determined geometry has been reported only for the Z rotamer of MF [3,4]. The QCISD/6-311G(d,p) optimized geometrical parameters for the Z rotamers of MF were within the uncertainty of the values derived from microwave experiment [4] (see Table 1). The optimized values of the geometrical parameters remained almost unchanged upon replacing the 6-311G(d, p) basis
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
set with the correlation consistent basis set, ccpVTZ (Table 1). Our results of the geometry optimizations for the Z and E rotamers at the QCISD/6-311G(d,p) level are in reasonable agreement with previously reported ab initio/DFT results for MF [16–21], as well as for TFMF [19,22]. Tables 3 and 4 summarize the results of single-point energy evaluations for MF and TFMF, respectively: the differences in potential energy between the rotational stationary points, the Z and E rotamers and the rotational transition state, are given. For MF, the potential energy differences at the HF level are already converged to 0.01 kcal/mol at cc-pV5Z (Table 3), while for TFMF the HF energy differences do not reach convergence even at cc-pV6Z (Table 4). Thus, we approximated the HF energy differences between the stationary points of TFMF at the complete basis set (CBS) limit via the following asymptotic form (1), which was originally proposed by Feller [23] EðnÞ ¼ ECBS
limit
þ B expðCnÞ:
ð1Þ
This asymptotic expression with assumption of geometric progression has been frequently used to obtain the CBS limit. As compared with the HF energies, the convergence of the energy differences at correlated levels was slower for both MF and TFMF (see Tables 3 and 4). Such slower convergence behavior of correlation energy was also pointed out in recent investigations [24]. To obtain the energy at the complete basis set (CBS) limit, Helgaker et al. [25] have proposed the following expression: E ¼ ECBS
limit
þ bX 3 :
ð2Þ
Cs asz ar et al. [26] have suggested that this asymptotic form may not be strongly operative unless the cc-pVQZ basis set or higher basis sets are employed. Thus, by using the results calculated with cc-pVQZ and cc-pV5Z basis sets, we extrapolated the energy differences to the CBS limits of MP2 the correlation energies at the MP2 level (E1 ) via the asymptotic form of Eq. (2). As can be seen in Tables 3 and 4, convergence of the correlation energies beyond the MP2 level appears to be faster than that at the MP2 level. In
185
their recent investigations on some small molecules, Park and Lee have reported the faster convergence behavior at the CCSD(T) level than at the MP2 level [24]. We estimated the contribution of correlation energy beyond the MP2 level as the differences between the CCSD(T) and MP2 results, d[CCSD(T)], calculated with the cc-pVQZ basis set (DCC ). Moreover, although the differences between the results calculated with the cc-pVnZ basis sets and the corresponding augmented basis sets, aug-ccpVnZ, were rather small (less than 0.1 kcal, Tables 3 and 4), we took the effects of the diffuse functions into account, i.e., the difference between the CCSD(T) results obtained with cc-pVTZ and augcc-pVTZ basis sets (Daug ). Finally, we considered the effect of the core-correlation, whose importance has recently been emphasized for some cases [14,27]. We carried out CCSD(T) calculations using the correlation consistent polarized core-valence basis set, cc-pCVnZ [14]. The results obtained from calculations with all electrons correlated were close to those obtained from frozencore approximation: the differences were less than 0.03 kcal/mol (Tables 3 and 4). Our estimates for the contribution of the core-correlation (DCORE ) are the differences between the energies calculated with all electrons correlated and with frozen-core approximation at the CCSD(T) level in conjunction with the cc-pCVTZ basis set. Our best estimates for the potential energy differences between rotational stationary points are HF MP2 obtained as DE1 þ dE1 þ DCC þ Daug þ DCORE . This expression provides estimates for the potential energy differences between the Z and E rotamers of 5.46 and 1.34 kcal/mol for MF and TFMF, respectively. Our estimates for the potential barrier heights on going from the Z rotamer to the rotational transition state are 13.55 and 7.50 kcal/mol for MF and TFMF (Tables 3 and 4). The change in the calculated values for the potential energy differences between the rotational stationary points result mainly from the changes in the contributions of the HF energies and those of the correlation energies at the MP2 level. With increase of the quality of the basis set employed, the contributions of the HF energies and those of the MP2 correlation energies change in the
186
Table 3 The potential energy differences between the rotational stationary points for methyl formate (MF)a n
cc-pVnZ
aug-cc-pVnZ
E–Z 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
TS-Z 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
TS-E 2 3 4 5 6 DElimit b
(76) (176) (340) (584) (924)
a
d[MP2]
d[CCSD(T)]
D
5.95 5.42 5.32 5.31 5.31 5.31
)0.28 0.00 0.13 0.18
)0.13 )0.15 )0.14
5.54 5.28 5.32
0.24
)0.14
5.41
12.61 12.20 12.14 12.13 12.13 12.13
1.41 1.69 1.79 1.83
)0.48 )0.46 )0.45
13.54 13.44 13.49
1.88
)0.45
13.56
6.67 6.78 6.82 6.82 6.82 6.82
1.69 1.68 1.66 1.65
)0.36 )0.31 )0.31
8.00 8.16 8.17
1.64
)0.31
8.15
D[HF] (128) (276) (504)
5.44 5.33 5.31
cc-pCVnZ d[MP2]
d[CCSD(T)]
0.05 0.12 0.18
)0.17 )0.14
D 5.33 5.32
DCORE
Daug )0.22 0.04
(92) (228)
0.04 (128) (276) (504)
12.26 12.13 12.13
1.62 1.74 1.83
)0.57 )0.47
13.31 13.40
)0.23 )0.03
0.01 (92) (228)
)0.03 (128) (276) (504)
6.82 6.80 6.82
1.57 1.61 1.65
)0.40 )0.33
7.99 8.08
)0.01 )0.08
)0.08
0.01 0.01
0.03 0.03
0.03 (92) (228)
5.46
13.55
0.02 0.02
0.02
8.10
Potential energy differences are given in kcal/mol. The symbol d indicates the increment in the potential energy difference with respect to the preceding level of theory, namely HF ! MP2 ! CCSD(T). The number of basis functions is given in parentheses. b See the text.
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
D[HF]
Table 4 The potential energy differences between the rotational stationary points for trifluoromethyl formate (TFMF)a n
cc-pVnZ
(103) (224) (415) (692) (1071)
TS-Z 2 3 4 5 6 DElimit b
(103) (224) (415) (692) (1071)
TS-E 2 3 4 5 6 DElimit b
(103) (224) (415) (692) (1071)
D[HF]
d[MP2]
d[CCSD(T)]
D
2.06 1.53 1.50 1.49 1.48 1.47
)0.44 )0.35 )0.28 )0.21
)0.01 )0.04 )0.04
1.60 1.13 1.18
)0.13
)0.04
1.29
7.73 7.42 7.41 7.40 7.39 7.39
0.06 0.20 0.25 0.28
)0.17 )0.19 )0.19
7.61 7.43 7.47
0.31
)0.19
7.51
5.66 5.90 5.92 5.91 5.92 5.92
0.50 0.55 0.53 0.49
)0.16 )0.15 )0.15
6.01 6.30 6.30
0.44
)0.15
6.21
(170) (345) (606)
cc-pCVnZ
D[HF]
d[MP2]
d[CCSD(T)]
D
Daug
1.36 1.46 1.48
)0.15 )0.24 )0.21
)0.05 )0.04
1.16 1.18
)0.44 0.05
DCORE (131) (315)
0.05 (170) (345) (606)
7.35 7.40 7.40
0.21 0.23 0.29
)0.27 )0.21
7.28 7.41
)0.33 )0.02
0.00 (131) (315)
)0.02 (170) (345) (606)
5.99 5.94 5.92
0.36 0.46 0.50
)0.22 )0.17
6.13 6.23
0.12 )0.07
)0.07
0.01 0.00
0.02 0.01
0.01 (131) (315)
1.34
7.50
0.01 0.01
0.01
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
E–Z 2 3 4 5 6 DElimit b
aug-cc-pVnZ
6.15
a
Potential energy differences are given in kcal/mol. The symbol d indicates the increment in the potential energy difference with respect to the preceding level of theory, namely HF ! MP2 ! CCSD(T). The number of basis functions is given in parentheses. b See the text.
187
188
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
Table 5 Energetics of the rotational stationary points of methyl formate (MF) and trifluoromethyl formate (TFMF)a E–Z
TS-Z
TS-E
CH3 CO(O)H (MF) DEe DZPE DH (298 K) DG (298 K)
5.46b (5.28) )0.47 5.21 (5.03) 4.59 (4.41)
13.55b (13.57) )0.81 12.50 (12.52) 12.91 (12.92)
8.10b (8.29) )0.34 7.30 (7.48) 8.33 (8.51)
F3 CO(O)H (TFMF) DEe DZPE DH (298 K) DG (298 K)
1.34b (1.21) )0.18 1.27 (1.14) 0.85 (0.72)
7.50b (7.52) )0.55 6.66 (6.68) 6.96 (6.98)
6.15b (6.31) )0.37 5.39 (5.55) 6.10 (6.26)
a b
The values are given in kcal/mol. The values calculated with CBS-APNO procedure are given in parentheses. See Tables 3 and 4.
opposite direction. As a result, our estimates for the energy differences between the rotational stationary points are rather close to the previously reported ab initio values obtained from MP2/MP3 calculations with a medium size basis set [5,16,22]. 1 To obtain the thermochemical values, we calculated the zero-point energy (ZPE) for each rotational stationary point using scaled HF/6-311G (d,p) harmonic vibrational frequencies (scale factor ¼ 0.9051) [28]. Table 5 lists the calculated values for the differences in enthalpy DH and in free energy DG between the rotational stationary points. It has been confirmed that the CBS-APNO procedure [29,30] provides quite reliable thermochemical values [31]. Thus, the values computed with the CBS-APNO procedure are also given in Table 5. Our estimate for DH between the Z and E rotamers of MF at 298 K is 5.21 kcal/mol. The
1
Wiberg and Laidig obtained the value of 5.59 kcal/mol for Z=E potential energy difference of MF from MP3/6-311+G(d,p) calculations, while Wallington et al. obtained the value of 1.2 kcal/mol for TFMF from MP2/TZ2P calculations. In addition, the MP3/6-311+G(d,p) level calculations of Wiberg and Laidig suggested that the MF rotamer with O@C–O–H torsional angle of 90° was higher by 12.83 kcal/mol in potential energy than the Z rotamer, while the MP2/TZ2P calculations of Wallington et al. suggested that the rotational transition state for TFMF was higher by 7.5 kcal/mol than its Z rotamer. MiyazawaÕs estimate of 13.1 kcal/mol for the potential barrier of MF was derived only from IR measurements. Noteworthy is that his estimate is quite close to the ab initio values.
corresponding CBS-APNO value is 5.03 kcal/mol. Both calculated values are still slightly larger than the upper edge of uncertainty of experimentally derived value of enthalpy difference (DH ) between the Z and E rotamers, 4.75 0.19 kcal/mol, reported by Blom and G€ unthard [7]. 2 For TFMF, DH value between the Z and E rotamers is significantly smaller than for MF: our estimate and the CBS-APNO value for DH at 298 K are 1.27 and 1.14 kcal/mol, respectively (see Table 5). The value of DH on going from the Z rotamer to the rotational transition state is estimated to be 12.50 kcal/mol at 298 K for MF. The corresponding DH estimate for TFMF is 6.66 kcal/mol (see Table 5). Our estimates for DH between the rotational transition states and the Z=E rotamers are again quite close to the corresponding CBSAPNO values (see Table 5). For ordinary esters, such as MF and methyl acetate, one important difference between the Z and E rotamers is found in their dipole moments: the dipole moments of the E rotamers are much larger than those of the Z rotamers. Bond and Schleyer [32] have suggested that the difference in dipole moment between the rotamers should be the primary factor determining the Z preference for
2 Blom and G€ unthard derived DH between the Z and E rotamers of MF from vanÕt Hoff plot in the temperature region from 540 to 885 K. Our calculation results suggest DH of 5.31 kcal/mol in this temperature region.
T. Uchimaru et al. / Chemical Physics Letters 373 (2003) 182–190
189
Table 6 Calculated values for dipole moment for CH3 OC(O)H (MF) and CF3 OC(O)H (TFMF)a Basis set
Z
E
TS
CH3 OC(O)H (MF) cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z Basis set limitb
1.6187 1.7253 1.7593 1.7740 1.78
3.8189 4.0143 4.1085 4.1548 4.20
2.5594 2.7143 2.7873 2.8212 2.85
CF3 OC(O)H (TFMF) cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z Basis set limitb
1.8742 1.9857 2.0353 2.0502 2.06
1.6243 1.7243 1.7564 1.7757 1.78
1.7982 1.8873 1.9274 1.9441 1.96
a b
The dipole moments calculated using the MP2 densities are given in unit of Debye. See the text.
ordinary esters. They found a direct relationship between the differences in dipole moment of the rotamers and their energy differences. The dipole moments of MF and TFMF calculated using the MP2 densities are given in Table 6. We have derived the values of dipole moments at the basis set limit according to FellerÕs extrapolation procedure [33], i.e., using an expression similar to Eq. (1). For MF, the magnitude of the dipole moment of the E rotamer (4.20 D) is considerably larger than that of the Z rotamer (1.78 D) and that of the rotational transition state (2.85 D) comes between those of the Z and E rotamers. Meanwhile, the difference in dipole moment between the Z and E rotamers is less significant for TFMF (2.06 and 1.78 D, respectively). The magnitude of the dipole moment for the rotational transition state (1.96 D) also comes between those of the Z and E rotamers for TFMF, but conversely to MF, TFMF shows slightly larger dipole moment for the Z rotamer than for the E rotamer. This should be related to the smaller energy difference between the Z and E rotamers, as well as the lower rotational barrier height, for TFMF as compared with those for MF.
4. Concluding remarks We have carried out ab initio energy evaluations on the Z and E rotamers, as well as the ro-
tational transition state connecting them, for methyl formate (MF) and trifluoromethyl formate (TFMF). With systematic increase of the quality of the basis set employed, the contributions of the HF energies and those of the correlation energies at the MP2 level to the potential energy differences between the rotational stationary points were found to change in the opposite direction. The contributions of the electron correlation energies at the MP2 level to the energy differences between the stationary points showed slower convergence than those of the HF energies and those of the electron correlation energies beyond the MP2 level. The addition of diffuse functions to the basis set utilized and the contributions of core-correlation did not significantly alter the estimates for the energy differences at the basis set limit. Our best estimate for the enthalpy difference at 298 K between the Z and E rotamers of MF was 5.21 kcal/mol, which is slightly larger than the upper edge of uncertainty of the experimentally derived value for enthalpy difference of 4.75 0.19 kcal/mol [7]. In accord with the findings of Wallington et al. [22], the estimates for the energy differences at the basis set limit have suggested that the Z/E energy difference, as well as the rotational barrier height, is significantly smaller for TFMF than for MF. This should be related with the fact that the differences in the magnitude of the dipole moments among the rotational stationary points are much smaller for TFMF than for MF.
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Acknowledgements T.U. would like to express his appreciation to Director Dr. Masaaki Yamabe, Director Dr. Kazuo Kitaura, and Deputy Director Dr. Masuhiro Mikami and the members of their group for their help and encouragement.
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