Ab initio analysis of the vibrational spectra of conformers of some branched alkanes

Journal of Molecular Structure 550–551 (2000) 67–91 www.elsevier.nl/locate/molstruc

Ab initio analysis of the vibrational spectra of conformers of some branched alkanes 夽 N.G. Mirkin, S. Krimm* Biophysics Research Division and Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA Received 25 June 1999; accepted 6 December 1999

Abstract A scaled ab initio HF/6-31G force field has been optimized that provides an accurate description of normal mode frequencies and eigenvectors of branched alkanes. This force field reproduces 159 observed non-CH stretch bands of 10 conformers of 2methylpropane, 2,2-dimethylpropane, 2-methylbutane, 2,2-dimethylbutane, and 3-methylpentane with an rms deviation of 6.1 cm ⫺1. A number of modes have been reassigned based on this vibrational analysis. The force field serves as the basis for the development of a spectroscopically accurate molecular mechanics energy function for saturated hydrocarbon chains. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Ab initio analysis; Vibrational spectra; Branched alkanes

1. Introduction In a previous paper [1] we developed scaled ab initio force fields for stable structures of n-pentane and n-hexane that could provide a detailed and accurate description of the normal mode frequencies and eigenvectors of the 14 conformers of these molecules. In this treatment, the rms deviation for 61 observed non-CH stretch (s) bands of all trans-n-pentane and nhexane was 4.8 cm ⫺1. Such force fields not only serve to provide more accurate analyses of the vibrational spectra of these molecules, but they are the basis for developing spectroscopically reliable molecular mechanics (MM) energy functions for macromolecules. This follows

夽 Dedicated to Professor James R. Durig on the occasion of his 65th birthday. * Corresponding author. Fax: ⫹ 1-734-764-3323. E-mail address: [email protected] (S. Krimm).

from our methodology of analytically transforming ab initio structures and scaled force fields into MM functions [2], producing what we call a spectroscopically determined force field (SDFF). We have in this way used the n-paraffin results [1] to produce an SDFF suitable for the polyethylene chain [3]. The present study is part of the program to produce SDFFs for the general (i.e. including branched) saturated hydrocarbon chain [4] as well as for hydrocarbon chains with olefinic unsaturation [5]. We have therefore selected for analysis branched alkanes with representative types of branching, viz. 2-methylpropane (isobutane), 2,2dimethylpropane (neopentane), 2-methylbutane (isopentane), 2,2-dimethylbutane, and 3-methylpentane. Their spectra have been re-analyzed, resulting in some infrared (IR) and Raman assignments that differ from those suggested by previous normal mode calculations based on empirical force fields. The overall reproduction of observed frequencies is very good, with an rms deviation for 159 non-CH s bands of 6.1 cm ⫺1.

0022-2860/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(00)00513-5

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Table 1 Local symmetry coordinate scale factors to HF/6-31G force constants for alkanes Symmetry coordinate a

Scale factor

CC s CH3 s CH2 s CH s CCC b CCH b CH3 sb CH3 ab CH3 r CH2 b CH2 r CH2 w CH2 tw CC t

0.873 0.830 0.813 0.830 0.829 0.767 0.760 0.779 0.775 0.773 0.790 0.772 0.788 0.997

a

s: stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, w: wag, tw: twist, t: torsion.

2. Calculations Ab initio calculations were performed with the gaussian 92 [6] and gaussian 94 [7] programs. For each molecule we obtained the optimized geometry and minimum energy at the Hartree–Fock (HF) level with 6-31G and 6-31G ⴱ basis sets, and at the secondorder Møller–Plesset perturbation level (MP2) with the 6-31G ⴱ basis set. The ab initio force constants in Cartesian coordinates were obtained by computing analytically the

Fig. 1. Stable conformer of 2-methylpropane (isobutane).

second derivatives of the energy at the optimized geometries with the HF/6-31G basis set. Our studies of the n-alkanes [1] showed that this basis set gave more accurate results (eigenvectors and interaction force constants) than HF/6-31G ⴱ and equivalent to MP2/6-31G ⴱ. Internal and local symmetry coordinates for each of the molecules followed our previous definitions [1], and normal mode calculations were carried out using the scaled ab initio force field at the optimized geometry. The HF ab initio calculated frequencies are significantly larger than the corresponding experimental values primarily due to neglect of contributions from electron correlation, and therefore it is necessary to scale the force field. We used the scale factors defined in terms of local symmetry coordinates that were obtained for the all-transpentane [1] based on well-established assignments. Additional scale factors were defined for those new coordinates specific to the branched alkanes (e.g. tertiary CH s and non-methyl group CCH bend (b)), and the whole set was then reoptimized for both linear and branched alkanes. The final scale factors in local symmetry coordinates, which are little changed from the earlier ones [1], are shown in Table 1.

3. Results and discussion 3.1. 2-Methylpropane (isobutane) There is one stable conformer of 2-methylpropane (isobutane) (see Fig. 1). Our MP2/6-31G ⴱ calculated barrier to internal rotation of the methyl groups, 3.85 kcal/mol, agrees satisfactorily with that obtained from microwave spectra [8] and from two thermodynamic results [9], 3.90, 3.62 and 3.87 kcal/mol. Isobutane has C3v symmetry and its 36 fundamental frequencies are distributed as follows: 8A1⫹4A2⫹ 12E. The A1 and E modes are both IR and Raman active, while the A2 fundamentals are forbidden in both Raman and IR. The observed and calculated symmetries, frequencies, and potential energy distributions (PEDs) are given in Table 2. The computed harmonic frequencies are in good agreement with the experimental data of Evans and Bernstein [10] and Snyder and Schachtschneider [11]. For the most part

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

69

Table 2 Observed and calculated frequencies (cm ⫺1) of 2-methylpropane (isobutane)

n (obs) Raman (liq.) c

IR (gas) c

2962

Symmetry a

Potential energy distribution b

2963

A1

2962

E

C3H3 as1(30) C7H3 as2(25) C11H3 as2(22) C11H3 as1(39) C7H3 as1(35) C7H3 as2(14) C11H3 as2(10)

2962 2956

E A2

2950

E

2950 2900

E A1

2891

E

2891

E

2881 1474

A1 A1

1467

E

1467

E

1454

E

1454

E

1449

A2

1389

A1

1366

E

1366 1327

E E

C11H3 sb(53) C7H3 sb(52) C3C2H b(43) C2C3 s(11) C7C2H b(11) C11C2H b(11)

1327 1191

E A1

1176

E

C7C2H b(33) C11C2H b(33) C3H3 rl(20) C7H3 r2(15) C11H3 r2(15) C2C3 s(18) C7H3 r1(16)

1176

E

IR (solid) d 2965

2958

n (calc)

2958 C3H3 as2(65) C7H3 as1(17) C3H3 as2(35) C7H3 as1(25) C11H3 as1(25) C7H3 as2(40) C11H3 as2(33) C11H3 as1(16)

2951 2907

2904

2889

2869

C3H3 C7H3 C3H3 C7H3

as1(66) C11H3 as2(16) ss(33) C11H3 ss(33) ss(32) ss(50) C11H3 ss(50)

2887

2880 1477

1468

2871 1475

C3H3 ss(67) C7H3 ss(16) C11H3 ss(16) C2H s(94) C3H3 ab1(31) C7H3 ab2(23) C11H3 ab2(23) C3H3 ab2(58) C7H3 ab1(14) C11H3 ab2(12)

1468

1450

C11H3 ab1(36) C7H3 ab1(31) C7H3 ab2(17) C3H3 ab1(61) C11H3 ab2(17) C7H3 ab1(12)

1459

1394

1373

2904

1371

1389

C7H3 ab2(40) C11H3 ab2(30) C11H3 ab1(18) C3H3 ab2(33) C7H3 ab1(25) C11H3 ab1(25) C3H3 sb(34) C7H3 sb(34) C11H3 sb(34) C3H3 sb(70) C7H3 sb(18) C11H3 sb(17)

1365

1327

1330

1330

1184

1177

1189

1169

1166

1173 C3H3 r2(22) C2C11 s(13) C2C7 s(13)

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N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 2 (continued)

n (obs) Raman (liq.) c

n (calc) IR (gas) c

966

917

Symmetry a

Potential energy distribution b

963

E

C2C3 s(35) C7H3 r1(14) C3H3 r1(10) C11H3 r2(10)

963

E

939

A2

909

E

C2C7 s(26) C2C11 s(26) C3H3 r2(16) C7H3 r2(11) C3H3 r2(34) C7H3 r1(26) C11H3 r1(26) C3H3 r1(48) C7H3 r2(19) C11H3 r1(16) C3C2H b(12)

909

E

IR (solid) d

961

918

913

799

797

796

788

A1

433

426

433

425

A1

364

E

364

E

272

E

272 224

E A2

367

C11H3 r2(35) C7H3 r2(19) C7H3 r1(18) C2C3 s(28) C2C7 s(28) C2C11 s(28) C3C2C7 b(12) C3C2C11 b(12) C7C2C11 b(12) C3C2H b(10) C7C2H b(10) C11C2H b(10) C3C2C7 b(37) C3C2C11 b(37) C3H3 r2(10)

367 C7C2C11 b(49) C3C2C11 b(12) C3C2C7 b(12) C2C3 t(57) C2C7 t(14) C2C11 t(14)

280 e 225 e

C2C7 t(43) C2C11 t(43) C2C7 t(43) C2C3 t(43) C2C11 t(43)

a

Symmetry species. Contributions ⱖ 10. See Fig. 1 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, t: torsion. c From Ref. [10]. d From Ref. [11]. e From Ref. [8]. b

we agree with their assignments, with the following exceptions. Snyder and Schachtschneider (SS) assign the tertiary CH s mode, to a band at 2904 cm ⫺1. Several arguments do not lend support to this assignment, and in agreement with others [12] we also do not follow it. For example, CH3 to CD3 deuteration experiments [13] show that this mode in isobutane is at 2869 cm ⫺1 in the liquid and at 2880 cm ⫺1 in the gas, shifting to 2887 and 2896 cm ⫺1, respectively, in the (CD3)3CH molecule (an effect due to the change in physical state and changes in Fermi resonance

interactions [14]). Furthermore, 2,2,3,3-tetramethylbutane has a band at 2906 cm ⫺1 [11] even though it has no tertiary CH group, making it unreasonable to assign this band to CH s in isobutane. The scale factor of 0.830 for the CH s force constant was chosen based on the frequency in the (CD3)3CH molecule because it has a pure CH s mode (this being a mixed mode in other molecules) and there is no possibility of Fermi resonances with CCH bend modes (which are near 1300 cm ⫺1). Choosing the liquid frequency of 2887 cm –1 for this mode, we calculate the CH s mode in (CH3)3CH at 2881 cm ⫺1. We attribute the

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91 Table 3 Observed and calculated frequencies (cm ⫺1) of isobutane-d1 [(CH3)3CD]

n (obs) a Raman (liq.)

n (calc)

Symmetry b

Potential energy distribution c

2962

E

2962

E A1

C11H3 as1(41) C7H3 as1(33) C7H3 as2(17) C3H3 as2(64) C7H3 as1(17) C3H3 as1(32) C11 H3 as2(26) C7H3 as2(25)

2962

A2

2950

E

2950 2899

E A1

2891 2891

E E

2125 1473

A1 A1

1466

E

1466

E

1454

E

1454

E

1449

A2

1389

A1

1366

E

1366 1242

E E

C11H3 sb(53) C7H3 sb(52) C2C3 s(30) C11H3 r1(13) C3C2D b(1) C7H3 r1(10)

1242

E

1174

A1

1064

E

C2C7 s(23) C2C11 s(23) C3H3 r2(20) C3H3 r1(21) C7H3 r2(16) C11H3 r2(16) C3H3 r1(33) C7H3 r1(14) C11H3 r2(14) C3C2D b(12)

1064

E

941

E

IR (gas)

2956

2903

2146

2904

2152 1477

C3H3 as2(35) C7H3 as1 (25) C11H3 as1(25) C7H3 as2(40) C11H3 as2(33) C11H3 as1(16) C3H3 as1(66) C11H3 as2(16) C7H3 ss(34) C11H3 ss(34) C3H3 ss(32) C7H3 ss(50) C11H3 ss(50) C3H3 ss(67) C7H3 ss(16) C11H3 ss(16) C2D s(100) C3H3 ab1(31) C7H3 ab2(23) C11H3 ab2(23) C3H3 ab2(59) C11H3 ab1(12) C11H3 ab2(12) C7H3 ab1(11)

1463 C7H3 ab1(34) C11H3 ab1(34) C7H3 ab2(17) C3H3 ab1 (63) C11H3 ab2(18) C7H3 ab1(10)

1450

1380

1358

1229

1166

1390

C7H3 ab2(40) C11H3 ab2(30) C11H3 ab1(17) C3H3 ab2(33) C7H3 ab1(25) C11H3 ab1(25) C3H3 sb(34) C7H3 sb(34) C11H3 sb(34) C3H3 sb(70) C7H3 sb(18) C11H3 sb(17)

1367

1233

1065 C7H3 r2(26) C11H3 r1(14) C11H3 r2(13) C2C7 s(30) C2C11 s(27) C3H3 r2(21)

71

72

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Table 3 (continued)

n (obs) a Raman (liq.) 944

813

n (calc)

Symmetry b

Potential energy distribution c

941

E

939

A2

802

E

C2C3 s(38) C11H3 r1(15) C2C11 s(11) C3H3 r2(34) C7H3 r1(26) C11H3 r1(26) C3C2D b(43) C3H3 r1(26) C11C2D b(11) C7C2D b(10)

802

E

IR (gas) 942

812

796

793

784

A1

426

432

420

A1

362

E

362

E

272

E

272 224

E A2

C7C2D b(33) C11C2D b(31) C11H3 r2(17) C7H3 r2(12) C2C3 s(28) C2C7 s(28) C2C11 s(28) C3C2C7 b(12) C3C2C11 b(12) C7C2C11 b(12) C3C2D b(10) C7C2D b(10) C11C2D b(10) C3C2C7 b(37) C3C2C11 b(36) C3H3 r2(10)

370 C7C2C11 b(49) C3C2C11 b(13) C3C2C7 b(12) C2C3 t(57) C2C7 t(14) C2C11 t(14) C2C7 t(43) C2C11 t(43) C2C7 t(43) C2C3 t(43) C2C11 t(43)

a

From Ref. [10]. Symmetry species. c Contributions ⱖ 10. See Fig. 1 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, t: torsion. b

shift to the observed band at 2869 (2871 [11]) cm ⫺1 to the proposed Fermi resonance [10] with the overtone of a CH3 bend mode. As we will see below, this scale factor for the CH s force constant yields calculated frequencies for the CH s mode that are also in excellent agreement with observed frequencies in 2methylbutane and 3-methylpentane. In the CH3 bend region, our calculations support assigning the higher of the calculated CH3 antisymmetric bends (ab), 1474 cm ⫺1, to an A1 mode [10]. This assignment differs from that of SS [11], who assign it to an E mode. This is also true of the observed frequency at 966 cm ⫺1, which we calculate at 963 cm ⫺1, and assign to an E mode, whereas Wilmshurst and Bernstein [13] assign it to an A1 mode. The

low frequency modes, calculated at 272 and 224 cm ⫺1, are in good agreement with the values estimated by Lide and Mann [8] from the relative intensities of microwave satellite lines, 280 ^ 20 and 225 ^ 20 cm ⫺1. There is extensive experimental data on deuterated isotopomers of isobutane, viz. (CH3)3CD [10], (CD3)3CH [13], and (CD3)3CD [13], and we have therefore calculated and assigned the modes of these molecules. The results are presented in Tables 3–5, and it can be seen that the observed and calculated values agree very well. However, we find that these assignments are often in disagreement with those previously proposed [10,13], with respect to assignment of fundamentals, character of the normal modes,

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91 Table 4 Observed and calculated frequencies (cm ⫺1) of isobutane-d9 [(CD3)3CH]

n (obs) a Raman (liq.)

IR (gas)

2887

2896

n (calc)

Symmetry b

Potential energy distribution c

2887 2194

A1 E

C2H s(101) C11D3 as1(40) C7D3 as1(36) C7D3 as2(14) C11D3 as2(11)

2194

E

2189

A1

2188

A2

2185

E

2185

E

2084

A1

2078 2078

E E

1303

E

C3D3 as2(66) C7D3 as1(15) C11D3 as1(11) C3D3 as1(32) C7D3 as2(26) C11D3 as2(26) C3D3 as2(35) C7D3 as1(25) C11D3 as1(25) C7D3 as2(39) C11D3 as2(36) C11D3 as1(14) C7D3 as1(11) C3D3 as1(69) C11D3 as2(14) C7D3 as2(10) C7D3 ss(34) C11D3 ss(34) C3D3 ss(32) C7D3 ss(50) C11D3 ss(50) C3D3 ss(68) C7D3 ss(16) C11D3 ss(16) C3C2H b(50) C2C3 s(14) C7C2H b(13) C11C2H b(13)

1303

E

1149

E

1149

E

1110

A1

1062

A1

1059 1059

E E

1052

E

1052

E

1048

A2

1032

A1

1003

E

1003

E

2219

2212

2082

1312

1152

2076

1315

1153

1122

1064

C7C2H b(38) C11C2H b(38) C2C7 s(11) C2C11 s(11) C2C3 s(40) C3D3 sb(22) C2C11 s(10) C2C7 s(10)

1071

C2C7 s(30) C2C11 s(30) C7D3 sb(17) C11D3 sb(17) C7D3 sb(23) C11D3 sb(23) C3D3 sb(22) C2C11 s(11) C2C3 s(11) C2C7 s(11) C3D3 ab1(33) C11D3 ab2(25) C7D3 ab2(24) C3D3 ab2(66) C11D3 ab1(16) C7D3 ab1(40) C11D3 ab1(34) C11D3 ab2(13) C7D3 ab2(12)

1052 C3D3 ab1(64) C7D3 ab2(14) C11D3 ab2(10) C11D3 ab2(38) C7D3 ab2(34) C7D3 ab1(13) C11D3 ab1(11) C3D3 ab2(34) C7D3 ab1(25) C11D3 ab1(25) C3D3 r1(14) C7D3 r2(11) C11D3 r2(11) C3D3 sb(41) C7D3 sb(11) C11D3 sb(10) C7D3 sb(31) C11D3 sb(31) C3D3 r2(10)

73

74

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 4 (continued)

n (obs) a Raman (liq.)

797

705

n (calc)

Symmetry b

Potential energy distribution c

789

E

C3D3 r2(27) C2C11 s(12) C2C7 s(12) C11D3 r1(12) C7D3 r2(11)

789

E

710

A2

703

E

C7D3 r1(21) C2C3 s(16) C11D3 r2(12) C11D3 r1(10) C3D3 r2(35) C11D3 r1(27) C7D3 r1(26) C3D3 r1(57) C7D3 r2(20) C11D3 r1(15)

703

E

IR (gas)

798

708

692

691

682

A1

359

360

352

A1

303

E

303

E

196

E

196 159

E A2

C11D3 r2(40) C7D3 r2(25) C7D3 r1(19) C2C3 s(21) C2C7 s(21) C2C11 s(21) C3D3 r1(12) C3C2C7 b(11) C3C2C11 b(11) C7C2C11 b(11) C3C2C7 b(36) C3C2C11 b(35) C3D3 r2(16)

306 C7C2C11 b(48) C3C2C11 b(12) C3C2C7 b(12) C7D3 r1(10) C2C3 t(58) C2C7 t(15) C2C11 t(14) C2C11 t(44) C2C7 t(43) C2C7 t(43) C2C3 t(43) C2C11 t(43)

a

From Ref. [13]. Symmetry species. c Contributions ⱖ 10. See Fig. 1 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, t: torsion. b

and correspondence between bands of different isotopomers. The self-consistency of our results over the set of branched molecules using the same scale factors suggests that the current assignments are the most reliable. 3.2. 2,2-Dimethylpropane (neopentane) Neopentane has only one stable conformer, a staggered conformation (t (H4C1C2C3) ⬃ 180⬚) with Td symmetry (see Fig. 2); there is also a transition state, an eclipsed conformation …t ⬃ 120⬚†; with C3v symmetry. The calculated relative energy of the two states is 4.13 (HF/6-31G), 4.25 (HF/6-31G ⴱ) and 4.41 (MP2/6-31G ⴱ) kcal/mol. The symmetric barriers for methyl group rotation in neopentane have been

obtained experimentally by several different methods: 4.29 kcal/mol, derived from combination bands of gas phase IR spectra [15]; 4.3 kcal/mol, derived from the low frequency modes of molecular crystals [16]; 4.4 kcal/mol, from thermodynamic measurements [9]; and 5.20 and 5.03 kcal/mol, from cold-neutron scattering studies [17,18]. The MP2/6-31G ⴱ value for this barrier, 4.41 kcal/mol, is in good agreement with the experimental values. The isolated neopentane molecule has 45 normal modes of vibration distributed as follows: 3A1 ⫹ A2 ⫹ 4E ⫹ 4F1 ⫹ 7F2. The A1 and E vibrations are only Raman active, the F2 modes are both Raman and IR active, and the A2 and F1 modes are forbidden in both Raman and IR. Table 6 shows the observed and calculated frequencies, and the corresponding

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91 Table 5 Observed and calculated frequencies (cm ⫺1) of isobutane-d10 [(CD3)3CD]

n (obs) a Raman (liq.)

2217

Symmetry b

Potential energy distribution c

2194

E

2194

E

2193

A1

2189

A2

2185

E

2185

E

2123 2084

A1 A1

2078

E

C11D3 as1(40) C7D3 as1(35) C7D3 as2(15) C11D3 as2(10) C3D3 as2(66) C7D3 as1(15) C11D3 as1(11) C3D3 as1(31) C11D3 as2(25) C7D3 as2(24) C3D3 as2(35) C7D3 as1(25) C11D3 as1(25) C7D3 as2(39) C11D3 as2(36) C11D3 as1(14) C7D3 as1(11) C3D3 as1(68) C11D3 as2(14) C7D3 as2(11) C2D s(95) C7D3 ss(33) C11D3 ss(33) C3D3 ss(32) C7D3 ss(50) 11D3 ss(50)

2078

E

1206

E

IR (gas)

2216

2073

2063

n (calc)

2067

1209

1208

1117

1118

1206 1104

E A1

1068

1062

A1

1060

E

1060

E

1055 1055

E E

1048

A2

1046

E

1046 1015

E A1

907

E

907

E

781

E

1056

786

C2C7 s(39) C2C11 s(39) C3D3 sb(26) C7D3 sb(26) C11D3 sb(26) C2C3 s(10) C2C7 s(10) C2C11 s(10) C3D3 ab1(33) C7D3 ab2(24) C11D3 ab2(24) C3D3 ab2(64) C7D3 ab1(13) C11D3 ab1(11) C11D3 ab1(37) C7D3 ab1(35) C7D3 ab2(14) C11D3 ab2(10)

1056

1020

918

C3D3 ss(68) C7D3 ss(16) C11D3 ss(16) C2C3 s(52) C2C7 s(13) C2C11 s(13) C3C2D b(11)

C3D3 ab1(58) C11D3 ab2(14) C7D3 ab2(36) C11D3 ab2(30) C11D3 ab1(14) C3D3 ab2(34) C7D3 ab1(25) C11D3 ab1(25) C3D3 sb(47) C7D3 sb(12) C11D3 sb(12) C7D3 sb(35) C11D3 sb(35) C3D3 r1(16) C7D3 r2(12) C11D3 r2(12) C3C2D b(25) C3D3 r1(12)

920

789

C7C2D b(19) C11C2D b(18) C7D3 r2(11) C3D3 r2(27) C2C7 s(15) C2C11 s(14)

75

76

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 5 (continued)

n (obs) a Raman (liq.)

690

345

n (calc)

Symmetry b

Potential energy distribution c

781

E

710

A2

681

A1

674

E

674

E

349

A1

302

E

C2C3 s(20) C7D3 r1(18) C11D3 r1(13) C3D3 r2(35)C7D3 r1(27) C11D3 r1(27) C2C3 s(21) C2C7 s(21) C2C11 s(21) C3D3 r1(52) C3C2D b(18) C7D3 r2(17) C11D3 r1(12) C11D3 r2(35) C7D3 r2(24) C7D3 r1(17) C7C2D b(14) C11C2D b(13) C3C2C7 b(11) C3C2C11 b(11) C7C2C11 b(11) C3D3 r1(11) C3C2C11 b(36) C3C2C7 b(35) C3D3 r2(15)

302

E

196

E

196 159

E A2

IR (gas)

687

359

304 C7C2C11 b(48) C3C2C11 b(12) C3C2C7 b(12) C7D3 r1(10) C2C3 t(58) C2C7 t(14) C2C11 t(14) C2C7 t(43) C2C11 t(43) C2C7 t(43) C2C3 t(43) C2C11 t(43)

a

From Ref. [13]. Symmetry species. c Contributions ⱖ 10. See Fig. 1 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, t: torsion. b

PEDs and symmetry species. The experimental frequencies come from IR studies of gaseous [15,19–22], crystalline [16], solid [11,22,23], and solution [22] samples, Raman spectra [20,24,25], and inelastic neutron scattering spectra [17,18,26] (for which, of course, optical selection rules do not apply). There are also various normal mode calculations reported in the literature using empirical force fields [11,26–29] and one with an unscaled ab initio 631G ⴱ force field [30]. Together with some vapor phase band contours, most of the vibrational modes have been assigned with certainty. However, there still are a few discrepancies. There are three predicted Raman active A1 modes and there is no problem with such an assignment of the CC s and CH3 symmetric stretch (ss) modes to the observed Raman bands at 733 and 2909 cm ⫺1, respectively. (The

reason for the apparently observed IR 733 cm ⫺1 band [15,19,23], expected to be inactive, as well as the observed IR 2907 cm ⫺1 band [19,21–23] is unclear.) The A1 mode corresponding to a CH3 symmetric bend (sb) has not been observed. We calculate it at 1392 cm ⫺1. Other normal mode calculations have obtained values of 1368 [11] and 1381 cm ⫺1 [19]. The A2 torsional mode is optically inactive, but could be observed by neutron scattering. In fact, such a band has been observed at 218 cm ⫺1 [26], which is consistent with our calculated value of 212 cm ⫺1. This mode has also been observed, at 221 cm ⫺1 [16], in far IR spectra of solid neopentane, in which the selection rule is relaxed because the molecule is on a site of lower symmetry in the crystal. This band shifts to 157 cm ⫺1 in neopentaned12 [16], in good agreement with our calculated value of 150 cm ⫺1.

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91 Table 6 Observed and calculated frequenceis (cm ⫺1) of neopentane

n (obs) IR c (gas)

IR d (solid)

2961

Symmetry a

Potential energy distribution b

2949

F2

2949

F2

2949

F2

2939

E

C1H3 as1(33) C7H3 as2(25) C11H3 as2(25) C3H3 as1(37) C11H3 as1(17) C7H3 as1(17) C11H3 as2(13) C7H3 as2(13) C1H3 as2(37) C3H3 as2(37) C11H3 as1(13) C7H3 as1(13) C1H3 as1(26) C3H3 as1(26) C11H3 as1(25) C7H3 as1(25)

2939

E

2938

F1

2938

F1

2938

F1

Raman e (gas)

2962

2953

n (calc)

2955 f

2907

2909 g

2909 f

2889

A1

2877

2877

2876

2877 2877

F2 F2

2877 1471

F2 F2

1471

F2

1471

F2

1451

E

1451

E

1445

F1

1445

F1

1445

F1

1392

A1

1361 1361

F2 F2

1361 1260

F2 F2

1260

F2

1477

1455 h

1375

1256

1472

1451 g

1361

1253

C7H3 as2(28) C11H3 as2(28) C1H3 as2(22) C3H3 as2(22) C11H3 as1(38) C7H3 as1(37) C3H3 as2(14) C1H3 as2(13) C1H3 as1(38) C3H3 as1(38) C7H3 as2(13) C11H3 as2(12) C1H3 as2(29) C3H3 as2(28) C11H3 as2(22) C7H3 as2(22) C1H3 ss(25)C7H3 ss(25) C11H3 ss(25) C3H3 ss(25) C7H3 ss(50) C11H3 ss(50) C1H3 ss(26) C7H3 ss(25) C11H3 ss(25) C3H3 ss(25) C3H3 ss(51) C1H3 ss(49) C7H3 ab1(24) C3H3 ab1(24) C11H3 ab1(21) C1H3 ab1(21) C1H3 ab2(34) C3H3 ab2(34) C11H3 ab1(13) C7H3 ab1(10) C7H3 ab2(34) C11H3 ab2(34) C1H3 ab1(13) C3H3 ab1(10) C7H3 ab1(25) C11H3 ab1(25) C3H3 ab1(25) C1H3 ab1(24)

1458

1370

1258

C1H3 ab2(25) C3H3 ab2(25) C11H3 ab2(24) C7H3 ab2(24) C1H3 ab1(37) C3H3 ab1(37) C11H3 ab2(13) C7H3 ab2(12) C3H3 ab2(27) C7H3 ab2(25) C11H3 ab2(24) C1H3 ab2(23) C7H3 ab1(37) C11H3 ab1(37) C1H3 ab2(14) C3H3 ab2(10) C1H3 sb(25) C7H3 sb(25) C11H3 sb(25) C3H3 sb(25) C3H3 sb(53) C1H3 sb(52) C1H3 sb(27) C11H3 sb(27) C7H3 sb(26) C3H3 sb(25) C7H3 sb(53) C11H3 sb(52) C2C3 s(20) C1C2 s(19)C7H3 r2(15) C11H3 r2(15) C1C2 s(10) C2C3 s(10) C2C7 s(10) C2C11 s(10) C1H3 r1(10) C7H3 r1(10) C11H3 r1(10) C3H3 r1(10)

77

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Table 6 (continued)

n (obs) IR c (gas)

IR d (solid)

n (calc)

Symmetry a

Potential energy distribution b

1260

F2

1055

E

C2C7 s(20) C2C11 s(20) C1H3 r2(15) C3H3 r2(15) C1H3 r1(19) C7H3 r1(19) C11H3 r1(19) C3H3 r1(19)

1055

E

933

F1

933

F1

933

F1

913

F2

913

F2

913

F2

Raman e (gas)

1060 i C1H3 r2(19) C7H3 r2(19) C11H3 r2(19) C3H3 r2(19) C7H3 r1(38) C11H3 r1(38) C1H3 r2(15) C3H3 r2(11)

940 i

926

923

927

733 j

733 g

733

719

A1

416 j

414 g

414 f

414 414

F2 F2

414

F2

325

E

325

E

283

F1

283 283 212

F1 F1 A2

335 j

335 g

280 i 218 i a

C1H3 r1(38) C3H3 r1(38) C11H3 r2(13) C7H3 r2(12) C3H3 r2(28) C7H3 r2(26) C11H3 r2(25) C1H3 r2(23) C2C3 s(34) C1C2 s(29) C7H3 r2(13) C11H3 r2(13) C1C2 s(19) C2C7 s(16) C2C11 s(16)C2C3 s(13) C2C7 s(32) C2C11 s(32) C1H3 r2(13) C3H3 r2(13) C1C2 s(22) C2C3 s(22) C2C7 s(22) C2C11 s(22) C1C2C3 b(33) C7C2C11 b(33) C1C2C7 b(17) C3C2C11 b(17) C3C2C7 b(16) C1C2C11 b(16) C1C2C11 b(17) C3C2C7 b(17) C1C2C7 b(16) C3C2C11 b(16) C1C2C3 b(31) C7C2C11 b(31)

334 C1C2C7 b(23) C1C2C11 b(23) C3C2C7 b(23) C3C2C11 b(23) C2C3 t(34) C2C11 t(22) C2C7 t(21) C1C2 t(12) C2C7 t(45) C2C11 t(45) C1C2 t(55) C2C3 t(34) C1C2 t(39) C2C3 t(39) C2C7 t(39) C2C11 t(39)

Symmetry species. Contributions ⱖ 10. See Fig. 2 for atom numbering. Symmetry coordinates follow our previous definitions [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, t: torsion. c From Ref. [21], unless otherwise noted. d From Ref. [11], unless otherwise noted. e From Ref. [25], unless otherwise noted. f From Ref. [20]. g From Ref. [23]. h From Ref. [19]. i From Ref. [26]. j From Ref. [15]. b

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

79

Fig. 2. Stable conformer of 2,2-dimethylpropane (neopentane).

There are four predicted doubly degenerate Raman active E modes. Bands at about 1455 and 335 cm ⫺1 (calculated at 1451 and 325 cm ⫺1) are observed in the Raman [20,24,25]. (Weiss and Leroi [15] and Young et al. [19] also observe a band at 335 cm ⫺1 in the IR, although this mode is expected to be IR inactive.) Several authors [19,25,27,30] assign an observed

band at 925 cm ⫺1 to the E species, corresponding to a CH3 rock (r) mode. However, our calculated frequency for this mode is 1055 cm ⫺1 which would agree with a band at 1060 cm ⫺1 observed by neutron scattering (and Raman) [26], and we prefer this assignment. The calculated 2939 cm ⫺1 CH3 as mode is best assigned to the 2955 cm ⫺1 band (see below)

Fig. 3. Stable conformers of 2-methylbutane (isopentane).

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N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 7 Relative energies (kcal/mol) and main torsion angles (⬚) of conformers of 2-methylbutane (isopentane) with different basis sets HF/6-31Gⴱ

HF/6-31G

trans gauche a b

MP2/6-31G ⴱ

t1 a

t2 b

DE

t1 a

t2 b

DE

t1 a

t2 b

DE

172.4 ⫺63.0

⫺64.0 63.1

0.0 0.91

172.9 ⫺63.2

⫺63.4 63.2

0.0 0.92

174.8 ⫺61.7

⫺62.7 62.9

0.0 0.80

t 1: C1C2C3C4 (see Fig. 3). t 2: C9C2C3C4 (see Fig. 3).

(discrepancies may be larger in this region because of Fermi resonances). The F1 modes are expected to be optically inactive, but the torsion mode is clearly observed at 280 cm ⫺1 by neutron scattering [26], in good agreement with our calculated value of 283 cm ⫺1. Far IR measurements [16] place it at 281 cm ⫺1, and it has also been estimated at 282 cm ⫺1 [15]. In the deuterated species, it shifts to 206 cm ⫺1, in good agreement with our calculated value of 202 cm ⫺1. The assignment of the CH3 r F1 mode has been the subject of controversy because of the expected presence of E and F2 modes in this region. If we accept the 1060 (E) cm ⫺1 assignment, then our calculations indicate that the observed 940 cm ⫺1 neutron scattering peak [26] should be assigned to the F1 mode, leaving the observed Raman and IR band at ⬃926 cm ⫺1 to be assigned to the F2 CC s mode. This would agree with assignments

proposed by some authors [9,11,20,26] although it would be in disagreement with those of others [19,25,27,28,30]. We think the present assignment is more compelling given the internal consistency of our ab initio calculations for the set of branched molecules. The F1 CH3 ab mode is difficult to assign, probably because its calculated value, 1445 cm ⫺1, is expected to fall close to that of the E mode at 1451 cm ⫺1, but the broad neutron scattering peak at 1451 cm ⫺1 [26] may contain contributions from this mode. The remaining F2 modes are assignable without ambiguity, except for some controversy about the CH3 as modes. Our assignment of the 2962 cm ⫺1 IR active band to the F2 mode, with the 2955 cm ⫺1 band being assigned to the E species, is accepted by most authors [11,19,26–28,30], although one group [25] assigns the former to E and/or F2.

Fig. 4. MP2/6-31Gⴱ rotational barrier for 2-methylbutane (isopentane), trans (175⬚, ⫺63⬚) ! gauche (⫺62⬚, 63⬚).

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

81

Table 8 Observed and calculated frequencies (cm ⫺1) of 2-methylbutane (isopentane)

n (obs) IR a (solid)

n (calc) Raman b (liquid)

2969

2962

2962

2952

2952 2938

2947 2944 2942

2926

2935

2908 2891 e 2883 e

2891 2886 2884 2878 2871 2855 1475 1469

2875 2852 1475

1466

1462

1466 1463 1460

1455

1455

1384 1377 1366 1351 1337

1381

1298 1268

1299 1269

1176 1149

1176 1149 1140

1368 1339

1037

1448 1384 1377 1366 1351 1337 1298 1269 1188 1179 1154

1042 1030

1011

969

1014

974

1015

968

trans

gauche

Potential energy distribution c

n (calc)

Symmetry d

C9H3 as2(42) C4H3 as2(31) C4H3 as1(12) C9H3 as1(11) C4H3 as2(39) C9H3 as2(29) C9H3 as1(12) C4H3 as1(10) C1H3 as1(67) C9H3 as1(21) C1H3 as2(44) C4H3 as1(32) C4H3 as1(43) C1H3 as2(23) C4H3 as2(22) C9H3 as1(42) C1H3 as2(25) C1H3 as1(23) C9H3 as2(11) C3H2 as(45) C4H3 ss(34) C2H s(12) C4H3 ss(34) C3H2 as(26) C9H3 ss(23) C9H3 ss(43) C4H3 ss(29) C1H3 ss(21) C1H3 ss(70) C9H3 ss(28) C2H s(74) C3H2 as(19) C3H2 ss(92) C9H3 ab1(49) C4H3 ab2(19) C4H3 ab1(38) C1H3 ab1(17) C4H3 ab2(14) C3H2 b(12) C9H3 ab2(33) C1H3 ab2(22) C1H3 ab1(17) C4H3 ab2(44) C1H3 ab2(25) C4H3 ab1(19) C3H2 b(25) C1H3 ab2(23) C9H3 ab2(22) C4H3 ab1(12) C9H3 ab1(31) C1H3 ab1(27) C1H3 ab2(15) C4H3 ab2(12) C3H2 b(45) C9H3 ab2(24) C1H3 ab1(18) C9H3 sb(50) C1H3 sb(41) C4H3 sb(94) C1H3 sb(52) C9H3 sb(49) C3H2 w(58) C1C2H b(13) C2C3 s(10) C9C2H b(30) C3C2H b(22) C3H2 tw(16) C2C3 s(26) C3H2 w(24) C3C2H b(22) C1C2H b(35) C3H2 w(26) C3C2H b(11) C3H2 tw(52) C4H3 r2(10) C3H2 r(17) C4H3 r2(14) C2C3 s(12) C1H3 r2(15) C2C9 s(12) C9H3 r1(10) C1C2 s(21) C9H3 r2(14) C4H3 r1(11) C4H3 r1(16) C1H3 r2(15) C9H3 r2(15) C3C4 s(11) C3C4 s(63) C4H3 r1(28) C2C3 s(14) C3H2 w(11) C9H3 r1(10) C1H3 r1(10) C4H3 r1(24) C1C2 s(14) C3H2 tw(24) C4H3 r2(22) C1C2 s(21) C2C9 s(21) C3C4 s(43) C4H3 r1(15) C9H3 r2(13) C1H3 r2(13) C3C2H b(11) C4H3 r2(18) C3H2 tw(16) C1H3 r1(16) C4H3 r1(15) C3C2H b(13)

2961

A 00

2956

A0

2946 2945 2944

A0 A 00 A 00

2940

A0

2896 2887 2886 2882 2877 2855 1473 1472

A0 A0 A 00 A 00 A0 A0 A0 A 00

1470

A0

1469

A0

1457

A 00

1453

A 00

1451 1385 1378 1367 1356 1341 1315

A0 A0 A0 A 00 A0 A 00 A0

1271 1191 1173

A 00 A0 A 00

1142

A0

1028

A0

1005

A 00

986

A0

82

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 8 (continued)

n (obs) IR a (solid)

n (calc) Raman b (liquid)

952 917 910

949 920 910

951 912 906

796

796

789

764

764

756

757 f 530 e 459

368

462

452

415

411

366

366 274 266

246

234

120

222 97

trans

gauche

Potential energy distribution c

n (calc)

Symmetry d

C9H3 r2(33) C1H3 r1(27) C1C2 s(13) C1H3 r2(46) C9H3 r1(34) C1C2 s(20) C2C9 s(20) C3C4 s(12) C2C3 s(12) C9H3 r2(12) C3H2 r(34) C4H3 r2(27) C2C3 s(14) C3H2 r(60) C4H3 r2(44) C3H2 r(27) C2C3 s(21) C2C9 s(19) C4H3 r2(14) C2C3 s(42) C1C2 s(17) C2C9 s(17) C2C3C4 b(38) C4H3 r1(11) C3C2C9 b(10) C1C2C3 b(10) C2C3C4 b(24) C1C2C9 b(14) C1C2C3 b(11) C3C2C9 b(41) C2C3C4 b(13) C1C2C3 b(33) C3C2C9 b(33) C3C4 t(15) C1C2C9 b(38) C1C2C3 b(20) C2C9 t(36) C3C4 t(19) C1C2 t(37) C2C3C4 b(27) C3C2C9 b(12) C2C9 t(41) C1C2 t(40) C2C3C4 b(11) C1C2 t(50) C2C3C4 b(23) C1C2C3 b(16) C3C4 t(12) C2C9 t(51) C3C4 t(50) C2C3 t(123) C3C4 t(21) C2C9 t(15)

952 912 897

A 00 A 00 A0

774

A 00

746 528

A0 A0

373

A 00

369 271 267

A0 A 00 A0

266

A0

215 93

A 00 A 00

a

From Ref. [11], unless otherwise noted. From Ref. [36], unless otherwise noted. c Potential energy distribution (contributions ⱖ 10) for trans conformer. When no trans band is given, the PED is for the gauche conformer. See Fig. 3 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, w: wag; tw: twist, t: torsion. d Symmetry species. e From Ref. [21], IR (gas). f From Ref. [31], Raman (gas). b

3.3. 2-Methylbutane (isopentane) 2-Methylbutane (isopentane) has two stable conformations with respect to the t 1(C1C2C3C4) and t 2(C9C2C3C4) torsion angles. These are trans (180⬚, ⫺60⬚) and gauche (⫺60⬚, 60⬚), with C1 and Cs symmetry, respectively (see Fig. 3). The relative energies (at the minima) of the two stable conformers, calculated at HF/6-31G, HF/631G ⴱ and MP2/6-31G ⴱ levels, are given in Table 7. At the Hartree–Fock level, expansion of the basis set from 6-31G to 6-31G ⴱ does not produce a significant change in the relative energies of the conformers.

The inclusion of electron correlation decreases the trans–gauche difference from ⬃0.92 to 0.80 kcal/ mol. From careful analysis of vapor phase Raman spectra, Verma et al. [31] obtained an energy difference between the C1 and Cs conformers of 809 ^ 50 cal/mol, in good agreement with our MP2/6-31G ⴱ level calculation. This energy difference indicates that at room temperature the concentration of trans-isopentane is about four times that of the gauche conformer. It is interesting to compare this to the trans–gauche energy difference in n-butane, which is given by recent calculations as 0.57 [32], 0.59 [33], and 0.62 kcal/mol [34], compared to an

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

83

Table 9 Comparison of some calculated frequencies (cm ⫺1) and potential energy distributions for trans and gauche 2-methylbutane (isopentane) trans a 1475 1460 1298 1188 1179 1154 1042 1015 968 756 452 411 274 266 234 222

gauche a

C9H3 ab1(49) C4H3 ab2(19) C3H2 b(25) C1H3 ab2(23) C1C2H b(35) C3H2 w(26) C3H2 r(17) C4H3 r2(14) C1H3 r2(15) C2C9 s(12) C1C2 s(21) C9H3 r2(14) C3C4 s(63) C4H3 r(24) C1C2 s(14) C4H3 r2(18) C3H2 tw(16) C3H2 r(27) C2C3 s(21) C2C3C4 b(24) C1C2C9 b(14) C3C2C9 b(41) C2C3C4 b(13) C2C9 t(36) C3C4 t(19) C1C2 t(37) C2C3C4 b(27) C1C2 t(50) C2C3C4 b(23) C2C9 t(51) C3C4 t(50)

1473 1457 1315 1191 1173 1142 1028 1005 986 746 528 373 271 267 266 215

C1H3 ab1(40) C9H3 ab1(39) C1H3 ab1(33) C9H3 ab1(33) C2C3 s(26) C3H2 w(24) C1H3 r1(18) C9H3 r1(18) C3H2 r(23) C4H3 r2(18) C4H3 r1(16) C1H3 r2(15) C4H3 r1(28) C2C3 s(14) C3H2 tw(24) C4H3 r2(22) C3C4 s(43) C4H3 r1(15) C2C3 s(42) C1C2 s(17) C2C3C4 b(38) C4H3 r1(11) C1C2C3 b(33) C3C2C9 b(33) C1C2 t(23) C2C9 t(21) C2C3C4 b(39) C2C9 t(41) C1C2 t(40) C3C4 t(51) C1C2 t(32)

a See Fig. 3 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, b: bend, ab: antisymmetric bend, r: rock, w: wag; tw: twist, t: torsion.

experimental gas phase enthalpy difference of 0.67 kcal/mol [35]. The trans ! gauche rotational barrier of isopentane, calculated at the MP2/6-31G ⴱ level, is shown in Fig. 4. For this calculation the t 1 torsion angle is kept at constant values between ⫺30⬚ and ⫺195⬚, in 15⬚ intervals, and all other bond lengths and angles are optimized. Our calculated value for this barrier is 5.7 kcal/mol. In n-butane, the experimental value for

this barrier is 3.62 kcal/mol [35], with calculated values being 3.49 [32] and 3.31 [33,34] kcal/mol. The observed and calculated frequencies and PEDs of the trans conformer are given in Table 8. The experimental results include IR spectra of the vapor [21] and of the solid deposited at ⫺196⬚C [11] and Raman spectra of liquid and solid samples [36]. The calculated frequencies are in general in good agreement with the experimental data. Our calculated PEDs

Fig. 5. Stable conformer of 2,2-dimethylbutane.

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Table 10 Observed and calculated frequencies (cm ⫺1) of 2,2-dimethylbutane

n (obs) a Symmetry b n (calc) Potential energy distribution c 2970 2961

2945

A 00 A0

2965 2960

A 00

2951

A

0 0

A A 00 A 2912

0

A 00

2948 2946 2943 2938 2937

A0 A0

2896 2888

2868

A 00 A 00 A0

2885 2881 2878

2856 1477

A0 A0

2855 1478

A 00

1474

A0

1471

2880

1458

A0 A 00 A0

1467 1465 1455

A 00

1452

A 00

1449

1391

A0 A0

1447 1391

1373 1368 1362

A0 A 00 A0

1378 1365 1364

1337 1308 1254 1232

A0 A 00 A0 A 00

1338 1308 1267 1231

1218

A0

1224

1080

A 00

1081

1074

A0

1074

C17H3 as2(83) C6H3 as2(32) C10H3 as2(32) C17H3 as1(12) C6H3 as1(10) C10H3 as1(10) C6H3 as2(20) C10H3 as2(20) C10H3 as1(19) C6H3 as1(19) C1H3 as2(11) C17H3 as2(11) C1H3 as1(48) C17H3 as1(13) C10H3 as1(12) C6H3 as1(12) C17H3 as1(74) C1H3 as2(74) C6H3 as2(11) C10H3 as2(11) C1H3 as1(47) C10H3 as1(19) C6H3 as1(18) C6H3 as1(29) C10H3 as1(29) C1H3 as2(15) C6H3 as2(14) C10H3 as2(14) C17H3 ss(81) C6H3 ss(31) C10H3 ss(31) C1H3 ss(18) C17H3 ss(18) C14H2 as(97) C6H3 ss(49) C10H3 ss(49) C1H3 ss(78) C6H3 ss(11) C10H3 ss(11) C14H2 ss(97) C6H3 ab1(24) C10H3 ab1(24) C1H3 ab1(23) C17H3 ab2(40) C6H3 ab1(20) C10H3 ab1(20) C1H3 ab2(15) C17H3 ab1(25) C6H3 ab2(24) C10H3 ab2(24) C17H3 ab1(57) C14H2 b(24) C1H3 ab2(45) C17H3 ab2(42) C1H3 ab1(47) C14H2 b(20) C6H3 ab1(11) C10H3 ab1(11) C6H3 ab2(27) C10H3 ab2(27) C6H3 ab1(12) C10H3 ab1(12) C1H3 ab2(10) C17H3 ab2(10) C1H3 ab2(25) C6H3 ab2(21) C10H3 ab2(21) C10H3 ab1(14) C6H3 ab1(14) C14H2 b(52) C1H3 ab1(23) C6H3 sb(32) C10H3 sb(32) C1H3 sb(27) C17H3 sb(94) C6H3 sb(52) C10H3 sb(52) C1H3 sb(68) C6H3 sb(17) C10H3 sb(17) C14H2 w(81) C5C14 s(10) C14H2 tw(52) C5C14 s(28) C1H3 r1(13) C14H2 r(19) C17H3 r2(18) C14H2 tw(16) C1C5 s(27) C6H3 r2(13) C10H3 r2(13) C1H3 r2(19) C14H2 r(15) C17H3 r2(15) C14H2 tw(12) C6H3 r2(10) C10H3 r2(10) C14C17 s(27) C17H3 r1(25)

Table 10 (continued)

n (obs) a Symmetry b n (calc) Potential energy distribution c 1019 990 980

A0 A0 A 00

1019 988 979

931

A 00

933

A 00

920

A0

918

A0

861

927 869

00

780 712

A A0

780 700

484 d

A0

484

A 00

419

411 d 361 d

A0 A 00

408 355

344 d

A0

332

A 00

292

260 d

A0 A 00 A0

279 256 253

194 d

A 00

209

A 00

84

C14C17 s(45) C5C14 s(12) C1H3 r1(41) C17H3 r1(27) C6H3 r2(22) C10H3 r2(22) C17H3 r2(16) C14H2 tw(15) C1H3 r2(38) C6H3 rl(22) C10H3 rl(22) C6H3 r2(10) C10H3 r2(10) C5C6 s(24) C5C10 s(24) C6H3 rl(16) C10H3 rl(16) C1H3 r2(14) C1C5 s(32) C1H3 rl(14) C6H3 r2(14) C10H3 r2(14) C5C14 s(26) C1C5 s(13) C17H3 rl(11) C5C6 s(10) C5C10 s(10) C14H2 r(57) C17H3 r2(47) C5C14 s(29) C5C6 s(19) C5C10 s(19) C1C5 s(12) C5C14C17 b(32) C14C5C6 b(11) C14C5C10 b(11) C1C5C6 b(18) C1C5C10 b(18) C14C5C6 b(15) C14C5C10 b(15) C6C5C10 b(27) C1C5C14 b(24) C6C5C10 b(30) C1C5C6 b(14) C1C5C10 b(14) C5C14C17 b(13) C14C5C6 b(24) C14C5C10 b(24) C1C5C6 b(20) C1C5C10 b(20) C1C5 t(26) C5C6 t(19) C5C10 t(19) C14C17 t(13) C5C6 t(40) C5C10 t(40) C1C5 t(61) C14C17 t(16) C5C14C17 b(40) C1C5C14 b(22) C14C17 t(48) C5C6 t(35) C5C10 t(35) C1C5 t(13) C5C14 t(144) C14C17 t(42) C5C10 t(13) C5C6 t(13) C1C5 t(10)

a

From Ref. [11], unless otherwise noted. Symmetry species. c Contributions ⱖ 10. See Fig. 5 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, w: wag; tw: twist, t: torsion. d From Ref. [38]. b

agree qualitatively with those of SS [11], with some quantitative differences. The only exception is the CH s mode which SS calculate at 2904 cm ⫺1 while we calculate it at 2871 cm ⫺1 and assign it to a band at 2875 cm ⫺1. Also shown in Table 8 are the calculated frequencies for the gauche conformer and the corresponding

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Fig. 6. Stable conformers of 3-methylpentane.

85

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N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

Table 11 Relative energies (kcal/mol) and main torsion angles (⬚) of conformers of 3-methylpentane with different basis sets HF/6-31Gⴱ

HF/6-31G

TT TG 0 GG TG G0G a b

MP2/6-31G ⴱ

t1 a

t2 b

DE

t1 a

t2 b

DE

t1 a

t2 b

DE

171.4 173.1 58.9 166.4 ⫺87.2

188.7 ⫺66.7 59.8 63.5 63.5

0.0 0.17 0.71 0.76 3.97

171.8 174.6 58.5 166.9 ⫺86.3

188.2 ⫺65.1 60.0 63.7 63.9

0.0 0.16 0.69 0.75 3.81

173.0 177.6 56.7 169.2 ⫺87.0

187.0 ⫺62.0 58.2 63.6 61.3

0.0 0.09 0.34 0.61 3.38

t 1: C1C2C3C4 (see Fig. 6). t 2: C2C3C4C5 (see Fig. 6).

symmetry species. Due to the Cs symmetry of this isomer, of the 45 normal modes of vibration, 25 are in-plane (A 0 ) and 20 are out-of-plane (A 00 ). While many of these retain the same or similar local character as in the trans conformer, even with different frequencies, others can be quite dissimilar, either with close or with very different frequencies. The latter are illustrated in Table 9, and emphasize the well-known sensitivity of eigenvectors and frequencies to conformation. Although early results [36] failed to identify bands definitively associated with the gauche conformer, Verma et al. [31] in their vapor phase Raman spectra were able to resolve a band at 757 cm ⫺1 that disappeared in the solid state and there-

fore could be assigned to the gauche conformer. Its intensity variation with temperature resulted in the aforementioned DH ˆ 809 cal=mol: Our calculated Dn (trans–gauche) ˆ 756 ⫺ 746 ˆ 10 cm ⫺1 agrees well with the observed Dn ˆ 764 ⫺ 757 ˆ 7 cm⫺1 ; and supports our suggestion of other assignments to the gauche conformer in the vapor and liquid phase spectra. 3.4. 2,2-Dimethylbutane There is one stable conformer of 2,2-dimethylbutane (t (C1C5C14C17) ˆ 180⬚; see Fig. 5) and a transition structure …t ˆ 0⬚†; both of Cs symmetry. The

Fig. 7. MP/6-31G ⴱ C2C3C4C5 rotational barrier for 3-methylpentane, TT (⬃180⬚, ⬃180⬚) ! TG 0 (⬃180⬚, ⬃⫺60⬚) ! TG(⬃180⬚, ⬃60⬚).

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

87

Fig. 8. MP2/6-31G ⴱ C1C2C3C4 rotational barrier for 3-methylpentane, TG (⬃180⬚, ⬃60⬚) ! GG(⬃60⬚, ⬃60⬚).

relative energy of the stable conformation with respect to the symmetric transition structure is 5.19 (HF/6-31G), 5.12 (HF/6-31G ⴱ), and 5.43 (MP2/631G ⴱ) kcal/mol. NMR studies of this barrier give a value 5.2 ^ 0.2 kcal/mol at 100 K [37]. Our MP2/631G ⴱ calculated value of 5.43 kcal/mol is in good agreement with this result. The observed and calculated frequencies and PEDs are given in Table 10. Experimental data for 2,2dimethylbutane are from SS [11] (IR) and Fenske et al. [38]. Our assignments differ significantly from those of SS, especially in the 1100–1400 cm ⫺1 region. SS do not assign the observed frequencies corresponding to the CCH3 sb region, viz. 1391, 1373, 1368 and 1362 cm ⫺1. However our calculated values, 1391, 1378, 1365 and 1364 cm ⫺1, are in excellent agreement with these experimental frequencies. Nor do they assign a CH2 wag (w) in this region, which we calculate at 1338 cm ⫺1 and assign to a weak band at 1337 cm ⫺1. They assign the CH2 w to a band at 1218 cm ⫺1, but in studying similar molecules, where the CH2 group is adjacent to a C(CH3)2 group, the CH2 w is near our value, viz. 1337 cm ⫺1 (2,2-dimethylhexane) [39], 1340 cm ⫺1 (2,3,3,-trimethylpentane) [40] and 1342 cm ⫺1 (3,3-dimethylpentane) [41]. We calculate the CH2 twist (tw) mode at 1308 cm ⫺1 and

assign it to a band observed at 1308 cm ⫺1. SS assign the CH2 tw to a band at 1173 cm ⫺1, while we do not have any calculated frequency in the 1100 cm ⫺1 region. SS assign the observed band at 1254 cm ⫺1 to CCH3 sb, CC s and CH2 w, while we assign it to mostly CC s and CCH3 r. Another observed frequency that they do not assign is at 1232 cm ⫺1, which we assign to CCH3 r and CH2 r and calculate at 1231 cm ⫺1. Our frequency agreement is significantly better than that of SS and we believe our assignments are more self-consistent. 3.5. 3-Methylpentane 3-Methylpentane has five stable conformations. The stable structures are shown in Fig. 6 and are characterized by the trans and gauche relationship of the t 1(C1C2C3C4) and t 2(C2C3C4C5) torsion angles: TT(⬃180⬚, ⬃180⬚), TG 0 (⬃180⬚, ⬃⫺60⬚), TG(⬃180⬚, ⬃60⬚), GG(⬃60⬚, ⬃60⬚), and G 0 G(⬃⫺90⬚, ⬃60⬚). The TT conformer has Cs symmetry and the other four have C1 symmetry. The relative energies of the five 3-methylpentane conformers, calculated at HF/6-31G, HF/6-31G ⴱ and MP2/6-31G ⴱ levels, are given in Table 11. Conformers TT, TG, TG 0 and GG are all within less than

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Table 12 Observed and calculated frequencies (cm ⫺1) of conformers of 3-methylpentane

n (obs) a

n (calc)

Potential energy distribution b

TT

TG 0

GG

TG

2968 2961 2953 2950 2943 2942 2897 2889 2888 2885 2880 2865 2857 2852 1480 1470 1469 1463 1462 1460 1456 1448 1380 1377 1375

2966 2960 2953 2943 2942 2941 2908 2890 2887 2885 2883 2868 2856 2855 1475 1471 1467 1464 1463 1461 1456 1449 1380 1378 1373

2961 2955 2950 2945 2943 2943 2900 2895 2893 2886 2884 2872 2864 2858 1476 1471 1470 1467 1463 1463 1454 1453 1380 1378 1376

2962 2959 2953 2948 2944 2943 2898 2895 2889 2886 2885 2871 2861 2853 1475 1471 1469 1466 1464 1462 1454 1451 1381 1379 1375 1360

1354

1352

1358

1357 1356

1351 1334 1314 1298

1351 1334

1350

1281 1272

1283 1272

1273

1269

1247

1249

1247

1250 1186

1174

1177

1178 1166

1463 1459

1377

1330 1318 1299

1347 1339

1301 1289

1152 1144 1123 1051 1040 1012 985 976

1160 1158 1149

1270 1260 1183 1168

1156 1142

1055 1044

1049 1039

1052

1018

1015 982

1022 1008 986

969

971

977

1131 1047 1038 1016 985

C12H3 as2(70) C1H3 as2(11) C5H3 as2(11) C1H3 as2(29) C5H3 as2(29) C12H3 as1(14) C5H3 as1(10) C1H3 as1(10) C12H3 as2(31) C1H3 as2(26) C5H3 as2(25) C12H3 as1(70) C5H3 asl(40) C1H3 asl(39) C1H3 asl(39) C5H3 asl(37) C1H3 as2(12) C5H3 as2(11) C2H2 as(36) C4H2 as(36) C3H s(12) C12H3 ss(44) C1H3 ss(21) C5H3 ss(21) C1H3 ss(43) C5H3 ss(43) C12H3 ss(45) C5H3 ss(23) C1H3 ss(22) C2H2 as(42) C4H2 as(42) C3H s(56) C2H2 ss(18) C4H2 ss(18) C4H2 ss(30) C3H s(29) C2H2 ss(29) C2H2 ss(49) C4H2 ss(49) C12H3 ab1(59) C1H3 ab2(13) C5H3 ab2(13) C5H3 ab1(26) C1H3 ab1(25) C5H3 ab2(20) C1H3 ab2(19) C1H3 abl(25) C5H3 ab1(25) C4H2 b(16) C2H2 b(16) C12H3 abl(12) C1H3 ab2(23) C5H3 ab2(23) C12H3 ab2(22) C1H3 ab1(15) C5H3 abl(14) C12H3 ab2(56) C2H2 b(11) C4H2 b(11) C1H3 ab2(29) C5H3 ab2(29) C5H3 ab1(12) C1H3 ab1(12) C12H3 ab1(10) C2H2 b(32) C4H2 b(32) C12H3 ab1(13) C2H2 b(37) C4H2 b(37) C12H3 ab2(16) C12H3 sb(41) C5H3 sb(31) C1H3 sb(30) C1H3 sb(52) C5H3 sb(51) C12H3 sb(49) C1H3 sb(19) C5H3 sb(19) C4H2 w(28) C12H3 sb(22) C4C3H b(17) C2H2 w(16) C2H2 w(18) C4H2 w(18) C12C3H b(14) C12H3 sb(12) C4H2 w(41) C4C3H b(20) C2H2 w(29) C4H2 w(29) C2C3 s(12) C2C3H b(12) C4C3H b(12) C3C4 s(12) C2H2 w(23) C4H2 w(23) C12C3H b(14) C2H2 w(20) C4H2 w(20) C2C3H b(16) C4H2 tw(11) C12C3H b(17) C4H2 tw(17) C4H2 w(15) C4C3H11 b(13) C2H2 tw(11) C4C3H b(27) C2H2 w(18) C3C4 s(12) C12C3H b(10) C4H2 w(10) C4C3H b(20) C2C3H b(19) C2H2 tw(11) C4H2 tw(11) C4H2 w(10) C2H2 w(10) C2H2 tw(21) C4H2 tw(21) C12C3H b(17) C4H2 tw(20) C2H2 tw(18) C2C3H b(13) C12C3H b(10) C2H2 tw(23) C4H2 tw(23) C2C3 s(19) C12H3 r2(11) C12H3 rl(16) C2H2 r(13) C4H2 r(13) C1H3 r2(11) C5H3 r2(11) C3C4 s(21) C12H3 r2(17) C5H3 rl(13) C3C12 s(15) C1H3 rl(11) C5H3 rl(11) C3C4 s(10) C2C3 s(10) C12H3 r2(26) C3C4 s(11) C2C3 s(11) C3C12 s(17) C1H3 rl(13) C4C5 s(14) C5H3 rl(13) C1C2 s(33) C4C5 s(33) C1H3 rl(22) C5H3 rl(22) C1C2 s(22) C2C3 s(16) C1C2 s(29) C4C5 s(29) C12H3 r2(26) C5H3 r1(18) C1H3 r1(10) C12H3 r2(29) C1H3 r2(10) C5H3 r2(10) C3C12 s(35) C1H3 r2(18) C2H2 tw(16) C4C5 s(10)

N.G. Mirkin, S. Krimm / Journal of Molecular Structure 550–551 (2000) 67–91

89

Table 12 (continued)

n (obs) a

n (calc) TT

Potential energy distribution b TG 0

960 947 880

961 943 871

946 873

814 798 768 750

808

805 764

GG

TG

950

957 944

867

869

799 761

785 768

756 754

738

732

741 722

549

546 525

467 447

464 452 432

436

443

383

383

406 390 370

370

373

321 312

308

304 299

278 260 232

191

214 200

228 220 218

260 254 230 222

266 261 215 212

129 104 86 79

103 84 78

59

C3C12 s(37) C1H3 rl(11) C5H3 rl(11) C12H3 rl(44) C2C3 s(22) C3C4 s(22) C12H3 r2(19) C4C5 s(12) C1C2 s(12) C2C3 s(20) C3C4 s(16) C12H3 r2(15) C4C5 s(13) C1H3 r1(12) C1C2 s(10) C5H3 r1(10) C1H3 r2(13) C12H3 r1(13) C5H3 r2(13) C2H2 r(12) C4H2 r(12) C2H2 r(33) C1H3 r2(32) C5H3 r2(11) C4H2 r(10) C2H2 r(47) C1H3 r2(27) C4H2 r(19) C5H3 r2(11) C2H2 r(36) C4H2 r(36) C1H3 r2(19) C5H3 r2(19) C3C12 s(24) C2H2 r(15) C4H2 r(15) C4H2 r(28) C2C3 s(22) C5H3 r2(10) C3C4 s(34) C2C3 s(16) C2H2 r(15) C3C4C5 b(35) C5H3 r1(12) C4C3C12 b(10) C3C4C5 b(36) C5H3 r1(11) C4C3C12 b(10) C3C4C5 b(32) C2C3C12 b(14) C1C2C3 b(13) C1C2C3 b(33) C3C4C5 b(33) C2C3C12 b(16) C4C3C12 b(16) C2C3C12 b(11) C4C3C12 b(11) C2C3C12 b(39) C1C2C3 b(24) C2C3C4 b(15) C2C3C12 b(10) C4C3C12 b(10) C4C3C12 b(31) C2C3C12 b(21) C1C2C3 b(12) C3C4C5 b(12) C4C3C12 b(11) C2C3C12 b(11) C3C4C5 b(17) C3C12 t(15) C1C2C3 b(12) C1C2 t(12) C1C2 t(24) C3C4C5 b(23) C1C2 t(22) C4C5 t(21) C3C12 t(17) C2C3C12 b(12) C4C3C12 b(12) C4C5 t(40) C1C2C3 b(21) C2C3C12 b(13) C1C2 t(11) C3C12 t(10) C1C2C3 b(28) C3C12 t(16) C2C3C12 b(13) C3C4C5 b(13) C2C3C4 b(13) C4C5 t(10) C1C2 t(24) C4C5 t(24) C3C12 t(76) C1C2 t(18) C2C12 t(70) C4C5 t(20) C1C2 t(20) C2C3C4 b(25) C1C2C3 b(24) C3C4C5 b(24) C1C2 t(17) C4C5 t(17) C2C3 t(59) C3C4 t(33) C4C5 t(29) C1C2 t(17) C3C4 t(58) C2C3 t(31) C4C5 t(27) C2C3 t(50) C3C4 t(47) C3C4 t(107) C2C3 t(103) C3C12 t(50) C4C5 t(17) C1C2 t(16) C2C3 t(157) C3C4 t(142) C3C12 t(32) C4C5 t(27) C1C2 t(20)

a

From Ref. [42]. Potential energy distributions (contributions ⱖ 10) for TT conformer, except when no TT band is given, in which case the PED is for the lowest energy conformer. See Fig. 6 for atom numbering. Symmetry coordinates follow our previous definition [1]. s: stretch, ss: symmetric stretch, as: antisymmetric stretch, b: bend, sb: symmetric bend, ab: antisymmetric bend, r: rock, w: wag; tw: twist, t: torsion. b

1 kcal/mol in their relative energies, while the G 0 G conformer is about 3 kcal/mol higher. The MP2/631G ⴱ values of DE of 90 and 610 cal/mol for the TG 0 and TG conformers, respectively, are interesting to compare to our MP2/6-31G ⴱ calculated DE for npentane of 670 cal/mol [1]. The TT ! TG 0 ! TG torsional barrier of 3-methylpentane with respect to t 2, calculated at MP2/6-31G ⴱ, is shown in Fig. 7. The calculated barrier heights are 2.66 kcal/mol for TT ! TG 0 and 5.76 kcal/mol for

TG 0 ! TG. Fig. 8 shows the TG ! GG torsional barrier with respect to t 1. In addition to the TG and GG minima, there are two equivalent higher energy minima at (⬃⫺90⬚, ⬃60⬚) and (⬃⫺60⬚, ⬃90⬚), separated by a small barrier of 0.21 kcal/mol. The calculated values for the other barriers are 5.42 (TG ! G 0 G), 4.38 (G 0 G ! GG), and 7.39 kcal/mol (GG ! G 0 G). There are no experimental values for these barriers. In Table 12 we compare the observed Raman

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(liquid) and IR (liquid and solid state) frequencies of 3-methylpentane [42] with the calculated values for the four lowest energy conformers, giving also the PEDs for the TT and some of the other conformers. All of the TT calculated frequencies can be assigned to observed bands. As to the presence of the other conformers, some observed bands can be assigned solely to one conformer: 1314 and 467 cm ⫺1 to TG 0 , and 1123 and 549 cm ⫺1 to TG. Since the higher energy conformer (TG) appears to be present, GG must also be present, even though no observed frequency is assignable solely to this conformer. Therefore, bands at 798 and 370 cm ⫺1 may well be due mostly to the GG conformer. The only other normal mode study of this molecule that we are aware of is due to Crowder and Hill [42], who used an empirical force field. For some bands, our assignments, both with respect to conformers as well as PEDs, differ substantially from theirs.

4. Conclusions As was the case in our previous ab initio analysis of the vibrational spectra of conformers of linear alkanes [1], we have shown that a scaled ab initio Hartree– Fock force field can account satisfactorily for the observed IR and Raman spectra of branched alkanes. With a set of 14 scale factors, most of the optimized values being close to those of the linear chains, we have reproduced 159 observed non-CH s frequencies of 10 conformers of 5 molecules with an rms deviation of 6.1 cm ⫺1. This analysis has resulted in the clarification and reassignment of a number of modes in individual molecules, and has enabled a self-consistent interpretation of the spectra of this class of molecules. The force constants provide the basis for the development of a spectroscopically reliable molecular mechanics energy function, an SDFF [2], for saturated hydrocarbon chains [4].

Acknowledgements This research was supported by NSF Grants DMR9627786 and MCB-9601006.

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