Infrared and Raman spectra, conformational stability, ab initio calculations of structure, and vibrational assignment of 2-hexyne

Infrared and Raman spectra, conformational stability, ab initio

calculations of structure, and vibrational assignment of 2-hexyneq

Stephen Bella, Xiaodong Zhub, Gamil A. Guirgisb, James R. Durigb,*

aDepartment of Chemistry, University of Dundee, Dundee, Scotland DD1 4HN, UKbDepartment of Chemistry and Geosciences, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA

Received 20 March 2002; revised 30 May 2002; accepted 30 May 2002

Abstract

The infrared spectra (3500–50 cm21) of the gas and solid and the Raman spectra (3500–50 cm21) of the liquid and solid

have been recorded for 2-hexyne, CH3–CxC–CH2CH2CH3. Variable temperature studies of the infrared spectrum (3500–

400 cm21) of 2-hexyne dissolved in liquid krypton have also been recorded. Utilizing four anti/gauche conformer pairs, the

anti(trans ) conformer is found to be the lower energy form with an enthalpy difference of 74 ^ 8 cm21 (0.88 ^ 0.10 kJ/mol)

determined from krypton solutions over the temperature range 2105 to 2150 8C. At room temperature it is estimated that there

is 42% of the anti conformer present. Equilibrium geometries and energies of the two conformers have been determined by ab

initio (HF and MP2) and hybrid DFT (B3LYP) methods using a number of basis sets. Only the HF and DFT methods predict the

anti conformer as the more stable form as found experimentally. A vibrational assignment is proposed based on the force

constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and on rotational band contours

obtained using the calculated equilibrium geometries. From calculated energies it is shown that the CH3 group exhibits almost

completely free rotation which is in agreement with the observation of sub-band structure for the degenerate methyl vibrations

from which values of the Coriolis coupling constants, z, have been determined. The results are compared to similar properties of

some corresponding molecules. q 2002 Elsevier Science B.V. All rights reserved.

Keywords: Infrared spectra; Conformational stability; Ab initio calculations; 2-hexyne

1. Introduction

We have been studying the vibrational spectra

and structural parameters of several alkynes [1–4]

and some fluorine substituted alkynes [5–9]. The

infrared and Raman spectra of 1-pentyne, HCxC–

CH2CH2CH3 [2,4], presents an interesting problem

concerning which conformer has the lower energy,

the anti (trans) or gauche form. For this molecule,

the anti rotamer was found to have the lower

enthalpy by 50 ^ 6 cm21 (0.60 ^ 0.07 kJ/mol) and

45 ^ 4 cm21 (0.54 ^ 0.05 kJ/mol) by variable

low-temperature infrared spectra of liquid xenon

and krypton solutions, respectively [4]. In the

infrared spectrum of 2-pentyne, CH3 – CxC –

CH2CH3, in the gas phase [3], some interesting

‘fine’ structure was observed involving three

nearly degenerate antisymmetric modes of the

0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.

PII: S0 02 2 -2 86 0 (0 2) 00 3 26 -5

Journal of Molecular Structure 616 (2002) 135–158

www.elsevier.com/locate/molstruc

q Taken in part from the thesis of X. Zhu which will be submitted

to the Department of Chemistry at the University of Missouri-

Kansas City in partial fulfillment of the PhD degree.* Corresponding author. Tel.: þ1-816-235-6038; fax: þ1-816-

235-5502.

E-mail address: [email protected] (J.R. Durig).

http://www.elsevier.com/locate/molstruc

methyl group adjacent to the CC triple bond

which show strong–weak–weak–strong sub-bands

much like that observed in the spectra of

symmetric top molecules such as the methyl

halides. For 2-pentyne, the sub-band structure

was assigned as arising from Coriolis coupling

of the vibrational angular momenta with the

almost-free internal rotation of the methyl group

adjacent to the triple bond.

Both of these features are allowed in the 5-fluoro-

2-pentyne CH3–CxC–CH2CH2F molecule [9] which

is like 2-pentyne exhibiting sub-band structure

associated with the methyl antisymmetrical

vibrational modes. For this molecule, sub-bands are

observed for only two modes, namely the antisym-

metric stretch and antisymmetric deformation, but not

for the antisymmetric rock, perhaps due to the close

proximity of the C–F stretch. For 5-fluoro-2-pentyne,

the anti rotamer was determined [9] to be lower in

energy than the gauche form with an enthalpy

difference of 273 ^ 15 cm21.

The 2-hexyne molecule CH3–CxC–CH2CH2CH3

is also expected to exhibit both of these interesting

features in its infrared spectrum. It can exist in two

conformers, the anti and gauche forms, like 1-pentyne

[2,4], and it may also exhibit Coriolis sub-band

structure like 2-pentyne [3] due to the almost

symmetric methyl group adjacent to the CC triple

bond. It is isoelectronic and isostructural with 5-

fluoro-2-pentyne apart from a methyl replacing the F

atom at the 5-position. This methyl group should not

have a low barrier to internal rotation but it should

have a value much like that in ethane or 1-pentyne.

Additionally, 2-hexyne is another example in a

series of 1,2-disubstituted ethane molecules, XCH2-

CH2Y, whose conformational stabilities and struc-

tural parameters have been of interest to chemists

for many years. The 1,2-difluoroethane molecule

has the gauche conformer as the more stable form

where the DH value has been determined [10] to be

280 ^ 30 cm21 (3.35 ^ 0.36 kJ/mol). However, for

both 1,2-dichloroethane [11] and n-butane [12] the

anti conformer is the more stable rotamer with DH

values of 318 ^ 25 cm21 (3.81 ^ 0.30 kJ/mol) and

234 ^ 33 cm21 (2.80 ^ 0.39 kJ/mol), respectively.

However, both 1-fluoropropane [13] and 1-chlor-

opropane [14] have the gauche conformers as the

more stable form where the enthalpy differences

from the rare gas solutions have been determined

to be 104 ^ 6 cm21 (1.24 ^ 0.07 kJ/mol) and

52 ^ 3 cm21 (0.62 ^ 0.06 kJ/mol), respectively.

With the replacement of the methyl group of 1-

fluoropropane by the ethynyl group, CxCH, i.e.

FCH2CH2CxCH (4-fluoro-1-butyne), the confor-

mational stability changes from the gauche con-

former to the anti rotamer being the more stable

form [5] by 215 ^ 22 cm21 (2.57 ^ 0.26 kJ/mol) in

krypton. This is a large change in conformational

stability which was rather unexpected although the

CxCH and CN groups have recently been shown to

have a pronounced effect on the relative stabilities

of the conformers of n-butane when they replace

one of the methyl groups [2,15]. The results from

these studies indicate that the conformational

stability for the series FCH2CH2X has additional

factors to the electronegativity and size of the

substituent X determining the rotamer that will be

the most stable form.

As a continuation of our conformational studies

of 1,2-disubstituted ethane molecules, we initiated

a Raman and infrared vibrational investigation of

2-hexyne, CH3CxCCH2CH2CH3 where the methyl

group of n-butane has been replaced by the

CxCCH3 group to determine the effect on the

conformational stability by the propynyl group as

well as by the replacement of the hydrogen atom

on the ethynyl moiety by the methyl group for the

1-pentyne molecule [2]. Therefore, we have

recorded the Raman spectra of the liquid and

solid along with the infrared spectra of the gas,

krypton solutions with variable temperatures, and

solid 2-hexyne. We have also carried out ab initio

calculations employing the 6-31G(d) basis set at

the level of restricted Hartree–Fock (RHF) as well

as with electron correlation with the 6-31G(d)

basis set by the Moller–Plesset method to the

second order (MP2) to obtain equilibrium geome-

tries, force constants, vibrational frequencies,

infrared and Raman intensities, and conformation-

al stabilities. Structural parameters and confor-

mational stabilities have also been obtained from

the larger basis sets of 6-311G(d,p) and 6-

311G(2df,2p) at the MP2 level and by density

functional theory (DFT) by the B3LYP method.

The results of these spectroscopic and theoretical

studies are reported herein.

S. Bell et al. / Journal of Molecular Structure 616 (2002) 135–158136

2. Experimental

The sample of 2-hexyne was purchased from

Aldrich Chemical Corp., Milwaukee, WI with a

stated purity of 99%. Further purification was

performed with a low-temperature, low-pressure

fractionating column. The sample was collected at

255 8C and the purity was checked by infrared

spectroscopy [16]. The sample was stored under

vacuum at low temperature.

The mid-infrared spectrum of the gas (Fig. 1A) was

recorded using a Perkin–Elmer model 2000 Fourier

transform spectrometer equipped with a Ge/CsI

beamsplitter and DTGS detector. Atmospheric water

vapor was removed from the spectrometer housing by

purging with dry nitrogen. The spectrum of the gas

was obtained using a 10 cm cell fitted with CsI

windows. The infrared spectrum of the solid (Fig. 1D)

was obtained by condensing the sample on a CsI

substrate held at the temperature of boiling liquid

nitrogen and housed in a vacuum cell fitted with CsI

window. The sample was condensed as an amorphous

or glassy solid and repeatedly annealed until no

further changes were observed in the spectrum.

The mid-infrared spectra of the sample dissolved in

liquid krypton as a function of variable temperatures

were recorded on a Bruker model ISF-66 Fourier

transform spectrometer equipped with a globar

source, a Ge/KBr beamsplitter and a TGS detector.

In all case 100 interferograms were collected at

1.0 cm21 resolution, averaged and transformed with a

boxcar truncation function. A specially designed

cryostat cell was used to obtain the spectral data. It

consists of a copper cell with a path length of 4 cm

with wedged silicon windows sealed to the cell with

indium gaskets. This cell was cooled by boiling liquid

nitrogen and the temperature was monitored with two

Pt thermoresistors. The complete cell was connected

to a pressure manifold, which allowed the filling and

evacuation of the cell. After the cell had cooled to the

desired temperature, a small amount of the compound

was condensed into the cell. Next, the pressure

manifold and the cell were pressurized with the

noble gas, which immediately started to condense in

the cell, allowing the compound to dissolve.

The far infrared spectrum of the gas (Fig. 2) was

recorded on a Bomem model DA3.002 Fourier

transform spectrometer equipped with a vacuum

bench, 6.25 and 25 mm Mylar beamsplitters, and a

liquid helium-cooled Si bolometer. The spectrum was

obtained from the sample contained in a 1-m folded

path cell equipped with mirrors coated with gold, and

fitted with polyethylene windows with an effective

resolution of 0.1 cm21. The far infrared spectra of the

amorphous and crystalline solids (Fig. 2) were

obtained with the Perkin – Elmer model 2000

equipped with a metal grid beamsplitter and a

DTGS detector.

The Raman spectra were recorded on a SPEX

model 1403 spectrophotometer equipped with a

Spectra-Physics model 164 argon ion laser operating

on the 514.5 nm line. The laser power used was 0.5 W

with a spectral bandpass of 3 cm21. The spectrum of

the liquid was recorded with the sample sealed in a

Pyrex glass capillary held in a Miller–Harney

apparatus [17]. Depolarization ratio measurements

were checked by measuring the depolarization values

of the Raman bands of CCl4 immediately before

depolarization measurements were made on the liquid

sample. The Raman wavenumbers are expected to be

accurate to ^2 cm21 and typical spectra are shown in

Fig. 1. All of the observed bands with significant

intensity in both the infrared and Raman spectra,

along with the proposed assignments, are listed in

Table 1.

3. Conformational stability

For 2-hexyne, many of the fundamentals for the

two conformers have nearly the same frequency.

Nevertheless, there are significant differences among

lower frequencies as indicated in the spectrum of 2-

hexyne in liquid krypton which is shown in Fig. 3. The

assignment of fundamentals of the gauche conformer

is according to ab initio MP2/6-31G(d) predication

calculations and in agreement with the anti conformer

being the only conformer existing in the annealed

solid state. The conformer pairs at 478/513, 740/1074,

740/820, and 740/513 cm21, where the first frequen-

cies are due to the anti conformer, were used to

determine the enthalpy difference between the two

conformers. With the sample dissolved in liquid

krypton, the spectral changes with variation of the

temperature are shown in Fig. 4. It is evident that the

increase in the intensity of the band assigned to

S. Bell et al. / Journal of Molecular Structure 616 (2002) 135–158 137

the anti conformer as the temperature decreases

confirms the ab initio prediction. In order to obtain

the enthalpy difference, spectral data at ten different

temperatures were obtained from these four pairs of

bands over the temperature range from 2105 to

2150 8C for the krypton solution as given in Table 2.

The enthalpy difference was calculated by the van’t

Hoff equation, 2ln K ¼ ðDH=RTÞ2 DS=R; with the

assumption that the value of DH is constant within the

temperature range utilized and It/Ig is substituted for

K. The value of DH for the four pairs of bands ranged

from a low value of 44 ^ 5 cm21 to a high value of

96 ^ 7 cm21 from the slope of the lines with the anti

conformer the more stable form. Using a least squares

Fig. 1. Vibrational spectra: (A) gas, infrared; (B) liquid, Raman; (C)

annealed solid, Raman; (D) annealed solid, infrared of 2-hexyne.

Fig. 2. Far infrared spectra of 2-hexyne: (A) gas phase and (B)

annealed solid.

Fig. 3. Mid-infrared spectrum (400–1100 cm21) of 2-hexyne

dissolved in liquid krypton at 2105 8C.

Fig. 4. Variation with temperature of the 740/1074 cm21 conformer

pair in liquid krypton.


Table 1

Observed infrared and Raman wavenumbers (cm21) for 2-hexyne

Gas Rel. Int. Infrared Raman Assignment

Krypton Rel. Int. Solid Rel. Int. Liquid Rel.Int. and Depol. Solid Rel. Int. ni

0 Approximate description

3076 m

2972 ’ 2976 vs 2972 s 2 964 sh 2972 m n1pCH3 antisymmetric stretch

2965 vs 2962 s 2964 2965 m n26pCH3 antisymmetric stretch

2958 m 2955 m n27 CH2 antisymmetric stretch

2955 sh S 2955 S 2955 m 2953 sh n2 CH3 antisymmetric stretch

2942 max vs 2941 vs 2945 s 2938 s 2945 m n28 CH3 antisymmetric stretch

2937 vs 2937 s 2939 m n29pCH2 antisymmetric stretch

2931 sh s 2925 vs 2920 s 2922 s 2921 s n3 CH2 symmetric stretch

2919 QC s 2914 s 2911 s 2908 vs n4pCH3 symmetric stretch

2909 s 2903 s 2904 s 2908 vs n5 CH3 symmetric stretch

2880 max s 2877 s 2873 s 2875 m 2884 m n6pCH2 symmetric stretch

2730 max 2730 m 2738 w 2738 w

2302 s 2296 s

2236 vs 2228 vs n7 CxC stretch, Fermi doublet

1462 QC s 1467 s 1467 s 1460 w n8 CH2 scissors

1453QC s 1457 s 1458 s 1453 m n30 CH3 antisymmetric deformation

1447 QC 1450 m 1447 m 1449 m n9 CH3 antisymmetric deformation

1435 QC s 1436 s 1421 s 1435 m n10pCH2 scissors

1450 ’ m 1448 s 1443 s 1443 m 1444 m n31pCH3 antisymmetric deformation

1436 m 1441 m n11pCH3 antisymmetric deformation

1390 QC m 1381 s 1387 m 1381 m 1394 m n12pCH3 symmetric deformation

1384 QA m 1372 m 1371 w n13 CH3 symmetric deformation

1380 P

1348 QC m 1353 m 1352 m 1349 w 1348 w n14 CH2 wag

1342 QC m 1341 m 1332 m n 014

1337QC m 1333 s 1332 m n 015

1332 P

1296 w 1294 vw 1296 w 1296 m n32 CH2 twist

1287 R

1282 QA w 1280 m 1277 s 1279 w 1283 w n15pCH2 wag

1277 P

1261 w n 032

1237 R

1231 QA vw 1230 w 1240 w n33pCH2 twist

1225 P

1217 w 1228 w n 033

(continued on next page)

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Table 1 (continued)




1135 max w 1147 w 1137 vw 1144 vw 1140 vw n16 C3C4 stretch

1103 R

1097 QC w 1101 w 1105 w 1095 m 1092 m n17 CH3 rock ip

1091 QC w 1096 m 1094 w n34pCH2 rock

1080 R

1074 QA w 1074 m 1071 w n 017

1067 P

1039 R

1036 QA w 1034 m 1037 w n18pCH3 rock ip

1032 QA w 1031 m 1034 w 1033 m 1035 m n19, n35 C5C6 stretch, pCH3 rock op

1028 P

1024 sh w 1024 w 1020 w n 018

1018 sh w 1013 w n 019

894 R

892 QC w 888 m 890 m 888 m 890 m n20 C4C5 stretch

889 QA w 879 w n 036

885 P

866 QC 865 w 866 w 866 vw n36 CH3 rock op

856 QC 855 w 855 m n 020

849 P

807 R

804 QA w 802 w 804 w n 037

800 P

740 w 754 w 755 vw 745 vw n21 C1C2 stretch

751 R

740 QC vw 739 m 730 w 734 vw 735 vw n37 CH2 rock

726 P

690 R

685 QC vw 686 w 687 w n 021

681 P

518 R

513 QA w 513 w 514 w n 022

508 P

483 R

478 ctr B vw 479 vw 475 w 479 w 476 w n22 C3C4C5 bend

474 P

399 R

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Table 1 (continued)




392 ctr B vw 382 vw 374 s 384 m n38 C2xC3C4 bend op

385 P

368 max vw 368 w n 038

359 sh vw 348 w 343 w 349 w n23 C4C5C6 bend

288 R

286 QC w 289 w n 039

280 R

272 QA m 298 m 285 w 282 w n24 C1C2xC3 bend ip

268 P

210 max m 243 m n40 C1C2xC3 bend op

202 QC m n 040

129 R

120 QC w n 025

115 sh w 141 w 139 m n25 C2xC3C4 bend ip

90 R

88 QC w 103 w 111 w n41 C6C5C4C3 torsion

86 P

92

91

75 Lattice mode

74

47

Abbreviations used: s, strong; m, medium; w, weak; v, very; ctr, center; A, B, C, and ’ refer to infrared band envelopes; P, Q, and R refer to the rotational–vibrational

branches. n indicates anti mode and n0 indicates gauche mode.

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fit of all of these data the value of DH is 74 ^ 4 cm21

(0.88 ^ 0.04 kJ/mol). The uncertainty is the statistical

uncertainty and does not take into account possible

overtone or combination bands contributing to the

intensities of the bands used for the DH determination.

Thus, the probably error is expected to be at least ten

percent, so a value of 74 ^ 8 cm21 (0.88 ^ 0.10 kJ/

mol) is a more realistic one.

4. Ab Initio calculations

The electronic structure calculations were per-

formed with GAUSSIAN98 program [18] with the

Gaussian type basis functions. The energies of 2-

hexyne were obtained from restricted Hartree–Fock

(RHF) calculations, Møller–Plesset perturbation cal-

culations at the second order (MP2) as well as hybrid

density functional theory (B3LYP) with the 6-31G(d)

and 6-311G(2d,2p) basis sets, and the results are given

in Table 3. The geometrical parameters have been

optimized for all the conformers considered. For each

of the calculation methods, potential energy functions

have been obtained from these energies by least

squares fit. It is evident from Table 3 and Fig. 5 that

the gauche conformer is predicted to be lower in

energy than the anti rotamer with the MP2 method for

any size of basis set. However, at both the Hartree–

Fock and B3LYP levels of calculation the anti

conformer is more stable with a small conformer

energy difference as found experimentally.

The optimized values of the structural parameters

obtained by computation are given in Table 4 for the

anti and the gauche form. The parameter symbols

adopted are also given in this table and in Fig. 6. The

GAUSSIAN98 program was also employed in calculat-

ing the force field in Cartesian coordinates for each of

the computational methods. In order to carry out a

normal coordinate analysis and attempt a complete

assignment of vibrational frequencies for 2-hexyne,

the internal coordinates defined in Table 4 and shown

in Fig. 6 were used to form the symmetry coordinates

listed in Table 5. The B-matrix elements were used to

convert the ab initio force field from Cartesian

coordinates into the force field in internal coordinates

[19]. These force constants were used in a mass-

weighted Cartesian coordinate calculation to repro-

duce the ab initio vibrational frequencies and to

determine the potential energy distributions (PED),

which are given in Table 6 for anti 2-hexyne and in

Table 7 for the gauche rotamer. The diagonal and off-

diagonal elements of the force field in internal

coordinates were then modified with scaling factors

of 0.88 for the carbon–hydrogen stretches, 0.9 for the

heavy atoms stretch and carbon–hydrogen bends, 1.0

for the skeletal bends except the CxCC motions with

a scaling factor of 1.5. The off-diagonal elements were

scaled by the geometric mean of the scaling factors.

The calculation was repeated to obtain the fixed

scaled force field and scaled vibrational frequencies.

To aid in the vibrational assignment for each of the

conformers, we simulated the Raman spectra for each

form. The Raman scattering activities were obtained

from the output of the ab initio calculations. The

Raman scattering cross sections, ›sj/›V, which are

proportional to the Raman intensities, can be

calculated from the scattering activities and the

predicted wavenumbers for each normal mode

[20–23]. To obtain the polarized Raman cross

sections, the polarizabilities are incorporated into Sj

by Sj[(1 2 rj)/(1 þ rj)], where rj is the depolarization

ratio of the jth normal mode. The Raman scattering

cross sections and the predicted scaled wavenumbers

were used together with a Lorentzian function to

obtain the calculated spectra.

The predicted Raman spectra of the pure anti

conformer of 2-hexyne is shown in Fig.7D and that of

Table 2

Temperature and intensity ratios for the conformational study of 2-

hexyne dissolved in liquid krypton

T (8C) 1000/K I478/513 I740/1074 I740/820 I740/513

2105 5.9471 0.6681 1.0841 – 1.061

2110 6.1293 0.7035 1.1424 0.400 1.096

2115 6.3231 0.7112 1.1540 0.425 –

2120 6.5295 0.7210 1.1908 0.445 1.141

2125 6.7499 0.7469 1.2004 0.453 –

2130 6.9857 0.7515 1.2513 0.474 1.198

2135 7.2385 0.7517 – 0.486 –

2140 7.5103 0.7632 1.3297 0.507 1.272

2145 7.8033 0.7693 1.3759 0.520 1.307

2150 8.1202 0.7888 1.4202 0.534 1.359

DHa (cm21) 44 ^ 5 82 ^ 3 96 ^ 7 77 ^ 1

a Average value of DH is 74 ^ 4 cm21 (0.88 ^ 0.04 kJ/mol) with

the anti conformer the more stable form.


pure gauche conformer in Fig. 7C. The predicated

Raman spectrum of the mixture of the two con-

formers, with an enthalpy difference of 74 cm21 with

the anti conformer the more stable rotamer at ambient

temperature, is shown in Fig. 7B. This result is

considered satisfactory when it is compared to the

experimental Raman spectrum (Fig. 7A) of the liquid.

One major difference is the doublet of the bands near

2250 cm21, which results from the Fermi resonance

of the CxC stretch with an overtone as in 2-pentyne

[3]. In general, the predicted Raman spectrum for the

lines in the region of 100–1500 cm21 showed very

Table 3

Calculated energies and energy difference for several conformations of 2-hexyne by ab initio and hybrid DFT methods

Method/basis Energy (Eh), Tse Energy differencesa (cm21)

Gse Cse Sse Teeb (V3 trans ) Geeb V3 gauche Tss

HF/3-21G 2231.692497 249.4 1752 1287 1069 1032 2.0

HF/6-31G 2232.889762 þ57.7 1826 1305 1026 1073 2.5

MP2(FC)/6-31G(d) 2233.747418 2145.8 1072 1171 3.8

MP2(full)/6-31G(d) 2233.776573 2148.3 1594 1292 1081 1179 3.8

MP2(full)/6-31G(d,p) 2233.859273 2142.6

MP2(full)/6-311G(2d,2p) 2234.088154 2153.9

B3LYP/6-31G(d) 2234.606622 þ26.3 1604 1217 1019 1086 4.2

B3LYP/6-31G(d,p) 2234.620509 þ27.0

B3LYP/6-31 þ G(d,p) 2234.629772 þ105.6

B3LYP/6-311G(2d,2p) 2234.683270 þ58.2

Conformation labels: capital letter refers to main skeletal torsional angle, C6C5C4C3, T ¼ trans or anti, G ¼ gauche, C ¼ cis or syn, and

S ¼ skew; lower case letters refer to methyl torsional angles, staggered or eclipsed, the first for the C6 methyl and the second for the C1 methyl.a Energies of conformations relative to Tse; A negative energy difference means gauche form is lower than trans conformer.b Tee energy is relative to Tse and Gee energy is relative to Gse to obtain methyl barriers.

Fig. 5. Potential energy function for torsion about the CH2–CH2 bond.


Table 4

Calculated structural parameters of the anti and gauche conformer of 2-hexyne

Parametersa HF 6-31G MP2(Full) 6-31G(d) B3LYP 6-31G(d) MP2(Full) 6-311G(d,p)

anti gauche anti gauche anti gauche anti gauche

C1–C2 S 1.4646 1.4646 1.4617 1.4639 1.4614 1.4658 1.4623 1.4624

C2xC3 T 1.1961 1.1963 1.2211 1.2215 1.2098 1.2101 1.2195 1.2198

C3–C4 U 1.4688 1.4700 1.4629 1.4618 1.4647 1.4615 1.4629 1.4641

C4–C5 V 1.5393 1.5406 1.5327 1.5339 1.5436 1.5456 1.5344 1.5359

C5–C6 X 1.5301 1.5296 1.5240 1.5228 1.5307 1.5303 1.526 1.5252

C1C2C3 z 180.06 180.12 180.47 180.40 180.38 180.43 179.27 179.32

C2C3C4 j 179.42 179.87 178.72 179.16 178.88 179.23 178.19 178.63

C3C4C5 u 113.05 113.55 112.70 112.67 113.37 113.73 112.66 112.51

C4C5C6 e 112.15 113.42 112.03 112.61 112.42 113.47 112.02 112.41

C3C4C5C6 t 180.0 64.08 180.0 61.47 180.0 62.62 180.0 61.78

C1H1 r1 1.0839 1.0838 1.0937 1.0937 1.0971 1.0971 1.0934 1.0934

C1H2 r2 1.0838 1.0838 1.0937 1.0937 1.0971 1.0971 1.0933 1.0934

C1H3 r3 1.0838 1.0838 1.0937 1.0937 1.0971 1.0971 1.0933 1.0934

C4H4 r4 1.0866 1.0867 1.0976 1.0978 1.1000 1.1001 1.0970 1.0973

C4H5 r5 1.0866 1.0859 1.0976 1.0968 1.1000 1.0990 1.0970 1.0960

C5H6 r6 1.0849 1.0864 1.0950 1.0964 1.0970 1.0979 1.0948 1.0959

C5H7 r7 1.0849 1.0850 1.0950 1.0952 1.0970 1.0972 1.0948 1.0951

C6H8 r8 1.0841 1.0845 1.0934 1.0935 1.0957 1.0958 1.0932 1.0934

C6H9 r9 1.0854 1.0854 1.0941 1.0944 1.0971 1.0973 1.0944 1.0947

C6H10 r10 1.0854 1.0832 1.0941 1.0926 1.0971 1.0952 1.0944 1.0929

C2C1H1 b1 110.98 111.01 111.02 111.04 111.36 111.37 110.86 110.85

C2C1H2 b2 111.03 110.99 111.04 111.02 111.40 111.36 110.84 110.87

C2C1H3 b3 111.03 111.06 111.04 111.05 111.40 111.44 110.84 110.84

C3C4H4 b4 108.99 108.03 108.84 108.41 108.83 107.95 109.52 109.33

C3C4H5 b5 108.99 108.98 108.84 108.79 108.83 108.78 109.52 109.26

C4C5H6 b6 109.27 109.22 109.67 109.44 109.62 109.43 108.65 108.46

C4C5H7 b7 109.27 108.92 109.67 109.43 109.62 109.33 108.65 108.69

C5C6H8 b8 111.05 110.92 111.23 111.18 111.18 111.11 111.25 110.87

C5C6H9 b9 111.20 110.99 110.97 110.77 111.29 111.13 110.77 110.64

C5C6H10 b10 111.20 111.09 110.97 110.65 111.29 110.86 110.77 110.55

H1C1C2C5 f1 0.0 22.81 0.0 12.85 0.0 16.68 0.0 8.62

H2C1C2C5 f2 119.98 142.76 119.98 132.80 119.98 136.61 119.99 128.80

H3C1C2C5 f3 2119.98 297.22 2119.98 2107.17 2119.98 2119.92 2119.99 2111.34

H4C4C3C5 f4 121.97 122.18 119.98 121.59 119.98 122.16 119.99 121.37

H5C4C3C5 f5 2121.97 2121.90 2121.89 2122.24 2122.15 2122.20 2121.71 2122.08

H6C5C4C6 f6 121.97 121.60 122.10 121.94 122.25 122.02 122.06 121.31

H7C5C4C6 f7 2121.97 2122.71 2122.10 2122.16 2122.25 2122.55 2122.06 2120.94

H8C6C5C4 f8 180.0 179.24 180.0 179.55 180.0 180.31 180.0 179.98

H9C6C5C4 f9 60.06 59.43 59.94 59.58 59.98 60.34 59.89 58.96

H10C6C5C4 f10 260.06 260.64 259.94 260.12 259.98 259.45 259.89 260.61

lmal 0.014 0.037 0.012 0.047 0.019 0.067 0.146 0.047

lmbl 0.142 0.070 0.170 0.090 0.137 0.069 0.087 0.090

lmcl 0.000 0.085 0.000 0.093 0.000 0.078 0.000 0.093

lmtl 0.143 0.116 0.170 0.138 0.139 0.123 0.170 0.138

A 18168 7876 17854 7735 17907 7755 17732 7721

B 1195 1586 1196 1616 1189 1588 1199 1618

C 1153 1402 1153 1421 1147 1400 1155 1423

k 20.9950 20.9431 20.9948 20.9382 20.9949 20.8407

F 6.0827 5.4956 5.9783 5.3940 5.9672 5.3809

F p 6.0858 5.6895 5.9783 5.5893 5.9731 5.5818

a Kinetic constants for methyl internal rotation: F applies to C6 methyl, F p to C1 methyl labeled pCH3.


good correspondence with the experimental spectrum

for 2-hexyne with the exception of the intensities of

the lines in the 250–380 cm21 region. The problem

here arises from the poor prediction of the out-of-

plane bend of the C2xC3–C4 group from the MP2/6-

31G(d) calculations. Without scaling this fundamental

which is the strongest predicted Raman line in this

region is predicted at 261 cm21 and with scaling at

299 cm21, whereas the band is actually observed

nearly 100 cm21 higher at 392 cm21. Excluding this

problem the predicted Raman spectrum is quite useful

for making the correct assignment of the observe

fundamentals for the two conformers.

Infrared intensities were calculated based on the

dipole moment derivatives with respect to the

Cartesian coordinates. The derivatives were taken

from the ab initio calculation transformed to normal

coordinates by

›mu

›Qi

� �¼X

j

›mu

›Xj

!Lij

where the Qi is the ith normal coordinate, Xj is the jth

Cartesian displacement coordinate, Lij is the trans-

formation matrix between the Cartesian displacement

coordinates and normal coordinates. The infrared

intensities were then calculated by

Ii ¼Np

3c2

›mx

›Qi

� �2

þ›my

›Qi

� �2

þ›mz

›Qi

� �2" #

In Fig. 8C and D are the predicated spectra of the pure

anti and gauche conformers, respectively. In Fig. 8B

the predicated spectrum of the mixture utilizing the

DH value of 74 cm21 is shown which is in good

agreement with the experimental spectrum of the

sample dissolved in liquid krypton solution (Fig. 8A)

at a temperature of 2105 8C. For example, it was

quite easy to identify the bands due to the anti and

gauche conformers in the region 1100–500 cm21

from the predicated spectrum (Fig. 3). Thus, the

predicted infrared spectrum made it relatively easy to

assign the fundamentals for both conformers.

5. Vibration assignment

The anti conformer of 2-hexyne has Cs symmetry

and the fundamental vibrations span the irreducible

representation 25A0 þ 17A00. The ab initio calculation

shows that the c principal axis of the anti conformer is

perpendicular to the symmetry plane (Table 4).

Therefore, the out-of-plane modes are expected to

give rise to C-type band contours in the infrared

spectrum, yield depolarized lines in the Raman spec-

trum and will not be observed in the Raman spectrum of

the gas, whereas the in-plane modes should give rise to

A-, B-, or A/B hybrid-type infrared contours. For the

gauche conformer, the infrared band contours can be A-,

B- and C-types and any hybrid of these three types

because it has only the trivial C1 symmetry. The

predicted vibrational–rotational infrared band contours

Fig. 6. Internal coordinates of 2-hexyne.

Fig. 7. Raman spectrum of 2-hexyne: (A) observed spectrum of the

liquid; (B) simulated spectrum of the mixture of anti and gauche

conformers with DH ¼ 74 cm21; (C) calculated for pure anti

conformer; (D) calculated for pure gauche conformer.


Table 5

Symmetry coordinates for vibrations of 2-hexyne

Description Symmetry coordinate

A0

pCH3 antisymmetric stretch S1 ¼ 2r1 2 r2 2 r3

CH3 antisymmetric stretch S2 ¼ 2r8 2 r9 2 r10

CH2 symmetric stretch S3 ¼ r6 þ r7pCH3 symmetric stretch S4 ¼ r1 þ r2 þ r3

CH3 symmetric stretch S5 ¼ r8 þ r9 þ r10pCH2 symmetric stretch S6 ¼ r4 þ r5

C2 xC3 stretch S7 ¼ T

CH2 scissors S8 ¼ (p

6 þ 2)d5 2 b6 2 b7 2 g6 2 g7 2 (p

6 2 2)u

CH3 antisymmetric deformation S9 ¼ 2a8 2 a9 2 a10pCH2 scissors S10 ¼ (

p6 þ 2)d4 2 b4 2 b5 2 g4 2 g5 2 (

p6 2 2)e

pCH3 antisymmetric deformation S11 ¼ 2a1 2 a2 2 a3pCH3 symmetric deformation S12 ¼ a1 þ a2 þ a3 2 b1 2 b2 2 b3

CH3 symmetric deformation S13 ¼ a8 þ a9 þ a10 2 b8 2 b9 2 b10

CH2 wag S14 ¼ b6 þ b7 2 g6 2 g7pCH2 wag S15 ¼ b4 þ b5 2 g4 2 g5

C3–C4 stretch S16 ¼ U

CH3 rock ip S17 ¼ 2b8 2 b9 2 b10pCH3 rock ip S18 ¼ 2b1 2 b2 2 b13

C5–C6 stretch S19 ¼ X

C4–C5 stretch S20 ¼ V

C1–C2 stretch S21 ¼ S

C3C4C5 bend S22 ¼ (p

6 þ 2)u 2 b4 2 b5 2 g4 2 g5 2 (p

6 2 2)d4

C4C5C6 bend S23 ¼ (p

6 þ 2)e 2 b6 2 b7 2 g6 2 g7 2 (p

6 2 2)d5

C1–C2xC3 bend ip S24 ¼ z

C2xC3–C4 bend ip S25 ¼ jpCH3 redundancy R1 ¼ a1 þ a2 þ a3 þ b1 þ b2 þ b3

CH3 redundancy R2 ¼ a8 þ a9 þ a10 þ b8 þ b9 þ b10pCH2 redundancy R3 ¼ e þ b4 þ b5 þ g4 þ g5 þ d4

CH2 redundancy R4 ¼ u þ b6 þ b7 þ g6 þ g7 þ d5

A00

pCH3 antisymmetric stretch S26 ¼ r2 2 r3

CH2 antisymmetric stretch S27 ¼ r6 2 r7

CH3 antisymmetric stretch S28 ¼ r9 2 r10pCH2 antisymmetric stretch S29 ¼ r4 2 r5

CH3 antisymmetric deformation S30 ¼ a9 2 a10pCH3 antisymmetric deformation S31 ¼ a2 2 a3

CH2 twist S32 ¼ b6 2 b7 2 g6 þ g7pCH2 twist S33 ¼ b4 2 b5 2 g4 þ g5pCH2 rock S34 ¼ b4 2 b5 þ g4 2 g5pCH3 rock op S35 ¼ b2 2 b3

CH3 rock op S36 ¼ b9 2 b10

CH2 rock S37 ¼ b6 2 b7 þ g6 2 g7

C2xC3–C4 bend op S38 ¼ j0

CH3 torsion S39 ¼ f

C1–C2xC3 bend op S40 ¼ z0

C6C5C4C3 torsion S41 ¼ tpCH3 torsion S42 ¼ f p

p Asterisks indicate the C atoms attached at both ends of the CxC bond.


Table 6

Calculated and observed vibrational wavenumbers (cm21) of anti 2-hexyne

Vib. No. Approximate descriptiona HF 6-31G B3LYP 6-31G(d) MP2 6-31G(d) MP2 6-3lG(d) b IR Raman act.e Depol. ratio PEDf

Obs.c Int.d

A0

n1pCH3 antisymmetic stretch 3258 3115 3194 2997 2972 26.5 97.7 0.75 99S1

n2 CH3 antisymmetric stretch 3255 3095 3185 2988 (2955) 10.0 92.6 0.62 100S2

n3 CH2 symmetric stretch 3198 3052 3115 2922 2931 24.9 77.1 0.18 97S3

n4pCH3 symmetric stretch 3190 3042 3102 2910 2919 17.0 226.8 0.01 98S4

n5 CH3 symmetric stretch 3182 3035 3101 2909 (2903) 30.0 208.3 0.01 99S5

n6pCH2 Symmetric stretch 3177 3016 3081 2891 2880 18.0 29.8 0.32 98S6

n7 C2xC3 stretch 2547 2371 2309 2191 2188 0.0 134.5 0.34 81S7

n8 CH2 scissors 1665 1538 1571 1491 1462 5.2 2.4 0.55 53S8, 38S9

n9 CH3 antisymmetric deformation 1653 1522 1557 1479 1447 0.7 32.8 0.74 55S9, 40S8

n10pCH2 scissors 1644 1510 1547 1468 1435 6.6 16.8 0.70 93S10

n11pCH3 antisymmetric deformation 1642 1506 1542 1464 1450 1.0 27.6 0.75 91S11

n12pCH3 symmetric deformation 1589 1445 1472 1397 1390 5.5 33.6 0.51 61S12, 35S13

n13 CH3 symmetic deformation 1579 1442 1471 1396 1382 0.2 1.4 0.67 58S13, 36S12

n14 CH2 wag 1529 1404 1433 1361 1348 3.3 8.8 0.54 49S14, 31S15

n15pCH2 wag 1463 1323 1342 1276 1282 10.4 7.7 0.52 50S15, 29S14

n16 C3–C4 stretch 1240 1175 1203 1142 1135 0.6 0.4 0.51 41S16, 42S21

n17 CH3 rock in-plane 1225 1120 1151 1104 1097 3.0 8.3 0.15 38S17, 26S20, 11S23

n18pCH3 rock in-plane 1196 1070 1091 1036 1036 0.7 0.3 0.64 65S18, 22S20

n19 C5–C6 stretch 1115 1046 1074 1025 1032 0.9 12.1 0.62 90S19

n20 C4–C5 stretch 971 900 929 884 893 3.3 18.0 0.34 35S20, 34S17, 18S18

n21 C1–C2 stretch 824 772 778 746 739 0.3 2.4 0.39 35S21, 25S16, 14S7

n22 C3C4C5 bend 604 487 441 453 478 2.6 14.8 0.59 47S22, 21S25, 12S16

n23 C4C5C6 bend 387 338 325 328 359 0.7 6.6 0.43 72S23, 14S25

n24 C1–C2xC3 bend in-plane 320 279 212 257 272 3.8 1.2 0.73 100S24

n25 C2xC3–C4 bend in-plane 115 102 92 105 115 1.1 1.5 0.73 79S25, 25S22

A00

n26pCH3 antisymmetric stretch 3258 3110 3192 2995 2972 44.0 95.4 0.75 84S26, 16S28

n27 CH2 antisymmetric stretch 3258 3095 3186 2989 2995 9.9 22.8 0.75 100S27

n28 CH3 antisymmetric stretch 3230 3083 3165 2969 2942 8.9 51.4 0.75 78S28, 16S26

n29pCH2 antisymme tric stretch 3206 3042 3126 2932 (2937) 7.5 145.2 0.75 94S29

n30 CH3 antisymmetric deformation 1656 1530 1564 1484 1453 7.6 23.7 0.75 93S30

n31pCH3 antisymmetric deformation 1642 1510 1547 1469 1450 6.0 25.5 0.75 94S31

n32 CH2 twist 1454 1337 1364 1294 1294 0.0 24.9 0.75 64S32, 27S33

n33pCH2 twist 1397 1274 1303 1236 1231 0.2 0.6 0.75 39S33, 25S36, 20S37

n34pCH2 rock 1260 1138 1156 1101 1091 0.5 0.1 0.75 26S34, 29S33, 19S37

n35pCH3 rock out-of-plane 1196 1070 1075 1025 1032 1.2 0.2 0.75 88S35


S.

Bell

eta

l./

Jou

rna

lo

fM

olecu

lar

Stru

cture

61

6(2

00

2)

13

5–

15

81

47

of both the anti and gauche conformers are shown in

Figs. 9 and 10. They have been calculated by an

asymmetric top program using the rotational constants

given in Table 4 as obtained from the B3LYP

calculations.

The major difference of the band contours is for

the pure B and C bands of the anti conformer

where the spacing for the R and P branches is

significantly larger so the rotational fine structure

will be more discernible for this conformer

compared to the corresponding bands of the gauche

conformer. This information was particularly

important for distinguishing the bands in the low

wavenumber spectral region. In the ‘fingerprint’

spectral region most of the fundamentals could be

assigned based on the ab initio predicted frequen-

cies, infrared intensities, and Raman activities,

particularly once the bands were identified for the

gauche conformer after their disappearance from

the spectrum of the solid. A previous vibrational

assignment has been given [16] based on exper-

iment spectra and normal coordinate calculations

with transferred force constants but before theTab

le6

(co

nti

nued

)

Vib

.N

o.

Ap

pro

xim

ate

des

crip

tio

na

HF

6-3

1G

B3

LY

P6

-31

G(d

)M

P2

6-3

1G

(d)

MP

26

-3lG

(d)

bIR

Ram

anac

t.e

Dep

ol.

rati

oP

ED

f

Ob

s.c

Int.

d

n36

CH

3ro

cko

ut-

of-

pla

ne

98

08

84

90

18

57

86

60

.51

.40

.75

36

S36,4

0S

34,

16

S32

n37

CH

2ro

ck8

24

75

17

63

72

67

40

2.7

0.4

0.7

55

4S

37,

28

S34,

12

S36

n38

C2x

C3–

C4

ben

do

tlt-

Of-

pla

ne

53

93

80

26

12

99

39

20

.62

1.1

0.7

54

1S

38,4

3S

39,1

6S

41

n39

CH

3to

rsio

n2

50

24

52

42

24

92

38

0.5

0.0

0.7

55

5S

39,

40

S38

n40

C1–

C2x

C3

ben

do

ut-

of-

pla

ne

24

12

21

20

62

46

22

06

.40

.00

.75

10

0S

40

n41

C6C

5C

4C

3to

rsio

n8

88

48

38

78

80

.30

.60

.75

70

S41,

28

S38

n42

pC

H3

tors

ion

12

16

14

14

0.0

0.0

0.7

51

00

S42

aA

ster

isks

indic

ate

Cat

om

sat

tach

edto

both

ends

of

the

Cx

Cb

on

d.

bS

cale

fact

ors

for

forc

eco

nst

ants

:0

.9fo

ral

lC

Cst

retc

hes

,0.8

8fo

rC

Hst

retc

hes

,0.9

for

CC

Hd

efo

rmat

ion

s,1

.0fo

rh

eav

y-a

tom

ben

ds

exce

pt1

.5fo

rCx

C–

Cli

nea

rb

end

s,an

d1

.0

for

tors

ion

s.e

Cal

cula

ted

Ram

anac

tivit

ies

inA

4/a

mu

atth

eM

P2

/6-3

1G

(d)

lev

el.

fC

alcu

late

dat

the

MP

2/6

-31

G(d

)le

vel

;co

ntr

ibu

tio

ns

less

than

10

%ar

eo

mit

ted.

cO

bse

rved

freq

uen

cies

are

fro

mth

ein

frar

edsp

ectr

um

of

the

gas

exce

pt

tho

sew

ith

inb

rack

ets

are

fro

mth

esp

ectr

um

of

the

soli

d.

dC

alcu

late

din

frar

edin

ten

siti

esin

km

/mo

lat

the

MP

2/6

-31

G(d

)le

vel

.

Fig. 8. Mid-infrared spectrum of 2-hexyne: (A) observed spectrum

in the krypton solution (at 2105 8C); (B) simulated spectrum of the

mixture of anti and gauche conformers with DH ¼ 74 cm21; (C)

calculated for pure anti conformer; (D) calculated for pure gauche

conformer.


Table 7

Calculated and observed vibrational wavenumbers (cm21) of gauche 2-hexyne

Vib. No. Approximate descriptiona HF 6-31G 3LYP 6-31G(d) MP2 6-31G(d) MP2 6-3lG(d)b IR Raman act.e Depol. ratio PEDf

Obs.c Int.d

n1pCH3 antisymmetric stretch 3258 3111 3191 2993 33.0 101.6 0.75 64S1,32S26

n2 CH3 antisymmetric stretch 3252 3095 3185 2988 9.6 69.2 0.64 57S2,43S27

n3 CH2 symmetric stretch 3190 3041 3103 2911 25.4 54.8 0.06 95S3

n4pCH3 symmetric stretch 3191 3046 3105 2913 19.4 448.1 0.04 99S4

n5 CH3 symmetric stretch 3183 3036 3101 2909 27.3 23.8 0.69 100S5

n6pCH2 symmetric stretch 3178 3020 3084 2893 19.6 51.4 0.30 98S6

n7 C2xC3 stretch 2545 2369 2306 2188 0.2 120.8 0.33 81S7

n8 CH2 scissors 1664 1538 1571 1491 5.4 2.8 0.75 72S8, 14S9

n9 CH3 antisymmetric deformation 1652 1518 1553 1474 1.1 34.6 0.74 79S9, 17S8

n10pCH2 scissors 1642 1510 1546 1467 6.3 19.3 0.74 92S10

n11pCH3 antisymmetric deformation 1642 1504 1539 1461 3.7 25.0 0.75 92S11

n12pCH3 symmetric deformation 1579 1442 1471 1396 4.7 2.4 0.60 86S12, 1013

n13 CH3 symmetric deformation 1589 1445 1474 1398 5.3 32.6 0.51 7813, 11S12

n14 CH2 wag 1532 1393 1418 1346 1342 3.2 2.3 0.60 70S14

n15pCH2 wag 1503 1380 1406 1334 1336 13.1 19.7 0.55 56S15, 24S32

n16 C3–C4 stretch 1259 1175 1203 1143 0.4 0.4 0.18 37S16, 37S21, 16S15

n17 CH3 rock in-plane 1202 1104 1133 1084 1073 2.2 5.2 0.71 29S17, 24S18, 15S34

n18pCH3 rock in-plane 1195 1070 1075 1026 1024 1.5 0.2 0.59 25S18, 20S20, 12S14

n19 C5–C6 stretch 1123 1043 1074 1021 1018 2.3 8.2 0.73 83S19

n20 C4–C5 stretch 928 867 896 853 856 0.2 16.3 0.28 20S20, 35S34, 289S17

n21 C1–C2 stretch 750 701 712 680 686 0.7 7.4 0.28 23S21, 27S16, 20S37

n22 C3C4C5 bend 622 523 505 512 513 1.2 10.8 0.59 34S22, 12S23, 25S25

n23 C4C5C6 bend 537 383 347 356 359 0.9 20.1 0.75 38S23, 26S18, 11S41

n24 C1–C2xC3 bend in-plane 261 243 221 255 210 4.5 0.0 0.58 61S24, 27S39

n25 C2xC3–C4 bend in-plane 140 127 123 137 120 1.6 0.9 0.69 40S25, 19S22, 24S41

n26pCH3 antisymmetric stretch 3270 3126 3205 3007 25.8 26.3 0.73 62S26, 36S1,

n27 CH2 antisymmetric stretch 3258 3095 3186 2988 9.7 99.8 0.75 57S27, 43S2

n28 CH3 antisymmetric stretch 3227 3080 3157 2961 19.7 66.6 0.74 88S28

n29pCH2 antisymmetric stretch 3215 3055 3132 2938 18.4 158.7 0.54 91S29

n30 CH3 antisymmetric deformation 1658 1529 1564 1484 5.6 12.3 0.64 77S30

n31pCH3 antisymmetric stretch 1642 1510 1547 1467 6.4 35.7 0.73 92S31

n32 CH2 twist 1427 1307 1332 1265 0.3 11.6 0.63 46S32, 17S36, 16S15

n33pCH2 twist 1389 1268 1291 1227 1217p 1.1 7.2 0.65 59S33

n34 CH2 rock 997 902 924 879 889 2.1 2.0 0.58 20S34, 27S17, 21S20

n35pCH3 rock out-of-plane 1196 1071 1077 1027 1.5 0.2 0.74 82S35

n36 CH3 rock out-of-plane 1244 1132 1157 1104 0.1 2.3 0.28 15S36, 12S33, 20S37, l2S33

n37 CH2 rock 897 816 830 793 804 3.4 1.3 0.41 31S37, 27S36

n38 C2xC3–C4 bend out-of-plane 440 382 289 323 368 1.0 6.7 0.74 41S38, 15S40, 15S23


S.

Bell

eta

l./

Jou

rna

lo

fM

olecu

lar

Stru

cture

61

6(2

00

2)

13

5–

15

81

49

widespread use of predicated frequencies from ab

initio calculations and spectra recorded with better

resolution or at low temperatures.

In the carbon–hydrogen stretching region there are

three modes from each of the two methyl groups and

two each for the two methylene groups for both

conformers, but we shall address the assignments for

these modes for the anti conformer first. Since thepCH3 rotor (methyl group attached to the triple bond)

is essentially a ‘free’ rotor, the two pCH3 antisym-

metric stretches are degenerate and readily assigned to

the vibrational–rotational fine structure which is

centered at 2972 cm21. For the CH3 group the two

antisymmetric stretches are split and assigned at 2953

and 2945 cm21 (n2 and n28) which are wavenumbers

from the Raman spectrum of the solid. However, it is

possible that the n2 fundamental is coincident with the

n1 fundamental at 2972 cm21 because the CH2

antisymmetric stretch is most reasonably assigned at

2955 cm21 or at 2972 cm21. The pCH2 antisymmetric

stretch is assigned at 2937 cm21 since it is predictedTab

le7

(co

nti

nued

)

Vib

.N

o.

Ap

pro

xim

ate

des

crip

tio

na

HF

6-3

1G

3L

YP

6-3

1G

(d)

MP

26

-31

G(d

)M

P2

6-3

lG(d

)bIR

Ram

anac

t.e

Dep

ol.

rati

oP

ED

f

Ob

s.c

Int.

d

n39

CH

3to

rsio

n3

30

24

32

55

28

22

86

0.1

1.5

0.4

13

3S

39,

23

S40,

36

S24

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ate

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)le

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.

Fig. 9. Rotational contours of the anti conformer, A-, B-, and C-

type.


to be more than 50 cm21 lower than the

corresponding mode for the CH2 group. The

symmetric methyl and methylene stretches (n3

through n6) are assigned consistent with the order

predicted from the ab initio calculations along

with the predicted infrared intensities and Raman

activities. These assignments must be considered

somewhat tentative and could be made only more

confidently if selected deuteration were made on

each carbon atom. Some of the wavenumbers

listed for these modes in Table 1 from the spectra

of the gas, krypton, or liquid, could be due to the

corresponding vibrations for the gauche conformer

which is in greater abundance in the fluid states even

though the anti conformer is the more stable form.

The predicted infrared intensity for the CxC

stretch is essentially zero and without the Raman

data it could not be assigned. The propyl group on one

side of the triple bond is not sufficiently different from

the methyl group on the other end of the triple bond to

give enough asymmetry for an observable dipole

change for the vibration. In fact, the band

(2259 cm21) readily observed in the infrared spectra

in this region is a combination band that falls between

the Fermi doublet at 2302 and 2236 cm21 for the CxC

stretch which is observed in the Raman spectrum.

Fig. 10. Rotational contours of the gauche conformer, A-, B-, and C-type.


There is also some ambiguity on the assignments

for two of the four methyl antisymmetric defor-

mations and the two methylene scissors. The twopCH3 antisymmetric deformations appear as a degen-

erate mode centered at 1450 cm21 with the typical

vibrational–rotational fine structure of a perpendicu-

lar symmetric top mode. The other four fundamentals

in this spectral region were assigned for the anti

conformer based on the scaled MP2/6-31G(d) ab

initio predicted wavenumbers and the observed bands

in the infrared and Raman spectra of the solid. The

remaining carbon–hydrogen bends, as well as the

heavy atom stretches, can be confidently assigned

from the ab initio predicted wavenumbers, infrared

intensities, Raman activities, and band contours.

However, the low frequency skeletal bends are better

predicted from the DFT calculations by the B3LPY

method than from the scaled ab initio calculations,

even with the scaling factor of 1.5 for the triple bond

bends. Nevertheless, there is little question concern-

ing their assignment for the anti conformer utilizing

the low wavenumber data from the infrared and

Raman spectra of the solid (Figs. 1 and 2).

For the gauche conformer, most of the funda-

mentals lower in wavenumber than the carbon–

hydrogen deformations could be assigned from their

disappearance from the spectra of the fluid phases

when the sample crystallizes to the solid phase. The

fundamental for this conformer in the higher wave-

number range, i.e. carbon–hydrogen stretches, CxC

stretch, and carbon–hydrogen deformations, are

expected to be in near coincident with the correspond-

ing modes of the anti conformer. For example, the

CxC stretch is predicted to only differ by three

wavenumbers for the two conformers. The complete

assignment of the normal modes of both anti and

gauche conformers are reported in Tables 6 and 7,

respectively.

6. Coriolis interaction

As in 2-pentyne [3] and 5-fluoro-2-pentyne [9],

the infrared spectrum of the gas exhibits sub-band

structure with strong–weak–weak–strong intensity

alternation associated with the antisymmetric pCH3

stretching vibrations and the antisymmetric pCH3

deformation modes (Figs. 11 and 12). This band

structure is typical of perpendicular bands of

symmetric top molecules such as the methyl

halides and 1-halo-propynes but in these molecules,

it is caused by the Coriolis interaction of the

overall rotational motion of the molecule with the

angular momentum of the E vibrations of

the methyl group. Similar sub-band structure has

been observed in the corresponding bands in the

infrared spectra of the 1-halo-2-butynes [7,24]

which are not symmetric top molecules. The Q

branches of the different sub-bands agree well with

the formula nsub0 ¼ c0 ^ c1m þ c2m2:

For a perpendicular band of a symmetric-top

molecule such as the degenerate fundamentals of a

methyl group, the formula for the sub-band structure

with the type of intensity alternation already men-

tioned has been given [25,26] by

nsub0 ¼ n0 þ ½A0ð1 2 zÞ2 2 B0�^ 2½A0ð1 2 zÞ2 B0�K

þ ½ðA0 2 B0Þ2 ðA00 2 B00Þ�K2

where z is the Coriolis coupling constant and the

factor (1 2 z )2 is used [25,26] rather than (1 2 2z ) as

in Herzberg [27] and Nyquist [28]. The single prime

refers to the upper state and double prime to the lower

state.

However, in the case of the 1-halo-2-butynes [7,

24], 2-pentyne [3], 5-fluoro-2-pentyne [9] and 2-

hexyne, the sub-band structure is due to the

interaction of the vibrational angular momentum of

the pseudo-degenerate vibrations with the internal

rotational angular momentum of the almost freely

rotating internal top and not with the overall rotation

of the molecule. From the energies of several ab initio

calculations of eclipsed and staggered configurations

of the C1 methyl of 2-hexyne (Table 3), it is evident

that the barrier to internal rotation of the pCH3 group

is very small, being only a few cm21 for all

calculation models used.

A quadratic equation can be derived from the first

principles using the appropriate Hamiltonian, but in

order to retain the z notation, the following equation

can be derived from the sub-band formula for overall

rotation of symmetric top molecules by elimination of

the kinetic constants for overall rotation, B or

(B þ C )/2, and by replacing the A constants with F1

which is h=8p2cIredt ; the inverse reduced moment of

inertia for internal rotation of the methyl top in the


slightly asymmetric top molecule

nsub0 ¼ ½n0 þ F0

1ð1 2 zÞ2� þ 2F01ð1 2 zÞm

þ ðF01 2 F00

1Þm2:

In 2-hexyne, the anti conformer is shown to be lower;

a complete vibrational analysis is given above, and it

is also more nearly a symmetric top than the gauche

conformer. The sub-band structure probably arises

from the near degeneracy of n1/n26 and n11/n31 of the

anti form. Values for kinetic constant F001 in the ground

vibrational state are obtained from ab initio optimized

geometric structures of the anti conformer given in

Table 4.

The measurements of the observed sub-bands shown

in Figs. 11 and 12 are given in Table 8. Fits to the sub-

band peaks have been made by the least-squares method

to the formula nsub0 ¼ c0 ^ c1m þ c2m2 and the coeffi-

cients are given in Table 8. For each of the bands, the

quadratic coefficient c2 is small; it is the change in the

internal rotational constant, F, between the ground and

excited states. Taking F00 ¼ 5:9731 cm21 from the

B3LYP geometric structure calculation, for the C–H

nearly degenerate stretching fundamental, n1/n26, we

obtain z ¼ 0:166 ^ 0:002 from the coefficient of the

linear term, 2F0ð1 2 zÞ; and from n0 þ F0ð1 2 zÞ2 the

band center, n0, is 2971.7 cm21. This value of

the antisymmetric pCH3 stretching fundamental is

very near that obtained for 2-pentyne [3].

The sub-band series is more difficult to discern for

the deformation fundamental, n11/n31 as the series is

interrupted in the middle with an interval of 22 cm21

instead of 14 cm21 and only the more obvious part is

used in a fit to obtain z ¼ 20:178 ^ 0:02 from the

linear term and the origin n0 is 1450.0 cm21.

However, this value for the deformational funda-

mental is in very good agreement with the value in 2-

pentyne and indeed it is within the range of

1451 ^ 2 cm21 for molecules considered with 1-

fluoro-2-butyne [7].

7. Discussion

The experimentally determined enthalpy differ-

ence of 74 ^ 8 cm21 for 2-hexyne is slightly lower

than the value of 50 ^ 6 cm21 obtained for 1-pentyne

[4] with the anti form the more stable conformer in

each case. Thus, the methyl group attached to the

carbon–carbon triple bond does not significantly

affect the conformational stability of 2-hexyne.

However, it should be noted that the ab initio MP2

calculations incorrectly predict the conformer stab-

ility and there is little difference in the predicted

energy difference with a small basis set of 6-31G(d)

with frozen core (146 cm21) and the much larger

basis set of 6-311G(2d,2p) with full electron corre-

lation (154 cm21). However, it should be noted that

all of the DFT calculations predict the correct

conformer stability. The similar problem exists for

Fig. 11. Sub-band structure in the degenerate CH3 antisymmetric

stretching band due to Coriolis interaction.

Fig. 12. Sub-band structure in the degenerate CH3 antisymmetric

deformation band due to Coriolis interaction.


1-pentyne where the ab initio MP2 calculations with

the 6-31G(d) basis set also incorrectly predicted the

gauche conformer as the more stable form by

122 cm21. Also, the MP2/g-311 þ G(d,p) calcu-

lations predicted the gauche conformer as the more

stable rotamer by 103 cm21. Because the ab initio

MP2 calculations predict such a long CxC bond, the

relative predicted energies for the two conformers is

in error for both molecules.

Apart from the frequency for the torsion of the

methyl group on the CxC (which is essentially free)

bond, the lowest frequency (Tables 6 and 7)

calculated for each of the conformers is the asym-

metric skeletal torsion: anti, 84.6, 83.2, and

86.8 cm21 from the B3LYP, MP2, MP2 scaled

calculations, respectively; and gauche, 89.4, 86.2,

and 93.9 cm21 from the B3LYP, MP2, MP2 scaled

calculations, respectively. From a calculation of the F

series for the kinetic part of the torsional problem and

from the potential function obtained from the B3LPY

energies of the four conformers in Table 3 and plotted

in Fig. 5, the torsional fundamentals are predicted as

83.5 and 86.0 cm21 for the anti and gauche

conformers, respectively. The absorption hump

around 90 cm21 is clearly to be identified with

asymmetric torsion. In view of the fact that the

gauche torsional fundamental is calculated as higher

than the anti fundamental, the small peak at 91 cm21

is assigned to the anti fundamental and the shoulder at

87 cm21 to the gauche fundamental. The value of DH

obtained from temperature-dependent infrared spectra

of 74 cm21 (Table 2) is used as the 0 þ (g ) ˆ 0(t )

transition energy. Using these torsional intervals, the

torsional angle of 62.68 of the gauche conformer, and

the F series from the B3LYP parameters an

experimental potential energy function is obtained

Table 8

Coriolis structure of nearly degenerate CH3 antisymmetric stretch and deformation bands of 2-hexyne

m CH3 antisymmetric stretch CH3 antisymmetric deformation

nobs nobs 2 ncalc nobs nobs 2 ncalc

13 3097.40 20.46

12 3089.19 0.24

11 3080.16 0.20 1605.10 20.27

10 3071.04 0.16 1592.63 0.04

9 3061.62 20.12 1580.32 0.63

8 3052.64 0.13 1566.69 0.02

7 3043.30 0.10 1553.05 20.48

6 3033.99 0.17 1540.30 0.03

5 3024.26 20.10 1526.70 20.20

4 3014.44 20.37 1513.60 0.19

3 3005.20 0.01 1499.83 0.03

2 2995.54 0.04 1477.56

1 2985.80 0.08 1464.91

0 2975.10 20.76 1448.02

21 2966.60 0.67 1434.59

22 1419.11

23 1404.98

24 1391.76

25 1377.85

26 1363.26

St. dev. 0.36 0.36

c0 2975.86 ^ 0.19 1458.3 ^ 0.9

c1 9.8947 ^ 0.0716 14.020 ^ 0.292

c2 20.0392 ^ 0.0057 20.059 ^ 0.021

z 0.166 ^ 0.002 20.178 ^ 0.024

n0 2971.74 ^ 0.2 1450.0 ^ 0.9


by fit. The constants are V1 ¼ 218; V2 ¼ 220; V3 ¼

1475; V4 ¼ 2104 cm21 with the DH of 72.2 cm21.

This function is also plotted in Fig. 5.

The predicted structural parameters for the two

conformers do not differ significantly with the bond

distances having variations of usually 0.001–0.002 A.

There are only slightly more variations in the angles

with the most apparent ones the dihedral angles.

However, such small changes are not expected to give

rise to large variations in the force constants. This is

exactly what is found with the variations usually less

than 2%. The exceptions are for several of the angle

bends.

The major difference in force constant values,

excluding those for the torsional modes, is found for

the C3C4C5 and C4C5C6 angle bends which are 11.8

and 8% smaller, respectively, for the anti conformer

compared to the corresponding ones for the gauche

form, i.e. 0.635 versus 0.710 and 0.710 versus

0.767 mdyn/A. Smaller differences of 4.9 and 3.2%

are obtained for the C2C3C4 and C1C2C3 in-plane

bends with those for the anti conformer again having

the lower values (0.389 versus 0.408 and 0.373 versus

0.385 mdyn/A). Another noteworthy difference is the

C6C5H7 bending force constant which is 3.4% lower

for the anti conformer (0.562 versus 0.581 mdyn/A).

Major differences are also predicted for the force

constants for the asymmetric and CH3 torsions with

values of 37 and 8.9% lower for the anti conformer.

Therefore, most of the significant differences in

frequencies for the normal modes are due to the

differences in the PEDs rather than differences in the

force constants.

The PEDs are reasonably pure for the anti

conformer with major mixing of the pCH2, CH2,pCH3 and CH3 rocks, along with some of the carbon–

carbon stretches. Several of these fundamentals have

only 35–41% contributions of the symmetry coordi-

nate for which the band is assigned. For most of these

vibrations there are significant contributions from

three symmetry coordinates. For the gauche con-

former which has no symmetry elements, the mixing

is much more extensive. For example, n17 and n18

which are methyl rocks and n20 and n21 which are

carbon–carbon stretches have only 20–29% of those

indicated symmetry coordinates contributing to these

bands. Similarly, n36 which is designed as the CH3

rock, has only 15% of S36 contributing to this mode,

with the other three contributions greater than 10%

being only 12, 12 and 20%. Therefore, the approxi-

mate descriptions given for the fundamentals of the

gauche conformer are much less an indication of the

motions than those for the anti conformer.

Assuming the internal rotation of the C5 methyl

group as an independent coordinate and from the

methyl barriers given in Table 3 and the F value given

in Table 4, the methyl torsional fundamental is

predicted to be at 220 cm21 in the anti conformer

and at 216 cm21 in the gauche form. These are a little

lower than predicted by the harmonic vibrational

force field but the symmetry coordinates are con-

siderably mixed as shown in the PED.

Taking the heavy atom torsional motion as a

separate coordinate and from a F series determined

from the geometrical structures of both anti and

gauche forms, the fundamental transitions for

C3C4C5C6 torsion are predicted to be at 111 cm21

for the anti conformer and at 98 cm21 in the gauche

form. These fundamental frequencies are a little

higher than indicated by the harmonic force field but

more in agreement with the magnitudes of the

observed and assigned far infrared bands.

In the earlier proposed assignment [15] many of

the fundamentals for the anti conformer were

assigned as being accidentally degenerate since only

the infrared spectra of the liquid and solid and the

Raman spectrum of the liquid were utilized for the

identification of the fundamentals. For example, in

the carbon–hydrogen stretch region only five of the

ten fundamentals were identified and the carbon–

hydrogen deformations only three individual bands

were assigned for the eight fundamentals. Similar dual

assignments were given for several of the funda-

mentals in the fingerprint region whereas others were

predicated form normal coordination calculations but

left unassigned, i.e. predicated fundamentals at 1102,

1019, and 911 cm21 which we observed at 1091,

1032, and 892 cm21, respectively.

Similar multiple assignments were previously

given [15] for some of the carbon–hydrogen bending

or carbon–carbon stretching modes for the gauche

conformer. However, from the spectral data from the

krypton solution it was possible to assign most of the

fundamentals in the fingerprint region to the gauche

conformer to individual bands that were not present in

the spectra of the solid. However, it should be noted


that many of these fundamentals were predicated

reasonably well from the earlier [15] normal coordi-

nate calculation which was obtained from transferred

force constants from 1- and 2-butyne and 2-pentyne.

Nevertheless, many of the fundamentals for the two

conformers were predicated to be nearly degenerate,

particularly those associated with the two methyl

groups.

There does not appear to have been a structural

determination of 2-hexyne by the electron diffraction

Table 9

Comparison of the structural parameters (bond distances in A, angles in degrees, rotational constants in MHz, dipole moments in Debye, and

energies in Hartree) for anti and gauche 1-pentyne (all columns except the last two are for 1-pentyne) and 2-hexyne from experimental values

and ab initio calculations

MP2/6-311 þ G(d,p) EDa MWb ro-adjustedc 2-hexyne (MP2/6-311G(d,p))

anti gauche anti gacuhe anti gauche anti gauche

r(C2–C3) 1.219 1.219 1.2220(7) 1.210 1.210 1.209 1.209 1.220(1.210) 1.220(1.210)

r(C3–C4) 1.462 1.464 1.4604(30) 1.460 1.460 1.462 1.463 1.463 1.464

r(C4–C5) 1.535 1.536 1.5372(15) 1.544 1.544 1.536 1.537 1.534 1.536

r(C5–C6) 1.526 1.525 1.5262 1.536 1.536 1.526 1.525 1.526 1.525

r(C4–H4) 1.096 1.095 1.1072(9) 1.094 1.094 1.096 1.095 1.097 1.100

r(C4–H5) 1.096 1.097 1.1072(9) 1.094 1.094 1.096 1.097 1.097 1.099

r(C5–H6) 1.095 1.096 1.095 1.096 1.095 1.098

r(C5–H7) 1.095 1.095 1.095 1.095 1.095 1.097

r(C6–H9) 1.094 1.095 1.094 1.095 1.094 1.097

r(C6–H10) 1.094 1.093 1.094 1.093 1.094 1.095

r(C6–H8) 1.094 1.093 1.094 1.093 1.093 1.096

/C2C3C4 178.3 178.9 180.0 180.0 180.0 178.3 178.9 178.2 179.2

/C3C4C5 112.6 112.4 113.5(4) 111.5 111.5 112.3 112.1 112.7 112.5

/C4C5C6 111.9 112.4 111.7(5) 111.5 112.4 112.9 113.5 112.0 112.4

/C3C4H4 109.2 109.0 110.0(5) 109.5 109.5 109.4 109.1 109.5 109.3

/C3C4H5 109.2 109.1 109.5 109.5 109.4 109.2 109.5 109.3

/H3C4H5 106.8 106.9 106.8 106.9 106.6 106.8

/C4C5H6 108.7 108.2 108.2 107.7 108.7 108.5

/C4C5H7 108.7 108.9 108.2 108.3 108.7 108.7

/H6C5H7 106.9 107.2 106.9 107.2 106.8 107.2

/H6C5C6 110.3 110.0 109.5 109.5 110.3 110.0 110.3 110.0

/H7C5C6 110.3 110.0 109.5 109.5 110.3 110.0 110.3 110.0

/C5C6H9 111.1 110.6 110.14 110.14 111.1 110.6 1.094 110.6

/C5C6H10 110.8 110.8 110.14 110.14 110.8 110.8 1.094 110.6

/C5C6H8 110.8 111.1 110.14 110.14 110.8 111.1 111.2 111.2

/H9C6H10 107.9 108.0 107.9 108.0 108.0 108.0

/H9C6H8 107.9 108.0 107.9 108.0 108.0 108.1

/H10C6H8 108.0 108.3 108.0 108.3 108.0 108.3

/C3C4C5C6 180.0 61.4 64.9(1.1) 180 65(3) 180.0 63.5 180.0 67.8

A 23393 9817 23340.0 9921.1 23340.2 9921.7

B 2226 3209 2230.6 3172.8 2229.6 3172.0

C 2113 2651 2116.4 2634.0 2115.2 2636.3

lmal 0.902 20.761

lmbl 0.068 0.329

lmcl 0.000 20.002

lmtl 0.905 0.829

2 (E þ 194) 0.8023933 0.8032195

DE (cm21 181

a Ref. [29].b Ref. [30].c Ref. [4].


technique or from a microwave study. Since the

dipole moment is so small (predicted value of 0.17D

for the anti form and 0.13D for gauche conformer) for

the 2-hexyne molecule it would be a very difficult

microwave problem. However, an electron diffraction

study [29] and the microwave spectrum has been

reported [30] for 1-pentyne which has larger dipole

moments of 0.92 and 0.82D for the anti and gauche

conformers, respectively. It is expected that the

determined structural parameters for 1-pentyne will

be very nearly the same as those for 2-hexyne.

Therefore, we have listed (Table 9) the previously

reported structural parameters for 1-pentyne along

with those predicted from MP2/6-311G(d,p) ab initio

calculations for both 1-pentyne and 2-hexyne. The

major difference in the r0 adjusted parameters for 1-

pentyne and those from the electron diffraction study

[29] or the ab initio predictions is the triple bond

distance of 1.209 A which does not differ significantly

with difference substitutes on the CxC triple bond.

Therefore, the predicted structural parameters from

the MP2/6-311G(d,p) calculations for 2-hexyne

should provide C–H distances within 0.003 A,

whereas all of the C–C distances except for the triple

bond are expected to be a little too short. The CxC

bond distance is predicted too long from MP2

calculations by 0.010–0.012 A, so the actual value

is expected to be near the value of 1.210 A which is

the distance predicted from the B3LYP/6-31G(d)

calculations. Making these adjustments to the car-

bon–carbon distances, it is expected that the predicted

values for the distances relative to the actual values

will be 0.005 A for the carbon–carbon distances and

0.003 A for the carbon–hydrogen distances. These

adjusted ab initio parameters are expected to be as

accurate as they can be experimentally measured. The

uncertainty for all of the angles is 0.58 except for the

gauche dihedral angle, C3C4C5C6, which is expected

to be 1.58.

Acknowledgments

J.R. Durig acknowledges the University of Kansas

City Trustees for a Faculty Fellowship award for

partial financial support of this research.

References

[1] G.A. Guirgis, J.R. Durig, S. Bell, J. Mol. Struct. 196 (1989)

101.

[2] S. Bell, G.A. Guirgis, Y. Li, J.R. Durig, J. Phys. Chem., A 101

(1997) 5987.

[3] S. Bell, G.A. Guirgis, S.W. Hur, J.R. Durig, Spectrochim. Acta

A 55 (1999) 2361.

[4] J.R. Durig, B.R. Drew, J. Mol. Struct. 560 (2001) 247.

[5] G.A. Guirgis, S. Bell, J.R. Durig, Spectrochim. Acta A 52

(1996) 1861.

[6] G.A. Guirgis, X. Zhu, S. Bell, J.R. Durig, J. Phys. Chem. A

105 (2001) 363.

[7] G.A. Guirgis, S. Bell, J.R. Durig, Spectrochim. Acta 57 (2001)

1235.

[8] G.A. Guirgis, S. Bell, J.R. Durig, J. Raman Spectrosc. 31

(2000) 987.

[9] S. Bell, X. Zhu, G.A. Guirgis, J.R. Durig, Phys. Chem. Chem.

Phys. 3 (2001) 776.

[10] J.R. Durig, J. Liu, T.S. Little, J. Phys. Chem. 96 (1992)

8224.

[11] W.A. Herrebout, B.J. van der Veken, J. Phys. Chem. 100

(1996) 9671.

[12] W.A. Herrebout, B.J. van der Veken, A. Wang, J.R. Durig,

J. Phys. Chem. 99 (1995) 578.

[13] G.A. Guirgis, X. Zhu, J.R. Durig, Struct. Chem. 10 (1999)

445.

[14] J.R. Durig, X. Zhu, S. Shen, J. Mol. Struct. 570 (2001) 1.

[15] J.R. Durig, B.R. Drew, A. Koomer, S. Bell, Phys. Chem.

Chem. Phys. 3 (2001) 766.

[16] G.A. Crowder, P. Blankenship, J. Mol. Struct. 196 (1989)

125.

[17] F.A. Miller, B.M. Harney, Appl. Spectrosc. 24 (1970) 291.

[18] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A.

Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery,

Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam,

A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi,

V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.

Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala,

Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck,

K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz,

B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,

R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham,

C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe,

P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres,

C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople,

GAUSSIAN98 (Revision A.5), Gaussian Inc., Pittsburgh, PA,

1998.

[19] G. Guirgis, X. Zhu, Z. Yu, J.R. Durig, J. Phys. Chem. A 104

(2000) 4383.

[20] M.J. Frisch, Y. Yamagushi, J.F. Gaw, J.F. Schaefer III, J.S.

Binkley, J. Chem. Phys. 84 (1986) 531.

[21] R.D. Amos, Chem. Phys. Lett. 124 (1986) 376.

[22] P.L. Polavarapu, J. Phys. Chem. 94 (1990) 8106.

[23] G.W. Chantry, in: A. Anderson (Ed.), (1971) The Raman

Effect, vol. 1, Chapter 2, Marcel Dekker, New York, NY.

[24] R.D. McLachlan, Spectrochim. Acta A 23 (1967) 1793.


[25] D.W. Davidson, H.J. Bernstein, Can. J. Chem. 33 (1955) 1226.

[26] E.W. Jones, R.J.L. Popplewell, H.W. Thomson, Spectrochim.

Acta 22 (1966) 639.

[27] G. Herzberg, Molecular Spectra and Molecular Structure. II.

Infrared and Raman Spectra of Polyatomic Molecules, van

Nostrand, Princeton, 1945, p. 429.

[28] R.A. Nyquist, Spectrochim. Acta 21 (1965) 1245.

[29] M. Traetteberg, P. Bakken, H. Hopt, J. Mol. Struct. 509 (1999)

213.

[30] F.J. Wodarczyk, E.B. Wilson, J. Chem. Phys. 56 (1972)

166.


Documents

Infrared and Raman spectra, conformational stability, ab initio calculations of structure, and vibrational assignment of 2-hexyne