Infrared and Raman spectra and ab initio calculations for 2-pentyne

Spectrochimica Acta Part A 55 (1999) 2361–2374

Infrared and Raman spectra and ab initio calculations for2-pentyne

Stephen Bell a, Gamil A. Guirgis b,1, Seung Won Hur b, James R. Durig b,*a Department of Chemistry, Uni6ersity of Dundee, Dundee DDI 4HN, UK

b Department of Chemistry, Uni6ersity of Missouri-Kansas City, Kansas City, MO 64110-2944, USA

Received 4 January 1999; accepted 11 January 1999

Abstract

The infrared spectra (3500–50 cm−1) of the gas and solid and the Raman spectrum (3500–30 cm−1) of solid2-pentyne, CH3CH2CCCH3, have been recorded. Additionally, the infrared spectrum (3500–400 cm−1) of a xenonsolution has been recorded. A complete vibrational assignment is proposed based on infrared band contours, relativeintensities, depolarization values, and group frequencies. The assignment is supported by normal coordinatecalculations utilizing ab initio force constants. The internal rotational barrier for the CH3 rotor of the ethyl group wasdetermined to be 1285 cm−1 from the torsional transitions whereas that for the CH3 rotor attached to the carbon ofthe triple bond has nearly free rotation. Complete equilibrium geometries have been determined employing severalbasis sets at the levels of restricted Hartree–Fock (HF), and/or with full electron correlation by the perturbationmethod to second order (MP2) as well as with a hybrid density functional theory (B3LYP). The results are discussedand compared to those obtained for some similar molecules. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: 2-Pentyne; Ab initio calculations; Infrared and Raman spectra; Structural parameters

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1. Introduction

In the initial vibrational studies of 1-butyne,CH3CH2CCH (ethyl acetylene), the torsional fun-damental was not observed [1,2] so we [3] carriedout a far infrared study of this molecule. The twolow frequency skeletal bending modes were ob-

served at 343.6 cm−1, n23(A%%), and 196.5 cm−1,n15(A%) in the spectrum of the gas. In the spectrumof the solid, these two bands were observed at 360and 223 cm−1. Therefore, a distinct torsionalmode was not observed for the 1-butyne moleculein either the spectra of the gas or solid. However,there were two pronounced Q branches at 212.8and 201.5 cm−1 amongst the rotational–vibra-tional transitions on the lower frequency skeletalbend which were assigned as the 1�0 and 2�1torsional transitions, respectively. These transi-tions were utilized to obtain the two coefficients(V3=1060 and V6= −30 cm−1) of the periodic

* Corresponding author. Tel.: +1-816-235-1136; fax: +1-816-235-5191.

E-mail address: [email protected] (J.R. Durig)1 Present address: Analytical R&D Department, Organic

Products Division, Bayer, Bushy Park Plant, Charleston, SC29411, USA.

1386-1425/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S1386 -1425 (99 )00033 -5

S. Bell et al. / Spectrochimica Acta Part A 55 (1999) 2361–23742362

potential function governing the internal rotationwhich gave a torsional barrier (1060 cm−1) lowerthan that obtained from the earlier microwaveresults [4–6] (1144 and 1089 cm−1) as well asthose predicted from ab initio calculations [3](1228 cm−1).

As a continuation of our studies of 1-butyne wehave investigated the far infrared spectrum of2-pentyne, CH3CH2CCCH3 (ethyl methylacetylene), to determine the torsional barrier ofthe methyl group on the ethyl moiety. The re-placement of the hydrogen atom with a methylgroup on the acetylenic carbon should result in amuch lower frequency for the skeletal bendingmode so the methyl torsional mode (ethyl moiety)should be more easily observed. The barrier forthe methyl group attached to the acetylenic car-bon will be very low, i.e. nearly free internalrotation and it should not interfere with the tor-sional mode of the other methyl rotor.

There has been one previous vibrational study[7] of 2-pentyne where the infrared spectrum ofthe gas and the Raman spectrum of the liquidwere reported. The methyl torsional mode wasnot observed and only one of the expected twolow frequency skeletal modes (143 cm−1) wasobserved although the second one was predictedto have a frequency of 112 cm−1. Additionally,several of the fundamentals were assigned as de-generate, such as the symmetric CH3 deforma-tions of the two different methyl groups.Therefore, a complete vibrational analysis wasundertaken utilizing higher resolution infraredspectrum of the gas along with the infrared spec-tra of xenon solution and the solid. The Ramanspectrum of the solid has also been recorded. Asan aid in the interpretation of the vibrationalspectra we have carried out ab initio calculationswith a variety of basis sets at the restrictedHartree–Fock level (HF) and with full electroncorrelation by the perturbation method [8] tosecond order (MP2). The optimized geometries,torsional barriers, harmonic force fields, infraredintensities, Raman activities, depolarization ra-tios, and vibrational frequencies have been ob-tained to compare with the experimental resultswhere applicable. Similar studies have recentlybeen carried out for the 1-pentyne molecule [9].

The results of these spectroscopic and theoreticalstudies are reported herein.

2. Experimental

The sample of 2-pentyne was obtained fromAldrich Chemical Company with stated purity of98%. It was further purified using a low-tempera-ture, low-pressure fractionation column.

The mid-infrared spectra of the gas and solid(Fig. 1) were obtained from 3500 to 400 cm−1 ona Perkin–Elmer model 2000 Fourier transformspectrometer equipped with a Ge/CsI beamsplitterand a DTGS detector. The gas was contained in a10 cm cell fitted with CsI windows. This spectrumwas obtained at 0.5 cm−1 resolution and trans-formed with boxcar truncation function. Thespectrum of the solid was obtained by condensingthe sample onto a liquid nitrogen cooled CsI platecontained in an evacuated cell equipped with CsIwindows, and 256 scans were collected for boththe reference and sample interferograms at 1cm−1 resolution and then transformed with aboxcar truncation function.

The mid-infrared spectra of the sample dis-solved in liquified xenon as a function of tempera-ture were recorded on a Bruker model IFS 66Fourier transform spectrometer equipped with aglobar source, a Ge/KBr beamsplitter and a

Fig. 1. Infrared spectra of 2-pentyne: (A) gas; (B) amorphoussolid; and (C) polycrystalline solid.

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Fig. 2. Far infrared spectrum of gaseous 2-pentyne. Topspectrum is that of water vapor.

of the crystalline solid (Fig. 3) was obtained withthe Perkin–Elmer model 2000 spectrometerequipped with a metal grid beamsplitter and aDTGS detector. The sample was condensed ontoa wedged Si plate cooled by liquid nitrogen, whichwas contained in an evacuated cell equipped withpolyethylene windows, and 128 scans were col-lected at 2 cm−1 resolution.

The Raman spectrum of the solid was recordedon a SPEX model 1403 spectrophotometerequipped with a Spectra-Physics model 164 argonion laser operating on the 514.5 nm line. The laserpower used was 0.5 W with a spectral band passof 3 cm−1. The spectrum was recorded with thesample sealed in a pyrex glass capillary held in aMiller–Harney apparatus [10]. The measurementsof Raman frequencies are expected to be accurateto92 cm−1 and a typical spectrum is shown inFig. 4. All of the observed bands in both theinfrared and Raman spectra, along with the pro-posed assignments, are listed in Table 1.

3. Ab initio calculations

The LCAO-MO-SCF restricted Hartree–Fockcalculations were performed with the Gaussian-94program [11] using Gaussian-type basis functions.The energy minima (Table 2) with respect to

DTGS detector. In all cases 100 interferogramswere collected at 1.0 cm−1 resolution, averagedand transformed with a boxcar truncation func-tion. For these studies a specially designedcryostat cell was used. It consisted of a copper cellwith a path length of 4 cm with wedged siliconwindows sealed to the cell with indium gaskets.The copper cell was enclosed in an evacuatedchamber fitted with KBr windows. The tempera-ture was maintained with boiling liquid nitrogenand monitored with two Pt thermoresistors. Thecomplete cell was connected to a pressure mani-fold, allowing the filling and evacuation of thesystem. After cooling to the desired temperature,a small amount of the compound was condensedinto the cell. Next, the system was pressurizedwith the noble gas, which immediately started tocondense in the cell, allowing the compound todissolve.

The far infrared spectrum of the gas (Fig. 2)was recorded with a Nicolet model 200 SXVFourier transform spectrometer equipped with avacuum bench, a 6.25 mm Mylar beamsplitter, anda liquid helium cooled Ge bolometer with awedged sapphire filter and polyethylene window.The spectra were obtained from the sample con-tained in a 1 m folded path cell equipped withmirrors coated with gold, and fitted withpolyethylene windows with an effective resolutionof 0.10 cm−1. To remove traces of water, anactivated 3A, molecular sieve was used to dry thesample. Interferograms were recorded 512 timesat a resolution of 0.10 cm−1 and transformedwith a boxcar truncation function. The spectrum

Fig. 3. Low wavenumber spectrum of solid 2-pentyne: (A)amorphous solid; and (B) annealed solid.

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Vibrational frequencies (cm−l) of 2-pentyne

B3LYP 6-Approximate MP2/6-31G(d)Vib. No. IR gas IR xenon IR solid Raman solid Rel. IR int. Raman activ-HF6-31G MP2/6-31G(d) DP ratios P.E.D.scaleddescriptiona ity31G(d)

3125.9 3003.6 2983 2976A% 2977CH3 antisym- 2977 26.7 100.4 0.70 99S1n1 3266.2 3202.0metric stretch

3093.7 2986.7 2977 2976 2973 2977 10.23184.1 96.9 0.74 100S23258.2*CH3 antisym-n2

metric stretch3056.0 2919.5 2943 2939 2940 2937 22.73112.3 254.7CH3 symmet- 0.02 99S3n3 3196.4

ric stretch3100.6*CH3 symmet- 3035.0 2908.6 2937 2920 2927 2931 26.6 167.4 0.01 99S4n4 3190.3

ric stretch3025.9 2904.3 2930 2920 2920 2921 21.2 55.9CH2 symmet- 0.22 99S5n5 3188.0 3096.0

ric stretch2282.5 2340 2336 2232 2236 0.12304.1 119.02371.7 0.33 81S62547.9C�C stretchn6

1569.0 1536.2 1488.5 1462 1464 1466 1462 2.4 8.4CH3 antisym- 0.60 85S7n7 1661.5metric defor-mation

1547.2 1510.7 1467.8 1459 1451 1449 14501647.7 6.7 32.4 0.72 69S8, 24S9*CH3 antisym-n8

metric defor-mation

n9 1509.2 1467.5 1449 1438 1434 1433 1.8 26.5 0.74 68S9,24S8CH2 scissors 1642.8 1546.71470.9 1446.0 1395.5 1390 – 1385 1392 3.21589.4 30.3*CH3 symmet- 0.52 96S10n10

ric deforma-tion

1578.0CH3 symmet- 1467.4 1436.3 1392.2 1376 1376 1380 1374 1.7 2.3 0.61 96S11n11

ric deforma-tion

1326.9 1326 1322 1321/1315 1323 18.6 14.3 0.47n12 74S12CH2 wag 1504.6 1397.8 1373.31177.7 1142.0 1150 1147 1140 1141 1.2 0.11202.5 0.741252.8 39S13,CH3–C�n13

stretch 39S17,16S12

1073.3 1071 1065 1069/1063 1069 2.6 0.1n14 0.55 48S14,31S16,CH3 rock 1196.3 1123.2 1092.610S18

1021.2 1035 1029 1036/1034 1034 1.51072.2 7.81069.4 0.21 88S151190.6*CH3 rockn15

966.6CH3–CH2 948.0 951 952 955 955 0.05 12.1 0.42 56S16, 20S14,n16 1033.5 998.3stretch 13S13

718.1 712.4 688.9 – 694 695 697756.7 0.1CH2–C� 7.7 0.35 36S17, 31S13,n17

16S6stretch505.9 473.0 494 495 504 505 3.0464.8 13.7620.2 0.58 60S18, 26S20n18 C–CH2–CH3

bend303.2 242.1 296 – 313 319 3.2 5.9 0.67*CH3–C�C 100S19n19 372.7 214.2

i.p. bend131.3 132.7 125 – 160 178 2.1149.3 1.0120.4 0.70 85S20, 19S18C�C–CH2 i.p.n20

bend3132.9 3013.6 2983 2976 2977 2977 22.2A%% 31.8CH3 antisym- 0.75 98S21n21 3278.3 3212.6

metric stretch3095.5 2989.8 2977 2976 2973 2977 10.23259.3 103.73187.0 0.75 100S22*CH3 antisym-n22

metric stretch3052.4CH2 antisym- 2945.6 2957 2958 2951 2956 10.6 122.4 0.75 98S23n23 3219.6 3140.0

metric stretch1559.3 1524.9 1479.3 1462 1464 1463 14561653.6 5.3CH3 antisym- 26.9 0.75 93S24n24

metric defor-mation

1642.1*CH3 antisym- 1546.4 1510.0 1466.9 1458 1451 1449 1450 6.2 24.4 0.75 94S25n25

metric defor-mation

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Table 1 (Continued)Vibrational frequencies (cm−l) of 2-pentyne

Vib. No. MP2/6-31G(d)Approximate MP2/6-31G(d) IR gas IR xenon IR solid Raman solid Rel. IR int. Raman activ- DP ratios P.E.D.B3LYP 6-HF6-31Gitydescriptiona 31G(d) scaled

– 1260 1263 1264n26 0.1CH2 twist 11.3 0.75 70S26, 23S271423.4 1326.4 1302.7 1258.41085.2 1088 1084 1086 1089 0.02 0.11123.0 0.75n27 33S27, 35S29,CH3 rock 1139.61246.1

23S26

n28 1068.8 1021.2 1035 1029 1036/1034 1034 1.6 0.1 0.75 86S28*CH3 rock 1196.0 1072.6n29 796.0 766.8 781 780 784 786/777 2.0 1.7 0.75 59s29, 35S27CH2 rock 882.9 806.7

385.8 324.2 377 – 382 384 1.2311.4 20.3*CH3–C�C o.p. 0.75 74S30, 30S32537.9n30

bendn31 267.5 235.5 252 – 273 277 2.4 0.2 0.75 100S31CH3 torsion 286.1 209.4

175.7C�C–CH2 o.p. 183.5 166 – 182 195 4.3 0.1 0.75 76S32, 20S30n32 193.8 166.8bend

15.1 – – - – 0.001 0.05 0.7515.1 100S3322.9n33 CH3 torsion 12.3

a Asterisk (*) indicates the methyl group attached to the ethylynic carbon.


Fig. 4. Comparison of (A) experimental and (B) calculatedRaman spectra of solid 2-pentyne.

In order to obtain a more complete descriptionof the molecular motions involved in the normalmodes, we have carried out a normal coordinateanalysis. The force fields in Cartesian coordinateswere calculated by the Gaussian-94 program [11]at the MP2/6-31G(d) and B3LYP/6-31G(d) levels.Internal coordinates (Table 3 and Fig. 5) wereused to calculate the G and B matrices using thestructural parameters from the two different cal-culations. Using the B matrix [13], the force fieldin Cartesian coordinates was then converted to aforce field in internal coordinates, and the puretheoretical vibrational frequencies were repro-duced. The resulting force constants may be ob-tained from the authors. Subsequently, scalingfactors of 0.87 for the carbon–hydrogen stretches,0.9 for the heavy atom stretches, and carbonhydrogen bends, 1.0 for the skeletal bends exceptfor the C�C–CH3 motions with a factor of 1.3were used. The geometric averages of the scalingfactors for the interaction force constants wereused to obtain the fixed scaled force field andresultant wavenumbers. A set of symmetry coor-dinates was used (Table 4) to determine the corre-sponding potential energy distributions (P.E.D.).A comparison between the observed and calcu-lated frequencies of 2-pentyne along with the cal-culated infrared intensities, Raman activities,depolarization ratios and P.E.D. are given inTable 1.

nuclear coordinates were obtained by the simulta-neous relaxation of all of the geometric parame-ters consistent with the symmetry restrictionsusing the gradient method of Pulay [12]. Thestructural optimization was carried out with ini-tial parameters taken from those from our earlierstudies of 1-pentyne. The 6-31G and 6-31G(d)basis sets were employed at the level of restrictedHartree–Fock (HF) and Moller–Plesset (MP2)perturbation to second order [8] with full electroncorrelation. Additionally, the 6-31(d) basis set wasused with a hybrid density functional theory(B3LYP). The determined structural parametersare listed in Table 3.

Table 2Energies for the stable conformera of 2-pentyne and energy difference to other conformers by various theoretical methods

Potential constant V6Energy stag/ecl* Energy differences

Ecl/Ecl*=V3 Nominal 30°/Ecl*Stag/stag*=V3*

−193.870947755 1194.33HF/6-31G 2.70 579.71 (31.21°) −55.41HF/DZ −26.03−193.888221360 1141.34 2.00 579.70 (31.17°)HF/6-31G(d) −72.94−193.940907494 1256.62 3.46 606.67 (31.55°)

−68.08596.06 (31.52°)2.57HF/DZ(d) 1229.52−193.964727547MP2/6-31G(d) −80.56−194.581458976 1266.27 4.16 604.32 (31.55°)

3.181205.36−194.590744406MP2/DZ(d) −73.87577.27 (31.52°)−195.292526571 −68.17547.67 (31.42°)4.991145.72B3LYP/6-31G(d)

a The stable conformer is given as stag/ecl* as the C5 methyl is staggered with respect to the CH2 neighbor but the C1 methyleclipses the CH2 group. The asterisk (*) refers to the C1 methyl rotor.


Table 3Geometrical parametersa for 2-pentyne obtained from ab initio calculations and microwave spectra

Parameter RHF/6-31GInternal coordinates MP2/6-31G(d) B3LYP/6-31G(d) Expt MWb

1.4646 1.4637C1C2 1.4614S 1.4601.1961 1.2226C2C3 1.2098T 1.2101.4696 1.4658U 1.4655C3C4 1.460

VC4C5 1.5361 1.5323 1.5402 1.536jC1C2C3 179.97 178.90 179.69 180.0

179.50 177.96x 178.97C2C3C4 180.0112.85 112.42C3C4C5 113.15u 111.5180.00 180.00t1 180.00C3C4C5H6 180.0

r1C1H1 1.0838 1.0940 1.0971 1.094b1C2C1H1 110.99 111.00 111.36 110.1

1.0838 1.0940r2,3 1.0971C1H2,3 1.094111.03 111.02C2C1H2,3 111.40b2,3 110.1119.99 119.98f2 119.98H1C2C1H2

c 120.0r4,5C4H4,5 1.0857 1.0965 1.0990 1.094g1,2C3C4H4,5 109.17 109.37 109.46 109.5

122.03 122.02f4 122.22C5C3C4H4c 120.0

1.0842C5H6 1.0940r6 1.0957 1.094110.40 110.57b6 110.43C4C5H6 110.1

t*2C5C2C1H1 0.00 0.00 0.00 0.00r7,8C5H7,8 1.0830 1.0925 1.0947 1.094

110.82 110.55b7,8 110.85C4C5H7,8 110.1119.99C6C4C5H7

c 120.15f7 120.09 120.0

Rotational constantsA 20303.2520778.63 20511.23 20481.02

2071.06 2065.01B 2058.85 2084.581950.51 1942.15 1938.60 1962.51C−0.9872 −0.9866 −0.9871 −0.9868k

Internal rotational constants3.1062 3.1667 3.1722 3.1896C5 Me It5.7134 5.5916F 5.5984 5.5572

C1 Me It* 3.0949 3.1532 3.1551 3.18966.2039 6.0868 6.0912F* 6.0337

a Bond lengths in A, , angles in degrees, rotational constants in MHz, It in amu A, 2, and F in cm−1.b MW parameters for 1-pentyne transferred: [19].c Dihedral angle of symmetrically equivalent H is negative value.

4. Results

There are several interesting features in theinfrared spectrum of 2-pentyne. Because of thenearly free internal rotation of the methyl group(*CH3 rotor), where the asterisk is used to distin-guish this methyl rotor from the one on the ethylgroup attached to the acetylenic carbon, thenearly degenerated vibrations of this methyl rotorresult in pseudo-symmetric top type spectra forthese vibrations. For example, in the carbon hy-drogen stretching region one clearly observes the

strong–weak–weak–strong–weak–weak transi-tions as a result of the statistical weights of theK=0, 3, 6 etc. levels. The observed frequenciesare listed in Table 5. Similar pseudo-symmetrictop spectra are also observed for the antisymmet-ric *CH3 deformations and the *CH3 rockingmodes. For the rocking modes, the fine structureis not as extensive and as well defined as thatfound for the antisymmetric *CH3 stretch anddeformation. The spacing is approximately whatone expects for the nearly pure free internal rota-tion of the methyl group.


Because of the overlapping bands resultingfrom the corresponding modes of the methylgroup of the ethyl moiety, it is difficult to identifythe band center of this fine structure. However, byrecording the infrared spectral data in a xenonsolution, the band center is approximatelydefined. These three nearly degenerate bands arebroader in the spectrum of xenon solution thanthe other vibrations of a similar nature for theother methyl rotor. Although one would expectsome shift in the frequency from the gas to thexenon solution, the observed frequencies shouldbe near the band center of these pseudo-symmet-ric top modes.

An interesting feature of the infrared spectrumof the gas is that many of the fundamental vibra-tions are extremely weak. In other words, theacetylenic bond behaves more like it were sym-metrically substituted, i.e. the ethyl group isnearly equivalent to the methyl group. This resultsin the C�C stretch having a predicted intensity of0.1 km mol−1 so that it is difficult to observe inthe infrared spectra. The C–C stretch of the ethylgroup has zero predicted intensity and that of theC–C stretch of the H2C–C�C– moiety has apredicted intensity of 0.2 km mol−1. Therefore, itwould be impossible to provide a vibrational as-signment without the Raman spectrum, wherethese modes are quite pronounced.

As was pointed out in the earlier vibrationalstudy [7] of this molecule, there is a strong Fermiresonance of the C�C stretching mode with anovertone mode. In fact, the second Raman line ofthis doublet is 2/3 the intensity of the fundamen-tal vibration (Fig. 4).

Table 4Symmetry coordinates for vibrations of 2-pentyne

DescriptionaSpecies Coordinate

CH3 antisymmetricA% S1=2r6−r7−r8

stretch*CH3 antisymmetric S2=2r1−r2−r3

stretchS3=r6+r7+r8CH3 symmetric

stretchS4=r1+r2+r3*CH3 symmetric

stretchS5=r4+r5CH2 symmetric

stretchS6=TC�C stretch

CH3 antisymmetric S7=2a6−a7−a8

deformationS8=2a1−a2−a3*CH3 antisymmetric

deformationCH2 scissors S9= (6+2)h−g4−g5

−d4−d5−(6−2)u*CH3 symmetric de- S10=a1+a2+a3−b1−b2

formation−b3

CH3 symmetric de- S11=a6+a7+a8−b6−b7

formation−b8

CH2 wag S12=g4+g5−d4−d5

S13=SCH3–C stretchCH3 rock S14=2b6−b7−b8

*CH3 rock S15=2b1−b2−b3

CH3–CH2 stretch S16=VCH2–C� stretch S17=UC–CH2–CH3 i.p. S18= (6+2)u−g4−g5

bend−d4−d5

− (6−2)h*CH3–C�C i.p. bend S19=j

C�C–CH2 i.p. bend S20=x

redundancy S1R=a6+a7+a8+b6

+b7+b8

redundancy S2R=a1+a2+a3+b1

+b2+b3

S3R=u+h+g4+g5+d4redundancy

+d5

A%% CH3 antisymmetric S21=r7−r8

stretch*CH3 antisymmetric S22=r1−r2

stretchS23=r4−r5CH2 antisymmetric

stretchS24=a7−a8CH3 antisymmetric

deformation*CH3 antisymmetric S25=a1−a2

deformationFig. 5. Internal coordinates for 2-pentyne.


Table 4 (Continued)

Species Descriptiona Coorinate

CH2 twist S26=g4−g5−d4+d5

CH3 rock S27=b7−b8

*CH3 rock S28=b1−b2

S29=g4−g5+d4−d5CH2 rockS30=j %*CH3–C�C o.p. bend

CH3 torsion S31=t1

S32=x %C�C–CH2 o.p. bendS33=t2*CH3 torsion

a Since there are two methyl groups, C1 is marked with anasterisk (*).

Raman spectrum of the liquid, whereas the otherbend was left unassigned. Similarly, the CH3 tor-sion was predicted at 237 cm−1 but it was notobserved in the Raman spectrum of the liquid andno far infrared data have previously been re-ported. It is clear from the far infrared spectrumof the gas that all three of these fundamentals areobserved along with another bending mode near300 cm−1. In order to analyze the band contoursof the fundamentals, we calculated the expectedcontours for the three different pure A, B and Cband types (Fig. 6). Clearly, it should be possibleto distinguish between the A% modes (A, B andA/B hybrid types) and the A%% modes, which giverise to C-type infrared band contours.

The band around 300 cm−1 appears to have anA-type contour with a central Q peak at 296cm−1 which can easily be assigned on the basis of

The most intriguing part of the infrared spec-trum is that found in the far infrared (Fig. 2)spectral region of the gas. In the previous vibra-tional study [7] of this molecule, one of the C�C–CH2 bends was assigned at 143 cm−1 from the

Table 5Frequencies of the sub-bands of the ‘degenerate’ *CH3 modes of the CH3–C�C moiety

*CH3 antisymmetric deformation CH3 rockK Relative intensity *CH3 antisymmetric stretch

PQkRQk RQkPQkPQk RQk

2976.10 s 1459.6 1035.21472.92966.92983.9aw1 1042.81446.5 1029.9

2965.32994.4 2957.9 1489.1 1433.12 1048.7w 1023.62996.0 2956.53004.8 2946.7 1502.7 1419.43 1053.8s 1018.03005.8

1059.81406.61515.02938.63014.2w43015.4

w 3023.6 2928.65 1528.6 1392.2 1066.53024.9

1070.61542.06 2920.63032.9s3034.9 2917.5

7 w 3042.2 1363.2 1077.43044.1

w 3051.38 1348.6 1083.63053.1

9 s 3060.83062.33070.2w103071.4

w 3079.2113080.83088.3s123090.5

a Not used in the least squares fit.


Fig. 6. Predicted pure A-, B-, and C-type infrared bandcontours.

There are a number of peaks from 120 to 180cm−1; first a strong Q peak at 166 cm−1, next abroad hump with a possible central peak at 139cm−1, then a weaker band with a possible Q peakat 125 cm−1. Since the internal rotation of theacetylenic methyl (C1) is effectively free, there areonly two other fundamentals, n20 and n32, to beidentified in this region of the far infrared spec-trum. This is confirmed by the far infrared spec-trum of the solid phase (Fig. 3) where two broadbands are observed although they have shifted tohigher frequencies.

In order to fit this complex band, we investi-gated how the pure contours would be changedby significant differences in the rotational con-stants in the excited vibrational state. Therefore,by taking an A-type band centered at 125 cm−1

with DA=0.04 cm−1 and DB=DC=0 and aC-type band with an origin at 166 cm−1 withDA=0 and DB=DC=0.0005 cm−1, the bandcontour of Fig. 8 is predicted. Although the con-tour does not fit exactly, it is clear that most ofthe absorption in this spectral region can be ade-quately accounted for by the two fundamentals at125 (n20, A%) and 166 cm−1 (n32, A%%). Therefore,the broad band centered at 139 cm−1 is not afundamental as previously assigned.

Fig. 7. Distortion of R and P branches of A-type contour forDA=0.05 cm−1.

the quantum chemical calculations, especiallyfrom the B3LYP frequencies in Table 1, as theskeletal bending vibration n19. However, it has astrange contour with a strong P branch showingK structure expected of a B- or C-type band (seethe contours in Fig. 6) and perhaps the rotationalorigin is nearer to the dip at 295 cm−1. Forexample, by decreasing the A rotational constantby 0.05 cm−1 the contour for the A type bandwithout the central Q-branch is shown in Fig. 7.Going to lower frequencies, after some further Kstructure, there is a series of peaks probably ofC-type bands starting at 252 cm−1, which oncomparison with predictions and consideration ofthe band type are undoubtedly the torsional tran-sitions (n31) of the C5 methyl group (ethyl moiety).


Fig. 8. Observed and predicted contours for (A) n20 and (B)n32 fundamentals (see text).

the B3LYP and MP2 calculations as shown inTable 1. The values of the kinetic constant F aregiven with the structural parameters in Table 3and an average of the MP2 and B3LYP values isemployed in Table 6. However, without V6, con-secutive torsional transitions should be spaced atleast 15 cm−1 apart and not the 5 cm−1 spacingobserved. With V6 included, the fundamental isshifted down and therefore when all four bandsare included in a fit the resulting V3 is much largerthan any of the predicted values in Table 2 and V6

is excessively negative. Hence the best fit is ob-tained by considering the four peaks as formingtwo series with alternate bands as consecutivetorsional transitions. This is similar to the treat-ment of the torsional transitions of 1-pentynewhere the fitted values for V3 and V6 also haverather large magnitudes. In both molecules, onereason for this may be found in the potentialenergy distributions of the symmetry coordinates,which show mixing of the torsion with the out-of-plane skeletal bending modes. This is not evidentin the potential energy distribution from the un-scaled MP2 components, where the C�C is exces-sively long but the distribution for unscaledB3LYP shows a component of 33% from S30

(Table 1).We predicted the Raman spectrum from the

HF/6-31G calculations. The evaluation of Ramanactivity by using analytical gradient methods has

5. Discussion

The progression of Q peaks from 252 to 235cm−1 are assigned to the C5 methyl torsion ingood agreement with the prediction by the forceconstant calculation using the B3LYP method.Torsional transitions can also be predicted from atorsional potential energy function derived fromthe ab initio or hybrid DFT conformer energies inTable 2. These give unreasonably high values ofV6 but by ignoring V6 the torsional fundamentalis calculated near the first observed band for both

Table 6Potential constants, kinetic constants and torsional transitions (in cm−1) for the C5-methyl torsion of 2-pentyne

B3LYP/6-31G(d) MP2/6-31G(d) Fit four bands Fit two bands Fit two bands

6.096.096.096.09 6.09F 6.096.091266.31145.71145.7V3 1411.61658.9 1284.81266.3

V6a 0 −68.2 0 −80.6 −132.9 −40.6 3.9

Transitions Obs.b

252.0252.0250.4224.8248.91�0 215.1236.0252.0240.8 235.7220.02�1 208.6247.2 233.1 219.4 248.9

240.8 202.1 198.8 215.33�2 210.4 243.3190.1178.5173.4235.74�3 233.3193.8

a Ab initio potential constants give the fundamental transition (1�0) fairly near to observed especially MP2 calculations if theV6 is ignored. However, without a negative V6 term the calculated transitions are more separated than observed, but large negativevalues of V6 lower the value of the fundamental.

b A fit to all four observed bands (with V3 and V6) yields a very high barrier (V3=1659) and an excessively negative V6. A fit toalternative bands as consecutive transition gives the best results (last column).


been developed [14,15]. The activity Sj can beexpressed as:

Sj=gj(45a j2+7b j

2)

where gj is the degeneracy of the vibrational modej, aj is the derivative of the isotropic polarizabilityand bj is that of the anisotropic polarizability.The Raman scattering cross sections, #sj/#V,which are proportional to the Raman intensities,can be calculated from the scattering activitiesand the predicted wavenumbers for each normalmode using the relationship [16,17]:

(sj

(V=�24p4

45�: (60−6j)4

1−exp�−hc6j

kTn;� h

8p2c6j

�Sj

where n0 is the exciting wavenumber, nj is thevibrational wavenumber of the jth normal mode,and Sj is the corresponding Raman scatteringactivity. To obtain the polarized Raman scatter-ing cross sections, the polarizabilities are incorpo-rated into Sj by Sj [(1−rj)/(1+rj)] where rj is thedepolarization ratio of the jth normal mode. TheRaman scattering cross sections and calculatedwavenumbers obtained from the standard Gaus-sian program [11] were used together with aLorentzian function to obtain the calculated spec-tra. Since the calculated wavenumbers are approx-imately 10% higher than those observed, thewavenumber axis of the theoretical spectrum wascompressed by a factor of 0.9.

The predicted Raman spectrum is shown in Fig.4B. The experimental Raman spectrum of theliquid is shown in Fig. 4A for comparison pur-poses and the agreement is satisfactory except forthe region below 500 cm−1. Also, the predictedintensity of the C�C stretch is drastically underes-timated. Because the HF/6-31G* calculationspoorly predict the CH3–C�C bending modes, oneexpects the predicted Raman spectrum in thelower wavenumber region to be rather poor.

We also calculated the infrared spectrum andwe used the MP2/6-311G* calculations for thispurpose. Infrared intensities were calculated basedon the dipole moment derivatives with respect tothe Cartesian coordinates. The derivatives weretaken from the ab initio calculations transformed

Fig. 9. Observed infrared spectrum of 2-pentyne in: (A) xenonsolution; and (B) the predicted spectrum.

to normal coordinates by:�(mu

(Qi

�=%

j

�(mu

(Xj

�Lij

where Qi is the ith normal coordinate, Xj is the jthCartesian displacement coordinate, and Lij is thetransformation matrix between the Cartesian dis-placement coordinates and normal coordinates.The infrared intensities were then calculated by:

Ii=Np

3c2

��(mX

(Qi

�2

+�(my

(Qi

�2

+�(mz

(Qi

�2nThe predicted infrared spectrum is shown in

Fig. 9B and the observed spectrum of the xenonsolution in 9A. The calculated spectrum is in goodagreement with the mid-infrared spectrum of thexenon solution and demonstrates the utility of theinfrared intensities in aiding vibrational assign-ments for these types of molecules.

The infrared spectra (Fig. 1) show clearly thatthree bands have resolvable fine structure whichhave the strong, weak, weak intensity alterationscharacteristic of perpendicular vibrations of sym-metric top molecules with a three fold axis ofsymmetry. The band in the C–H stretching regionhas an average spacing of 9.4 cm−1 (Fig. 10)whereas the one attributed to the CH3 antisym-metric deformation has an average spacing of 13.8cm−1. It is more difficult to assign the fine struc-ture on the CH3 rock but the spacing appears to


be about 5.9 cm−1. This rotational structure mustbe due to nearly free rotation of the CH3 groupabout the C–C�C axis since the Q-branch spacingis much too large to be due to rotation of theentire molecule and the difference in spacing mustbe due to Coriolis coupling. The fact that theseQ-branches are split into doublets indicates thatthere is a small barrier to the internal rotation ofthe methyl group.

The energy expression for a symmetric top withfree internal rotation is given [18] by:

F(J, K, k1, k2)=BJ(J+1)−BK2+A1k12+A2k2

2

where A1 and A2 are the rotational constants ofthe freely rotating parts of the molecule and k1

and k2 are the quantum numbers of the angularmomentum of the respective parts about the rota-tion axis. The selection rules for the Q-branchesof perpendicular bands due to vibration of part 1of the molecule, which is considered here to be theCH3 group, are:

DJ=0 Dk2=0 Dk1=DK=91

This yields the following expression for the Q-branches of the sub-bands:

60sub=60+ (A %1−B %)92(A %1k1−B %K)

+ [(A %1−A¦1)k12− (B %−B¦)K2]

If this expression is modified to include the asym-metry of the molecule and Coriolis coupling, thefollowing expression is obtained [18]:

60sub=60+

�A %1(1−z)

B %+C %2

n+2A %[(1−z)k1− (B %+C %)K ]

+ (A %1−A¦1)k12

−�(B %−B¦)+ (C %−C¦)

2K2n

Since the term in K2 is expected to be very small,the perpendicular bands should consist of Q-branches with a spacing of [2A1(1−z)− (B%+C%)]. Each of these Q-branches should consist of(unresolved) bands with a spacing of (B%+C%).

The frequencies of the Q-branches (Fig. 10) ofthe degenerate C–H stretching fundamental werefound to fit by the least squares method thefollowing equation:

Fig. 10. Fine structure of ‘degenerate’ *CH3 stretch.

60sub=2976.0899.461K−0.007K2

The band center, n0, is calculated to be 2976.1cm−1 and z is 0.216, which is consistent with thevalue for z found for the corresponding motion ofCH3D and the methyl halides [18]. The bandcenter agrees very well with the value obtainedfrom the xenon solution.

The Q-branches of the degenerate deformationare also quite evident but their assignment is notas readily made as those for the degenerate car-bon–hydrogen stretch. This made the leastsquares fit of the 60

sub of the antisymmetric defor-mation a little suspect but the result is:

60sub=1460.72913.75K+0.03K2

with a z value of−0.137. Again, the z value isconsistent with the z value for the correspondingmotion for the methyl halides, which range invalue [18] from−0.23 to−0.29. For the degener-ate *CH3 rock, the least squares fit of the Q-branches gives 60

sub of 1036.0596.05K−0.02K2

and a z value of 0.50. This value is slightly-lowerthan the value of 0.66 obtained for this corre-sponding motion in CH3D and somewhat higherthan the values of 0.21–0.28 obtained for thismode in the methyl halides. These results clearlyindicate that the internal rotational barrier of themethyl group attached to the carbon of the triplebond is very small and for purposes of explaining


the spacings of the near-degenerate modes of thisgroup one can treat the methyl group as freelyrotating.

The far infrared spectrum of the solid is quiteinteresting since the n32 fundamental has a muchhigher frequency in the amorphous solid than inthe polycrystalline solid. With repeated annealingthe band at 182 cm−1 sharpens and clearly shiftsto lower frequency (Fig. 3). It should also benoted that n20 has a very large shift from the gasphase (125 cm−1) to that for the solid (160cm−1). Such shifts are frequently found for tor-sional modes but not for skeletal bending modes.

The methyl barrier of 1284 cm−1 for the CH3

rotor of the ethyl group using only two torsionalbands is in reasonable agreement with the mi-crowave value for this rotor in ethyl acetylene(1144 and 1089 cm−1) [4–6] and agrees with theab initio predictions. It is probable that the twotransitions between the 252.0 (1�0) and 235.7(2�1) bands are due to ‘hot bands’ associatedwith the low frequency bending mode rather thansuccessive transitions of the torsional mode.

Acknowledgements

JRD would like to acknowledge partial supportof these studies by the University of Missouri-Kansas City Faculty Research Grant program.

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Infrared and Raman spectra and ab initio calculations for 2-pentyne