Spectrochimica Acta Part A 61 (2005) 1471–1477

Ab initio study of the barriers to methyl torsion andtorsional frequencies of acetyl molecules�

Stephen Bell∗

Faculty of Life Sciences, Carnelley Building, University of Dundee, Dundee DD14HN, Scotland, UK

Received 14 October 2004; accepted 29 October 2004

Abstract

A wide range of ab initio and hybrid density functional methods and basis sets have been employed to calculate the barriers to methylinternal rotation in a range of molecules with the acetyl moiety. Comparison is made of the computed torsional frequency with the experimentaltorsional frequency,νobs, for each molecule. With the MP2/6-311+G(3df,2p) combination of method and basis set, the agreement is betterthan 4 cm−1 for most of the molecules, whereνobs or theV3 barrier is well-determined experimentally.© 2004 Elsevier B.V. All rights reserved.

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eywords: Acetyl molecule; Internal rotation; Methyl torsion; Far infrared spectra; Microwave spectra; Potential function

. Introduction

Over the years, Dr. Durig has published several studiesf the infrared spectra, particularly the far infrared spectra,f almost all the compounds considered in this study[1–14].his ab initio study of the internal rotation of the methyl

op in acetyl molecules, that is, molecules with the methylroup adjacent to a carbonyl, includes comparisons with ex-erimental values of internal rotational parameters found bypectroscopic methods. These comparisons are of particular

nterest because of the low methyl barriers in such moleculesV3 of order 400 cm−1) and the extensive experimental stud-es, at least, of the parent molecule, which have providedrecise torsional data for acetaldehyde[15–20]. This is notn experimental study but purely a quantum chemical studyf these molecules.

In some of these experimental studies, the torsional fun-amental has been observed in the gas phase spectrum. Inthers, the torsional fundamental is observed only in con-ensed phases where agreement with ab initio predictions is

likely to be poorer. Only two of the molecules considerednot in the list of molecules whose infrared spectra havestudied by Dr. Durig’s group; for these the barrier has bdetermined by splittings in microwave spectra alone[21–22].At least one basic type of acetyl molecule is not considin this study; acetamide is excluded because of difficultieoptimization caused by non-planar amine geometries anfar infrared information is available for this molecule.

At the outset it should be realised that all the methodsbasis sets yield potential energy functions for internal rtion of the methyl group of the correct phase and withriers in the correct ball-park even at the Hartree–Fock (level with the 3-21G basis set; hence, its inclusion to sthat approximate barriers can be calculated at little comtational expense. This is perhaps surprising becausesmall energy differences between different configurationthe molecules.

2. Methods

� Presented in honor of Prof. James R. Durig, colleague for 17 years andriend, on the occasion of his 70th birthday.∗ Tel.: +44 1382 344705; +44 1382 542315.

E-mail address:s.bell@dundee.ac.uk.

All the calculations have been made with Gaussian 98[23]. The methods considered are restricted Hartree–Fock,the hybrid density-functional method called B3LYP and theMoller–Plesset perturbation method to second order, MP2.

d.

386-1425/$ – see front matter © 2004 Elsevier B.V. All rights reserveoi:10.1016/j.saa.2004.10.047

1472 S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477

For the MP2 calculations, electron correlation of all elec-trons is used including the innermost shell, i.e., MP2 = full inGaussian notation. Other methods have been used but not re-ported because of the computing effort required for so manymolecules. In the interest of the best agreement with experi-ment and economy at the same time, a wide range of basis setshas been employed including the Pople sets (3-21G, 6-31G,etc.)[23], the Dunning–Huzinaga basis set often labeled DZ[24] and the more recent Dunning sets (cc-pVXZ)[25].

For most molecules, the eclipsed (minimum) and stag-gered (saddle point) configurations having a planar skeletonhave Cs symmetry, which is used in geometric optimization.For all the configurations with the methyl group in an eclipsedor a staggered situation, the geometrical parameters have beenfully optimized in the appropriate symmetry (except whereindicated) and the vibrational frequencies calculated for theoptimized structure.

The barriers orV3 values are obtained from ab initio ener-gies for staggered and eclipsed methyl geometries. Zero-pointenergy (ZPE) differences to be used as corrections toV3 areobtained from the vibrational frequencies of both the eclipsedand staggered configuration but the zero-point energy of themethyl torsional mode itself is omitted.

For fully optimized methyl groups, the group does nothave an exact C3 structure. In spite of this, an exactly

three-fold potential energy function (i.e., noV1, V2, etc.terms) is obtained by the use of an effective torsional angledefined asτeff = (τ1 + τ2 + τ3)/3 [26]. This is particularlyrelevant at the 30◦ configuration, which is used on orderto determine the required higher potential energy term,V6.For this study, one H of the methyl is fixed at 30◦ and thedihedral angle of the other H atoms optimized; the effectiveangle is usually around 31◦.

In order to go from ab initio values ofV3 to predictedtorsional fundamental frequencies, the kinetic constant forinternal rotation,F, is required. This is calculated only for theeclipsed (minimum) configurations using the program CART.To calculate torsional transitions from kinetic constants,F,and potential energy constants,V3, the program ASTOR isemployed. Some transition frequencies are obtained with theV6 term included in some cases.

3. Results

The molecules listed inTables 1a–cand studied byDr. Durig are acetaldehyde (X = H)[1], acetyl chlo-ride (X = Cl) [2,3], acetyl bromide (X = Br)[3], acetone(X = CH3) [4], acetyl cyanide (X= C≡N) [5], acetyl acety-lene (X = C≡CH)[6], methyl vinyl ketone (X = CH CH2)

TE ules, C

Cl

622c, 4162.8c

647.2428.4451.1385.5384.8415.3420.5

426.8444.2591.2451.1384.2

482.9

able 1axperimental and ab initio barriers,V3, for methyl torsion in acetyl molec

X H F

ExperimentalV3 or V3eff 407.95a 364b

νobs 143.86i 121j

HF/3-21G 397.4 443.6HF/6-31G 332.3 416.7HF/6-31G(d) 359.1 401.9B3LYP/6-31G(d) 387.5 353.6B3LYP/6-31G(d,p) 393.8 352.2MP2/6-31G(d) 349.2 398.9MP2/6-31G(d,p) 363.6 397.5MP2/6-31+G(d) 309.9 359.7MP2/6-311G(d) 379.9 392.6MP2/6-311+G(d) 334.5 365.2MP2/6-311+G(d,p) 360.5 366.9MP2/6-311+G(3df,2p)k 407.5 347.8HF/DZ 401.3 387.5HF/DZ(d) 399.0 372.8B3LYP/DZ(d) 376.2 318.8B3LYP/DZ(d,p) 376.4MP2/DZ(d) 397.8 354.3MP2/DZ(d,p) 413.7

a Ref. [20].b Ref. [21].c Ref. [2].d Ref. [27].

e Refs.[2,3].f Ref. [28].g Ref. [22].h Refs.[4,32].i Refs.[1,15].j Calculated fromV3.k At geometry of MP2/6-311+G(d,p).

H3COX

Br OH trans CH3

53d (689)e, 456f 169g 251h

, 137j (168)e, 135j 82j b1125.16h

524.2 288.1 322.4567.1 238.5 243.4556.9 209.8 240.7446.2 133.8 226.1

530.8 186.6 267.3523.2 185.6 267.1

447.0 145.3 203.5465.3 140.2 229.7

232.3 238.1182.1 211.886.5 131.3

104.6 154.3

S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477 1473

Table 1bExperimental and ab initio barriers for methyl torsion in acetyl molecules, CH3COX

X C≡N C≡CH CH CH2 cis CH CH2 trans CH2CH3 trans CH2CH3 gauche

ExperimentalV3 or V3eff 400a 346b 361c 420d, 430e 183f

νobs 126.06a 117.94b 121c 125d (137)g, 124g 142g

HF/3-21G 423.7 390.1 407.7 561.0 253.4 263.6HF/6-31G 369.4 343.9 326.7 408.8 180.3 203.2HF/6-31G(d) 405.4 370.0 370.5 428.1 188.5 227.8B3LYP/6-31G(d) 355.1 312.1 316.2 307.6 172.9 223.1MP2/6-31G(d) 435.9 438.1 370.1 447.7 210.8 233.5MP2/6-31G(d,p) 424.5 420.7MP2/6-311+G(d,p) 395.7 367.6 355.7 396.5 136.0 169.5MP2/6-311+G(3df,2p)h 411.0 373.5 373.7 404.1 160.3 196.0

a Ref. [5].b Ref. [6].c Ref. [7].d Ref. [7]; V3 = 384 cm−1 using ab initioF-value.e Ref. [29].f Refs.[30,31].g Ref. [8], observed in spectrum of solid, ab initio in italics, butν = 84 cm−1 from MW V3 = 183 cm−1.h At geometry of MP2/6-311+G(d,p).

[7], 2-butanone (X = CH2CH3) [8], acetyl isocyanate(X = NCO) [9,10], acetyl isothiocyanate (X = NCS)[11],methyl cyclopropyl ketone (X =cC3H4) [12,13] and ace-tophenone (X = C6H5) [14].

Two other acetyl molecules, acetyl fluoride (X = F)[21]and acetic acid (X = OH)[22], are included for complete-ness although acetamide is omitted as explained above. InTable 1a, the substituent, X, contains only one first-row ornon-hydrogen atom; inTable 1b, the X group contains twofirst-row atoms and inTable 1c, it involves three or more suchatoms. The labelscis andtrans refer to the configuration ofthe X-group atoms with respect to the carbonyl double bondexcept in 2-butanone and acetic acid, where it is defined rel-ative to the methyl group.

Most of the experimentalV3 barriers given inTables 1a–care derived from observed torsional transition frequencies,νobs, using a value of the reduced internal rotation constant,F, and a few are derived from microwave splittings. In thestable configuration of each of these acetyl molecules, bothexperimentally and by ab initio calculation, one hydrogen

of the methyl group is in plane and eclipsing the carbonyloxygen presumably because of a weak hydrogen bond.The ab initio calculated values ofV3 in Tables 1a–careobtained by taking the differences in energy between thelowest configuration and that with the methyl rotatedby 180◦.

In the entries for acetyl chloride[2,27], acetyl bro-mide [2,3,28], methyl vinyl ketone[7,29] and 2-butanone[8,30,31], more than one value of the experimental barrieris given because of microwave determinations of the barrierheight[27–31]being different from far infrared.

The effects of different basis sets and ab initio methodon raw barrier heights are manifest inTables 1a–c, the rangeof methods/basis sets for acetaldehyde being particularly ex-tensive. Barriers are estimated cheaply using HF/3-21G andthey are all of the correct sign but all too high for all themolecules except X = H. In acetaldehyde,V3 from calcula-tions using 6-31G and all the bases derived from it are mostlya little low except for the largest set, 6-311+G(3df,2p), and forB3LYP calculations. The DZ basis yields surprisingly good

Table 1cExperimental and ab initio barriers for methyl torsion in acetyl molecules, CH3COX

X NCO cis NCO trans NCScis NCS trans Cyclopropyl H-trans Phenyl

ExperimentalV3 or V3eff 381c

131b

499.4364.7384.9269.0362.6309.4328.0

νobs 138a 147a

HF/3-21G 438.5 –HF/6-31G 327.7 –HF/6-31G(d) 365.8 397.0B3LYP/6-31G(d) 281.8 316.0MP2/6-31G(d) 373.1 441.2MP2/6-311+G(d,p)e 325.2 371.2MP2/6-311+G(2df,2p)e 337.5 380.4

a Refs.[9,10] ab initio harmonic frequency.b Ref. [11] ab initio harmonic frequency.c Refs.[12,13].d Not observed in Ref.[14].e At MP2/6-31G(d) geometry.

150b 124.8c n.o.d

– 452.5 733.6– 387.4 603.5– 419.3 624.5

316.9 355.8 502.8440.0 407.7 654.0392.6 389.4 570.8373.2

1474 S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477

agreement for the HF and MP2 methods but low results forB3LYP. The DZ basis set has also been used for acetyl cyanide[5] and acetyl acetylene[6] for which barriers are predictedhigher than observed. The gap inTable 1afor X = Br is dueto Gaussian functions being unavailable for Br in the DZ set.However, the peculiarity of DZ is that it sometimes yieldsfreak low results as for acetic acid and acetone; hence, it isnot trusted for larger molecules.

The effect of adding diffuse functions (+) to smaller bases,such as in MP2/6-31G(d), is to reduce barrier drastically,at least in acetaldehyde and acetyl fluoride and hence, thiscombination is discontinued for other molecules. The effectof going from double-split valence shell, MP2/6-31G(d), totriple-split MP2/6-311G(d) appears to be to raise the pre-dicted barrier by a small amount.

For molecules other than acetaldehyde, the effect ofadding p polarization functions to the hydrogen basis set(e.g., going from B3LYP/6-31G(d) to B3LYP/6-31G(d,p),MP2/6-31G(d) to MP2/6-31G(d,p) or MP2/6-311+G(d) toMP2/6-311+G(d,p)), is quite negligible (contrary to theassumptions of some manuscript reviewers). For acetalde-hyde, the addition ofp functions is to cause a small increasepresumably because of the hydrogen atom adjacent to theoxygen of the carbonyl group (X = H), which is absentin all the other molecules. Therefore, results for addingpf

o omt onlya rc of theo rnalr them ls asir witht rnalt lt fort kindo l oft thylv

ap-p Thebm Z,r alsos put-i ts art

gree-m lv pre-d osttO few

examples makes negligible difference to the prediction usingthe MP2/6-311+G(d,p) geometry.

3.1. Zero-point energy correction

In the treatment of torsional transitions in the far infraredspectra, it is usual to represent the internal rotation as a one-dimensional problem separate from other vibrational coordi-nates of the molecule. In the analysis of microwave spectra,the interaction of internal rotation and overall rotation mustbe considered but not the interaction with other vibrations.Hence, the experimental potential energy function so derivedeffectively includes the difference in the zero-point energiesof all the 3N-7 vibrations[26]. The ab initio potential energyfunction can be made to correspond more correctly with ex-perimental by the addition of the ZPE differences obtainedfrom ab initio harmonic vibration frequencies of the 3N-7vibrations excluding methyl torsion.

In Table 2are listed for acetaldehyde all the ZPE correc-tions to be applied to the rawV3 also listed obtained by simpledifferences between ab initio energies of eclipsed and stag-gered configurations. It is clear that these corrections are notnegligible and that the family of bases built on the Pople ba-sis sets have larger ZPE corrections (13–20 cm−1) than thosewhere the Dunning basis sets are used (1–11 cm−1). Addi-t db thee theB singt

onicf basiss nalf ionaT ta edf sedgf lf

etylm ibra-t giveni -ta lla se toV sedb

3

r ro-t red,a iven

unctions is discontinued at acetyl acetylene (X =C≡CH).The barrier heights calculated for acetone (X = CH3) are

btained by the rotation of only one methyl group frhe eclipsed to staggered position and are therefore,

form of effective barrier,V3eff. It is included here foompleteness and as an exact analog of the treatmentther acetyl molecules. The correct treatment of inteotation in acetone is to include the coupling betweenethyl tops at both the kinetic and potential energy leve

n the analysis given by Groner et al.[4,32]. It may be for thiseason that the results for acetone are rather low evenhe MP2/6-311 + G(3df,2p) basis. The neglect of inteop–top coupling may also be the reason for the low resuhe large bases in acetic acid (X = OH). Perhaps somef multidimensional treatment should be applied to al

he molecules with more than one internal top from meinyl ketone (X = CH CH2) onwards inTables 1b and 1c.

The Dunning correlated bases cc-pVXZ have beenlied in calculations for acetaldehyde and acetyl fluoride.arriers in acetaldehyde are 488, 446 and 418 cm−1 by theethods MP2/cc-pVDZ, MP2/cc-pVTZ and MP2/cc-pVQ

espectively. The calculated barriers in acetyl fluoride areomewhat higher than the observed. Considering the comng cost and poor results, it appears that these basis seoo expensive for the present purpose.

Almost no method/basis set gives consistently good aent of the calculated value ofV3 with the experimenta

alue for all molecules across the tables. However, theictions of the MP2/6-311+G(3df,2p) seem to be the m

rustworthy in spite of the low values for X = OH and CH3.ptimizing the geometry with this method/basis for a

e

ion of the ZPE correction to the rawV3 raises the predictearrier in all cases but this yields good agreement withxperimental barrier for a number of methods, notably3LYP results with the 6-31G bases and some results u

he DZ basis.Since in order to determine ZPE differences, harm

requencies have been obtained for all methods andets for acetaldehyde (X = H), the ab initio methyl torsiorequencies,νharm, obtained in the harmonic approximatre also given inTable 2. The torsional frequencies,νper, inable 2have been determined from rawV3 barriers withoupplying any correction. TheF rotational constants employ

or this have been calculated from the optimized eclipeometry. With aV3 of 400 cm−1 and anF of 7.66 cm−1,

or each increase toV3 of 10 cm−1, the periodic torsionarequency is increased by only 2.0 cm−1.

The zero-point energy corrections for all the other acolecules have also been calculated from harmonic v

ional frequencies and a few representative results aren Table 3. For X = Cl, C≡N, andcis CH CH2, the correcions are even larger (17–36 cm−1) than for X = H or F. WithV3 of 400 cm−1 and anF of 5.48 cm−1, the average for acetyl molecules other than acetaldehyde, for an increa3 of 20 cm−1 the periodic torsional frequency is increay only 3.4 cm−1.

.2. The effect of V6 on torsional fundamental

When more than one torsional transition is observed oational transitions of excited torsional levels are measusmall departure from an exact three-fold potential is g

S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477 1475

Table 2Torsional parameters for methyl torsion in acetaldehyde from ab initio calculations

V3 νharma ZPE V6 F νper

b

Experimental 407.95 −12.92 7.6559 143.86HF/3-21G 397.4 162 18.6 −5.5 7.8303 148.5HF/6-31G 332.3 147 19.0 −5.8 7.8052 134.7HF/6-31G(d) 359.1 152 14.7 −7.2 7.8412 140.7B3LYP/6-31G(d) 387.5 154 15.4 −9.2 7.6739 145.2B3LYP/6-31G(d,p) 393.8 155 14.7MP2/6-31G(d) 349.2 148 14.7 −8.1 7.6457 137.0MP2/6-31G(d,p) 363.6 150 15.2 −9.7 7.7027 140.5MP2/6-31+G(d) 309.9 138 17.0MP2/6-311G(d) 379.9 154 12.6MP2/6-311+G(d) 334.5 144 15.1MP2/6-311+G(d,p) 360.5 147 19.9 −11.3 7.6795 139.6MP2/6-311+G(3df,2p) 407.5 7.6795 149.2HF/DZ 401.3 162 9.7 −8.8 7.7969 149.0HF/DZ(d) 399.0 160 8.7 −9.1 7.8323 148.9MP2/DZ(d) 397.8 155 6.5 −10.6 7.5913 146.5MP2/DZ(d,p) 413.7 158 1.2B3LYP/DZ(d) 376.2 151 6.5 −7.4 7.6562 142.7B3LYP/DZ(d,p) 376.4 151 4.7MP2/cc-pVDZ 488.3 171 1.0MP2/cc-pVTZ 446.0 170 1.8MP2/cc-pVQZ 417.6B3LYP/cc-pVTZ 419.0 159 11.4

a Torsional fundamental derived from harmonic force constants.b Derived from periodic potential functionV3.

but a smallV6 term is usually sufficient to give a good fit. Anab initio determination ofV6 is obtained by calculating theenergy at some methyl torsional angle other than eclipsedor staggered. In this study, 30◦ is chosen but the true ef-fective torsional angle,τeff, of the set of hydrogens mustbe used.

For acetaldehyde, calculated values ofV6 are given forsome methods inTable 2. It is evident that for acetaldehydethey are negative like the experimental value (−12.92 cm−1)although all are underestimates. For a negative value ofV6,the derived torsional frequency is lowered. For acetalde-hyde, aV6 of −10 cm−1 reduces the frequency by 3.8 cm−1.This magnitude of correction would bring the prediction forMP2/6-311+G(3df,2p) into very good agreement with ex-perimental fundamental. However, the torsional frequencies,νper, in Table 2have been determined from rawV3 barrierswithout applying any correction because it is evident that theZPE correction and theV6 correction cancel each other.

TheV6 corrections for a few representative molecules andmethods are given inTable 4. V6 values are usually nega-tive but two acetyl molecules treated here have computed

positive values for most methods. However, for the largestmethod/basis set employed, the values are all negative.

With aV3 of 400 cm−1 a value ofV6 of ±10 cm−1 changesthe predicted torsional frequency by±3.7 cm−1.

3.3. Comparison of experimental and ab initio torsionalfrequencies

Just as no one method and basis set combination gives con-sistently good agreement of the calculated value ofV3 withthe experimental value for all molecules across the tables,so none of the versions of ab initio torsional vibrational fre-quencies are consistently in good agreement with observedtorsional fundamentals.

Since in order to determine ZPE differences, harmonicfrequencies have been obtained for most methods and basissets, the ab initio methyl torsional frequencies in the har-monic approximation,νharm, are given inTable 5for twomethods/basis sets. Although one might expect them to beconsistently higher than observed fundamental frequenciesand also higher than torsional transitions calculated from the

Table 3Zero-point energy corrections to be added to raw ab initioV3 values for some CH3COX molecules

X H F Cl CN cis CH CH2 NCO

HF/3-21G 18.635.25.18.22.16.

HF/6-31G 19.0 17.6HF/6-31G(d) 14.7 17.1B3LYP/6-31G(d) 15.4 7.7MP2/6-31G(d) 14.7 11.9MP2/6-311+G(d,p) 19.9 13.1

6 30.2 31.4 21.98 27.8 25.8 1.99 24.3 26.5 10.24 16.4 30.4 2.55 20.4

1476 S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477

Table 4V6 values for some CH3COX molecules

X H F Cl CN cis CH CH2 NCO

HF/3-21G −5.5 −7.8 −12.7 4.8 −1.2 14.7HF/6-31G −5.8 −13.3 −7.5 2.4 −4.0 6.0HF/6-31G(d) −7.2 −6.2 −10.0 4.6 −4.1 7.8B3LYP/6-31G(d) −9.2 −9.1 −12.4 2.6 −5.6 8.9MP2/6-31G(d) −8.1 −10.7 −13.1 3.3 −9.4 7.3MP2/6-311+G(d,p) −11.3 −14.8 −18.7 −6.1 −15.6 −2.7

torsional potential function, some of them are remarkablynear to experimental. At least they can be used to settle dis-agreements in assignment.

Since MP2/6-31G(d) is an inexpensive method ofobtaining frequencies for all molecules and since the MP2/6-311+G(3df,2p) combination is fairly consistent, only thesetwo methods are chosen for the tabulation of the torsional fre-quencies obtained from the periodic potential,νper, inTable 5.

The agreement of the final column ofνper with the firstcolumn, νobs, is very good for all the cases where thereis a well measured observed torsional transition. For ac-etaldehyde (X = H), acetyl fluoride (X = F), acetyl cyanide(X = C≡N), acetyl acetylene (X =C≡CH), methyl vinylketone (X = CH CH2) both cis and trans, and methyl cy-clopropyl ketone (X =cC3H4) the agreement is better than4 cm−1.

There are three cases of disagreement between a farinfrared assignment and the torsional frequency derivedfrom the microwave spectrum: acetyl chloride (X = Cl)[2,3,27], acetyl bromide (X = Br)[3,28] and 2-butanone(X = CH2CH3) [8,30,31]. There is excellent agreement, likethat for the molecules above, of the ab initioνper valuewith the microwave value. The agreement for the verylow torsional frequency of 84 cm−1 in trans 2-butanone(X = CH2CH3) is only slightly less good. However, thereis a problem withtrans2-butanone in that B3LYP/6-31G(d)and MP2/6-311+G(d,p) do not give an optimized geometrywith a plane of symmetry, the methyl and ethyl groups be-ing slightly rotated. The same problem arises with the largebasis set for acetone. The predictions for acetone cannot beexpected to give good agreement when top–top coupling isignored.

Table 5Experimental and ab initio torsional fundamental frequencies for acetyl molecules, CH3COX

X νobsa νharm

c

MP2/6-31G(d)νharm

c MP2/6-311 + G(d,p)

F MP2/6-31G(d)

F MP2/6-311 + G(d,p)

νperb

MP2/6-31G(d)νper

b MP2/6-311 + G(3df,2p)

H 147.86d 147.6 147.0 7.646 7.680 137.0 149.2F 121e 144.0 133.5 5.660 5.575 128.6 118.4Cl 162.8, 137f 151.1 142.3 5.472 5.470 129.5 134.4Br 168, 135g 163.0 141.4 5.390 5.394 147.2 137.0

equen

transOH 82h 91.6 61.1CH3 125.16 b1142.1 b1127.6C≡N 126.06 141.0 128.6C≡CH 117.9 137.1 119.3CH CH2 cis 121 136.1 128.6CH CH2 trans 125 152.9 133.8CH2CH3 trans 124, 84i 110.3 107.0CH2CH3 gauche 142 149.2 140.2NCO cis 138 134.2NCO trans 147 152.5NCScis 131 131.7NCS trans 150 150.8Cyclopropyl H-trans 124.8 144.0Phenyl in-plane 150.7

a SeeTables 1a–cfor Durig references, italics for ab initio harmonic frb Derived from periodic potential function,V3.c Derived from harmonic force constants.d Ref. [15].e Calculated fromV3 of Ref. [21].f Calculated fromV of Ref. [27].

3g Calculated fromV3 of Ref.[28].h Calculated fromV3 of Ref. [22].i Calculated fromV3 of Refs.[30,31].j FromV3 of MP2/6-311+G(2df,2p).k FromV3 of MP2/6-311+G(d,p).

5.675 5.683 85.7 75.15.632 5.626 103.0 95.05.458 5.450 132.9 128.55.462 5.453 133.3 121.95.585 5.574 122.6 123.25.444 5.436 134.7 127.25.583 5.575 90.5 78.95.457 5.445 94.4 86.15.543 5.545 122.8 116.2j

5.351 5.351 132.6 122.1j

5.512 5.512 120.5 114.1j

5.313 5.313 131.9 120.5j

5.484 5.484 128.3 124.4k

5.359 5.359 164.6 152.8k

cy.

S. Bell / Spectrochimica Acta Part A 61 (2005) 1471–1477 1477

There are four molecules for which no torsional frequen-cies have been observed or assigned. The predictions foracetic acid (X = OH) are for very low methyl barriers andvery low torsional frequencies, but that is as expected fromthe microwave barrier. The best value is only a few cm−1 fromthe value derived from that barrier using theF-values calcu-lated. Clearly for X = NCO and NCS, the torsional frequen-cies derived from the periodic potential function should berelied upon rather than those from harmonic force constantswhich are clearly too high in most cases but particularly forX = NCO and NCS. For acetophenone, the best prediction isfor a torsional frequency of 153 cm−1.

For the four molecules for which no torsional bands havebeen observed in the far infrared spectrum, this study pro-vides clear guidance as to where to search. In all these acetylmolecules, the methyl torsional transitions are calculated byab initio methods to be very weak and such weak featuresmay have been overlooked before.

For all the other acetyl molecules studied except acetone,there is a very pleasing agreement between the computed fre-quencies and the experimental torsional frequencies obtainedfrom either far infrared spectra or microwave spectra.

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