ORIGINAL RESEARCH

The r0 structural parameters of equatorial and axialchlorocyclobutane, conformational stability from temperaturedependent infrared spectra of xenon solutions, and vibrationalassignments

James R. Durig Æ Joshua J. Klaassen ÆArindam Ganguly Æ Todor K. Gounev ÆGamil A. Guirgis Æ Wei Lin

Received: 3 August 2008 / Accepted: 26 August 2008 / Published online: 19 September 2008

� Springer Science+Business Media, LLC 2008

Abstract Variable temperature (-55 to -100 �C) studies

of the infrared spectra (4,000–400 cm-1) of chlorocyc-

lobutane, c-C4H7Cl, dissolved in liquid xenon have been

carried out. The infrared spectrum (4,000–100 cm–1) of the

gas has also been recorded. For this puckered ring molecule

the enthalpy difference between the more stable equatorial

conformer and the axial form, has been determined to be

361 ± 17 cm-1 (4.32 ± 0.20 kJ/mol). This stability order

is consistent with that predicted by ab initio calculations

but the DH is much lower than the average energy value of

646 ± 73 cm-1 obtained from the MP2 ab initio calcula-

tions or 611 ± 28 cm-1 from the B3LYP density

functional theory calculations. The percentage of the axial

conformer present at ambient temperature is estimated to

be 15 ± 1%. By utilizing previously reported microwave

rotational constants for both conformers combined with

ab initio MP2(full)/6–311?G(d,p) predicted structural

values, adjusted r0 parameters have been obtained. The

determined heavy atom structural parameters for the

equatorial conformer are: the distances C–Cl = 1.783(5),

C1–C4 = 1.539(3), C4–C6 = 1.558(3) A, and angles

\C6C4C1 = 86.9(5), \C4C1C5 = 89.7(5)�, and for the

axial conformer are: the distances C–Cl = 1.803(5),

C1–C4 = 1.547(3), C4–C6 = 1.557(3) A, and angles

\C6C4C1 = 86.3(5), \C4C1C5 = 88.9(5) and the pucker-

ing angles for the equatorial and axial conformers are

30.7(5)� and 22.3(5)�, respectively. The conformational

stabilities, harmonic force fields, infrared intensities,

Raman activities, depolarization ratios and vibrational

frequencies have been obtained for both conformers from

MP2(full)/6-31G(d) ab initio calculations and compared to

experimental values where available. The results are dis-

cussed and compared to the corresponding properties of

some similar molecules.

Keywords Infrared spectrum � Xenon solutions �Conformational stability � r0 Structural parameters �Ab initio calculations � Chlorocyclobutane

Introduction

Structural studies of monosubstituted derivatives of cyc-

lobutanes in the vapor phase have shown the four-

membered rings usually adopt a non-planar equilibrium

conformation. For most molecules studied to date, the most

stable conformation is the one in which the substituent is in

the equatorial position relative to the puckered ring. For

several of the molecules it was initially proposed that the

axial conformer has only one bound state so no ring-

puckering mode was observed for the axial conformer of

Cl, Br, F, NH2 [1–5]. However, initially the cyclobutyl

silane molecule was shown to have both an equatorial and

axial form with the latter one having more than one energy

level for the ring-puckering mode by microwave studies

[6]. Additionally, cyclobutanol was also initially proposed

Taken in part from the thesis of Arindam Ganguly, which will be

submitted in partial fulfillment of the Ph.D. degree.

J. R. Durig (&) � J. J. Klaassen � A. Ganguly � T. K. Gounev

Department of Chemistry, University of Missouri-Kansas City,

Kansas City, MO 64110, USA

e-mail: durigj@umkc.edu

G. A. Guirgis

Department of Chemistry and Biochemistry, College of

Charleston, Charleston, SC 29424, USA

W. Lin

Department of Natural Science and Mathematics,

University of Saint Mary, Leavenworth, KS 66048, USA

123

Struct Chem (2008) 19:935–948

DOI 10.1007/s11224-008-9378-8

[7] to have an axial well with more than one energy level

for the ring-puckering mode. Since these initial studies

several microwave investigations [8–10] have been carried

out where the spectra have been assigned for the axial

conformer, i.e., F, CN, and Cl; for these monosubstituted

cyclobutanes. However, for the fluoride only one energy

level for the ring-puckering mode was proposed in the axial

well but for the cyanide and chloride a second energy level

was proposed based on the observation of rotational tran-

sitions from an excited state. Therefore, it should be

possible to observe the ring-puckering mode for the axial

conformer of chlorocyclobutane, and we initiated a vibra-

tional investigation in search of it.

Although there have been extensive microwave studies

of several monosubstituted cyclobutanes only the parame-

ters for chlorocyclobutane were initially proposed [2] from

one isotopomer with 13C rotational constants, 6 isotopo-

mers with various deuterium substitutions and the normal

species with 35Cl and 37Cl. The parameters from this study

were used to predict the rotational constants for the cor-

responding alcohol [11]. Electron diffraction studies [12]

have been used to obtain average values for the C–C and

C–Cl distances for both conformers of chlorocyclobutane

but small differences in bond length between the con-

formers could not be determined but the two different

puckering angles were reported. Therefore, of major

interest is the difference of the structural parameters

between the two conformers which should be obtainable

from the previously reported six rotational constants for

each conformer [10].

Finally we were interested in the enthalpy difference

between the two conformers in the gas for comparison to

the value reported for the liquid which could be signifi-

cantly affected by the condensed state. Also, the earlier

reported value from the temperature dependent Raman

spectrum of the gas was determined from a single pair of

bands. Ab initio predicted energy differences between the

two conformers are much larger than the experimentally

reported enthalpy difference. With these goals we initiated

the vibrational and theoretical study of chlorocyclobutane,

and the results of these investigations are reported therein.

Experimental

The sample of chlorocyclobutane was purchased from

Aldrich Chemical Co., with stated purity of 97%. The

sample was further purified by low-temperature, low-

pressure fractionation column and the purity of the sample

was verified by comparing the infrared spectrum with that

previously reported [3].

The mid-infrared spectra of the gas and solid were

obtained from 4,000 to 220 cm-1 on a Perkin-Elmer model

2000 Fourier transform spectrometer equipped with a Ge/

CsI beamsplitter and a DTGS detector. Atmospheric water

vapor was removed from the spectrometer housing by

purging with dry nitrogen. The theoretical resolution used

to obtain the spectrum of the gas was 0.5 and 2.0 cm-1 for

the spectra of the solid. One hundred twenty eight inter-

ferograms were added and transformed with a boxcar

truncation function. The frequencies for the predicted and

observed fundamentals are listed in Tables 1 and 2.

The mid-infrared spectra (4,000–400 cm-1) of the

sample dissolved in liquefied xenon (Fig. 1a) at ten dif-

ferent temperatures (-55 to -100 �C) were recorded on a

Bruker model IFS-66 Fourier transform spectrometer

equipped with a globar source, a Ge/KBr beamsplitter,

and a DTGS detector. In all cases, 100 interferograms

were collected at 1.0 cm-1 resolution, averaged and

transformed with a boxcar truncation function. For these

studies, a specially designed cryostat cell was used. It

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

wedged silicon windows sealed to the cell with indium

gaskets. The copper cell was enclosed in an evacuated

chamber fitted with KBr windows. The temperature was

maintained with boiling liquid nitrogen and monitored by

two Pt thermo resistors. A very small sample was intro-

duced into the cell after cooling to the designated

temperature. The system was then pressurized with the

noble gases, which condensed in the cell, allowing the

compound to dissolve.

The Raman spectra (Fig. 2) were recorded on a Spex

model 1403 spectrophotometer equipped with a Spectra-

Physics model 2017 argon ion laser operating on the

514.5 nm line. The laser power used was 1.5 W with a

spectral bandpass of 3 cm-1. The spectrum of the liquid

was recorded with the sample sealed in a Pyrex glass

capillary. The measurements of the Raman frequencies are

expected to be accurate to ±2 cm-1. All the observed

bands in the spectrum of the liquid with their proposed

assignments are listed in Tables 1 and 2.

Ab initio calculations

The LCAO-MO-SCF restricted Hartree–Fock calculations

were performed with the Gaussian-03 program [13] using

Gaussian-type basis functions. The energy minima with

respect to nuclear coordinates were obtained by the

simultaneous relaxation of all geometric parameters using

the gradient method of Pulay [14]. A variety of basis sets as

well as the corresponding ones with diffuse functions were

employed with the Møller-Plesset perturbation method [15]

to the second order MP2(full) as well as with the density

functional theory by the B3LYP method. The predicted

conformational energy differences are listed in Table 3.

936 Struct Chem (2008) 19:935–948

123

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Struct Chem (2008) 19:935–948 937

123

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[26]

938 Struct Chem (2008) 19:935–948

123

In order to obtain a complete description of the molec-

ular motions involved in the fundamental modes of

chlorocyclobutane, a normal coordinate analysis has been

carried out. The force field in Cartesian coordinates was

obtained with the Gaussian 03 program at the MP2(full)

level with the 6-31G(d) basis set. The internal coordinates

used to calculate the G and B matrices are given in Table 4

with the atomic numbering shown in Fig. 3. By using the B

matrix [16] the force field in Cartesian coordinates was

converted to a force field in internal coordinates. Subse-

quently, scaling factors of 0.88 for CH and 0.90 for all

other coordinates were used, along with the geometric

average of scaling factors for interaction force constants, to

obtain the fixed scaled force field and resultant wave-

numbers. A set of symmetry coordinates was used

(Table 5) to determine the corresponding potential energy

distributions (P.E.Ds). A comparison between the observed

and calculated wavenumbers, along with the calculated

infrared intensities, Raman activities, depolarization ratios

and potential energy distributions for the Eq and Ax con-

formers, which are given in Tables 1 and 2, respectively.

The infrared spectra were predicted from the MP2(full)/

6-31G(d) calculations. The predicted scaled frequencies

Fig. 2 Comparison of experimental and calculated Raman spectra of

chlorocyclobutane: (a) observed Raman spectrum of the gas; (b)

observed Raman spectrum of the liquid; (c) simulated spectrum of the

mixture of equatorial and axial conformer at 25 �C with

DH = 361 cm-1; (d) simulated Raman spectrum of axial (Cs); (e)

simulated Raman spectrum of equatorial (Cs); (f) annealed solid

Fig. 1 Comparison of experimental and calculated infrared spectra of

chlorocyclobutane: (a) infrared spectrum of the Xe solution at

-70 �C; (b) simulated infrared spectrum of mixture of equatorial and

axial at -70 �C with DH = 361 cm-1; (c) simulated spectrum of

axial (Cs); (d) simulated spectrum of equatorial (Cs); (e) annealed

spectrum of solid

Struct Chem (2008) 19:935–948 939

123

were used together with a Lorentzian function to obtain the

calculated spectra. Infrared intensities determined from

MP2(full)/6-31G(d) calculations were obtained based on

the dipole moment derivatives with respect to Cartesian

coordinates. The derivatives were transformed with respect

to normal coordinates by ðolu=oQiÞ ¼P

j

ðolu=oXjÞLij;

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

displacement coordinate, and Lij is the transformation

matrix between the Cartesian displacement coordinates

and the normal coordinates. The infrared intensities

were then calculated by [(Np)/(3c2)] [(qlx/qQi)2 ? (qly/

qQi)2 ? (qlz/qQi)

2]. In Fig. 1, a comparison of the exper-

imental and simulated infrared spectra of chlorocyclobutane

is shown. Infrared spectrum of the of chlorocyclobutane in

Xe at -70 �C (Fig. 1a), and the predicted infrared spectra

for the pure equatorial (Fig. 1d) and axial (Fig. 1c) con-

formers, as well as the mixture (Fig. 1b) of the two

conformers with relative concentrations calculated for the

equilibrium mixture at -70 �C by using the experimentally

determined enthalpy difference are presented. The spectrum

of the mixture should be compared to that of the xenon

solution. The predicted spectrum is in relatively good

agreement with the experimental spectrum which indicates

the utility of the scaled predicted frequencies and intensities

for supporting the vibrational assignment.

Also, to further support the vibrational assignments, we

have simulated the Raman spectra from the ab initio

MP2(full)/6-31G(d) results. The evaluation of Raman

activity by using the analytical gradient methods has been

developed [17–20]. The activity Sj can be expressed as:

Sj = gj (45a2j ? 7bj

2), where gj is the degeneracy of the

vibrational mode j, aj is the derivative of the isotropic

polarizability, and bj is that of the anisotropic polarizabil-

ity. To obtain the polarized Raman scattering cross

sections, the polarizabilities are incorporated into Sj by

multiplying Sj with (1 - qj)/(1 ? qj), where qj is the

depolarization ratio of the jth normal mode. The Raman

scattering cross sections and calculated wavenumbers

obtained from the Gaussian 03 program were used together

with a Lorentzian function to obtain the simulated Raman

spectra. Comparison of experimental Raman spectra of the

gas (Fig. 2a), liquid (Fig. 2b), solid (Fig. 2f) and the pre-

dicted Raman spectra for the pure equatorial (Fig. 2e) and

axial (Fig. 2d) conformers as well as the mixture (Fig. 2c)

of the two conformers with relative concentrations calcu-

lated for the equilibrium mixture at 25 �C by using the

Table 3 Calculated energies

(H) and energy differences

(cm-1) for the two conformers

and transition state of

chlorocyclobutane

a Energy of equatorialconformer is given as

–(E ? 615) Hb Difference is relative to

equatorial form and given in

cm-1

Method/basis set Energya, E Energy differencesb, D

Equatorial Axial D Planar ring

RHF/6-31G(d) 0.004753 0.001952 615

MP2(full)/6-31G(d) 0.684422 0.681119 725 1,231

MP2(full)/6-31?G(d) 0.694032 0.690757 719

MP2(full)/6-31G(d,p) 0.741896 0.738454 755

MP2(full)/6-31?G(d,p) 0.750538 0.747190 735

MP2(full)/6-311G(d,p) 0.922859 0.920160 592 1,578

MP2(full)/6-311?G(d,p) 0.927873 0.925299 565 1,476

MP2(full)/6-311G(2d,2p) 0.998447 0.995541 638

MP2(full)/6-311?G(2d,2p) 1.001589 0.998883 594

MP2(full)/6-311G(2df,2pd) 1.094710 1.091892 619

MP2(full)/6-311?G(2df,2pd) 1.097565 1.094897 586

MP2(full)/aug-cc-pVTZ 1.095940 1.093315 576 990

Average MP2(full) 646 ± 73

B3LYP/6-31G(d) 1.814566 1.811570 657 666

B3LYP/6-31?G(d) 1.820667 1.817654 661

B3LYP/6-311G(d,p) 1.885003 1.882303 593

B3LYP/6-311?G(d,p) 1.886542 1.883820 597 607

B3LYP/6-311G(2d,2p) 1.893272 1.890576 592

B3LYP/6-311?G(2d,2p) 1.894304 1.891614 590

B3LYP/6-311G(2df,2pd) 1.898975 1.896193 611 589

B3LYP/6-311?G(2df,2pd) 1.899936 1.897168 608 598

B3LYP/aug-cc-pVTZ 1.910347 1.907623 598 599

Average B3LYP 611 ± 28

940 Struct Chem (2008) 19:935–948

123

experimentally determined enthalpy difference are shown.

The predicted spectrum of the mixture should be compared

to that of the Raman spectrum of the liquid at room tem-

perature, although there may be some difference between

the predicted and that obtained experimentally due to the

hydrogen bonding in the liquid. Nevertheless, the predicted

spectrum is in good agreement with the experimental

spectrum which again indicates the utility of the scaled

predicted frequencies and intensities of the Raman spectra

for supporting the vibrational assignment.

Table 4 Structural parameters (A and degree), rotational constants (MHz), and dipole moments (Debye) for equatorial and axial

chlorocyclobutane

Structural parameters Int. Co. MP2(full)/6-311?G(d,p) EDa Microwave Adjusted r0

Eq Ax Eq Ax Eqb,c Axd Eq Ax

rC1–Cl R1 1.777 1.785 1.786(4) 1.786(4) 1.775(5) 1.785 1.783(5) 1.803(5)

rC1–C4,C5 R2 1.534 1.541 1.545(2) 1.545(2) 1.525(5) 1.539(3) 1.547(3)

rC6–C4,C5 R3 1.551 1.549 1.560(2) 1.560(2) 1.550(5) 1.558(3) 1.557(3)

rC1–H3 r5 1.092 1.090 1.098(4) 1.098(4) 1.10(1) 1.092(2) 1.090(2)

rC4–H7,C5–H9 r1 1.093 1.091 1.098 (4) 1.098(4) 1.085(1) 1.093(2) 1.091(2)

rC4–H8,C5–H10 r2 1.092 1.095 1.098(4) 1.098(4) 1.085(1) 1.092(2) 1.095(2)

rC6–H11 r3 1.091 1.091 1.098(4) 1.098(4) 1.10(1) 1.091(2) 1.091(2)

rC6–H12 r4 1.093 1.091 1.098(4) 1.098(4) 1.10(1) 1.093(2) 1.091(2)

\Cl2C1C4 /1 118.7 111.4 118.6 111.4 117* 118.1(5) 110.6(5)

\C4C1C5 h2 89.02 88.27 88.9 89.4 90.8(5) 88.62 89.7(5) 88.9(5)

\C6C4C1 h3 86.55 88.02 86.5* 86.9(5) 89.3(5)

\C4C6C5 h4 87.84 87.72 86.8* 88.3(5) 88.1(5)

\H3C1C4 r1 111.3 119.1 106* 111.6(5) 119.5(5)

\H3C1Cl2 r2 107.1 106.9 106.6 106.6 114(2) 107.1(5) 106.9(5)

\H7C4C1 k1 110.1 117.4 114(1) 110.1(5) 117.4(5)

\H7C4C6 k2 110.4 119.1 115* 107.7(5) 122.4(5)

\H8C4C1 k3 118.1 109.6 115(1) 118.1(5) 109.6(5)

\H8C4C6 k4 119.5 111.1 118* 121.7(5) 106.3(5)

\H7C4H8 k5 110.1 109.8 109.8 109.8 112(1) 110.1(5) 109.8(5)

\H11C6C4 p1 117.6 111.1 119* 118.4(5) 108.4(5)

\H12C6C4 p2 111.4 117.9 113* 110.2(5) 120.2(5)

\H11C6H12 p3 109.6 109.6 109.8 109.8 110(1) 109.6(5) 109.6(5)

Puckering anglee 33.9 30.5 30 21 20(1) 28.2 30.7(5) 22.3(5)

A(MHz) 10273.6 7951.6 10095.0 8043(1) 10094.7 8044.9

B(MHz) 2521.2 2931.9 2520.9 2859.0 2521.6 2858.7

C(MHz) 2199.7 2701.2 2196.3 2610.5 2195.9 2611.1

|la| 2.457 2.204 2.11(6) 1.97

|lb| 0.000 0.000 0.00 0.00

|lc| 0.451 0.897 0.57(7) 0.98

|lt| 2.498 2.380 2.20(7) 2.20

a Reference [12]b Structural parameters were taken from [2], while the rotational constants and dipole moments were taken from reference [10]c Parameters indicated with an asterisk are dependent parameters where the values with listed uncertainties are independent parametersd Adjusted parameters using the microwave data from [10] for the given ground statese Puckering angle is defined as the angle between the planes CbCcCb0 and CbCaCb0

Fig. 3 Chlorocyclobutane showing atomic numbering

Struct Chem (2008) 19:935–948 941

123

Structural parameters

We have [21] shown that ab initio MP2(full)/6-

311?G(d,p) calculations predict the r0 structural param-

eters for more than fifty carbon-hydrogen distances better

than 0.002 A compared to the experimentally determined

values from isolated CH stretching frequencies which are

compared [22] to previously determined values from

earlier microwave studies. Thus, all the carbon-hydrogen

parameters can be taken from the MP2(full)/6-311?

G(d,p) predicted values for chlorocyclobutane. Also, we

have found [23] that we can obtain good structural

parameters by adjusting the structural parameters from the

ab initio calculations to fit the rotational constants

obtained from the microwave experimental data. In order

to reduce the number of independent variables, the

structural parameters are separated into sets according to

their types. Bond lengths in the same set keep their rel-

ative ratio which results in only two heavy atoms

distances for chlorocyclobutane. Also, the bond angles

and torsional angles in the same set keep their differences

in degrees. This assumption is based on the fact that the

errors from ab initio calculations are systematic. There-

fore, it should be possible to obtain ‘‘adjusted r0’’

structural parameters for the equatorial and axial con-

former of chlorocyclobutane by utilizing the previously

reported [2, 10] microwave rotational constants.

Two microwave studies have been conducted on the

chlorocyclobutane molecule and in the first investigation

[2] only the equatorial conformer for the normal species

and eight of its isotopomers was assigned. Initially, we [24]

made an attempt to determine the r0 structural parameters

using the rotational constants from this earlier [2] study.

However, we could not achieve a satisfactory fit of the

rotational constants which prompted us to refer to the more

recent microwave study of chlorocyclobutane where the A

rotation constants were much more accurately determined

to obtain the r0 structural parameters.

Table 5 Symmetry

coordinatesa for

chlorocyclobutane

a Not normalized

Species Description Symmetry coordinatea

A0 b-CH2 symmetric stretch S1 = r2 - r1 ? r4 - r3

b-CH2 asymmetric stretch S2 = r1 ? r2 ? r3 ? r4

c-CH2 asymmetric stretch S3 = r5 - r6

c-CH2 symmetric stretch S4 = r5 ? r6

CH symmetric stretch S5 = r7

c-CH2 deformation S6 = 4m6 - m2 - m3 - m4 - m5

b-CH2 deformation S7 = 4a4 ? 4b4 - a2 - a3 - a5 - a6 - b2 - b3 - b5 - b6

c-CH2 rock S8 = m3 - m2 ? m5 - m4

CH in-plane bend S9 = 2h2 - d1 - d2

b-CH2 wag S10 = a2 ? a3 - a5 - a6 ? b2 ? b3 - b5 - b6

b-CH2 rock S11 = a2 - a3 ? a5 - a6 ? b2 - b3 ? b5 - b6

Ring breathing S12 = R3 ? R4

b-CH2 twist S13 = a2 - a3 - a5 ? a6 ? b2 - b3 - b5 ? b6

Ring deformation S14 = a1 ? b1 - m1 - h1

Ring deformation S15 = R1 ? R2

CCl stretch S16 = R5

CCl in-plane-bend S17 = u1 ? u2

Ring puckering S18 = a1 ? b1 ? m1 ? h1

A00 b-CH2 asymmetric stretch S19 = r2 - r1 ? r3 - r4

b-CH2 symmetric stretch S20 = r1 ? r2 - r3 - r4

b-CH2 deformation S21 = 4a4 - a2 - a3 - a5 - a6 - 4b4 ? b2 ? b3 ? b5 ? b6

b-CH2 rock S22 = a3 - a2 - a5 ? a6 ? b2 - b3 ? b5 - b6

CH out-of-plane bend S23 = d1 - d2

c-CH2 twist S24 = m2 - m3 - m4 ? m5

c-CH2 wag S25 = m4 ? m5 - m2 - m3

Ring deformation S26 = R3 - R4

b-CH2 wag S27 = a5 ? a6 - a2 - a3 ? b2 ? b3 - b5 - b6

b-CH2 twist S28 = a3 - a2 ? a5 - a6 ? b2 - b3 - b5 ? b6

Ring deformation S29 = R1 - R2

CCl out-of-plane bend S30 = u1 - u2

942 Struct Chem (2008) 19:935–948

123

In the second study [10], the authors reinvestigated and

reassigned the microwave spectrum of the equatorial con-

former of the normal species and 37Cl isotopomer of

chlorocyclobutane. In the same investigation the authors

were also successful in assigning the spectrum for the axial

conformer of the chlorocyclobutane also for the normal

species and 37Cl isotopomer and some of the excited states

for both the conformers. We utilized these data containing

six rotational constants corresponding to each of the con-

formers to determine the r0 structural parameters. The fit of

these rotational constants is shown in Table 6 where six of

the rotational constants are fit to better than one MHz for

the equatorial conformer. An equivalent fit was obtained

for the axial conformer except for the A rotational constant

of the normal species. The resulting adjusted r0 parameters

obtained for both the conformers are listed in Table 4,

where the C1–C4(C5) and C6–C4(C5) distances should be

accurate to ±0.003 A, the C–H distances should be accu-

rate to ±0.002 A and the angles to within ±0.5�.

The ab initio predicted structural parameters for the

equatorial and the axial conformers are quite distinct. For

example, the C–Cl bond distance for the equatorial form is

0.008 A shorter than the corresponding distance in the

axial form. In addition the Ca–Cb bond distance is pre-

dicted to be 0.007 A shorter than the corresponding

distance in the axial form which is probably due to the

positioning of the Cl atom with respect to the ring. Another

difference is the Ca–H3 bond distance which is as expected

predicted to be longer in the equatorial conformer by

0.002 A again due to the position of the Cl atom with

respect to the ring. Other perceptible differences are the

Cb–H distances where for the hydrogen atoms which are

positioned on top of the ring with chlorine atom, the Cb–H

distances in equatorial form is predicted to be 0.002 A

longer than the axial form. For the Cb–H distance for the

hydrogens which are placed below the ring, the distances

for the equatorial form is predicted to be 0.003 A shorter.

The Cc–H distance for the hydrogens positioned on top of

the ring are equal for both the conformers, whereas for the

other hydrogen atom the distance is 0.002 A longer for the

equatorial form compared to the axial. Further, we observe

that the difference in the ab initio predicted puckering

angles between the two conformers is relatively small. The

ab initio predicted difference is approximately 3.1�, com-

pared to 9 and 8.2�, as obtained from ED and MW,

respectively. The ab initio predicted ClCaCb angles for the

equatorial and axial forms differs considerably at 118.7�and 111.4�, respectively, which agrees with the electron

diffraction value and is only slightly smaller than the dif-

ference obtain in this study.

Vibrational assignment

There have been three extensive vibrational assignments

[3, 25, 26] for chlorocyclobutane where in the earlier one

the a-C-d and b-C2-d4 isotopomers were used to assign

many of the molecular motions. In the most recent study

[26] ab initio calculations with the 3-21G(d) basis set with

two scaling factors of 0.9 for stretches and 0.8 for the bends

were used to predict frequencies for the fundamentals and

potential energy distributions. These new data resulted in

some significant changes in a few of the descriptions of the

motions contributing to some of the bands. In particular the

two ring deformations were assigned to lower frequency

bands which had been assigned as CH2 rocking modes.

There was also a few major changes in the vibrational

assignment where C–H out-of-plane bend was reassigned

as accidently degenerate with the corresponding in-plane

motion of 1,207 cm-1 rather than the *300 cm-1 differ-

ence as originally assigned. Our experimental results

support the higher assignment for these two modes with

Table 6 Comparison of

rotational constants (MHz)

obtained from ab initio

MP2(full)/6-311?G(d,p)

predictions and from microwave

spectra and the adjusted

structural parameters for

chlorocyclobutane

a Reference [10]b Difference between

microwave determined values

and adjusted r0 structural

parameters

Isotopomer Rotational

constant

MP2(full)/

6-311?G(d,p)

Experimentala Adjusted r0 |D|b

eq-C4H735Cl A 10273.6 10094.98 10094.28 0.7

B 2521.2 2520.84 2521.51 0.7

C 2199.7 2196.38 2195.86 0.5

eq-C4H737Cl A 10278.0 10090(2) 10091.80 0.0

B 2453.3 2454.78 2455.31 0.5

C 2147.6 2146.17 2145.60 0.6

ax-C4H735Cl A 7951.6 8043(1) 8044.97 1.0

B 2931.9 2859.02 2858.80 0.2

C 2701.2 2610.55 2611.16 0.6

ax-C4H737Cl A 7941.4 8037(2) 8036.28 0.0

B 2859.6 2787.54 2787.31 0.2

C 2640.7 2551.75 2552.26 0.5

Struct Chem (2008) 19:935–948 943

123

them being separated by only 18 cm-1. The predicted

infrared band contours for the gas along with the predicted

infrared intensities and Raman activities provides consid-

erably more spectral information for making the vibrational

assignment.

The earlier assignments of the two b-CH2 twists with the

A0 mode to a band about 100 cm-1 lower than the pre-

dicted value and the A00 mode to a band about the same

difference except to a higher frequency have been reas-

signed to bands nearly to the predicted values since there

are both infrared and Raman bands that are consistent with

the frequencies predicted. This reassignment required the

band at 1,039 cm-1 in the A0 symmetry block and the

1,123 cm-1 band (A00) to not be assigned as fundamentals

as initially given [3] since neither of these bands were

observed in our spectra. These bands had been later iden-

tified [25] as probably due to impurity bands and our

current assignment of the fundamentals is consistent with

those proposed by these more recent investigators.

Our major contribution for the vibrational assignments

is for the fundamentals for the axial conformer. We have

identified six more fundamentals for the axial conformer

than those assigned earlier [25, 26]. These assignments

were based on band contours, relative intensities, and the

predicted frequencies from the ab initio calculations,

P.E.Ds and the spectra in Xe solution Fig. 4.

Conformational stability

To determine the enthalpy difference between the two

conformers, the mid-infrared spectra of chlorocyclobutane

dissolved in liquefied xenon as a function of temperature

from -55 to -100 �C were recorded. Only small interac-

tions are expected to occur between the dissolved sample

and the surrounding xenon atoms, and consequently, only

small frequency shifts are anticipated when passing from

the gas phase to the liquefied noble gas solutions [27–30].

A significant advantage of this study is that the conformer

bands are better resolved in comparison with those in the

infrared spectrum of the gas. From ab initio calculations,

the dipole moments of the two conformers are predicted to

have similar values and the molecular sizes of the two

rotamers are nearly the same, so the DH value obtained

from the temperature-dependent FT-IR study is expected to

be close to that for the gas [27–31].

A careful comparison between the infrared spectrum of

the xenon solutions at the highest (-55 �C) and the lowest

temperature (-100 �C) indicated two bands that were

clearly due to the axial conformer in the solution with

corresponding bands in the gas. These two bands in the

spectra of the xenon solutions at 1,013 cm-1 [ring

breathing (m12)] (Fig. 5) and 1,268 cm-1 [CH in-plane

bend (m9)] disappear in the spectrum of the solid. Both

bands are sufficiently separated from the equatorial bands

at 938 and 1,258 cm-1 which makes them satisfactory for

DH determinations.

Five equatorial bands, all of them but one well resolved

and well separated, were used for the conformational sta-

bility determination. The intensities of the infrared bands

were measured as a function of temperature and their ratios

were determined. By application of the van’t Hoff equation

-lnK = DH/(RT) - DS/R, DH was determined from a plot

of -lnK versus 1/T, where DH/R is the slope of the line and

K is substituted with the appropriate intensity ratios, i.e.,

Fig. 4 Mid-infrared spectra of chlorocyclobutane (a) gas; (b) Xe

solution at -70 �C

Fig. 5 Infrared spectra of chlorocyclobutane in xenon solution at

different temperatures

944 Struct Chem (2008) 19:935–948

123

Iequatorial/Iaxial. It was assumed that DH is not a function of

temperature in the temperature range studied.

By combining the two axial and the five equatorial con-

former bands, six pairs of bands were utilized for the

determination of the enthalpy difference, and the resulting

values with statistical uncertainties are listed in Table 7. The

statistical average of these six values is 361 ± 17 cm-1

where the error limit is derived from the statistical standard

deviation of one sigma of the measured intensity data where

the data were taken as a single set. The van’t Hoff plot for

each sets are also shown in Fig. 6. These error limits do not

take into account small associations with the liquid xenon or

the interference of overtones and combination bands in near

coincidence with the measured fundamentals. The variations

in the individual values are undoubtedly due to these types of

interferences, but by taking several pairs the effect of such

interferences should cancel. The abundance of the less stable

axial conformer present at ambient temperature is 15 ± 1%.

Ring puckering and barrier to planarity

The fundamental ring-puckering vibration of the equatorial

conformer has been observed [26] at 157.6 cm-1 (Fig. 7a)

as a strong Q-branch as expected for a predicted band

contour of 37% A-type and 63% C-type. The correspond-

ing band is observed in the Raman spectrum of the gas at

158 cm-1 (Fig. 7b). This frequency is much lower than the

value of 190 cm-1 (180 cm-1 with scaling factor 0.9)

predicted from the MP2(full)/6-31G(d) calculations which

raises a question concerning the reasonableness of the

predicted barrier to planarity and the puckering angle.

There are clearly two ‘‘hot bands’’ at 149.3 cm-1

(Raman 150 cm-1) and 139.8 cm-1 (Raman 141 cm-1) in

the far infrared spectrum with the second one possibly split

in both the infrared and Raman spectra. The next observed

lower frequency band is a very weak Q-branch at

130.1 cm-1 with a stronger one at 128.1 cm-1 with the

corresponding Raman line very broad which indicates it is

arising from two transitions. These two infrared bands were

assigned [26] as the third overtone of the ring-puckering

mode at 130.1 cm-1 for the equatorial conformer and the

stronger one to the fundamental of this mode for the axial

conformer. With this assignment there is again a very large

difference between the predicted frequency of 164 cm-1

(156 cm-1 with scaling 0.9) but the difference is consistent

with the difference obtained for the equatorial conformer.

We then checked to see if an improvement of the predicted

frequency could be obtained with the larger basis set of 6-

311?G(d,p) with both the MP2(full) and B3LYP calcula-

tions. With the larger basis set the B3LYP calculations

predict the ring-puckering mode for the equatorial con-

former at 150 cm-1 and for the axial form 98 cm-1. These

values are not significantly lower than values of 155 cm-1

Table 7 Temperature and intensity ratios of the equatorial and axial bands of chlorocyclobutane

T (�C) 1/T(910-3 K-1)

I938/I1013 I1258/

I1268

I1237/I1268 I1226/

I1268

I1202/

I1268

I1163/

I1268

Liquid

xenon

-55.0 4.584 0.954 1.190 0.901 0.165 1.071 0.269

-60.0 4.692 1.016 1.286 0.817 0.135 0.952 0.274

-65.0 4.804 1.048 1.381 0.889 0.144 0.990 0.269

-70.0 4.923 1.000 1.500 1.014 0.154 1.048 0.322

-75.0 5.047 1.223 1.391 1.059 0.167 1.157 0.333

-80.0 5.177 1.282 1.739 1.204 0.184 1.229 0.363

-85.0 5.315 1.365 1.833 1.365 0.183 1.345 0.386

-90.0 4.460 1.437 1.960 1.457 0.218 1.437 0.426

-95.0 5.613 1.480 2.038 1.637 0.226 1.574 0.458

-100.0 5.775 1.569 2.192 1.768 0.242 1.647 0.500

DHa 343 ± 41 368 ± 63 462 ± 30 315 ± 45 324 ± 32 375 ± 32

a Average value DH = 361 ± 17 cm-1 (4.32 ± 0.20 kJ mol-1) with the equatorial conformer the more stable form and the statistical

uncertainty (1r) obtained by utilizing all of the data as a single set

Fig. 6 van’t Hoff plot of -ln(Iequatorial/Iaxial) as a function of 1/T

Struct Chem (2008) 19:935–948 945

123

for the equatorial form and 103 cm-1 for the axial con-

former with the smaller 6-31G(d) basis set by the DFT

calculations. Although these values for the ring-puckering

vibration are in better agreement with the experimental

values the barrier to planarity is clearly predicted too low

compared to the predicted energy difference between the

conformers (Table 3). By using the larger basis set with the

MP2 calculations the ring-puckering mode was predicted

slightly higher at 194 cm-1 for the equatorial conformer,

and for the axial conformer it is predicted higher at

182 cm-1. Thus, these predictions are even poorer when

compared to the experimental values.

By utilizing the four transitions for the equatorial con-

former along with the fundamental transition for the axial

form the potential function governing the ring-puckering

motion of chlorocyclobutane was obtained [26]. The bar-

rier to planarity of 827 cm-1 and an enthalpy difference of

449 cm-1 along with puckering angles of 22� and 17� for

the equatorial and axial forms, respectively, (Fig. 7c). The

uncertainties in the values for the angles are dependent on

the reduced mass assumed for the molecular vibration. This

potential has three bound energy levels for the axial form

which is one more than the proposed potential suggested

from the microwave study [10] where a barrier

*800 cm-1 has been proposed. The ab initio calculations

contribute little to providing reasonable predictions to the

barrier at the planar position between the two wells where

the value of 1,578 cm-1 is predicted from the MP2(full)/6-

311G(d,p) calculation and is lowered to 990 cm-1 with

aug-cc-pVTZ basis set which still seems too high. Of

particular note is the large energy difference between the

two conformers from the B3LYP calculations with the

planar energy of essentially the same value so no bound

energy state would be present for the second conformer.

Therefore, we concluded that the potential function previ-

ously proposed [26] seems to be most consistent with all

the known experimental data.

Discussion

The determined structural parameters obtained in this study

for the equatorial conformer are really significantly dif-

ferent for several of the distances even when the

uncertainties are taken into account. The most obvious one

is the C1–C4(C5) distance which is relatively short at

1.525(5) A compared to the value of 1.539(3) A obtained

in this study. This experimental value is in agreement with

the average value of 1.545(2) A for both conformers for the

C1–C4 distance with C6–C4 average distance of 1.560(2) A.

This latter value is in excellent agreement with the value of

1.558(3) A for the equatorial (1.557(3) A for the axial

form) conformer. Also it should be noted that the C–H

distances reported earlier from the microwave study [2]

have very large uncertainties, i.e., 1.10(1) A, for the two

C6–H distances and the C1–H distance, whereas the values

from this study are 1.093(2) A, C6–H12; 1.091(2) A, C6–

H11; and 1.092(2) A for C1–H3 for the equatorial

Fig. 7 Low frequency spectra of chlorocyclobutane: (a) far-infrared

gas; (b) Raman spectra of gas; (c) potential function for the ring

puckering motion (data taken from [26])

946 Struct Chem (2008) 19:935–948

123

conformer. From the early study the CH distances for the

C4 and C5 carbons the uncertainty is small 1.085(1) A, but

the value differs substantially from the values of 1.093(2)

and 1.092(2) A obtained from this study.

The parameter that makes the largest difference is the

puckering angle which was reported in the earlier micro-

wave study to be 20 ± 1�, but from this study we obtained

a value of 30.7 ± 0.5� for the equatorial conformer which

is essentially the same value of 30� obtained in the electron

diffraction study [12]. Our value of 22.3(5)� for this angle

for the axial form also agrees with the value of 21� from

the electron diffraction study [12]. We found the puckering

angle was very sensitive to the value of the A rotational

constants and the values of A previously reported [2] of

10086.7(5) MHz for 35Cl and 10085(5) MHz for 37Cl but

the more accurate values recently determined [10] have

values of 10094.98(1) and 10090(2) MHz for the 35Cl and37Cl isotopomers, respectively. This difference for 35Cl of

8.2 MHz for A constant which was the most accurately

determined one was surprising but undoubtedly led to the

much smaller puckering angle and the large uncertainty on

the A constants obtained for the other isotopomer (various

deuterated species) makes it very difficult to use for r0

structural parameters [24].

In support of the determined parameters for chlorocyc-

lobutane a comparison with the heavy atom parameters of

cyclobutane which were obtained from a microwave study

[32] with the determined distances of: CC = 1.5555(2),

and CH = 1.0910(6), with equal parameters for the axial

and equatorial conformers and ring-puckering angle of

28.58(9)�. The comparison indicates a reasonable reduction

of the CC distance where the chlorine atom is attached with

a slight elongation of the other CC distance with consistent

CH distances and puckering angle. Therefore, it is believed

that the determined parameters reported herein for chlo-

rocyclobutane are as accurate as can be obtained for the

gas.

The ab initio MP2(full)/6-31G(d) predicted frequencies

with only two scaling factors of 0.88 and 0.9 provided

values for the A0 fundamentals within an average differ-

ence of 10 cm-1, which is an average error of 0.6% and for

the A00 an average difference of 7.6 cm-1, which is a

percentage error of 0.7%. Only a very few scaling factors

are needed to provide frequencies which are sufficient to

support the vibrational assignment rather than several

scaling factors to predict the observed frequencies. At one

time this was important so the force constants could be

transferred but now it is possible to calculate the force

constants for practically any bond of interest.

The P.E.D. distributions for the equatorial conformer

indicate extensive mixing of the ring modes with the CCl

motions for both the A0 and A00 species. For example m16 is

assigned as the CCl stretch with only 28% S16 and 41%S14

but m14 has 39% S14 and 22% S16. Thus, there is significant

contribution from the CCl stretch to m14, m15, and m16 so the

designation of m16 as the CCl stretch is more for book-

keeping then describing the molecular motion. There are

four other vibrations where significant contributions are

indicated by four different symmetry coordinates. Never-

theless, it is believed that these approximate descriptions

are useful for comparison of similar vibrations for corre-

sponding molecular such as other mono-substituted four-

membered rings.

The determined DH value of 361 ± 17 cm-1

(4.32 ± 0.20 kJ/mol) from the xenon solution is in excel-

lent agreement with the value of 325 ± 40 cm-1

(3.89 ± 0.48 kJ/mol) previously reported [26] from the

variable temperature study of the Raman spectrum of the

gas from a single pair of bands. However, the value

obtained from the xenon solution has a significant lower

uncertainty. Previously a value of 334 cm-1 was reported

from the electron diffraction study [12] which utilized a

dynamic model which was obtained by introducing a single

Boltzmann population to determine the potential function

of the puckering motion. This value was preferred to a

static model with two conformers vibrating in separate

wells which gave a value of 500 cm-1 for the enthalpy

difference. It is clear from the determined enthalpy dif-

ference that the preferred model is consistent with the

experimentally determined enthalpy difference.

The ab initio predicted energy difference from the MP2

calculations is 646 ± 73 cm-1 (7.73 ± 0.87 kJ/mol) and

is way too large compared to all the experimental data

which include the determined DH value, the amount of the

axial conformer present at ambient temperature, the iden-

tification of the second conformer in the microwave

spectrum, and the need for a second conformer to analysis

the electron diffraction data. With the energy difference of

646 cm-1 there would be only 4% of the axial conformer

present at ambient temperature which is not consistent with

the intensities of the observed bands in the infrared or

Raman spectra. The MP2 calculations with medium size

basis sets are frequently found to predict large energy

differences for organo-chlorides, and it appears that

B3LYP calculations also give similar results.

Three of the quadratic distortion constants, DJ, DJK, and

dJ, were obtained from the most recently obtained [10]

microwave data for the equatorial 35Cl isotopomer and two

constants, DJ, and DJK, for the 37Cl isotopomer as well as

for both isotopomers for the axial conformer (Table 8). We

have obtained all five distortion constants for both isotop-

omers for both conformers from the force constants

predicted from the MP2(full)/6-31G(d) calculations and

these values are listed in Table 8 for comparison to the

experimentally determined values. For the equatorial 35Cl

isotopomer the values from the force constants agree very

Struct Chem (2008) 19:935–948 947

123

well with those obtained from the microwave, data whereas

those for the equatorial 37Cl the agreement is not quite as

good but satisfactory. However, the experimental values

may not be as good as the listed uncertainties since the

value for dJ for this isotopomer as well as for both iso-

topomers for the axial conformer were held to be 0.0.

Therefore, we believe those obtained from the force con-

stants from the ab initio calculations for the equatorial 37Cl

isotopomer are more accurate than the two experimental

determined values, and we expect it may be the similar

case for both isotopomers of the axial conformer.

Acknowledgment JRD acknowledges the University of Missouri-

Kansas City for a Faculty Research Grant for partial financial support

of this research.

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Table 8 Quadratic centrifugal distortion constants (kHz) for equatorial and axial chlorocyclobutane

Equatorial Axial

C4H735Cl C4H7

37Cl C4H735Cl C4H7

37Cl

MP2(full)/ 6-31G(d) Exp.a MP2(full)/ 6-31G(d) Exp.a MP2(full)/ 6-31G(d) Exp.a MP2(full)/ 6-31G(d) Exp.a

DJ 0.31 0.34(2) 0.30 0.53(6) 1.03 1.2(1) 0.99 1.8(2)

DJK 1.31 1.31(4) 1.25 0.8(2) -1.97 -3.6(3) -1.91 -5(1)

DK 5.37 – 5.46 – 6.25 – 6.21 –

dJ 0.0336 0.0449(8) 0.0316 0.0 -0.0286 0.0 -0.0265 0.0

dK 1.21 – 1.18 – 0.71 – 0.68 –

a Values taken from [10]

948 Struct Chem (2008) 19:935–948

123