Conformational stability from variable temperature infrared spectra of krypton solutions, ab initio calculations, and vibrational assignment of bromocyclopentane

Journal of Molecular Structure 645 (2003) 89–107 www.elsevier.com/locate/molstruc

Conformational stability from variable temperature infrared spectra of krypton solutions, ab initio calculations, and vibrational assignment of bromocyclopentane H.M. Badawia, W.A. Herreboutb, T.A. Mohamedc,1, B.J. van der Vekenb, J.F. Sullivand, D.T. Durige, C. Zhengf, K.S. Kalasinskyg,2, J.R. Durigf,* a

Department of Chemistry, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Department of Chemistry, Universitair Centrum Antwerpen, 171 Groenenborglaan, Antwerpen 2020, Belgium c Department of Chemistry, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt d Medical University of South Carolina, 11 Meeting Street, Charleston, SC 29425, USA e Departments of Chemistry and Physics, The University of the South, Sewanee, TN 37383, USA f Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA g Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, USA

b

Received 1 August 2002; accepted 9 September 2002

Abstract The infrared spectra from 3500 to 80 cm21 of krypton solutions of bromocyclopentane, c-C5H9Br, at variable temperatures (2 105– 2 150 8C) have been recorded and only the axial and equatorial conformers are present which supports the ab initio calculations that the twisted form is a transition state. From the temperature dependence of five conformer pairs an enthalpy difference of 233 ^ 23 cm21 (2.79 ^ 0.28 kJ/mol) has been obtained with the axial conformer the more stable form. From these data, it is estimated that 75 ^ 2% of the axial form is present at ambient temperature. The Raman spectra (3500 – 40 cm21) of liquid and solid c-C5H9Br and c-C5D9Br have been recorded as well as the infrared spectrum of the normal species in the gaseous and solid states. A complete vibrational assignment is provided for the axial conformer and several of the low frequency fundamentals for the equatorial conformer have been assigned. The conformational stabilities, harmonic force constants, fundamental frequencies, infrared intensities, Raman activities, and depolarization values have been obtained from MP2/6-31G(d) calculations. These quantities have been compared to the experimental values when appropriate. The optimized geometries and conformational stabilities have also been obtained from ab initio MP2/6-311 þ G(d,p) calculations and from density functional theory calculations by the B3YLP method with several different basis sets. The barriers to the twisted conformer is predicted to be too large for pseudorotation. However, the predicted low frequencies for the ring twisting modes indicate many excited states are populated at ambient temperature which could explain the better fit of the radial distribution curve by a pseudorotational model in the electron diffraction study. The adjusted-r0 structural parameters have been obtained for both conformers by combining the ab initio data with the previously reported microwave rotational constants and the values are compared to those reported from the electron * Corresponding author. Tel.: þ 1-816-235-6038; fax: þ1-816-235-2290. E-mail address: [email protected] (J.R. Durig). 1 Present address: Department of Chemistry, Faculty of Science, Box 17551, UAE University, Al-Ain, UAE. 2 Present address: Armed Forces Institute of Pathology, Rockville, MD 20850, USA. 0022-2860/03/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 2 ) 0 0 5 3 9 - 2

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diffraction study. Many of these results are compared to the corresponding quantities of some similar molecules. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Conformational stability; FT-IR spectra; Krypton solutions; Ab initio calculations; Structural parameters; Bromocyclopentane

1. Introduction Recently an electron diffraction investigation of bromocyclopentane, c-C5H9Br, was reported [1] and from these studies it was concluded that the radial distribution curve could be better fit with a pseudorotational model rather than a model with the axial and equatorial conformers. It was further concluded that the barrier to pseudorotation was rather low which suggested the presence of forms intermediate between the more stable axial conformer and the higher energy equatorial form which had been identified from its microwave spectrum [2]. The enthalpy difference between the conformers was reported [1] to be 260 ^ 140 cm21 (3.11 ^ 1.67 kJ/mol) which indicates a population of the axial form in the range of 55 –71% (^ 8%) at ambient temperature. It has been shown that enthalpy determinations for conformers from rare gas solutions may be near those for the vapor if the conformers have similar dipole moments and sizes [2 –7]. Therefore, we initiated an investigation of the conformational stability of bromocyclopentane utilizing variable temperature FT-IR spectra of krypton solutions. Additionally, the infrared and Raman spectra of the c-C5D9Br isotopomer have been recorded and analyzed. To aid in the vibrational assignments and to provide information on the relative barrier to conformational interchange we have carried out a number of ab initio and density functional theory calculations. We have obtained the harmonic force fields, infrared intensities, Raman activities, depolarization ratios, and vibrational frequencies from MP2/6-31G(d) ab initio calculations with full electron correlation by the perturbation method with frozen core [8]. We have also carried out MP2/6-311G(d,p) and MP2/6-311þ þ G(d,p) calculations to obtain the optimized geometries for both stable conformers. Additionally, density functional theory (DFT) calculations have been made by the B3LYP method with the two basis sets 6-31G(d) and 6-311G(d,p) as well as, with diffuse functions to predict the conformational

stabilities. The results of these spectroscopic and theoretical studies are reported herein.

2. Experimental The bromocyclopentane sample was purchased from Aldrich Chemical Co., Milwaukee, WI with a stated purity of 99%. Further purification was carried out with a low-temperature, low-pressure vacuum fractionation column. The c-C5D9Br sample was purchased from Merck and used without further purification. The mid-infrared spectra of gaseous and solid bromocyclopentane were obtained using a Perkin – Elmer model 2000 Fourier transform spectrometer equipped with a nichrome wire source, a Ge/CsI beamsplitter, and a DTGS detector. The spectrum of the gas (Fig. 1(A)) was obtained by using a 10 cm cell fitted with CsI windows. The spectrum of the solid

Fig. 1. Infrared spectra of bromocyclopentane: (A) liquid, (B) solid.

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

(Fig. 1(B)) was obtained by condensing the sample on a CsI substrate held at , 77 K by boiling liquid nitrogen, housed in a vacuum cell fitted with CsI windows. The sample was repeatedly annealed until no further changes were observed in the spectrum. The theoretical resolution used to obtain the spectra of both the gas and the solid was 1.0 cm21. For the c-C5D9Br isotopomer the mid-infrared spectra were recorded on a Digilab model FTS-15B spectrometer. The Raman spectra were recorded on a Cary model 82 spectrophotometer equipped with a SpectraPhysics model 171 Ar ion laser operating on the ˚ line. The Raman spectra of the liquids (Fig. 2) 5145 A c-C5H9Br and the d9-isotopomer (Fig. 3) were obtained by using a sealed glass capillary with a bulb on the end [9] and the Raman spectra of the solids (Fig. 4) were obtained by condensing the samples onto a blackened brass block that is fixed at

Fig. 2. Comparison of experimental and calculated Raman spectra of bromocyclopentane: (A) observed Raman spectrum of bromocyclopentane in liquid; (B) simulated Raman spectrum of a mixture of axial and equatorial conformers (DH ¼ 233cm21); (C) simulated Raman spectrum of the equatorial conformer; (D) simulated Raman spectrum of the axial conformer.

91

Fig. 3. Raman spectrum of liquid bromocyclopentane-d9.

1.58 from the normal to the incident radiation and cooled by boiling liquid nitrogen. The far infrared spectrum of the gas was recorded with the sample contained in a 1 m cell at a resolution of 0.1 cm21 with a Nicolet model 200 SXV spectrometer. This spectrometer is equipped with a vacuum bench, a 6.25 or 25 mm Mylar beamsplitter, a Globar source and a liquid helium cooled germanium barometer. Interferograms were recorded 256 times, averaged, and transformed with a boxcar truncation function for both sample and reference cells. The far infrared spectra of the amorphous and crystalline solids (Fig. 5) were obtained on the Digilab model 15B by utilizing 6.25 mm Mylar beamsplitter and DTGS detector. The samples were contained in a cryostat cell with polyethylene windows and the samples were deposited on a silicon substrate held at , 77 K by boiling liquid nitrogen and annealed until no further spectral changes were observed.

Fig. 4. Raman spectra of solid bromocyclopentane: (A) d0isotopomer, (B) d9-isotopomer.

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Fig. 5. Far infrared spectrum of bromocyclopentane: (A) amorphous, (B) annealed phase.

The mid-infrared spectra of the sample dissolved in the liquefied krypton as a function of temperature (Fig. 6(A)) were recorded on a Bruker model IFS-66 Fourier transform spectrometer equipped with a globar source, a Ge/KBr beamsplitter, and a DTGS detector. The temperature studies ranged from 2 110 to 2 150 8C and were performed in a specially designed cryostat cell consisting of a 4 cm path length copper cell with wedged silicon windows sealed to the cell with indium gaskets. The complete system is attached to a pressure manifold to allow for the filling and evacuation of the cell. The cell is cooled by boiling liquid nitrogen and the temperature is monitored by two Pt thermoresistors. Once the cell is cooled to a designated temperature, a small amount of sample is condensed into the cell. The system is then pressurized with the rare gas, which immediately starts to condense, allowing the compound to dissolve. For each temperature investigated, 100 interferograms were recorded at a 1.0 cm21 resolution, averaged, and transformed with a boxcar truncation function. A similar cell with a seven cm path length was used for the far infrared studies. The far infrared spectra of the krypton solutions (Fig. 7) were recorded on a Bruker model IFS-66V Fourier transform spectrometer, equipped with a Globar source, 6.0 mm Mylar beamsplitter, and a liquid helium cooled Si bolometer. The interferograms for these studies were recorded at a resolution

Fig. 6. Comparison of experimental and calculated infrared spectra of bromocyclopentane: (A) observed infrared spectrum of bromocyclopentane in liquid krypton; (B) simulated infrared spectrum of a mixture of axial and equatorial conformers (DH ¼ 233 cm21); (C) simulated infrared spectrum of the equatorial conformer; (D) simulated infrared spectrum of the axial conformer.

of 0.5 cm21 and were averaged over 250 scans, and transformed by a Blackmann – Harres apodization function. The observed fundamentals for the light compound are listed in Tables 1 and 2 for the axial and equatorial conformers, respectively. The observed frequencies

Fig. 7. Far infrared spectrum (50– 350 cm21) of bromocyclopentane in liquid krypton.

Table 1 Observed and calculated wavenumbers (cm21) and potential energy distributions for axial bromocyclopentane Sym. Vib. No. Description

IR int.c Raman Observed Ab initioa Fixed scaledb act.d IRgas IRKr

dp Ratiod PEDe Rliq

IRsolid

g-CH2 antisymmetric stretch a-CH stretch b-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation b-CH2 wag b-CH2 twist a-CH bend (in plane) g-CH2 wag g-CH2 twist Ring deformation b-CH2 rock Ring deformation Ring breathing g-CH2 rock Ring deformation C –Br stretch Ring puckering C –Br bend (in plane)

3198 3188 3182 3137 3099 1579 1549 1395 1368 1295 1266 1175 1098 993 959 924 829 726 550 323 150

3000 2991 2985 2943 2907 1498 1470 1323 1298 1229 1201 1115 1042 942 910 877 786 689 522 323 150

35.9 9.7 0.9 28.5 28.1 3.8 6.1 1.7 11.5 43.8 1.0 0.1 1.6 2.9 6.2 0.4 1.8 10.0 10.9 1.4 0.5

52.3 103.9 102.5 134.3 171.0 8.1 7.1 0.6 7.3 7.3 13.1 4.9 6.2 1.6 5.2 14.0 0.6 4.8 12.0 3.2 0.4

3000 2985 2958 2918 2883 1472 1448 1321 1288 1227 1207 1133 1038 945 910 884 790 690 528 310 153

2994 2976 2957 2918 2879 1451 1445 1322 1290 1222 1207 1135 1035 942 908 884 792 691 524 310 153

2994 2986 2969 2973 2948 2958 2916 2912 2874 2869 1473 1456 1449 1436f 1315 1326 1282 1287 1219 1215 1209 1204 1066 1134 1028 1038 935 944 903 913 886 885 – 795 – 687 515 514 305 310 – 153

0.74 0.13 0.66 0.06 0.20 0.58 0.61 0.53 0.71 0.54 0.72 0.71 0.73 0.62 0.55 0.07 0.51 0.34 0.23 0.25 0.66

82S1, 15S3 91S2 62S3, 16S1, 14S5 99S4 80S5, 18S3 87S6, 13S7 86S7, 13S6 57S8, 26S11 29S9, 30S11, 16S8, 14S12 52S10, 15S12, 14S14 25S11, 25S9, 22S12 24S12, 26S10, 24S9, 12S21 38S13, 28S15, 10S11 46S14, 20S15, 18S12 17S15, 36S16, 25S13 59S16, 16S13, 13S15 45S17, 34S18 27S18, 36S17, 15S21 62S19, 12S18, 10S14, 10S20 50S20, 26S19, 13S21 60S21, 28S20

A00

n22 n23 n24 n25 n26 n27 n28 n29 n30 n31 n32 n33 n34 n35 n36 n37

b-CH2 antisymmetric stretch g-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation g-CH2 wag b-CH2 wag a-CH bend (out-of-plane) g-CH2 twist b-CH2 twist Ring deformation g-CH2 rock Ring deformation b-CH2 rock Ring deformation

3187 3175 3129 3093 1553 1534 1394 1342 1334 1275 1227 1115 1047 939 846 643

2990 2978 2935 2901 1473 1455 1322 1273 1266 1210 1164 1058 993 891 803 610

7.1 5.5 17.3 7.7 4.8 4.0 1.8 0.1 0.9 0.5 1.6 0.6 0.3 3.3 0.0 0.3

62.8 9.3 30.3 14.0 7.1 20.8 0.6 0.1 5.5 6.4 4.3 7.5 1.7 0.0 0.4 1.6

2976 2958 – 2855 1472 1437 1321 ,1280 ,1270 1198 1175 1069 – ,890 796 613

2971 2957 2904 2853 1451 1436 1319 1284 1270 – 1172 1065 1001 893 796 –

2969 2967 2948 2948 2890 2890 2849 2833 1449 1441 1433 1429 1315 1316 – 1284 – 1268 1209 1198 1178 1173 1066 1066 1003 1006f 886 885 808 803 – 623

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

62S22, 25S23, 12S25 74S23, 18S25 99S24 80S25, 20S22 89S26, 10S27 89S27, 10S26 50S28, 18S30, 16S29 55S29, 29S31 31S30, 40S31, 12S28 44S31, 17S84, 10S32, 10S80 45S32, 16S33 22S33, 17S32, 16S36, 16S30, 11S29, 11S34 28S34, 25S33, 12S29, 11S36 71S35, 10S30 46S36, 19S34, 15S37 70S37, 13S36 (continued on next page)

A00

93

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 n18 n19 n20 n21

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

A0

94

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

for the fundamentals of the axial conformer for the d9isotopomer are listed in Table 3.

f

e

c

d

MP2/6-31G(d) predicted values. MP2/6-31G(d) fixed scaled frequencies with factors of 0.88 for CH stretches, 0.90 for CH bends and heavy atom stretches, and 1.0 for all other modes. Infrared intensities in km/mol from MP2/6-31G(d) calculations. ˚ 4/amu and depolarization ratios from MP2/6-31G(d) calculations. Raman activities in A From the MP2/6-31G(d) calculations and contributions of less than 10% are omitted. From Raman spectrum of the solid. a

b

283 132 289 – 285 120 289 115 0.8 0.1 0.2 0.1 294 96 294 96 C –Br bend (out-of-plane) Ring twisting

n38 n39

Sym. Vib. No. Description

Table 1 (continued)

Ab initioa Fixed IR int.c Raman Observed scaledb act.d IRgas IRKr

Rliq

IRsolid

0.75 0.75

dp Ratiod PEDe

96S38 93S39

3. Ab initio calculations The LCAO-MO-SCF restricted Hartee – Fock calculations were performed with the GAUSSIAN -98 program [10] using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all the geometric parameters using the gradient method of Pulay [11]. Calculations were also carried out with electron correlation with frozen core by the perturbation method [8] to second order up to the 6311þ þ G(d,p) basis set. DFT calculations utilizing the B3LYP method were also carried out up to the 6311G(2d,2p) basis set. The results of these calculations are listed in Table 4 and there are significant differences in the results. For example the lowest energy difference predicted from the ab initio MP2 calculations is 261 cm21 from the 6-311G(d,p) basis set whereas the B3LYP/6-311þ þ G(d,p) calculations predict this difference to be only 115 cm21. Also the twisted transition state is predicted to be at a significantly lower energy in the 500 cm21 range whereas this energy difference is in the , 900 cm21 range from the MP2 calculations. In order to obtain a complete description of the molecular motion involved in the normal modes, the force field in Cartesian coordinates was calculated by the GAUSSIAN -98 program with MP2/6-31G(d) basis set. The internal coordinates are listed in Table 5 and they were used to form the symmetry coordinates listed in Table 6. The B matrix was used to convert the ab initio force field in Cartesian coordinates to a force field in internal coordinates [12]. The frequencies were obtained from the MP2/6-31G(d) calculations, utilizing a set of scaling factors of 0.88 for the CH stretches, 0.9 for the CH bends and heavy atom stretches and 1.0 for all other coordinates with the geometric average for the off diagonal terms. The potential energy distributions (PED) expressed in terms of the symmetry coordinates are listed in Tables 1– 3. The predicted fixed scaled frequencies, infrared intensities, Raman scattering activities and depolarization ratios obtained from the ab initio MP2/631G(d) calculations are also given in Tables 1– 3, for

Table 2 Observed and calculated wavenumbers (cm21) and potential energy distributions for equatorial bromocyclopentane Sym.

Vib. no.

Description

Ab initioa

Fixed scaledb

IR int. c

Raman act.d

IRgas A0

A00

g-CH2 antisymmetric stretch a-CH stretch b-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation b-CH2 wag b-CH2 twist a-CH bend (in-plane) g-CH2 wag g-CH2 twist Ring deformation b-CH2 rock Ring deformation Ring breathing g-CH2 rock Ring deformation C–Br stretch Ring puckering C–Br bend (in-plane)

3181 3154 3196 3130 3122 1581 1559 1392 1365 1305 1266 1188 1091 962 920 1008 745 819 302 461 162

2984 2959 2998 2936 2929 1500 1479 1321 1295 1238 1201 1127 1035 913 873 956 707 777 302 437 162

3.8 3.9 42.6 32.6 11.6 0.8 7.3 9.6 1.8 15.3 15.5 6.5 1.8 1.7 1.7 2.1 15.3 19.6 3.2 0.1 0.3

n22 n23 n24 n25 n26 n27 n28 n29 n30 n31 n32 n33 n34 n35 n36 n37

b-CH2 antisymmetric stretch g-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation g-CH2 wag b-CH2 wag a-CH bend (out-of-plane) g-CH2 twist b-CH2 twist Ring deformation g-CH2 rock Ring deformation b-CH2 rock Ring deformation

3186 3167 3121 3120 1556 1544 1372 1289 1392 1325 1229 1155 1004 989 847 631

2989 2971 2928 2927 1476 1465 1302 1223 1321 1257 1166 1096 952 938 804 599

11.7 6.0 29.9 0.03 3.3 0.8 0.5 1.8 0.3 0.002 0.8 0.0002 1.0 2.9 0.01 1.1

113.6 51.9 48.7 195.9 82.4 9.7 6.2 5.9 9.7 2.6 5.9 10.5 9.6 4.7 10.7 1.7 9.0 8.3 7.0 1.6 0.3 64.2 16.6 11.8 25.2 5.3 21.0 0.7 9.0 4.3 5.5 2.3 1.5 0.8 1.6 0.2 1.3

PEDe

722 756 – – –

–

Rliq

1027 916 – – 724 794 292 – –

0.43 0.63 0.63 0.04 0.16 0.64 0.74 0.47 0.74 0.54 0.55 0.71 0.71 0.66 0.07 0.07 0.23 0.21 0.27 0.40 0.41

56S1, 35S3 88S2 51S3, 43S1 92S4 88S5 72S6, 27S7 72S7, 28S6 60S8, 21S11 36S9, 37S11, 11S12 20S10, 26S12, 16S14 28S11, 38S9, 14S15 28S12, 26S10, 17S8, 42S13, 24S15, 18S11 37S14, 36S15 14S15, 35S16, 24S13 45S16, 22S12, 10S14 57S17, 15S19, 10S18 31S18, 28S17, 19S19 55S19, 16S21 25S20, 30S18, 18S14, 16S21 35S21, 59S20

716 742 – 452 –

580

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

84S22, 13S23 83S23, 11S22 60S24, 33S25 61S25, 37S24 68S26, 31S27 68S27, 31S26 63S28, 12S29 37S29, 48S37 59S30, 13S32 34S31, 33S29, 18S29, 11S30 46S32, 24S34, 11S36 49S33, 19S35, 13S37, 23S34, 29S32, 18S30, 18S36 56S35, 17S33 46S36, 23S34, 12S37 70S37, 13S36 (continued on next page)

584

IRkr

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

A00

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 n18 n19 n20 n21

dp Ratiod

Observed

95

e

c

d

a

b

PEDe

229 60 231 – C–Br bend (out-of-plane) Ring twisting

n38 n39

234 46

234 46

0.4 0.02

1.1 0.01

228 –

IRkr IRgas

Rliq

0.75 0.75

dp Ratiod Observed Raman act.d IR int. c Fixed scaledb Ab initioa Description Vib. no. Sym.

Table 2 (continued)

MP2/6-31G(d) predicted values. MP2/6-31G(d) fixed scaled frequencies with factors of 0.88 for CH stretches, 0.90 for CH bends and heavy atom stretches, and 1.0 for all other modes. Infrared intensities in km/mol from MP2/6-31G(d) calculations. ˚ 4/amu from MP2/6-31G(d) calculations. Raman activities in A From the MP2/6-31G(d) calculations and contributions of less than 10% are omitted.

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

97S38 94S39

96

the axial and equatorial conformers of the light molecule and for the axial conformer for the d-isotopomer, respectively. To aid in the vibrational assignment the theoretical infrared and Raman spectra for the normal species were calculated utilizing the predicted intensities (Tables 1 and 2) from the MP2/6-31G(d) ab initio calculations. The infrared intensities were calculated based on the dipole moment derivatives with respect to the Cartesian coordinates. The derivatives were taken from the ab initio calculations MP2/6-31G(d) transformed to normal coordinates by: !
 X ›m u ›mu Lij ¼ ›Q i › Xj j where Qi is the ith normal coordinate, Xj is the jth Cartesian displacement coordinates, and Lij is the transformation matrix between the Cartesian displacement coordinates and normal coordinates. The predicted infrared spectra of the axial and equatorial conformers are shown in Fig. 6(D) and (C), respectively, with the mixture of the two conformers shown in Fig. 6(B). The calculated spectrum is in reasonably good agreement with the experimental spectrum of the sample dissolved in krypton (Fig. 6(A)) and demonstrates the utility of the calculated infrared intensities for analytical purposes. The dominance of the bands (Fig. 6) due to the axial conformer in the spectrum of the krypton solution in the 500 –1000 cm21 region is clearly indicated, which supports the conclusion that the axial rotamer is the more stable form. The theoretical Raman (Fig. 2) spectra have been calculated using the scaled wavenumbers and Raman scattering activities determined from the MP2/631G(d) ab initio calculations. The Raman scattering cross sections, ›sj =›V; which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted wavenumber for each normal mode [13 – 16]. To obtain the polarized Raman scattering cross sections, the polarizabilities are incorporated into Sj by Sj ½ð1 2 rj Þ= ð1 þ rj Þ; where rj is the depolarization ratio of the jth normal mode. The Raman scattering cross sections and calculated frequencies were used, together with a Lorentzian function, to obtain the calculated spectrum. The predicted Raman spectra of the axial and

Table 3 Observed and calculated wavenumbers (cm21) and potential energy distributions for axial bromocyclopentane-d9 Sym.

A0

A00

Description

Ab initioa

Fixed scaledb

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 n18 n19 n20 n21

g-CD2 antisymmetric stretch a-CD stretch b-CD2 antisymmetric stretch g-CD2 symmetric stretch b-CD2 symmetric stretch g-CD2 deformation b-CD2 deformation b-CD2 wag b-CD2 twist a-CD bend (in-plane) g-CD2 wag g-CD2 twist Ring deformation b-CD2 rock Ring deformation Ring breathing g-CD2 rock Ring deformation C– Br stretch Ring puckering C– Br bend (in-plane)

2371 2350 2361 2287 2260 1183 1124 1221 1069 870 849 995 1193 757 793 830 578 720 481 277 137

2224 2206 2217 2148 2122 1122 1066 1158 1014 825 805 948 1131 718 752 799 548 683 456 277 137

n22 n23 n24 n25 n26 n27 n28 n29 n30 n31 n32 n33 n34 n35 n36 n37

b-CD2 antisymmetric stretch g-CD2 antisymmetric stretch g-CD2 symmetric stretch b-CD2 symmetric stretch g-CD2 deformation b-CD2 deformation g-CD2 wag b-CD2 wag a-CD bend (out-of-plane) g-CD2 twist b-CD2 twist Ring deformation g-CD2 rock Ring deformation b-CD2 rock Ring deformation

2357 2364 2278 2256 1132 1112 1220 802 1062 954 840 1228 1010 749 544 710

2212 2218 2139 2118 1077 1058 1157 760 1008 907 803 1150 962 710 525 689

IR intc

19.3 5.8 0.3 12.1 12.6 4.3 3.6 0.7 54.7 0.3 0.1 2.9 2.8 1.0 4.3 0.1 9.2 0.8 4.6 0.8 0.5 3.4 0.2 9.6 4.2 0.7 2.4 0.7 0.5 0.2 0.6 0.3 2.2 0.9 1.5 0.2 0.04

Raman act.d

28.4 50.7 51.7 76.7 73.8 0.4 1.8 0.1 6.4 14.9 6.0 7.8 0.7 1.5 1.7 7.6 5.7 1.4 8.2 1.9 0.3 3.4 35.2 13.7 7.2 4.7 5.2 0.1 3.8 0.5 5.4 6.2 0.3 0.6 0.3 0.8 0.6

Observed

dp Ratiod

PEDe

IRsolid

2232 2332 2166 2149 2111 1116

2232 2228 2175 2145 2110 1121 1062 1155 1004 836 816 949 1148 728 759 797 541 690 454 266 138

0.71 0.30 0.56 0.05 0.19 0.44 0.74 0.74 0.50 0.26 0.74 0.72 0.63 0.04 0.74 0.17 0.30 0.46 0.23 0.26 0.70

91S1 94S2 79S3 96S4 89S5 49S6, 12S7, 10S15 48S7, 28S6, 11S11 33S8, 34S16, 11S13 15S9, 20S14, 21S21, 14S10 19S10, 42S15, 18S9 60S11, 21S13 38S12, 27S9 27S13, 26S7, 13S11, 12S16 23S14, 20S9, 18S8, 12S18 22S15, 19S8, 18S18, 15S14, 14S12 35S16, 35S10, 115S21 32S17, 18S19 26S18, 11S10, 65S18, 56S19, 19S14, 11S17 38S20, 19S19, 16S21, 12S14 36S21, 46S20

2228 2209 2157 2122 1062 1049 1162 774 1021 913 816 1162 972 690 531 690

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

71S22, 21S24 77S23, 21S22 98S24 90S25 84S26 79S27, 13S28 17S28, 33S33, 17S35, 11S29 39S29, 19S33, 17S28 21S30, 38S29, 36S28 79S31 55S32, 15S30 30S33, 29S35, 16S30 52S34, 17S32, 14S36 40S35, 31S30, 15S32 36S36,28S37, 18S34 40S37, 26S36 (continued on next page)

1153 1000 836 816 948

798 682 449 270 138

1044

97

Rliq

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A00

Vib. no.

e

c

d

0.7 0.1 0.3 0.1 256 77 256 77 C– Br bend (out-of-plane) Ring twisting

n38 n39

MP2/6-31G(d) predicted values. MP2/6-31G(d) fixed scaled frequencies with factors of 0.88 for CH stretches, 0.90 for CH bends and heavy atom stretches, and 1.0 for all other modes. Infrared intensities in km/mol from MP2/6-31G(d) calculations. ˚ 4/amu and depolarization ratios from MP2/6-31G(d) calculations. Raman activities in A From the MP2/6-31G(d) calculations and contributions of less than 10% are omitted. a

b

86S38 92S39 0.75 0.75 251 65

IRsolid Rliq

Description Vib. no. Sym.

Table 3 (continued)

Ab initioa

Fixed scaledb

IR intc

Raman act.d

Observed

PEDe

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

dp Ratiod

98

equatorial conformers are shown in Fig. 2(D) and (C), respectively. In Fig. 2(B), the mixture of the two conformers with the determined DH of 233 cm21 (Section 5), with the axial conformer the more stable rotamer, is shown. This spectrum should be compared to the experimental Raman spectrum (Fig. 2(A)) of the liquid. The calculated spectrum has some differences from the experimental spectrum, especially in the relative intensities of the bands in the low frequency region. Nevertheless, it provides support for making the vibrational assignments.

4. Vibrational assignment In order to determine the conformational stability it is necessary to assign the spectra to the individual conformers. To aid in distinguishing the vibrational modes the band contours were calculated for the two conformers by utilizing the reported rotational constants from the microwave study [2]. The contours for the axial conformer are shown in Fig. 8 and those for the equatorial form are nearly indistinguishable. Since both conformers are neat symmetric tops the type A and C bands are very similar with very strong Q-branches which will be the contours for the A0 modes. The A00 modes should be distinguishable by their type-B contours. Both conformers have low frequency ring twisting modes with many excited states populated at ambient temperature which may obscure the minimum for the type-B bands. Thus most of the bands appeared with non-descript contours except a few with well defined Q-branches (A0 fundamentals). By utilizing the predictions from the scaled ab initio calculations along with band contours and depolarization values, it is possible to give a reasonable confident assignment for the fundamentals for the axial conformer since this is the rotamer in the solid state. The only questionable assignments are for one of the carbon-hydrogen stretches and one of the CH2 deformations. The lowest assigned CH2 stretch (n25 ) at 2855 cm21 could be part of a Fermi doublet with the band at 2879 cm21 where this would then be the lowest frequency for the carbon – hydrogen stretches. The difference then between the predicted and observed frequency would be more in line with the differences found for the other carbon – hydrogen

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

99

Table 4 Ab initio and DFT energies (Hartree) and energy differences between conformers (cm21) for bromocyclopentane Energy axial

MP2/6-31G(d) MP2/6-31 G(d,p) MP2/6-31 þ G(d,p) MP2/6-311G(d,p) MP2/6-311þ þG(d,p) MP2/6-311(2d,2p) B3LYP/6-31G(d) B3LYP/6-31G(d,p) B3LYP/6-31 þ G(d,p) B3LYP/6-311G(d,p) B3LYP/6-311þ þG(d,p) B3LYP/6-311G(2d,2p) a b

0.245043 0.317490 0.344016 2.873151 2.878064 2.924455 2.666755 2.679532 2.704288 5.158717 5.160194 5.162624

Energy differencesa, (DE ) Equatorial

Twist(TS)b

Planar(TS)b

589 574 329 261 298 322 289 298 174 122 115 124

1062 1044 828 907 904 936 692 675 548 543 525 519

2977 2953 2803 2774 2771 2924 2119 2111 2053 1887 1862 1813

Energy of axial conformer is given as 2(E þ 2765) Hartree. Difference is relative to axial form which is the lowest energy conformer. Transition state and not stable conformer.

Table 5 Internal coordinate definitions and force constants from MP2/6-31G(d) calculations for bromocyclopentane Coordinate

C1 –C2 stretch C1 –C3 stretch C2 –C4 stretch C3 –C5 stretch C4-C5 stretch C1 –H6 stretch C2 –H7 stretch C2 –H8 stretch C3 –H9 stretch C3 –H10 stretch C4 –H11 stretch C4 –H12 stretch C5 –H13 stretch C5 –H14 stretch C1 –Br15 stretch C2C1C3 bend C1C2C4 bend C1C3C5 bend C2C4C5 bend C3C5C4 bend C2C1Br15 bend C3C1Br15 bend Br15C1H6 bend C2C1H6 bend C3C1H6 bend a

Definition

V1 V2 Y1 Y2 Z Q D1 T1 D2 T2 P1 S1 P2 S2 R a b1 b2 g1 g2 p1 p2 u d1 d2

˚. Force constants in mdyn/A

Force constantsa Axial

Equatorial

3.511 3.511 3.362 3.362 3.266 4.901 4.881 4.684 4.881 4.684 4.848 4.824 4.848 4.824 2.637 0.661 0.852 0.852 0.815 0.815 1.002 1.002 0.541 0.564 0.564

3.531 3.531 3.329 3.329 3.228 4.814 4.782 4.855 4.782 4.855 4.828 4.793 4.828 4.793 2.761 0.662 0.800 0.800 0.802 0.802 0.794 0.794 0.528 0.573 0.573

Coordinate

C1C2H7 bend C1C3H9 bend C4C2H7 bend C5C3H9 bend C4C2H8 bend C5C3H10 bend C1C2H8 bend C1C3H10 bend H7C2H8 bend H9C3H10 bend C2C4H11 bend C3C5H13 bend C5C4H11 bend C4C5H13 bend C5C4H12 bend C4C5H14 bend C2C4H12 bend C3C5H14 bend H11C4H12 bend H13C5H14 bend C1C3C5C4 torsion C1C2C4C5 torsion

Definition

f1 f2 v1 v2 m1 m2 r1 r2 k1 k2 S1 S2 D1 D2 H1 H2 L1 L2 G1 G2 t2 t2

Force constantsa Axial

Equatorial

0.538 0.538 0.532 0.532 0.557 0.557 0.562 0.562 0.457 0.457 0.550 0.550 0.578 0.578 0.535 0.535 0.544 0.544 0.471 0.471 0.405 0.405

0.583 0.583 0.552 0.552 0.528 0.528 0.533 0.533 0.451 0.451 0.536 0.536 0.535 0.535 0.573 0.573 0.545 0.545 0.473 0.473 0.281 0.281

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Table 6 Symmetry coordinates for bromocyclopentane Species

Description

Symmetry coordinatesa

A0

g-CH2 antisymmetric stretch a-CH2 stretch b-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation b-CH2 wag b-CH2 twist a-CH bend (in plane) g-CH2 wag g-CH2 twist Ring deformation b-CH2 rock Ring breathing Ring deformation g-CH2 rock Ring deformation C –Br stretch Ring puckering C –Br bend (in plane)

S1 ¼ P1 2 S1 þ P2 2 S2 S2 ¼ Q S3 ¼ D1 2 T1 þ D2 þ T2 S4 ¼ P1 þ S1 þ P2 þ S2 S5 ¼ D1 þ T1 þ D2 2 T2 S6 ¼ 2S1 2 L1 2 D1 2 H1 þ 4G1 2 S2 2 L2 2 D2 2 H2 þ 4G2 S7 ¼ 2f1 2 r1 2 v1 2 m1 þ 4k1 2 f2 2 r2 2 v2 2 m2 þ 4k2 S8 ¼ f1 þ r1 2 v1 2 m1 þ f2 þ r2 2 v2 2 m2 S9 ¼ f1 2 r1 2 v1 þ m1 þ f2 2 r2 2 v2 þ m2 S10 ¼ 2d1 2 p1 2 d2 2 p2 þ 4u S11 ¼ S1 þ L1 2 D1 2 H1 þ S2 þ L2 2 D2 2 H2 S12 ¼ S1 2 L1 2 D1 þ H1 þ S2 2 L2 2 D2 þ H2 S13 ¼ 2V1 2 V2 2 Y1 2 Y2 þ 4Z S14 ¼ f1 2 r1 þ v1 2 m1 þ f2 2 r2 þ v2 2 m2 S15 ¼ V1 þ V2 þ Y1 þ Y2 þ Z S16 ¼ V1 þ V2 2 Y1 2 Y2 S17 ¼ S1 2 L1 þ D1 2 H1 þ S2 2 L2 þ D2 2 H2 S18 ¼ 3a 2 2:5b1 2 2:5b2 þ g1 þ g2 S19 ¼ R S20 ¼ t1 2 t2 S21 ¼ 2d1 þ p1 2 d2 þ p2

A00

b-CH2 antisymmetric stretch g-CH2 antisymmetric stretch g-CH2 symmetric stretch b-CH2 symmetric stretch g-CH2 deformation b-CH2 deformation g-CH2 wag b-CH2 wag a-CH bend (out of plane) g-CH2 twist b-CH2 twist Ring deformation g-CH2 rock Ring deformation b-CH2 rock Ring deformation C –Br bend (out of plane) Ring twisting

S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39

A00

a

¼ D1 2 T1 2 D2 þ T2 ¼ 2P1 þ S1 þ P2 2 S2 ¼ 2P1 2 S1 þ P2 þ S2 ¼ D1 þ T1 2 D2 2 T2 ¼ S1 þ L1 þ D1 þ ð1 24G1 2 S2 2 L2 2 D2 2 H2 þ 4G2 ¼ f1 þ r1 þ v1 þ m1 2 4k1 2 f2 2 r2 2 v2 2 m2 þ 4k2 ¼ 2S1 2 L1 þ D1 þ ð1 þS2 þ L2 2 D2 2 H2 ¼ 2f1 2 r1 þ v1 þ m1 þ f2 þ r2 2 v2 2 m2 ¼ d1 2 d2 ¼ 2S1 þ L1 þ D1 2 ð1 þS2 2 L2 2 D2 þ H2 ¼ 2f1 þ r1 þ v1 2 m1 þ f2 2 r2 2 v2 þ m2 ¼ 2V1 þ V2 þ Y1 2 Y2 ¼ 2S1 þ L1 2 D1 þ ð1 þS2 2 L2 þ D2 2 H2 ¼ 2V1 þ V2 2 Y1 þ Y2 ¼ 2f1 þ r1 2 v1 þ m1 þ f2 2 r2 þ v2 2 m2 ¼ 2b1 þ b2 þ g1 2 g2 ¼ p1 2 p2 ¼ t1 þ t2

Not normalized.

stretching modes. In the CH2 deformation region there are only three pronounced bands in the infrared spectrum for the four fundamentals expected in this spectral region. Therefore, the Raman line at 1436 cm21 which is indicated with a star in Table 1 is assigned as the fourth CH2 deformation. The Raman band at 1006 cm21 was used for n34 but the predicted

infrared intensity of this fundamental is only 0.3 km/ mol so the fact that it was not observed in the infrared spectrum of the solid is not too surprising. Six of the fundamentals for the axial conformer were not observed in the Raman spectrum of the liquid but four of these had very small predicted activities. The spectra from the krypton solutions with the sharp,

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101

Fig. 9. Temperature dependent infrared spectrum (1000 – 1080 cm21) of bromocyclopentane in liquid krypton.

452, 584, 724, 743 and 1027 cm21. These bands do not appear in the infrared spectrum of a well annealed solid and they are predicted as fundamentals for the equatorial conformer within a few wavenumbers. Therefore they have been assigned as fundamentals for this rotamer and they are listed in Table 2. Although several of the fundamentals have been assigned for the equatorial conformer there is a very limited number which can be used for the enthalpy determination.

5. Conformational stability

Fig. 8. Predicted pure A-, B- and C-type infrared contours for the axial conformer of bromocyclopentane.

narrow bands made it possible to identify several of the modes which were quite close to each other in frequency, as well as, to predict the band centers of several of the fundamentals in the gas phase. With the assignment of the fundamentals for the axial conformer there are a significant number of bands in the infrared spectrum of the krypton with corresponding bands in the spectrum of the gas which have not been assigned particularly in the low frequency region. The obvious ones are at 229, 292,

With confident assignments for several of the fundamentals of the equatorial conformer, it was expected to be possible to obtain the enthalpy between the two forms by variable temperature infrared studies of rare gas solutions. Since most of the fundamentals for the equatorial conformer were in close proximity of the fundamentals of the axial conformer, krypton was chosen rather than xenon since the infrared bands would be narrower which makes there intensity more easily measured. However, for such a large molecule as bromocyclopentane the solubility in krypton is expected to be relatively low. Initially the 1027 cm21 equatorial band (Fig. 9) was chosen along with the

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Table 7 Temperature and intensity ratio from the temperature study of bromocyclopentane dissolved in liquid krypton T (8C)

1000/T (K)

I310a/292e

I285a/292e

I310a/301e

I1035a/1027e

I1065a/1027e

2100 2105 2110 2115 2120 2125 2130 2135 DHa (cm21)

5.7753 5.9471 6.1293 6.3231 6.5296 6.7499 6.9857 7.2385

1.2537 1.3361 1.4491 1.5818 1.7245 1.8910 2.0946 2.3129 295 ^ 2

0.29222 0.30446 0.31463 0.33380 0.35274 0.37315 0.39419 0.42437 178 ^ 3

7.0396 7.3649 8.1170 8.7081 9.1798 9.4690 10.490 10.764 207 ^ 14

– 3.8679 4.0984 4.3333 4.5517 – 5.5476 5.7222 222 ^ 13

– – 1.4754 1.6167 1.7414 1.7368 2.2381 2.3333 294 ^ 42

a

Average enthalpy difference between the two conformers is 233 ^ 11 cm21 with the axial form more stable.

two axial bands nearly at 1035 and 1065 cm21. In order to obtain an estimate of the enthalpy difference, infrared spectral data at seven different temperatures were obtained (Table 7) from this pair of bands over the temperature range from 2 110 to 2 135 8C. Attempts to obtain data at 2 140 8C and above failed because the spectrum indicated that solid was accumulating on the cell windows. The enthalpy difference was calculated by the van’t Hoff equation, 2ln k ¼ ðDH=RTÞ 2 DS=R; with the assumption that the value of DH is constant within the temperature range utilized and Ia/Ie is substituted for K. The values of DH for the I1035/I1027 and I1065/I1027 pairs are 222 ^ 13 and 294 ^ 42 cm21, respectively, from the slopes of the lines with the axial conformer the more stable rotamer. The large differences in these two values is probably due to underlying bands of the combination modes. We also used the two low frequency axial bending modes at 310 and 285 cm21 with the 292 cm21 equatorial mode (Fig. 10) to obtain the enthalpy difference. However, there is a clear overtone band at 301 cm21 which makes it difficult to obtain a good measurement of the peak area of the 310 cm21 band. Again it was not possible to obtain spectral data below 2 135 8C since the sample began to condense on the cell windows. The far infrared cell was constructed so it could withstand a much higher pressure than the mid-infrared cell so data was collected to 2 100 8C so that eight data points could be obtained. The observed changes in these four bands are shown in Fig. 11 and the data obtained from utilizing all four of them is listed in Table 7 where the peak intensities were used

rather than the band areas. Again the enthalpy differences were obtained by the van’t Hoff equation and the values ranged from a high value of 295 ^ 2 cm21 to a low value of 178 ^ 3 cm21. It is expected that the most reliable value is the one due to the two most intense and well resolved bands which gives the larger value with a statistical uncertainty of only two wavenumbers which is much lower than the method can justify. Taking all the five values together gives an average value of 233 ^ 11 cm 21 (2.79 ^ 0.13 kJ/mol) with the axial rotamer the more stable form. The statistical uncertainty does not take into account any interfering bands so the errror should be at least 10% which results in a value of the enthalpy of 233 ^ 23 cm21 (2.79 ^ 0.28 kJ/ mol) which is probably the lower limit.

Fig. 10. Far infrared spectrum (260– 340 cm21) of bromocyclopentane in krypton solution with the four bands resolved (2110 8C).

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

Fig. 11. Temperature dependent infrared spectrum (260–340 cm21) of bromocyclopentane in liquid krypton.

6. Discussion Although many of the fundamentals can be described by the major contribution of the dominate symmetry coordinates there are a few modes where such descriptions are not really adequate. This is particularly true for the two CH2 rocks and four of the ring modes of the A0 symmetry block. For example n17 and n18 have similar contribution from the ring deformation and the g-CH2 rock. Also the three ring modes indicated by n13, n15 and n16 all have significant contributions to both the fundamentals at 910 and 884 cm21 although the lower frequency band has 59% contribution from the ring breathing mode. The other ring mode assigned at 1038 cm21 which has

103

38% contribution from the S13 symmetry coordinate has 28% contribution from S15. Similar mixing is also found for the b-CH2 twist, g-CH2 wag, and g-CH2 twist where the maximum contributions from any one symmetry coordinate is only 24– 30%. In the A00 symmetry block the n33 (ring formation) and n34 (g-CH2 rock) have extensive mixing where the maximum contribution to the ring mode is only 22% from S33 and there are five other contributions ranging from 17 to 11% which are carbon hydrogen bending motions, i.e. CH2 rocks, CH2 wag, CH2 twist, and CH bend. For most of the other modes in this symmetry block they are relatively pure with large contributions from one symmetry coordinate. Since the mixing is significantly different for the ring modes and the carbon – deuterium bending modes for the c-C5D9Br isotopomer, it is difficult to describe some of the modes in a consistent way so the expected shift can be attributed to the deuterium substitution for the corresponding CH2 bends. For example the ring modes appear to be at higher frequencies than the corresponding ones in the normal species and some of the bending modes appear to shift more than the predicted amount expected for the substitution of hydrogen by a deuterium atom. However, these differences are mainly due to the differences in the mixing of the symmetry coordinates. The values of the corresponding force constants for the two conformers have significantly different values for many of them, particularly for many of the angle bending constants. However, most of the stretching force constants have values which different by only 1% or less. One of the largest differences is for the CCBr bend which is 20% smaller for the equatorial conformer compared to the similar one for the axial rotamer (Table 5). Also many of the CCH bending force constants have values which differ by about 8% between the conformers, i.e. f1 ; f2 ; D1 ; D2 ; etc. Because of these relatively large differences the order of the carbon –hydrogen bending modes relative to the ring deformations differs between the two conformers (Tables 1 and 2). By utilizing only two scaling factors of 0.88 for the C– H stretches and 0.9 for the C –H bends and heavy atom stretches, and 1.0 for the remaining ones with the predictions of the ab initio MP2/6-31G(d) calculations the differences between the frequencies of the observed fundamentals and the theoretical ones

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are less than 1%. The average error for the A0 block for the axial conformer is 10 cm21 with a significant amount of the error arising from the C –H stretches and the CH2 deformations. The average error for the other thirteen fundamentals is 6 cm21. The average error for the A00 is slightly higher at 12 cm21 but again the major differences are from the predictions for the carbon – hydrogen stretches. Although the ab initio MP2/6-31G(d) calculations predict the fundamental frequencies rather well, the predicted infrared intensities are rather poor compared to what is usually found for monohalohydrocarbons (Fig. 6). The major difference appears in the 900 cm21 region where there is extensive mixing of the CH2 bends with the ring deformations. The mixing and intensities are significantly affected by the scaling factor in this spectral region where there are some major changes from the predicted spectrum from the ab initio calculations with and without the scaling factor of 0.9. Undoubtably the ring deformations is an important factor here. A similar problem does not appear with the prediction of the Raman spectrum (Fig. 2) where the observed spectrum of the liquid is in good agreement with the theoretical one. The experimently determined enthalpy difference of 233 ^ 23 cm21 (2.79 ^ 0.28 kJ/mol) is in reasonable agreement with the ab initio predicted values from the MP2 calculations where the energy differences ranged from a low value of 261 cm21 from the 6-311G(d,p) basis set to maximum value of 329 cm21 with the 6-31 þ G(d,p) basis set. Using diffuse functions on the small basis set decreased the energy difference by more than 200 cm21 whereas with the larger basis set it increases the energy difference by only about 40 cm21. However, the DFT calculations predict in general a much lower energy difference but with only a little difference with diffuse functions. These calculations do not appear to be significantly affected by the larger basis sets. Thus, the ab initio calculations give a better prediction of the energy difference. The planar transition state is approximately 2800 cm21 (33.5 kJ/mol) higher in energy than the axial conformer whereas the twisted transition state is only about 900 cm21 (10.8 kJ/mol) higher than the axial form. Therefore, conformational interchange is expected to go through this twisted state rather than the planar form (Table 4). Since the equatorial form

has a very low value for the frequency of the ring twisting fundamental there will be many excited states of this mode for this conformer at ambient temperature. For this reason it is believed that the pseudorotational model used for analyzing the electron diffraction data [1] cannot be justified. These authors used a dynamic model with nine conformers between the phase angles of 0 and 1808. Since there is such a large predicted difference between the C – Br distance ˚ for the axial conformer and the 1.948 A ˚ of 1.966 A C– Br distance for the equatorial conformer excited vibrational states of the ring twisting mode will have signficantly different C –Br distances. These distances will have a pronounced effect on the calculated ˚ for ‘Br· · ·C4 amplitutes where the r(Br· · ·C4) ¼ 3.4 A ˚ for the the axial form and r(Br· · ·C4) ¼ 4.2 A equatorial conformer. Thus, it is believed that using this part of the radial distribution curve to conclude the presence of forms intermediate between the axial and equatorial conformers is in error because of the differences in the C –Br distances as a result of excited vibrational twisting modes. With the relatively high barrier of the twisting transition state the two conformer model is more appropriate for bromocylopentane. We have found [17] that we can obtain good structural parameters by adjusting the structural parameters obtained from the ab initio calculations to fit rotational constants (computer program A and M, ab initio and Microwave, developed in our laboratory) 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 relative ratio, and bond 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. The microwave spectra of two isotopomers of each conformer have been reported [2] so there are 12 rotational constants for the determination of six heavy atom parameters. Since the MP2/6-311 þ G(d,p) calculations [18] predict r0 C – H distances for ˚ of well known parameters hydrocarbons to 0.002 A obtained from ‘isolated’ C –H stretching frequencies [19] we have kept the carbon – hydrogen parameters the same as those predicted from the MP2/6-311þ G(d,p) calculations. For the axial conformer

H.M. Badawi et al. / Journal of Molecular Structure 645 (2003) 89–107

the calculated A value is too small by 11 MHz whereas the B and C constants are larger by 10 and 11 MHz, respectively, from the MP2/6-311 þ G(d,p) calculations compared to the experimentally determined values (Table 8). For the equatorial conformer the fit of the predicted rotational constants to the experimental ones is even better with values of only 13, 3, and 3 MHz, respectively (Table 8). Therefore, only very minor adjustments need to be made for the parameters of the axial conformer to fit all six of the rotational constants (79Br and 81Br isotopomers) previously reported from the microwave study [2]. For example, by increasing the C – Br distance by ˚ and the angle Br to ring by 0.68 the calculated 0.003 A

105

rotational constants are 4395, 1510, 1430 MHz for the Br, and 4394, 1496, and 1418 MHz for 81Br isotopomer compared to the experimental values of 4395, 1511, 1429, 4392, and 1417 MHz, repectively. This is an excellent fit of the experimental rotational constants and we believe the maximum errors for these structural parameters should not be more than ˚ for the C –H distances, 0.005 A ˚ for the heavy 0.002 A atom parameters and 0.58 for the angles. For the equatorial conformer the adjustment needed is smaller with a slight increase of the C – Br distance ˚ which provides a very satisfactory fit of by 0.001 A the six experimental rotational constants. There are some significant difference in these parameters and 79

Table 8 ˚ and degrees), total dipole moment (Debye), and rotational constants (MHz) of bromocyclopentane Structural parameters (A Parameter

Microwavea Axial

r(C1 –C2yC1 –C3) r(C2 –C4yC3 –C5) r(C4 –C5) r(C1 –Br) r(C1 –H6) r(C2 –H7yC3 – H9) r(C2 –H8yC3 – H10) r(C4 –H11yC5 –H13) r(C4 –H12yC5 –H14) /(C2C1C3) /(C2C4C5yC3C5C4) /(Br-ring) /(H6-ring) /(H6C1Br) /(H7C2C1yH9C3C1) /(H8C2C1yH10C3C1) /(H11C4C2yH13C5C3) /(H12C4C2yH14C5C3) /(H7C2H8yH9C3H10) /(H11C4H12yH13C5H14) t(H7C2C1C4yH9C3C1C5) t(H8C2C1C4yH10C3C1C5) t(H11C4C2C5yH13C5C3C4) t(H12C4C2C5yH14C5C3C4) uc m(t) A B C a b c

Ref. [2]. Ref. [1]. Ring puckering angle.

Equatorial

1.524 1.543 1.558 1.966 1.090 1.092 1.098 1.092 1.093 103.1 105.6 128.0 127.9 104.1 113.6 107.2 110.3 111.2 107.5 106.9

1.523 1.543 1.559 1.948 1.094 1.095 1.092 1.092 1.093 103.5 105.7 127.2 127.1 105.7 107.9 113.2 111.8 110.2 108.4 107.5

40.0

43.1

4396 1511 1429

6442 1176 1040

Electron diffractionb

MP2/6-311 þ G(d,p)

Adjusted ro

Axial

Axial

Equatorial

Axial

1.526 1.543 1.555 1.966 1.091 1.092 1.098 1.093 1.093 102.9 105.6 123.6 131.3 105.1 113.5 107.0 110.2 111.2 108.1 107.4 124.1 116.8 119.1 121.9 40.2 2.584 4385 1521 1441

1.525 1.543 1.559 1.948 1.095 1.096 1.093 1.093 1.094 103.4 105.7 129.9 124.8 105.4 108.6 113.6 110.2 111.4 108.2 107.3 117.1 122.6 121.9 119.2 44.0 2.718 6445 1172 1038

1.527 1.544 1.553 1.974(7) 1.093(7) 1.093(7) 1.093(7) 1.093(7) 1.093(7)

111.9(11) 111.9(11) 111.9(11) 111.9(11) 111.9(11)

Equatorial 1.527 1.546 1.553 1.954(7) 1.093(7) 1.093(7) 1.093(7) 1.093(7) 1.093(7)

111.9(11) 111.9(11) 111.9(11) 111.9(11) 111.9(11)

1.526 1.543 1.555 1.969 1.091 1.092 1.098 1.093 1.093 102.9 105.6 124.2 131.3 105.1 113.5 107.0 110.2 111.2 108.1 107.4 124.1 116.8 119.1 121.9 40.2 4397 1510 1430

Equatorial 1.525 1.543 1.559 1.947 1.095 1.096 1.093 1.093 1.094 103.4 105.7 129.6 124.8 105.4 108.6 113.6 110.2 111.4 108.2 107.3 117.1 122.6 121.9 119.2 44.0 6442 1175 1040

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those published [2] previously, where the C – H distances were permitted to change and the relative value of the angles between the two conformers were also allowed to change. With this greater freedom some of the other distances changed by as much as ˚ and several of the angles changed by 1.18. 0.003 A With these changes the twelve rotational constants were not fit nearly as well and no consideration was given to the fact that the A rotational constants for the two isotopomers of the equatorial conformer were poorly determined with only A-type transitions observed. Therefore, the presently proposed parameters are expected to be much better determined. The limited number of structural parameters determined from the electron diffraction study are also listed in Table 8 where the C –C distances were fixed to the ab initio predicted values but with the same values for both conformers. The C – Br distance should be the best determined value from the electron diffraction study and taking the uncertainity in the reported value there is agreement with the adjusted r0 value for this parameter obtained from this study. Therefore, it is believed that the structural parameter reported herein are as accurate as can be experimentally determined. Further the reported differences between the various C – H distances should be as ˚ which cannot be obtained accurate as 0.001 A experimentally. The Raman spectrum of the annealed solid of bromocylopentane was obtained in a cryostat at 155 K. Upon warming, the crystal underwent a visual change at 194 K from a white crystalline solid to a clear glassy solid. The spectrum of this glassy solid was much weaker than the spectrum of the annealed solid. This weaker spectrum was characterized by broad peaks with intensity differences from that of other spectra for the solid and liquid. The sample could be recooled with the white solid reappearing at 186 K and then rewarmed with glassy solid reappearing at 194 K. The glassy solid could be held on the angled sample plate for several hours without change. This indicated that it was not a super cooled liquid which would have exhibited fluid motion after some time. This was interpreted to be a plastic phase of the bromocyclopentane with the transition point from crystal II to the warmer crystal I at 190 ^ 4 K. Dunning [20] reported that the kinetics of the phase transformation for solid states within a plastic

crystal typically are such that undercooling and superheating are necessary to observe the crystal changes in reasonable time frames. Therefore, it appears that bromocyclopentane has a plastic crystal phase before it melts. Timmermans [21] noted that almost spherical or globular molecules exhibit a new phase of matter he terms ‘plastic crystals’. These compounds are characterized by an unusually low entropy of fusion, near that of monoatomic crystals. This suggests that rotational degrees of freedom have been activated at some lower than the melting point and only the centers of gravity gain mobility on melting. An alternate theory submits that if the barrier between two positions of minimum potential energy is small enough, the molecule will be able to convert relatively rapidly from one orientation to another, then the molecules in the plastic phase can have a random distribution between different orientations. For bromocylopentane this explanation could explain its plastic phase since the barrier between the two stable conformers is rather small. Thus, an X-ray study of solid bromocyclopentane could be quite interesting to see if such disorder existed in the plastic phase.

Acknowledgements WAH and BJV thank the FWO-Vlaanderen for their assistance toward the purchase of the spectroscopic equipment used in this study. WAH, BJV and JRD thank the Flemish Community for financial support through the Special Research Fund (BOF) and the Scientific Affairs Division of NATO for travel funds. The authors also thank Ahmed Badawi for his assistance with the preperation of this manuscript.

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