Conformational Stability from Variable-Temperature Infrared Spectra

May 27, 2011 - pubs.acs.org/JPCA. Conformational Stability from Variable-Temperature Infrared. Spectra of Xenon Solutions, r0 Structural Parameters, a...
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Conformational Stability from Variable-Temperature Infrared Spectra of Xenon Solutions, r0 Structural Parameters, and Vibrational Assignment of Pyrrolidine† James R. Durig,* Ahmed M. El-Defrawy, Arindam Ganguly, Savitha S. Panikar, and Mamdouh S. Soliman‡ Department of Chemistry, University of Missouri-Kansas City, Kansas City, Missouri 64110, United States

bS Supporting Information ABSTRACT: The infrared spectra of gaseous and variable-temperature liquid xenon solutions of pyrrolidine have been recorded. The enthalpy difference has been determined to be 109 ( 11 cm1 (1.30 ( 0.13 kJ mol1) with the envelope-equatorial conformer more stable than the twist form with 37 ( 3% present at ambient temperature. Ab initio calculations utilizing various basis sets up to MP2(full)/aug-ccpVTZ have been used to predict the conformational stabilities, energy at the equatorialaxial saddle point, and barriers to planarity. From previously reported microwave rotational constants along with MP2(full)/6-311þG(d,p) predicted structural values, adjusted r0 parameters have been obtained for both conformers. Heavy atom distances (Å) of equatorial[twist] conformer are as follows: N1C2 = 1.469(3)[1.476(3)], N1C3 = 1.469(3)[1.479(3)], C2C4 = 1.541(3)[1.556(3)], C3C5 = 1.541(3)[1.544(3)], C4C5 = 1.556(3)[1.543(3)]; and angles (deg) — N1C2C4 = 102.5(5)[107.6(5)], — N1C3C5 = 102.5(5)[105.4(5)], — C2C4C5 = 104.3(5)[104.6(5)], — C3C5C4 = 104.3(5)[103.7(5)], — C2N1C3 = 104.1(5)[103.9(5)], τC2C4C5C3 = 0.0(5)[13.5(5)]. A complete vibrational assignment is proposed for both conformers.

’ INTRODUCTION The saturated five-membered ring molecules are structurally interesting, since they can be in one or more of the three stable conformers, i.e., twisted, envelope, and planar forms. Furthermore, the energy difference between these forms can be very small with the barrier for the molecule to go from one form to another sufficiently small, where instead of going through the planar form, it may go through a series of twisted forms where one atom moves out perpendicular to a hypothetical plane of the rest of the atoms. This concept was called pseudorotation14 and was first experimentally observed for cyclopentane.4 As a continuation of our earlier investigations of five-membered rings, we more recently initiated variable-temperature infrared studies of rare gas solutions of several molecules some of which we had investigated earlier.5,6 We have determined the enthalpy difference between the two stable, envelope-axial and envelopeequatorial, forms of cyclopentyl chloride and cyclopentyl bromide by this method and the experimental values are 145 ( 15 cm1 (1.73 ( 0.18 kJ mol1) and 233 ( 23 cm1 (2.79 ( 0.28 kJ mol1), respectively, with the axial conformer as the more stable form for both molecules. Also, from studies of the variable-temperature infrared spectra of rare gas solutions of silacyclopentane7 and germacyclopentane,8 we found these molecules have only one stable twist (C2) conformer present in all physical states. From the initial vibrational study9,10 of cyclopentyl fluoride it was concluded that two conformers were present in the fluid states and they were the envelope-axial and envelope-equatorial conformers with the equatorial form the r 2011 American Chemical Society

more stable conformer. However, from a later vibrational investigation11 of the Raman spectrum of the liquid, it was concluded that there was only one form present and it was the equatorial form. This conclusion was supported by a theoretical prediction by a CNDO/2 calculation12 which predicted only the equatorial conformer as the stable form. However, we recently carried out13 a study of the variable temperature infrared spectrum of xenon solutions of cyclopentyl fluoride and determined that there was only one conformer present in the fluid states but it was the twisted (C1) form. This conclusion was supported by ab initio predictions as well as by the determined microwave rotational constants. Therefore, it is expected that the conformational conclusions of the structural stabilities of some of the other substituted five-membered rings may be in error. Another saturated five-membered ring molecule of considerable conformational interest is pyrrolidine, c-C4H8NH, which has received much scientific interest due to its presence in biologically important molecules such as peptides, proteins, and amino acids. It has been the subject of several experimental and theoretical conformational studies. From the first conventional microwave study, Caminati et al.14 reported that the pyrrolidine molecule exists in an envelope-axial form but there was no spectroscopic evidence for the envelope-equatorial form. In a subsequent electron diffraction study,15 which was supported Received: January 22, 2011 Revised: May 25, 2011 Published: May 27, 2011 7473

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The Journal of Physical Chemistry A by HF/4-21N* ab initio calculations, again the envelope-axial form was reported to be the more stable conformer with the envelope-equatorial conformer higher in energy by 339 cm1 (4.05 kJ mol1) and the barrier to pseudorotation was predicted to be 580 cm1 (6.94 kJ mol1). However, from a more recent microwave study, Caminati et al.16 discovered transitions of the equatorial conformer during the investigation of rotational free jet spectrum of pyrrolidinewater adduct. In this microwave investigation, it was observed that the axial conformer relaxes to the equatorial conformer when the cooling conditions were increased, which clearly shows that the equatorial form is the more stable conformer. To estimate the enthalpy difference from the relative intensity of the microwave lines the dipole moments were predicted by utilizing the vectorial compositions of the bond moments. An arbitrary uncertainty value of the dipole moments was taken to be 0.4 D. These predicted dipole moment values for both conformers were utilized (only the |μc|) which gave an estimated enthalpy difference to be ΔE0,0 (=Eax  Eeq) = 80 ( 300 cm1. However, by combining this value with the cooling effects of the jet which shows the equatorial conformer to be more stable, the predicted enthalpy difference of 0 < ΔE0,0 < 200 cm1 was obtained.16 In order to obtain an experimentally determined enthalpy difference, we initiated an investigation of the vibrational spectrum of pyrrolidine with a study of the infrared spectra of the gas and xenon solutions at variable temperatures. To obtain reliable enthalpy determinations from variable-temperature infrared spectrum in xenon solutions, it is essential to have a confident vibrational assignment for both forms particularly in the spectral region where the conformer pair or pairs are selected for the enthalpy determination. Therefore, assignments need to be made for the fundamentals for each of the conformers which is facilitated by utilizing ab initio calculations at the MP2 level with full electron correlation by the perturbation method.17 In the last three vibrational investigations,1820 no assignments were made for any of the fundamentals of the less stable conformer. Additionally, the structure of the less stable conformer has not been definitively determined since it was proposed to be the axial form as the most stable conformer from the initial microwave14 and electron diffraction studies15 and it seems to be accepted without experimental verifications. Also, we were interested in obtaining the r0 structural parameters for both the stable conformers. The results for these spectroscopic and theoretical studies are reported herein.

’ EXPERIMENTAL AND THEORETICAL METHODS The sample of pyrrolidine was purchased from Aldrich Chemical Co., with stated purity of 98%. The sample was further purified by a low-temperature, low-pressure fractionation column, and the purity of the sample was verified by comparing the infrared spectrum with previously reported ones.1820 The mid-infrared spectrum of the gas was obtained from 3500 to 300 cm1 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 cm1. Sixty-four interferograms were added and transformed with a boxcar truncation function. The mid-infrared spectrum of the solid was obtained with the sample deposited on a silicon substrate at 77 K, and multiple annealings were performed in order to obtain a good polycrystalline sample.

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The far-infrared spectrum of the sample was recorded on the previously described Perkin-Elmer 2000 spectrometer. A grid beamsplitter was used to record the spectrum of the gas with the sample contained in a 12 cm cell equipped with polyethylene windows. The spectra were recorded at a spectral resolution of 0.5 cm1 and, typically, 256 scans were used for both the sample and the reference data to give a satisfactory signal-to-noise ratio. The interferograms were averaged and then transformed with a boxcar truncation function. All of the observed bands of the fundamentals for both conformers are listed in Tables 1 and 2. The mid-infrared spectra (3500400 cm1) (Figure 1A) of the sample dissolved in liquefied xenon as a function of temperature, ranging from 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. For all spectra, 100 interferograms were collected at 1.0 cm1 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 thermoresistors. The LCAO-MO-SCF restricted HartreeFock calculations were performed with the Gaussian 03 program21 by using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all geometric parameters by using the gradient method of Pulay.22 A variety of basis sets with and without diffuse functions were employed with the MøllerPlesset perturbation method17 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. The infrared spectra were predicted from the MP2(full)/ 6-31G(d) calculations. The predicted scaled frequencies 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 (∂μu/∂Qi) = ∑j(∂μu/∂Xj)Lij, 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 (Nπ)/(3c2)[(∂μx/ ∂Qi)2 þ (∂μy/∂Qi)2 þ (∂μz/∂Qi)2]. In Figure 1, a comparison of experimental and simulated infrared spectra of pyrrolidine is shown. The predicted spectrum is in good agreement with the experimental spectrum which shows the utility of the scaled predicted frequencies and predicted intensities for supporting the vibrational assignment. In order to obtain a complete description of the molecular motions involved in the fundamental modes of pyrrolidine, a normal-coordinate analysis was 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 Figure 2. By using the B matrix,23 the force field in Cartesian coordinates was converted to a force field in internal coordinates. Subsequently, scaling factors of 0.88 for CH2 stretches and CH2 7474

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Table 1. Calculateda and Observed Frequencies (cm1) for Envelope-Equatorial (Cs) Form of Pyrrolidine infrared sym block A

0

A00

vib no.

approx description

ab initio

fixed scaledb

IR intensity

band contour

gas

liq Xe

PEDc

A

B

C

ν1

NH str

3535

3353

0.4

3351

3348

100S1

2



98

ν2

β-CH2 antisym str

3200

3002

45.2

2986

2985

98S2

4



96

ν3

R-CH2 antisym str

3158

2962

9.6

2971

2965

60S3, 33S5

2



98

ν4

β-CH2 sym str

3138

2944

34.0

2944

2943

94S4

100





ν5

R-CH2 sym str

3015

2828

115.2

2828

2826

66S5, 34S2

3



97

ν6

R-CH2 def

1591

1492

0.8

1476

1475

77S6, 21S7

3



97

ν7

β-CH2 def

1568

1471

4.4

1463

1458

78S7, 20S6

71



29

ν8 ν9

R-CH2 wag β-CH2 wag

1439 1364

1365 1294

1.8 1.9

1351 1288

1348 1286

79S8 58S9, 26S10

81 96

 

19 4

ν10

R-CH2 twist

1284

1218

0.8

1222

1221

52S10, 17S9, 12S13

12



88

ν11

β-CH2 twist

1268

1202

8.2

1203

1197

55S11, 16S13

1



99

ν12

ring def

1111

1054

0.7

1054

1041

18S12, 32S14, 14S9,

1



99

ν13

R-CH2 rock

1041

987

6.3

984

977

30S13, 21S12, 16S16, 17S11

3



97

ν14

ring def/breathing

982

931

2.5

933

929

27S14, 37S15, 12S11

44



56

ν15

ring breathing/def

941

893

6.5

896

898

58S15, 22S14

7



93

ν16 ν17

NH in-plane bend/ring def β-CH2 rock

921 798

874 757

69.5 22.9

792 739

791 733

36S16, 47S12 70S17, 10S16

30 45

 

70 55

ν18

ring def

596

565

43.3

568

568

76S18, 12S17, 10S13

41



59

ν19

ring puckering

318

302

4.9

302

288

98S19

100





ν20

β-CH2 antisym str

3182

2985

0.9

2981

2980

95S20



100



ν21

R-CH2 antisym str

3155

2959

52.9

2967

2966

62S21, 32S23



100



ν22

β-CH2 sym str

3130

2937

16.0

2937

2936

98S22



100



ν23

R-CH2 sym str

3013

2826

35.1

2826

2824

67S23, 33S21



100



ν24 ν25

R-CH2 def β-CH2 def

1573 1547

1476 1451

1.2 0.9

1472 1450

1464 1449

93S24 93S25

 

100 100

 

ν26

NH out-of-plane bend

1469

1394

5.6

1400

1399

56S26, 26S28, 10S33



100



ν27

β-CH2 wag

1366

1296

9.3

1283

1282

48S27, 22S29, 13S26



100



ν28

R-CH2 wag

1341

1272

15.0

1281

1281

42S28, 33S27, 13S29



100



ν29

β-CH2 twist

1283

1217

7.7

1208

1209

57S29, 13S34, 11S28



100



ν30

R-CH2 twist

1233

1170

0.8

1174

1172

63S30, 10S31



100



ν31

ring def

1169

1109

10.0

1114

1112

42S31, 25S32



100



ν32 ν33

R-CH2/β-CH2 rocks ring def

1140 971

1081 921

0.5 0.3

1080 916

1076 910

30S32, 29S34, 18S31, 68S33, 12S31

 

100 100

 

ν34

β-CH2/R-CH2 rocks

900

854

2.7

855

853

35S34, 31S32, 12S35



100



ν35

ring def

639

606

0.6

600

598

73S35, 10S32



100



ν36

ring twist

67

64

0.2

65



95S36



100



MP2(full)/6-31G(d) ab initio calculations, scaled frequencies, infrared intensities (km mol1), and potential energy distributions (PEDs). str = stretch; def = deformation. b Scaled frequencies with scaling factors of 0.88 for CH2 stretches and CH2 deformations and 0.90 for all other modes. c Symmetry coordinates with PED contribution less than 10% are omitted. a

deformations and 0.90 for all other coordinates were applied, along with the geometric average of scaling factors for interaction force constants, to obtain the fixed scaled force field and resultant wavenumbers. Comparisons between the observed and calculated wavenumbers, along with the calculated infrared intensities and potential energy distributions for equatorial and twist forms, are listed in Tables 1 and 2, respectively.

’ VIBRATIONAL ASSIGNMENT To obtain reliable enthalpy determinations from variabletemperature infrared spectra, it is essential to have confident assignments for both forms particularly in the spectral region where the

conformer pairs are being selected for the enthalpy determination. With significantly more information than what was utilized in making the earlier vibrational assignment such as ab initio predicted intensities, fundamental frequencies for the second conformer, and gas-phase contours, we have utilized all of these data as well as infrared spectra from xenon solutions where the sharp bands make it possible to identify closely spaced fundamentals. We expected to be able to assign all of the fundamentals for the more stable conformer and many of those for the second conformer particularly in the “fingerprint” spectral region (Figure 3). The assignments in the carbonhydrogen stretching region are nearly the same as those given earlier18 for the gas of the more stable conformer but it is possible to assign several of the 7475

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Table 2. Calculateda and Observed Frequencies (cm1) for Twist (C1) Form of Pyrrolidine infrared vib no.

approx description

ab initio

fixed scaledb IR intensity gas

band contour PEDc

liq. Xe

ν1

NH str

3500

3320

0.4

3324

ν2

β-CH2 antisym str

3190

2993

64.7

(2986)

ν3

R-CH2 antisym str

3181

2984

17.1

2981

ν4

R-CH2 antisym str

3174

2977

0.8

2971

ν5

β-CH2 antisym str

3164

2968

12.3

2961

ν6

β-CH2 sym str

3128

2934

28.2

ν7

β-CH2 sym str

3114

2922

ν8 ν9

R-CH2 sym str R-CH2 sym str

3113 3108

2920 2915

ν10

β-CH2 def

1580

ν11

R-CH2 def

1562

3322

100S1

A

B

C

15

2

83

3

1

96

72S3, 18S5

7

81

12

57S4, 31S2

10

67

23

76S5, 16S3

12

85

3

2932

78S6, 16S7

70

30



41.4

2922

67S7, 18S6

20

58

22

20.3 34.6

2925 2909

53S8, 24S9, 16S7 63S9, 27S8

39 6

14 67

47 27

1482

1.1

(1467)

63S10, 35S11

91

6

3

1465

3.6

1457

54S11, 36S10

22

3

75

65S12, 24S13, 10S11

2

90

8

70S13, 27S12

4



96

65S2, 30S4

1456

ν12

R-CH2 def

1558

1462

1.8

(1457)

ν13

β-CH2 def

1549

1453

0.5

1463

ν14

NH out-of-plane bend

1500

1423

7.3

1419

1419

78S14, 11S21

1

99



ν15

R-CH2 wag

1410

1338

2.7

1341

1336

84S15

88



12

ν16 ν17

R-CH2 twist R-CH2 twist

1386 1371

1315 1301

0.6 1.7

1315 1302

1315 1297

24S16, 24S18,15S17,12S20, 11S19 48S17, 12S16,10S18, 10S19

88 90

5 10

7 

ν18

β-CH2 wag

1340

1271

1.0

1271

1269

ν19

β-CH2 wag

1329

1260

1.0

1261

1457

55S18, 36S16



99

1

34S19,15S27, 10S16

18

81

1

ν20

β-CH2 twist

1292

1226

2.0

1226

53S20, 16S22, 10S27

30

70



ν21

R-CH2 wag

1255

1190

3.4

1188

1182

36S21, 13S19, 10S22

85

14

1

ν22

β-CH2 twist/R-CH2 wag

1247

1183

4.7

1186

1182

17S22, 24S21, 13S31, 10S20

94

3

3

ν23

ring def

1148

1089

20.3

1089

1083

64S23, 22S28



100



ν24 ν25

ring def β-CH2/R-CH2 rocks

1083 1080

1028 1025

0.7 2.4

1020 1013

39S24, 11S29, 11S19 30S25, 25S31, 17S21, 12S14

35 4

41 95

24 1

ν26

R-CH2 rock/β-CH2 twist

1028

975

25.0

975

962

27S26, 27S22, 20S24

94

1

5

ν27

ring def/breathing

973

923

10.5

923

919

25S27, 52S29, 18S30

94



6

ν28

ring def

958

908

0.5

909

59S28, 19S23

81

17

2

ν29

ring breathing/NH bend

930

883

8.1

885

883

24S29, 51S30, 12S24

98





ν30

NH in-plane bend/R-CH2

894

848

84.0

848

842

15S30, 31S26, 12S34, 11S24

90



10

784

15S31, 23S25, 18S26, 12S32 61S32, 13S34, 10S25

84 3

1 23

15 74 23

rock ν31 ν32

R-CH2/β-CH2 rocks β-CH2 rock

884 817

838 775

33.5 1.8

838 787

ν33

ring def

664

630

1.7

630

39S33, 32S34

28

49

ν34

ring def

616

584

0.9

591

28S34, 30S33, 13S32, 10S27

21

64

15

ν35

ring puckering

308

292

8.0

288

91S35

21



79

ν36

ring twist

38

36

0.3

39

91S36

5

28

67

MP2(full)/6-31G(d) ab initio calculations, scaled frequencies, infrared intensities (km mol1), and potential energy distributions (PEDs). str = stretch; def = deformation. b Scaled frequencies with scaling factors of 0.88 for CH2 stretches and CH2 deformations and 0.90 for all other modes. c Symmetry coordinates with PED contribution less than 10% are omitted. a

fundamentals to the second conformer in this spectral region. Beginning with the CH2 deformations and the remaining bands in the “fingerprint” region, the assignments for many of the fundamentals of the more stable conformer are different than those given earlier since many of the corresponding vibrations of the second conformer are quite pronounced. Most of the CH2 bending vibrations have expected frequencies based on group frequencies but there is significant mixing among the CH2 rocks and heavy atom ring vibrations. There is also considerable mixing with the NH bends which makes the description sometimes arbitrary. Nevertheless, three-fourths of the vibrations have major contributions of 50% or greater so that the descriptions

are useful for comparison of corresponding vibrations in similar molecules. On this basis, the assignments of several of the ring modes are of interest with the ring breathing vibrations at 896 and 885 cm1 with the latter one for the second conformer but extensively mixed with the NH bend. This latter band was assigned earlier18 to this vibration but the other four bands previously assigned as ring modes in the 8001100 cm1 region do not agree with the proposed assignment presented in this study. Also, only one of the lower frequency assigned ring modes agrees with those previously proposed18 but it should be noted that the earliest assigned ones made based on ab initio prediction were for the axial conformer as the most stable form. After the 7476

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second microwave investigation was reported16 with the equatorial conformer as the more stable form, ab initio predictions were used to estimate the frequencies for the equatorial form and the bands from the earlier reported spectra were reassigned to the equatorial form but none of them were assigned as arising from the less stable conformer. The other assignment reported18 for

Figure 1. Comparison of experimental and calculated infrared spectra of pyrrolidine: (A) observed infrared spectrum in xenon; (B) simulated infrared spectrum of a mixture of envelope-equatorial and twist conformers at 100 C with ΔH = 109 cm1; (C) simulated infrared spectrum of twist (C1) form; (D) simulated infrared spectrum of equatorial (Cs) form.

the equatorial form was made from the spectrum of the liquid where significant association is expected due to hydrogen bonding of the amine. Therefore, bands at 923, 909, and 885 cm1 are now assigned as ring modes for the second conformer, whereas, all three bands had been assigned18 as fundamentals for the equatorial form with two of them ring modes. Thus, only one of the five ring modes above 800 cm1 assigned in the current study agrees with those assigned earlier18 but two of the four ring modes below 700 cm1 agree with those assigned18 earlier. It should be noted that for the equatorial form only one of the vibrations has contributions from four symmetry coordinates but 10 of them have significant contributions from three symmetry coordinates. This mixing makes it impossible to assign the NH in-plane bend, CH2 rocks, and three of the ring deformations to mainly a single vibration which has resulted in several different vibrations contributing significantly to the NH bend. Therefore, some of the descriptions of these modes are more for bookkeeping than to convey a description of the major atom motions involved. Although the descriptions of several of the band contours in the fingerprint spectral region are ambiguous, definitive assignments for most of them to one or the other of the conformers can be confidently made. This is possible from the spectral data of the xenon solution where the bands are relatively sharp and the band centers for the broad B-type bands for the gas can be clearly identified. For example, the broad band in the 10001050 cm1 region of the xenon solution has clear bands at 1020 and 1013 cm1 which can be assigned to the second conformer whereas the band at 1041 cm1 must be assigned to the equatorial form. This example shows that the relatively weak broad bands can be assigned to the individual conformers. With the vibrations which are assigned to the individual conformers and not badly overlapped, it should be possible to obtain the enthalpy difference between the conformers from variable-temperature studies of the infrared spectra of the xenon solutions. Relatively small interactions are expected to occur between xenon and the sample and, thus, small frequency shifts are anticipated when passing from gas to the liquefied xenon solutions. A significant advantage of this

Table 3. Calculated Electronic Energies (Hartrees) and Energy Differencesa (cm1) for the Envelope-Equatorial (Cs), Twist (C1), Envelope-Axial (Transition State) (Cs), and Planar (Transition State) (Cs) Conformers of Pyrrolidine method/basis set MP2(full)/6-31G(d) MP2(full)/6-31þG(d)

no. of basis functions

envelopeequatorial

twist

ΔEEeqT

ΔEEeqEax

planar

ΔEEeqP

93

211.850047

211.850122

16

211.850115

15

211.840341

2130

113

211.863522

211.862925

131

211.862888

139

211.853918

2108

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

144

212.070241

212.070741

110

212.070548

67

212.060696

2095

MP2(full)/6-311þG(d,p)

164

212.077306

212.077220

19

212.077050

56

212.068326

1971

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

196

212.132264

212.132212

11

212.132159

23

212.122841

2068

MP2(full)/6-311þG(2d,2p) MP2(full)/6-311G(2df,2pd)

216 276

212.137810 212.217237

212.137472 212.216998

74 52

212.137446 212.216869

80 81

212.128537 212.207550

2035 2126

MP2(full)/6-311þG(2df,2pd)

296

212.222209

212.221736

104

212.221664

119

212.212711

2085

MP2(full)/6-311þþG(2df,2pd)

305

212.222513

212.222009

111

212.221944

125

212.212996

2089

MP2(full)/aug-cc-pVTZ

565

212.232642

212.232319

71

212.232291

77

212.223483

82 ( 24

averageb

96 ( 24

2010 2069 ( 46

93

212.581750

212.582016

58

212.582023

60

212.574451

1602

B3LYP/6-31þG(d)

113

212.591062

212.590634

94

212.590641

92

212.583712

1613

B3LYP/6-311G(d,p) B3LYP/6-311þG(d,p)

144 164

212.642045 212.646368

212.642152 212.646034

23 73

212.642160 212.646043

25 71

212.634865 212.639520

1576 1503

B3LYP/6-31G(d)

a

envelopeaxial

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

196

212.651253

212.651322

15

212.651331

17

212.644739

1430

B3LYP/6-311þG(2d,2p)

216

212.655218

212.654989

50

212.655000

48

212.648727

1425

Energy differences of the twist, axial, and planar forms are relative to the equatorial form. b Average values are for the five largest basis sets. 7477

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Table 4. Structural Parameters (Å and deg) and Rotational Constants (MHz) for Equatorial and Twist Forms of Pyrrolidine adjusted r0

MP2(full)/6-311þG(d,p) struct parameters

a

a

internal coord

equatorial

twist

ED axial

equatorial

twist

r(NC2)

R1

1.463

1.473

1.469(10)

1.469(3)

1.476(3)

r(NC3)

R2

1.463

1.466

1.469(10)

1.469(3)

1.479(3)

r(C2C4) r(C3C5)

R3 R4

1.536 1.536

1.557 1.535

1.543(8) 1.543(8)

1.541(3) 1.541(3)

1.556(3) 1.544(3)

r(C4C5)

R5

1.551

1.542

1.543(8)

1.556(3)

1.543(3)

r(NH6)

r1

1.016

1.017

1.020

1.016(2)

1.017(2)

r(C2H7)

r2

1.104

1.093

1.090(4)

1.104(2)

1.093(2)

r(C2H9)

r3

1.093

1.094

1.090(4)

1.093(2)

1.094(2)

r(C3H10)

r4

1.104

1.093

1.090(4)

1.104(2)

1.093(2)

r(C3H8)

r5

1.093

1.096

1.090(4)

1.093(2)

1.097(2)

r(C5H11) r(C5H13)

r6 r7

1.092 1.092

1.095 1.093

1.090(4) 1.090(4)

1.092(2) 1.092(2)

1.095(2) 1.093(2)

r(C4H14)

r8

1.092

1.093

1.090(4)

1.092(2)

1.093(2)

r(C4H12)

r9

1.092

1.094

1.090(4)

1.092(2)

1.093(2)

— N1C2C4

ϕ1

102.5

107.7

104.6

102.5(5)

107.6(5)

— N1C3C5

ϕ2

102.5

105.4

104.6

102.5(5)

105.4(5)

— C2C4C5

ϕ3

104.2

104.2

104.9

104.3(5)

104.6(5)

— C3C5C4

ϕ4

104.2

102.8

104.9

104.3(5)

103.7(5)

— C2N1C3 — C2N1H6

ψ σ1

103.8 111.8

104.1 108.4

105.2(35) 107.0

104.1(5) 111.7(5)

103.9(5) 108.4(5)

— C3N1H6

σ2

111.8

107.9

111.7(5)

108.0(5)

— H7C2N1

R1

112.0

110.0

112.0(5)

110.0(5)

— H9C2N1

R3

111.1

108.3

111.1(5)

108.3(5)

— H10C3N1

R2

112.0

110.7

112.0(5)

110.7(5)

— H8C3N1

R4

111.1

108.2

111.1(5)

108.2(5)

— H7C2C4

R5

109.6

112.9

109.6(5)

113.0(5)

— H9C2C4 — H10C3C5

R6 R7

113.1 109.6

110.1 113.9

113.1(5) 109.6(5)

110.1(5) 113.9(5)

— H8C3C5

R8

113.1

110.2

113.1(5)

110.2(5)

— H7C2H9

γ1

108.5

107.7

108.5(5)

107.7(5)

— H10C3H8

γ2

108.5

108.2

108.5(5)

108.2(5)

— H11C5C3

β1

111.6

108.9

111.6(5)

109.0(5)

— H13C5C3

β3

110.1

113.6

110.1(5)

113.6(5)

— H14C4C2

β2

111.6

112.0

111.6(5)

112.0(5)

— H12C4C2 — H11C5C4

β4 β5

110.1 112.6

110.6 110.4

110.1(5) 112.5(5)

110.6(5) 110.0(5)

— H13C5C4

β6

110.4

112.9

110.4(5)

112.4(5)

— H14C4C5

β7

112.6

111.8

112.5(5)

111.6(5)

— H12C4C5

β8

110.4

110.8

110.4(5)

110.6(5)

— H11C5H13

ε1

107.8

108.1

107.9(5)

108.1(5)

— H14C4H12

ε2

107.8

107.5

107.9(5)

107.5(5)

τN1C2C4C5

τ1

27.5

4.25

27.0(5)

10.0(5)

τN1C3C5C4 τC2C4C5C3

τ2 τ3

27.5 0.0

36.9 19.2

27.0(5) 0.0

32.8(5) 13.5(5)

τC2N1C3C5

τ4

46.5

40.1

45.8(5)

39.4(5)

τC3N1C2C4

τ5

46.5

27.3

45.8(5)

30.6(5)

A

6914.6

6884.4

6865.2

6833.9

B

6828.3

6715.9

6792.6

6678.6

C

3934.6

3924.9

3902.1

3888.9

39.0(14)

Values taken from ref 15. 7478

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Figure 2. Planar (Cs) conformer of pyrrolidine showing atom numbering.

Figure 4. Temperature (55 to 100 C) dependent mid-infrared spectrum in the 525600 cm1 region of pyrrolidine dissolved in liquid xenon.

Figure 3. Mid-infrared spectra (5001500 cm1) of pyrrolidine: (A) gas in transmittance; (B) liquid xenon solution in absorbance.

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 (Table 3) and the molecular sizes of the rotamers are nearly the same, so that the ΔH value obtained from the temperature-dependent FT-IR study is expected to be comparable to the value for the gas.2428

’ CONFORMATIONAL STABILITY Once the vibrational assignments were made for most of the observed bands in the spectral region from 400 to 1400 cm1, the bands to be used to obtain the enthalpy difference need to be selected. Lowest frequency bands are best selected since the number of overtone or combination bands will increase significantly for the higher wavenumber bands. Thus, the first fundamental considered for the equatorial conformer was ν18 which is mainly due to a ring deformation. However, the second conformer has a fundamental on the high-frequency side as well as ν35 for the equatorial conformer. Also, there is a distinct band on the low-frequency side with a pronounced Q branch which is tentatively assigned as the overtone of ν35 of the less stable conformer. There is also a second weaker band slightly below the overtone band and the breadth of ν18 makes it difficult to obtain the relative intensity change with the decrease in temperature. Thus, the value of the uncertainty when this band is used is larger than normally obtained. Nevertheless, this fundamental is

mainly (76%) due to a ring mode which is desirable since bands associated with an NH mode can be significantly affected by association in the solution. Another fundamental for the equatorial conformer is the 1041 cm1 band which has a highfrequency shoulder but it is sufficiently separated so its intensity can be reasonably well measured. The third equatorial fundamental chosen was the 1112 cm1 band which is relatively sharp in the xenon solution and has significant contribution from S31(42%), a ring mode. The final two bands chosen were the 791 (47S12, ring deformation) and 1282 cm1 where both have sufficient intensity to be used with the most intense band being used for the second conformer. The bands chosen for the second conformer were the very pronounced 1083 cm1 which is a ring deformation and the weak doublet at 1013 and 1020 cm1 with the latter one also a ring deformation. The five equatorial bands and the three from the second conformer made it possible to obtain six individual enthalpy differences. The intensities of the chosen infrared bands were measured as a function of temperature (Figure 4) and their ratios were determined. By application of the van’t Hoff equation ln K = ΔH/(RT)  ΔS/R, the enthalpy differences were determined from a plot of ln K versus 1/T, where ΔH/R is the slope of the line and K is substituted with the appropriate intensity ratios, i.e., IformA/IformB. It was assumed that ΔH is not a function of temperature in the range studied. By combining the intensity of the bands of the equatorial conformer with those of the second form, six individual ΔH values were obtained where different values ranged from a high value of 134 cm1 to the lowest one of 71 cm1 but with different statistical uncertainties ranging from 41 to 6 cm1 with an arithmetic average of 24 cm1. However, by combining these six pairs into a single set the determined ΔH value 7479

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ARTICLE

is 109 ( 11 cm1 (1.30 ( 0.13 kJ mol1) (Table 5). This error limit was derived from the statistical standard deviation of 1σ of the measured intensity data where the data from the six pairs were taken as a single set. 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 are undoubtedly due to these types of interferences but by taking six pairs it is hoped that the effect of such interferences would be minimized. From these results the abundance of the less stable conformer at ambient temperature is estimated to be 37 ( 3%. The experimentally determined enthalpy difference is in satisfactory agreement with the energy difference predicted from the ab initio calculations for a second conformer which could be either the envelope-axial or the twist form. However, the ab initio calculations have a negative frequency for the axial form which indicates that it is a first-order saddle point and not a stable conformer. However, the energy differences are relatively small from the calculations with the predictions from the MP2(full)/ aug-cc-pVTZ expected to be the best estimate.

changes, 11 of the 15 rotational constants are fit to 0.4 MHz or better with the other four differing by 0.6, 0.7, and 1.3 MHz (Table 6). The estimated uncertainties for the individual parameters are listed in Table 4. For the second conformer which is predicted from the ab initio calculations to be the twisted form with no symmetry, there are Table 6. Comparison of Rotational Constants (MHz) Obtained from ab Initio MP2(full)/6-311þG(d,p) Predictions, Microwave Spectra, and Adjusted r0 Structural Parameters for Pyrrolidine conformer

isotopomer

equatorial

C4H8NH

rotational const

obsda

calcd

|Δ|

A

6864.7

6865.2

0.6

B

6791.9

6792.6

0.7

C

3902.3

3902.1

0.2

A

6865.6

6865.2

0.4

B C

6405.8 3771.1

6405.6 3771.3

0.2 0.2

A

6803.2

6803.6

0.4

B

6709.7

6709.6

0.1

C

3858.5

3857.2

1.3

A

6845.1

6845.4

0.3

B

6661.0

6661.0

0.0

C

3851.6

3852.3

0.7

A B

6856.1 6665.0

6855.9 6665.3

0.2 0.3

C

3862.3

3862.7

0.4

A

6834.5

6833.9

0.6

B

6677.8

6678.5

0.7

C

3888.1

3888.9

0.8

A

6707.4

6707.6

0.2

B

6403.8

6404.5

0.7

C A

3834.6 6735.6

3834.3 6735.7

0.3 0.1

B

6635.8

6634.9

0.9

C

3843.9

3843.2

0.7

A

6803.6

6804.3

0.7

B

6560.0

6559.0

1.0

C

3838.4

3838.6

0.2

C4H8ND

2-13C

’ STRUCTURAL PARAMETERS We29 have shown that ab initio MP2(full)/6-311þG(d,p) calculations predict the r0 structural parameters for 50 substituted hydrocarbons for the carbonhydrogen distances better than 0.002 Å compared to the experimentally determined values from isolated CH stretching frequencies30 which agree with previously determined values from earlier microwave studies. Therefore, all of the carbonhydrogen distances can be taken from the MP2(full)/6-311þG(d,p) predicted values for pyrrolidine. We have also shown31 that we can obtain good structural parameters by adjusting the structural parameters obtained from the ab initio calculations to fit the rotational constants obtained from microwave experimental data. For the pyrrolidine equatorial conformer there are three heavy atom distances, three heavy atom angles, and two dihedral angles to be determined from the 12 microwave determined (excluding the N-D isotopomer) rotational32 constants by adjusting the predicted parameters from the MP2(full)/6-311þG(d,p) calculation. The adjusted r0 parameters are given in Table 4, and the three heavy atom distances are increased by 0.006 and 0.005 Å and — CCC increased by 0.1, and the — CNC is increased by 0.3 and one of the dihedral angles changes by 0.7. With these very small

3-13C

C4H815NH

C4H8NH

twist

C4H8ND

2-13C

3-13C

a

Values for the rotational constants taken from ref 32.

Table 5. Temperature and Intensity Ratios of the Equatorial and Twist Bands of Pyrrolidine T (C) liquid xenon

ΔHa (cm1)

1/T (103 K1)

I568/I1083 

I791/I1083

I1282/I1083

I1112/I1020

I1041/I1020

I1041/I1013

55.0

4.584





0.360

2.409

2.154

60.0

4.692

1.333

0.899

0.309

0.357

2.207

1.919

65.0

4.804

1.280

0.842

0.314

0.345

2.442

1.921

70.0 75.0

4.923 5.047

1.250 1.231

0.823 0.881

0.283 0.332

0.345 0.337

2.154 2.355

1.824 2.010

80.0

5.177

1.250

0.809

0.274

0.332

2.189

1.931

85.0

5.315

1.232

0.845

0.303

0.327

2.276

1.846

90.0

4.460

1.121

0.802

0.271

0.326

1.979

1.742

95.0

5.613

1.118

0.766

0.262

0.322

2.025

1.778

100.0

5.775

1.068

0.765

0.263

0.320

1.813

1.615

130 ( 16

88 ( 21

119 ( 41

71 ( 6

134 ( 32

116 ( 27

a Average value ΔH = 109 ( 11 cm1 (1.30 ( 0.13 kJ mol1) with the equatorial conformer the more stable form and the statistical uncertainty (1σ) obtained by utilizing all of the data as a single set.

7480

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The Journal of Physical Chemistry A now five heavy atom distances, five angles, and five dihedral angles which must be determined from the 12 microwave reported rotational constants. 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 which results in only three heavy atom distances for the twisted form. Also, the bond angles in the same set keep their differences in degrees which reduces them to three. This assumption is based on the fact that the errors from ab initio calculations are systematic. By this process there are 11 parameters to be adjusted so it should be possible to obtain “adjusted r0” structural parameters for the twisted conformer by utilizing the 12 determined microwave rotational constants from this conformer. The parameters obtained for the twist conformer are listed in Table 4 along with the estimated uncertainties of the parameters. From the microwave studies14,16 of pyrrolidine the centrifugal distortion constants were reported for both conformers. From the predicted force constants by utilizing two different basis sets from MP2(full) ab initio calculations and with the same basis sets from density functional calculations, the centrifugal distortion constants have been calculated for the envelope-equatorial and twist conformers (Table S1 in the Supporting Information). In the case of the envelope-equatorial conformer, only the ΔJ and δJ values were obtained from the microwave study16 and the remaining quartic centrifugal distortion parameters were fixed to zero because they could not be determined from the experimental data. The three distortion constants which were set to zero have been predicted to have significant values (Table S1) which makes the values reported for the other two distortion constants with statistical uncertainties unrealistic. The experimental distortion constants for the twist conformer were originally attributed incorrectly to the envelope-axial conformer.14 This misassignment has been rectified in Table S1 but the agreement of the predicted values from the MP2(full)/6-311þG(d,p) calculations is only satisfactory for the ΔJ and ΔK constants but the other three constants have very large differences (2 orders of magnitude).

’ DISCUSSION The frequency predictions from the ab initio calculations for the A0 modes of the envelope-equatorial conformer are on the average within 5.6 cm1 which represents an error of 0.4%. For the A00 modes for this conformer the predictions are within 4.9 cm1 which is an error of 0.3%. These predictions were obtained with only two scaling factors with the ab initio calculation from the relatively small 6-31G(d) basis set by second-order perturbation with full electron correlation. Similar predictions are expected for the second conformer, so the present assignment for this less stable form is expected to be very good. For the envelope-equatorial conformer which has a plane of symmetry, the mixing of the normal modes is relatively minor except for the two highest frequency ring modes and the NH bend in the A0 symmetry block. Except for these four modes the approximate descriptions given represent a reasonable description of the major atomic motions for the vibrations. However, for the twisted form where there are no symmetry elements, several of the modes are given approximate descriptions more for bookkeeping than to convey the major atomic displacements. For example, ν16 has contributions from five different symmetry coordinates with contributions greater than 10% and six of them with contributions from four symmetry coordinates. Therefore, the

ARTICLE

Figure 5. ν30 and ν31 modes of the twist form predicted and observed at 848 and 838 cm1of the gas.

descriptions for the modes for the twisted form are not as meaningful as those for the equatorial conformer. We investigated the difference in the predicted frequencies for the axial and twist forms and found most of the values were only 2 or 3 cm1 apart except for ν9, ν17, ν18, ν29, ν35, and ν36 which differ by 5 or 6 cm1 (Table S2 in the Supporting Information). However, the ν35 and ν18 which are ring modes are predicted to be 20 cm1 lower and 16 cm1 higher, respectively, for the axial form than the corresponding modes for the twist form. It should be noted that these modes are predicted at 630 and 584 cm1 and observed at 630 and 591 cm1 for the twist conformer whereas they are predicted at 610 and 600 cm1, respectively, for the axial form. These ab initio predictions support the twist conformer as the second conformer. A more interesting observation is the predicted and observed intensities of the ν30 and ν31 modes of the twist form where they are predicted at 848 and 838 cm1, and observed at exactly these frequencies. Their predicted intensities are 84.0 and 33.5 km mol1 and both with A/C contours with a strong Q-branch (Figure 5). However, for these two modes for the axial conformer they are predicted 848 and 834 cm1 with intensities of 116.5 and 0.9 km mol1, respectively, with A/C contour for the higher frequency band but a B-type contour for this conformer which has a plane of symmetry. Therefore, these vibrational data provide convincing experimental evidence that the less stable conformer is the twist form. The data obtained from the variable low temperature study in xenon has provided some excellent information for determining the correct assignment for the normal modes of both of the conformers. It is clear that the previous proposed assignments are in error in several cases. The lack of agreement between those proposed earlier and the ones obtained from the current studies arises from the much larger amount of data available in this study such as the band contours, the relative predicted intensities from the ab initio calculation, and the intensity changes from the variable temperature study. Additionally, much of the earlier data 7481

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The Journal of Physical Chemistry A

Figure 6. Mid-infrared spectra (3001500 cm1) of pyrrolidine: (A) gas; (B) liquid xenon solution; (C) solid.

were obtained from condensed-phase samples rather than for the gas. For the liquid there must be significant association which can significantly shift the band frequencies as well as change the intensities. Association can also be present in the solution but with liquid xenon the 4 cm cell makes it possible to utilize a very dilute solution of approximately 104 M which significantly reduces the association. For the solid the lower frequency region is drastically changed as can be seen in Figure 6 where the pronounced fundamentals in the gas [xenon] at 568 [568], 739 [733], and 792 [791] cm1 either disappear or shift to ∼900 cm1. These spectra dramatically show that an assignment made from spectral data from the condensed phases cannot be compared to one for the gas for the monomer. Therefore, we believe that the current proposed vibrational assignments for the two conformers are based on good scientific evidence for the monomeric species. An attempt was made to obtain the conformational stability by utilizing two bands observed in the far-infrared spectrum of a krypton solution which was initially thought to be due to the two different conformers. However, on determining the enthalpy difference for these two bands a value of 550 cm1 was obtained and, therefore, it was concluded that this enthalpy value was not between the two forms of pyrrolidine but was due to the dimerization arising from the NH association from one molecule to the electron pair on other molecules based on the much lower temperature of the krypton solution. This enthalpy value was certainly too large based on the amount of the second conformer present at ambient temperature as well as the predicted energy difference from the ab initio and density function theory calculations. The enthalpy difference of 109 ( 11 cm1 (1.30 ( 0.13 kJ mol1) has the expected 10% uncertainty which is usually found by using the variable-temperature technique of rare gas solutions. The spread in values is not unusual particularly when the higher frequencies in the fingerprint region have to be used, so there are many opportunities for some interferences for each conformer. Also, even with the very low concentration of the sample one does expect some association as the temperature is lowered which could lead to slight lowering of the experimentally

ARTICLE

determined enthalpy value. However, the predicted value from the ab initio calculations can vary extensively from the different calculations. For example, it has been shown that only theoretical methods that incorporate correlation effect in conjunction with large basis sets provided satisfactory predictions for allyl amine.33 The structural parameters (Table 4) determined by utilizing the previously reported microwave rotational constants along with the predicted parameters from MP2(full)/6-311þG(d,p) calculations have provided excellent distances and angles which we believe to have small uncertainties such as 0.003 Å for the heavy atom distances, 0.002 Å for the CH and NH distances, and 0.5 for the angles. These parameters are probably as good as can be obtained experimentally by any technique for the gas phase. It is interesting to compare the CN distance of pyrrolidine with other secondary amines. For example, the CN distance for dimethylamine has the reported34 rs value of 1.462 ( 0.005 Å and the CNC angle of 112.2 ( 0.2. The r0 parameters for ethylmethylamine35 are 1.462(5) and 1.461(5) Å for the two CN distances and 112.1(5) for the CNC angle which are essentially the same as those for the dimethyl compound. Disregarding the uncertainties, these CN distances are slightly smaller than the value of 1.469(3) Å for pyrrolidine. Of course, the CNC angle is much smaller at 104.1(5), as expected, since the angle in the ring must be much smaller than those in straight-chain molecules. There are no structural parameters for N-methylpyrrolidine obtained from spectroscopic data but they were reported from an electron diffraction study36 where the ra values are 1.455(3) Å for the CN, 1.542(4) Å for the two CC, and 1.555(4) Å for the unique CC distance and the CNC angle is 107.4(17) for the envelope-equatorial form. These electron diffraction parameters provided rotational constants which satisfactorily predicted the rotational constants obtained later from the microwave study.37 Also, these parameters are in good agreement with those obtained in the current study for this conformer of pyrrolidine. It is rather surprising that the second most stable conformer for pyrrolidine is the twisted form rather than the envelope-axial form which has been found for most of the previously studied fivemembered rings which have two stable conformers. Therefore, it would be of interest to investigate whether there are other five membered rings with two conformers where the equatorial form is the more stable conformer and the second most stable form the twisted conformer. For example, N-methylpyrrolidine should have a second conformer but from the several spectroscopic studies there has not been a second conformer reported. Therefore, studies of some additional N-substituted pyrrolidines would be of considerable interest. If there are additional ones with the second conformer the twisted form it would be of interest to learn what the major factors are which contribute to the difference.

’ ASSOCIATED CONTENT

bS

Supporting Information. Table S1, quadratic centrifugal distortion constants (kHz) for isotopomers of twist and equatorial pyrrolidine.Table S2, calculated frequencies (cm1) for the envelopeaxial (Cs) and twist (C1) forms of pyrrolidine. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: 01-816-235-6038. Fax: 01 816-235-2290. E-mail: durigj@ umkc.edu. 7482

dx.doi.org/10.1021/jp200692t |J. Phys. Chem. A 2011, 115, 7473–7483

The Journal of Physical Chemistry A Present Addresses ‡

Department of Chemistry, Mansoura University, Mansoura, Egypt.

Notes †

Taken in part from the theses of A.M.E. and A.G., which were submitted in partial fulfillments of their Ph.D. degrees, and in part from the thesis of S.S.P., which will be submitted in partial fulfillment of her Ph.D. degree.

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