ARTICLE pubs.acs.org/JPCA
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.
ARTICLE
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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