J. Phys. Chem. 1996, 100, 15073-15078
15073
Molecular Structures and Vibrational Spectra of Pyrrole and Carbazole by Density Functional Theory and Conventional ab Initio Calculations Sang Yeon Lee† and Bong Hyun Boo*,§ Department of Chemistry, Chungnam National UniVersity, Taejon 305-764, Korea, and Center for Molecular Science, 373-1 Kusung-dong, Yusung-gu, Taejon 305-701, Korea ReceiVed: March 27, 1996; In Final Form: June 26, 1996X
Ab initio Hartree-Fock, MP2, and Becke 3-Lee-Yang-Parr (B3LYP) density functional theory calculations using 6-31G*, 6-311G**, and 6-311G(2df,p) basis sets were carried out to study molecular structures and vibrational spectra of pyrrole and carbazole. We report the results of the molecular structures and fundamental vibrational frequencies obtained on the basis of the calculations. The assignments of frequencies show a one-to-one correspondence between the observed and calculated fundamentals.
Introduction The electronic-vibrational spectra of weakly bound van der Waals (vdW) complexes of carbazole (CZ) are the subject of ongoing spectroscopic investigations.1-5 The CZ molecule, like fluorene, a structural analog of CZ, is well-known to fluoresce efficiently upon excitation of S0 to S1.6 Thus excited state dynamics of CZ6 and its derivatives, N-ethylcarbazole6,7 and polyvinylcarbazole,8 have been studied by fluorescence or absorption spectroscopy. Published results indicate that the vibrational frequencies appended to the 000 band origin of CZ consist of fundamentals, overtones, and combination bands.2,6,9,10 Thus correct assignment of the ground-state fundamentals is necessary in order to elucidate the electronic-vibrational spectra. In 1968, Bree and Zwarich (BZ) reported fundamentals and modes of CZ assigned Via polarized infrared and Raman spectroscopies11 and low-temperature absorption spectroscopy.9 It is evident that the work of BZ is excellent in the assignment of the observed vibrational frequencies. There are, however, no assignments to a2 modes owing to the forbidden infrared selection rule and to the very weak Raman intensities of the modes. And also there is some ambiguity in the assignments of fundamental modes of other symmetries due to their low intensities. Thus a reliable theoretical study is required to predict the frequencies of a2 modes in the vibrational spectra and to assign fundamentals and their modes among the peaks in the spectra. Computational methods based on density functional theory (DFT) are becoming widely used. These methods predict relatively accurate molecular structures and vibrations with moderate computational effort. Published results show that DFT methods reproduce experimental vibrational frequencies with higher accuracy than do the HF and MP2 calculations.12-18 Even when a uniform scaling is performed for the computed vibrational frequencies, DFT methods give better agreement with the experimental frequencies than do the HF and MP2 methods.12a,13,14 Some examples of the calculation on the vibrational frequencies of benzene are represented by Handy et al.13 and Wheeless et al.,15 in which MP2 calculations obtained by using the 6-311G(d,p) basis set still underestimate the vibrational frequencies corresponding to the ring torsion and overestimate the vibrational frequency corresponding to a b2u †
Postdoctoral fellow at Center for Molecular Science. Chungnam National University and Center for Molecular Science. X Abstract published in AdVance ACS Abstracts, August 15, 1996. §
S0022-3654(96)00921-5 CCC: $12.00
mode which tends to dissociate into three acetylene molecules. On the other hand, these frequencies are accurately predicted by the DFT calculation using the Becke-Lee-Yang-Parr (BLYP) functional.13,15 Rauhut and Pulay (RP) employed the BLYP functional and the B3LYP functional methods to predict fundamentals of 20 small molecules such as benzene, ether, and methanol, whose vibrational frequencies are exactly assigned. They then derived uniform scaling factors of 0.995 and 0.963, having root mean square (rms) deviations of 26.2 and 18.5 cm-1, respectively.16 When these workers also applied these scaling factors to another 11 molecules such as aniline, ethanol, and oxetane, the root mean square deviations turned out to be 26.9 and 19.7 cm-1 for the BLYP and B3LYP methods, respectively. We calculated molecular structure and performed the normal vibrational mode analyses of CZ at the HF and B3LYP levels using the 6-31G* basis set, resulting in reassignment of some of the fundamentals. Almost one-to-one correspondence is unambiguously achieved between the calculated frequencies and the experimental values reported by BZ. But there still exist some ambiguities in the reassignment of the fundamentals, and one fundamental shows sizable deviations from the experimental data reported by BZ. To deduce whether the sources giving rise to large deviations come from wrong identification or from the size of the basis set employed such as 6-31G*, we first performed a quality test by comparing the B3LYP method with conventional ab initio calculations using a given basis set, 6-31G*. We then checked the accuracy of the B3LYP method as a function of the size of the basis set. For this purpose, we assumed that the pyrrole (PR) molecule is an appropriate model since PR is small enough to make feasible the use of large basis sets such as 6-311G(2df,p), since it is almost a subunit of CZ, and since its molecular structure19 and fundamental frequencies20-26 are well determined experimentally. A number of experimental studies of vibrational spectra of PR have been done by liquid phase infrared20-25 and Raman20-22,26 spectroscopy and by gas phase infrared spectroscopy.22-25 To date, only a few ab initio studies using the HF27 and B3LYP16 methods have been done to reproduce the vibrational spectra of PR, and the theoretical predictions of the fundamentals have been achieved only with a variety of optimized scale factors.16,27 Here we report the results of molecular parameters and fundamentals of PR and CZ obtained from a variety of calculated methods. It is confirmed again in this study that the ab initio approach at the level of B3LYP is sufficiently powerful © 1996 American Chemical Society
15074 J. Phys. Chem., Vol. 100, No. 37, 1996
Lee and Boo
Figure 1. Comparison of the calculated and X-ray structural parameters of pyrrole.
to predict fundamentals via the use of a uniform scaling factor as well as to estimate the structural parameters of CZ of satisfactory accuracy with moderate effort. Calculations The molecular geometries of PR and CZ were optimized at the HF, MP2 and B3LYP levels of theory with a variety of basis sets of 6-31G* and/or 6-311G**, 6-311G(2df,p), by using the Gaussian 94 program.28 Vibrational frequencies were computed with the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, B3LYP/6-311G**, and B3LYP/6-311G(2df,p) methods for PR and with the HF/6-31G* and B3LYP/6-31G* methods for CZ. They were scaled by 0.8929 (HF/6-31G*), 0.95 (MP2/6-31G*), 0.963 (B3LYP/6-31G* and B3LYP/6-311G**) and 0.968 [B3LYP/6-311G(2df,p)]. The frequencies and normal modes for PR and CZ were determined by diagonalizing the massweighted force constant matrix. Results and Discussion Geometric Structures. The PR and CZ molecules have been shown to have C2V symmetry in the gas phase. The numbering of the atoms is depicted in Figures 1 and 2. The optimized bond lengths and angles of PR and CZ calculated by the HF, MP2, and B3LYP methods are displayed in Tables 1 and 2, and some of the structural parameters are also represented in Figures 1 and 2. The molecular parameters determined from the microwave spectra of PR19 and from X-ray studies of CZ29,30 are included for comparison. It is well-known that the HF method underestimates bond lengths and that inclusion of electron correlation at the MP2 level improves the agreement with experiment. This pattern is also found for the PR and CZ molecules. As seen in Figure 1, bond lengths and angles of PR determined by microwave spectroscopy are quite consistent with the optimized values. For the given basis set of 6-31G*, MP2 results for PR show slightly
Figure 2. Comparison of the calculated and X-ray structural parameters of carbazole.
TABLE 1: Equilibrium Geometrical Parameters of Pyrrole in the Ground State
parameter N-H N-C2 C2-C3 C3-C4 C2-H C3-H H-N-C2 C2-N-C5 N-C2-C3 C2-C3-C4 N-C2-H C2-C3-H a
B3LYP/ HF/ MP2/ B3LYP/ B3LYP/ 6-311G 6-31G* 6-31G* 6-31G* 6-311G** (2df,p) expta 0.992 1.363 1.358 1.427 1.070 1.071 125.3 109.5 108.2 107.1 121.1 126.0
1.011 1.373 1.383 1.418 1.081 1.082 124.9 110.2 107.4 107.5 121.2 125.6
1.008 1.376 1.378 1.425 1.081 1.082 125.1 109.8 107.7 107.4 121.1 125.8
1.007 1.375 1.378 1.425 1.080 1.081 125.1 109.8 107.7 107.4 121.2 125.7
1.005 1.370 1.373 1.421 1.077 1.078 125.1 109.8 107.7 107.4 121.3 125.7
0.996 1.370 1.382 1.417 1.076 1.077 125.1 109.8 107.7 107.4 121.5 125.5
Reference 19.
better agreement with the microwave data19 than do the B3LYP results. The optimized parameters of CZ at the MP2 and B3LYP levels are in good agreement with the reported X-ray data, but they show somewhat larger deviation from the experimental data than do the PR results. In particular, significant disagreement is observed between the X-ray and the optimized values for the pyrrole ring in CZ. The relatively large deviations in CZ may be attributed to the crystal packing force. The experimental bond lengths of the C-H and the N-H bonds are much shorter than the optimized ones. The large deviations from experiment may arise from the low scattering factors of hydrogen atoms in the X-ray diffraction experiment. The difference between the bond lengths of C2-C3 and C3C4 in PR is much smaller than that between those of C10-C11
Vibrational Spectra of Pyrrole and Carbazole
J. Phys. Chem., Vol. 100, No. 37, 1996 15075
TABLE 2: Equilibrium Geometrical Parameters of Carbazole in the Ground State parameter
HF/ 6-31G*
MP2/ 6-31G*
B3LYP/ 6-31G*
X-raya
C1-C2 C2-C3 C3-C4 C4-C11 C11-C12 C1-C10 C10-C11 C10-N C1-H C2-H C3-H C4-H N-H
1.380 1.397 1.380 1.391 1.455 1.389 1.401 1.378 1.076 1.076 1.075 1.076 0.992
Bond Length 1.392 1.409 1.391 1.403 1.443 1.399 1.419 1.383 1.088 1.088 1.087 1.089 1.012
1.393 1.407 1.392 1.400 1.450 1.397 1.421 1.387 1.087 1.087 1.086 1.087 1.008
1.390 1.398 1.395 1.400 1.467 1.395 1.404 1.414 0.897 0.981 1.070 0.983 0.964
C1-C2-C3 C2-C3-C4 C3-C4-C11 C4-C11-C12 C1-C10-C11 C2-C1-C10 C4-C11-C10 C10-C11-C12 C10-N-C13 C11-C10-N C2-C1-H C3-C2-H C4-C3-H C11-C4-H
121.5 120.5 119.2 134.0 121.8 117.7 119.5 106.5 109.4 108.8 121.0 119.3 120.0 121.5
Bond Angle 121.4 120.9 118.8 133.8 122.0 117.4 119.4 106.8 109.7 108.4 121.1 119.4 119.7 120.6
121.3 120.7 119.2 134.1 121.9 117.6 119.2 106.7 109.7 108.4 120.1 119.4 119.8 120.4
121.3 120.4 119.5 134.1 122.3 117.7 118.8 107.1 108.2 108.8 118.4 118.4 120.8 120.3
a
Reference 30.
and C11-C12 in the pyrrole ring in CZ, indicating that the C11-C12 bond has a relatively single bond character due probably to the delocalization effect in the phenyl ring. Assignment of Fundamentals. Pyrrole. We have performed a variety of normal vibrational mode analyses. We increased the size of the basis sets from 6-31G* to 6-311G(2df,p) in the hope that the use of the larger basis set could successfully reproduce fundamentals of PR. For a relatively larger molecule such as CZ, we employed the relatively smaller basis set of 6-31G*. The use of the large basis set such as 6-311G(2df,p) reduces the discrepancy between calculated and experimental frequencies for six fundamentals. The six fundamentals are in the low-frequency range from 461 to 878 cm-1. Quantum mechanical calculation indicates that the PR molecule includes 24 fundamentals having various symmetries of 9a1 + 3a2 + 4b1 + 8b2. Unambiguous identification of the 24 fundamentals is straightforward due to the well-separated spectral positions and to the sophisticated theoretical methods. The scaled fundamentals are listed in Table 3 together with experimental fundamentals.22 The scaling factor of 0.963 for B3LYP/6-31G* is a reported value by RP, and the factors of 0.963 and 0.968 for B3LYP/6-311G** and B3LYP/6-311G(2df,p), respectively, are optimized in this study to give the best fit for all the experimental frequencies. Interestingly, the optimized scaling factors for 0.963 for 6-311G** and 0.968 for 6-311g(2df,p) are the same as or similar to the value of 0.963 reported by RP.16 The rms deviations of computed frequencies from experiment are found to be 31.90, 43.86, 21.82, 18.66, and 17.43 cm-1 for HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, B3LYP/6-31G**, and B3LYP/6-311G(2df,p), respectively. It is noticed that this does not mean that the HF/6-31G* calculation is better than MP2/6-31G*. For HF/6-31G*, a relatively smaller scaling
factor of 0.8929 is applied, and a larger scaling factor near unity (0.950) is employed for MP/6-31G*. It can be seen that the B3LYP method reproduces fundamentals better than does the MP2 method. All of the experimental frequencies reported in the literature22 were measured by gas phase infrared absorption spectroscopy except those for a2 symmetry modes, which were measured by liquid phase Raman spectroscopy.20-22,26 The frequencies corresponding to the a2 mode are infrared inactive. Intermolecular motion may cause discrepancies between liquid phase frequencies and gas phase frequencies. One of the examples is shown in fundamental 4 (at 712 cm-1) that very much deviates from theory, although the deviation can be reduced significantly by using the B3LYP method with the 6-311G(2df,p) basis set. The B3LYP results of PR are not sensitive to the size of basis set. However, use of the expanded basis set 6-311G(2df,p) significantly improves agreement with experiment for fundamentals 1, 4, and 6, but unexpectedly, agreement with experiment worsens for the fundamentals corresponding to the C-H stretching vibrations. Nevertheless, the overall deviation is less at the B3LYP/6-311G(2df,p) level of calculation, and the assignment of the experimental frequencies is unambiguous. Carbazole. The B3LYP/6-31G* method was used to determine fundamental frequencies. Establishment of a one-to-one correspondence between the observed and calculated frequencies results in reassignment of some fundamentals of CZ. Fundamentals in the region ν e 1643 cm-1 are well separated, and thus the assignment is relatively straightforward. Assignments of fundamentals 51-59 are less straightforward due to the slight band separations and/or probably due to the band overlapping. Our frequencies scaled with a factor of 0.963, the value reported by RP, are in excellent agreement with fundamentals reported by BZ,11 giving rise to reassignment of some fundamentals as listed in Table 4. However, fundamentals ν52 and ν60 are still overestimated by the theory. Serious disagreement is, however, observed between the peak positions of the experimental frequencies and the HF values. As seen in Table 4, the HF calculation greatly underestimates fundamentals such as ν1, ν34, ν35, ν39, ν41, ν55, ν56, ν57, ν58, and ν59 and greatly overestimates ν28 and ν60. This is the reason why Xie et al. use the scaled factors in the wide range from 0.450 to 0.930 in the prediction of fundamentals of PR.27 The newly assigned fundamentals are in better agreement with the scaled fundamentals and are found to have a quite low value of the root mean square deviation of 21.4 cm-1 for B3LYP. By contrast, the fundamentals extracted by BZ deviate very much, 59.4 and 51.5 cm-1 for B3LYP and HF, respectively. Therefore we conclude that the newly assigned fundamentals are well correlated with the calculated fundamentals almost without exception and that among the methods the B3LYP calculations are quite reliable in predicting the fundamentals. From the reliable one-to-one correspondence, we derive the spectral positions of the missing lines and distinguish fundamentals from the various vibrational frequencies reported previously by BZ. Also our assigned fundamentals show a one-to-one correspondence with fundamentals of the fluorene molecule obtained experimentally31 and calculated with the B3LYP method.32 It is uncertain the reason why the vibrational frequencies of PR deviate largely from experiment in comparison with those of CZ. We only presume that the large deviation is attributed to the strained ring deformation and torsions in the pyrrole ring since the use of the expanded basis set reduces discrepancy between the calculated frequencies and observed frequencies corresponding to the vibrational modes.
15076 J. Phys. Chem., Vol. 100, No. 37, 1996
Lee and Boo
TABLE 3: Comparison of the Observed and Calculated Vibrational Spectra of Pyrrolea sym no.b freq a1
a2 b1
b2
d
HF/6-31G* IIR IRam
ν9 ν10 ν12 ν14
864 991 1037 1129
0.7 25.7 26.2 2.7
ν16
1382
ν18
1472
1.3 0.2 2.8 34.1
DPc
MP2/6-31G* B3LYP/6-31G* B3LYP/6-311G** B3LYP/6-311G(2df,p) exptd freq IIR freq IIR freq IIR freq IIR freq
0.56 857 0.71 1017 0.13 1078 0.21 1135
0.2 25.8 4.9 2.2
866 1006 1063 1138
0.1 26.4 7.8 2.6
865 1004 1061 1137
0.2 26.2 7.9 2.7
878 1006 1063 1143
0.2 27.8 8.0 2.1
880 1018 1074 1134
7.2
45.6 0.41 1398
5.8
1386
4.7
1384
4.4
1378
4.2
1391
15.7
14.9 0.27 1462
6.8
1464
9.0
1461
9.4
1462
6.2
1470
ν21 ν23 ν24 ν2 ν4 ν7 ν1 ν3 ν5 ν6 ν8
3063 10.2 33.0 0.48 3137 3.2 3085 0.1 202.5 0.13 3156 0.1 3507 83.8 82.6 0.28 3500 73.0 607 0.0 0.2 0.75 557 0.0 719 0.0 1.7 0.75 601 0.0 844 2.6 3.5 0.75 835 1.1 430 121.0 1.6 0.75 438 71.5 611 0.1 0.8 0.75 605 7.3 741 137.5 0.7 0.75 671 123.5 863 0.4 0.1 0.75 733 31.1 892 0.0 1.4 0.75 749 0.0
3141 3162 3534 607 647 845 431 618 705 788 839
7.3 0.1 49.4 0.0 0.0 1.2 79.9 0.9 114.4 5.4 0.0
3138 3160 3553 607 654 843 444 618 707 795 845
5.8 0.1 54.7 0.0 0.0 1.3 77.6 1.0 110.6 3.6 0.0
3148 3168 3570 615 674 858 461 627 711 811 851
4.6 0.2 58.0 0.0 0.0 1.2 75.1 0.0 137.2 1.4 0.0
3125 3148 3527 615 712 863 474 602 720 826 866
ν11 ν13
1041 1118
18.5 1.5
2.9 0.75 1039 6.2 0.75 1139
23.3 2.8
1039 1127
22.7 2.2
1036 1122
22.8 2.3
1040 1127
25.2 2.1
1049 1148
ν15
1283
1.2
0.3 0.75 1270
1.8
1273
1.8
1270
1.9
1281
1.1
1287
ν17 ν19
1424 1558
10.3 9.3
2.6 0.75 1445 0.8 0.75 1518
15.1 3.6
1420 1540
7.4 4.6
1416 1536
7.3 4.1
1412 1534
6.1 4.3
1424 1548
ν20 ν22
3052 3080
4.7 14.4
96.3 0.75 3127 5.8 0.75 3151
1.9 3.8
3129 3157
3.5 8.6
3127 3154
3.2 6.9
3137 3163
3.0 4.9
3116 3140
approx mode descrpte ring defm, C-H ip bend C-H ip bend, ring defm ring defm (C-C,C-N) str, C-H ip bend ring defm, C3,4-H ip bend C2,5-H ip bend, ring defm C-H str tot sym C-H str N-H str ring tor C-H oop bend, ring tor C-H oop bend, ring tor N-H oop bend ring tor C-H oop bend C-H oop bend ring defm, (N-H,C2-H) ip bend C-H ip bend, ring defm N-H ip bend, C2,5-H ip bend (C-H,N-H) ip bend, ring defm N-H ip bend, ring defm CdC str, ip (N-H,C-H) bend C-H str C-H str
a Vibrational frequencies in cm-1. b Mode numbers are extracted from the output result of the B3LYP/6-31G* calculation. c Depolarization ratio. Reference 22. e Mode descriptions are from the B3LYP/6-31G*; ip, in-plane; oop, out-of-plane.
Almost all the modes are delocalized over the whole molecule and thus cannot be assigned to several local bonds. This is a characteristic feature of cyclic compounds, particularly aromatic compounds.33 Therefore we provide in Tables 3 and 4 only the approximate mode descriptions. a1 Modes. Under C2V symmetry, the CZ molecule involves 60 fundamentals having various symmetries of 21a1 + 9a2 + 10b1 + 20b2. Twenty-one frequencies that we identify as a1 fundamentals are 220, 425, 658, 747, 856, 1012, 1107, 1136, 1205, 1288, 1307, 1334, 1449, 1481, 1576, 1625, 3039, 3055, 3077, 3084, and 3421 cm-1. It is noticed that the fundamental at 910 cm-1 identified as a a1 mode by BZ is replaced by a fundamental at 1307 (ν40). The fundamental at 1307 cm-1 is actually observed in the polarized infrared spectra and has already been assigned to a mode of a1 symmetry11 corresponding to the in-plane CH and CCC bending. The fundamental at 1307 cm-1 is also well correlated with the calculated values of 1300 (B3LYP/6-31G*) and 1266 cm-1 (HF/ 6-31G*). It is shown in the B3LYP calculation that most of the a1 fundamentals involve totally symmetric vibrations of C-H and/ or N-H in-plane bending and stretching, and ring deformations. a2 Modes. Since a2 modes are infrared inactive and Raman active, there are many unidentified spectral positions as shown in Table 4. Only two fundamentals at 104 and 299 cm-1 are observed in the Raman spectrum.11 Straightforward identification of the a2 fundamentals is impossible due to the infrared inactive vibrations and to the low intensities in the Raman spectra. Our B3LYP calculations predict nine fundamentals identifiable as a2, 147, 286, 438, 563, 727, 762, 831, 891, and 930 cm-1. Most of the fundamentals correspond to C-H outof-plane bending and ring torsions.
b1 Modes. Among 10 fundamentals attributable to b1, nine fundamentals identified correspond to 139, 310, 445, 566, 722, 741, 830, 880, and 926 cm-1. As seen in Table 4, the fundamental at 830 cm-1 is a new member instead of the peak at 1152 cm-1, which has previously been assigned as a b1 fundamental by BZ.11 It is noticed that the peak at 830 cm-1 is not observed in the crystal spectra but is observed in massselective ground-state vibrational spectra of jet-cooled CZXe vdW complexes.5 Fundamental 4 (271 cm-1 for B3LYP/ 6-31G*) is not observed experimentally, although the theoretical intensity is as high as 26.93 for B3LYP and 88.54 for HF. Fundamental 1 is observed experimentally, although the theoretical intensity is much lower than the ν4 intensity. This may be attributed to the inadequacy of the HF and B3LYP methods using 6-31G* methods in predicting the intensities of the low frequencies of the molecules. The nine fundamentals are in excellent agreement with our calculations. Most of the fundamentals involve C-H out-ofplane bending and ring torsions. b2 Symmetry. Among the 20 b2 modes, only 19 modes can we identify: 505, 548, 616, 835, 995, 1022, 1118, 1158, 1204, 1233, 1320, 1380, 1452, 1490, 1594, 1643, 3030, 3050, and 3094 cm-1. Most of the vibrations include C-H in-plane bending and stretching modes, and ring deformations. Among these fundamentals, the peak at 1643 cm-1 is a new member for the b2 group. It is reported that the fundamental at 1643 cm-1 is observed as a shoulder in the polarized infrared spectra.11 The low intensities may lead to the wrong identification in the assignments of fundamentals. Serious disagreement in fundamental ν52 is observed between our calculation and the reported value by BZ. If we include the value for ν52 of 2940 cm-1 as one of the fundamentals, the
Vibrational Spectra of Pyrrole and Carbazole
J. Phys. Chem., Vol. 100, No. 37, 1996 15077
TABLE 4: Comparison of the Observed and Calculated Vibrational Spectra of Carbazolea HF/6-31G* sym
no.b
freq
a1
ν3 ν8 ν15 ν18 ν24
a2
b1
b2
exptd
B3LYP/6-31G*
IIR
IRam
DPc
freq
IIR
BZe
newf
refg
210 412 640 724 852
0.41 1.47 0.21 0.00 0.72
1.02 6.61 1.02 21.96 22.11
0.35 0.27 0.15 0.12 0.16
212 419 644 731 856
0.28 1.14 0.56 0.01 0.26
220 425 658 747 856
214 430 652 746 868
ν30 ν32 ν34 ν36 ν39 ν40 ν42 ν44 ν46 ν48 ν51 ν53 ν55 ν57 ν59 ν60 ν2 ν5 ν9 ν13 ν17 ν20 ν22 ν26 ν27 ν1 ν4 ν6 ν7 ν12 ν16 ν19 ν21 ν25 ν28
998 1080 1093 1174 1227 1266 1296 1442 1479 1580 1631 2995 3003 3013 3025 3499 145 289 441 568 747 771 861 948 982 93 225 313 422 559 728 755 858 947 983
0.67 19.32 0.92 5.22 5.20 21.15 0.25 48.31 0.23 2.42 4.07 2.50 1.69 70.16 7.37 75.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.14 88.54 30.92 8.02 10.67 30.91 121.01 2.23 3.38 0.16
45.16 20.76 5.57 54.19 20.12 124.64 82.70 21.67 49.66 70.64 213.17 38.79 153.82 52.56 552.40 90.96 0.03 9.04 0.63 0.06 2.27 0.03 0.84 0.65 0.21 0.59 1.53 0.62 0.01 0.00 0.34 0.53 5.21 0.12 0.03
0.12 0.14 0.16 0.23 0.12 0.30 0.24 0.50 0.30 0.60 0.39 0.72 0.69 0.41 0.11 0.21 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
1008 1095 1140 1195 1273 1300 1336 1439 1477 1571 1619 3063 3070 3079 3091 3530 147 286 438 563 727 762 831 891 930 101 271 338 418 555 714 735 826 891 932
0.27 2.16 6.56 6.22 4.81 0.40 9.50 32.42 0.01 0.01 3.54 3.81 0.99 58.94 5.70 47.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.00 26.93 70.00 6.62 10.86 41.76 65.63 0.37 1.49 0.00
220 425 658 747 856 910 1012 1107 1136 1205 1288
1012 1107 1136 1205 1288 1307 1334 1449 1481 1576 1625 3039 3055 3077 3084 3421 104 299
1016
139 ? 310 445 566 722 741 830 880 926
101
ν10 ν11 ν14
491 541 605
5.36 0.61 7.49
0.77 10.06 0.05
0.75 0.75 0.75
495 542 608
3.93 0.16 6.09
ν23 ν29 ν31 ν33 ν35 ν37 ν38 ν41 ν43 ν45 ν47 ν49 ν50 ν52 ν54 ν56 ν58
824 974 1006 1098 1113 1187 1201 1262 1384 1460 1492 1592 1613 2994 3001 3012 3024
7.43 3.48 2.31 44.77 18.87 38.16 80.46 5.46 42.67 52.42 47.86 7.41 53.24 0.01 7.38 7.31 69.98
1.34 0.64 0.13 0.01 15.33 6.00 2.06 1.15 2.19 0.93 0.91 10.05 6.02 26.01 46.53 120.36 6.46
0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
834 982 1012 1108 1147 1200 1224 1320 1389 1456 1488 1576 1605 3063 3069 3079 3090
2.27 4.47 3.61 8.19 0.22 0.63 76.92 67.08 11.11 32.36 35.23 1.93 39.34 0.04 4.01 5.90 58.19
1334 1449 1481 1576 1625 3039 3055 3077 3084 3421 104? 299
139 310 445 566 722 741 880? 926 1152 505 548 616 737 835 995 1022 1118 1158 1204 1233 1320 1380 1452 1490 1594 2940 3030 3050 3094
505 548 616 835 995 1022 1118 1158 1204 1233 1320 1380 1452 1490 1594 1643 ? 3030 3050 3094
1286
552 628 844
approx mode descrpth ring defm ring defm ring defm ring defm, C-H ip bend ring defm, C-H ip bend ring defm, C-H ip bend ring defm, C-H ip bend C-H ip bend C-H ip bend + ring defm C-H ip bend + ring defm C-H ip bend, ring defm C-H ip bend + ring defm C-H ip bend + ring defm C-H ip bend + ring defm C-H ip bend + ring defm C-C str C-H str C-H str C-H str tot sym C-H str N-H str ring tor ring tor C-H oop bend + ring tor ring tor C-H oop bend, ring tor C-H oop bend + ring tor C-H oop bend, ring tor C-H oop bend, ring tor C-H oop bend, ring tor N-H oop bend + ring tor N-H oop bend, ring tor N-H oop bend ring tor ring tor, C-H oop bend ring tor + C-H oop bend C-H oop bend + ring tor C-H oop bend, ring tor C-H oop bend, ring tor C-H oop bend, ring tor ring defm C-H ip bend + ring defm C-H ip bend + ring defm ring defm, C-H ip bend ring defm, C-H ip bend ring defm, (C-H,N-H) ip bend C-H ip bend, ring defm (C-H,N-H) ip bend N-H ip bend C-H ip bend + ring defm C-H ip bend + ring defm, N-H ip bend N-H ip bend, C-H ip bend + ring defm C-H ip bend + ring defm, N-H ip bend (C-H + N-H) ip bend + ring defm (C-H + N-H) ip bend + ring defm C-C str, N-H ip bend C-H str C-H str C-H str C-H str
fluorenei 217 421 628 743 857 1016 1089 1143 1186, 1231 1291 1349 1440 1480 1570 1612 3048 3064 3072 3094 134j 269j 427j 556j 718j 772, 788j 852j 905j 943j 119 260 410 470 693 735 841 873 910, 950 487 542 618 773 994 1023 1103 1146 1172 1188 1303 1336 1440 1471 1582 1635 3040 3062 3084
a Vibrational frequencies in cm-1. b Mode numbers are extracted from the output result of the B3LYP/6-31G* calculation. c Depolarization ratio. The italicized numbers indicate the previous assignment by Bree and Zwarich; the numbers noted by bold face refer to our new assignment. e Assigned by Bree and Zwarich (ref 11). f Our vibrational frequencies assignment on the basis of the ab initio calculations. g In supersonic molecular beam study from ref 4 except for ν39 (1286 cm-1) from ref 2. h Mode descriptions are from the B3LYP/6-31G*; ip, in-plane; oop, out-of-plane; the modes assigned are sorted in the order of their contributions to the vibrational motions. i The experimental values from ref 31. j Fundamentals calculated with the B3LYP/6-31G* method (ref 32). d
rms values turned out to be too large, 27.3 and 34.6 cm-1 for the B3LYP and HF calculations, respectively. Maximum
deviation of the B3LYP calculation from experiment is less than 39 cm-1 except for the N-H stretching mode, which deviates
15078 J. Phys. Chem., Vol. 100, No. 37, 1996 by 109 cm-1. Also the ab initio study indicates that the fundamental has a very low intensity of 0.04 for B3LYP and 0.01 for HF. Thus the large deviation of 123 cm-1 and the low intensity of ν52 suggest that the fundamental reported by BZ (2940 cm-1) may be the result of wrong identification. Acknowledgment. The present studies were supported by the Basic Science Research Institute Program, Ministry of Education, Korea, 1995-1996, Project No. BSRI-95-3432, which is gratefully acknowledged. B.H.B. is grateful to Center for Molecular Science (CMS) for partial financial support. S.Y.L. thanks CMS for a postdoctoral fellowship. References and Notes (1) Leutwyler, S.; Bo¨siger, J. Chem. ReV. 1990, 90, 489. (2) Honegger, E.; Bombach, R.; Leutwyler, S. J. Chem. Phys. 1986, 85, 1234. (3) Bu¨rgi, T.; Droz, T.; Leutwyler, S. Chem. Phys. Lett. 1994, 225, 351. (4) Droz, T.; Bu¨rgi, T.; Leutwyler, S. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 429. (5) Droz, T.; Bu¨rgi, T.; Leutwyler, S. J. Chem. Phys. 1995, 103, 4035. (6) Auty, A. R.; Jones, A. C.; Phillips, D. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1219. (7) Isoshima, T.; Wada, T.; Zhang, Y.-D.; Brouye´re, E.; Bre´das, J.-L.; Sasabe, H. J. Chem. Phys. 1996, 104, 1042. (8) Klo¨pffer, W. J. Chem. Phys. 1969, 50, 2337. (9) Bree A.; Zwarich, R. J. Chem. Phys. 1968, 49, 3355. (10) Chakravotry, S. C.; Ganguly, S. C. J. Chem. Phys. 1970, 52, 2760. (11) Bree A.; Zwarich, R. J. Chem. Phys. 1968, 49, 3344. (12) (a) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (b) Devlin, F. J.; Finley, J. W.; Stephens, P. J.; Frisch, M. J. J. Phys. Chem. 1995, 99, 16883. (13) (a) Handy, N. C.; Maslen, P. E.; Amos, R. D.; Andrews, J. S.; Murray, C. W.; Laming, G. J. Chem. Phys. Lett. 1992, 197, 506. (b) Handy,
Lee and Boo N. C.; Murray, C. W.; Amos, R. D. J. Phys. Chem. 1993, 97, 4392. (14) El-Azhary, A. A.; Suter, H. U. J. Phys. Chem. 1995, 99, 12751. (15) Wheeless, C. J. M.; Zhou, X.; Liu, R. J. Phys. Chem. 1995, 99, 12488. (16) Rauhut, G.; Pulay, P. J. Phys. Chem. 1995, 99, 3093. (17) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993, 98, 5612. (18) Langhoff, S. R. J. Phys. Chem. 1996, 100, 2819. (19) Nygaad, L.; Nielson, J. T.; Kirchheiner, J.; Maltesen, G.; RastrupAndersen, J.; Sorensen, S. O. J. Mol. Struct. 1969, 3, 491. (20) Lord, R. C.; Miller, F. A. J. Chem. Phys. 1942, 10, 328. (21) Lautie, A.; Novak, A. J. Chem. Phys. 1972, 69, 1332. (22) Navarro, R.; Orza, J. M. An. Quim., Ser. A 1983, 75, 557. (23) Mirone, P. Gazz. Chim. Ital. 1956, 86, 165. (24) Morcillo, J.; Orza, J. M. An. Real. Soc. Esp. Fis. Quı´m. B 1960, 56, 231, 253. (25) Cataliotti, C.; Paliani, G. Can. J. Phys. 1975, 54, 2451. (26) Sicorov, N. K.; Kalashnikova, L. P. Opt. Spectrosc. 1968, 26, 247. (27) Xie, Y.; Fan, K.; Boggs, J. E. Mol. Spectrosc. 1986, 58, 401. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision B.2; Gaussian Inc.: Pittsburgh, PA, 1995. (29) Lahiri, R. N. Acta. Crystallogr. 1969, 25, 127. (30) Batra, I. P.; Bagus, P. S.; Clementi, E.; Seki, H. Theor. Chim. Acta 1974, 32, 279. (31) Bree, A.; Zwarich, R. J. Chem. Phys. 1969, 51, 912. (32) Lee, S. Y.; Boo, B. H. J. Phys. Chem. 1996, 100, 8782. (33) Szczepanski, J.; Vala, M.; Talbi, O.; Parisel, O.; Ellinger, Y. J. Chem. Phys. 1993, 98, 4494.
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