17786
J. Phys. Chem. 1996, 100, 17786-17790
Density Functional, Hartree-Fock, and MP2 Studies on the Vibrational Spectrum of Phenol D. Michalska* and D. C. Bien´ ko Institute of Inorganic Chemistry, Technical UniVersity of Wrocław, Smoluchowskiego 23, 50-370 Wrocław, Poland
A. J. Abkowicz-Bien´ ko and Z. Latajka Faculty of Chemistry, UniVersity of Wrocław, Joliot-Curie 14, 50-383 Wrocław, Poland ReceiVed: May 13, 1996; In Final Form: August 16, 1996X
Vibrational spectra of phenol are calculated with ab initio Hartree-Fock and MP2 methods as well as with density functional theory (DFT) using the 6-31G(d,p) basis set. A clear-cut assignment of the vibrational frequencies is reported on the basis of the potential energy distribution (PED) calculated at the three theory levels. These results are compared with the previously reported ab initio data and with the experiment. Several reassignments are suggested for the phenol modes: OH bend, 9b, 17a, 8a, and 8b. It is demonstrated that the MP2/6-31G(d,p) level fails in predicting the frequencies for two modes, labeled 14 and 4 in phenol. The calculated frequency of the former is about 140 cm-1 too high, and that of the latter is 220 cm-1 too low. Very similar results at the MP2 level have been reported earlier for the corresponding ω14 and ω4 in benzene. The HF/6-31G(d,p) method provides incorrect results for the modes related to the OH bend in phenol. It is remarkable that DFT with the BLYP functional gives excellent agreement between the calculated and observed frequencies for phenol. In particular, the modes 4 and 14 are predicted to within 11 and 6 cm-1, respectively, which confirms the reliability of DFT (BLYP) in reproducing vibrational frequencies.
Introduction Vibrational spectra of phenol and clusters with water, methanol, and ammonia have gained much interest in recent years.1-14 Phenol is the simplest aryl alcohol and serves as a basic unit of larger molecules, e.g., tyrosine residues in proteins. The hydrogen-bonded phenol complexes with simple solvent molecules are important models for investigation of H-bonding and proton transfer in proteins and nucleic acids. The intra- and intermolecular vibrations of phenol clusters have been extensively studied with cluster ion dip spectroscopy (CIDS),1-2 dispersed fluorescence,2-6 resonant two photon ionization (R2PI),4,7-8 ionization detected stimulated Raman spectroscopy (IDSRS),9 and other laser spectroscopic techniques in molecular beam experiments.6,10 To help assign the observed vibrational bands, several ab initio Hartree-Fock calculations and normal coordinate analyses have been performed for these systems.4,5,10-14 It is anticipated that the normal modes of phenol which involve stretching, bending, and torsion vibrations of the OH group undergo substantial changes in frequency due to hydrogen bonding. The frequency shifts of these modes provide direct information on the H-bond interaction. Therefore, unequivocal assignment of these “marker bands” in the infrared spectrum of a bare phenol is indispensable for a clear understanding of the spectral changes in the hydrogen-bonded complexes. Unfortunately, despite extensive and careful investigations by previous workers,4,10-14 some inconsistencies still exist in the reported ab initio results concerning, in particular, the assignment of the OH in-plane bending mode of phenol. This vibration has been observed at 1176.5 cm-1 in the infrared spectrum of phenol vapor.15,16 Schu¨tz et al.11 first performed the HF/6-31G(d,p) studies and assigned the frequency at 1197.3 cm-1 (1081 scaled value) to the OH-bending vibration. * Author for correspondence. X Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)01376-7 CCC: $12.00
In the other studies with a more elaborate basis set4 a very similar assignment has been made. Furthermore, it has been suggested that the frequency of this band increases by about 115 cm-1 upon complexation with a water molecule. Gerhards et al.13 performed HF/4-31G(d) calculations for phenol (Ph) and the Ph‚CH3OH complex and assigned the frequencies according to refs 4 and 11. Recently, Schiefke et al.10 carried out experimental studies complemented by the HF/6-31G(d,p) on the Ph‚NH3 complex and made a different assignment for the OH-bending vibration. Moreover, these authors10 predicted frequency shifts different from those reported in the previous ab initio calculations. Vibrational frequencies of phenol have also been computed at the MP2/6-31G (d,p) level.12 Unfortunately, the assignment of the MP2 frequencies is very ambiguous since some of the calculated modes of the a′ symmetry have been attributed to the experimental a′′ modes and vice versa. For instance, the MP2/6-31G (d,p) frequency 633 cm-1 (a′ symmetry) has been assigned to the ring-puckering mode (no. 4) observed at 686 cm-1; however, the latter is of the a′′ symmetry. In our earlier MP2/6-31G (d,p) studies on carbon clusters (C4)17 and other small molecules,18 we have demonstrated that this level of theory enabled us to determine the structure of these molecules and to predict their infrared spectra. Handy and co-workers,19,20 as well as Raghavahari et al.,21 have shown however, that the MP2 method is deficient for certain vibrations of multiple bonds and also for some asymmetric vibrations, such as the one in ozone. In those cases, density functional theory appears to be more reliable for prediction of frequencies than the MP2 method.19,20 In this paper, we present the results from calculations of the vibrational spectra of phenol at three levels: ab initio HartreeFock and MP2 as well as density functional theory (DFT) with the BLYP functional.22,23 The 6-31G (d,p) basis set has been used in all calculations in order to facilitate comparison with the previously reported ab initio results. © 1996 American Chemical Society
Vibrational Spectrum of Phenol
Figure 1. Comparison of the optimized geometries with the available experimental data for phenol.
To get a detailed insight into the nature of normal modes, the potential energy distributions (PEDs)24 were calculated at each theory level. This enabled us to make unequivocal assignment of the harmonic frequencies of phenol. Methods The HF, MP2, and DFT(BLYP) calculations were performed using the 6-31G (d,p) basis set with the Gaussian 92/DFT program25 on the IBM RS/6000 SP2 computer. For each theory level the geometry optimization of phenol was performed under relaxation of all internal degrees of freedom assuming planarity of the molecule (Cs symmetry). The harmonic vibrational frequencies and eigenvectors as well as infrared intensities were subsequently calculated using the analytical second derivatives for ab initio methods and numerical differentiation of analytical gradients for the BLYP functional. Then the force constant matrices obtained in the Cartesian coordinates were transformed to the internal coordinates which allowed us to perform normal coordinate analysis as described by Schachtschneider.26 The matrices of the potential energy distribution (PED)24 were calculated at three theory levels. PED elements provide a measure of each internal coordinate’s contribution to the normal coordinate. The nonredundant set of 33 symmetrized (3n - 6) internal coordinates for phenol has been derived as recommended by Fogarasi and Pulay.27 Perhaps the most important information obtained from such calculations is the extent of mixing of various internal coordinates in the normal mode. It seems that such data are more reliable for making vibrational assignment than the comparison of diagrams of atomic displacements, especially in the case of strongly coupled modes. A. Geometry. Although the theoretical geometries (i.e., minimum energy geometries) for phenol are not the main focus of this investigation, we should like to comment briefly on these results. The bond lengths and angles optimized at the three theory levels are displayed in Figure 1 along with the available experimental data.28 It is apparent that the DFT/BLYP method with 6-31G (d,p) basis set yields bond lengths for phenol that are too long. The atom distances are overestimated as follows: the C-H by about 1-1.6%, the C-C by 0.9%, the O-H by 2.2%, and the C-O by 1.3%, as compared to the experiment. The DFT prediction for the C-C-O bond angle lies between the MP2 and HF values. Both the DFT and MP2 methods
J. Phys. Chem., Vol. 100, No. 45, 1996 17787 produce very similar values for the C-O-H bond angle being closer to the experiment than that computed at the HF level. It follows from these results that the MP2/6-31G(d,p) geometry shows the best overall agreement with experiment, as it was noted earlier.12 The agreement between the DFT/BLYP-calculated structure of phenol and experiment would have been better if a more extended basis set were used within this approximation. Handy and co-workers19,20 have demonstrated in the density functional studies with the BLYP functional that the use of the larger basis sets (TZ2P or TZ2Pf) yields significant improvement of the calculated bond lengths for benzene. In our work we have used the 6-31G (d,p) basis set for both geometry optimization and frequency calculation, to compare our results with those previously obtained in the ab initio studies of phenol.4,10-12 It is interesting to note that, although the DFT/BLYP/6-31G (d,p) level overestimates both the O-H and the C-O bond length, it produces frequencies of the corresponding O-H and C-O stretching vibrations in excellent agreement with experiment, as we will show in the next section. B. Vibrational Spectra. The calculated harmonic frequencies and infrared intensities are shown in Table 1 and compared to the available experimental data.9,15,16,29 The discrepancies concerning empirical assignment of some bands have also been indicated in the table. The labeling of the vibrational modes is taken from Bist et al.,15 since it has been used in the earlier ab initio studies.4,10-13 It should be noted, however, that it differs, for some modes, from the convention used by Varsanyi30 and other authors,9,31 namely the modes designated as 1, 12, 9b, 15, and 18b in ref 15 correspond, respectively, to 12, 1, 15, 18b, and 9b in refs 9, 30, and 31. The energetic sequence of the experimental frequencies given in Table 1 is followed by the same sequence of normal modes calculated with the DFT method. Minor inconsistencies appear in the order of frequencies obtained at both the MP2 and HF levels. All the vibrational frequencies calculated at the HF/631G(d,p) level are overestimated with respect to the experimental values; therefore, they were scaled by the factor 0.90283, derived for phenol by Schu¨tz et al.11 In Table 2 is given a detailed description of the normal modes of phenol (vibrational assignment) based on the potential energy distribution (PED) obtained from the DFT, MP2, and HF calculations. It should be emphasized that these three theoretical methods yielded almost identical or very similar PED values for 26 corresponding normal modes of phenol. Different PED’s obtained for the remaining seven modes have been indicated under the Table 2. OH Vibrations. The most indicative frequency shifts, due to complexation of phenol, are associated with the OH stretching, OH bending, and the torsion vibration about the C-O axis. As can be seen from Table 1, the frequency of the OHstretching vibration (Q33) calculated with the DFT method, 3664.2 cm-1, is in nearly perfect agreement with the recently reported experimental value, 3656.7 cm-1.9 The frequency of this mode obtained at the MP2 level is overestimated by about 6%, whereas that computed at the HF level is overestimated by 14.8% with respect to the experiment. As already mentioned, an assignment of the OH in-plane bending vibration is still controversial in the ab initio calculated spectra.4,10-12 Bist et al.15 have assigned this mode to a very intense band, observed at 1176.5 cm-1 in the infrared spectrum of phenol vapor. The other authors29-31 have confirmed this assignment and also noted that the OH in-plane bending enters into strong
17788 J. Phys. Chem., Vol. 100, No. 45, 1996
Michalska et al.
TABLE 1: Comparison of Experimental Vibrational Frequencies (νj, cm-1) and Infrared Intensities (IRel) with the Theoretical Harmonic Frequencies (ω j , cm-1) and Infrared Intensities (A, km mol-1) Calculated with Density Functional Theory Using the BLYP Functional (DFT/BLYP) and with ab Initio MP2 and HF Methods expta mode no.
sym
label
νj
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q31 Q32 Q33
a′′ a′′ a′ a′′ a′′ a′ a′ a′′ a′′ a′′ a′ a′′ a′′ a′′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′
11 OH torsion 18b 16a 16b 6a 6b 4 10b 10a 12 17b 17a 5 1 18a 15 9b 9a OH bend 7a 3 14 19b 19a 8b 8a 13 7b 2 20b 20a OH stretch
244.5 309.2 403.1 408.5 502.8 526.6 618.7 685.9 750.6 817.2 823.2 881 958b,c (995.2?a) 972.5 999.3d 1026.1d 1072.4 1150.7 1168.9 1176.5 1261.7d 1277.4 1343 1472 1501 1603b,d (1610a?) 1610b,d (1603a?) 3027 3049 3074.5c (3063a) 3070a(?) 3086.6c 3656.7c
DFT (BLYP)/6-31G(d,p) ω j
A
ω je
225.4 384.6 394.0 406.6 499.2 520.7 616.1 674.8 732.2 788.9 805.0 846.2 911.1 939.5 982.7 1017.4 1069.8 1156.6 1165.7 1173.3 1254.0 1329.7 1349.3 1468.8 1495.5 1589.5 1602 3079 3100.2 3107.9 3123.9 3131.4 3664.2
0.2 108 9 0.9 6 1 0.3 8 44 0.0 17 3 0.0 0.1 2 3 10 8 5 146 64 7 29 28 34 37 32 19 0.2 27 27 7 25
226.8 327.5 404.9 403.3 522.0 535.1 632.6 464.8 736.0 814.3 837.1 849.7 904.8 913.4 1024.8 1064.5 1117.0 1205.6 1218.1 1221.0 1320.3 1388.2 1478.5 1531.9 1567.2 1681.2 1695.6 3241.9 3261.4 3269.6 3284.3 3290.6 3881.8
Irel 47 5 0.0 26 5 50 52 0.0 20 12 0.0 1 5 8 10 38 70 80 62 31 23 54 70
50
MP2/6-31G(d,p)
HF/6-31G(d,p)
A
ω jf
A
ω j scg
0.8 126 10 0.9 3 1 0.3 4 78 0.2 18 0.7 0.5 0.1 0.3 5 12 10 0.5 157 66 22 12 22 54 27 39 12 0.1 16 15 5 53
256.2 314.2 440.6 461.2 568.2 574.3 678.6 767.8 846.7 924.2 892.0 996.0 1090.1 1111.4 1085.2 1122.8 1176.9 1197.0 1282.1 1291.0 1404.4 1488.6 1370.5 1635.2 1671.2 1797.8 1810.6 3326.4 3343.7 3354.1 3370.9 3379.6 4197.2
5 141 11 0.3 7 2 0.3 13 83 0.0 20 13 0.0 0.6 3 4 10 33 0.4 85 114 36 53 29 76 45 66 16 0.2 29 28 7 84
231 284 398 416 513 518 613 693 764 834 805 899 984 1003 980 1013 1063 1081 1157 1156 1268 1344 1238 1476 1509 1623 1635 3003 3019 3028 3043 3052 3789
a
The experimental frequencies were taken from ref 15a, otherwise as indicated: b Reference 16; c Reference 29; d Reference 9. e MP2/6-31G(d,p) frequencies first reported by Feller and Feyereisen12 (with incorrect assignment of several modes, as shown in this paper). f HF/6-31G(d,p)) frequencies first reported by Schu¨tz et al.11 (with incorrect assignment of the OH bend). g The HF frequencies were scaled by the factor 0.90283, derived in ref 11.
coupling with skeletal vibration of the same symmetry, which gives rise to another band at about 1340 cm-1 in the spectra of phenols. The latter corresponds to the mode 14 of benzene and is sensitive to the association conditions and to the deuteration of the phenolic OH group. Therefore, it has been concluded that the OH in-plane bending vibration contributes mainly to the fundamental at 1176.5 cm-1 (Q20) and also to the mode at 1343 cm-1 (Q23) in the spectrum of phenol vapor.29-31 It is remarkable that, of the three theoretical methods used in this work, only the DFT (BLYP) predicted both the frequencies and forms of these modes. It is seen from Table 1 that the DFT frequencies, 1173.3 cm-1 (Q20) and 1349.3 cm-1 (Q23), are in excellent agreement with the corresponding experimental data; the differences are only 3 and 6 cm-1, respectively. From the PED shown in Table 2, it is apparent that the mode Q20 has mainly the “OH-bend” character due to the predominant contribution (55%) from the δOH internal coordinate. Some mixing with the aromatic (C-C) stretch and CH bend is also noted. The normal mode 14 (Q23) can be described as a strongly coupled vibration involving (C-C) stretching, OH bending, and CH bending, which confirms earlier experimental assignment.29-31 The other two theoretical methods failed in predicting the nature of these modes. Although the MP2-calculated frequency of the mode Q20 (OH bend) is in fairly good agreement with the experimental value and the corresponding potential energy distribution is identical with that obtained from the DFT studies, the MP2 method gave the wrong results for the mode 14 (Q23). The MP2-calculated frequency of this planar vibration is
overestimated by 136 cm-1 . Moreover, mode 14 becomes an almost pure CdC stretching vibration (at the MP2 level), as shown in Table 2. From the examination of the carbon atom displacements, it is clear that they lead to one of the Kekule structures of the benzene ring. Further distortion of the molecule along this normal coordinate will eventually break the three C-C single bonds. It should be emphasized that very similar effects have been observed for the analogous mode 14 (B2u) of benzene calculated with the MP2 method using more extended basis sets.19,32 The MP2 frequency of mode 14 in benzene is about 150 cm-1 above the experimental value,19 and the form of this mode resembles that obtained in our studies. It appears that the MP2 description of this mode is incorrect. Unfortunately, the results obtained at the Hartree-Fock level for the phenol modes Q20 and Q23 are inconsistent with the experimental and the DFT results. According to the PED computed at the HF level, the OH in-plane bending vibration contributes only in 26% to mode Q20 (labeled “OH bend”) whereas it predominates (32%) in mode Q23 (these values are shown under the Table 2). Thus, one may anticipate that in the calculated vibrational spectrum of the H-bonded phenol complexes, at the Hartree-Fock level, mode 14 (Q23) will show a more significant frequency shift than mode Q20. And indeed, this result has been obtained in the ab initio HF/6-31G(d,p) studies on the phenol-ammonia complex10 in which the calculated mode 14 shows an upward frequency shift of 44.2 cm-1, whereas the mode ”OH bend” (Q20) shifts only by 22.8 cm-1. This is in agreement with the PED values presented in this work; however, it should be emphasized that the form of
Vibrational Spectrum of Phenol
J. Phys. Chem., Vol. 100, No. 45, 1996 17789
TABLE 2: Assignment of the Vibrational Modes of Phenol Based on the Potential Energy Distribution (PED) Calculated at the Three Theory Levels: DFT (BLYP), MP2, and HF (Atom Numbering Shown in Figure 1) mode no.
label
sym
assignment, PED (%)a,b
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q31 Q32 Q33
11 OH torsion 18b 16a 16b 6a 6b 4 10b 10a 12 17b 17a 5 1 18a 15 9b 9a OH bend 7a 3 14 19b 19a 8b 8a 13 7b 2 20b 20a OH strech
a′′ a′′ a′ a′′ a′′ a′ a′ a′′ a′′ a′′ a′ a′′ a′′ a′′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′
τ3 ring (52) + τ2 ring (18) + γCO(17) + τ1 ring (10) τ(O-H) (100) δCO(81) τ2 ring (76) + τ3 ring (24) γCO (46) + τ3 ring (30) + τ1 ring (13) δ2 ring def.(77)+ ν(C-O) (12) δ3 ring def.(83) τ1 ring (90) γC4H(31) + γCO(23) + γC3H(15) + γC2H(12) + γC5H(11) γC2H(53) + γC6H(22) + γC5H(17) ν(C-O) (25) + δ1 ring def.(19) + ν(C1-C2) (17)+ ν(C1-C6) (17) + δ2 ring def.(14) γC6H(42) + γC4H(26) + γC2H(21) + γC3H(17) γC3H(52) + γC5H(22) + γC6H(17) + γC2H(12) γC5H(44) + γC4H(22) + τ1 ring(13) + γC6H(12) + γC3H(10) δ1 ring def.(65)+ ν(C1-C6) (10) ν(C5-C4) (32) + ν(C4-C3) (26) + δCHc(25) ν(C3-C2) (22) + ν(C6-C5) (19) + δC6H(13) + ν(C4-C3) (11) + δC4H(11) + δC2H(10) δC4H(36) + δC5H(23) + δC6H(12) + δC3H(11) δC3H(27) + δC2H(26) + δC6H(14) + δC5H(10) δOH(55) + ν(C1-C6) (13) + δC6H(10) ν(C-O) (52) + ν(C-C)c (20) δC2H(18) + δC6H(18) + δC5H(18) + δC3H(14) + δC4H(12) ν(C-C)c (56) + δOH(21) + δC5H(22) δC4H(25) + δC3H(13) + ν(C6-C5) (13) + ν(C3-C2) (13) + δC6H(10) δC5H(19) + δC2H(16) + ν(C4-C3) (13) + δC3H(12) ν(C2-C1) (25) + ν(C5-C4) (22) ν(C1-C6) (21) + ν(C6-C5) (17) + ν(C3-C2) (16) + ν(C4-C3) (14) ν(C2-H) (90) + ν(C3-H) (10) ν(C5-H) (52) + ν(C4-H) (26) + ν(C3-H) (13) ν(C3-H) (58) + ν(C5-H) (28) ν(C4-H) (50) + ν(C6-H) (33) + ν(C3-H) (17) ν(C6-H) (61) + ν(C4-H) (19) + ν(C5-H) (18) ν(O-H) (100)
a
b c d
e f g
a Abbreviations: ν, stretching; δ, in-plane bending; γ, out-of-plane bending; τ, torsion; def., deformation; δ1, δ2, and δ3 ring deformations and τ1, τ2, and τ3 torsions are the linear combinations of internal coordinates for benzene ring taken from ref 27. b PEDs elements lower than 10% are not included. Different PEDs obtained with the HF or MP2 methods are indicated in the last column: (a) MP2, τ3(57) + τ1(19) + τ2(19); (b) MP2, γCO(81) + τ3(11); (c) MP2, τ1(81) + τ3(19); (d) MP2, γCHc(90) + CO(10); (e) SCF, δOH(26) + δC3H(26) + δC4H(19) + ν(C1-C6) (11); (f) SCF and MP2, +δOH(15); (g) MP2, ν(C-C)c(89); SCF, δOH(32) + ν(C-C)c (25) + δC2H(13) + δC4H(11) + δC6H(10). c Include all atoms.
these modes, predicted at the Hartree-Fock level, is not supported by the experimental data. In view of the results obtained in this work and the data reported by Schiefke et al.,10 it seems that both the assignment of the OH in-plane bending vibration in phenol and its frequency shift upon complexation, reported in the earlier ab initio studies at the HF/6-31G(d,p) level, are incorrect. The HF frequency 1197 cm-1 (1081 cm-1 upon scaling) assigned to the OH bend in refs 4 and 11-13 corresponds to our mode Q18. According to the PED for Q18, shown in Table 2, this mode should be assigned to the mixed CH in-plane vibrations, since the contribution from the OH bending motion is negligible (less than 2% at both the MP2 and DFT levels and only 7% at the HF level). In fact, this mode, labeled 9b,15 is observed in the spectrum of phenol vapor at 1150.7 cm-1 and its frequency is very well reproduced by the DFT method (1156.6 cm-1). Evans16 and Green et al.29 studied the OH torsional vibration in the spectra of monomeric phenol and its derivatives and concluded that it does not mix with the ring vibrations. This is in accordance with our results, shown in Table 2. The mode Q2 corresponds to the pure OH torsion vibration. As can be seen from Table 1, the DFT method somewhat overestimates the frequency of this mode. However, it should be noted that all the remaining frequencies in the low-frequency region 225800 cm-1, as well as the frequencies of the OH bending and OH stretching, calculated with the DFT method, are in a very good agreement with the experimental data. The MP2 frequency of the OH torsional vibration is overestimated by 18.3 cm-1, whereas the HF scaled frequency is
underestimated by 25.2 cm-1 with respect to the experimental value, 309.2 cm-1.15 CO Group. Six modes involve considerable motion of both the phenyl ring and CO group and are described as X-sensitive modes.15,30-31 These modes are labeled 7a (Q21), 12 (Q11), 6a (Q6), 16b (Q5), 18b (Q3), and 11 (Q1).15 The computed DFT and MP2 frequencies as well as the scaled HF frequencies of these modes are quite close to the corresponding experimental values. According to PED obtained at the three theory levels, the C-O stretching vibration contributes mainly to the band observed at 1261.5 cm-1 (Q21) and also to the band at 823.2 cm-1 (Q11). Phenyl Ring. The phenyl ring modes are due to the CH inplane bending, CH out-of-plane bending, and ring deformation vibrations. These modes are not particularly sensitive to the nature of the substituent. In phenol there are five modes associated with the CH in-plane bending vibrations: 18a (Q16), 15 (Q17), 9b (Q18), 9a (Q19), and 3 (Q22).15,29-31 As can be seen from Table 1, the frequencies of these modes calculated with the DFT (BLYP) method are in nearly perfect agreement with the corresponding experimental data. The MP2 frequencies are overestimated by about 4%, except for the mode 3 (Q22), which is computed with a larger error (8%). The scaled Hartree-Fock frequencies of the modes Q16, Q17, and Q19 agree well with the experimental values; however, that of Q18 is underestimated by 70 cm-1 and that of Q22 is overestimated by 67 cm-1. The infrared intensities of these modes computed at the DFT and MP2 levels are quite similar and can be compared with the
17790 J. Phys. Chem., Vol. 100, No. 45, 1996 relative experimental data; however, a large discrepancy is noted for mode Q19 (9a). This mode is observed in the infrared spectrum of phenol at 1168.9 cm-1, very close to the mode at 1176.5 cm-1 (Q20) of the same symmetry (a′).15 Both of these bands have a high intensity in the experimental spectrum, whereas the computed infrared intensities are different. For instance, the intensity of the former is very low, A ) 0.5 km/mol, and that of the latter is the highest (A ) 157 km/ mol) at the MP2 level. A plausible explanation of this effect is Fermi resonance which may occur in this range, as noted by Green et al.29 These two modes almost overlap; the difference between the calculated frequencies of Q19 and Q20 at the MP2 level is only 3 cm-1. In the anharmonic resonance coupling the weak mode Q19 may “borrow” intensity from a very intense fundamental, Q20, since the symmetry of these modes is the same. Assignment of the out-of-plane CH vibrations in phenol merits some discussion. As revealed by PED in Table 2 the modes Q9 (10b), Q10 (10a), Q12 (17b), Q13 (17a), and Q14 (5) are associated with the out-of-plane γCH vibrations. Numerous authors have reported that mode 17a occurs at a lower frequency than mode 5.16,29-31 Evans16 in the infrared spectrum of phenol assigned the bands at 958 and 972 cm-1 to modes 17a and 5, respectively. However, Bist et al.15 deduced that mode 17a occurs at 995.2 cm-1. From the results obtained in this work, it seems that the latter assignment is incorrect since the calculated frequency of mode 17a is always lower than that of 5, at the three theory levels. It is quite conceivable that the questioned frequency, 995.2 cm-1, observed in the spectrum of phenol, is due to some overtone or combination tone being in anharmonic resonance with a fundamental transition. It should also be noted that the three theoretical methods predict higher frequency for mode 8a than for 8b. Both of these modes correspond to the CdC aromatic stretching vibration in the benzene ring. This result is entirely consistent with the assignment reported in several experimental studies;16,29-31 however, it is opposite to that suggested by Bist et al.15 In view of our data, it seems that the assignments of modes 8a and 8b in ref 15 should be reversed. The most striking result obtained in this work is the fact that the frequency of the ring puckering mode, 4 (Q8), calculated at the MP2/6-31G(d,p) level is 220 cm-1 below the experimental value. Furthermore, a similar effect has also been reported for the corresponding mode 4 (B2g) in benzene which was calculated too low by as much as 300 cm-1 at the MP2/6-311G(d,p) level.32 Handy et al.19 have shown that in order to correct this error it is necessary to include f basis functions for MP2 calculations. The HF/6-31G(d,p) frequency for this mode in phenol (Q8) is too high by about 80 cm-1; however, this difference decreases upon frequency scaling. The DFT (BLYP) frequencies for this mode as well as for the remaining out-of-plane vibrations of phenol are in very good agreement with experiment. Evidently, the MP2/6-31G(d,p) level of calculations fails in predicting two vibrations of the aromatic ring, labeled 14 and 4, which correspond to the in-plane and out-of-plane bending vibrations, respectively. It should be noted that we have met such a failure of the MP2 method in calculating vibrational spectra of bicyclobutene (C4H4), which is nonplanar, highly strained molecule with the double-bond carbons significantly pyramidalized.33 At the MP2/6-31G(d,p) level, two modes were considerably shifted (one to higher frequencies and the other to lower frequencies) and good results were obtained with the TCSCF and two-reference CISD methods.33 Apparently, the description of some vibrations in such molecules requires ab initio methods based on multireference wave function.
Michalska et al. It is therefore remarkable that the DFT (BLYP) method overcomes this problem and reproduces the frequencies of phenol in excellent agreement with experiment. Acknowledgment. The authors thank the Wroclaw Centre of Networking and Supercomputing for the granted computer time. References and Notes (1) Stanley, R. J.; Castleman, A. W., Jr. J. Chem. Phys. 1991, 94, 7744. (2) Ebata, T.; Furukawa, M.; Suzuki, T.; Ito, M. J. Opt. Soc. Am. 1990, B7, 1890. (3) Abe, H.; Mikami, N.; Ito, M.; Udagawa, Y. J. Phys. Chem. 1982, 86, 2567. (4) Schu¨tz, M.; Bu¨rgi, T.; Leutwyler, S.; Fisher, T. J. Chem. Phys. 1993, 98, 3763. (5) Bu¨rgi, T.; Schu¨tz, M.; Leutwyler, S. J. Chem. Phys. 1995, 103, 6350. (6) Schmitt, M.; Henrichs, U.; Mu¨ller, H.; Kleinermanns, K. J. Chem. Phys. 1995, 103, 9918. (7) Fuke, K.; Kaya, K. Chem. Phys. Lett. 1983, 94, 97. (8) (a) Lipert, R. J.; Colson, S. D. J. Chem. Phys. 1988, 89, 4579. (b) Lipert, R. J.; Colson, S. D. Chem. Phys. Lett. 1989, 161, 303. (c) Lipert, R. J.; Colson, S. D. J. Chem. Phys. 1989, 94, 2358; J. Phys. Chem. 1989, 93, 135. (9) Hartland, G. V.; Henson, B. F.; Venturo, V. A.; Felker, P. M. J. Phys. Chem. 1992, 96, 1164. (10) Schiefke, A.; Deusen, C.; Jacoby, C.; Gerhards, M.; Schmitt, M.; Kleinermanns, K.; Hering, P. J. Chem. Phys. 1995, 102, 9197. (11) Schu¨tz, M.; Bu¨rgi, T.; Leutwyler, S. J. Mol. Struct. (THEOCHEM) 1992, 276, 117. (12) Feller, D.; Feyereisen, M. W. J. Comput. Chem. 1993, 14, 1027. (13) Gerhards, M.; Beckman, K.; Kleinermanns, K. Z. Phys. 1994, D29, 224. (14) Gerhards, M.; Kleinermanns, K. J. Chem. Phys. 1995, 103, 7392. (15) Bist, H. D.; Brand, J. C. D.; Williams, D. R. J. Mol. Spectrosc. 1967, 24, 402. (16) Evans, J. C. Spectrochim. Acta 1960, 16, 1382. (17) Michalska, D.; Chojnacki, H.; Hess, B. A., Jr.; Schaad, L. J. Chem. Phys. Lett. 1987, 141, 376. (18) Michalska, D.; Hess, B. A., Jr.; Schaad, L. J. Int. J. Quantum Chem. Symp. 1986, 29, 1127. (19) Handy, N. C.; Maslen, P. E.; Amos, R. D.; Andrews, J. S.; Murray, C. W.; Laming, G. J. Chem. Phys. Lett. 1992, 197, 506. (20) Handy, N. C.; Murray, C. W.; Amos, R. D. J. Phys. Chem. 1993, 97, 4392. (21) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Replogle, E. Chem. Phys. Lett. 1989, 158, 207. (22) Becke, A. D. Phys. ReV. A 1988, 38, 3098; J. Chem. Phys. 1993, 98, 5648. (23) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (24) Califano, S. Vibrational States; Wiley: New York, 1976. Mallick, P. K.; Strommen, D. P.; Kincaid, J. R. J. Am. Chem. Soc. 1990, 112, 1686. (25) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A.: Gaussian 92, Revision C; Gaussian Inc.: Pittsburgh, PA, 1992. (26) Schachtschneider, J. H. Vibrational Analysis of Polyatomic Molecules. Technical Report Nos. 231-64 and 57-65, Shell Development Co., Emeryville, CA. (27) Fogarasi, G.; Pulay, P. Ab initio Calculation of Force Fields and Vibrational Spectra. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: New York. 1985; Vol. 13, pp 162-163. (28) Pedersen, T.; Larsen, N. W.; Nygaard, L. J. Mol. Struct. 1969, 4, 59. (29) Green, J. H. S.; Harrison, D. J.; Kynaston, W. Spectrochim. Acta 1971, 27A, 2199. (30) Varsanyi, G. Vibrational Spectra of Benzene DeriVatiVes; Academic Press: New York, 1969. (31) Dollish, F. R.; Fateley, W. G.; Bentley, F. F. Characteristic Raman Frequencies of Organic Compounds; John Wiley and Sons: New York, 1974; Chapter 13. (32) Goodman, L.; Ozkabak, A. G.; Thakur, S. N. J. Phys. Chem. 1991, 95, 9044. (33) Hess, B. A.; Allen, W. D.; Michalska, D.; Schaad, L. J.; Schaefer, H. F., III. J. Am. Chem. Soc. 1987, 109, 1615.
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