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Analysis of vibrational spectra of chlorotoluene based on density function theory calculations
Spectrochimica Acta Part A 58 (2002) 1553– 1558 www.elsevier.com/locate/saa
Analysis of vibrational spectra of chlorotoluene based on density function theory calculations Zhengyu Zhou a,b,*, Hongwei Gao a, Li Guo a, Yuhui Qu a, Xueli Cheng a b
a Department of Chemistry, Qufu Normal Uni6ersity, Shandong, Qufu 273165, People’s Republic of China State Key Laboratory Crystal Materials Shandong Uni6ersity, Shandong, Jinan 250100, People’s Republic of China
Received 3 July 2001; accepted 27 July 2001
Abstract The conformational behavior and structural stability of chlorotoluene were investigated by utilizing ab initio calculations with 6-31G* basis set at restricted Hartree-Fock (RHF) and density function theory (DFT) levels. The vibrational frequencies of chlorotoluene were computed at the RHF and DFT levels. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. RHF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 10 cm − 1. Two hybrid DFT methods are found to yield frequencies, which are generally higher than the observed fundamental frequencies. When the calculated results are compared with ‘experimental’ frequencies, B3LYP method is found to be slightly more accurate for CH stretching modes. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Density functional theory; Vibrational spectra; Chlorotoluene molecule
1. Introduction In the past few years, the structural stability of toluene molecule have been investigated. But the analysis of vibrational spectra using DFT methods is very few. Modern vibrational spectrometry has proven to be an exceptionally powerful technique for solving many chemistry problems. It has * Corresponding author. Tel.: + 86-537445-6765; fax: + 86537445-8216. E-mail address: [email protected] (Z. Zhou).
been extensively employed both in the study of chemical kinetics and chemical analysis. Several theoretical methods are useful in analyzing vibrational spectra of organic molecules. These methods can be roughly divided into the following groups: classical mechanics, semi-empirical quantum mechanical methods, ab initio quantum mechanical method and ab initio followed by empirical scaling of the force constants. Ab initio molecular orbital calculation is the relatively successful approaches to vibrational problems of closed shell organic molecules. However, raw frequency values computed at the Hartree-Fock level
1386-1425/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 1 ) 0 0 6 0 9 - 6
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Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
contain known systematic errors due to neglecting electron correlation and basis set incompleteness resulting in overestimate of about 10– 12%. Therefore, it is necessary to scale frequencies predicted at the Hartree-Fock level. The most popular and accurate scaled ab initio approach is the scaled quantum mechanical (SQM) force field procedure which employs different scale factors for different coordinates. A less ambitious approach is to scale all the calculated frequencies or force constants by a constant [1–4]. Over the past two decades, scaled ab initio calculations have been quite successful in predicting vibrational spectra of closed shell organic molecules. However, the scaling requires considerable empirical knowledge and makes the scaling procedure arbitrary and difficult when the empirical knowledge is not readily available. For much open shell and some conjugated closed shell molecules, however, errors due to neglecting electron correlation are far from systematic and can not be corrected by a scaling procedure. Even for molecules as simple as toluene, effect of electron correlation already appears less systematic errors. Therefore, in many cases, the Hartree-Fock methods even fail to give a qualitatively corrected description. Recently, density functional theory (DFT) [5– 8] has been accepted by the ab initio quantum chemistry community as a cost-effective approach to molecular properties. Unlike the Hartree-Fork theory, DFT recovers electron correlation in the self-consistent Kohn-Sham procedure through the functions of electron density and gives good descriptions for systems, which require sophisticated treatments of electron correlation in the conventional ab initio, approach, so it is a cost effective and a reliable method. DFT calculations of vibrational spectra of small organic systems [9– 12] have shown promising conformity with experimental results. In a recent comprehensive study, Rauhut and Pulay [13] have shown that the raw BLYP and B3LYP frequencies and force constants approximate the experimental results much better than the Hartree-Fock results. To gain a better understanding of the performance and limits of different DFT methods as a general approach to the vibrational problems of organic molecules, we have focussed our attention
in this study on chlorotoluene molecule. It was found that the combination of Becke’s exchange and Lee-Yang-Parr’s correlation functional (BLYP) reproduces the observed fundamental vibrational frequencies satisfactorily. The B3LYP frequencies are generally higher than observed fundamental frequencies, but appear to be closer to the available ‘experimental’ harmonic frequencies.
2. Calculations All calculations were carried out using the Gaussian 94 program package. Five popular DFT methods are used in this study. They are: Slater’s (local spin density) exchange functional [14] in conjunction with Vosko-Wilk-Nusair correlation functional [15] (LSDA), Becke’s gradient-corrected exchange functional [16,17] in conjunction with Lee-Yang-Parr gradient-corrected exchange functional [18] (BLYP), Becke’s gradient-corrected exchange functional in conjunction with Perdew gradient corrected correlation functional [19] (BP86), Becke’s three-parameter method [20] with Perdew correlation functional (B3P86) and Becke’s three-parameter method with Lee-YangParr correlation functional (B3LYP). The 6-31G* basis set was used throughout. This basis set was chosen on the basis of the findings that the 631G* DFT results on structures, energies, and force constants are obviously superior to results of smaller basis sets [21]. Further enlarging the basis set, however, increases the computational cost significantly and, therefore, is not practical for studying larger systems. All molecular structures were fully optimized prior to analytic second derivative calculations and vibrational analysis.
3. Results and discussion
3.1. Structure Chlorotoluene belong to C1 point group. A comparison of the calculated CC, CCl and CH bond lengths of chlorotoluene by different methods is presented in Fig. 1. From experimental
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
values of literature[15], CC single bond length is 1.5037 A, , HC single bond length is 1.0853 A, and CCl bond length is 1.8247 A, for chlorotoluene. Taking account of the effect of conjugation, our calculated values of chlorotoluene molecule is in reasonable agreement with the above-mention experimental data. The HF/6-31G* bond lengths are slightly shorter, while the BLYP/6-31G* bond lengths are slightly exaggerated electron correlation effect while the HF theory neglecting this effect. Compared with the experimental values, the B3LYP/6-31G* bond lengths are the best.
3.2. Vibrational frequencies The calculated harmonic frequencies of chlorotoluene molecule are compared with observed frequencies in Table 1. All the assignments and activities are in good agreement with the earlier normal coordinate analysis and experimental determinations. In order to investigate the performance and limits of different DFT methods in predicting the vibrational frequencies, the mean deviation, mean absolute deviation and standard deviation (S.D.) between the calculated harmonic and observed fundamental vibrational frequencies for each method are also given in Table 2, respectively. It can be noted that the calculated results are harmonic frequencies while the observed frequencies contain anharmonic contributions. The latter is generally lower than the former due to the anhar-
Fig. 1. Comparison of the calculated structure parameters of chlorotoluene by different methods. The bond lengths are given in Angstroms. The experimental values are obtained from [15].
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monic nature of molecular vibrations. In principle, one should compare the calculated frequencies with experimental harmonic frequencies. However, as all the vibrations are more or less anharmonic, harmonic frequencies are not directly observable. Although they can be deduced theoretically, it requires detailed knowledge of both quadratic and anharmonic (cubic and higher) force constants and is only feasible for very small molecules. It should be pointed out that reproduction of observed fundamental frequencies more desirable practically because they are directly observable in a vibrational spectrum. Comparison, therefore, between the calculated and the observed vibrational spectra helps us to understand the observed spectral features. Results in Table 1 indicate that frequencies calculated by the two hybrid DFT methods are higher than observed fundamental frequencies but that B3LYP results are significantly closer to available ‘experimental’ harmonic frequencies for CH (D) stretching vibrations. The mean absolute and standard deviations between the observed and the calculated frequencies are 61.7 and 72.8 cm − 1 for B3LYP, 66.9 and 80.0 cm − 1 for B3P86, respectively. As we can see, most of the BLYP non-CH stretching frequencies are slightly lower than reliable experimental assignments, and the best agreement between the calculated and observed fundamental vibrational frequencies is achieved by the BLYP. The average mean absolute and standard deviations are 20.6 and 25.3 cm − 1, while for BP86 (21.5 and 27.4 cm − 1) and LSDA (32.2 and 41.7 cm − 1), the results are not as good as BLYP. According to above results, five DFT methods have similar accuracy when the calculated results compared with ‘experimental’ harmonic frequencies while B3LYP yields the slightly higher level of conformity. Compared with the observed frequencies, when the CH stretching vibrations are excluded, deviations of five DFT methods all reduce to some extent. B3P86 (66.9 and 80.0 cm − 1) gives the largest deviations in five DFT methods, whereas BLYP (20.6 and 25.3 cm − 1) and BP86 (21.5 and 27.4 cm − 1) perform very similarly with deviations of BLYP results being slightly smaller. These results indicate anharmonicity affects CH stretching modes most
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
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Table 1 Calculated and experimental fundamental vibrational frequencies of chlorotoluene Number
Experimenta
BLYP
LSDA
BP86
B3LYP
B3P86
HF
Assignment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
3074 3064 3055 3046 3043 3040 2982 1601 1583 1484 1461 1443 1320 1316 1247 1185 1168 1151 1130 1064 1010 974 944 912 882 881 813 785 742 674 604 603 531 446 387 305 245 92 28
3124 3114 3105 3096 3093 3090 3032 1600 1582 1499 1476 1458 1335 1331 1262 1200 1183 1166 1145 1079 1025 989 959 927 897 896 828 800 757 689 619 618 546 461 402 320 260 107 43
3144 3135 3124 3112 3111 3091 3028 1658 1640 1512 1468 1441 1428 1304 1270 1231 1169 1151 1146 1087 1046 996 962 926 896 895 825 823 774 693 691 616 555 473 400 313 267 106 19
3133 3120 3110 3100 3098 3088 3028 1612 1594 1496 1464 1455 1359 1319 1264 1208 1178 1161 1148 1080 1028 988 955 924 895 891 823 804 757 686 646 614 548 463 398 315 262 106 38
3211 3201 3192 3183 3180 3173 3114 1665 1646 1547 1516 1504 1369 1362 1313 1241 1214 1195 1185 1113 1058 1019 1000 968 932 924 858 826 786 712 666 635 568 480 415 328 272 111 39
3227 3217 3207 3197 3195 3183 3121 1681 1662 1550 1510 1506 1389 1363 1317 1251 1213 1194 1190 1116 1064 1020 1002 970 932 925 857 832 790 712 691 633 569 482 413 325 273 110 35
5662 3904 3346 3338 3327 3317 3310 3085 1776 1766 1730 1656 1588 1462 1348 1304 1285 1173 1131 1116 1108 1103 1065 1048 963 895 812 799 675 655 482 469 449 353 214 207 194 186 54
CH stre. CH stre. CH stre. CH ste. CH ste. CH ste. CH ste. CC stre.+CH ipb. CC ste. CH ipb. CC stre. CCH in-plane bend CCH in-plane bend CCH in-plane bend CCH in-plane bend CH ipb.+CC stre. CH ipb.+CC stre. CH ipb.+CC stre. CH ipb.+CC stre. CH ipb. CH ipb. CH wag. CH wag. CCl stre. CCl stre. CCl wag. CCl wag. CH wag. CH wag. CH wag. Ring bending Ring bending Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion
a
Values are obtained from [22].
significantly, as the experimental harmonic frequencies of the CH stretching modes are over 100 cm − 1 higher than the corresponding fundamental frequencies. As we can see, this CH stretching modes are of much higher energy do not couple with other fundamental vibrational modes and are less important than frequencies of the fingerprint region for chemical analysis.
The calculated harmonic frequencies of HF methods at 6-31G* basis set also listed in Table 1. As we can see, the worst agreement between the calculated and observed results is found with HF/ 6-31G* results (249.2 and 527.7 cm − 1). There is a large overestimation of the frequencies at HF level, this may be due to the slightly too short bond lengths resulting from neglecting electron
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
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Table 2 Mean deviations, mean absolute deviations and standard deviations between the calculated and observed fundamental vibrational frequencies
Mean deviation Mean absolute deviation Standard deviation
BLYP
LSDA
BP86
B3LYP
B3P86
HF
20.5 20.6 25.3
31.1 32.2 41.7
21.8 21.5 27.4
61.7 61.7 72.8
67.8 66.9 80.0
−35.0 249.2 527.7
correlation in the HF theory. Even the scale factors considered, the results are still worse than DFT methods. Even though B3LYP is superior to BLYP for many properties, the fact that the BLYP frequencies are closer to observed fundamental vibrational frequencies has important implications for interpreting observed vibrational spectra. As discussed by Rauhut and Pulay, the high level of conformity between BLYP results and the observed fundamental frequencies may be due to error cancellation. Our geometry optimization indicates that due to slight exaggeration of electron correlation by BLYP method, the BLYP bond lengths are slightly longer than the corresponding B3LYP bond distances. The BLYP force constants and vibrational frequencies are, therefore, slightly smaller than the corresponding B3LYP results. As the effect of anharmonicity is also to lower the vibrational frequencies, the high level of conformity between BLYP harmonic frequencies and the observed results is likely to be attributable to overestimation of the bond length by the BLYP method. Agreement between the experimental and simulated spectral features indicates that the BLYP infrared intensities are qualitatively correct. Therefore, the high level of conformity between the observed and calculated spectral features indicates that BLYP, without any empirical adjustment is a more straightforward and practical approach to deduce the observed fundamental vibrational frequencies for many molecules whose vibrational spectra are not well understood.
4. Conclusions DFT and HF calculations on the vibrational frequencies of chlorotoluene molecule have been carried out. On the basis of the comparison between calculated and experimental results, assignments of fundamental vibrational modes are examined. It is found that DFT using BLYP reproduces the observed fundamental vibrational frequencies very well with the mean absolute deviations about 20.6 cm − 1 and S.D. about 25.3 cm − 1 between the calculated and observed results. This accuracy is desirable for resolving disputes in vibrational assignments and provides valuable insight for understanding the observed spectral features. Therefore, it is a promising approach for identifying an unknown compound by comparing its vibrational spectrum with calculates results of a few candidates and the BLYP calculated results could serve as a guide for a further experimental search for the missing fundamentals of the target molecule. Furthermore, since the DFT results without any empirical adjustment can be compared directly with experimental results, it will gain more and more popularity in the calculation of vibration frequencies.
Acknowledgements This work was supported by the Natural Science Foundation of Shandong Province, the National Key Laboratory Foundation of Crystal
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Material and the National Natural Science Foundation of China (2967305).
References [1] P. Paulay, G. Fogarasi, G. Pongor, J.E. Boggs, A. Vargha, J. Am. Chem. Soc. 105 (1983) 7073. [2] P. Botschwina, Chem. Phys. Lett. 29 (1974) 98. [3] C.E. Blom, C. Altona, Mol. Phys. 31 (1976) 1377. [4] G. Fogarasi, P. Paulay, K. Molt, W. Sawodny, Mol. Phys. 33 (1977) 1565. [5] R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules. Oxford, New York, 1989. [6] R.O. Jones, O. Gunnarsson, Rev. Mol. Phys. 61 (1989) 689. [7] T. Ziegler, Chem. Rev. 91 (1991) 651. [8] W. Kohn, L.J. Sham, Phys. Rev. A140 (1965) 11133. [9] N.C. Handy, C.W. Murray, R.D. Amos, J. Phys. Chem. 97 (1993) 4392.
[10] X.F. Zhou, J.A. Krauser, D.R. Tate, A.S. Vanburen, J.A. Clark, P.R. Moody, R.F. Liu, J. Phys. Chem. 100 (1996) 16822. [11] Z.hou Zhengyu, D.u Dongmei, J. Mol. Struct. (Theochem) 505 (2000) 247. [12] Zhou Zhengyu, Fu Aiping, Du Dongmei, Int. J. Quant. Chem. 78 (2000) 186. [13] G. Rauhut, P. Pulay, J. Phys. Chem. 99 (1995) 3093. [14] J.C. Slater, Quantum Theory of Molecules and Solids, vol. 4, The Self Consistent Field for Molecules and Solids, McGraw, New York, 1974. [15] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [16] A.D. Becke, Phys. Rev. A38 (1988) 3098. [17] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B37 (1988) 785. [18] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 157 (1989) 200. [19] J.P. Perdew, Phys. Rev. B33 (1986) 8822. [20] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [21] J. Florian, B.G. Johnson, J. Phys. Chem. 98 (1994) 3681. [22] H.M. badawi, W. Forner, A.A. Saadi, J. Mol. Struct. 505 (2000) 19.
Analysis of vibrational spectra of chlorotoluene based on density function theory calculations Zhengyu Zhou a,b,*, Hongwei Gao a, Li Guo a, Yuhui Qu a, Xueli Cheng a b
a Department of Chemistry, Qufu Normal Uni6ersity, Shandong, Qufu 273165, People’s Republic of China State Key Laboratory Crystal Materials Shandong Uni6ersity, Shandong, Jinan 250100, People’s Republic of China
Received 3 July 2001; accepted 27 July 2001
Abstract The conformational behavior and structural stability of chlorotoluene were investigated by utilizing ab initio calculations with 6-31G* basis set at restricted Hartree-Fock (RHF) and density function theory (DFT) levels. The vibrational frequencies of chlorotoluene were computed at the RHF and DFT levels. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. RHF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 10 cm − 1. Two hybrid DFT methods are found to yield frequencies, which are generally higher than the observed fundamental frequencies. When the calculated results are compared with ‘experimental’ frequencies, B3LYP method is found to be slightly more accurate for CH stretching modes. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Density functional theory; Vibrational spectra; Chlorotoluene molecule
1. Introduction In the past few years, the structural stability of toluene molecule have been investigated. But the analysis of vibrational spectra using DFT methods is very few. Modern vibrational spectrometry has proven to be an exceptionally powerful technique for solving many chemistry problems. It has * Corresponding author. Tel.: + 86-537445-6765; fax: + 86537445-8216. E-mail address: [email protected] (Z. Zhou).
been extensively employed both in the study of chemical kinetics and chemical analysis. Several theoretical methods are useful in analyzing vibrational spectra of organic molecules. These methods can be roughly divided into the following groups: classical mechanics, semi-empirical quantum mechanical methods, ab initio quantum mechanical method and ab initio followed by empirical scaling of the force constants. Ab initio molecular orbital calculation is the relatively successful approaches to vibrational problems of closed shell organic molecules. However, raw frequency values computed at the Hartree-Fock level
1386-1425/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 1 ) 0 0 6 0 9 - 6
1554
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
contain known systematic errors due to neglecting electron correlation and basis set incompleteness resulting in overestimate of about 10– 12%. Therefore, it is necessary to scale frequencies predicted at the Hartree-Fock level. The most popular and accurate scaled ab initio approach is the scaled quantum mechanical (SQM) force field procedure which employs different scale factors for different coordinates. A less ambitious approach is to scale all the calculated frequencies or force constants by a constant [1–4]. Over the past two decades, scaled ab initio calculations have been quite successful in predicting vibrational spectra of closed shell organic molecules. However, the scaling requires considerable empirical knowledge and makes the scaling procedure arbitrary and difficult when the empirical knowledge is not readily available. For much open shell and some conjugated closed shell molecules, however, errors due to neglecting electron correlation are far from systematic and can not be corrected by a scaling procedure. Even for molecules as simple as toluene, effect of electron correlation already appears less systematic errors. Therefore, in many cases, the Hartree-Fock methods even fail to give a qualitatively corrected description. Recently, density functional theory (DFT) [5– 8] has been accepted by the ab initio quantum chemistry community as a cost-effective approach to molecular properties. Unlike the Hartree-Fork theory, DFT recovers electron correlation in the self-consistent Kohn-Sham procedure through the functions of electron density and gives good descriptions for systems, which require sophisticated treatments of electron correlation in the conventional ab initio, approach, so it is a cost effective and a reliable method. DFT calculations of vibrational spectra of small organic systems [9– 12] have shown promising conformity with experimental results. In a recent comprehensive study, Rauhut and Pulay [13] have shown that the raw BLYP and B3LYP frequencies and force constants approximate the experimental results much better than the Hartree-Fock results. To gain a better understanding of the performance and limits of different DFT methods as a general approach to the vibrational problems of organic molecules, we have focussed our attention
in this study on chlorotoluene molecule. It was found that the combination of Becke’s exchange and Lee-Yang-Parr’s correlation functional (BLYP) reproduces the observed fundamental vibrational frequencies satisfactorily. The B3LYP frequencies are generally higher than observed fundamental frequencies, but appear to be closer to the available ‘experimental’ harmonic frequencies.
2. Calculations All calculations were carried out using the Gaussian 94 program package. Five popular DFT methods are used in this study. They are: Slater’s (local spin density) exchange functional [14] in conjunction with Vosko-Wilk-Nusair correlation functional [15] (LSDA), Becke’s gradient-corrected exchange functional [16,17] in conjunction with Lee-Yang-Parr gradient-corrected exchange functional [18] (BLYP), Becke’s gradient-corrected exchange functional in conjunction with Perdew gradient corrected correlation functional [19] (BP86), Becke’s three-parameter method [20] with Perdew correlation functional (B3P86) and Becke’s three-parameter method with Lee-YangParr correlation functional (B3LYP). The 6-31G* basis set was used throughout. This basis set was chosen on the basis of the findings that the 631G* DFT results on structures, energies, and force constants are obviously superior to results of smaller basis sets [21]. Further enlarging the basis set, however, increases the computational cost significantly and, therefore, is not practical for studying larger systems. All molecular structures were fully optimized prior to analytic second derivative calculations and vibrational analysis.
3. Results and discussion
3.1. Structure Chlorotoluene belong to C1 point group. A comparison of the calculated CC, CCl and CH bond lengths of chlorotoluene by different methods is presented in Fig. 1. From experimental
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
values of literature[15], CC single bond length is 1.5037 A, , HC single bond length is 1.0853 A, and CCl bond length is 1.8247 A, for chlorotoluene. Taking account of the effect of conjugation, our calculated values of chlorotoluene molecule is in reasonable agreement with the above-mention experimental data. The HF/6-31G* bond lengths are slightly shorter, while the BLYP/6-31G* bond lengths are slightly exaggerated electron correlation effect while the HF theory neglecting this effect. Compared with the experimental values, the B3LYP/6-31G* bond lengths are the best.
3.2. Vibrational frequencies The calculated harmonic frequencies of chlorotoluene molecule are compared with observed frequencies in Table 1. All the assignments and activities are in good agreement with the earlier normal coordinate analysis and experimental determinations. In order to investigate the performance and limits of different DFT methods in predicting the vibrational frequencies, the mean deviation, mean absolute deviation and standard deviation (S.D.) between the calculated harmonic and observed fundamental vibrational frequencies for each method are also given in Table 2, respectively. It can be noted that the calculated results are harmonic frequencies while the observed frequencies contain anharmonic contributions. The latter is generally lower than the former due to the anhar-
Fig. 1. Comparison of the calculated structure parameters of chlorotoluene by different methods. The bond lengths are given in Angstroms. The experimental values are obtained from [15].
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monic nature of molecular vibrations. In principle, one should compare the calculated frequencies with experimental harmonic frequencies. However, as all the vibrations are more or less anharmonic, harmonic frequencies are not directly observable. Although they can be deduced theoretically, it requires detailed knowledge of both quadratic and anharmonic (cubic and higher) force constants and is only feasible for very small molecules. It should be pointed out that reproduction of observed fundamental frequencies more desirable practically because they are directly observable in a vibrational spectrum. Comparison, therefore, between the calculated and the observed vibrational spectra helps us to understand the observed spectral features. Results in Table 1 indicate that frequencies calculated by the two hybrid DFT methods are higher than observed fundamental frequencies but that B3LYP results are significantly closer to available ‘experimental’ harmonic frequencies for CH (D) stretching vibrations. The mean absolute and standard deviations between the observed and the calculated frequencies are 61.7 and 72.8 cm − 1 for B3LYP, 66.9 and 80.0 cm − 1 for B3P86, respectively. As we can see, most of the BLYP non-CH stretching frequencies are slightly lower than reliable experimental assignments, and the best agreement between the calculated and observed fundamental vibrational frequencies is achieved by the BLYP. The average mean absolute and standard deviations are 20.6 and 25.3 cm − 1, while for BP86 (21.5 and 27.4 cm − 1) and LSDA (32.2 and 41.7 cm − 1), the results are not as good as BLYP. According to above results, five DFT methods have similar accuracy when the calculated results compared with ‘experimental’ harmonic frequencies while B3LYP yields the slightly higher level of conformity. Compared with the observed frequencies, when the CH stretching vibrations are excluded, deviations of five DFT methods all reduce to some extent. B3P86 (66.9 and 80.0 cm − 1) gives the largest deviations in five DFT methods, whereas BLYP (20.6 and 25.3 cm − 1) and BP86 (21.5 and 27.4 cm − 1) perform very similarly with deviations of BLYP results being slightly smaller. These results indicate anharmonicity affects CH stretching modes most
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
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Table 1 Calculated and experimental fundamental vibrational frequencies of chlorotoluene Number
Experimenta
BLYP
LSDA
BP86
B3LYP
B3P86
HF
Assignment
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
3074 3064 3055 3046 3043 3040 2982 1601 1583 1484 1461 1443 1320 1316 1247 1185 1168 1151 1130 1064 1010 974 944 912 882 881 813 785 742 674 604 603 531 446 387 305 245 92 28
3124 3114 3105 3096 3093 3090 3032 1600 1582 1499 1476 1458 1335 1331 1262 1200 1183 1166 1145 1079 1025 989 959 927 897 896 828 800 757 689 619 618 546 461 402 320 260 107 43
3144 3135 3124 3112 3111 3091 3028 1658 1640 1512 1468 1441 1428 1304 1270 1231 1169 1151 1146 1087 1046 996 962 926 896 895 825 823 774 693 691 616 555 473 400 313 267 106 19
3133 3120 3110 3100 3098 3088 3028 1612 1594 1496 1464 1455 1359 1319 1264 1208 1178 1161 1148 1080 1028 988 955 924 895 891 823 804 757 686 646 614 548 463 398 315 262 106 38
3211 3201 3192 3183 3180 3173 3114 1665 1646 1547 1516 1504 1369 1362 1313 1241 1214 1195 1185 1113 1058 1019 1000 968 932 924 858 826 786 712 666 635 568 480 415 328 272 111 39
3227 3217 3207 3197 3195 3183 3121 1681 1662 1550 1510 1506 1389 1363 1317 1251 1213 1194 1190 1116 1064 1020 1002 970 932 925 857 832 790 712 691 633 569 482 413 325 273 110 35
5662 3904 3346 3338 3327 3317 3310 3085 1776 1766 1730 1656 1588 1462 1348 1304 1285 1173 1131 1116 1108 1103 1065 1048 963 895 812 799 675 655 482 469 449 353 214 207 194 186 54
CH stre. CH stre. CH stre. CH ste. CH ste. CH ste. CH ste. CC stre.+CH ipb. CC ste. CH ipb. CC stre. CCH in-plane bend CCH in-plane bend CCH in-plane bend CCH in-plane bend CH ipb.+CC stre. CH ipb.+CC stre. CH ipb.+CC stre. CH ipb.+CC stre. CH ipb. CH ipb. CH wag. CH wag. CCl stre. CCl stre. CCl wag. CCl wag. CH wag. CH wag. CH wag. Ring bending Ring bending Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion Ring torsion
a
Values are obtained from [22].
significantly, as the experimental harmonic frequencies of the CH stretching modes are over 100 cm − 1 higher than the corresponding fundamental frequencies. As we can see, this CH stretching modes are of much higher energy do not couple with other fundamental vibrational modes and are less important than frequencies of the fingerprint region for chemical analysis.
The calculated harmonic frequencies of HF methods at 6-31G* basis set also listed in Table 1. As we can see, the worst agreement between the calculated and observed results is found with HF/ 6-31G* results (249.2 and 527.7 cm − 1). There is a large overestimation of the frequencies at HF level, this may be due to the slightly too short bond lengths resulting from neglecting electron
Z. Zhou et al. / Spectrochimica Acta Part A 58 (2002) 1553–1558
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Table 2 Mean deviations, mean absolute deviations and standard deviations between the calculated and observed fundamental vibrational frequencies
Mean deviation Mean absolute deviation Standard deviation
BLYP
LSDA
BP86
B3LYP
B3P86
HF
20.5 20.6 25.3
31.1 32.2 41.7
21.8 21.5 27.4
61.7 61.7 72.8
67.8 66.9 80.0
−35.0 249.2 527.7
correlation in the HF theory. Even the scale factors considered, the results are still worse than DFT methods. Even though B3LYP is superior to BLYP for many properties, the fact that the BLYP frequencies are closer to observed fundamental vibrational frequencies has important implications for interpreting observed vibrational spectra. As discussed by Rauhut and Pulay, the high level of conformity between BLYP results and the observed fundamental frequencies may be due to error cancellation. Our geometry optimization indicates that due to slight exaggeration of electron correlation by BLYP method, the BLYP bond lengths are slightly longer than the corresponding B3LYP bond distances. The BLYP force constants and vibrational frequencies are, therefore, slightly smaller than the corresponding B3LYP results. As the effect of anharmonicity is also to lower the vibrational frequencies, the high level of conformity between BLYP harmonic frequencies and the observed results is likely to be attributable to overestimation of the bond length by the BLYP method. Agreement between the experimental and simulated spectral features indicates that the BLYP infrared intensities are qualitatively correct. Therefore, the high level of conformity between the observed and calculated spectral features indicates that BLYP, without any empirical adjustment is a more straightforward and practical approach to deduce the observed fundamental vibrational frequencies for many molecules whose vibrational spectra are not well understood.
4. Conclusions DFT and HF calculations on the vibrational frequencies of chlorotoluene molecule have been carried out. On the basis of the comparison between calculated and experimental results, assignments of fundamental vibrational modes are examined. It is found that DFT using BLYP reproduces the observed fundamental vibrational frequencies very well with the mean absolute deviations about 20.6 cm − 1 and S.D. about 25.3 cm − 1 between the calculated and observed results. This accuracy is desirable for resolving disputes in vibrational assignments and provides valuable insight for understanding the observed spectral features. Therefore, it is a promising approach for identifying an unknown compound by comparing its vibrational spectrum with calculates results of a few candidates and the BLYP calculated results could serve as a guide for a further experimental search for the missing fundamentals of the target molecule. Furthermore, since the DFT results without any empirical adjustment can be compared directly with experimental results, it will gain more and more popularity in the calculation of vibration frequencies.
Acknowledgements This work was supported by the Natural Science Foundation of Shandong Province, the National Key Laboratory Foundation of Crystal
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Material and the National Natural Science Foundation of China (2967305).
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