Structure and Vibrational Spectra of the Azabenzenes. A Density

Vibrational analysis of precursors of compounds of biomedical interest. M.Fernández Gómez , A.Navarro Rascón , T.Peña Ruiz , M.P.Fernández Liencr...
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J. Phys. Chem. 1996, 100, 6973-6983

6973

Structure and Vibrational Spectra of the Azabenzenes. A Density Functional Study Including Exact Exchange Contributions Jan M. L. Martin Department SBG, Limburgs UniVersitair Centrum, UniVersitaire Campus, B-3590 Diepenbeek, Belgium, and Institute for Materials Science, Department of Chemistry, UniVersity of Antwerp (UIA), UniVersiteitsplein 1, B-2610 Wilrijk, Belgium

C. Van Alsenoy* Institute for Materials Science, Department of Chemistry, UniVersity of Antwerp (UIA), UniVersiteitsplein 1, B-2610 Wilrijk, Belgium ReceiVed: October 27, 1995; In Final Form: February 1, 1996X

The geometry and vibrational spectra of pyridine, pyridazine, pyrimidine, pyrazine, s-triazine, 1,2,3-triazine, 1,2,4-triazine, and s-tetrazine have been computed using the B3LYP density functional method and correlation consistent basis sets of spd and spdf quality. Empirical corrections have been applied to the computed bond distances. Computed harmonic frequencies are in very good to excellent agreement with the available experimental data; the only real deficiency seen is for the Kekule´-type vibration, which appears to have some multireference character. Significant basis set effects are seen for the Kekule´ modes and for “pinwheel”type hydrogen motions. Empirically corrected B3LYP/cc-pVDZ and B3LYP/cc-pVTZ bond distances are in essentially complete agreement for CH distances, excellent agreement (0.001 Å) for CC distances, and good agreement (0.002 Å) for CN distances, but differ markedly (0.003-4 Å) for NN distances. Computed B3LYP/ cc-VTZ dipole moments are in excellent agreement with the available experimental values (about 0.05-0.1 D too low). The calculations are found to be valuable in verifying a number of less certain experimental vibrational assignments.

I. Introduction studies1-4

triggered a revived interest in A number of recent the DFT methodology. Indeed, these studies showed that use of the B3LYP (Becke three-parameter Lee-Yang-Parr) exchange-correlation functional5,6 leads to results whose accuracy is comparable to those obtained using coupled cluster methods such as CCSD(T).7 An avalanche of papers using the B3LYP approach5,6 or one of its predecessors resulted, covering the complete range of static quantities,8-10 comprehensive studies of organic reactions,11 and studies of vibrational spectra,12 metallic clusters, and organometallic complexes13 (the field where DFT methods were traditionally used). For a more extensive list of references we refer to Ziegler,14,15 Labanowski et al.,16 and Seminario et al.17 To assess the performance of B3LYP-DFT in reproducing property shifts of a series of closely related compounds, the structure and harmonic frequencies of eight members of the azabenzene series are calculated using basis sets of spd and spdf quality and compared with experiment. In a previous study using the B3LYP method and correlation consistent18 basis sets, excellent agreement with the available experimental data was found for the parent molecule benzene: it would be interesting to see whether this still holds true as progressively more nitrogen atoms are introduced into the ring. Upon successively substituting N atoms for C-H entities in benzene, one arrives at 12 possible azabenzenes, one monoazine, three of each of the diazines, triazines, and tetrazines, one pentazine, and one hexazine. Eight members of this family will be studied, namely, pyridine, pyridazine, pyrimidine, pyrazine, 1,2,3-triazine, 1,2,4-triazine, 1,3,5-triazine (sym-triazine), and 1,2,4,5-tetrazine (sym-tetrazine). Of the mono-, di-, and triazX

Abstract published in AdVance ACS Abstracts, April 1, 1996.

0022-3654/96/20100-6973$12.00/0

ines, all possible homologues were included, while of those containing four N atoms only the symmetric tetrazine is studied. The more heavily substituted structures containing five and six N atoms were omitted because the ground state of these systems is not a planar six-membered ring. For pentazine only some MP2/6-31G* calculations19 are available, while the issue of the equilibrium structure of N6 (of which hexazine, or hexaazabenzene, does not appear to be the lowest energy structure20,21) is a problem in itself (for more details, see for example refs 2023) and is beyond the scope of the present paper. The importance of the members of this series can hardly be exaggerated, as they form the basic building blocks for many compounds fulfilling important physiological functions in man, animals, and plants. The nitrogenous bases of the DNA nucleotides are either substituted pyrimidines (thymine, cytosine) or substituted purines (adenine, guanine), a fused ring system of pyrimidine with imidazole. Many inhibitors of reverse transcriptase used in the treatment of AIDS24 contain either pyrimidine (AZT) or pyridine (Nevirapine). Pteridine, a fused ring system of pyrazine and pyrimidine, is found in a number of pigments isolated from butterfly wings and “less lovely parts of other insects”.25 The important growth factor folic acid (vitamin B10) also contains a pteridine ring system, as does riboflavin (vitamin B2), the yellow pigment in egg yolk. Melamine, a derivative of sym-triazine, is used for making melamine-formaldehyde plastics. Finally, s-tetrazine is a promising-looking candidate for usage in the area of data storage at the molecular level26 due to the fact that one of the relaxation mechanisms of its S1 exited state leads to 2HCN + N2. In view of the importance of these compounds, individual elements of these series were the subject of a large number of studies, too numerous to review. Those directly relevant to the present study will be cited in section III. A review of ab initio © 1996 American Chemical Society

6974 J. Phys. Chem., Vol. 100, No. 17, 1996

Martin and Van Alsenoy

TABLE 1: Geometry (Å, deg) of Pyridine

rN,C1 rC1,C2 rC2,C3 rC1,H1 rC2,H2 rC3,H3 RCNC RNCC RC1,C2,C3 RC2,C3,C4 RN,C1,H1 RC1,C2,H2 RC2,C3,H3

B3LYP cc-pVDZ

B3LYP cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

expt30 rs

expt37 r0

expt38 rg

1.3406 1.3981 1.3964 1.0957 1.0921 1.0927 116.89 123.9 118.43 118.44 115.9 120.2 120.78

1.3338 1.3901 1.3883 1.0844 1.0813 1.0819 117.31 123.58 118.5 118.54 116.13 120.23 120.73

1.3316(32) 1.3891(32) 1.3874(32) 1.0821(37) 1.0785(37) 1.0791(37)

1.3336(22) 1.3899(22) 1.3881(22) 1.0819(21) 1.0788(21) 1.0794(21)

1.3376(4) 1.3938(6) 1.3916(4) 1.0865(4) 1.0826(4) 1.0818(2) 116.94(3) 123.80(3) 118.53(3) 118.40(3) 116.01(3) 120.12(3) 120.80(2)

1.3402 1.3958 1.3944 1.0857 1.0819 1.0811 116.98 123.79 118.5 118.45 116.05 120.12 120.78

1.344 1.399 1.398 1.096 1.092 1.094 116.1 124.6 117.8 119.1 115.2 119.3 120.5

studies on tetrazine up to 1987 was published by Scheiner and Schaefer.27 Pang et al.28 and Wiberg29 studied a subset of the azabenzenes studied in this work. An extensive review of experimental data on the azabenzenes was published by Innes, Ross, and Moomaw (IRM).30 II. Computational Methods All calculations have been carried out using the Gaussian 94 package31 running on IBM RS/6000 Model 580 workstations at the Limburgs Universitair Centrum. The B3LYP exchangecorrelation functional5,6 has been used throughout. This consists of the Lee-Yang-Parr5 correlation functional in conjunction with a hybrid exchange functional first proposed by Becke.6 The latter is a linear combination of local density approximation, Becke’s gradient correction,32 and the Hartree-Fock exchange energy based on Kohn-Sham33 orbitals. Using the adiabatic connection34 argument, Becke demonstrated that this is the simplest form of the exchange-correlation functional that correctly describes the limiting cases of Hartree-Fock behavior and long-distance interaction. Two “correlation consistent” basis sets due to Dunning18 have been used throughout. The first, cc-pVDZ or correlation consistent polarized valence double ζ, is a [3s2p1d/2s1p] contraction of a (9s4p1d/4s1p) primitive set. The second, ccpVTZ or correlation consistent polarized valence triple ζ, is a [4s3p2d1f] contraction of a (10s5p2d1f/5s2p1d) primitive set. It has conclusively been shown35 that the former is the smallest basis set that will yield useful harmonic frequencies in a correlated calculation and that the latter bridges most of the one-particle basis set incompleteness gap, generally yielding harmonic frequencies within 10 cm-1 of experiment if advanced coupled cluster methods are used for electron correlation. In a very recent basis set convergence study in DFT calculations,36 it was found that B3LYP/cc-pVDZ harmonic frequencies are often in surprisingly good agreement with experiment and that the improvement upon going from cc-pVDZ to cc-pVTZ is by no means as marked as for a very accurate electron correlation method. Hence, while the change between cc-pVDZ and cc-pVTZ basis sets will be very indicative of which frequencies are basis set sensitive, the expense of investigating even larger basis sets is not warranted. In that same paper,36 however, it has been found that the errors in computed bond distances at the B3LYP level are fairly systematic (for a given basis set) and that using the average overestimates for single-, double-, and triple-bond lengths in a number of reference molecules as empirical corrections lead to bond distances within a few milliangstroms of experiment. Those at the B3LYP/cc-pVTZ level are markedly better than

at the B3LYP/cc-pVDZ level, illustrating the greater basis set sensitivity of geometries as opposed to harmonic frequencies (see also ref 35). Encouraging results have previously been obtained36 for the geometry and particularly the harmonic frequencies of benzene, pyrrole, and furane, with the latter usually being within 20-50 cm-1 of experiment. We expect the same level of accuracy for the azabenzenes under study here. III. Results and Discussion A. Pyridine. Computed and observed geometries for pyridine are given in Table 1. Three different sets of experimental data are available: an older r0 geometry,37 an electron diffraction rg geometry from the Antwerp group,38 and an rs microwave substitution structure from the IRM review.30 Among these, one would normally expect the rs geometry to be closest to the re geometry. For brevity, in the following discussion we shall adopt the notation of Innes et al.30 for the vibrational frequencies, in which, for example, na1 means the nth highest frequency of symmetry a1. As expected, the B3LYP/cc-pVDZ and B3LYP/cc-pVTZ geometries differ fairly substantially in the bond distances. This, however, is due to known basis set effects. Martin et al.36 derived an empirical correction for B3LYP/cc-pVnZ (n ) 2-4) bond lengths that uses different additive corrections for single, double, and triple bonds. Since the average bond order in the six-membered ring, like in benzene, is expected to be 1.5, we will use the average of the single- and double-bond corrections for bond lengths in the ring. This leads to the bond lengths labeled as “corrected” in Table 1, where the uncertainties in parentheses are the mean absolute errors found for the reference molecules in ref 36. It is seen immediately that the corrected CH bond lengths are in nearly perfect agreement with each other for the two basis sets: they are probably the most accurate re values that can be obtained by any method at the present time. Very good agreement is also obtained for the CC bond lengths: the only significant deviation is seen for the CN bond, which the corrected B3LYP/cc-pVDZ calculations predict to be 0.002 Å shorter than their corrected B3LYP/cc-pVTZ counterparts. Nevertheless, both values are within each other’s uncertainty: we would probably regard the corrected B3LYP/ cc-pVTZ value to be the more reliable of the two in view of the smaller uncertainty and the smaller extent of the correction, which accidentally nearly cancels out for bond order 3/2 at the B3LYP/cc-pVTZ level. All rs bond lengths within the ring are about 0.004 Å longer than our best calculation of the re counterparts; the rs - re difference for the CH bonds decreases

Structure and Vibrational Spectra of the Azabenzenes TABLE 2: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of Pyridine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available) B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

a1 3202(7.6) 3177(5.2) 3149(9.1) 1636(23.0) 1507(3.1) 1236(2.6) 1089(3.8) 1048(4.7) 1009(8.0) 611(4.3) b2 3193(26.7) 3146(30.0) 1628(9.4) 1466(25.3) 1369(0.02) 1306(0.2) 1159(1.8) 1076(0.02) 665(0.3)

3195(7.4) 3171(5.2) 3147(6.8) 1626(23.8) 1518(3.2) 1244(3.4) 1096(3.0) 1052(7.7) 1012(5.7) 617(4.7) 3186(26.7) 3144(29.9) 1621(8.9) 1477(27.2) 1391(0.1) 1283(0.07) 1173(2.4) 1080(0.1) 670(0.2)

HF/ 6-311++G47 expt40 In-Plane 3375 3353 3332 1759 1639 1339 1178 1125 1077 674 3366 3345 1752 1594 1507 1317 1223 1156 731

Out-of-Plane b1 1018(0.0004) 1023(0.02) 1153 957(0.01) 964(0.003) 1078 763(5.5) 769(5.9) 796 719(44.6) 721(63.1) 840 420(3.0) 422(3.5) 478 a2 1002 1011 1135 897 899 1008 385 385 444

3070 3057 3025 1581 1483 1217 1069 1030 991 603 3079 3034 1574 1437 1355 1227b 1146 1069 654

expt41 3094(0.0a) 3073(1.5(1.0) 3030(8.5(1.0) 1584(17.9(1.8) 1483(4.0(0.4) 1218(4.3(0.4) 1072(4.5(0.5) 1032(7.7(0.8) 991(5.4(0.5) 601(4.4(0.4) 3087(15.9(1.6) 3042(5.1(1.5) 1581(7.3(1.8) 1442(31.1(3.1) 1362(0.5(0.2) 1227(0.0a) 1143(3.6(0.4) 1079(0.0a) 652(1.1(0.2)

1007 1007(0.0a) 941 937(0.0a) 747 744(12.9(1.3) 703 700(67.5(6.7) 406 403(7.2c) 980 966 884 871 380 373

a Band only detected in Raman in ref 41. b Affected by severe Fermi resonance. c Intensity taken from Kakiuti et al., J. Mol. Spectrosc. 1976, 61, 164 in ref 41.

in the order ortho > meta > para. The B3LYP/cc-pVTZ computed bond angles and their rs counterparts agree quite well with each other, except for the CNC angle, which the calculations find about 0.4° wider. It is hard to say whether this is a deficiency of the calculations or an actual feature of the difference between rs and re geometries. Computed harmonic frequencies and observed fundamentals are given in Table 2, together with computed double-harmonic infrared intensities for the active vibrations. Agreement with experiment for the out-of-plane modes can only be termed impressive, given the relatively low computational cost of the B3LYP calculations. For the in-plane modes, agreement is likewise very good for the lower lying bending modes (with one exception, see below), while the difference for the CH stretches is consistent with the expected anharmonicity of 100140 cm-1 for these modes. (The well-known39 annoying tendency of BLYP to underestimate XH stretching frequencies is completely absent in B3LYP.36) Differences for the remaining modes (such as ring stretches) are more or less in line with the expected effects of anharmonicity. As a whole, the performance of the B3LYP calculations can only be termed very satisfactory. There is only one fly in the ointment: the 5b2 band, which is calculated at 1283 and observed at 1227 cm-1. The error is still larger for the B3LYP/cc-pVDZ calculations, which predict it at 1306 cm-1. Since this error is so out of character with that for the other vibrations, the experimental data deserve closer attention. DiLella and Stedham40 note, however, the proximity of another band at 1290 cm-1, which they ascribe to a combination of the 406 (b1) and 884 (a2) bands. Our calculations place the zero-order interval between these two states at

J. Phys. Chem., Vol. 100, No. 17, 1996 6975 only 38 cm-1 using the cc-pVTZ and only 11 cm-1 using the cc-pVDZ basis set. This suggests that a severe Fermi resonance may be involved and that the deperturbed frequency should be a lot closer to our calculations. The differences between the computed frequencies using the cc-pVDZ and the much larger cc-pVTZ basis set suggest a conspicuously small basis set effect for most modes. The two exceptions to this rule are the 4b2 and 5b2 bands observed at 1355 and 1227 cm-1, for which the basis set effect amounts to +22 and -23 cm-1, respectively. 5b2 corresponds to a pinwheel-type motion (for which a substantial basis set effect was also seen in benzene36); 4b2 is the Kekule´-type ring stretch whose normal mode corresponds to breakup into 2C2H2 + HCN, similar to the corresponding mode in benzene which leads to 3C2H2, and is also found to be sensitive to the basis set.36 Infrared intensities agree reasonably well between the two basis sets for the more intense modes, but differ quite appreciably for the less intense modes. Needless to say, the ccpVTZ values should be the more reliable ones. Pyridine is the only molecule for which full experimental intensity information is available.41 From Table 2, we see that reasonable to excellent agreement with experiment is achieved for most modes, with the notable exception of the CH stretching modes, for which even qualitative differences are observed. Since these modes are also by far the most anharmonic ones, this might suggest that the observed intensities contain appreciable anharmonic contributions. An indirect indication of the reliability of our computed double-harmonic intensities (which are related to geometrical derivatives of the dipole moment) is afforded by the quality of the computed dipole moment. The most precise experimental value available is 2.215 ( 0.01 D from Stark effect measurements;42 other literature values include 2.17 D from the CRC Handbook,43 2.23 D in an older compilation,44 and 2.15 ( 0.05 D.45 While the B3LYP/cc-pVDZ value of 2.04 D is clearly too low, the B3LYP/cc-pVTZ value of 2.18 D agrees very nicely with the available experimental data. This would appear to suggest that the B3LYP/cc-pVTZ intensities, within the limitations of the approximation, should give a good approximation to the double-harmonic part of the actual intensities. IRM mention that an alternative assignmentsof absorptions at 936 and 884 cm-1swas proposed in their refs 90 and 93 for the two highest b1 modes. They, however, reject this assignment on the basis of ab initio calculations (scaled quantum mechanical force field) by Pulay and co-workers;46 this decision appears to be vindicated by the present B3LYP results, which are utterly incompatible with the alternative assignment. The suggestion in ref 90 of IRM that the 5b2 band lies at 1293 cm-1 rather than 1362 cm-1 is not supported by the present calculations. The quality of the SCF/6-311++G frequencies of Yang and Schatz47 leaves something to be desired, as expected; that of the HF/6-31+G* frequencies scaled by 0.9 of Wiberg29 is a lot better, although the errors are much more erratic than those of our B3LYP/cc-pVDZ calculations. Summarizing, we can state that the performance of B3LYP/ cc-pVTZ for the properties of the pyridine molecule is as good as can be expected from a method of its relatively modest computational cost. B. Pyridazine. Computed and observed geometries for pyridazine are given in Table 3. The principal source for an experimental geometry is relatively recent electron diffraction measurements.48 The B3LYP/cc-pVTZ computed bond angles agree very well with the experimental r0R values. For the computed bond distances, the same correction as for pyridine is applied. We find the corrected B3LYP/cc-pVDZ

6976 J. Phys. Chem., Vol. 100, No. 17, 1996

Martin and Van Alsenoy

TABLE 3: Geometry (Å, deg) of Pyridazine

rNN rN,C1 rC1,C2 rC2,C3 rC1,H1 rC2,H2 RNNC RNCC RCCC RN,C1,H1 RC1,C2,H2

B3LYP cc-pVDZ

expt48 rR0

B3LYP cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

SCF71 DZ

SCF71 TZVP

1.3332 1.3380 1.4001 1.3865 1.0942 1.0921 119.38 123.90 116.73 114.84 121.00

1.3370(21) 1.3379(15) 1.4000(9) 1.3846(19) 1.0787(20) 1.0707(20) 119.38(5) 123.76(7) 116.86(5) 114.91(17) 120.67(13)

1.3287 1.3304 1.3921 1.3779 1.0829 1.0813 119.47 123.63 116.90 115.03 120.87

1.3242(32) 1.3290(32) 1.3911(32) 1.3775(32) 1.0806(37) 1.0785(37)

1.3285(22) 1.3302(22) 1.3919(22) 1.3777(22) 1.0804(21) 1.0788(21)

1.3319 1.3322 1.4010 1.3818 1.0796 1.0801 120.03 122.70

1.3052 1.3077 1.3919 1.3646 1.0729 1.0727 120.04 123.28

115.49 120.50

115.41 120.75

TABLE 4: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of Pyridazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available) B3LYP/ cc-pVDZ a1

b2

a2

b1

a

B3LYP/ cc-pVTZ IR/Raman

expt50 IR/Raman

expt51

expt30

3204(7.6) 3172(0.8) 1615(5.6) 1475(1.2) 1198(0.03) 1160(0.05) 1094(12.6) 1018(7.4) 677(3.1) 3189(17.8) 3168(10.7) 1613(3.7) 1429(17.5) 1302(2.5) 1080(0.8) 1052(1.9) 629(0.04)

In-Plane 3197(8.2) 3085/3083 3168(0.3) 3056/3052 1615(5.6) 1570/1572 1482(1.2) 1446/1450 1181(0.001) 1159/1160 1174(0.01) 1131/1129 1091(11.8) 1061/1063 1010(7.7) 963/964 682(3.3) 664/667 3183(18.1) 3068/3064 3164(10.2) 3056/3052 1607(4.0) 1563/1566 1446(17.4) 1415/1417 1316(2.8) 1283/1283 1088(1.7) 1061/1063 1063(1.1) -/1012 636(0.1) 629/630

-/3080 -/3080 1555/1570 1440/1441 1153/1150 -/1055/1063 960/963 663/660 -/3070 -/3041 1540/1564 1408/1401 1283/1287 1058/1052 -/632/622

3064 3052 1564 1410 1348 1150 1062 970 665 3085 3056 1566 1450 1283 1129 1023 630

1023 943 774 376 981(0.01) 763(29.2) 377(8.1)

Out-of-Plane 1031 -/989 951 -/938 784 -/753 380 -/410a 991(0.02) 963/767(40.3) 760/759 377(8.9) 369/370

-/986 -/-/-/363a -/970 760/755 372/370

[989] 861 730 410 [938] 760 370

Labeled “doubtful” in SQM paper.

and B3LYP/cc-pVTZ bond distances to be in very good agreement with each other, with the notable exception of the NN bond, for which the cc-pVTZ value is 0.0043 Å longer. (A large basis set effect for an NN bond does not really come as a surprise.) As seen above for pyridine, the agreement for the corrected CH bond distances with the two different basis sets is almost total, suggesting empirically corrected B3LYP calculations as perhaps the most reliable source of re(CH) distances. As expected for an rR geometry, the observed CH distances are shorter and the others lower than our best calculations. Agreement between our B3LYP/cc-pVTZ harmonic frequencies (Table 4) and the available experimental fundamentals follows the same pattern as for pyridine: differences in line with expected anharmonicities for the CH stretches and less so for the ring stretches; very good agreement for the out-of-plane modes. Again, significant differences are seen between computed intensities using the cc-pVDZ and cc-pVTZ basis sets. The observed dipole moment is very high: 4.22 ( 0.06 D.49 B3LYP/cc-pVTZ puts in a handsome 4.10 D, while B3LYP/ cc-pVDZ yields a too low value of 3.89 D. This again provides

us with the conclusion that the B3LYP/cc-pVTZ intensities should be useful in comparing to the experiment. Of the assignments suggested by IRM, that of 1348 cm-1 to 5a1 is untenable in light of the present calculations (1181 cm-1): other assignments of 1160 or 1150 cm-1 50,51 appear more plausible. For the top a2 mode, Stidham and Tucci50 suggest a value of 936 cm-1, which is incompatible with the present computed results: this is much less the case for the IRM value of 989 cm-1. The IRM value for 1b1 of 938 cm-1 is indicated by them to be only an estimate based on force field calculations: while the difference with our computed value is implausible large, there is no such problem with the IR50 and Raman51 measurements of 963 and 970 cm-1, respectively. We agree with the SQM paper of Berces et al.52 that the assignment of 410 cm-1 to 4a2 is doubtful. Appreciable basis set effects are found for the 5a1, 6a1 (to a lesser extent), 4b2, and 5b2 modes: -17, +14, +17, +14 cm-1. The 5a1 mode corresponds to a Kekule´-type vibration which at infinite amplitude leads to dissociation to 2C2H2 + N2 in one limit and 2HCN + C2H2 in the other limit. Animation of 6a1 reveals that a lot of NN stretching is involved, for which a significant basis set effect would be expected. 4b2 and 5b2 are both pinwheel-type motions similar to the one noted above for pyridine; in 4b2 mostly the inner and in 5b2 mostly the outer H atoms move. It is rather hard to compare the performance of the SQM force field with that of our B3LYP calculations, since the parametrization in the former attempts to absorb anharmonic and rovibrational coupling effects into its parametrization, in a force field whose physical form is that of a rigid rotor-harmonic oscillator one. Summarizing, we again find excellent performance for pyridazine. C. Pyrimidine. Computed and observed geometries for pyrimidine can be found in Table 5. There are two experimental rR geometries available from electron diffraction: an older one due to Fernholt and Rømming,53 in which equality constraints were introduced between the two symmetry-distinct CN bonds, as well as the three symmetry-distinct CH bonds, and a newer determination of Cradock et al.,54 in which no such constraints were assumed. It should be noted that the CN bonds ((0.007 Å) are associated with fairly large error bars in this determination. Comparing the corrected B3LYP/cc-pVDZ and B3LYP/ccpVTZ bond distances with each other, we again see nearly perfect agreement for the CH bond distances, excellent agreement for the CC bond, and a somewhat larger deviation of about 0.002 Å (although the error bars still overlap to a large extent) for the CN bonds. It is noteworthy that both treatments find the two symmetry-distinct CN bond distances to be within less than 0.001 Å of each other, validating at least one of the symmetry constraints in ref 53 but in sharp contrast with the

Structure and Vibrational Spectra of the Azabenzenes

J. Phys. Chem., Vol. 100, No. 17, 1996 6977

TABLE 5: Geometry (Å, deg) of Pyrimidine expt53 ra

B3LYP cc-pVDZ rC1,N rN,C2 rC2,C3 rC1,H1 rC2,H2 rC3,H3 RNCN RC1,N,C2 RN,C2,C3 RC2,C3,C4 RH1,C1,N RN,C2,H2 RC2,C3,H3 a

B3LYP cc-pVTZ

1.340(2)a 1.340(2)a 1.393(2) 1.099(7)b 1.099(7)b 1.099(7)b 127.6(3) 115.5(2) 122.30 116.80 116.20 115.3(28) 121.60

1.3392 1.3399 1.3953 1.0956 1.0957 1.0914 127.60 115.54 122.43 116.46 116.20 116.43 121.77

1.3321 1.333 1.3873 1.0841 1.0844 1.0806 127.05 115.96 122.19 116.64 116.47 116.60 121.68

corrected cc-pVDZ

corrected cc-pVTZ

expt54 rR

1.3302(32) 1.3309(32) 1.3863(32) 1.0820(37) 1.0821(37) 1.0778(37)

1.3319(22) 1.3328(22) 1.3871(22) 1.0816(21) 1.0819(21) 1.0781(21)

1.328(7) 1.350(7) 1.393(3) 1.082(4) 1.079(2) 1.087(3) 121.2(3) 117.8(2) 120.9(3)

Constrained to be equal. b Constrained to be equal.

TABLE 6: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of Pyrimidine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available) B3LYP/cc-pVDZ

B3LYP/cc-pVTZ

expt30

In-Plane a1

b2

b1

a2

3204(9.5) 3160(16.7) 3150(14.8) 1618(43.2) 1429(54.4) 1159(2.0) 1081(1.5) 1011(5.1) 692(3.8) 3153(26.0) 1620(79.4) 1488(7.3) 1379(0.2) 1263(2.8) 1225(6.7) 1090(3.1) 630(11.6) 1025(0.002) 980(0.02) 824(2.7) 739(32.0) 354(2.9) 998 407

3198(10.0) 3160(15.3) 3147(15.5) 1611(42.3) 1439(60.6) 1164(2.2) 1084(1.4) 1011(4.3) 697(3.3) 3151(22.9) 1610(83.0) 1499(7.0) 1398(0.3) 1255(8.4) 1214(4.1) 1097(2.8) 636(12.4) Out-of-Plane 1035(0.004) 992(0.1) 830(4.4) 742(41.2) 354(3.1) 1007 410

3074 3052 3038 1570 1398 1147 1065 991 677 3086 1568 1466 1370 1225 1159 1071 623 980 955 811 721 344 [927] 399

difference of 0.022 Å (admittedly (0.014 Å) in ref 54. The two CH bond lengths that are vicinal to an N atom are predicted to be nearly equal, while the remaining CC bond is found to be about 0.004 Å shorter. Interestingly, the electron diffraction data in ref 54 display the opposite trend. On the whole, it might be that the older data of ref 53 are actually the more reliable. Computed and observed geometries for pyrimidine can be found in Table 6. For the in-plane modes, agreement with the experimental results from the IRM compilation is similar to that observed for pyridine and pyridazine. This is somewhat less so for the out-of-plane frequencies, where the experimental assignments are far less certain. Two alternative assignments can be eliminated with certainty on the basis of our calculations. In refs 1 and 94 of IRM it was suggested that the 1a2 frequency (for which the IRM value of 927 cm-1 is only an estimate) should be 868 cm-1, which is irreconcilable with our computed values of 998 (B3LYP/ccpVDZ) and 1007 (B3LYP/cc-pVTZ) cm-1. In refs 100 and 102 of IRM it was suggested to deassign the 955 cm-1 band from 2b1 and add either the 708 cm-1 (ref 100) or 775 cm-1 (ref 102) absorptions to the b1 pool.

Wiberg,29 on the basis of his scaled HF/6-31+G* frequencies, suggested that the 955 cm-1 band be deassigned and the 980 cm-1 band be reassigned to 2b1, while an unassigned band at 1024 cm-1 might correspond to 1b1. These revised assignments are in excellent agreement with our calculations: the 955 cm-1 band could correspond to one of the following combinations: 8b2 + 2a2 or 9a1 + 5b1. (The experimental difficulties in assigning the 1b1 and 2b1 bands become apparent when one considers the very small computed intensities for these bands.) Our calculations also seem to confirm Wiberg’s suggestion that the 927 cm-1 estimate for 1a2 is incorrect. Comparing now the B3LYP/cc-pVDZ and B3LYP/cc-pVTZ frequencies, we find that only the 4b2 band (which goes up by 19 cm-1) has any appreciable effect: this again corresponds to the “pinwheel-type” motion of the hydrogens. The basis set effect on the computed intensities exhibits the same trend as for the previous compounds. An accurate dipole moment of 2.33 ( 0.01 D is known from Stark effect measurements:55 again, the B3LYP/cc-VDZ value of 2.13 D is somewhat too low, but the B3LYP/cc-pVTZ value of 2.28 D is in as good an agreement as one may expect. We hence would be inclined to give some credit to the B3LYP/cc-pVTZ computed dipole derivatives, viz., intensities. In short, the performance of B3LYP/cc-pVTZ for pyrimidine is again as good as can be hoped for. D. Pyrazine. There are only three symmetry-unique bond distances in pyrazine (Table 7). The difference between the corrected B3LYP/cc-pVDZ and B3LYP/cc-pVTZ distances follows the familiar pattern: virtually identical values for r(CH), excellent agreement for r(CC), a difference of almost 0.002 Å for r(CN). The bond angles turn out to be relatively sensitive to the basis set, the change of 0.5° in the CNC angle being the most noteworthy. Two experimental geometries are available: an older rg geometry56 and a relatively recent rR determination from the work of Cradock et al.54 In the former, r(CH) and a(NCH) both have clearly erroneous values, and the difference between their rg(CC) and our re(CC) is outside the realm of the expected as well. No such remarks apply to the rR structure, which seems to be fairly reliable. As seen in Table 8, the vibrational assignments for pyrazine appear to be well established. The only discrepancies outside the ordinary with our B3LYP calculations are seen for the 1au and 3b2u modes. The experimental value for the former (which is neither IR nor Raman active) is only an estimate, while the 3b2u mode corresponds to dissociation into 2HCN + C2H2. Indeed, the only two modes for which a significant basis set effect is seen are 3b3g (the pinwheel motion) and 3b2u, namely, +31 and -26 cm-1, respectively.

6978 J. Phys. Chem., Vol. 100, No. 17, 1996

Martin and Van Alsenoy

TABLE 7: Geometry (Å, deg) of Pyrazine B3LYP cc-pVDZ

expt56 rg

B3LYP cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

expt54 rR

MP272 DZP

MP257 6-31G*

1.3392 1.3986 1.0952 122.24 115.52 116.99 120.77

1.339(2) 1.403(4) 1.115(4) 122.2(4) 115.6(4) 113.9(10) 123.9(12)

1.3321 1.3905 1.0838 121.97 116.06 117.19 120.84

1.3302(32) 1.3896(32) 1.0816(37)

1.3319(22) 1.3903(22) 1.0813(21)

1.3376(13) 1.3968(30) 1.0831(37) 122.18(12) 115.65(24) 117.87(20) 119.96(8)

1.346 1.402 1.085 122.3 115.3 116.8 120.85

1.3446 1.3958 1.0880 122.35 115.30 116.65 121.00

rCN rCC rCH RNCC RCNC RNCH RCCH

TABLE 8: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of Pyrazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available)

ag

b3g

b1u

b2u

au b1g b2g b3u a

B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

3171 1628 1246 1043 607 3149 1584 1358 716 3149(7.6) 1508(1.1) 1162(5.1) 1032(38.2) 3165(70.3) 1436(32.3) 1242(2.1) 1089(8.8)

3169 1617 1255 1042 613 3147 1578 1379 721 3148(5.2) 1518(1.2) 1166(4.7) 1037(38.8) 3162(71.5) 1446(31.5) 1216(3.8) 1092(11.9)

expt30 In-Plane 3055 1580 1233 1016 602 3040 1525 1346 704 3012 1483 1130 1018 3069.09 1411 1149 1063

expt73 3055 1582 1230 1015 596 3040 1525 1346 704 3012 1484 1136 1021 3063 1416 1149 1063

Out-of-Plane 1000 1011 [960]a [960]a 351 351 350 341 942 949 927 919 987 999 983 983 776 784 756 756 803(21.1) 808(28.2) 785 785 431(18.7) 437(22.8) 418 420

MP2/ MP2/ 6-31G*57 DZP72 3244 1641 1281 1041 605 3225 1589 1395 717 3225 1531 1176 1040 3240 1470 1365 1113 960 343 944 949 747 801 423

3280 1633 1265 1027 597

914

Denoted to be only a rough estimate in IRM.

The discrepancy between theory and experiment for the 3b2u mode may reflect a methodological deficiency of B3LYP for this mode, which is likely to exhibit some multireference character, but also a Fermi resonance perturbation by, for example, 1b1g + 2b3u or 2au + 1b2g (harmonic band origins, which are expected to be upper limits, calculated at 1345 and 1337 cm-1, respectively). A proposed reassignment (refs 103 and 104 in IRM) of 3b2u to 1346 cm-1 is simply unthinkable: it is, however, not implausible that said band is the aforementioned Fermi resonance partner. Another alternative assignment that can be dismissed immediately on the basis of our calculations is the suggestion in refs 81, 106, and 107 of IRM that the 704 cm-1 band is actually b2g and that the 983 cm-1 band would then be b3g. Interestingly, the MP2/6-31G* frequencies of Zhu and Johnson57 agree fairly well with our B3LYP calculations, with

the notable exception of 3b2u. Since MP2 is known to break down for even modest levels of multireference character, this does suggest that the mode might be fairly sensitive to the level of theory. Computed intensities follow the same general trends as above. B3LYP/cc-pVDZ and B3LYP/cc-pVTZ agree well for intense modes and less well for weak ones. Evidently, the larger basis set values are to be preferred. E. s-Triazine or 1,3,5-Triazine. For the geometry of s-triazine (Table 9), both an older r0 geometry58 from Raman spectroscopy and newer rg and r0R geometries from the Antwerp group59 are available. There are only two unique bond distances, r(CN) and r(CH). Again, r(CH) is in nearly complete agreement between corrected B3LYP/cc-pVDZ and B3LYP/cc-pVTZ geometries, while there is a difference of about 0.002 Å for r(CN). The CH distance of 1.084 Å in the Raman experiments was an assumed value and appears to have been well chosen. Our computed CNC bond angle (all other angles are related by symmetry) agrees well with the electron diffraction experiments, but disagrees with the Raman experiments. The discrepancies between our computed re and the observed rg geometries are in line with expected rg - re differences. An overview of computed and observed frequencies can be found in Table 10. Agreement with the fundamentals from the compilation of IRM is very pleasing throughout, if one takes account of the magnitude of expected anharmonicities (about 120 cm-1 on a CH stretch). The “experimental” values of Califano and Crawford60 for the two a′2 modes (which are neither IR nor Raman active) are actually rough estimates based on empirical force fields and are not listed for that reason in IRM. The large disagreement with the present calculations is therefore not surprising. It is noteworthy that both these modes exhibit significant basis set sensitivity: the change from B3LYP/cc-pVDZ to B3LYP/ cc-pVTZ amounts to +18 and -28 cm-1, respectively, for 1a′2 and 2a′2. Not surprisingly, these modes turn out to correspond to the H pinwheel motion and to dissociation into 3HCN, respectively. A further significant basis set effect (+16 cm-1 for the same criterion) is seen for the symmetric out-ofplane H motion 1a′′2. Computed IR intensities exhibit tendencies similar to those of the other azabenzenes. F. 1,2,3-Triazine. For this compound, which was newly synthesized in 1981,61 only a routine IR spectrum by the discoverers61 was available at the time of writing of IRM. Since then, a detailed IR and Raman study has been published by

TABLE 9: Geometry (Å, deg) of s-Triazine

rCN rCH RCNC RNCN RHCN

B3LYP cc-pVDZ

B3LYP cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

expt58 Raman

expt59 rg

expt59 rR0

1.3383 1.0963 113.84 126.16 116.92

1.3314 1.0847 114.29 125.71 117.14

1.3293(32) 1.0827(37)

1.3312(21) 1.0822(21)

1.338(1) [1.084] 113.2(15) 126.8(15) 116.6(15)

1.338(1) 1.106(8) 113.9(1) 126.1 116.9

1.335(1) 1.092(8) 113.9(1) 126.1 116.9

Structure and Vibrational Spectra of the Azabenzenes

J. Phys. Chem., Vol. 100, No. 17, 1996 6979

TABLE 10: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of s-Triazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available) B3LYP/ cc-pVDZ a′1 a′2 e′

a′′2 e′′

B3LYP/ cc-pVTZ

expt74,75

expt60

expt30

3042 1132 992

3082 1130 989 [1556]a [1381]a 3081 1560 1404 1168 666

3042 1137 989

3161 1154 1014 1386 1194 3156(54.3) 1605(265.5) 1433(124.5) 1197(1.2) 689(34.5)

In-Plane 3161 1160 1011 1404 1166 3156(49.0) 1594(270.8) 1443(145.3) 1197(1.6) 693(33.9)

941(0.1) 759(28.5) 1036 350

Out-of-Plane 957(0.006) 762(32.5) 737 1050 1032 354 340

3059 1556 1410 1172 675

3059 1556 1410 1173 676 925 737 1034 339

a Estimated from rough force field calculations. Not listed for this reason in ref 30.

Fischer et al.,62 supplemented with scaled HF/6-31G* and MP2/ 6-31G* calculations to aid in the assignments. Structurally speaking, only X-ray data are available.63 The corrected B3LYP/cc-pVDZ and B3LYP/cc-pVTZ bond distances (Table 11) exhibit the by now familiar pattern by which only the NN bond distance differs significantly between the two levels of theory. While the bond angles in the ring agree reasonably well between the calculations and the experimental X-ray data, the angles involving H differ by 2° or more. The inadequacy of the MP2/6-31G* method is the clearest for the NN bond distance, which it overshoots by 0.024 Å. HF/ 6-31G* undershoots the same by 0.025 Å. For the frequencies (Table 12) which could be determined experimentally (i.e., excluding 1a2 and the extremely weak 1b1 band) agreement with our calculation is quite satisfying. The MP2/6-31G* frequencies scaled64 by 0.9426 were very helpful in the experimental analysis,62 but perform fairly erratically compared to the present B3LYP results. Performance would appear to be better for the CH stretches, but only because the scaling factor actually seeks to absorb the anharmonicity as well. For the undetected 1b1 and 1a2 modes, the difference between scaled MP2/6-31G* and the present work amounts to 10% of the actual frequency. Differences with HF/6-31G* frequencies scaled by 0.892964 reach or exceed 100 cm-1 for many modes. Fischer et al.62 also refined a Urey-Bradley force field: they were unable to include 4b2 in this refinement, and their final force field, which produces frequencies in excellent agreement with their other data, affords a highly erratic value of 1329 cm-1 for 4b2, which would normally indicate a Fermi resonance.

Interestingly, the calculated B3LYP frequency for this mode is in very good agreement with experiment and does not warrant concluding that a Fermi resonance exists. The band which exhibits the largest basis set sensitivity, 7b2 (-26 cm-1 change from B3LYP/cc-pVDZ to B3LYP/cc-pVTZ), is a mixture of both hydrogen wagging and asymmetric motion of the nitrogens. The latter probably adds to the great basis set sensitivity. The pattern of the observed relative intensities only partly parallels our B3LYP/cc-pVDZ calculations. Although no real attempt to obtain quantitative intensities was made experimentally, and the KBr matrix may affect results too, this might be an indication that the behavior of intensities is not completely double-harmonic for 1,2,3-triazine. Finally, the molecule is predicted to have an unusually high gas-phase dipole moment of 4.88 D at the B3LYP/cc-pVTZ level (only 4.68 D with the smaller basis set). Extrapolating from the behavior for pyridazine, we expect a dipole moment in the range 4.9-5.0 D, which would be among the highest recorded dipole moments for organic compounds. G. 1,2,4-Triazine. For this molecule, the only available data are a routine infrared spectrum.65 Sixteen bands are listed (Table 13) spanning a range 700-3100 cm-1, while 21 bands are available. Of these, however, three (15a′, 5a′′, and 6a′′) fall outside the range of interest, and two others (1a′′ and 2a′′) have near-zero intensities. The remaining frequencies are trivially matched to the observed bands (Table 13), except for a possible interchange among the two uppermost bands, the harmonic frequencies of which are calculated to be very close. The dipole moment is calculated to be 2.57 D at the B3LYP/cc-pVTZ level (2.45 D using the smaller basis set): extrapolating from the small remaining errors in pyridine and pyrimidine, we expect the actual value to be in the 2.60-2.70 D range. Computed and empirically corrected geometries can be found in Table 14. Between the two levels of theory, the principal difference in the corrected geometries is again the NN bond distance, although some of the angles around N change by as much as 0.5° as well. We would venture that the corrected B3LYP/cc-pVTZ geometry is probably as close as anyone will come to a reliable structure for 1,2,4-triazine at the present time. H. s-Tetrazine. This molecule has been the subject of two in-depth ab initio studies: the former by Scheiner and Schaefer,27 the latter very recently by Lu¨thi and co-workers.66 For the geometry (Table 15), only a crude X-ray structure67 and a fairly rough rs structure68 are available. Particularly on r(CH), error bars are too large to permit a real comparison with our calculations. The corrected B3LYP geometries with the two different basis sets again agree well except for a 0.003 Å discrepancy in r(NN). The one unique angle agrees well with experiment, insofar that that is significant at all. For the harmonic frequencies (Table 16), the CCSD(T)/6311G** calculations of Lu¨thi and co-workers66 are of particular

TABLE 11: Geometry (Å, deg) of 1,2,3-Triazine

rN1,N2 rN1,C1 rC1,C2 rC1,H1 rC2,H2 RN1,N2,N3 RC1,C2,C3 RC2,C1,H1 RC1,C2,H2 a

At 100 K.

HF/ 6-31G*

MP2/ 6-31G*

expt63 X-raya

B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

1.292 1.322 1.375 1.074 1.073 121.8 114.3 122.7 122.9

1.341 1.346 1.388 1.087 1.086 121.1 115.3 122.7 122.4

1.326 1.346 1.382 1.085 1.085 121.6 115.4 124.5 120.2

1.3262 1.3418 1.3892 1.0943 1.0915 121.61 114.67 122.45 122.66

1.3204 1.3347 1.3806 1.0828 1.0807 121.44 114.96 122.52 122.52

1.3172(32) 1.3328(32) 1.3802(32) 1.0807(37) 1.0779(37)

1.3202(22) 1.3345(22) 1.3804(22) 1.0803(21) 1.0782(21)

6980 J. Phys. Chem., Vol. 100, No. 17, 1996

Martin and Van Alsenoy

TABLE 12: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of 1,2,3-Triazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available)c IR62

Raman62

a1

3107(1.2)

b2

1597(0.6) 1336(5.8) 1080(0.5) 1069 979(3.5) 660 3046(1.4) 1545(10.0) 1410(2.3) 1195(0.6) 1124(0.5) 935(2.8) 653(4.3)

3110(2.9) 3045(3.4) 1594(1.2) 1329(0.9) 1088(2.5) 1064(2.1) 977(10.) 660(1.3) 1547(1.5) 1198(1.3) 1127(1.0)

b1 819(3.6) 769(3.3) 318 a2 365(0.9) a

B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

MP2/ 6-31G*62,a

HF/ 6-31G*62,b

In-Plane 3204(6.5) 3170(1.4) 1596(0.02) 1383(14.1) 1137(1.1) 1091(0.5) 1013(5.0) 678(0.2) 3175(12.6) 1596(45.4) 1428(4.4) 1218(0.03) 1098(0.1) 991(13.0) 663(6.1)

3199(7.5) 3167(2.0) 1592(0.01) 1387(15.3) 1139(0.5) 1099(0.7) 1010(4.3) 682(0.1) 3172(11.5) 1591(47.1) 1444(3.6) 1225(0.2) 1105(0.1) 965(12.7) 668(6.5)

3079(1.0) 3056(0.2) 1514(0.7) 1306(3.7) 1044(0.3) 1044(0.0) 927(1.4) 633(0.2) 3062(2.7) 1524(10.0) 1370(2.7) 1193(0.8) 1088(1.0) 989(3.0) 621(1.9)

3054(0.9) 3031(0.2) 1597(0.4) 1401(2.7) 1122(0.5) 1053(0.0) 1007(1.1) 662(0.0) 3040(2.3) 1585(10.0) 1422(1.2) 1201(0.1) 1075(0.0) 899(0.8) 649(1.0)

Out-of-Plane 1017(0.001) 823(3.4) 780(13.2) 306(1.4) 988 360

1031(0.0001) 832(4.2) 789(19.1) 310(1.5) 1001 366

907(0.1) 761(6.0) 713(1.9) 286(0.5) 915(0.0) 310(0.0)

1015(0.0) 819(1.2) 762(2.5) 358(0.3) 996(0.0) 401(0.0)

b

Scaled by 0.9426. Scaled by 0.8929. c All intensities except the B3LYP ones have been arbitrarily normalized to 10.0 for the 2b2 band in the original source.62

TABLE 13: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of 1,2,4-Triazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available) B3LYP/cc-pVDZ

B3LYP/cc-pVTZ

expt65

In-Plane a′

3185(5.6) 3180(18.8) 3152(10.6) 1608(10.0) 1567(23.8) 1466(1.2) 1391(29.5) 1307(11.2) 1178(7.5) 1154(10.0) 1100(3.2) 1067(21.4) 1023(5.9) 728(3.2) 630(2.1)

a′′

1010(0.003) 986(0.007) 859(4.7) 791(6.7) 379(10.8) 321(11.5)

3177(2.5) 3174(22.3) 3147(10.1) 1597(9.4) 1565(24.8) 1472(1.2) 1406(29.6) 1319(13.4) 1182(10.5) 1141(9.9) 1098(1.2) 1068(20.2) 1013(9.0) 731(3.1) 637(2.2) Out-of-Plane 1024(0.01) 1002(0.03) 870(6.9) 799(8.1) 387(12.2) 323(12.7)

3090 3060 3035 1560 1529 1435 1380 1295 1163 1136 1113 1050 955 713

851 768

interest, as B3LYP/6-311G** calculations readily allow a comparison between the performance of B3LYP and the CCSD(T) method, which is usually considered to yield frequencies close to the exact basis set value for “well-behaved” molecules. It should be noted, however, that all electrons were correlated in ref 66, which, in a basis set that is only of minimal quality in the core orbitals like 6-311G**, is known to result in errors in excess of 20 cm-1. For the in-plane modes, the two methods agree well except for 3b2u, where they differ by 54 cm-1. Differences are more pronounced for the out-of-plane modes, for which the 85 cm-1 discrepancy in the ring folding (calculated CCSD(T)/6-311G** frequency 257 cm-1) is probably the most problematic case.

TABLE 14: Geometry (Å, deg) of 1,2,4-Triazine

rN2,N1 rC3,N2 rN4,C3 rC5,N4 rC6,C5 rC6,N1 rH3,C3 rH5,C5 rH6,C6 RN1,N2,C3 RN2,C3,N4 RC3,N4,C5 RN4,C5,C6 RC5,C6,N1 RC6,N1,N2 RN2,C3,H3 RN4,C5,H5 RC5,C6,H6 RN4,C3,H3 RC6,C5,H5 RN1,C6,H6

B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

1.3339 1.3371 1.3429 1.3308 1.4002 1.3351 1.0944 1.0956 1.0937 118.04 127.39 114.01 120.68 121.75 118.12 115.41 117.72 122.13 117.20 121.60 116.11

1.3290 1.3298 1.3361 1.3231 1.3931 1.3274 1.0832 1.0848 1.0828 118.11 126.92 114.53 120.52 121.60 118.32 115.68 117.88 122.11 117.40 121.60 116.29

1.3249(32) 1.3281(32) 1.3339(32) 1.3218(32) 1.3912(32) 1.3261(32) 1.0811(32) 1.0820(32) 1.0801(32)

1.3288(22) 1.3296(32) 1.3359(32) 1.3229(32) 1.3929(32) 1.3272(32) 1.0807(32) 1.0823(32) 1.0803(32)

TABLE 15: Geometry (Å, deg) of s-Tetrazine

rCN rNN rCH RHCN

B3LYP cc-pVDZ

B3LYP cc-pVTZ

corrected cc-pVDZ

corrected cc-pVTZ

expt68 rs

1.3400 1.3241 1.0932 116.67

1.3329 1.3182 1.0818 116.86

1.3310(32) 1.3151(32) 1.0796(37)

1.3327(22) 1.3180(22) 1.0793(21)

1.3405 1.3256 1.0726 116.82

There are three main sets of experimental data: the IRM compilation, the values compiled by Scheiner and Schaefer27 (S2), and an older Russian compilation work69 in which most of the values for s-tetrazine are actually rough force field-based estimates and which shall not be considered further here. The main differences between S2 and IRM are as follows. (1) 3b1u is left unassigned in S2, but is assigned to a band at 1093 by IRM. Our B3LYP calculations endorse the assignment, as does the CCSD(T)/6-311G* frequency (which was not noted

Structure and Vibrational Spectra of the Azabenzenes

J. Phys. Chem., Vol. 100, No. 17, 1996 6981

TABLE 16: Computed Harmonic and Observed Fundamental Frequencies (cm-1) of s-Tetrazine (Infrared Intensities in km/mol for IR Active Modes Are Given in Parentheses Where Available)

ag

b1u b2u b3g

au b2g b3u

SCF/ DZP27

SCF/ 6-311G**66

MP2/ 6-311G**66

CCSD/ 6-311G**66

3423 1739 1171 817 3421 1373 1183 1640 1269 888 1789 1440 705

3395.5 1722.9 1169.8 824.1 3393.4 1369.2 1193.0 1637.1 1267.7 848.8 1780.4 1438.9 706.0

3250.6 1435.3 1012.6 746.7 3250.0 1218.9 1103.4 1464.6 1211.5 1079.6 1544.3 1325.1 633.8

3252.6 1524.3 1058.6 757.8 3251.2 1250.0 1109.0 1504.7 1167.1 844.6 1611.2 1344.8 648.1

449 1087 896 1022 405

448.6 1095.9 899.1 1032.2 410.4

328.6 974.8 797.5 922.4 271.3

343.8 984.6 802.9 930.0 297.2

CCSD(T)/a 6-311G**66

B3LYP/ 6-311G**

B3LYP/ cc-pVDZ

B3LYP/ cc-pVTZ

3200 1472 1045 757 3198 1231 1099 1473 1150 962 1557 1325 650

3200 1482 1050 755 3199(7.8) 1232(59.1) 1099(3.1) 1469(2.4) 1154(10.3) 993(33.3) 1570 1314 647

342 995 827 931 258

341 994 828 924(0.9) 259(50.2)

In-Plane 3223.1 1455.9 1017.9 741.4 3221.9 1211.7 1087.6 1471.4 1137.5 908.0 1557.6 1321.0 636.9 Out-of-Plane 256.6 946.7 772.2 896.2 228.4

exptb

expt69

expt30

3196 1472 1050 756 3194(8.1) 1236(63.9) 1102(1.1) 1479(2.6) 1151(9.6) 964(35.8) 1559 1330 656

3010 1415 1009 736 3090c 1200c 1435 1103c 882d 1525 1291 640

3040 1489 990 737 3070 1200 1106 1434 1187 1085 1543 1278 679

3010 1415 1009 736 3086 1204 1093 1448 1104 883 1525 1290 640

354 1011 837 940(1.5) 258(53.5)

254 994 801 904 255

319 925 775 890 340

335 994 801 929 254

a All electrons correlated. b Reference 76 unless denoted otherwise. c Reference 77. d Reference 78. The assignment is denoted “highly tentative” in ref 30.

TABLE 17: Potential Energy Distribution of Ring-Mode Frequencies coord

benzene36

pyridine

pyridazine

pyrimidine

pyrazine

trigoa

1030(100%,b1u)

1052(47%,a1) 1012(41%,a1)

1063(84%,b2)

1166(25%,b1u) 1037(76%,b1u)

chaird

769(67%,b1) 721(31%,b1) 617(89%,a1) 670(90%,b2) 422(85%,b1) 385(87%,a2)

784(86%,a2)

asym1b asym2c boate twistf

1021(19%,b2g) 726(83%,b2g) 624(66%,e2g) 624(66%,e2g) 413(59%,e2u) 413(59%,e2u)

682(87%,a1) 636(91%,b2) 377(85%,b1) 380(86%,a2)

1164(27%,a1) 1084(38%,a1) 1011(44%,a1) 830(39%,b1) 742(64%,b1) 697(91%,a1) 636(89%,b2) 354(85%,b1) 410(93%,a2)

coord

benzene

s-triazine

1,2,3-triazine

1,2,4-triazine

s-tetrazine

trigo

1030(100%,b1u)

1102(83%,b1)

1021(19%,b2g) 726(83%,b2g) 624(66%,e2g) 624(66%,e2g) 413(59%,e2u) 413(59%,e2u)

1139(28%,a1) 1099(64%,a1) 832(51%,b1) 789(49%,b1) 682(90%,a1) 668(87%,b2) 310(88%,b1) 366(89%,a2)

1067(60%,a′)

chaird

1160(73%,a′1) 1011(40%,a′1) 957(28%,a′′2) 762(99%,a′′2) 693(90%,e′) 693(90%,e′) 354(95%,e′′) 354(95%,e′′)

a

asym1b asym2c boate twistf

784(90%,b2g) 613(88%,ag) 721(94%,b3g) 437(84%,b3u) 351(91%,au)

798(84%,a′)

837(94%,b2g)

637(84%,a′) 730(87%,a′) 387(85%,a′,) 322(79%,a′,)

755(89%,ag) 655(95%,b3g) 258(75%,b3u) 354(100%,au)

a Trigonal deformation: R - R + R - R + R - R . b Asymmetric deformation 1: 2R - R - R + 2R - R - R . c Asymmetric deformation 1 2 3 4 5 6 1 2 3 4 5 6 2: R2 - R3 + R5 - R6. d Chair deformation: δ1 - δ2 + δ3 - δ4 + δ5 - δ6. e Boat deformation: -δ1 + δ3 - δ4 + δ5. f Twist deformation: -δ1 + 2δ2 - δ3 - δ4 + 2δ5 - δ6.

in ref 66). The older assignment of 882 cm-1 is simply untenable, and the present assignment frees up the 882 cm-1 band for 3b2u. (2) The au ring folding is given as 254 cm-1 by S2, but as 335 cm-1 by IRM. The CCSD(T) values support the former, the B3LYP results the latter assignment. Interestingly, the CCSD value66 is close to our B3LYP result, which may suggest that an unusually large effect of triple excitations is involved. (3) While IRM puts the 1b3u band at 929 cm-1, S2 puts it at 904 cm-1. The B3LYP calculations would appear to support the latter, the CCSD(T) ones the former assignment, but both levels of theory can be reconciled with either value without undue stretching of the imagination. Our calculations show the 3b2u band to be highly basis set sensitive, which is not really surprising given that the normal mode corresponds to the “Kekule´” motion, in this case leading to 2HCN + N2. For this particular mode, which may exhibit multireference character, CCSD(T)/6-311G** puts the frequency

only 26 cm-1 too high, rather than the full 80 cm-1 seen for B3LYP/6-311G**. Wiberg,29 on the basis of his scaled HF/6-31+G* frequencies, suggests that the 1415 cm-1 band is misassigned and that the original assignment of 1521 cm-1 for 2ag is correct. Both our B3LYP and the CCSD(T) calculations of ref 66 contradict this and suggest the 1415 cm-1 assignment to be correct. This mode is essentially a symmetric NN stretch combination, and SCF is especially deficient for such, leading to a significant overestimate even after scaling by 0.9. It is very encouraging that the very low 2b3u frequency of 254 cm-1 is reproduced almost exactly by the B3LYP calculations. Interestingly, CCSD(T)/6-311G** (all electrons) underestimates this frequency. Finally, it should be remarked that SCF is woefully inadequate for this molecule and that MP2 appears to capture most of the important correlation effects, with the notable exception of the Kekule´ mode and, to a lesser extent, the NN symmetric stretch: the deficiency of MP2 for describing

6982 J. Phys. Chem., Vol. 100, No. 17, 1996 NN bonds is well-known.70 CCSD and B3LYP agree quite well, overall, with the exception of the Kekule´ mode, for which only CCSD(T) yields a frequency in good agreement with experiment. Evidently, the curtain has not quite fallen over the issue of the harmonic frequencies of s-tetrazine, and a more accurate calculation would be of considerable interest. IV. General Observations From the above, we can infer a number of conclusions. (1) Performance of B3LYP for the harmonic frequencies of the azabenzenes is evidently more than satisfactory. (2) The only mode for which B3LYP appears to exhibit some deficiencies is the “Kekule´”-type vibration, which eventually leads to dissociation into lC2H2+mHCN+nN2 (where l + m + n ) 3, m + n ) the number of nitrogen atoms, and n ) the number of NN groups) and therefore can be understood to be a multireference problem. (3) The two principle modes which exhibit a significant basis set effect are the Kekule´-type vibration and the “pinwheel”type hydrogen motion. (4) Empirically corrected B3LYP/cc-pVnZ bond distances for n ) 2 and n ) 3 are essentially in complete agreement for CH distances, in excellent agreement (deviation about 0.001 Å) for CC distances and somewhat less good agreement (about 0.002 Å) for CN distances and differ markedly (0.003-0.004 Å) for NN distances. The predicted trend28,38 of a decrease by 2° of the CNC valence angles upon introduction of every additional N atom in the ring is confirmed for the diazines and triazines but not for pyridine, the decrease being 3° in the latter case. (5) Computed B3LYP/cc-pVTZ dipole moments appear to be in excellent agreement with experiment for the azabenzenes where experimental information is available (about 0.05-0.1 D too low). (6) The calculations turn out to be of great value in checking and/or correcting vibrational assignments. (7) From a comparison of the potential energy distribution of ring-mode frequencies given in Table 17 it can be concluded that in comparison with benzene36 in-plane modes resonate at higher frequencies, while out-of-plane modes are found to resonate at lower frequencies. The shift of the in-plane modes can be understood in terms of the more rigid nature of the N atom valence angles, while the lower frequencies for out-ofplane modes would indicate a decrease in aromaticity. Summarizing, we have presented another example of the invaluable tool that B3LYP with a sufficiently large basis set provides for understanding the structure and vibrational spectroscopy of “well-behaved” medium-sized organic molecules. Acknowledgment. J.M. is an NFWO/FNRS (National Science Foundation of Belgium) Senior Research Associate (“Onderzoeksleider”), and C.V.A. an NFWO/FNRS Research Director (“Onderzoeksdirecteur”). J.M. thanks the computer center of the LUC Business School for making idle time available on the IBM RS/6000 Model 580. References and Notes (1) Oliphant, N.; Bartlett, R. J. J. Chem. Phys. 1995, 100, 6550. (2) Gill, P. M. W.; Johnson, B. G.; Pople, J. A. Int. J. Quantum Chem. Symp. 1992, 26, 319. (3) Handy, N. C.; Maslen, P. E.; Amos, R. D.; Andrews, J. S.; Murray, C. W.; Laming, G. J. Chem. Phys. Lett. 1992, 197, 506. (4) Scuseria, G. E. J. Chem. Phys. 1992, 97, 7528. (5) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (6) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (7) Purvis, G. D., III; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F., III. J. Chem. Phys. 1988, 89, 7382. Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon,

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