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A theoretical study of the vibrational spectra of imidazole and its different forms
247
Journal of Molecular Structure, 274 (1992) 247-257 Elsevier Science Publishers B.V., Amsterdam
A theoretical study of the vibrational imidazole and its different forms
spectra of
J. Sadlej, A. Jaworskil and K. Miaskiewicz2 Laboratory of Intermolecular Interactions, Warsaw University, PL-02-093 Warsaw, ul. Pasteura 1 (Poland) (Received 19 May 1992)
Abstract The equilibrium geometry, vibrational frequencies, and infrared and Raman intensities for imidazole, the protonated imidazole cation, the deprotonated imidazole anion and the imidazole ylide have been calculated at the SCF 4-21 G level. Infrared spectra predicted at this level of calculation reproduce the experimental spectra and enable the interpretation of the SERS spectra of imidazole adsorbed on a silver electrode to be confirmed in terms of the cationic, anionic and ylide forms of imidazole.
INTRODUCTION
This work is the continuation of an experimental study of the SERS spectra of the imidazole molecule adsorbed on an Ag surface. In a previous paper [l], the SERS spectra of imidazole adsorption on the Ag electrode and on metallic silver are reported. The SERS spectra have indicated that different forms of imidazole (the anionic, cationic, neutral and ylide forms) can be observed at the Ag surface [l]. In other papers [2,3], the SERS spectra proved to be useful in the study of polymerization reactions on an Ag electrode surface. Vibrational spectra of imidazole have been the subject of numerous experimental studies in matrix, in solution and in the solid phase [4-111. The vapor-phase [4] and matrix-isolation experiments [5] are the only ones in which the N-H vibrations are not obscured by intermolecular effects in Correspondence to: Dr. J. Sadlej, Laboratory of Intermolecular Interactions, Warsaw University, PLO2993 Warsaw, ul. Pasteura 1, Poland. ‘Permanent address: Laboratory of Molecular Spectroscopy, Institute of Physics, Warsaw University of Technology, PL-00-662 Warsaw (Poland). ‘Permanent address: The Mount Sinai Medical Center, Mount Sinai School of Medicine, Box 1218, New York, NY 16629-6574 (USA).
0022-2860/92/$05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
248
J. Sadlej et al.lJ. Mol. Struct., 274 (1992) 247-257
solution and in the solid phase. Thus, the prediction of the vibrational spectrum of imidazole is important and has been the subject of several theoretical studies including ab initio [12] and classical normal coordinate analysis [9]. Imidazole behaves like a base in aqueous solutions and forms cations (ImH+ ). In strongly basic solutions, neutral imidazole undergoes deprotonation and the ionic form is formed (Im-). Another form of imidazole, the ylide form, is a reactive species in the exchange process [13]. It is a neutral, dipolar tautomer of imidazole. The vibrational spectra of the cationic and anionic forms of imidazole are known, although without assignment. The spectrum of the ylide tautomer is unknown. In the present study we performed 4-21 G SCF calculations to optimize the geometry and to obtain IR frequencies for the four forms of imidazole. Comparison between the experimental and theoretical results has enabled an assignment of the absorption bands in the IR spectra of these forms to be made. The comparison could also support the interpretations of the SERS spectra of imidazole on an Ag electrode, in terms of the anionic, cationic and ylide forms. DETAILS OF CALCULATIONS
Geometry optimizations for the four forms of imidazole were performed at the ab initio SCF level with the 4-21 G basis set [14], using the MONSTERGAUSS program [15]. The optimization was carried out under the assumption that the molecules are planar. As far as these calculations are concerned, the optimized planar geometry corresponds to a minimum on the potential energy hypersurface in all cases reported. This was confirmed by the subsequent calculations of the vibrational frequencies (GAUSSIAN 88 program [IS]). As a result of the anharmonicity of the molecular vibrations, particularly of stretching, the calculated force fields are sensitive functions of the molecular geometries. It is therefore important to use accurate geometry. Experimental geometries have been suggested [17], or empirical bond length corrections for the ab initio geometries [12]. As experimental geometries are unknown for the cationic, anionic and ylide forms of imidazole, we prefer to use calculated geometries. The frequencies and intensities of the IR absorption bands were calculated at the 4-21 G level. The standard PED analysis of the calculated force field enabled the presentation of the form of the calculated normal modes [19]. The convention for atom numbering is shown in Fig. 1 and the internal coordinates used in the PED calculations are listed in Table 1.
249
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
=8\
=8\
c6-N4 II
J/Y
10
=9
Cation form
Imidazole-neutral
Q\
cc-N4
/y
N3
cc-N4 II
II
II
II
l/L
/=
/y1 N3
H9
H8\
10
II
II
II 1
/= c6-N4
1
/kNgc2 I H9
Anion form
Ylide form
Fig. 1. Numbering scheme for the various forms of imidazole. RESULTS AND DISCUSSION
Geometries The optimized geometries for the different forms of imidazole are shown in Table 2, together with the available experimental microwave spectroscopic data for imidazole [Ml. The labelling of the atoms is presented in Fig. 1. It is seen from Table 2 that, in general, the geometry predicted for imidazole agrees well with the experimental data. In the case of the bond lengths between heavy atoms, the greatest discrepancies between the predicted and experimental data are not higher than O.OlLO.02A. The predicted bond lengths involving H atoms are calculated to be longer by 0.01 Hi in comparison with microwave spectroscopic data. The predicted bond angles between the heavy atoms generally differ from the experimental values by not more than l-2’. The same is true for the bond angles involving H atoms. The optimized geometries of the cationic and anionic forms, having C,, symmetry, are not very different from those of imidazole. The C,N, and C,N, bonds are equivalent. The H-atom substitution on N, changes the CN
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
250 TABLE 1
Definition of the internal coordinates” for the C, ionic forms of imidazole and for the neutral imidazole molecule
No.
Cation
Anion Ylide Imidazole
ql
r(2,3) + r(W)
ql
ql
q2
r(4,6) + r(3,5) r(l,2) r(56) r(68) + r(5,7) r(3,9) + r(4,lO) (4,3,2) + o((2,6,3) + (2~5~3))+ W(4,5,6) + (3,6&i)) (856) - (8,4,6) + (7965) - (7,3,5) (10,2,4) - (10,6,4) + (9,2,3) - (9,5,3) ~(2~3)- r(2,4) ~(436) - 4375) r(68) - 4597) r(3,9) - r(4,lO) (a - b)(- (2,6,4) + (253)) + (1 - o)((3,6,5) - (4,5,6)) (1,4,2) - (1,3,2) (8,576) - (8,4,6) - (7,675) + (7,3,5) (10,2,4) - (10,6,4) - (9,293) + (9,573) ((a - b)((2,3,5,6) - (2,4,6,5)) + (1 - a)((4,2,3,5) + (3,2,4,6)) 1 out (4,2,3) 8 out (4,6,5) + 7 out (6,5,3) 10 out (2,4,6) + 9 out (5,3,2) (3,5,6,4) + W(4,2,3,5,) + (3,2,4,6) + a((2,3,5,6) + (2,465))) 8 out (4,6,5) - 7 out (6,5,3) 10 out (2,4,6) - 9 out (5,3,2)
q2 q3 q4 q5 _
q2 q4 q5 q3 q6 q8 q7 q9 ql0 q12 qll q13 -
q3 94 cl5
q6 97 q8 q9
ql0 qll
ql2 ql3 ql4
915 ql6 ql7 ql8
919 920 q21 q22 q23 44
q6 q7 q8 q9 ql0 _ qll q12 q13
q17
q15 q14 q16 ql8 q17 ql9
ql8 _
q21 q20
q14 q15 q16 _
r(2,3) = ql r(2,4) = q2 r(4,6) = q3 F(5,6) = q4 (r(3,5) = q5 r(3,9) = q6 r(5,7) = q7 r(6,B) = q8 r(1,2) = q9 q10 = q7 qll = q14 (9,3,2) - (9,3,5) (7,395) - (7,695) (8,496) - (8,536) (1,3,2) - (1,4,2) q16 = q22 q17 = q18 q18 = q19 q19 = out 7 q20 = out 9 q21 = q18 _
‘a = - 0.809, b = - 0.309. Number pairs are bond lengths; number triples are bond angles; number quartets are dihedrals; out (a, b, c) refers to the motion of the proton out of the plane defined by a, b, c atoms.
bond distances by 0.045& and the HCH and CNC angles by 4’. Opposite changes are observed in the anionic form and the CNC angle; these are smaller than in the neutral form of imidazole. However, it is also seen from Table 2 that the changes caused by the simultaneous substitution of an H atom on N, and the removal of an H atom from C!, are significant; both the NCN and the CNC angles change considerably. Vibrational frequencies, and IR and Raman intensities To our knowledge, no previous calculations of the force field for the cationic, anionic and ylide forms appear in the literature, apart from one ab initio calculation of the force field for imidazole [12]. The fundamental vibrational frequencies of the four imidazole forms calculated without any
J. Sadkj et al./J. Mol. Strut.,
251
274 (1992) 247-257
TABLE 2 The 4-21 G optimized geometry for imidazole and its different forms Imidazole
Cation
Anion
Ylide
C,
C,”
Czv
CZV
Bond lengths (A) 1.3686 N3C2 1.3018 N4C2 1.4003 N4C6 1.4000 N3C5 1.3501 c4c5 0.9917 H9N3 1.0637 HlC2 1.0625 HSC6 1.0631 H7C5
1.3236 1.3236 1.4003 1.4003 1.3490 0.9987 1.0648 1.0624 1.0624
1.3471 1.3471 1.3782 1.3782 1.3721 _ 1.0706 1.0701 1.0701
Angles (deg.) N3C2N4 C2N4C6 N4C6C5 C2N3H9
111.37 105.92 109.84 126.69
107.64 109.65 108.25 125.15
115.44 103.19 110.52 _
N3C2Hl N4C6H8
122.63 121.31
126.18 122.04
122.28 121.79
Ml
1.3742 1.3742 1.4033 1.4033 1.3592 0.9933 _ 1.0633 1.0633 100.50 113.59 110.31 122.25 _ 123.14
- 224.312083
- 224.708534
- 223.706567
- 224.287115
/0)
3.964
1.773
1.284
2.903
ZPE (u)
0.076988
0.092276
0.061784
0.076983
E,,(u)
EXP
1.363 1.312 1.381 1.376 1.362 0.998 1.077 1.070 1.071 112.0 110.7 110.7 126.2 122.5 127.9
scaling factor are reported in Tables 3-6, along with the experimental measurements. A complete assignment of the fundamental vibrations is available only for imidazole [12]. For the cationic and anionic forms, there are only experimental frequencies [7,8], which we assigned by comparing the experimental data with the calculated spectra. First, as expected, the vibrational frequencies predicted using the SCF force field are higher than the experimental ones. Calculations with higher accuracy would require the use of a larger basis set and a treatment of electron correlation. Our results for imidazole are in general agreement with those of Fan et al. [12]. However, some comments should be made regarding a few of the spectral assignments. There is some controversy about the assignment of some bands of imidazole in the literature. First, consider the group of ~10, vll and v12 frequencies. According to ref. 12, v10 = 1253cm-’ should be assigned to NH deformation, vll = 1164cm-l to ring deformation and v12 = 1136cm-l to CH deformation. We found vll to be mainly a ring deformation with only 10% NH deformation. There is also some doubt
J. S’adlej et al./J. Mol. Struct., 274 (1992) 247-257
252 TABLE 3
4-21 G calculated frequencies (cm-‘), IR intensities (kmmol-I), Raman intensities (A’u) and potential energy distribution, PED, (“/o) among the internal coordinates for imidazole No.
v
Intensity IR
Raman
Al modes 1 3885 2 3495 3 3461 4 3464 5 1689 6 1612 7 1529 8 1440 9 1395 10 1253 11 1164 12 1136 13 1113 14 1040 15 996
101.6 2.2 0.9 3.6 25.2 13.8 21.3 12.3 2.6 1.4 4.9 34.5 36.2 1.9 13.1
79.1 104.7 55.1 56.6 2.9 17.7 8.4 15.5 12.4 16.7 3.4 10.4 5.6 0.6 2.1
A2 modes 16 1065 17 1004 18 900 19 740 20 704 21 695
0.7 9.2 45.3 24.1 120.3 101.9
1.7 0.1 2.3 0.9 2.4 0.1
PED”
Approx. description
q’X102) qW1), q7WW qW5L 418) qW’% q’WO),qW9)
qW9, qW2), qW6) qW% qW8) qW% qWW, qW6) dW1) qW0)
NH stretch CH stretch C2Hl stretch CH stretch CC stretch + CNH def. HCN def., CN stretch HNC def., HCC def. HCC def., CN stretch HCBN def., CN stretch HCN def., CC stretch CN stretch, HNC def. CN stretch CN stretch, CNC def. Ring def. Ring def.
@1OW,G=WW qW’2) GW), qWW qlW7) qWW, qlW8) qlWW, qW39)
CH wag, NH wag CH wag C2H wag Tors. ring NH wag, tors. ring Tors. ring, NH wag
@W), qWW, qW6)
qW25h !l2w%qww q12@5),q1(14), q14(14)
q14(33),q2(wL qW4)
qww, @cw qww, Hw, ql(17)
“PEDs lower than 10% are not included.
about this frequency in the experimental data. NH deformation was not assigned in the vapor spectrum by Perchard et al. [4]. Colombo et al. [6] and Saloma and Spiro [ll] assigned this mode in the region 1400-1500 cm-l. It seems more reasonable to us to adopt v7 = 1529cm-’ as &NH). Another controversy is the assignment of ~15 = 996cm-’ and v14 = 1040cm-‘. According to our calculations, Fan et al. [12] and Siiman et al. [lo], these two modes are ring deformations, while Saloma and Spiro [ll] and Colombo et al. [6] found ~15 to be the out-of-plane CH mode. It seems that the theoretical assignment is correct, as this mode is quite characteristic. The above mode assignments were, thus, used as a guide for interpreting the SERS spectra of imidazole on an Ag electrode. The vibrational spectra of imidazole can be divided into three regions: (i) the stretching frequencies; (ii) the region of deformation fundamentals; (iii) the out-of-plane vibrations. The second region is the ‘most interesting from
253
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
TABLE 4 4-21 G calculated frequencies (cm-‘), IR intensities (km mall’), Raman intensities (A” u) and potential energy distribution, PED (%), for the cationic form of imidazole No.
v
Intensity
PED
Approx. description
qW9) q5G-W q3W9 qW), qW1), qW5) ew2), PNw, qW5)
NH stretch CH stretch C2H stretch CC stretch, HNC def. HNC def., CC stretch CN stretch, HNC def. HCC def., CN, CC stretch CN stretch Ring def.
Raman
IR Al modes 1 3810 2 3513 3 3474 4 1765 5 1597 6 1311 7 1227 8 1118 9 1041
31.1 16.9 38.9 94.7 22.8 7.0 12.7 2.2 0.1
A2 modes 10 1092 11 893 12 684
0.1 0.1 0.0
1.9 1.1 1.3
Gww q24W
Bl modes 1125 13 14 925 15 870 16 707
16.3 5.1 495.1 19.3
0.6 2.0 0.1 0.4
qww,
B2 modes 17 3800 18 3489 19 1654 20 1574 21 1426 22 1293 23 1096 24 1016
470.1 25.9 4.8 24.8 8.5 9.1 35.5 6.5
13.9 39.1 0.3 5.2 3.1 3.0 3.5 1.5
qw1w Gv9)
95.9
75.5 37.0 3.3 49.2 21.6 7.7 7.5 0.7
qW0, WW, @Wl) qW% qW% q4W
dW) q7m
CH wag NH wag Tors. ring
q22(108)
CH wag, HNC def. CH wag NH wag Tors. ring
!?21(22)
q2OW qW5h
q18(108)
qlwo
qlWO), ql5(35)
qlW5) qW’1)
qww, qww qllW), ql4W) qlW% qW8)
qlW4
NH stretch CH stretch CN stretch, HCBN def. HCN def. HCC def. HC2N def., CN stretch CN stretch, CNC def. Ring def., CN stretch
the point of view of changes caused in the imidazole molecule by substitution and removal of an H atom. However, this is the most difficult region to interpret. Contributions from the ring-stretching vibrations are spread over many normal modes with frequencies in the region 1600900cm-’ and the corresponding bands are not characteristic. The imidazole cation has 24 normal modes, so there are three new fundamentals (~15, v17 and ~20, see Table 4) in comparison with neutral imidazole. The imidazole anion has eighteen normal vibrations (Table 5). The
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
254 TABLE 5
4-21 G calculated frequencies (cm-‘), IR intensities (km mol-I), Raman intensities (A4u) and potential energy distribution, PED, (%), for the anionic form of imidaxole No.
v
Intensity
PED
Approx. description
q5W) qw4 Pm09 qW1) qW0, @.W8) mw7 !?W) Gw4 qW’3),ql(W
CH stretch C2H stretch CC stretch, HCN def. CN stretch, CNC def. NCH def., CC stretch CN stretch NCN def., CN stretch
IR
Raman
Al modes 1 3391 2 3355 3 1555 4 1304 5 1198 6 1182 7 1033
41.1 143.3 0.9 7.1 1.1 3.6 7.0
158.7 67.1 11.8 23.0 9.6 16.6 3.7
A2 modes 8 965 9 751
0.1 0.1
0.3 1.6
q18(111) q17(111)
CH wag Tors. ring
Bl modes 10 956 11 875 12 774
6.4 47.4 25.9
2.8 2.7 0.4
q15(105) q16(100) q14(106)
CH wag CH wag Tors.
B2 modes 13 3351 14 1575
58.4 9.1
CH stretch HCC def., CN stretch
15 16 17
1419 1267 1146
0.9 11.3 19.3
9.1 1.0 8.0
qlO(100) ql2(38), ql3(31), ql8(18) ql3(51), ql2(44) q8(77), q9(12) q9(49), qll(27), q3(15)
18
1027
41.5
2.0
quw
78.4 1.7
HCC def., HCPN def. CN stretch CN stretch, NCH def. Ring def.
ylide form has 21 normal vibrations, of which ~13, ~15 and v17 are new ones caused by the second N-H bond, in comparison to the neutral molecule. In the first region, the most characteristic changes are the shift of the NH stretching vibration to lower frequencies in the cationic form, with the same values for the ylide form. These changes are accompanied by the lowering of the IR intensities of these modes in the cationic, anionic and ylide forms; these frequencies can only be compared with the gas-phase experiments, because of the H-bonding. The CH bands are shifted towards higher frequencies in the cationic form, in the opposite direction in the anionic form, and for the ylide form, the frequencies are close to the neutral imidazole. The intensities of the CH modes are very weak in neutral imidazole and become much stronger in the other forms.
255
J. Sadlej et ak/J. Mot. Struct., 274 (1992) 247-257 TABLE 6
4-21 G calculated frequencies (cm-‘), IR and Raman intensities, and potential energy distribution, PED (%), for the ylide form of imidazole No.
v
Intensity IR
Al modes 1 3886 2 3492 3 1767 4 1565 1261 5 1169 6
PED
Approx. description
4mw qW8) @W’h q’W% @W qve, q4(W, qW0) qWlh qlU5) qlw?, q2cw, qW8)
NH stretch CH stretch CC stretch, HCN def. HCN def., CC stretch HCC def., CN stretch CN stretch, HCN def. CN stretch NCN def.
Raman
7.6 1.0 13.6 86.0 1.7 1.4
137.2 79.8 17.2 14.6 19.9 2.3
1128 1008
1.7 2.6
14.1 1.1
A2 modes 9 1039 10 819 11 684
0.1 0.1 0.1
2.9
Bl modes 12 865 13 807 14 676
129.7 22.9 18.7
2.6 1.3 0.1
q18@2)
CH wag NH wag Tors. ring
B2 modes 15 3866 16 3463 17 1532 18 1484 1200 19 20 1074 21 1015
151.1 0.5 5.9 0.4 3.3 39.4 6.3
26.5 55.3 7.9 1.8 1.3 0.9 4.1
qww qww
NH stretch CH stretch HCN def. HCC def., NC def. CN stretch, CNC def. CN stretch, HCC def. CNC def., CN stretch
7 8
4.6 2.5
qW5h qW6) cKW9) @l(lW
q20(102) q19(113)
q17(102) q16(101)
qlW6) qlW4, om5) q~76), qW4) qlO@W,qlW5) ql3Wh &‘W
CH wag NH wag Tors. ring
The second region contains the ring, CH and NH deformation modes. Except for the ~12, v14 and ~15 ring deformations, all the others are not characteristic modes. Imidazole has the N-H deformation mode at 1529 cm-‘. In the cationic form, this frequency is shifted to 1597 cm-’ and a new band appears at 1574 cm-‘. The anionic form does not have this mode. The 1565 and 1532 cm-l bands are the NH deformation frequencies in the ylide form and they are both higher than the value for the neutral molecule. The other frequencies in this region caused small changes in comparison with neutral imidazole. In the third region, the most important changes caused by H-atom sub-
256
J. Sad&j et al./J. Mol. Struct., 274~~992) 247-257
stitution are the shifts of the NH wagging modes to higher frequencies for the cationic and ylide forms. According to ref. 1, the new intense bands at 1640, 1490, 1375, 1300 and 920cm-‘, which appear in the spectrum at an electrode potential more positive than - 0.6 eV, are due to Im- . All these bands, except the one at 1640 cm-‘, can be found in the calculated spectra of the imidazole anion. The bands at 1130, 1215 and 1450 cm-’ are present in our spectrum of Im+ . The ylide form is the source of the bands at 1025, 1285 and 1350 cm-‘, according to ref. 1. We agree with this interpretation, since all but the 1285cm-l band are present in our ImY calculated spectrum. CONCLUSIONS
The main conclusions from this study are as follows. (i) The 4-21 G ab initio calculations of the equilibrium geometry of neutral imidazole give geometrical parameters that lie very close to the experimental ones. (ii) The force fields obtained at this level of calculation for imidazole and its different forms reproduce the trends in experimental frequencies and the changes caused in the imidazole molecule by adding or removing a proton. (iii) We agree with the interpretation proposed in ref. 1 that the SERS spectra of imidazole adsorbed at an Ag electrode could be interpreted in terms of the anionic and dipolar-ylide forms of imidazole. ACKNOWLEDGMENTS
We are grateful to Drs. K. Jackowska and J. Bukowska for suggesting the topic of this study and for helpful discussions. We would like to thank L. Lapinski for help with the PED program. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
J. Bukowska, A. Kudelski and K. Jackowska, J. Electroanal. Chem., 309 (1991) 251. J. Bukowska and K. Jackowska, Synthetic Metals, 35 (1990) 135. J. Bukowska, K. Jackowska, Synthetic Metals, 35 (1990) 143. C. Perchard, A.M. Bellocq and A. Novak, J. Chem. Phys., 62 (1965) 1344. S.T. King, J. Phys. Chem., 74 (1970) 2133. L. Colombo, P. Bleckmann, B. Schrader, R. Schneider and Th.Plesser, J. Chem. Phys., 61 (1974) 3270. M.D. Walters and T.G. Spiro, Inorg. Chem., 22 (1982) 4014. D. Garflukel and J.T. Edsoll, J. Am. Chem. Sot., 80 (1958) 3807. M. Cordes and J.L. Walter, Spectrochim. Acta, Part A, 24 (1968) 237. 0. Siiman, R. Rivellini and R. Patel, Inorg. Chem., 27 (1988) 3940. S. Saloma and T.G. Spiro, J. Am. Chem. Sot., 100 (1978) 1105. K. Fan, Y. Xie and J.E. Boggs, J. Mol. Struct. (Theochem), 136 (1986) 339. R.J. Sundberg and R.B. Martin, Chem. Rev., 74 (1974) 471.
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257
14 P. Pulay, G. Fogarasi, F. Pany and J.E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. 15 M.R. Peterson and R.A. Poirier, MONSTERGAUSS program, University of Toronto, Ont., 1981. 16 GAUSSIAN ss,M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topiol and J.A. Pople, Gaussian Inc., Pittsburgh, PA, U.S.A. 17 P. Pulay, G. Fogarasi, X. Zhon and P.W. Taylor, Vibr. Spectrosc., 1 (1990) 159. 18 D. Christen, J.H. Griffiths and J. Sheridan, Z. Naturforsch., Teil A, 37 (1981) 1378. 19 S. Califano, Vibrational States, Wiley, New York, 1976.
Journal of Molecular Structure, 274 (1992) 247-257 Elsevier Science Publishers B.V., Amsterdam
A theoretical study of the vibrational imidazole and its different forms
spectra of
J. Sadlej, A. Jaworskil and K. Miaskiewicz2 Laboratory of Intermolecular Interactions, Warsaw University, PL-02-093 Warsaw, ul. Pasteura 1 (Poland) (Received 19 May 1992)
Abstract The equilibrium geometry, vibrational frequencies, and infrared and Raman intensities for imidazole, the protonated imidazole cation, the deprotonated imidazole anion and the imidazole ylide have been calculated at the SCF 4-21 G level. Infrared spectra predicted at this level of calculation reproduce the experimental spectra and enable the interpretation of the SERS spectra of imidazole adsorbed on a silver electrode to be confirmed in terms of the cationic, anionic and ylide forms of imidazole.
INTRODUCTION
This work is the continuation of an experimental study of the SERS spectra of the imidazole molecule adsorbed on an Ag surface. In a previous paper [l], the SERS spectra of imidazole adsorption on the Ag electrode and on metallic silver are reported. The SERS spectra have indicated that different forms of imidazole (the anionic, cationic, neutral and ylide forms) can be observed at the Ag surface [l]. In other papers [2,3], the SERS spectra proved to be useful in the study of polymerization reactions on an Ag electrode surface. Vibrational spectra of imidazole have been the subject of numerous experimental studies in matrix, in solution and in the solid phase [4-111. The vapor-phase [4] and matrix-isolation experiments [5] are the only ones in which the N-H vibrations are not obscured by intermolecular effects in Correspondence to: Dr. J. Sadlej, Laboratory of Intermolecular Interactions, Warsaw University, PLO2993 Warsaw, ul. Pasteura 1, Poland. ‘Permanent address: Laboratory of Molecular Spectroscopy, Institute of Physics, Warsaw University of Technology, PL-00-662 Warsaw (Poland). ‘Permanent address: The Mount Sinai Medical Center, Mount Sinai School of Medicine, Box 1218, New York, NY 16629-6574 (USA).
0022-2860/92/$05.00 0 1992 Elsevier Science Publishers
B.V. All rights reserved.
248
J. Sadlej et al.lJ. Mol. Struct., 274 (1992) 247-257
solution and in the solid phase. Thus, the prediction of the vibrational spectrum of imidazole is important and has been the subject of several theoretical studies including ab initio [12] and classical normal coordinate analysis [9]. Imidazole behaves like a base in aqueous solutions and forms cations (ImH+ ). In strongly basic solutions, neutral imidazole undergoes deprotonation and the ionic form is formed (Im-). Another form of imidazole, the ylide form, is a reactive species in the exchange process [13]. It is a neutral, dipolar tautomer of imidazole. The vibrational spectra of the cationic and anionic forms of imidazole are known, although without assignment. The spectrum of the ylide tautomer is unknown. In the present study we performed 4-21 G SCF calculations to optimize the geometry and to obtain IR frequencies for the four forms of imidazole. Comparison between the experimental and theoretical results has enabled an assignment of the absorption bands in the IR spectra of these forms to be made. The comparison could also support the interpretations of the SERS spectra of imidazole on an Ag electrode, in terms of the anionic, cationic and ylide forms. DETAILS OF CALCULATIONS
Geometry optimizations for the four forms of imidazole were performed at the ab initio SCF level with the 4-21 G basis set [14], using the MONSTERGAUSS program [15]. The optimization was carried out under the assumption that the molecules are planar. As far as these calculations are concerned, the optimized planar geometry corresponds to a minimum on the potential energy hypersurface in all cases reported. This was confirmed by the subsequent calculations of the vibrational frequencies (GAUSSIAN 88 program [IS]). As a result of the anharmonicity of the molecular vibrations, particularly of stretching, the calculated force fields are sensitive functions of the molecular geometries. It is therefore important to use accurate geometry. Experimental geometries have been suggested [17], or empirical bond length corrections for the ab initio geometries [12]. As experimental geometries are unknown for the cationic, anionic and ylide forms of imidazole, we prefer to use calculated geometries. The frequencies and intensities of the IR absorption bands were calculated at the 4-21 G level. The standard PED analysis of the calculated force field enabled the presentation of the form of the calculated normal modes [19]. The convention for atom numbering is shown in Fig. 1 and the internal coordinates used in the PED calculations are listed in Table 1.
249
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
=8\
=8\
c6-N4 II
J/Y
10
=9
Cation form
Imidazole-neutral
Q\
cc-N4
/y
N3
cc-N4 II
II
II
II
l/L
/=
/y1 N3
H9
H8\
10
II
II
II 1
/= c6-N4
1
/kNgc2 I H9
Anion form
Ylide form
Fig. 1. Numbering scheme for the various forms of imidazole. RESULTS AND DISCUSSION
Geometries The optimized geometries for the different forms of imidazole are shown in Table 2, together with the available experimental microwave spectroscopic data for imidazole [Ml. The labelling of the atoms is presented in Fig. 1. It is seen from Table 2 that, in general, the geometry predicted for imidazole agrees well with the experimental data. In the case of the bond lengths between heavy atoms, the greatest discrepancies between the predicted and experimental data are not higher than O.OlLO.02A. The predicted bond lengths involving H atoms are calculated to be longer by 0.01 Hi in comparison with microwave spectroscopic data. The predicted bond angles between the heavy atoms generally differ from the experimental values by not more than l-2’. The same is true for the bond angles involving H atoms. The optimized geometries of the cationic and anionic forms, having C,, symmetry, are not very different from those of imidazole. The C,N, and C,N, bonds are equivalent. The H-atom substitution on N, changes the CN
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
250 TABLE 1
Definition of the internal coordinates” for the C, ionic forms of imidazole and for the neutral imidazole molecule
No.
Cation
Anion Ylide Imidazole
ql
r(2,3) + r(W)
ql
ql
q2
r(4,6) + r(3,5) r(l,2) r(56) r(68) + r(5,7) r(3,9) + r(4,lO) (4,3,2) + o((2,6,3) + (2~5~3))+ W(4,5,6) + (3,6&i)) (856) - (8,4,6) + (7965) - (7,3,5) (10,2,4) - (10,6,4) + (9,2,3) - (9,5,3) ~(2~3)- r(2,4) ~(436) - 4375) r(68) - 4597) r(3,9) - r(4,lO) (a - b)(- (2,6,4) + (253)) + (1 - o)((3,6,5) - (4,5,6)) (1,4,2) - (1,3,2) (8,576) - (8,4,6) - (7,675) + (7,3,5) (10,2,4) - (10,6,4) - (9,293) + (9,573) ((a - b)((2,3,5,6) - (2,4,6,5)) + (1 - a)((4,2,3,5) + (3,2,4,6)) 1 out (4,2,3) 8 out (4,6,5) + 7 out (6,5,3) 10 out (2,4,6) + 9 out (5,3,2) (3,5,6,4) + W(4,2,3,5,) + (3,2,4,6) + a((2,3,5,6) + (2,465))) 8 out (4,6,5) - 7 out (6,5,3) 10 out (2,4,6) - 9 out (5,3,2)
q2 q3 q4 q5 _
q2 q4 q5 q3 q6 q8 q7 q9 ql0 q12 qll q13 -
q3 94 cl5
q6 97 q8 q9
ql0 qll
ql2 ql3 ql4
915 ql6 ql7 ql8
919 920 q21 q22 q23 44
q6 q7 q8 q9 ql0 _ qll q12 q13
q17
q15 q14 q16 ql8 q17 ql9
ql8 _
q21 q20
q14 q15 q16 _
r(2,3) = ql r(2,4) = q2 r(4,6) = q3 F(5,6) = q4 (r(3,5) = q5 r(3,9) = q6 r(5,7) = q7 r(6,B) = q8 r(1,2) = q9 q10 = q7 qll = q14 (9,3,2) - (9,3,5) (7,395) - (7,695) (8,496) - (8,536) (1,3,2) - (1,4,2) q16 = q22 q17 = q18 q18 = q19 q19 = out 7 q20 = out 9 q21 = q18 _
‘a = - 0.809, b = - 0.309. Number pairs are bond lengths; number triples are bond angles; number quartets are dihedrals; out (a, b, c) refers to the motion of the proton out of the plane defined by a, b, c atoms.
bond distances by 0.045& and the HCH and CNC angles by 4’. Opposite changes are observed in the anionic form and the CNC angle; these are smaller than in the neutral form of imidazole. However, it is also seen from Table 2 that the changes caused by the simultaneous substitution of an H atom on N, and the removal of an H atom from C!, are significant; both the NCN and the CNC angles change considerably. Vibrational frequencies, and IR and Raman intensities To our knowledge, no previous calculations of the force field for the cationic, anionic and ylide forms appear in the literature, apart from one ab initio calculation of the force field for imidazole [12]. The fundamental vibrational frequencies of the four imidazole forms calculated without any
J. Sadkj et al./J. Mol. Strut.,
251
274 (1992) 247-257
TABLE 2 The 4-21 G optimized geometry for imidazole and its different forms Imidazole
Cation
Anion
Ylide
C,
C,”
Czv
CZV
Bond lengths (A) 1.3686 N3C2 1.3018 N4C2 1.4003 N4C6 1.4000 N3C5 1.3501 c4c5 0.9917 H9N3 1.0637 HlC2 1.0625 HSC6 1.0631 H7C5
1.3236 1.3236 1.4003 1.4003 1.3490 0.9987 1.0648 1.0624 1.0624
1.3471 1.3471 1.3782 1.3782 1.3721 _ 1.0706 1.0701 1.0701
Angles (deg.) N3C2N4 C2N4C6 N4C6C5 C2N3H9
111.37 105.92 109.84 126.69
107.64 109.65 108.25 125.15
115.44 103.19 110.52 _
N3C2Hl N4C6H8
122.63 121.31
126.18 122.04
122.28 121.79
Ml
1.3742 1.3742 1.4033 1.4033 1.3592 0.9933 _ 1.0633 1.0633 100.50 113.59 110.31 122.25 _ 123.14
- 224.312083
- 224.708534
- 223.706567
- 224.287115
/0)
3.964
1.773
1.284
2.903
ZPE (u)
0.076988
0.092276
0.061784
0.076983
E,,(u)
EXP
1.363 1.312 1.381 1.376 1.362 0.998 1.077 1.070 1.071 112.0 110.7 110.7 126.2 122.5 127.9
scaling factor are reported in Tables 3-6, along with the experimental measurements. A complete assignment of the fundamental vibrations is available only for imidazole [12]. For the cationic and anionic forms, there are only experimental frequencies [7,8], which we assigned by comparing the experimental data with the calculated spectra. First, as expected, the vibrational frequencies predicted using the SCF force field are higher than the experimental ones. Calculations with higher accuracy would require the use of a larger basis set and a treatment of electron correlation. Our results for imidazole are in general agreement with those of Fan et al. [12]. However, some comments should be made regarding a few of the spectral assignments. There is some controversy about the assignment of some bands of imidazole in the literature. First, consider the group of ~10, vll and v12 frequencies. According to ref. 12, v10 = 1253cm-’ should be assigned to NH deformation, vll = 1164cm-l to ring deformation and v12 = 1136cm-l to CH deformation. We found vll to be mainly a ring deformation with only 10% NH deformation. There is also some doubt
J. S’adlej et al./J. Mol. Struct., 274 (1992) 247-257
252 TABLE 3
4-21 G calculated frequencies (cm-‘), IR intensities (kmmol-I), Raman intensities (A’u) and potential energy distribution, PED, (“/o) among the internal coordinates for imidazole No.
v
Intensity IR
Raman
Al modes 1 3885 2 3495 3 3461 4 3464 5 1689 6 1612 7 1529 8 1440 9 1395 10 1253 11 1164 12 1136 13 1113 14 1040 15 996
101.6 2.2 0.9 3.6 25.2 13.8 21.3 12.3 2.6 1.4 4.9 34.5 36.2 1.9 13.1
79.1 104.7 55.1 56.6 2.9 17.7 8.4 15.5 12.4 16.7 3.4 10.4 5.6 0.6 2.1
A2 modes 16 1065 17 1004 18 900 19 740 20 704 21 695
0.7 9.2 45.3 24.1 120.3 101.9
1.7 0.1 2.3 0.9 2.4 0.1
PED”
Approx. description
q’X102) qW1), q7WW qW5L 418) qW’% q’WO),qW9)
qW9, qW2), qW6) qW% qW8) qW% qWW, qW6) dW1) qW0)
NH stretch CH stretch C2Hl stretch CH stretch CC stretch + CNH def. HCN def., CN stretch HNC def., HCC def. HCC def., CN stretch HCBN def., CN stretch HCN def., CC stretch CN stretch, HNC def. CN stretch CN stretch, CNC def. Ring def. Ring def.
@1OW,G=WW qW’2) GW), qWW qlW7) qWW, qlW8) qlWW, qW39)
CH wag, NH wag CH wag C2H wag Tors. ring NH wag, tors. ring Tors. ring, NH wag
@W), qWW, qW6)
qW25h !l2w%qww q12@5),q1(14), q14(14)
q14(33),q2(wL qW4)
qww, @cw qww, Hw, ql(17)
“PEDs lower than 10% are not included.
about this frequency in the experimental data. NH deformation was not assigned in the vapor spectrum by Perchard et al. [4]. Colombo et al. [6] and Saloma and Spiro [ll] assigned this mode in the region 1400-1500 cm-l. It seems more reasonable to us to adopt v7 = 1529cm-’ as &NH). Another controversy is the assignment of ~15 = 996cm-’ and v14 = 1040cm-‘. According to our calculations, Fan et al. [12] and Siiman et al. [lo], these two modes are ring deformations, while Saloma and Spiro [ll] and Colombo et al. [6] found ~15 to be the out-of-plane CH mode. It seems that the theoretical assignment is correct, as this mode is quite characteristic. The above mode assignments were, thus, used as a guide for interpreting the SERS spectra of imidazole on an Ag electrode. The vibrational spectra of imidazole can be divided into three regions: (i) the stretching frequencies; (ii) the region of deformation fundamentals; (iii) the out-of-plane vibrations. The second region is the ‘most interesting from
253
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
TABLE 4 4-21 G calculated frequencies (cm-‘), IR intensities (km mall’), Raman intensities (A” u) and potential energy distribution, PED (%), for the cationic form of imidazole No.
v
Intensity
PED
Approx. description
qW9) q5G-W q3W9 qW), qW1), qW5) ew2), PNw, qW5)
NH stretch CH stretch C2H stretch CC stretch, HNC def. HNC def., CC stretch CN stretch, HNC def. HCC def., CN, CC stretch CN stretch Ring def.
Raman
IR Al modes 1 3810 2 3513 3 3474 4 1765 5 1597 6 1311 7 1227 8 1118 9 1041
31.1 16.9 38.9 94.7 22.8 7.0 12.7 2.2 0.1
A2 modes 10 1092 11 893 12 684
0.1 0.1 0.0
1.9 1.1 1.3
Gww q24W
Bl modes 1125 13 14 925 15 870 16 707
16.3 5.1 495.1 19.3
0.6 2.0 0.1 0.4
qww,
B2 modes 17 3800 18 3489 19 1654 20 1574 21 1426 22 1293 23 1096 24 1016
470.1 25.9 4.8 24.8 8.5 9.1 35.5 6.5
13.9 39.1 0.3 5.2 3.1 3.0 3.5 1.5
qw1w Gv9)
95.9
75.5 37.0 3.3 49.2 21.6 7.7 7.5 0.7
qW0, WW, @Wl) qW% qW% q4W
dW) q7m
CH wag NH wag Tors. ring
q22(108)
CH wag, HNC def. CH wag NH wag Tors. ring
!?21(22)
q2OW qW5h
q18(108)
qlwo
qlWO), ql5(35)
qlW5) qW’1)
qww, qww qllW), ql4W) qlW% qW8)
qlW4
NH stretch CH stretch CN stretch, HCBN def. HCN def. HCC def. HC2N def., CN stretch CN stretch, CNC def. Ring def., CN stretch
the point of view of changes caused in the imidazole molecule by substitution and removal of an H atom. However, this is the most difficult region to interpret. Contributions from the ring-stretching vibrations are spread over many normal modes with frequencies in the region 1600900cm-’ and the corresponding bands are not characteristic. The imidazole cation has 24 normal modes, so there are three new fundamentals (~15, v17 and ~20, see Table 4) in comparison with neutral imidazole. The imidazole anion has eighteen normal vibrations (Table 5). The
J. Sadlej et al./J. Mol. Struct., 274 (1992) 247-257
254 TABLE 5
4-21 G calculated frequencies (cm-‘), IR intensities (km mol-I), Raman intensities (A4u) and potential energy distribution, PED, (%), for the anionic form of imidaxole No.
v
Intensity
PED
Approx. description
q5W) qw4 Pm09 qW1) qW0, @.W8) mw7 !?W) Gw4 qW’3),ql(W
CH stretch C2H stretch CC stretch, HCN def. CN stretch, CNC def. NCH def., CC stretch CN stretch NCN def., CN stretch
IR
Raman
Al modes 1 3391 2 3355 3 1555 4 1304 5 1198 6 1182 7 1033
41.1 143.3 0.9 7.1 1.1 3.6 7.0
158.7 67.1 11.8 23.0 9.6 16.6 3.7
A2 modes 8 965 9 751
0.1 0.1
0.3 1.6
q18(111) q17(111)
CH wag Tors. ring
Bl modes 10 956 11 875 12 774
6.4 47.4 25.9
2.8 2.7 0.4
q15(105) q16(100) q14(106)
CH wag CH wag Tors.
B2 modes 13 3351 14 1575
58.4 9.1
CH stretch HCC def., CN stretch
15 16 17
1419 1267 1146
0.9 11.3 19.3
9.1 1.0 8.0
qlO(100) ql2(38), ql3(31), ql8(18) ql3(51), ql2(44) q8(77), q9(12) q9(49), qll(27), q3(15)
18
1027
41.5
2.0
quw
78.4 1.7
HCC def., HCPN def. CN stretch CN stretch, NCH def. Ring def.
ylide form has 21 normal vibrations, of which ~13, ~15 and v17 are new ones caused by the second N-H bond, in comparison to the neutral molecule. In the first region, the most characteristic changes are the shift of the NH stretching vibration to lower frequencies in the cationic form, with the same values for the ylide form. These changes are accompanied by the lowering of the IR intensities of these modes in the cationic, anionic and ylide forms; these frequencies can only be compared with the gas-phase experiments, because of the H-bonding. The CH bands are shifted towards higher frequencies in the cationic form, in the opposite direction in the anionic form, and for the ylide form, the frequencies are close to the neutral imidazole. The intensities of the CH modes are very weak in neutral imidazole and become much stronger in the other forms.
255
J. Sadlej et ak/J. Mot. Struct., 274 (1992) 247-257 TABLE 6
4-21 G calculated frequencies (cm-‘), IR and Raman intensities, and potential energy distribution, PED (%), for the ylide form of imidazole No.
v
Intensity IR
Al modes 1 3886 2 3492 3 1767 4 1565 1261 5 1169 6
PED
Approx. description
4mw qW8) @W’h q’W% @W qve, q4(W, qW0) qWlh qlU5) qlw?, q2cw, qW8)
NH stretch CH stretch CC stretch, HCN def. HCN def., CC stretch HCC def., CN stretch CN stretch, HCN def. CN stretch NCN def.
Raman
7.6 1.0 13.6 86.0 1.7 1.4
137.2 79.8 17.2 14.6 19.9 2.3
1128 1008
1.7 2.6
14.1 1.1
A2 modes 9 1039 10 819 11 684
0.1 0.1 0.1
2.9
Bl modes 12 865 13 807 14 676
129.7 22.9 18.7
2.6 1.3 0.1
q18@2)
CH wag NH wag Tors. ring
B2 modes 15 3866 16 3463 17 1532 18 1484 1200 19 20 1074 21 1015
151.1 0.5 5.9 0.4 3.3 39.4 6.3
26.5 55.3 7.9 1.8 1.3 0.9 4.1
qww qww
NH stretch CH stretch HCN def. HCC def., NC def. CN stretch, CNC def. CN stretch, HCC def. CNC def., CN stretch
7 8
4.6 2.5
qW5h qW6) cKW9) @l(lW
q20(102) q19(113)
q17(102) q16(101)
qlW6) qlW4, om5) q~76), qW4) qlO@W,qlW5) ql3Wh &‘W
CH wag NH wag Tors. ring
The second region contains the ring, CH and NH deformation modes. Except for the ~12, v14 and ~15 ring deformations, all the others are not characteristic modes. Imidazole has the N-H deformation mode at 1529 cm-‘. In the cationic form, this frequency is shifted to 1597 cm-’ and a new band appears at 1574 cm-‘. The anionic form does not have this mode. The 1565 and 1532 cm-l bands are the NH deformation frequencies in the ylide form and they are both higher than the value for the neutral molecule. The other frequencies in this region caused small changes in comparison with neutral imidazole. In the third region, the most important changes caused by H-atom sub-
256
J. Sad&j et al./J. Mol. Struct., 274~~992) 247-257
stitution are the shifts of the NH wagging modes to higher frequencies for the cationic and ylide forms. According to ref. 1, the new intense bands at 1640, 1490, 1375, 1300 and 920cm-‘, which appear in the spectrum at an electrode potential more positive than - 0.6 eV, are due to Im- . All these bands, except the one at 1640 cm-‘, can be found in the calculated spectra of the imidazole anion. The bands at 1130, 1215 and 1450 cm-’ are present in our spectrum of Im+ . The ylide form is the source of the bands at 1025, 1285 and 1350 cm-‘, according to ref. 1. We agree with this interpretation, since all but the 1285cm-l band are present in our ImY calculated spectrum. CONCLUSIONS
The main conclusions from this study are as follows. (i) The 4-21 G ab initio calculations of the equilibrium geometry of neutral imidazole give geometrical parameters that lie very close to the experimental ones. (ii) The force fields obtained at this level of calculation for imidazole and its different forms reproduce the trends in experimental frequencies and the changes caused in the imidazole molecule by adding or removing a proton. (iii) We agree with the interpretation proposed in ref. 1 that the SERS spectra of imidazole adsorbed at an Ag electrode could be interpreted in terms of the anionic and dipolar-ylide forms of imidazole. ACKNOWLEDGMENTS
We are grateful to Drs. K. Jackowska and J. Bukowska for suggesting the topic of this study and for helpful discussions. We would like to thank L. Lapinski for help with the PED program. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
J. Bukowska, A. Kudelski and K. Jackowska, J. Electroanal. Chem., 309 (1991) 251. J. Bukowska and K. Jackowska, Synthetic Metals, 35 (1990) 135. J. Bukowska, K. Jackowska, Synthetic Metals, 35 (1990) 143. C. Perchard, A.M. Bellocq and A. Novak, J. Chem. Phys., 62 (1965) 1344. S.T. King, J. Phys. Chem., 74 (1970) 2133. L. Colombo, P. Bleckmann, B. Schrader, R. Schneider and Th.Plesser, J. Chem. Phys., 61 (1974) 3270. M.D. Walters and T.G. Spiro, Inorg. Chem., 22 (1982) 4014. D. Garflukel and J.T. Edsoll, J. Am. Chem. Sot., 80 (1958) 3807. M. Cordes and J.L. Walter, Spectrochim. Acta, Part A, 24 (1968) 237. 0. Siiman, R. Rivellini and R. Patel, Inorg. Chem., 27 (1988) 3940. S. Saloma and T.G. Spiro, J. Am. Chem. Sot., 100 (1978) 1105. K. Fan, Y. Xie and J.E. Boggs, J. Mol. Struct. (Theochem), 136 (1986) 339. R.J. Sundberg and R.B. Martin, Chem. Rev., 74 (1974) 471.
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14 P. Pulay, G. Fogarasi, F. Pany and J.E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. 15 M.R. Peterson and R.A. Poirier, MONSTERGAUSS program, University of Toronto, Ont., 1981. 16 GAUSSIAN ss,M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J. Baker, R.L. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topiol and J.A. Pople, Gaussian Inc., Pittsburgh, PA, U.S.A. 17 P. Pulay, G. Fogarasi, X. Zhon and P.W. Taylor, Vibr. Spectrosc., 1 (1990) 159. 18 D. Christen, J.H. Griffiths and J. Sheridan, Z. Naturforsch., Teil A, 37 (1981) 1378. 19 S. Califano, Vibrational States, Wiley, New York, 1976.