Electron-vibrational spectra of pyridine, pyrazine and pyrimidine. Molecular structure in excited electron states

Journal of Molecular Structure (Theochem), 137 (1986) 91-111 Elsevier Science Publishers B.V., Amsterdam -Printed in The Netherlands

ELECTRON-VIBRATIONAL SPECTRA OF PYRIDINE, PYRAZINE AND PYRIMIDINE. MOLECULAR STRUCTURE IN EXCITED ELECTRON STATES

V. I. BARANOV,

G. N. TEN and L. A. GRIBOV

V. I. Vernadsky Institute of Geochemistry and Analytical Chemistry, of Science, 117975 Moscow (U.S.S.R.)

U.S.S.R. Academy

(Received 17 June 1985)

ABSTRACT Direct computations are given of the electron-vibrational spectra for pyridine, pyrazine, pyrimidine and their deuterosubstituted analogues. A detailed analysis is given of the nature of the first allowed nn*-transition of these molecules, by using charts of redistribution of electronic densities. Selection of molecular models of excited electron states was made using the previously suggested methods, i.e., variations in the bond lengths and force constants of the bonds were established from semi-empirical correlations between the length, force constant and n-order (index) of the bond; whilst variations in thevalence angles were defined by a semi-empirical method based upon the use of an hybridized-A0 basis for the approximation of electronic density distribution in the combination electronic states (the HA0 method). The possibility of determining the direction of HAOs corresponding to the unshared electron pairs (which must be predetermined when using the HA0 method), effected with the aid of the electronic-density charts, is illustrated. Electron-vibrational spectra have been interpreted. The computed spectra are quantitatively in agreement with experiment, thus offering further proof that the chosen molecular models are adequate for describing the real molecular structure in the excited state, and to the viability and efficiency of the method as a whole. INTRODUCTION

Recent years have witnessed the development and increasingly wide application of theoretical methods of analysis and interpretation of electronvibrational spectra of polyatomic molecules. This is accounted for, by the need to investigate and elucidate the structure of polyatomic molecules in excited electron states. It is worth noting here that, at present, electronvibrational spectra seem to be the only source of experimental data for these excited states. In addition, a marked advance in the experimental techniques enables fine-structure electron-vibrational spectra to be obtained, which cannot be interpreted in detail without the use of the relevant theoretical methods. To carry out a direct computation of the electron-vibrational spectrum of a polyatomic molecule, it is necessary to solve two generally independent 0166-1280/86/$03.50

o 1986 Elsevier Science Publishers B.V.

92

problems. The first problem is that of computing all the matrix elements occurring in the theory (vibrational wavefunction overlap integrals and electron-vibrational interaction integrals). This problem may be considered as having been solved by the development of pertinent computational methods and their implementation in the form of FORTRAN computer programs [ 1, 21. The second problem is the choice of a suitable model of a molecule in an excited electron state (molecular geometry and force field). Quantum-mechanical calculation of the geometry and force constants in polyatomics does not solve this problem, as variations in the molecular geometry and force constants under excitation are of the same order of magnitude (or even lower) as the errors inherent in the computational methods. It seems likely that a more promising solution is the use of semi-empirical methods and correlations; in particular they may be used to establish variations in bond lengths and force constants upon excitation of the molecule by using their correlation with bond indices (or n-orders) [2-41. Application of this type of method to the computation of the absorption and fluorescence spectra of a variety of molecules has demonstrated its high validity and dependability [2, 4, 51. In many cases, however, (especially in o?r*-states) the molecular valence angles are also appreciably changed upon excitation; these variations can become predominant from the point of view of formation of the electronvibrational spectrum. This paper presents a computational technique for establishing variations in the valence angle upon excitation. The essence of the method resides in the use of hybridized atomic orbit& (HAOs) for the purpose of approximation of the molecular electron-density distribution in the combination-electronic states. The HA0 basis is chosen on the principle of the maximum HA0 overlap for the bound atoms, which is why HA0 directions practically coincide with the bond directions and the angles between HAOs are consistent with the valence angles in a polyatomic molecule. Variations in the distribution of electronic density upon excitation of a molecule are interpreted as changes in hybridization, thus resulting in changes in the angles between HAOs, which represent the required changes in the molecular valence angles. The method may be modified to account for the way in which the charges are redistributed on the HAOs. The following modifications of the method can be used: (I) charges are considered to be the same on the HAOs in a given atom; (II) charges on the HAOs in an excited state are proportional to those on respective HAOs in the ground state; (III) charges are redistributed between the u-type HAOs of a given atom in proportion to variations in the u-charge on the corresponding bonds. What is more, redistribution of charges between the HAOs in the atom can be determined either by (a) taking into account the total charge on the atoms and bonds, or (b) by considering separately the charges of u- and n-types (methods IIa, IIIa and IIb, IIIb, respectively). Calculation of changes in the molecular valence angles upon excitation is reduced to the solution of simultaneous linear equations (on the assumption

93

that variations

in charges are relatively

small) as follows:

8,s’

where [A = A&a/Q* and &a = AQis/QAB are the relative variations in charges on the atom A and bond AB in the i-th excited state; K$ = Ad,/C, and 6d& = A&,/d, are the relative variations upon excitation in the coefficients in the representation of the r-th HA0 through the AOs in a given atom; @FAo = CrCsd,.&to, t, = C$E)C,’ and {cl = d,d,~,~S~~/C,,s~d,d,~,~S~~ are the relative contributions made by the r-th HA0 to the charge on the atom A, as well as the contribution made by the s-th and s’-th A0 overlap to the r-th and r’-th HA0 overlap in the atoms A and B. Coefficients d, determine the hybridization, i.e., the direction of the r-th HA0 (while C, are the normalizing coefficients, the square of which is equal to the charge on the r-th HAO, being determined to within a sign). This approach has been used by the authors to compute variations in the valence angles as applied to the molecules of HNO, H&O, CzHzOz and C4H4NZ upon transition to the first excited state. The results of the computations are in good agreement with the data given in the literature. It has been shown that method IIa is the optimum one for all three molecules, and a rule has been formulated for choosing the signs of the coefficients CA, CL in accordance with the variations in the charges on the AB bond. A detailed analysis of the method and the results of these computations will be published separately. In this paper, the presently suggested technique is used to compute the geometry of the excited states and the electron-vibrational spectra of molecules of pyridine, pyrazine, pyrimidine (Figs. 1, 2 and 3) and their deuterosubstituted analogues.

Fig. 1. Molecular diagram of the molecule of pyridine with the atom numbering, charge variations at the atoms (in parentheses) and o-components of the bond indices ca (in brackets). Fig. 2. Molecular diagram of the molecule of pyrazine with the atom numbering, charge variations at the atoms (in parentheses) and u-components of the bond indices, t”, (in brackets).

94

Fig. 3. Molecular diagram of the molecule of pyrimidine with the atom numbering, charge variations at the atoms (in parentheses) and u-components of the bond indices ta (in brackets). ELECTRONIC STRUCTURE OF MOLECULES IN THE GROUND AND FIRST-EXCITED ELECTRON STATES

The CNDO/S method has been used to compute the electronic molecular structure in the combination states, the energies and the probabilities of electronic transitions; 36 singly excited configurations were taken into account. The results of the computation of energies and oscillator strengths of the transitions are generally in good agreement with experiment (Table 1). The most recent experiments have demonstrated that the oscillator strength (f,,) of the vx* transition for ‘Al + lB2 in the range 7-7.5 eV is equal to 0.7 (c.f. the previously adopted value of f,,, = 1.3), and it is suggested that f,,,, for the corresponding transition in the pyrimidine and pyrazine molecules is also lower than that previously found by a factor of about two [6]. These data are in good agreement with the results of our computations. The first electronic transition, within the molecules under consideration, is commonly classified as a nn*-type transition. Here, as a rule, analysis is given to the type of configuration which determines the electronic wavefunction of the excited state and variation in the u- and n-charges on the atoms. Indeed, configurations which determine the electronic wavefunction of the first excited state of the molecules under consideration, are consistent with the transition of an electron from the MO of u-type to the n-type MO, wherein the maximum coefficients in the LCAO for these MOs contain the AOs of the nitrogen atoms. This is also in line with the nature of the changes in charges at the atoms; the major changes are the lowering of the u-charge and the increase of the n-charge on the nitrogen atoms. This consideration is, however, not sufficient for a comprehensive and detailed interpretation of the transition. The quantities of charges at the atoms and bonds, as obtained in quantum-mechanical computations, offer an integral characteristic of the charge distribution. They do not provide detailed information on the spatial

95 TABLE 1 Energies (E, eV) and oscillator strengths (f,,,,) pyridine, pyrazine and pyrimidinea Band characteristics

Molecule

E

nn*-trans.

1h-line

nn*-trans.

B,, h-lines

1

2

1

‘La-line 1 2

1

2

4.3

4.9 0.0056

4.8 5.2 0.04 0.0625

6.2 0.2 0.1

7.0 1.3 0.7

6.9; 7.1 22, 23 0.7826 7, 23 0.6388 6, 7

‘B,

‘B,

f osc 0.003

2

0.03 Pyrazine

IB, 3.8 0.01

Pyrimidine

of electron transitions in the molecules of

3.5 0.0055

4.8 0.1

‘B,

‘A,

4.5 0.0093

5.0 5.4 0.02 0.0744 0.05

6.5 0.1 0.01

‘B, 3.9 0.0069 0.0072

5.2 0.1625

6.3 0.145

6.1 0.0075

Ref.

‘B, ; ‘B, 6.3 0.1976

7.5; 7.5 1.0 0.7-0.8

7.6; 7.6 22, 23 0.6740 7, 23 0.3489 6

‘B 6.6 0.0948

7.2 1.0 0.5-0.6

7.3; 7.5 22, 23 0.5401 23 0.6747 6, 7

“( 1) Literature data; (2) calculated in this work.

distribution of electronic density and its variations upon excitation of the molecules nor, in particular, do they give information on the localization or delocalization of charges within certain structural groupings of the molecule. Furthermore they do not describe the quantity and nature of distribution of charges beyond these structural groupings. The above factors present a severe problem in making a complete interpretation of the electronic transition, especially in the case of small changes in the charges at the atoms and bonds, where the major role is played by the change in the character of the charge distribution in the regions immediately adjacent to individual structural elements of the molecule (atoms, bonds). It will be seen, from the following discussion, that in establishing the variations in the structure of molecules upon excitation, substantial importance is attached to the information concerning the spatial localization of the electronic density. The latter is consistent with the unshared electron pairs, without which the directions of the corresponding HAOs cannot be identified and, hence, a complete computation of changes in geometry cannot be performed. All of these problems can be readily solved by the setting up and the analysis of charts of the spatial distribution of electronic density, and its redistribution upon excitation of the molecules [8]. Of particular importance here is the illustrative nature of the data obtained and their high

96

information content. Some charts for the distribution of electronic density and its variations upon excitation, as computed for the molecules of pyridine, pyrazine and pyrimidine, are shown in Figs. 4, 5 and 6. The charts for the variations in the distribution of electronic density of molecules upon excitation, which characterize changes in the o-charges (Figs. 4a, 5a and 6a), show that the a-charge is diminished within the region of the molecule. The largest changes in the o-charge occur in the region of unshared electron pairs of the nitrogen atoms; a large portion of the overall change in the a-charge is represented by the changes at the carbon atoms

Z=0

Fig. 4. Variation in the distribution of electron density (Ap) in the molecule of pyridine upon transition to the first excited state: (a) in the plane of the molecule (Z = 0); (b) over the plane of the molecule (Z = 0.5 A).

(b)

Y,~

2 4

z=n

I

Fig. 5. Variation in the distribution of electron density (~p) in the molecule of pyrazine upon transition to the first excited state: (a) in the plane of the molecule (Z ffi 0); (b) over the plane o f the molecule (Z = 0.5 A).

97

Fig. 6. Variation in the distribution of electron density (Ap) in the molecule of pyrimidine upon transition into the first excited state: (a) in the plane of the molecule (2 = 0); (b) over the plane of the molecule (2 = 0.5 A).

(especially for pyrimidine). At a distance of 0.5 A above the molecular plane, the charge (n-charge) is seen to increase. Upon excitation of the molecule, the u-charge of the unshared electron pairs is transformed into the n-charge of the nitrogen and carbon atoms. It is worth noting that, for the pyrazine molecule, the x-charge increases mainly on the nitrogen atoms, whilst for the pyridine and pyrimidine molecules, the change on the carbon atom in the n-charge is comparable with, or even a little larger than, that on the nitrogen atom. Despite the fact that the molecules of pyridine and pyrazine differ from one another in the number of nitrogen atoms (and in the symmetry of the molecules), the redistribution of charges in these molecules upon excitation are very similar. The charts for the distribution of electronic density and its changes upon excitation of a molecule enable the region of localization of a charge on the unshared electron pairs in heteroatoms (i.e., respective HAO) and variations in this region upon excitation of the molecules to be determined. These data are indispensable in computing changes in the geometry of the molecules in excited states when using the HA0 method. This matter is discussed in detail in the next section. VARIATION IN THE MOLECULAR

GEOMETRY

UPON EXCITATION

Variations in the electronic densities occurring upon transition to the first excited state, as computed for the molecules of pyrazine, pyridine and pyrimidine, enable the changes in the lengths and force constants of the bonds and changes in valence angles to be determined. Changes in the lengths

98

and force constants of the bonds are determined from the computed, changes in the orders (or indices) of the bonds with the aid of the known correlations [3, 41. The values thus obtained are given in Table 2. The HA0 method, when used to find variations in the molecular valence angles upon excitation, does not provide information on the directions of the HAOs corresponding to the unshared electron pairs on the heteroatoms. In a number of cases where a molecule is symmetrical, this ambiguity can easily be eliminated. For example, it will be readily appreciated that due to the symmetry of the molecule of pyrazine, the HAOs in the molecule corresponding to the unshared electron pairs of the nitrogen atoms, are directed along the bisector of the respective angles. Another example is the glyoxal molecule for which the direction of the HAOs corresponding to the unshared electron pairs on the oxygen atoms are not known. However, due to the symmetry of the molecule changes in the valence angles upon excitation can be computed using the HA0 method without data on the direction of these HAOs. In other cases, additional assumptions should be used to eliminate such an ambiguity. The charts of the molecular electron density distribution in the combination states can be of material help in solving this problem. The charts of the molecular electron density distribution show a maximum electron density in the region of the unshared electron pairs. The direction towards this maximum electron density can be taken as the direction of the HA0 corresponding to this unshared pair (if there are two maxima, as is sometimes the case, the direction can be taken as the bisector of the respective angle). TABLE 2 Calculated changes in bond orders ( Ap, AC), bond lengths (A I) and force constants (AK) upon transition into the first excited state of the molecules of pyridine, pyrazine and pyrimidine Molecule

Bond

Ground state l(A)

K (X106 cm-‘)

Excited state A& At

Al (a) 0.051 0 0.005 0.005 0.001 0.0025

Pyridine

N,C, C,C, CSC, C,H, C,H, C,H,

1.355 1.378 1.397 1.092 1.080 1.080

11.5870 10.2402 10.3631 8.5650 8.5650 8.5650

-0.270 0 -0.012 -0.005 -0.001 -0.003

Pyrazine

NC cc CH

1.334 1.378 1.050

12.000 11.200 8.565

-0.175 0.003 -0.002

0.030 -0.005 0.001

Pyrimidine

CC!, N,C, N,C, C,H,, C,H, C,H,

1.395 1.355 1.335 1.085 1.085 1.085

11.0807 11.4111 11.0898 8.565 8.565 8.565

-0.011 -0.235 -0.016 0 -0.008 -0.0003

0.007 0.045 0.003 0 0.007 0

K(X106 -2.0 0 -0.2 -0.18 -0.05 -0.08 -1.5 0.02 -0.05 -0.2 -1.8 -0.1 0 -0.25 0

cm-*)

99

The validity of such an approach is substantiated by computations made for the molecule of glyoxal. If, in applying the HA0 method, the angle between the unshared pairs is set equal to 120” (which is the common practice), then variations in the angle upon excitation will become significant, ca. 2”. The chart for the electron density distribution within the plane of the glyoxal molecule (Fig. 7) shows that the angle between directions to the HA0 of the unshared pairs and CO bonds is 90”, remaining constant upon excitation of the molecule (angle variations less than 1”). This angle value in the HA0 method yields variations in the HAOs of the unshared electron pairs of ca. 0.1”) which is negligible and corresponds well with the variations obtained from charts of electron density. The HAOs, corresponding to the unshared electron pairs of pyridine and pyrazine are directed along the bisectors of the respective angles, and remain constant upon excitation of the molecules; this can be attributed to the symmetry of these molecules. In the pyrimidine molecule the unshared electron pairs are shifted with respect to the bisector of the respective angle towards the N3Cz bond by 6” (Fig. 8), and their direction remains invariable upon excitation of the molecule. Coefficients, Ci, the squares of which are equal to the charge on the r-th HAO, are determined according to the HA0 method to an accuracy of a sign. In principle, any combination of signs of these coefficients is possible, and this results in an ambiguity in solving the problem. The number of possible

Y

Y 0.5 a

0.58

Fig. 7. Chart of distribution of electron density (p) of the molecule of glyoxal in the plane of the molecule. (0) 1.7 *10e3; (1) 1.5 *lo-‘; (2) 2.9 *lo-‘; (3)4.4 *lo-‘; (4) 5.9 *lo-‘; (5) 7.4 010-r; (6) 8.8 ~10~~; (7) 1.0; (8) 1.2; (9) 1.3 a.u. Direction of unshared pair of an oxygen atom is shown by a dotted line. Fig. 8. Chart of distribution of electron density (p) of the molecule of pyrimidine in the plane of themolecule. (0)~ = 5.9~10-~;(1)9.5*10-2;(2)1.8~10~‘;(3) 2.8*10-‘;(4)3.8* 10-r; (5) 4.7 l10-r; (6) 5.7 *lo-‘; (7) 6.5 *lo-‘; (8) 7.6 *lo-‘; (9) 8.5 *lo-’ a.u. Direction of an unshared pair of the nitrogen atom is shown by a dotted line.

100

alternatives can be substantially reduced by using an empirical rule which was derived by the authors when computing the geometry of HNO, H,CO, CzHzOl and C4H4H2 molecules; i.e., the increase and decrease in the electronic density on various molecular bonds are associated with different signs of the Ck coefficients for the HAOs corresponding to these bonds. This rule may be illustrated by taking the molecule of pyridine as an example (see Fig. 1). In compliance with this rule, the C!: coefficients should be taken as positive (negative) for the C& bond, and as negative (positive) for the C4H9, C3Hs, C&, i.e., there are only two possible alternatives, while the total number of combinations of signs for C’i for the entire molecule is four (T T + I). In certain cases charge variation on a bond can be zero (for example,’ Alo’= 0 for the CIHlo bond in the molecule of pyrimidine). In these cases the number of alternatives is increased. However, a correct solution to the problem can be readily chosen from the existing alternatives. This can be done either on the basis of the qualitative picture of the molecular geometry variation, or by comparing the results of calculations with the experimental data (in particular, from the vibrational structure of the electronic spectra). It has already been mentioned that the HA0 method for computing variations in the molecular valence angles upon excitation, requires a number of modifications depending upon how the redistribution of charges on the HAOs of the atoms is taken into account (methods I, II, III and their a- and b-modifications). It should be noted that any one of these methods may be applied to all of the atoms in the molecule, or different methods may be applied to different atoms. Previous investigations of the HNO H&O, C2H202 and C4H4NZ molecule have shown that method IIa ensures correct results for all four molecules. This can be attributed, in particular, to the fact that variations in the n-charge in these molecules upon excitation represents a large percentage of the entire redistribution of charges. If only the variations in the u-charges were considered (for example using method IIb) the overall picture of the redistribution of charges would not be adequately reflected and thus a correct geometry of the molecule in the excited state would not be obtained. Investigations made by the authors have demonstrated that method IIa should be used, as a rule, in those cases where the order of magnitude of changes in the bond indices, t”, are about lo-’ for CH, and lo-’ for CC and CN. However, in each particular case, variations in charges on the atoms should also be taken into account. For example, in the pyridine molecule variation in E” for the C3C4 bond is an order of magnitude lower (see Fig. 1) than for the other CC bonds, but since variations in the u-charge on the C3 and C4 atoms are also rather small (-0.003 and -0.066, respectively), method IIa can also be used here. Calculated variations in the valence angles of the molecules of pyridine, pyrazine and pyrimidine appear in Table 3. Comparison of the results of these calculations with the data reported in the literature show that method IIa yields the most correct picture of changes

101 TABLE 3 Variations in the valence angles in the molecules of pyridine, pyrazine and pyrimidine upon transition to the first excited electron state Molecule

Pyridine

Angle

Ground state (Y*

Excited state Literature Methodsb values I

C,N,C, 114.8 125.05 C,C,C, 118.4 C,C,C, 118.3 N,C,I-$ 114.3 120.5

CombinaHa

-3.3

-5.4

-5.4 -

+

CNC 122.4

-1.3

CCH Pyrimidine

+ -

ti0n

-3.9

6.0

1.1 + +

Pyrazine

IIb

C,N,C, 115.1 N,C,N5 128.2 N&C, 122.6 C&C, 116.4 N,C,H,117.1

8.od -9.7 -3.5 0.7 0.1

16.8 -8.8 0.0 -9.8 0.5

-1.8

2.7 -10.0

3.0 -1.8 -6.1 -5.4 -0.8 -1.7 3.0 -0.5 0.3 -6.1 -O.l

12.6 -1.8 -o.2 -8.0 -0.1

10.0 -8.8 -5.5 -0.2 9.0

aIn degrees [24, 25, 261. bAngle calculated using HA0 method (Aor = aeKc - ati). CRefs.

17, 27 and 31, respectively. dRef. 27.

in the valence angles in the pyraxine molecule, which is as might have been expected. In the case of pyrimidine, however; not only method IIa but all the methods fail to provide results which would be in agreement with the reported data available. The reasons for this lie in the rather complicated redistribution of charges upon excitation, thus necessitating the use of different methods for different atoms. It has been inferred from the analysis of charge variations on the atoms and pertinent bonds in the molecule of pyrimidine that method I should be used for the atoms C4 and H8, while method III is best suited to the C1 atom since the charge variation at the bond CIHlo is zero, while at the bond Cl& this quantity has a value common to CC bonds (-0.011). Charge variation typical of method IIa is observed at the Cz atom and at the respective bonds. Application of a combination method (methods I, IIa and III) to the calculation of the valence angle variations in the pyrimidine molecule, yielded the results given in Table 3, which are in good agreement with the available calculation data obtained by other methods. Incidentally, calculations carried out by the authors have made it possible to choose the models for the molecules of pyridine, pyrimidine and pyrazine in the first electron excited state. Parameters characterising these models appear in Tables 2 and 3 (in Table 3 see method IIa for the molecules of pyridine and pyrazine, and a combination method for pyrimidine).

102

The final judgement on whether or not these models are adequate in describing the real structure of molecules in their excited states can be made only after their electron-vibrational spectra are computed and compared with experiment. As a preliminary step, known methods have been used to compute vibrations of these molecular models [9]. The results of the computations are given in Table 4 (for the vibrations active within the electronvibrational spectra). VIBRATIONAL

STRUCTURE OF ELECTRONIC SPECTRA

Pyridine The vibrational analyses of the molecular absorption spectra (transition So -+ 23,) for pyridine and pyridine-d, have been reported previously [ 10,111. TABLE 4 Frequencies of vibrations (active in electron spectra) of the molecules of pyridine, pyrazine and pyrimidinea Molecule

Pyridine

Symmetry

A1

4 Pyrazine

A

4 B, A

Pyrimidine

A,

A, 4 aFrequencies bRefs. 11,16,

for completely 23 and 28.

Wilson vibration number 12 1 6a 10a 16~ 16b

Frequencies of excited state This work

Ex~.~ 995( 954) 968

-

542( 535) 331(253) 60?

975(1008) 929( 892) 599( 586) 893(703) 366(324) 399( 364)

1 6a 80 9a 10a 4 5 160 17a 11 16b

966(831) 583( 564) 1373 llOl(978) 383( 292) 621 517 399(351) 234( 210)

971(882) 582(573) 1541(1532) 1230(944) 922(727) 755(628) 962( 395) 346(304) 946( 770) 781(773) 433( 696)

1 12 9a 6a 16a 16b

941 1012(1002?) 1109(929?) 613( 595) 238 366

959( 852) 1047(1057) 1129(929) 676(657) 406( 360) 349( 305)

deuterosubstituted

molecules

are given in parentheses.

103

Despite the fact that the above analyses were carried out proceeding from an incorrect assumption on the possibility of an analogy existing with the spectrum corresponding to the transition ‘B, + ‘A, in a molecule of benzene, the interpretation of completely-symmetric vibrations thus obtained has been further corroborated as a whole. Incompletely-symmetric vibrations have been investigated by Jesson et al. [ 121, where the vibrational component with frequency voo + 139 cm-’ (pyridine) had been assigned to the 16bZ, transition, i.e., to a transition initiating an overtone of frequency V1&.It has been further shown that the 10a vibration shows up in the spectra on account of electron-vibrational interaction between the excited state under consideration and the nearest excited RIT*state (‘&). Interpretation of the voo + 139 cm-’ component is somewhat doubtful. In particular, for the SVL fluorescence from the 16bi state, the spectrum is lacking the progression of the 16b vibration and consequently, this line in the spectrum corresponds to an unexcited band of a certain vibration [13]. Figures 9 and 10 show the computed absorption spectra for the pyridine and pyridine-d, molecules using the molecular models obtained for the firstexcited electron states (both with and without taking into account changes in the valence angles). For the sake of comparison, Figs. 9 and 10 include experimental absorption spectra of pyridine and pyridine-d5 in the benzene matrix at T = 4.2 K [ 141. These experimental spectra, as distinct from the absorption and fluorescence spectra in vapors [14, 151, show that for pyridine-d, the Fermi resonance is missing between vibrations 6~: and 12:

Fig. 9. Absorption spectrum of the molecule of pyridine: (A) experimental [14] ; (B) calculated with no account of the valence angles; (C) calculated with due account of changes in the valence angles (method IIa). Fig. 10. Absorption spectrum of the molecule of pyridine-d,: (A) experimental (B) calculated with due account of changes in the valence angles (method IIa).

[14];

104

due to a small (about 10-30 cm-‘) change in frequencies of the corresponding vibrations. Comparison of the computational results with experiment has shown that, first, the vibrational structure of the spectra is accounted for primarily by the changes in the valence angles in a molecule upon transition to the firstexcited electron state. A spectrum, when computed with variations in the bond lengths alone being accounted for, is far from consistent with experiment. In such a spectrum only the two components which correspond to the valence vibrations of ring 1 and 8a are seen; the intensity of these bands is lowered substantially. Secondly, a spectrum computed with regard to changes in both the bond lengths and the bond angles, agrees well with experiment both qualitatively and quantitatively. It can be concluded then that the model chosen is capable, as a whole, of adequately representing the actual molecular structure in an excited state, and that an interpretation of the spectrum may be performed. A strong band, comparable with the intensity of the O-O transition and, corresponding to vibration 6~; is observed in the spectra, which also include low-intensity bands consistent with other completely symmetrical vibrations. A component assigned to the vibration 12; in pyridine-ds has a lower intensity as compared with experiments; nonetheless, the behavior of intensity exhibited by the component upon transition from pyridine to pyridine-d5 is presented correctly in a qualitative sense (about a two-fold increase in intensity). The lack of a lOO%-quantitative agreement can be attributed in this case, we believe, to the fact that the molecular models used do not take into account variations in the angular force constants. The absorption spectra exhibit components due to the electron-vibrational interaction which correspond to vibrations 16b and 16~. In the case of component 16a, the major contribution is made by the interaction between the first excited state and the nearest excited nn*-state; component 16b is mainly accounted for by the interaction with the second and third states owing to the symmetry of these states, which leads to different polarization of these components (see Table 5). Consequently, it is vibration 16~ which shows up in the spectra, rather than the incompletely symmetrical vibration lOa as had been previously suggested [ 141. The voo + 139 cm-’ band should be assigned to the 16bh vibration rather than the 16b& Pyrazine Of the three molecules under consideration, pyrazine presents the greatest challenge from the point of view of interpretation of its electron-vibrational spectrum. This has caused appreciable differences in the interpretation of the vibrational structure of the absorption and fluorescence spectra of the pyrazine molecule (and, hence, its structure in an excited state) as reported by various authors [ 16,171. It can be seen from the vibrational structure of the absorption spectra of

105 TABLE 5

ES- ef) of electron-vibrational Coefficients 8,((tIaU,,/aQiIp)(pI~IS))/( molecule of pyridinea Vibration

Polarization Y

x

100 170 16a 11 4 5 lob 16b

interaction of the

0.1895 0.3248 0.5667 0.2373 0.4951 -0.5047 0.8308 0.4020

10-l lo-’ 10-l 10-l lo-* lo-= lo+ 10”

0 0 0 0.5079 0.8732 0.2519 -0.1955 -0.1537

1o-2 lo-* lo-* 1o-2 10-l

*Refs. 1 and 2.

pyrazine, that the frequencies of non-planar vibrations lOa, 5 and.l6b, which are active within the electron-vibrational spectrum, are substantially lowered upon transition of the molecule into the excited state ‘Bgu (nn*), while the frequency of vibration 16a is increasing. Thus, for example, the frequencies of vibration 1Oa in pyrazine in the ground- and excited-states are 919 and 383 cm-‘, respectively (for pyrazined,, these are 721 and 292 cm-‘, i.e., variations are about 60 per cent). So far as vibrations 5, 16b and 16~ are concerned, these changes are smaller, though still appreciable (5,32%; 16b, 44%; 16a, 17%) [ 161. These changes can be attributed to either a strong electronvibrational interaction between states lBgu (3.8 eV) and ‘Bzu (4.8 eV) [ 18, 191, or by a non-planar configuration of the molecule in an excited molecular state, with the symmetry going down from DZh to C,, [20]. The existence of a non-planar configuration of a molecule in an excited state is corroborated by the computation of the potential surface [17] and by investigation of the properties of the hydrogen-bound complexes [20], whilst its existence is very unlikely since the moment of inertia of pyrazine under excitation shows even smaller variations than in the case of pyrimidine and tetrazine [ 211. The absorption and fluorescence spectra computed for pyrazine and pyrazined, are shown in Figs. 11-14. It can be easily seen (Fig. 11) which of the possible models (consistent with different combinations of signs, see Table 3) is most closely related to the real molecule in an excited state, i.e., model 4 (method IIa;). The spectra computed for model 4 are in good agreement with experiment, illustrating the model’s consistency with the real molecular geometry in state ‘BgU. The calculation procedure reproduces well not only the relative intensities of the vibrational components of the absorption and fluorescence spectra produced by pyrazine, but also the intensity variations upon transition to pyrazine-&. Intensities of the components

-v-T-

3x-

315

320

325

0

nm

500

1500

2000

3000

3500

Fig. 11. Absorption spectrum of the molecule of pyrazine: (A) experimental [ 161; (B) calculated with no account of changes in the valence angles; (C) calculated with due account of changes in the valence angles (method IIa;); (D) as C (method IIa:); (E) as C (method IIa:). Fig. 12. Fluorescence spectrum of the molecule of pyrazine: (A) experimental (B) calculated with due account of changes in the valence angles (method IIa;).

310

315

320

nm

0

1000

2000

3000

Fig. 13. Absorption spectrum of the molecule of pyrazine-d,: (A) experimental (B) calculated with due account of changes in the valence angles (method IIa;).

[16];

cm-’

[16];

Fig. 14. Fluorescence spectrum of the molecule of pyrazine-d,: (A) experimental [16]; (B) calculated with due account of changes in the valence angles (method IIa;).

corresponding to vibrations 1 A and 9& increase upon the passage to the spectra produced by pyrazine-d, which is completely in line with experiment. It is worth noting that in the absorption spectrum for pyrazine the component corresponding to vibration 9J has greater wavelength than for

107

6a$ This is accounted for by the fact that model 4 takes no account of changes in the angle force constants. Consequently, this method is also of help in studying the finer effects which occur in the electron-vibrational spectra in connection with deuterosubstitution. Table 6 gives the results of the computation of the electron-vibrational interaction integrals made within the frame of the Herzberg-Teller approximation. One electron-vibrational interaction of state ‘Bgu can be observed not only with the nearest state, ‘BzU, of the ~g* type (the third excited state), but also with a higher state of the TV* type (for example, the seventh excited state). However, electron-vibrational interaction of pyrazine as a whole appears in the spectra only weakly, with the intensity of the respective vibrational components not exceeding 1% of the O-O transition intensity. High intensities of the vibrational components, consistent with the non-planar vibrations in the absorption and fluorescence spectra, and drastic reduction in the corresponding frequencies upon excitation of a molecule cannot, therefore, be attributed to a strong electron-vibrational interaction. The authors believe that these factors are accounted for by the lowering of the molecular symmetry upon excitation. Pyrimidine The results of the computation of the absorption and fluorescence spectra produced by pyrimidine are shown in Figs. 15-18 and Table 7. Calculation of the coefficients of the electron-vibrational interaction has shown that the planar vibrations of the pyrimidine molecule (both completely symTABLE6

Integrals ((tl(aU,,laQi)lp)) and coefficient-s ~:p((tl(aU,/aQi)lp)(~l~ls)} of the electronvibrational interaction of the pyrazine moleculea Electron states O-l 2-l 3-l 4-l 5-l 6-l 7-l 8-l 9-l

Vibration number 16~

170

10a

5

4

11

16b

0.0084 0.0063 -0.0046 0.0128 -0.0102 -0.0014 -0.0235 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.0104 -0.0041 -0.0052 -0.0031 -0.0023 -0.0048 -0.0022 -0.0003 -0.0029 0.0012 0.0019 -0.0094 0.0036-0.0109 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0021-0.0015 0.0072 0.0020 0.0017 0.0027 -0.0008 -0.0040 0.0028 -0.0012 -0.0013 0.0084 -0.0041 0.0128 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.0027 -0.0008 0.0011 -0.0002 -0.0010 0.0014-0.0029

(x) 1.076 0.2331 Coefficientb (y) 0.3110-0.05908

0.2040 0.2075 0.09234 0.2934 0.08966 0.1140-0.4883 0.01975 0.0167 -0.1857

aRefs.1 and 2.bCoefficient of electron-vibrational

interaction, 10'.

B B

2000 cm-’

1000

0

Fig. 15. Absorption spectrum of the molecule of pyrimidine: (A) experimental [28]; (B) calculated with due account of changes in the valence angles (combination method). Fig. 16. Fluorescence spectrum of the molecule of pyrimidine: (A) experimental [28] ; (B) calculated with due account of changes in the valence angles (combination method). TABLE 7 Coefficients {~p((tIav,,/aQiIp)(p(iIs))/(E~ the molecule of pyrimidinea Vibration

E!)} of electron-vibrational

interaction of

Polarization x

170 160 5 11 lob 4 16b

-

0.2860 0.2610 0.8033 0.8253 -0.6324 0.5413 0.1246

N

lo-* 1O-2 10” 1O-2 lo-* 10-z 10”

-c.9031 -0.3179 -0.1538 0.9999 -0.3236 0.2505 0.5061

10” 10-Z lo-* 1o-3 1O-3 1O-z lo-’

aRefs. 1 and 2.

metrical and incompletely symmetrical) do not “mix” the excited electron states; the Herzberg-Teller integrals differ from zero only for the first and second, and for the first and third nn*-states, but the probabilities of the respective transitions are zero. In the case of the non-planar vibrations the

109

coefficients of electron-vibrational interaction have the same order of magnitude as for the pyrazine molecule. The largest coefficient (0.1 X 10-l) corresponds to vibration 16b. The electron-vibrational interaction is, therefore, low and exerts no substantial impact on the vibrational structure of the absorption or fluorescence spectrum of the pyrimidine molecule. It is primarily the components corresponding to vibrations 1, 12, 9a and 6a that are most clear in the absorption and fluorescence spectra of pyrimidine and pyrimidined,. The results of the calculations represent well the changes in the intensity of component 12 upon transition from the spectrum of pyrimidine to pyrimidined+ There is generally good agreement between the calculated and experimental spectra. CONCLUSION

The calculations made in this work have shown that both the lengths and the force constants of the bonds and the valence angles are substantially changed upon excitation of the molecules of pyridine, pyrazine and pyrimidine, and that it is variations in the bond angles that determine the vibrational structure of their electronic spectra. This can be attributed to the fact

n

mm

HW

YZIO

Jam cm”

%a0

SD0

3uw

3wo cm*

Fig. 17. Absorption spectrum of the molecule of pyrimidine-d, (A) experimental [29] ; (B) calculated with due account of changes in the valence angles (combination method). Fig. 18. Fluorescence spectrum of the molecule of pyrimidine-d,: (A) experimental [30] ; (B) calculated with due account of changes in the valence angles (combination method).

110

that, as applied to the electron transitions discussed above (of the nn*-type), the u-charges in the molecules undergo a material change. Agreement between the calculated and experimental spectra reinforces the overall adequacy of the excited molecular models chosen to predict the real structure. This in turn corroborates that the assumptions made were correct, and that it is possible to use these methods to predict and to analyse the structure of these molecules .in their excited states. The computed spectra are representative not only of the qualitative distribution of the vibrational components and their intensity, but also of fairly subtle quantitative effects, such as for example, variations in intensities of the vibrational components upon deuterosubstitution. REFERENCES 1 V. I. Baranov, F. A. Savin and L. A. Gribov, Programmy Rascheta EIektronnoKolebatelnykh Spektrov Mnogoatomnykh Molekul (Programs for Computing ElectronVibrational Spectra of Polyatomic Molecules), NAUKA, Moscow, 1983. 2 L. A. Gribov, V. I. Baranov and B. K. Novosadov, Metody Rascheta EIektronnonKolebatelnykh Spektrov Mnogoatomnykh Molekul (Methods for Computing ElectronVibrational Spectra of Polyatomic Molecules), NAUKA, Moscow, 1984. 3 E. M. Popov and G. A. Kogan, Teor. Eksp. Khim., 1 (1965) 295. 4 V. I. Baranov and L. A. Gribov, Opt. Spectrosk., 47 (1979) 91. 5 V. I. Baranov and A. N. Solov’ev, Zh. Prikl. Spectrosk., 40 (1984) 780. 6 G. Ya. Zelikina, T. B. Mamchenko and T. G. Meister, Opt. spectrosk., 54 (1983) 332. 7 M. A. Kovner and S. K. Potapov, Usp. Khim., 36 (1967) 1460. 8M. M. Raikhshtat and V. V. Zhogina, Zh. PrikI. Spectrosk., 41(1984) 455. 9 L. A. Gribov and V. A. Dement’ev, Metody i AIgoritmy Vychisleniy v Teorii Kolebatelnykh Spektrov Molekul (Calculation Methods and Algorithms in the Theory of the Molecular Vibrational Spectra), NAUKA, Moscow, 1981. 10 H. Sponer and H. Stucklen, J. Chem. Phys., 14 (1946) 19. 11 J. V. Shukla, K. N. Upadhya and S. N. Thakur, Appl. Spectrosc., 26 (1972) 283. 12 J. P. Jesson, H. W. Kroto and D. A. Ramsay, J. Chem. Phys., 56 (1972) 6257. 13 Y. Mochizuki, K. Kaya and M. Ito, Chem. Phys., 54 (1981) 375. 14 Y. Mochizuki, K. Kaya and M. Ito, J. Chem. Phys., 65 (1976) 4163. 15 K. Sushida, M. Fujita, I. Yamazaki and H. Baba, Bull. Chem. Sot. Jpn., 56 (1983) 2228. 16 Y. Udagawa and M. Ito, Chem. Phys., 46 (1980) 237. 17 D. A. Kleier, R. L. Martin, W. R. Wadt and W. R. Moomaw, J. Am. Chem. Sot., 104 (1982) 60. 18 N. Kanamaru and E. C. Lim, Chem. Phys., 10 (1975) 141. 19 W. H. Henneker, A. P. Penner, W. Siebrand and M. Z. Zgierski, J. Chem. Phys., 69 (1978) 1884. 20 D. L. Narva and D. S. McClure, Chem. Phys., 11 (1975) 151. 21 K. K. Innes, A. H. Kalanter, A. Y. Khan and T. J. Durnick, J. Mol. Spectrosc., 43 (1972) 477. 22 G. Herzberg, Elektronnie Spektry i Stroenye Mnogoatomnykh Molecule (Electron Spectra and Structure of Polyatomic Molecules), MIR, Moscow, 1969. 23 K. K. Innes, J. P. Bume and I. G. Ross, J. Mol. Spectrosc., 22 (1967) 125. 24 C. W. N. Cumper, Trans. Farady Sot., 54 (1958) 1266. 25 Yu. 0. Gabel, Heterotsikhcheskie Soedinenya (Heterocyclic Compounds), Goskhimizdat, Moscow, 1941.

111 26 M. A. Kovner, B. N. Snigirev, A. V. Chaplik, V. I. Berezin, Yu. S. Korostelev and M. N. Zizin , Fizicheskie Problemy Spectroskipii (Physical Problems in Spectroscopy), U.S.S.R. Acad. Sci., l(l962) 376. 27 F. Zuccarello, A. Raudino and G. Buemi, Chem. Phys., 84 (1984) 209. 28 A. E. W. Knight, C. M. Lawburgh and C. S. Parmenter, J. Cbem. Phys., 63 (1975) 4336. 29 K. K. Innes, H. 0. McSwiney, J. D. Simmons and S. G. Tilford, J. Mol. Spectrosc., 31 (1969) 76. 30 R. M. Hochstrasser and C. J. Mazzacco, J. Mol. Spectrosc., 42 (1972) 75. 31 V. I. Berezin, Matth. L. Sverdlov, Depos., in TsNII Elektronika, No. 382284 Dep., 1984.