Adiabatic semi-empirical parametric method for computing electronic-vibrational spectra of complex molecules part 3. Azines

Journal of

MOLECULAR STRUCTURE ELSEVIER

Journal of Molecular Structure 407 (1997) 209-216

Adiabatic semi-empirical parametric method for computing electronic-vibrational spectra of complex molecules Part 3. Azines V.I. Baranov, L.A. Gribov*, V.O. Djenjer, D.Yu. Zelent'sov Vernadsky Institute of Geochemistry and Analytical Chemistry Russian Academy of Sciences, Kosygin Str. 19, 117975, Moscow, Russia

Received 5 August 1996; accepted 4 October 1996

Abstract

Calculations of the excited state structure and absorption and emission spectra of azines (pyridine, pyrimidine, pyrazine and their deutero-substituted derivatives) were performed using the parametric method described previously. It is shown that the fragmentary approach for molecular model construction is suitable for heteroaromatic compounds with relatively small structural grou~s of the form rt>o, and c/N'~c taken as primary fragments. Compared with H>O., the "first approximation model" of c / x c has an additional parameter of the o-type that accounts for the peculiarities of the electronic density redistribution of n - r * transitions and affects primarily the changes in valence angles on excitation of the molecule. The major peculiarities of the vibrational structure of the experimental electronic spectra are well reproduced in the calculations and the parameters of the adiabatic molecular model obtained correlate well with the data estimated by other methods. © 1997 Elsevier Science B.V. Keywords: Azines; Excited state property; Vibronic spectra calculation

1. Introduction

In previous papers (Parts 1 and 2 [1,2]), we suggested a new parametric approach in the theory of electronic-vibrational states and spectra of complex polyatomic molecules. The method rests on the adiabatic molecular model and a new parameter set that specifies the model. Qualitative analysis and quantitative estimations have shown that these parameters (namely the first and second derivatives of the matrix of coulombic and resonant one-electron integrals with respect to the internal coordinates c3He/aq° and

* Corresponding author. Fax: +7 095 938 2054.

oZHe/(Oq°Oq°)) have clear physical meaning and possess all the required properties: "locality" (dependence on peculiarities of small-sized local atomic groups of molecules), transferability in a homologous series of related compounds, independence from small electronic density change, possibility to be ranked by their values, a small number of most significant parameters, etc. The conventional parameters of the adiabatic molecular model (location of the minimum of the potential surface and its curvature in the system of normal coordinates) in combining electronic states are directly defined by these matrix elements. Changes in geometry (As) and force constants (Au) of the molecule on excitation to the nth electronic state may be expressed

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becomes possible to predict both qualitatively and quantitatively the peculiarities of the molecule's structural changes on excitation and the vibrational structure of the electronic spectrum. The accuracy achieved is quite sufficient to analyse the spectral data in detail; moreover, if need be, it may be increased by the solution of the inverse vibronic problem [5]. In this paper, we apply this method to heteroaromatic molecules, namely to the molecules from the azine series: pyridine, pyrazine, pyrimidine and their deutero-substituted derivatives (for bond numbering, see Fig. 1). These molecules are of interest because, on the one hand, they include a new structural group of the form c/N-,c different from that considered earlier [1,2] and, on the other, their electronic density redistribution on excitation affects not only the 7relectrons but the (r-electrons as well (i.e. there are electronic transitions of n-Tr*-type) drastically differing from that in polyenes, diphenylpolyenes and acenes. This peculiarity of the matrix of the electronic density change AP n may force the use of qualitatively different parametrization of the ,molecular fragments. Moreover, as opposed to 7r-Tr transitions in polyenes, acenes and other molecules, the changes in the valence angles play a far more important role in the formation of the vibrational structure of the electronic spectrum than the changes in bond lengths [6]. The possibility of the qualitative reproduction of such an effect with the help of the parametric method is also considered in this paper.

to close approximation by the relations [1] -

(1)

Au~t=Sp(AP,, OqOOql) 02H~ )

(2)

where AP" is the matrix of electronic density change, A and L°q are the matrices of the squared vibrational frequencies and vibrational forms in the ground state, Hc=H+SV, H is the matrix of the coulombic and resonant one-electron integrals, S is the matrix of atomic orbital (AO) overlap integrals and V : Y~..I,(Z.Zb/r.b) is the nuclear potential energy. It is important that the method's parameters OHe/ ~gq0and 02He/(Oq°Oql~)are equal for the ground and all the excited states; changes in molecular structure on excitation are determined by the matrix of electronic density change, which can be easily calculated with the standard quantum chemical techniques (in particular, with the CNDO/S method or any other semiempirical or ab initio method). The application of our method to the calculation of the excited state structure and vibronic spectra of polyenes, diphenylpolyenes [1] and acenes [2] has confirmed its high efficiency even for the simplest "first approximation model" when only the most significant parameters are taken into account. There are only two such parameters (OH~/c)qbiand 02H~/(c)q~)2) for the explored molecules and they are equal for all the molecules of the given homologous series and for all the structural groups of the form n>c.. An important point in this method is that it is possible to isolate a primary structural unit of the molecule (molecular fragment), which is typical for each homologous series, and to use the fragmentary approach [3,4] and special data banks containing the parameters of such fragments to compute the vibronic spectra and molecular structure in the excited states. By this means, it 7

2. R e s u l t s a n d d i s c u s s i o n

Pyridine (PD), pyrazine (PZ) and pyrimidine (PM) ground state molecular models (force fields) were determined earlier [6,7] with the help of the inverse problem solution based on the experimental IR 7"

o -(2 4

7

o -(2

Iq

Fig. I. Bond numberingof pyridine, pyrazineand pyrimidine.

4

V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 209-216

spectra and data on the molecular geometry. The electronic density in the ground and excited states and the energies and oscillator forces for the pure electronic transitions were calculated by the semi-empirical CNDO\S method [8]. The vibrational structure of the electronic absorption and emission spectra for the given excited state models was calculated with the previously devised original methods [4,9-11[. To describe the molecular model in the excited electronic states, we use the parameters for the molecular fragment n>c. determined previously for the acenes [2] unchanged, together with additional parameters for the c/N-,c group containing a nitrogen atom. Their values were taken as follows

OH~

,t2H ~

Oq--T=O.08 a.u. and ~=0.3(Oqi) a.u.

(3)

for the n>c. group (b designates CC bond) and

--=0.05 ~3qb

Pyridine 1 2 3 1-6 1-2 2-3 3-4 2-7 3-8 Pyrazine 1 2 1-6 1-2 2-7 Pyrimidine I 2 3 1-6 1-2 2-3 3-4 2-7

a.u., - - =

- 0 . 0 4 a.u. and

Oq~

02Hr~ = 0.3 a.u.

(4)

(cgqb) 2

for the c/~-,c group (b designates CN bond, a designates CNC angle). The use of the additional (non-zero) angular parameter OHr~/Oqa of o-type for the c,'N-,c group as distinct from the n>o , group is caused by the fact that the electronic transition to the first excited state is of n-Tr*-type for the molecules under consideration, and an essential redistribution of the electronic density of the nitrogen's unshared electron pair occurs. Hence the respective Ap matrix elements of the o-type

Table 1 Changes in lengths (~/, A), valence angles (Ao~, rad) and force constants (z~u, 10 Bond. angle a

211

cm -) of azmes on going to the first excited state

AI, Ae¢

Au

Model Ib

Model II b

BOLF ~

0.015 -0.018 0.046 -0.002 0.013 0.004 -0.032 0.006 -0.028

0.022 -0.011 0.032 0.047 --0.001 -0.077 0.109 0.013 0.013

0.005 0.000 0.051 0.122 -0.058 -0.038 0.066 0.140 -0.054

0.030 -0.030 -0.021 0.010 0.018

0.027 -0.024 0.074 -0.037 0.043

0.030 -0.005 0.063 -0.031 -0.014

-0.002 0.038 0.003 0.008 -0.002 -0.006 0.008 -0.016

0.007 0.036 -0.008 0.026 -0.029 0.063 -0.072 0.001

0.003 0.045 0.007 -0.004 -0.096 0.175 -0.154 0.157

Literature values J

0.035 0.070 0.060

Model II ~

BOLF ~

-0.33 0.33 - 1.62

-0.20 0.00 -2.00

- I .05 0.60

-1.50 0.02

0.00 -1.35 -0.14

-0. I0 -1.80 -0.20

0.012 -0.061 0.140 -0.170 0.002

For the bond numbering, refer to Fig. 1. Calculation with (model II) and without (model I) accounting for the angular a-type parameter OHm,/OqT. Evaluation with the use of the semi-empirical BOLF relationship [12] for the bonds and the RAO method [6] for the angles. d Refs. [13-15].

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V.l. Baranov et al./Journal of Molecular Structure 407 (1997) 209-216

become of the same order as (or even more than) those of the r-type. Thus, even for the "first approximation model", they cannot be neglected when computing the change in molecular structure on excitation with Eq. (1). In particular, accounting for this parameter results in significant changes in the valence angles which are of crucial importance in the formation of the vibrational structure of the absorption and emission spectra of azines [6]. The description of the molecular model with the help of a limited number of most significant parameters certainly causes the optimal values to be different from those calculated by ab initio methods; therefore any parametric method is semi-empirical in nature. Taking this fundamental peculiarity into account, we performed an empirical fitting of these parameter values for PZ and, in so doing, based our evaluation on the experimental spectral data and indirect calculations of the molecular geometry in the excited state via the semi-empirical bond order/bond length/force constant (BOLF) relationship [12] and the method of rehybridization of atomic orbitals (RAO) [6]. The parameters obtained for the molecular fragments of PZ were used to compute the excited state structure and spectra of PD and PM without any correction. In Table 1, we present the results of the calculation of the geometry changes for PZ, PD and PM on going to the first excited state. Accounting for the angular

, , ) % . , °/

i

o

I

I

iooo

I

Wavenumbers (era -I)

Fig. 2. Experimental [20] (a) and calculated (b) absorption spectra of pyridine. parameter OH~,lOq~ (model II) leads to non-essential corrections to the bond lengths and force constants compared with the results of model I, which does not account for this parameter. Their values, as a whole, agree well with the values obtained with the BOLF relationship [12]. By contrast, the changes in the valence angles for model II are generally several times greater than those for model I and correlate with the RAO evaluations [6] and with the data reported in the literature (see Refs. [ 13-15]). Therefore the "first approximation model" (Eq. (3) and Eq. (4)) for PZ, PD and PM gives an adequate picture of the change in molecular geometry on excitation. Nevertheless, the final judgement on whether or not this model adequately describes the actual molecular

Table 2 Excited state vibrational frequencies (cm-~) of the totally symmetric fundamentals of pyridine, pyrazine and pyrimidine~ Molecule

Wilson vibration number

Observedb

Pyridine

6a 1 12 18a 8a 6a 1 9a 8a 6a 1 12 9a 19a

557, 542 (535, 523) 968 995, 982 (954, 950) 1089 (823)

Pyrazine

Pyrimidine

583 (564) 966 (831) 1101 (978) 1373 613 (595) 941 1012 (1002) 1109 (929)

Frequencies of the totally deutero-substituted derivatives are given in parentheses. Refs. [16-20].

Calculated 595 (580) 958 (925) 1019 (1017) 1067 (836) 1582 (1563) 594 (583) 975 (944) 1234 (890) 1582 (1568) 663 (645) 972 (852) 1034 (1053) 1158 (941) 1503 (1486)

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V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 209-216

I

a

J

o

'

idoo

'

'

Wovenumbers (cm-~)

Fig. 3. Experimental [20l (a) and calculated (b) absorption spectra

of pyridine-ds.

structure in the excited state can be made only after the vibronic spectra have been calculated and compared with the experimental spectra. The results of such calculations and a comparison of the totally symmetric vibrational modes are presented in Table 2 and Figs. 2 - 1 0 (we also present the spectra of the deuterosubstituted molecules). For convenience, in some instances, we outline these totally symmetric vibrations by a full line in the experimental spectral curves. The presence of the non-totally symmetric vibrations (broken line) in the spectra can be attributed either to strong vibronic coupling between the first and the following excited states [22,23] or to a non-planar configuration of the molecules in the excited state (of C2v symmetry [22]). As the previous calculation [6] shows, vibronic coupling in these molecules only affects the spectra slightly, with respective corrections to the band intensities of no more than 1% of the 0 - 0 transition intensity. Therefore the high intensity of the non-totally symmetric vibrations presented in the experimental spectra cannot be attributed to strong vibronic

1

i

|

0

_Lt 1

Iooo

i

i

Wovenumber$ (cm- i )

Fig. 5. Experimental [17] (a) and calculated (for model II (b) and model I (c)) fluorescence spectra of pyrazine.

coupling and is caused mainly by the reduction of the molecular symmetry group on excitation. However, since we were interested in the investigation of the devised parametric method in computing the major spectral peculiarities and molecular structure in the excited electronic states, we restricted ourselves to the simplest case of a planar molecular model. The effects caused by non-planar deformations call for special quantum chemical investigations and may be considered in another paper. On this basis, it can be concluded that the

o

.,,,,

• i I!

....

/ •

I

i

•

|

i I I ",-J 4

l\

tl~l

b

i

o

i

i

Iooo

I

,¢1

Wavenumbers (cm-*)

Fig. 4. Experimental [17] (a) and calculated (b) absorption spectra of pyrazine,

A

IObO Wovenumber$ (cm-t )

Fig. 6. Experimental [17] (a) and calculated (b) absorption spectra of pyrazine-da.

214

V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 209-216

o

0

O

I

-

b 0.9-

I

o

I

ltl

I

A

0.8 0.7

I000

0.6

Wovenumbers (cm-')

Fig. 7. Experimental [17] (a) and calculated (b) fluorescence spectra of pyrazine-d4.

o.5 i

0.3

calculated absorption and emiss]on spectra agree satisfactorily with the experimental data (Figs. 2 10). All the experimentally observed totally symmetric vibronic bands were present in the calculated spectra, which is sufficient for sophisticated analysis of the experimental vibrational structure; the inverse vibronic problem [5] can be solved to gain better agreement of the molecular parameters. The calculated intensity of the most active fundamental 6a (and its overtones) in the spectra of azines is in good quantitative agreement with the experimental value (the difference is less than 20%) for PD, PZ and their deutero-substituted derivatives. In the

O"I = 0.2 0.1

'I

I AA A

500

I

4

I000

1500

fooo

15bo

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

L:'.,

0.1 0i

5bo

Wavenumbers (cm -j ) I

31000

3/800

!

32000

32600

Wovenumbers (cm -~ )

Fig. 8. Experimental [19] (a) and calculated (b) absorption spectra of pyrimidine.

Fig. 9. Experimental [19] (a) and calculated (for model II (b) and model I (c)) fluorescence spectra of pyrimidine.

theoretical spectra of PM, the intensity of this band (as well as all other bands) is underestimated compared with the intensity of the 0 - 0 transition (electronic origin), but the ratios of the totally symmetric band intensities are correct as a whole. The calculated spectra for molecular model I (which accounts only for the parameters of the 7rtype, as in the case of polyenes and acenes [1,2]) do not agree with the experimental spectra even qualitatively. The major vibronic band 6a and its overtones and many other important bands are absent in the

V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 209-216

og I

60,*

~2,* 1

60,*120,

60 °

1

i,~o 601012°e

~2

215

analysis in Ref. [6], where it was shown that consideration of the atomic charges is also important when calculating n-Tr* transitions of heteroaromatic compounds.

3. Conclusions

A

A~ A ~

0

5()0

AA

IC~)

15~) 20~ Wovenumbers (cm -~)

Fig. 10. Experimental [21] (a) and calculated (b) fluorescence spectra of pyrimidine-d4.

calculated spectra. Fig. 5 and Fig. 9 illustrate this peculiarity for PZ and PM respectively. Consequently, it is essential that the parameters of a-type should be taken into account for the correct calculation of the n-Tr* transitions in heteroaromatic compounds. To the first approximation, only one additional angular parameter OH°,/Oq~ (Eq. (4)) need be used. This parameter affects only slightly the changes in bond lengths but considerably improves the changes in valence angles (see Table 1), so that the deformation vibrations become the most active in the vibronic spectra. An important point is that the use of only one parameter "centred" on the heteroatom leads to a significant change in all the valence angles of the molecule (not only immediately adjacent to the heteroatom, but also situated far from it; see, for example, angle 1-6 of PD in Table 1 and Fig. 1). This confirms the validity of the fragmentary approach and the use of quite small molecular groups (of the form c/U-,c and H>c.) as primary units even for strongly conjugated systems. It should be noted that the parameter 8H~J8qa is diagonal on the basis of hybrid atomic orbitals, and therefore its impact on the molecular model in the excited states is caused primarily by the changes in the atomic charges, in contrast with the parameter aH~J8q~, which is "coupled" with the changes in bond charges. This corresponds with the results of

The calculations of azines and their deuterosubstituted derivatives show that it is possible to use the semi-empirical parametric method to compute the major peculiarities of the excited state structure and vibronic spectra of heteroaromatic molecules. As in the case of polyenes, diphenylpolyenes and acenes, the fragmentary approach for the construction of the molecular models can be used with the relatively small structural group of the form c/N,,c taken as the primary fragment accounting for the heteroatom. The simplest "first approximation model" provides a satisfactory qualitative and quantitative description of the main regular trends in the changes in the molecular geometry and spectra. It is important that an additional angular parameter of the o-type, corresponding to the nitrogen unshared electron pair, is used for the calculation of the n-Tr transitions because of the significant redistribution of the c/N,,c group electronic density. This parameter has a large impact on the change in valence angles resulting in an increase in the most active deformation vibration 6a in the calculated spectra. The adiabatic molecular model in the excited states (bond lengths, valence angles and force constants) may be refined both by the inclusion of additional non-zero parameters of the molecular groups (by this means, going to the "second approximation model") and by the solution of the inverse vibronic problem.

Acknowledgements The authors gratefully acknowledge partial financial support of this investigation by the Russian Foundation of Fundamental Research, Grant No. 9603-34460.

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References [1] V.l. Bamnov, L.A. Gribov, V.O. Djenjer and D.Yu. Zelent'sov, J. Mol. Struct., 407 (1997) 177. [2] V.I. Baranov, L.A. Gribov, V.O. Djenjer and D.Yu. Zelent'sov, J. Mol. Struct., 407 (1997) 199. [3] L.A. Gribov, in Y.M. Kolotyrkin (Ed.), Physical Chemistry, Contemporary Problems, Khimiya, Moscow, 1987 (in Russian). L.A. Gribov, A.T. Todorovsky and S.Ya. Plotkin, J. Mol. Struct., 212 (1989) 1. [4] L.A. Gribov and W.J. Orville-Thomas, Theory and Methods of Calculation of Molecular Spectra, Wiley, Chichester, 1988. [5] V.L Baranov and L.A. Gribov, Zh. Prikl. Spektrosk., 51 (1989) 80 (in Russian). V.I. Baranov, Zh. Prikl. Spektrosk., 51 (1989) 296 (in Russian). [6] V.I. Baranov, G.N. Ten and L.A. Gribov, J. Mol. Struct., 137 (1986) 91. [7] V.L Baranov and G.N. Ten, Izvestiya TSHA, (1985) 168, 183 (in Russian). [8] J. Del Bene and H.H. Jaffe, J. Chem. Phys., 48 (1968) 1807, 4050; 49 (1968) 1221. R.L. Ellis, G. Kuehnlenz and H.H. Jaffe, Theor. Chim. Acta, 26 (1972) 131. G.A. Segal (Ed.), Semiempirical Methods of Electronic Structure Calculation, Part A: Techniques, Part B: Applications, Plenum, New York, 1977. [9] L.A, Gribov, V.I. Baranov and B.K. Novosadov, Methods for Calculating Electronic-Vibrational Spectra of Polyatomic Molecules, Nauka, Moscow, 1984 (in Russian). [10] V.I. Baranov and D.Yu. Zelent'sov, J. Mol. Struct., 328 (1994) 179, 199. V.I. Baranov, L.A. Gribov and D.Yu. Zelent'sov, J. Mol. Struct., 328 (1994) 189; 376 (1996) 475.

[11] L.A. Gribov and V.A. Dementiev, Methods and Algorithms of Calculation in the Theory of Molecular Vibrational Spectra, Nauka, Moscow, 1981 (in Russian). V.I. Baranov, F.A. Savin and L.A. Gribov, Programs for Computing ElectronicVibrational Spectra of Polyatomic Molecules, Nauka, Moscow, 1983 (in Russian). [12] L. Salem, Molecular Orbital Theory of Conjugated Systems, Benjamin, New York, 1966. A. Julg, J. Chem. Phys., 65 (1968) 541. E.M. Popov, G.A. Kogan and V.M. Zheltova, Teor. Eksp. Khim., 6 (1970) 14 (in Russian). V.I. Baranov and L.A. Gribov, Opt. Spektrosk., 47 (1979) 91 (in Russian). [13] D.A. Kleier, R.L. Martin, W.R. Wadt and W.R. Moomaw, J. Am. Chem. Soc., 104 (1982) 60. [14] F. Zuccarello, A. Raudino and G. Buemi, Chem. Phys., 84 (1984) 209. [15] V.I. Berezin, Sverdlov Matth. L. Depos., in TsNII Elektronika, No. 3822-84 Dep., 1984. [ 16] J.V. Shukla, K.N. Upadhya and S.N. Thakur, Appl. Spectrosc., 26 (1972) 283. [17] Y. Udagawa, M. ho and I. Suzuka, Chem. Phys., 46 (1980) 237. [18] K.K. Innes, J.P. Byme and I.G. Ross, J. Mol. Spectrosc., 22 (1967) 125. [19] A.E.W. Knight, C.M. Lawburgh and C.S. Parmenter, J. Chem. Phys., 63 (1975) 4336. [20] Y. Mochizuki, K. Kaya and M. Ito, J. Chem. Phys., 65 (1976) 4163. [21] R.M. Hochstrasser and C.J. Mazzacco, J. Mol. Spectrosc., 42 (1972) 75. [22} N. Kanamaru and E.C. Lim, Chem. Phys., 10 (1975) 141. [23] W.H. Henneker, A.P. Penner, W. Siebrand and M.Z. Zgierski, J. Chem. Phys,, 69 (1978) 1884.