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Adiabatic semi-empirical parametric method for computing electronic-vibrational spectra of complex molecules part 2. Acenes
J o u r n a l of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 407 (1997) 199-207
Adiabatic semi-empirical parametric method for computing electronic-vibrational spectra of complex molecules Part 2. Acenes V.I. Baranov, L.A. Gribov*, V.O. Djenjer, D.Yu. Zelent'sov Vernadsky_ Institute for 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 acenes (benzene, naphthalene, anthracene and tetracene) have been performed using the devised parametric method. A relatively small structural group H~C = is used as the primary fragment for acenes, as well as for polyenes and diphenylpolyenes. Within the framework of the given method, the simplest "first approximation model", which uses only two common parameters for all the groups (SHTJOq b = 0.08 a.u. and 02H~/(8qb 2 = 0.3 a.u.), maintains the accuracy of the calculation to approximately 20 cm -~ for the excited state frequencies and 0.1 for the relative intensities of the vibrational fundamentals. The major peculiarities of the electronic spectra and the fine effects (such as mirror symmetry breakdown) are reproduced in the calculations. Thus quantitative computer simulation of the molecular structural properties, sophisticated treatment of the spectral data and fitting of the model parameters are made possible by the use of this semi-empirical parametric approach, together with the special data bank of molecular parameters. © 1997 Elsevier Science B.V. Keywords: Acene; Excited state property; Vibronic spectra calculation
1. Introduction The possible accurate theoretical simulation and prediction of the vibrational structure of molecular absorption and fluorescence spectra is of importance due to the high-level experimental techniques required for the recording of fine structure vibronic spectra of complex polyatomic molecules. This requires the development of a parametric theory of vibronic spectra which uses physically justified molecular models with parameters accumulated in special * Corresponding author. Fax: 00 7 095 938 2054.
data banks [1,2]. Such parametric semi-empirical methods find wide application in quantum chemical calculations of molecular structure and properties and in the theory of the IR spectra of polyatomics (see, for example, Refs. [2,3]). The possible application of the parametric approach to the calculation of the electronic-vibrational spectra of polyatomic molecules has been discussed previously [4,5], and a new parameter set suitable for both adiabatic and non-adiabatic variants of the theory has been suggested. In Part 1 [6], we examined the adiabatic variant of the theory in more detail and showed that changes in the molecular potential surface on excitation can be
0022-2860/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S0022-2860(96)09612-3
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V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
represented to sufficiently close approximation by the relations As" =-Lq°A -
3He LqSp(APn~qO)
I -0
(1)
( °2He
Au~t=Sp APnoqOOqO j
(2)
where AP" is the matrix of electronic density change on excitation to the nth excited state, A and L ° are the matrices of the squared vibrational frequencies and vibrational forms in the ground state, He=H+SV, H is the matrix of coulombic and resonant one-electron integrals, S is the matrix of the atomic orbital (AO) overlap integrals and V= •a,b(ZaZb/rab) is the nuclear potential energy. The quantities 3HJOq° and 02He/(Oq°Oq °) possess all the required properties for the parameters of semiempirical theory [4-6]. In particular, they offer distinct local peculiarities, transferability in a homologous series of related compounds, independence from small electronic density changes and the possibility to be ranked by their values. An important peculiarity of the method is its stability to small variations in these parameters. Calculations of polyenes and diphenylpolyenes [6] have shown that, to a first approximation, only two parameters common to all polyene structural groups of the form H>C = may be taken to describe molecular models in the excited electronic states, where the first parameter determines the change in geometry and the second the change in force constants. The theoretical spectra obtained for such molecular models agree well / \
\2
/
\~
, //3
\
• //'
/
\~
~__~/
/ >
\
/
/ \
\ /
,
o
/ \
\ /
/ \
\ /
\
/
Fig. 1. Bond numbering of naphthalene, anthracene and tetracene.
not only qualitatively but also quantitatively with the experimental spectra. However, in these calculations, we failed to determine the parameter values for the similar group H>0 = of the phenyl fragments because the latter were of little importance in the vibrational structure of the electronic spectra of diphenylpolyenes. In addition, it is of interest to investigate the application of the method to other homologous series of organic molecules. In this paper, we present calculations for the first four molecules of the acene series: benzene, naphthalene, anthracene and tetracene (see Fig. 1 for the bond numbering of naphthalene, anthracene and tetracene).
2. Results and discussion
The choice of meaningful parameters for the given homologous series, the determination of their values and the extent of transferability in the series are of fundamental importance in the description of the molecular structure in the excited states and the prediction of vibronic spectra using this method. This method, like any parametric technique, is semi-empirical in nature, because the description of the molecular model using a limited small number of most significant parameters results in the determination of the difference between the optimal values and the values obtained from ab initio calculations. The parameters were chosen by fitting their values to obtain the best agreement with the experimental data for the first two molecules of the series: benzene and naphthalene. Since direct experimental data on the molecular structure in the excited states are not available and the size of the molecules of interest renders extensive ab initio calculations impractical, we used indirect data obtained from spectral measurements and semi-empirical bond order/bond length/ force constant (BOLF) relationships [2,7,8] as an information source. These parameters of the acene group H;,C= were then used, without any correction, to compute the structures and spectra of the next two molecules (anthracene and tetracene) and to compare them with the experimental data. This allowed an estimation of the quality of the chosen parametrization, the extent of transferability of the parameters and the predictive ability of the method as a whole.
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
Molecular vibrations in combining electronic states and the vibronic structure of the electronic spectra were calculated using the previously devised original methods [2,7,9-11 ]. The calculations of the electronic density distribution, energy and oscillator strength for the pure electronic transition were carried out using the semi-empirical CNDO/S method [3,12]. The distinctive view of Ap" for the lowest energy electronic transitions of acenes allows us to conclude that, as with polyenes and diphenylpolyenes, r-type parameters for bonds qb are the most significant. Therefore, to a first approximation, we can take only 2 ~r b 2 two non-zero parameters, OH~/Oqp and 0 HrJ(Oqi) , common to all groups I'I>t3= where r and s designate the atomic 7r-orbitals of the atoms forming the ith bond ("first approximation model" (FAM)). This model can then be improved using second-order parameters. However, in this paper, we investigate the possibility of calculating the excited state structure of complex molecules and their spectra using this method, and therefore restrict our considerations to the crude model.
2.1. Benzene and naphthalene Adiabatic molecular models of benzene (BZ) and naphthalene (NL) in the ground state have been determined previously [13] on the basis of the calculation and treatment of their IR spectra; we use these models without any correction in this work. An analysis of the vibrational structure of the BZ absorption spectrum [14-17] shows that the major change in structure on excitation to the first excited singlet state $1 involves an increase in the CC bond lengths by 0.04 A, whereas the frequency of the active totally symmetric vibration decreases by approximately 70 cm -~. These data make it possible to evaluate the desired parameters of the FAM. We take the values OH~/Oqbi =0.08 a.u. and 02HTJ(Oq~) 2 = 0.3 a.u., which give A l c c = 0.043 ,~ for the change in bond length and AVcc = - 53 cm -1 for the change in vibrational frequency. These results also agree qualitatively with those obtained with the BOLF relationship for both BZ and NL (see Table 1). The sign and order of magnitude of the changes in the bond lengths and force constants and their ratios are well reproduced in the calculations. For example, the ratios of the change in
201
the second bond length to that of the fourth bond length (A12]AI4), calculated with this method and using the BOLF relationship, are equal to 0.43 and 0.48 respectively, and the similar ratios between the force constants are 0.33 and 0.39 for Au l/Au4 and 0.5 and 0.6 for Auz/AU4. The difference in sign for Al3 is of no importance because of its negligibly small absolute value (less than 5%, i.e. within the method's accuracy), and does not significantly affect the vibrational structure of the electronic spectrum. Compared with the BOLF evaluation, the slightly overestimated changes in the bond lengths do not necessitate a decrease in the parameter OHr/Oq~hi, because a major test of the model's validity is the agreement between the calculated vibrational frequencies and relative intensities and the experimental spectral data. A comparison between the calculated intensities of progression A 0 of BZ and the experimental data (see Table 2) shows good quantitative agreement: the difference is about 0.15, and the scatter in the experimental data [14-16] is also of the same order. The calculated BZ and NL vibrational frequencies in the excited state also agree well with the experimental values (Table 3). When fitting the parameters of the acene group H>C = , we did not use the experimental relative intensities of the vibronic bands of NL, because they are primarily determined by the extent of vibronic coupling in NL rather than by the change in the molecular potential surface. It should be noted that the devised method is not limited only by the FranckCondon approximation and can also be used in the case of strong vibronic coupling (Herzberg-Teller Table 1 Changes in the lengths (Al, ,~) and force constants (Au, 10 -~ cm -2) of carbon-carbon bonds for benzene and naphthalene on going to the first excited state Bond a
AI
Au
Benzene 0.043 Naphthalene 1 0.008 2 0.036 3 -0.006 4 0.083
0.032 b
-1.00
-1.37 b
0.017 0.025 0.004 0.052
-0.42 -0.64 -0.10 - I .28
-0.58 -0.93 -0.00 -1.49
a For the bond numbering, see Fig. 1. b Calculated using the BOLF relationship [8].
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
202
Table 2 Relative intensities for the A ° = u0o + 521 + n.923 cm -~ progression of the benzene absorption spectrum n
Calc.
Obs. [15]
Obs. [16]
Obs. [14]
I 2 3 4
0.73 1.00 0.66 0.28
0.71 1.00 0.82 0.45
0.74 1.00 0.77 0.40
0.87 1.00 0.87 0.46
approximation). The matrix elements o f vibronic coupling can be directly expressed in terms o f the parameters OHe/Oq ° and a2Hj(Oq°Oq °) and the matrix Ap, but, in order for the vibronic effects to be quantitatively reproduced, the c h o i c e o f appropriate m o l e c u l a r parametrization calls for special analysis and will be discussed elsewhere.
2.2. Anthracene The vibrational frequencies and forms of anthracene (AC) in the ground state have been calculated in Ref. [13]. A g o o d a g r e e m e n t b e t w e e n the results obtained and the experimental IR and R a m a n spectra supports the validity o f the ground state force field and m o l e c u l a r m o d e l as a whole. T o find the g e o m e t r y and force field o f A C in the first excited state and to c o m pute the vibrational structure o f the absorption and fluorescence spectra, we used this adiabatic m o d e l Table 3 Totally symmetric vibrational frequencies (cm -~) of benzene and naphthalene Ground state Benzene 991 3073 Naphthalene 485 773 1011
Excited state 993 a 3073
948 3071
923 a 3130
5130 761 1020
484 747 985
500 ° 702 987
1380
1310 1424 1543 3007 3044
1152
1360 1435 1593 3007 3045
1143
a Ref. [17], experimental data. o Ref. [18], experimental data.
1308
o f the ground state. Then, using the parameter values OH~/Oqbi=o.08 a.u. and OZH~J(Oq~)2 = 0.3 a.u. obtained f r o m B Z and NL, we found the changes in g e o m e t r y and force field o f A C on excitation using Eq. (1) and Eq. (2). W e present these data, together with those obtained using the Q C F F / P I m e t h o d [19] and B O L F relationship [20], in Table 4. The average difference in the bond length changes is 0.01 A and that of the force constant changes is 0.1 x 10 -6 c m -2, which are less than 1% o f the values o f the C C bond lengths and force constants in the ground state. This indicates that our F A M is adequate for the description o f the actual structure o f A C in the excited state, because the calculations [ 19,20] provide sufficiently accurate relative intensities of the vibrational bands in the absorption and e m i s s i o n spectra o f AC, and our results are not very different from those in Refs. [19,20], A c o m p a r i s o n o f the calculated and experimental spectra o f A C supports this conclusion. For example, the frequencies (see Table 5) differ, on average, by 15 c m -~ from the experimental values, with a maxim u m difference o f 44 c m -j for the v'2 = 1498 c m -1 band. Taking into account the underestimation by a p p r o x i m a t e l y 30 c m -~ of this m o d e f r e q u e n c y in the ground state (as well as o f the band ~"9 = 356 c m - l ) , the a g r e e m e n t should be considered as Table 4 Changes in the lengths (AI, ~) and force constants (Au, 10 ° cm -2) of carbon-carbon bonds for anthracene and tetracene on going to the first excited state Bond a Anthracene 1 2 3 4 5 Tetracene 1 2 3 4 5 6 7
Al
AU
-0.028 0.043 -0.032 0.011 0,030
-0.016 b 0.027 -0.013 0.004 0.021
-0.019 0.029 -0.030 -0.012 0.042 -0.007 0.007
-0.012 ° 0.017 -0.015 -0.007 0.020 0.000 0.000
-0.032 c 0.036 -0.028 0.009 0.016
a For the bond numbering, refer to Fig. 1. b Calculated using the BOLF relationship [8]. c Calculated with the QCFF/PI method [19].
0.37 -0.72 0.34 -0.04 -0.51
0.52 b -0.87 0.43 -0.12 -0.70
0.36 -0.50 0.32 0.15 -0.55 -0.01 -0.01
0.45 b -0.62 0.41 0.19 -0.68 -0.01 -0.01
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
203
Table 5 Totally symmetric vibrational frequencies (cm -~) of anthracene Mode
Ground state
1 2 3 4 5 6 7 8 9
1564 1456 1404 1255 1161 1021 735 578 356 " Ref. b Ref. Ref. d Ref. e Ref.
1568 a 1409 1267 1163 1020 759 629 394
Excited state 1566 b 1486 1408 1263 1165 1012 753 624 390
1562 ¢ 1411 1268 1175 1020 755 621 398
1557 d 1482 1403 1260 1163 1007 753 622 395
1564 1454 1390 1247 1161 1019 731 578 355
1501 a 1420 1380 9 1168 1019 755 583 385
1503 b ? 1399 1247 1157 1030 744 590 389
?c 9 1396 1239 1169 1028 733 590 392
1552 d 1498 1390 1218 1164 1026 737 587 393
1598 ~ 1516 1370 1249 1159 1046 773 715 390
[21], spectrum in n-heptane. [22], jet expansion spectrum. [23], spectrum in fluorine. [24], spectrum in 9,10-dihydroanthracene crystal. [19], calculated by the QCFF/PI method.
wholly satisfactory. It should be noted that our model of the AC force field reproduces the excited state vibrational frequencies much better than the QCFF/ PI model [19]; the latter has an average discrepancy of 30 cm -l, with a maximum value of more than 120 cm -1 for the u'8 = 590 cm -l mode. Since frequencies are determined primarily by the second derivatives of H e (see Eq. (2)), these data show that the parameter 02HTfl(Oq~) 2 = 0.3 a.u., obtained for BZ and NL, appropriately describes the changes in the force field of AC. The absorption and emission spectra of AC are depicted in Fig. 2 and Fig. 3. It is evident that the vibrational structure, as a whole, is well reproduced in the calculation; therefore the parameter OHTJOq b = 0.08 a.u., obtained for BZ and NL, also adequately describes the geometry of AC. Quantitative analysis demonstrates that the relative intensities of the AC totally symmetric fundamentals agree well with the experimental values [25] (see Table 6); the average difference is 0.05 (the maximal value is approximately 0.14 for the 4~ and 40 bands with a frequency of approximately 1250 cm-1). Some doubts are cast on the assignment of the 91 fundamental of the absorption spectrum in Ref. [25], because the intensity of the respective 90 band of the emission spectrum [25,26] is equal to 0.2, which is approximately twofold less. Moreover, the Dushinsky effect for this mode is small and so are the non-Condon corrections to the intensity (evaluated in Ref. [19]); therefore the absorption and emission spectra must have
approximate mirror symmetry. Therefore we consider the value of 0.2 for the relative intensity of the 9~ band presented in Ref. [26] to be more realistic. Small differences between the absorption and emission spectra are also represented correctly in
b
L &
0
I0oo
W~venumbers (cm -I ) Fig. 2. Calculated (a) and experimental [26] (b) absorption spectra of anthracene in 77 K n-hexane.
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
204
b
&
I000
0
0
IO00
Wa, v e n u m b e r s
(ern -1 )
Fig. 3. Calculated (a) and experimental [26] (b) absorption and emission spectra of anthracene in 4 K n-hexane.
our calculation. The major difference involves a decrease in the relative intensity of the most active 30 band in the emission spectrum by 0.1 compared with the intensity of the 30I band in the absorption spectrum. The QCFF/PI calculation [19] gives the opposite ratio of these values and an average error
for the relative intensities of the order of 0.1 (with a maximal value of more than 0.2). Therefore this method does not give such a good description of the molecular model in the excited states as our parametric method, Finally, it should be noted that, as with polyenes
Table 6 Relative intensities of the totally symmetric fundamentals of anthracene Absorption
Emission
Band
Calc.
Obs."
Calc. b
Band
Calc.
Obs."
Calc.b
Oo° I~ 2~ 3~ 40J 50~ 6~ 7g 80' 90j
1.oo 0.10 -< 0.02 0.54 0.15 0.07 0.03 0.09 -< 0.02 0.09
i.oo 0.17
l.OO 0.15
0.55 0.02 0.17 0.08 0.07
0.57 0.33 0.01 0.04 0.06
Oo° 1° 2~ 30 40 50 60 70 80 90
1.00 0.15 --< 0.02 0.45 0.20 0.07 --< 0.02 0.08 -< 0.02 0.08
1.00 0.14 0.42 0.06 0.06 0.03 0.02 0.02 0.16
1.00 0.05 0.04 0.68 0.01 0.03 0.0 I 0.02 0.06
-
0.41?
a Ref. [25], spectra in n-heptane. b Ref. [19], calculated by the QCFF/P1 method.
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
and diphenylpolyenes, changes in valence angles play an important role in the formation of the vibrational structure of the electronic spectrum. Although these changes are less (approximately five times) than those of the bond lengths and are not the decisive factor in computing the relative intensities, taking them into consideration essentially improves the agreement between the calculated and experimental spectra. For instance, for the most active 3~ fundamental (lob~ = 0.55 [25]), the calculated intensity increases by more than twofold and becomes very nearly equal to the experimental value (A/ -< 0.01) if the changes in angles are taken into account, and the same is also true for the 3 o band in the emission spectrum.
2.3. Tetracene To clarify the possibility of fast simulation of the main spectral and structural regularities of complex molecules using the devised method, we tried to compute the tetracene (TC) molecular model. This calculation has a model nature, and is based on the fragmentary method [10] for constructing molecular models in the ground state and the parametric method for constructing molecular models in the excited state with the parameters OH~/Oq~=O.08 a.u. and cq2Hrs/ (Oqbi)2 =0.3 a.u., obtained for BZ and NL. The ground state model was constructed from two
205
identical fragments, each consisting of AC without one terminal ring. As in all the other calculations, this was performed with the help of the LEV program [10] and the special data bank which now contains more than 300 molecules and molecular fragments [27]. Parameters of common carbon-carbon bonds and their nearest environments were taken from the appropriate group of AC. Contrary to the simple conjunction of two NL molecules, this method allows us to account for the peculiarities of the interior rings of TC more correctly. Quite satisfactory agreement between the calculated IR frequencies and the experimental data (Au <_ 20 cm -~, see Table 7) is achieved using such a simple and crude model. The changes in the molecular model on excitation, calculated by the parametric method and using the BOLF relationship, are given in Table 4. The calculated absorption and emission spectra (see Fig. 4 and Fig. 5) reproduce reasonably well (considering the crude model of the ground state) the observed vibrational structure only with respect to the vibrational frequencies (see Table 7). In this calculation, we failed to obtain quantitative agreement between the relative intensities of all the vibronic bands; in some cases, the calculated intensity is significantly less than the experimental value (for instance, we obtained lou~ 0.4 and Icalc ~ 0.05 for the 300 cm -r band and lob s 0.6 and Icalc ~ 0.1 for the 1450 cm -I band in the absorption spectrum).
Table 7 Totally symmetric vibrational frequencies (cm -~) of tetracene Excited state
G r o u n d state Calc.
Obs. a
300 600 719 757 968 1094 1157 1202 1364 1380 1441 1540
307 612 738
"Ref. [28]. Ref. [29].
986 1149 1381 1431 1536
Obs. b
Calc.
Obs. a
Obs. b
311 616 758 762 996 1013 1154 1198 1385 1446 154(I
297 598 716 757 971 1078 1145 1201 1364 1383 1448 1543
314 600 750 1159 1225 1362 1442 1551
308 609 746 755 1009 1151 1213 1361 1415 1549
206
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
number of parameters in the ground and excited states to obtain wholly satisfactory results. Nevertheless, even such a poor calculation allows us to evaluate the major structural changes in TC on excitation and to carry out a detailed treatment of the spectra. To obtain better agreement of the results, the parameters of the TC ground and excited state models may be fitted by solving the inverse vibronic problem, since the existing agreement is quite sufficient to state and solve such a problem correctly [30].
3. Conclusions 5()0
0
IO00
1500
Wa,venumbers (ore-')
Fig. 4. Calculated (a) and experimental [28] (b) absorption spectra of tetracene in supersonic jet.
This is caused primarily by the very crude model of the ground state and probably by the application limit of the FAM. Therefore, in this case, we may be forced to use a more sophisticated model with a larger
3000
2500
2600
iS00
1000
500
0
Wa,veuumbem (ern -1) Fig. 5. Calculated (a) and experimental [28] (b) fluorescence spectra of tetracene in supersonic jet.
The calculations of the molecular structure in the excited states and the vibronic spectra of acenes (benzene, naphthalene, anthracene and tetracene) confirm the high efficiency and performance of the parametric semi-empirical method in the adiabatic theory of polyatomic vibronic spectra [4-6]. As in the case of polyenes and diphenylpolyenes [6], a comparatively small structural group H~,C= can be used as a primary fragment for the acenes. The small number of parameters and the good extent of transferability in a homologous series enable an adiabatic molecular model to be constructed which adequately describes the actual excited state molecular structure, and also reproduces quantitatively the fine vibrational structure of the electronic spectra with a high degree of accuracy. The simplest model within the framework of this method, which uses only two common parameters for 2 7r b2 all the structural groups, aHffJOqbi and a t-lrJ(Oqi ) , provides an accuracy of calculation of the parameters to within 20 cm -~ for the vibrational frequencies and 0.1 for the relative intensities of the vibronic fundamentals. Even for such a crude molecular model, all the major peculiarities of the vibrational structure present in the calculated spectra (not only the most intense bands) are well reproduced; bands with comparatively small relative intensity (0.1 or less) are also reproduced well. Fine features (such as mirror symmetry breakdown due to normal mode mixing) are also well reproduced, and thus a sophisticated treatment of the spectra is available. If need be, further refinement of adiabatic molecular models is possible via the solution of the inverse vibronic problem.
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
Acknowledgements The authors gratefully acknowledge partial f i n a n c i a l s u p p o r t o f this i n v e s t i g a t i o n b y the R u s s i a n F o u n d a t i o n o f F u n d a m e n t a l R e s e a r c h , G r a n t No. 9603-34460.
References [1] 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. [2] L.A. Gribov and W.J. Orville-Thomas, Theory and Methods of Calculation of Molecular Spectra, Wiley, Chichester, 1988. [3] G.A. Segal (Ed.), Semiempirical Methods of Electronic Structure Calculation, Part A: Techniques, Part B: Applications, Plenum, New York, 1977. [4] V.I. Baranov and L.A. Gribov, Zh. Prikl. Spektrosk., 48 (1988) 963 (in Russian). V.I. Baranov and L.A. Gribov, Opt. Spektrosk., 67 (1989) 32 (in Russian). [5] L.A. Gribov and V.I. Baranov, J. Mol. Struct., 224 (1990) 45. [61 V.I. Baranov, L.A. Gribov, V.O. Djenjer and D.Yu. Zelent'sov, J. Mol. Struct., 407 (1997) 177. [7] L.A. Gribov, V.I. Baranov and B.K. Novosadov, Methods for Calculating Electronic-Vibrational Spectra of Polyatomic Molecules, Nauka, Moscow, 1984 (in Russian). [8] 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. Griboy, Opt. Spektrosk., 47 (1979) 91 (in Russian). [9] V.1. 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. [ 10] L.A. Gribov and V.A. Dementiev, Methods and Algorithms of Calculation in the Theory of Molecular Vibrational Spectra, Nauka, Moscow, 1981 (in Russian). [ 11] V.I. Baranov, F.A. Savin and L.A. Gribov, Programs for Computing Electronic-Vibrational Spectra of Polyatomic Molecules, Nauka, Moscow, 1983 (in Russian).
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[12] 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. [13] L.A. Gribov and V.A. Dementiev, Tables of Parameters for Calculation of Vibrational Spectra of Polyatomic Molecules, SO AN SSSR, Novosibirsk, 2nd edn., 1982 (in Russian). [14] H. Sponer, G. Nordheim, A.L, Sklar and E. Teller, J. Chem. Phys., 7 (1939) 207. [15] J.W. Eastman and S.J. Rehfeld, J. Phys. Chem., 74 (1970) 1438. [16] W.D. Gwinn, J. Chem. Phys., 55 (1971) 477. O.E. Weigang and E.C. Ong, J. Chem. Phys., 50 (1969) 4558. [17] F.M. Garforth, C.K. Ingold and H.G. Poole, J. Chem. Soc., (1948) 406. A.E.W. Knight, C.S. Parmenter and M.W. Schuyler, J. Am. Chem. Soc., 97 (1975) 1993. M.J. Robey and E.W. Schlag, J. Chem. Phys., 67 (1977) 2775. [18] F.M, Behlen, D.B. McDonald, V. Sethuraman and S.A. Rice, J. Chem. Phys., 75 (1981) 5685. [19] F. Zerbetto and M.Z. Zgierski, Chem. Phys., 127 (1988) 17. [20] V.I. Baranov and A.N. Solovyev, Zh. Fiz. Khim., 59 (1985) 1720 (in Russian). [21] A.V. Bree and S. Katagiri, J. Mol. Spectrosc., 17 (1965) 24. [22] A.V. Bree, S. Katagiri and S.R. Suart, J. Chem. Phys., 44 (1966) 1788. [23] G. Orlandi, G. Foggi and F. Zerbetto, Chem. Phys. Lett., 115 (1985) 253. [24] V.L. Broude and A.V. Laiderman, Luminescence and absorption spectra of anthracene in 9,10-dihydroanthracene crystal, IFFT AN SSSR, Chemogolovka, 1976, preprint (in Russian). [25] A.V. Bree, Chem. Phys. Lett., 131 (1986) 65. [26] T.N. Bolomikova, V.A. Zhukov, L.F. Utkina and V.I. Shaposhnikov, Opt. Spektrosk., 53 (1982) 823 (in Russian). [27] L.A. Gribov, V.A. Dementiev and A.T. Todorovsky, Interpreted Vibrational Spectra of Alkanes, Alkenes and Benzene Derivatives, Nauka, Moscow, 1986 (in Russian). L.A. Gribov, V.A. Dementiev and O.V. Novoselova, Interpreted Vibrational Spectra of Hydrocarbons: Cyclohexane and Cyclopentane Derivatives, Nauka, Moscow, 1988 (in Russian). [28] A. Amirav, U. Even and J. Jortner, J. Chem. Phys., 75 (1981) 3770. [29] N. Kruse and G.J. Small, J. Chem. Phys., 56 (1972) 2985. [30] V.I. Baranov and L.A. Gribov, Zh. Prikl. Spektrosk., 51 (1989) 80 (in Russian). V.I. Baranov, Zh. Prikl. Spektrosk., 51 (1989) 296 (in Russian).
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 407 (1997) 199-207
Adiabatic semi-empirical parametric method for computing electronic-vibrational spectra of complex molecules Part 2. Acenes V.I. Baranov, L.A. Gribov*, V.O. Djenjer, D.Yu. Zelent'sov Vernadsky_ Institute for 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 acenes (benzene, naphthalene, anthracene and tetracene) have been performed using the devised parametric method. A relatively small structural group H~C = is used as the primary fragment for acenes, as well as for polyenes and diphenylpolyenes. Within the framework of the given method, the simplest "first approximation model", which uses only two common parameters for all the groups (SHTJOq b = 0.08 a.u. and 02H~/(8qb 2 = 0.3 a.u.), maintains the accuracy of the calculation to approximately 20 cm -~ for the excited state frequencies and 0.1 for the relative intensities of the vibrational fundamentals. The major peculiarities of the electronic spectra and the fine effects (such as mirror symmetry breakdown) are reproduced in the calculations. Thus quantitative computer simulation of the molecular structural properties, sophisticated treatment of the spectral data and fitting of the model parameters are made possible by the use of this semi-empirical parametric approach, together with the special data bank of molecular parameters. © 1997 Elsevier Science B.V. Keywords: Acene; Excited state property; Vibronic spectra calculation
1. Introduction The possible accurate theoretical simulation and prediction of the vibrational structure of molecular absorption and fluorescence spectra is of importance due to the high-level experimental techniques required for the recording of fine structure vibronic spectra of complex polyatomic molecules. This requires the development of a parametric theory of vibronic spectra which uses physically justified molecular models with parameters accumulated in special * Corresponding author. Fax: 00 7 095 938 2054.
data banks [1,2]. Such parametric semi-empirical methods find wide application in quantum chemical calculations of molecular structure and properties and in the theory of the IR spectra of polyatomics (see, for example, Refs. [2,3]). The possible application of the parametric approach to the calculation of the electronic-vibrational spectra of polyatomic molecules has been discussed previously [4,5], and a new parameter set suitable for both adiabatic and non-adiabatic variants of the theory has been suggested. In Part 1 [6], we examined the adiabatic variant of the theory in more detail and showed that changes in the molecular potential surface on excitation can be
0022-2860/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S0022-2860(96)09612-3
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V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
represented to sufficiently close approximation by the relations As" =-Lq°A -
3He LqSp(APn~qO)
I -0
(1)
( °2He
Au~t=Sp APnoqOOqO j
(2)
where AP" is the matrix of electronic density change on excitation to the nth excited state, A and L ° are the matrices of the squared vibrational frequencies and vibrational forms in the ground state, He=H+SV, H is the matrix of coulombic and resonant one-electron integrals, S is the matrix of the atomic orbital (AO) overlap integrals and V= •a,b(ZaZb/rab) is the nuclear potential energy. The quantities 3HJOq° and 02He/(Oq°Oq °) possess all the required properties for the parameters of semiempirical theory [4-6]. In particular, they offer distinct local peculiarities, transferability in a homologous series of related compounds, independence from small electronic density changes and the possibility to be ranked by their values. An important peculiarity of the method is its stability to small variations in these parameters. Calculations of polyenes and diphenylpolyenes [6] have shown that, to a first approximation, only two parameters common to all polyene structural groups of the form H>C = may be taken to describe molecular models in the excited electronic states, where the first parameter determines the change in geometry and the second the change in force constants. The theoretical spectra obtained for such molecular models agree well / \
\2
/
\~
, //3
\
• //'
/
\~
~__~/
/ >
\
/
/ \
\ /
,
o
/ \
\ /
/ \
\ /
\
/
Fig. 1. Bond numbering of naphthalene, anthracene and tetracene.
not only qualitatively but also quantitatively with the experimental spectra. However, in these calculations, we failed to determine the parameter values for the similar group H>0 = of the phenyl fragments because the latter were of little importance in the vibrational structure of the electronic spectra of diphenylpolyenes. In addition, it is of interest to investigate the application of the method to other homologous series of organic molecules. In this paper, we present calculations for the first four molecules of the acene series: benzene, naphthalene, anthracene and tetracene (see Fig. 1 for the bond numbering of naphthalene, anthracene and tetracene).
2. Results and discussion
The choice of meaningful parameters for the given homologous series, the determination of their values and the extent of transferability in the series are of fundamental importance in the description of the molecular structure in the excited states and the prediction of vibronic spectra using this method. This method, like any parametric technique, is semi-empirical in nature, because the description of the molecular model using a limited small number of most significant parameters results in the determination of the difference between the optimal values and the values obtained from ab initio calculations. The parameters were chosen by fitting their values to obtain the best agreement with the experimental data for the first two molecules of the series: benzene and naphthalene. Since direct experimental data on the molecular structure in the excited states are not available and the size of the molecules of interest renders extensive ab initio calculations impractical, we used indirect data obtained from spectral measurements and semi-empirical bond order/bond length/ force constant (BOLF) relationships [2,7,8] as an information source. These parameters of the acene group H;,C= were then used, without any correction, to compute the structures and spectra of the next two molecules (anthracene and tetracene) and to compare them with the experimental data. This allowed an estimation of the quality of the chosen parametrization, the extent of transferability of the parameters and the predictive ability of the method as a whole.
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
Molecular vibrations in combining electronic states and the vibronic structure of the electronic spectra were calculated using the previously devised original methods [2,7,9-11 ]. The calculations of the electronic density distribution, energy and oscillator strength for the pure electronic transition were carried out using the semi-empirical CNDO/S method [3,12]. The distinctive view of Ap" for the lowest energy electronic transitions of acenes allows us to conclude that, as with polyenes and diphenylpolyenes, r-type parameters for bonds qb are the most significant. Therefore, to a first approximation, we can take only 2 ~r b 2 two non-zero parameters, OH~/Oqp and 0 HrJ(Oqi) , common to all groups I'I>t3= where r and s designate the atomic 7r-orbitals of the atoms forming the ith bond ("first approximation model" (FAM)). This model can then be improved using second-order parameters. However, in this paper, we investigate the possibility of calculating the excited state structure of complex molecules and their spectra using this method, and therefore restrict our considerations to the crude model.
2.1. Benzene and naphthalene Adiabatic molecular models of benzene (BZ) and naphthalene (NL) in the ground state have been determined previously [13] on the basis of the calculation and treatment of their IR spectra; we use these models without any correction in this work. An analysis of the vibrational structure of the BZ absorption spectrum [14-17] shows that the major change in structure on excitation to the first excited singlet state $1 involves an increase in the CC bond lengths by 0.04 A, whereas the frequency of the active totally symmetric vibration decreases by approximately 70 cm -~. These data make it possible to evaluate the desired parameters of the FAM. We take the values OH~/Oqbi =0.08 a.u. and 02HTJ(Oq~) 2 = 0.3 a.u., which give A l c c = 0.043 ,~ for the change in bond length and AVcc = - 53 cm -1 for the change in vibrational frequency. These results also agree qualitatively with those obtained with the BOLF relationship for both BZ and NL (see Table 1). The sign and order of magnitude of the changes in the bond lengths and force constants and their ratios are well reproduced in the calculations. For example, the ratios of the change in
201
the second bond length to that of the fourth bond length (A12]AI4), calculated with this method and using the BOLF relationship, are equal to 0.43 and 0.48 respectively, and the similar ratios between the force constants are 0.33 and 0.39 for Au l/Au4 and 0.5 and 0.6 for Auz/AU4. The difference in sign for Al3 is of no importance because of its negligibly small absolute value (less than 5%, i.e. within the method's accuracy), and does not significantly affect the vibrational structure of the electronic spectrum. Compared with the BOLF evaluation, the slightly overestimated changes in the bond lengths do not necessitate a decrease in the parameter OHr/Oq~hi, because a major test of the model's validity is the agreement between the calculated vibrational frequencies and relative intensities and the experimental spectral data. A comparison between the calculated intensities of progression A 0 of BZ and the experimental data (see Table 2) shows good quantitative agreement: the difference is about 0.15, and the scatter in the experimental data [14-16] is also of the same order. The calculated BZ and NL vibrational frequencies in the excited state also agree well with the experimental values (Table 3). When fitting the parameters of the acene group H>C = , we did not use the experimental relative intensities of the vibronic bands of NL, because they are primarily determined by the extent of vibronic coupling in NL rather than by the change in the molecular potential surface. It should be noted that the devised method is not limited only by the FranckCondon approximation and can also be used in the case of strong vibronic coupling (Herzberg-Teller Table 1 Changes in the lengths (Al, ,~) and force constants (Au, 10 -~ cm -2) of carbon-carbon bonds for benzene and naphthalene on going to the first excited state Bond a
AI
Au
Benzene 0.043 Naphthalene 1 0.008 2 0.036 3 -0.006 4 0.083
0.032 b
-1.00
-1.37 b
0.017 0.025 0.004 0.052
-0.42 -0.64 -0.10 - I .28
-0.58 -0.93 -0.00 -1.49
a For the bond numbering, see Fig. 1. b Calculated using the BOLF relationship [8].
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
202
Table 2 Relative intensities for the A ° = u0o + 521 + n.923 cm -~ progression of the benzene absorption spectrum n
Calc.
Obs. [15]
Obs. [16]
Obs. [14]
I 2 3 4
0.73 1.00 0.66 0.28
0.71 1.00 0.82 0.45
0.74 1.00 0.77 0.40
0.87 1.00 0.87 0.46
approximation). The matrix elements o f vibronic coupling can be directly expressed in terms o f the parameters OHe/Oq ° and a2Hj(Oq°Oq °) and the matrix Ap, but, in order for the vibronic effects to be quantitatively reproduced, the c h o i c e o f appropriate m o l e c u l a r parametrization calls for special analysis and will be discussed elsewhere.
2.2. Anthracene The vibrational frequencies and forms of anthracene (AC) in the ground state have been calculated in Ref. [13]. A g o o d a g r e e m e n t b e t w e e n the results obtained and the experimental IR and R a m a n spectra supports the validity o f the ground state force field and m o l e c u l a r m o d e l as a whole. T o find the g e o m e t r y and force field o f A C in the first excited state and to c o m pute the vibrational structure o f the absorption and fluorescence spectra, we used this adiabatic m o d e l Table 3 Totally symmetric vibrational frequencies (cm -~) of benzene and naphthalene Ground state Benzene 991 3073 Naphthalene 485 773 1011
Excited state 993 a 3073
948 3071
923 a 3130
5130 761 1020
484 747 985
500 ° 702 987
1380
1310 1424 1543 3007 3044
1152
1360 1435 1593 3007 3045
1143
a Ref. [17], experimental data. o Ref. [18], experimental data.
1308
o f the ground state. Then, using the parameter values OH~/Oqbi=o.08 a.u. and OZH~J(Oq~)2 = 0.3 a.u. obtained f r o m B Z and NL, we found the changes in g e o m e t r y and force field o f A C on excitation using Eq. (1) and Eq. (2). W e present these data, together with those obtained using the Q C F F / P I m e t h o d [19] and B O L F relationship [20], in Table 4. The average difference in the bond length changes is 0.01 A and that of the force constant changes is 0.1 x 10 -6 c m -2, which are less than 1% o f the values o f the C C bond lengths and force constants in the ground state. This indicates that our F A M is adequate for the description o f the actual structure o f A C in the excited state, because the calculations [ 19,20] provide sufficiently accurate relative intensities of the vibrational bands in the absorption and e m i s s i o n spectra o f AC, and our results are not very different from those in Refs. [19,20], A c o m p a r i s o n o f the calculated and experimental spectra o f A C supports this conclusion. For example, the frequencies (see Table 5) differ, on average, by 15 c m -~ from the experimental values, with a maxim u m difference o f 44 c m -j for the v'2 = 1498 c m -1 band. Taking into account the underestimation by a p p r o x i m a t e l y 30 c m -~ of this m o d e f r e q u e n c y in the ground state (as well as o f the band ~"9 = 356 c m - l ) , the a g r e e m e n t should be considered as Table 4 Changes in the lengths (AI, ~) and force constants (Au, 10 ° cm -2) of carbon-carbon bonds for anthracene and tetracene on going to the first excited state Bond a Anthracene 1 2 3 4 5 Tetracene 1 2 3 4 5 6 7
Al
AU
-0.028 0.043 -0.032 0.011 0,030
-0.016 b 0.027 -0.013 0.004 0.021
-0.019 0.029 -0.030 -0.012 0.042 -0.007 0.007
-0.012 ° 0.017 -0.015 -0.007 0.020 0.000 0.000
-0.032 c 0.036 -0.028 0.009 0.016
a For the bond numbering, refer to Fig. 1. b Calculated using the BOLF relationship [8]. c Calculated with the QCFF/PI method [19].
0.37 -0.72 0.34 -0.04 -0.51
0.52 b -0.87 0.43 -0.12 -0.70
0.36 -0.50 0.32 0.15 -0.55 -0.01 -0.01
0.45 b -0.62 0.41 0.19 -0.68 -0.01 -0.01
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
203
Table 5 Totally symmetric vibrational frequencies (cm -~) of anthracene Mode
Ground state
1 2 3 4 5 6 7 8 9
1564 1456 1404 1255 1161 1021 735 578 356 " Ref. b Ref. Ref. d Ref. e Ref.
1568 a 1409 1267 1163 1020 759 629 394
Excited state 1566 b 1486 1408 1263 1165 1012 753 624 390
1562 ¢ 1411 1268 1175 1020 755 621 398
1557 d 1482 1403 1260 1163 1007 753 622 395
1564 1454 1390 1247 1161 1019 731 578 355
1501 a 1420 1380 9 1168 1019 755 583 385
1503 b ? 1399 1247 1157 1030 744 590 389
?c 9 1396 1239 1169 1028 733 590 392
1552 d 1498 1390 1218 1164 1026 737 587 393
1598 ~ 1516 1370 1249 1159 1046 773 715 390
[21], spectrum in n-heptane. [22], jet expansion spectrum. [23], spectrum in fluorine. [24], spectrum in 9,10-dihydroanthracene crystal. [19], calculated by the QCFF/PI method.
wholly satisfactory. It should be noted that our model of the AC force field reproduces the excited state vibrational frequencies much better than the QCFF/ PI model [19]; the latter has an average discrepancy of 30 cm -l, with a maximum value of more than 120 cm -1 for the u'8 = 590 cm -l mode. Since frequencies are determined primarily by the second derivatives of H e (see Eq. (2)), these data show that the parameter 02HTfl(Oq~) 2 = 0.3 a.u., obtained for BZ and NL, appropriately describes the changes in the force field of AC. The absorption and emission spectra of AC are depicted in Fig. 2 and Fig. 3. It is evident that the vibrational structure, as a whole, is well reproduced in the calculation; therefore the parameter OHTJOq b = 0.08 a.u., obtained for BZ and NL, also adequately describes the geometry of AC. Quantitative analysis demonstrates that the relative intensities of the AC totally symmetric fundamentals agree well with the experimental values [25] (see Table 6); the average difference is 0.05 (the maximal value is approximately 0.14 for the 4~ and 40 bands with a frequency of approximately 1250 cm-1). Some doubts are cast on the assignment of the 91 fundamental of the absorption spectrum in Ref. [25], because the intensity of the respective 90 band of the emission spectrum [25,26] is equal to 0.2, which is approximately twofold less. Moreover, the Dushinsky effect for this mode is small and so are the non-Condon corrections to the intensity (evaluated in Ref. [19]); therefore the absorption and emission spectra must have
approximate mirror symmetry. Therefore we consider the value of 0.2 for the relative intensity of the 9~ band presented in Ref. [26] to be more realistic. Small differences between the absorption and emission spectra are also represented correctly in
b
L &
0
I0oo
W~venumbers (cm -I ) Fig. 2. Calculated (a) and experimental [26] (b) absorption spectra of anthracene in 77 K n-hexane.
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
204
b
&
I000
0
0
IO00
Wa, v e n u m b e r s
(ern -1 )
Fig. 3. Calculated (a) and experimental [26] (b) absorption and emission spectra of anthracene in 4 K n-hexane.
our calculation. The major difference involves a decrease in the relative intensity of the most active 30 band in the emission spectrum by 0.1 compared with the intensity of the 30I band in the absorption spectrum. The QCFF/PI calculation [19] gives the opposite ratio of these values and an average error
for the relative intensities of the order of 0.1 (with a maximal value of more than 0.2). Therefore this method does not give such a good description of the molecular model in the excited states as our parametric method, Finally, it should be noted that, as with polyenes
Table 6 Relative intensities of the totally symmetric fundamentals of anthracene Absorption
Emission
Band
Calc.
Obs."
Calc. b
Band
Calc.
Obs."
Calc.b
Oo° I~ 2~ 3~ 40J 50~ 6~ 7g 80' 90j
1.oo 0.10 -< 0.02 0.54 0.15 0.07 0.03 0.09 -< 0.02 0.09
i.oo 0.17
l.OO 0.15
0.55 0.02 0.17 0.08 0.07
0.57 0.33 0.01 0.04 0.06
Oo° 1° 2~ 30 40 50 60 70 80 90
1.00 0.15 --< 0.02 0.45 0.20 0.07 --< 0.02 0.08 -< 0.02 0.08
1.00 0.14 0.42 0.06 0.06 0.03 0.02 0.02 0.16
1.00 0.05 0.04 0.68 0.01 0.03 0.0 I 0.02 0.06
-
0.41?
a Ref. [25], spectra in n-heptane. b Ref. [19], calculated by the QCFF/P1 method.
V.I. Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
and diphenylpolyenes, changes in valence angles play an important role in the formation of the vibrational structure of the electronic spectrum. Although these changes are less (approximately five times) than those of the bond lengths and are not the decisive factor in computing the relative intensities, taking them into consideration essentially improves the agreement between the calculated and experimental spectra. For instance, for the most active 3~ fundamental (lob~ = 0.55 [25]), the calculated intensity increases by more than twofold and becomes very nearly equal to the experimental value (A/ -< 0.01) if the changes in angles are taken into account, and the same is also true for the 3 o band in the emission spectrum.
2.3. Tetracene To clarify the possibility of fast simulation of the main spectral and structural regularities of complex molecules using the devised method, we tried to compute the tetracene (TC) molecular model. This calculation has a model nature, and is based on the fragmentary method [10] for constructing molecular models in the ground state and the parametric method for constructing molecular models in the excited state with the parameters OH~/Oq~=O.08 a.u. and cq2Hrs/ (Oqbi)2 =0.3 a.u., obtained for BZ and NL. The ground state model was constructed from two
205
identical fragments, each consisting of AC without one terminal ring. As in all the other calculations, this was performed with the help of the LEV program [10] and the special data bank which now contains more than 300 molecules and molecular fragments [27]. Parameters of common carbon-carbon bonds and their nearest environments were taken from the appropriate group of AC. Contrary to the simple conjunction of two NL molecules, this method allows us to account for the peculiarities of the interior rings of TC more correctly. Quite satisfactory agreement between the calculated IR frequencies and the experimental data (Au <_ 20 cm -~, see Table 7) is achieved using such a simple and crude model. The changes in the molecular model on excitation, calculated by the parametric method and using the BOLF relationship, are given in Table 4. The calculated absorption and emission spectra (see Fig. 4 and Fig. 5) reproduce reasonably well (considering the crude model of the ground state) the observed vibrational structure only with respect to the vibrational frequencies (see Table 7). In this calculation, we failed to obtain quantitative agreement between the relative intensities of all the vibronic bands; in some cases, the calculated intensity is significantly less than the experimental value (for instance, we obtained lou~ 0.4 and Icalc ~ 0.05 for the 300 cm -r band and lob s 0.6 and Icalc ~ 0.1 for the 1450 cm -I band in the absorption spectrum).
Table 7 Totally symmetric vibrational frequencies (cm -~) of tetracene Excited state
G r o u n d state Calc.
Obs. a
300 600 719 757 968 1094 1157 1202 1364 1380 1441 1540
307 612 738
"Ref. [28]. Ref. [29].
986 1149 1381 1431 1536
Obs. b
Calc.
Obs. a
Obs. b
311 616 758 762 996 1013 1154 1198 1385 1446 154(I
297 598 716 757 971 1078 1145 1201 1364 1383 1448 1543
314 600 750 1159 1225 1362 1442 1551
308 609 746 755 1009 1151 1213 1361 1415 1549
206
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
number of parameters in the ground and excited states to obtain wholly satisfactory results. Nevertheless, even such a poor calculation allows us to evaluate the major structural changes in TC on excitation and to carry out a detailed treatment of the spectra. To obtain better agreement of the results, the parameters of the TC ground and excited state models may be fitted by solving the inverse vibronic problem, since the existing agreement is quite sufficient to state and solve such a problem correctly [30].
3. Conclusions 5()0
0
IO00
1500
Wa,venumbers (ore-')
Fig. 4. Calculated (a) and experimental [28] (b) absorption spectra of tetracene in supersonic jet.
This is caused primarily by the very crude model of the ground state and probably by the application limit of the FAM. Therefore, in this case, we may be forced to use a more sophisticated model with a larger
3000
2500
2600
iS00
1000
500
0
Wa,veuumbem (ern -1) Fig. 5. Calculated (a) and experimental [28] (b) fluorescence spectra of tetracene in supersonic jet.
The calculations of the molecular structure in the excited states and the vibronic spectra of acenes (benzene, naphthalene, anthracene and tetracene) confirm the high efficiency and performance of the parametric semi-empirical method in the adiabatic theory of polyatomic vibronic spectra [4-6]. As in the case of polyenes and diphenylpolyenes [6], a comparatively small structural group H~,C= can be used as a primary fragment for the acenes. The small number of parameters and the good extent of transferability in a homologous series enable an adiabatic molecular model to be constructed which adequately describes the actual excited state molecular structure, and also reproduces quantitatively the fine vibrational structure of the electronic spectra with a high degree of accuracy. The simplest model within the framework of this method, which uses only two common parameters for 2 7r b2 all the structural groups, aHffJOqbi and a t-lrJ(Oqi ) , provides an accuracy of calculation of the parameters to within 20 cm -~ for the vibrational frequencies and 0.1 for the relative intensities of the vibronic fundamentals. Even for such a crude molecular model, all the major peculiarities of the vibrational structure present in the calculated spectra (not only the most intense bands) are well reproduced; bands with comparatively small relative intensity (0.1 or less) are also reproduced well. Fine features (such as mirror symmetry breakdown due to normal mode mixing) are also well reproduced, and thus a sophisticated treatment of the spectra is available. If need be, further refinement of adiabatic molecular models is possible via the solution of the inverse vibronic problem.
V.L Baranov et al./Journal of Molecular Structure 407 (1997) 199-207
Acknowledgements The authors gratefully acknowledge partial f i n a n c i a l s u p p o r t o f this i n v e s t i g a t i o n b y the R u s s i a n F o u n d a t i o n o f F u n d a m e n t a l R e s e a r c h , G r a n t No. 9603-34460.
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