Berencz, Ferenc

Kolos, W.

Pauncz, Rezső

English

Berencz Ferenc

Kolos W.

Pauncz Rezső

University of Szeged

THEORETICAL EXAMINATION OF THE D I B E N Z O - D E M V A H V E S OF P E R Y L E N E By F. BERENCZ, W. KOLOS and R. PAUNCZ Institute of Theoretical Physics, The University, Szeged (Received May 4, 1956) The term systems o£ condensed aromatic hydrocarbons built up from anthra-cene and phenanthrene parts were examined using L. C. A. O. t reatment and fu r -thermore, calculations were performed regarding the applicability of the pertur-bation method. The most important properties of the spectra are obtained qualita-tively correctly from the results of the calculations, whereas the quantitative agreement is fa r lees good. 1. Introduction For a f e w years the pe r tu rba t ion me thod plays an i m p o r t a n t role in t h e theoret ical examina t ion of condensed a romat ic compounds, especially w h e n L. C. A. O. t r e a t m e n t is used (COULSON [1] and references therein) . I ts impor -tance consists in its r ende r ing possible the invest igat ion of s t ruc tu ra l changes in the molecule; e. g. on us ing it t he proper t ies of single a romat ic hyd roca r -bons can be examined as to h o w they a re a f fec ted on being condensed in to a grea te r compound. Recent ly PAUNCZ [2] used this me thod succesful ly fo r t h e invest igat ion of condensed a romat ic compounds buil t u p f r o m ident ical uni ts . The a im of this paper is to use the above-ment ioned p rocedure f o r t h e invest igat ion of molecules bui l t u p f r o m an th racene or p h e n a n t h r e n e pa r t s . The spectra of t h e fo l lowing compounds calculated by the L. C. A. O. m e t h o d will be examined : Of these compounds I and II can be puil t u p f r o m a n t h r a -cene-, III and IV f r o m p h e n a n t r e n e - and V and VI f r o m an th racene - and phenan t r ene - par ts . The m e m b e r s of the single pai rs of compounds (I—II, III—IV, V—VI) d i f fe r in the re la t ive position of the units . 2. The Method of Calculation For our t r e a t m e n t the we l l -known basic assumpt ions of the H O C K E L m e -thod are used. The calculat ion of the molecule t e r m system wi th the L. C. A. O. method consists in the evaluat ion of the roots of the fol lowing secular de t e r -minan t : | / / i t — e S a l = 0 , (1) where H n : ' ^ \ i h H u k d r , S ;k = \i£ukdx, (2) 4 F . BERENCZ, Vi. KOLOS and R. PAUNCZ Fig. 1 EXAMINATION OF THE DIBENZO-DEHIVATIVES OF PERYLENE u,- represents the n electron function belonging to atom i. H the effective Hamilton operator for a single electron, c the energy value. Relating to the matrixelements (Su.-, //,7.) the following simplifications are used: a) Sn: = dik, b) Hu=a, c ) Hiu only differs f rom zero when i and k are indices belonging to neighbouring atoms; let us denote this value with /3. The values of ¡3 occuring in the anthracene or phenanthrene parts are considered to be equal, while the value of Hik belonging to the bonds connect-ing the single anthracene or phenantrene unist is denoted by //?. Physical and chemical arguments suggest tha t the value of /. in the molecules investi-gated is smaller than 1; the lengths of the connecting bonds are greater than those of the other ones occuring in the molecules, i. e. the strengths of the corresponding bonds are smaller than those of the others. For instance, in the case of perylene the dibenzo-derivatives of which are all the six com-pounds the bond lengths of the bonds connecting the naphtalene parts measured Roentgenographically are 1.50 A, while the lengths of the remaining bonds are about 1,41 A (DONALDSON, ROBERTSON and WHITE [3]). On the other hand, the considerable independence of the two parts is shown by the fact tha t the value of the diamagnetic susceptibility of perylene can be calculated f rom those of naphtalene and hydrogen without any correction for the central hexa-gon (SHIBA and HAZATO [4], HAZATO [5]). Let us assume that also for the case when phenantrenes or anthracenes are joined instead of the two naphtalenes, the situation is analogous. Lacking Roentgenographical data we cannot give any definite value for / for this reason the term system of the molecules will be discussed in the ¿ = 0 a n d / —1 interval. The dependence of the t e rm system on y will be determined using the following two procedures: a) Perturbation method Let us take for the unperturbed problem the case when anthracene and phenantrene are not joined together and consider the formation of bonds between them as perturbation. The connecting links should be formed between the atoms a — a' and b — b% resp., where the atoms a and b belong to the first part, a' and b' to the second one. The first order perturbation energy belonging to the i-th level is according to DEWAR [6] and PAUNCZ [2] as follows: (c„;C„'i-{-CiiCvi)ifl, when the two units are identical (3) 0 when they are different," where c„,-, and C;„ mean the coefficients in the i-th molecular orbital belong-ing to atom a and b, resp. If the two units to be joined are different, the second order perturbation calculation should be used. In view of the fact, however, tha t the correspond-ing levels of anthracene and phenantrene are close to each other, the second order perturbat ion calculation does not give any acceptable results. b) Direct calculation Both for the examination of the latter case, and the investigation of the reliability of the perturbation treatment, in the former case, it seems useful to determine the dependence of the level on y by means of a straightforward calculation, too. 6 F. BERENCZ, Vi. KOLOS a n d R. PAUNCZ For this purpose each line of the secular determinant should be divided by and the following notation introduced: In the case of the single compounds the polynomial obtained by the reduction of . the secular determinant can be transformed into the following form: I. - IV. {Po(x) + lP,{x) + /}p,{x)) {P0(x)-?.P,(x) + m(x)} = 0 (5) V. — VI. P0(x) + ?J>P.2(x) + /SP4(x)=0. From equation (5) for all x, the "/. which makes the secular determinant to zero can be very simply determined. Performing the numerical calculation for all the given x, using a graphical method, it can easily be determined f rom the obtained results in which way the roots of the secular determinant depend on ?.. In the case of the compounds I. — IV., on the bases of (5), the possibi-lity for the factorisation of the polynomial obtained by the reduction of the secular determinant becomes evident,, thus the symmetrical and antisymme-trical levels in respect to reflection or inversion resp. can be treated separately. The comparison of the results of the direct calculation with those obtained wi th the perturbation method illustrates up to which value of ). the per tur -bation calculation gives reliable results. 3. Results of Calculation and Discussion The results of our calculations show that the term systems of the single pairs of compounds possess a high degree of resemblance, therefore in each case only one of the two term systems of the respective compound is shown in the following three figures. It is sufficient to plot the term systems cor-responding to all the positive x, as the level systems of the above mentioned al ternant hydrocarbons are symmetrical with respect to the x = 0 value. The result of the straightforward calculation is shown by a full line, that of the perturbat ion treatment by a dotted one. The examination, of the figures shows the following. f> On comparing the results obtained with the direct method with those received with the perturbation treatment it can be seen that their agreement up to / = 0,5 is excellent. For greater values of / a reliable agreement can be obtained only for the case if the distance of neighbouring levels is not too small, or they do not come too close together with increasing k. If this occurs the result of the first order perturbation calculation may be incorrect for I = 1. For instance, in Fig. 2 the order of the second and third levels changes. If our results of calculation are compared to the experiment the follow-ing can be established. a) According to the calculation the spectra of the corresponding pair of compounds should exhibit a high degree of resemblance. Experimentally the spectra of only one pair of compounds is known, its examination confirms this conclusion. EXAMINATION" OF THE DIBENZO-DERIVATIVES OF PERYLENE F ig. 2 8 F. BERENCZ, Vi. KOLOS and R. PAUNCZ b) F rom the calculations for the order of the f i rs t t rans i t ion the fo l low-ing can be obta ined: The t ransi t ion possessing the longest wave l eng th belongs to compounds buil t u p f r o m an th racene par ts , a shor te r wave l eng th corresponds to the compounds buil t u p f r o m a n t h r a c e n e and p h e n a n t h r e n e , and to the th i rd order belongs the pair of compounds consisting of two p h e n -a n t h r e n e par ts . This conclusion is in ag reemen t w i th the expe r imen ta l da t a as the wave leng th of t h e t rans i t ion are as fol lows: I, 558 m[ i II. 546 m p V. 503 m f t IV. 434 rn/t (CLAR [7], [8],i [9]). c) While the two f o r m e r qual i ta t ive conclusions have proved to be correct , the quan t i t a t ive agreement is f a r less good as a too high va lue is obta ined f o r the wave leng th of the f i r s t t ransi t ion. If t h e / va lue character iz ing t h e s t rength of the connect ing bonds is considered to be 0,5 the calculated va lue shif ts in the r ight direction diverging, however , still apprec iable f r o m t h e exper imenta l value. This fact shows tha t beside t h e above ment ioned fac tor , f u r t h e r r e f i nemen t s of the method mus t be t a k e n into account . Thus ins tead of the simplest va r i an t of the L. C. A. O. t r e a t m e n t the S. C. F. me thod m u s t be used (POPLE [10]) and the interact ion of the electrons should be considered. Such calculat ions are in progress. One of the au thors (W. K.) wishes to express his g ra t i t ude to the H u n -gar ian Academy of Sciences for its hospi tal i ty a t the Univers i ty of Szeged. References [1] Coulson, C. A.: Symposium on Molecular Physics at Nikko (1953), p. 23. [2] Pauncz, R.: Acta Phys. Acad. Sci. Hung, (to ibe published). [3] Donaldson, D. M., J. M. Robertson, J. G. White: Proc. Roy. Soc., A, 220, 311. (1953). [4] Shiba, H., G. Hazato: Bull. Chem. Soc. Japan, 22, 92 (1949). [5] Hazato, G.: Bull. Chem. Soc. Japan, 22, 151 (1949). [6] Dewar, M. J. S.: J. Am. Chem. Soc., 74, 3341 (1952). [7] Clar, E.: Aromatische Kohlenwasserstoffe. II. Aufl., Springer, Berlin (1952), p. 298. [8] Clar, E.: Ber., 65, 848 (1932). [9] Clar, E.: Ber., 82, 47 (1949). [10] Pople, J. A.: Trans. Farad. Soc., 49, 1375 (1953). 

Theoretical examination of the Dibenzo-derivatives of perylene

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Theoretical examination of the Dibenzo-derivatives of perylene

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