Calculation of the Positions of the α- and β-bands in the Electronic Spectra of Benzenoid Hydrocarbons Using the Method of Limited Configuration Interaction

The positions of the αand β-bands in the electronic absorption spectra of twenty aromatic benzenoid hydrocarbons were calculated by the semiempirical method of limited configuration interaction in the πelectron approximation using the Huckel molecular orbitals. The agreement of the experimental and calculated values is good for the β-band whereas a systematic deviation is observed for the α-band. This deviation cannot be removed by extending the configuration interaction of the monoexcited states constructed from the molecular orbitals considered. However, the consideration of electronic repulsion enables us to explain the character of the dependences of the experimental excitation energies on the excitation energies obtained by the simple Huckel method of molecular orbitals. Using a suitable choice of semiempirical parameters different for various electronic transitions (showing no large mutual differences) yields semiempirical interpolation formulas for the; p-, α-, and β-bands which give very good agreement with the corresponding experimental excitation energies for the compounds studied. Disciplines Atomic, Molecular and Optical Physics | Biochemical and Biomolecular Engineering | Engineering | Materials Science and Engineering | Semiconductor and Optical Materials Comments At the time of publication, author Vaclav Vitek was affiliated with the Czechoslovak Academy of Sciences. Currently, he is a faculty member at the Materials Science and Engineering Department in the School of Engineering and Applied Science at the University of Pennsylvania. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/mse_papers/226 CALCULATION OF THE POSITIONS OF THE IXAND P-BANDS IN THE ELECTRONIC SPECTRA OF BENZENOID HYDROCARBONS USING THE METHOD OF LIMITED CONFIGURATION INTERACTION J. KOUTECKY, J. PALDUS and V. ViTEK Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague, and Mathematical-Physical Faculty of the Charles University, Prague Received April 17th, 1962 The positions of the IXand tJ-bands in the electronic absorption spectra of twenty aromatic benzenoid hydrocarbons were calculated by the semiempirical method of limited configuration interaction in the n-electron approximation using the Huckel molecular orbitals. The agreement of the experimental and calculated values is good for the tJ-band whereas a systematic deviation is observed for the IX-band. This deviation cannot be removed by extending the configuration interaction of the monoexcited states constructed from the molecular orbitals considered. However, the consideration of electronic repulsion enables us to explain the character of the dependences of the experimental excitation energies on the excitation energies obtained by the simple Huckel method of molecular orbitals. Using a suitable choice of semiempirical parameters different for various electronic transitions (showing no large mutual differences) yields semiempirical interpolation formulas for the; PO, IX-, and tJ-bands which give very good agreement with the corresponding experimental excitation energies for the compounds studied. In a recent study! the positions of the p-bands (according to the Clarclassification) of twenty benzenoid hydrocarbons have been calculated using the method of limited configuration interaction in the n-electron approximation. The LCAO molecular orbitals in the Huckel approximation were used for the construction of the wave functions describing individual configurations. The positions of the IXand ,B-bands of the same group of compounds are estimated by the same method 1 in the work presented. Method of Calculation The method of calculation and the approximations employed are those used in the precedibg paperl (compare refs3 6). The distances between neighboring carbon atoms are taken equal to 1·39 A which, of course, is a rather crude approximation in some cases. The resonance integral between neighboring atomic orbitals is taken equal to -2·318 eV (see!) and the electronic repulsion integrals of the Coulomb type are approximated according to Mataga and Nishimoto 7 (1) 1468 Collection Czechoslov. Chern. Cominun. Calculation of the Positions of the (Xand ~-Bands where r IlV is the distance between the fi-th and o-th carbon atom. Otherwise, the approximations introduced by Pariser and Parr3 ,4 and Pople5 ,6 are used. The off-diagonal elements of the effective one-electron Hamiltonian F in the Huckel molecular orbital representation were neglected. We considered the monoexcited configurations to which the Huckel excitation energy lower than 1 IPI corresponds. The extent of the configuration interaction was investigated. Therefore, the excitation energies e~(k = ex, /3) which follow from the interaction of the configurations 11, 1 ~ 2') and 11, 2 --+ 1') of the same energy were also calculated (compare refs ). Here and hereforewith we use the designation, in which II, i --+ r) denotes the singlet monoexcited configuration formed by the substitution of the ith bonding molecular orbital with the jth virtual orbital in the monodeterminantal ground state wave function. The orbitals are arranged according to the increasing absolute values of the diagonal matrix elements F jj • The bonding orbitals are denoted by 1, 2 ... N/2 and the virtual orbitals by 1', 2' ... N' /2, where N is the number of carbon atoms of the hydrocarbon. In the cases of naphthacene, pentacene, and dibenzo[b,deJJchrysene both the ransitions formed by the interaction of 11, 1 ~ 2') and 11,2--+ 1') are, however, torbidden. These monoexcited configurations belong to the irreducible representafion BIg in naphthacene and pentacene (D Zh) and to the irreducible representation Ag tn dibenzo[b,deJJchrysene. Table I Assignment or Irreducible Representations to Monoexcited States for Various Transitions According to Clar Classification Group D6h DZh C Zy C Zh C lh Compound 1,20 2, 4, 6, 9, 11, 3,5,10,12,14, 7,15,19 8, ]3 16 17,18 p B zu B zu Bz Bu A' BI:! B3u a Al B} A' {3 E lu a Pentacene is an exception as its mono excited configurations producing the (X-transition belong to the irreducible representation BIg' b Dibenzo[bdeflchrysene is an exception as its monoexcited configurations producing the (X-transition belong to the irreducible representation A g • The full configuration interaction was considered for four compounds: anthracene (D Zh)' chrysene (CZh)' benzo[aJanthracene (Clh) and benzo[e]pyrene (CzJ. The configuration interaction for coronene (D6h) was extended so that it included the configurations formed by excitations from the nine highest bonding molecular orbitals to the nine lowest virtual orbitals. The consideration of the configurations with the Huckel excitation energy up to 1 IPI for benzene and naphthalene includes all monoexcited configurations. As the off-diagonal elements of the Hamiltonian in the repre-