Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization

TLDR: In this article, Levitt and Levitt developed a method for the consistent calculation of ground and excited state potential surfaces of conjugated molecules, which is based on the formal separation of u and 7r electrons, the former being represented by an empirical potential function and the latter by a semi-empirical model of the Pariser-Parr-Pople type corrected for nearest-neighbor orbital overlap.

Abstract: A formulation is developed for the consistent calculation of ground and excited state potential surfaces of conjugated molecules. The method is based on the formal separation of u and 7r electrons, the former being represented by an empirical potential function and the latter by a semiempirical model of the Pariser-Parr-Pople type corrected for nearest-neighbor orbital overlap. A single parameter set is used to represent all of the molecular properties considered; these include atomization energies, electronic excitation energies, ionization potentials, and the equilibrium geometries and vibrational frequencies of the ground and excited electronic states, and take account of all bond length and bond angle variations. To permit rapid determination of the potential surfaces, the u potential function and SCF-MO-CI energy of the r electrons are expressed as analytic functions of the molecular coordinates from which the first and second derivatives can be obtained. Illustrative applications to 1,3butadiene, 1,3,5-hexatriene, a,w-diphenyloctatetraene, and 1,3-cyclohexadiene are given. detailed interpretation of electronic transitions and A concomitant photochemical processes in conjugated molecules requires a knowledge of the ground and excited state potential surfaces. The determination of such surfaces has long been a goal of theoretical chemistry. Difficulties in a reliable a priori approach to the problem for a system as simple as ethylene2 are such that calculations for more complicated molecules are prohibitive at present. Consequently, a variety of methods that utilize experimental data have been introduced. Completely empirical treatments, in which the energy surface is expressed as a function of potential parameters fitted to the available information (1) Supported in part by Grant EY00062 from the National Institute of Health. (2) U. Kaldor and I. Shavitt, J . Chem. Phys., 48, 191 (1968); R. J. Buenker, S. D. Peyerimhoff, and W. E. Kammer, ibid., 55, 814 (1971). (equilibrium geometry, vibrational frequencies, etc.), have had considerable success in applications to molecules for which a localized electron description is app l i~ab le .~ The great advantage of this type of approach, which leaves open questions of reliability when extended from one class of molecules to another, is the ease and speed of the calculations; this had made possible applications to systems as large as certain nucleic acids and globular proteins. For conjugated molecules, however, the importance of delocalization introduces difficulties into such an empirical treatmenL5 (3) (a) See, for example, J. E. Williams, P. J . Stand, and P. v. R. Schleyer, Annu. Reu. Phys. Chem., 19, 531 (1969); (b) S. Lifson and A. Warshel, J . Chem. Phys., 49, 5116 (1968); A. Warshel and S . Lifson, ibid., 53, 8582 (1970). (4) M. Levitt and S. Lifson, J. Mol. B i d , 46, 269 (1969); M. Levitt, Nature (London), 224, 759 (1969). ( 5 ) C. Tric, J . Chem. Phys., 5 1 , 4778 (1969). Journal of the American Chemical Society 1 94:16 1 August 9, 1972