Collective electron excitations in long molecules with conjugated bonds (cyclic and linear polyenes)

Conclusions The technique used above for calculating electronic excitations is equivalent to the random phase approximation, but permits a clearer understanding of the approximations made. The linearization with respect to Ø in the derivation of the equations for the excited states means that the approximation made is valid only for small changes in the spin (or electron) density in the atoms in the excited states from that in the ground state. This is always the case for fairly small excitation energies. The proposed calculation technique may be used to calculate excitations both in long conjugated molecules and in ordinary molecules just as well as the Pariser-Parr-Pople and random phase approximations [14, 17, 18].We note that another approach was used in [6] to find the energy of the first triplet level in polyenes. In that paper the wave function of the generalized Hartree-Fock approximation was projected onto a singlet (ground) and a triplet state. The latter was treated as a very low triplet excited state. However, as shown in [1, 2], the energies of these (the singlet and triplet) states differ by a quantity that decreases like N^–2 or even faster as N. On the other hand, as shown in [7], the energy of the first triplet excitation should decrease like ₁ 1/N as N. This implies that the interaction between electrons above the generalized Hartree-Fock approximation must be taken into account in order to obtain the first triplet state.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 10, No. 6, pp. 723–731, November–December, 1974.