By Per-Olov Löwdin
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Example text
25 27 27 29 30 31 34 38 39 39 40 41 42 43 45 1. Introduction and Summary In theoretical investigations of the electronic structure of large molecules with more or less complicated conformation complete theoretical calculations cannot be carried out at present or in the near future. All methods applied to large molecules must therefore include considerable simplifications. Especially, investigators of unsaturated systems have almost invariably assumed that it is a satisfactory approximation to study the distribution of the mobile electrons within a frame of the nuclei and the localized electrons with fixed distribution.
It is shown that the electronic charge on the atom ,u in the OAO basis, 'PPap, is approximately equal to the gross atomic population, NPr, in the A 0 basis [Eqs. (57) and (58)]. An approximate relationship between the bond orders in the two bases is given in Eq. (61). In Section I11 the connection of the Hiickel method with the PariserParr-Pople method is discussed. Two features are especially stressed, uiz. the connection with the o technique [Eqs. (66) and (67)J and the difference between Hiickel parameters pertinent to spectral features on the one hand and to the total energy on the other hand [see Eqs.
The following derivation is slightly different from those published previously but most closely related to the much more elaborate and complete presentations of Ruedenberg and of Del Re and Parr. In the self-consistent field case the total rc electron energy En can be written En = 4 Tr{P(Hcore+ F)}. (70) The total energy of the system, E,,,, is the sum of En and the interaction between the positively charged core atoms, Erepuls, which can be written (cf. , Del Re and Parr, 1963): 42 lnga Fischer-Hjalmars Using Eqs.