Advances in quantum chemistry. / Volume 5 by Per-Olov Löwdin

By Per-Olov Löwdin

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If we finally consider the third step of Eq. (23), it is clearthat the energy is further lowered due to the additional flexibility in the wave function permitting deformation of the atomic orbitals. Each of the three steps in Eq. (23) corresponds, therefore, to a lowering of the total energy. In order to carry out the program suggested in Section 11, it is now necessary to provide physical pictures to account for these lowerings. In the present section, this problem will be solved by partitioning the energy according to a geometric division of the molecule into atomic and bond regions; in Section V the same problem will be analyzed from an orbital viewpoint.

Et, POLYDOROPOULOS, C. (1967). Compi. Rend. 264, 1368. , and MASSE,J. L. (1955). Bull. Sac. Chim. , 625. BOWEN,E. J. (1963). Advan. Photochem. 1, 23. Strictly valid only for alternant hydrocarbons. Photochemical Reactivity of Organic Molecules 25 BROWN,R. , (1949). Australian J. Sci. 2A, 564. BROWN,R. D. and HARCOURT, R. D. (1959). J. Chem. ,3451. BURKITT, F. , COULSON, C. , and LONGUET-HIGGINS, H. C. (1951). Trans. Faraday SOC. 47, 553. Buu-Hoi, N. , and SANDORFY, C. (1951). Bull. Chim. France 18, 132.

V. Orbital Analysis of the Ground State A. Basis for Orbital Partitioning The three steps of Eq. (23), which formed the basis for the preceding analysis, were selected in such a way that the energy integral was lowered in each of them. This choice was convenient for variational reasoning, but it entailed the need for a geometrical analysis in order to extract the two essential ingredients of bond formation.

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