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10) is fulfilled to the order E'. Zero Differential Overlap 37 For the homonuclear case it is possible to reformulate Eqs. (28), (32), and (41) in an interesting way. The Coulomb part of the penetration integral, UCoul, is found to satisfy the following approximate relations : (1 I U p l l l ) w (1 I UFu'(l)S:( 1 + 2S,)/3, (42) (1 I U y q 2 ) w (1 I Uyll)S:( 1 - S,). (43) By the aid of Eqs. (26), (42), and (43), Eqs. (28) and (32) can be written: "llT12) = -(llT12)(1 - S,)/S,, (44) "11uy12) z -(lluy"'i2)(l - S,)/(2S1).
J. (1951). Rev. Mod. Phys. 23,69. PARR,R. ,and JOY,H. W. (1957). J. Chem. Phys. 26,424. ,and TOMASI, J. (1961). Mol. Phys. 4, 193. Zero Differential Overlap in n-EIect ron Theories TNGA FlSCHER-HJALMARS Institute of Theoretical Physics University of Stockholm Stockholm, Sweden I. Introduction and Summary . 11. Basis of Zero Differential Overlap . A. Assumptions in the ZDO Scheme . B. Justification of the ZDO Assumptions by C. Orthogonalized Atomic Orbital Basis D. Expansion Method . E. Application to the Fock Operator .
1961). J. Chem. Phys. 34, 1914. ORLOFF,M. D. D. (1963). J. Am. Chem. 85, 3721. , and PARR,R. G. (1953). J. Chem. Phys. 21, 466 and 767. PARR,R. G. (1952). J . Chem. Phys. 20, 1499. PARR,R. G . (1960). J. Chem. Phys. 33, 1184. PARR,R. G. (1963). ” Benjamin, New York. 46 lnga Fircher-Hjalmarr PARR,R. , and PARISER, R. (1955). J. Chem. Phys. 23, 711. E. (1959). J . Chem. 3241. POPLE,J. A. (1953). Trans. 49, 1375. POPLE,J. A. (1955). Proc. Phys. (London) A68, 81. POPLE,J. A. (1957). J. Phys. Chem.
Advances in quantum chemistry. / Volume 2 by Per-Olov Löwdin