By Stuart A Rice; I Prigogine
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Extra resources for Advances in Chemical Physics [Vol 14]
This reduced list of index pairs, expressing QP in terms of excitations from @, is used to determine whether the integral vanishes, or to select the appropriate formula, Eqs. (6) or (7) with X 0 replaced by S‘, for , non-diagonal matrix elements. Diagonal elements are computed from Eq. (15). Matrix elements of &, are expressed in terms of XJ0by use of Eq. (12). 4O Two-electron integrals of the form indicated in Eq. 8 The coefficients in these linear combinations represent integrals over spherical harmonics and spin summations.
Chem. , 38, 2248 (1963). Kelly, H. , Phys. , 131, 684 (1963); 186, B896 (1964). , J . Chem. , 41, 2689 (1964). Nesbet, R. , in Quantum Theory of Atoms, Molecules, and the Solid State, Ed. -0. Lowdin, Academic Press, New York, 1966, pp. 157165; Colloques Internationaux du CNRS, No. 164 (1967). pp. 87-94. 34 R. K. NESBET 34. , IBM J . Res. , 9, Supplement (1965). Tables 4-1, 10-1. 35. Nesbet, R. , Phys. , 156, 99 (1967). 36. Mittleman, M. , Phys. , 147,69 (1966). 37. , Kgl. Fys. Sallskapets Lund F6rhaladE..
43) (c = 1,2) and the operators: (44) (c = 1,2) where T represents the sequence of numbers A;, A ; , . . A;, A; Furthermore, we shall associate the operator Pi,,(Pi,,)with every oriented line labelled A j ( A ; ) and entering (leaving) some vertex of the T diagram. Using the notation specified above, the operator may be expressed in the form %n i' =1-1 2 W$(t) 2 &(t, T) T (45) (c = 1,2) A set of T skeletons is called an M skeleton. J, etc. The M skeletons are designated S,(m), where m represents a sequence of indices t, of the T skeletons involved, the order of the individual indices being immaterial.