Expansion in a basis of orbital wave functions

The /V-clcctron Hamiltonian is a sum of one- and two-electron operators, H = h(i) + Y-H) j). A reference state b is defined as a single Slater deter- 

Taking spin indices into account, all two-electron integrals are of the form (ij u kl) = (ij u kl) - (ij u lk), with the convention that orbitals with different spin indices are orthogonal. It is convenient to truncate summations by the use of occupation numbers // which are in principle determined by Fermi-Dirac statistics. At zero temperature, occupation numbers are determined by the structure of the reference state. Then m = 1, na = 0 for i N a. A convention used for double summation indices is ij i j N,ab N a b. 

With these conventions of notation, simple formulas exist for all matrix elements of H in the basis of Slater determinants generated by virtual excitations from a reference state [72], Denoting the latter by b0, and defining an effective one-electron operator TL = h + nj(ij u ij) for b0, the sequence of nondiagonal 

All such matrix elements vanish if more than two occupied orbitals are replaced, because H contains only a two-electron interaction operator. Given (0 // 0) = ni(i h i) + nittj(ij u /j), diagonal elements follow a simple rule  

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