Configuration interaction integral transformation

This section briefly discusses two elements common to all configuration interaction programs transformation of integrals, and iterative subspace diagonal-ization of the Hamiltonian. 

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

The K-matrix method is essentially a configuration interaction (Cl) performed at a fixed energy lying in the continuum upon a basis of "unperturbed funetions that (at the formal level) includes both diserete and eontinuous subsets. It turns the Schrodinger equation into a system of integral equations for the K-matrix elements, which is then transformed into a linear system by a quadrature upon afinite L basis set. 

Theorem 2 For a Coulomb Hamiltonian, in an actual configuration-interaction -type calculation with one-particle square-integrable, analytic functions as basis sets, all overlap, one- and two-particle integrals remain invariant under transformations of the type u r)... 

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