A novel approach for calculating correlation energy based on the two‐electron density matrix formalism

Abstract

The two-particle density matrix contains all information which is "readable" by one-and two-particle operators. This work discusses the building of a two-electron density matrix, which is perfectly N-representable by construction. The 2-matrix of a pure quantum state is obtained without the intermediate determination of the wave function. The procedure is illustrated by computations on atomic and small molecular systems.

N-representability of two-electron densities and density matrices and the application to the few-body problem

“…The problem has been solved in two different ways, either by direct construction of valid density matrices from wavefunctions 3 or by an algebraic method 4 . The complexity is large in both methods, as presently implemented, and at least the algebraic method is so far computationally very demanding 3,5 . The wavefunction method is very direct, but gives no information about whether density matrices and densities may or may not be added.…”

“…If the number of proper basis functions is finite (as is always true in practice) it will be necessary to use differences instead of differentials, when minimizing Eqn. (5). This means that we cannot use |x 1 ´-x 1 |< ε and |x 2 ´-x 2 | < ε, with a very small ε, in the twoparticle density matrix as the differences will then always be zero, which is nonsense.…”