A variational matrix decomposition applied to full configuration-interaction calculations

A matrix decomposition method for the determination of the lowest eigenvalue of a Hermitian matrix is formulated as an approach to full configuration-interaction calculations on the ground state of many-electron systems. For a wavefunction of the form | ψ 〉 = ∑ | α,β 〉 C αβ the expansion coefficients are written as a separable sum of product terms, P α Q β The elements P a and Q β are then determined from the variation principle for each term. The corresponding Hermitian eigenvalue problem has a dimension which is essentially the square root of the dimension of the original problem. Preliminary calculations on the ground state of the beryllium atom indicate that nearly full configuration-interaction results can be obtained using a comparatively small number of product terms.