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> = Σ | α, β>Cαβthe expansion coefficients are written as a separable sum of product terms PαQPβ. The elements Pαand Qβare 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. © 1992.