Anti-Hermitian Contracted Schrödinger Equation: Direct Determination of the Two-Electron Reduced Density Matrices of Many-Electron Molecules

Two-electron reduced density matrices (2-RDMs) of many-electron molecules are directly determined without calculation of their wave functions by solving the anti-Hermitian contracted Schrödinger equation. Approximation of the 3-RDM in the anti-Hermitian contracted Schrödinger equation by a corrected cumulant expansion [Mazziotti, Phys. Rev. A 60, 3618 (1999)] permits the direct calculation of the energy and 2-RDM with many high-order correlation effects included. The method is illustrated for the molecules ${\mathrm{BeH}}_2$, ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{NH}}_3$, ${\mathrm{CH}}_4$, and CO as well as the dissociation of BH. Correlation energies are obtained within 95%–100% of full-configuration interaction, and 2-RDMs very nearly satisfy known $N$-representability conditions.

Figure 1

For BH the ACSE energy as a function of $\lambda$, converges to 0.3 mhartree above the FCI energy.

Figure 2

The potential curve of BH from the ACSE with NY reconstruction is compared with the curve from MP4 and FCI.