Direct Determination of the Quantum-Mechanical Density Matrix Using the Density Equation

Abstract

With the use of the density equation [H. Nakatsuji, Phys. Rev. A 14, 41 (1976)], the second-order density matrices are directly determined without any use of the wave functions. The third- and fourth-order reduced density matrices (RDM's) are decoupled into lower-order ones using the Green's function technique. This method is applied to Be, Ne, ${\mathrm{H}}_{2}$O, ${H}_{3}{O}^{+}$, N${\mathrm{H}}_{3}$, C${\mathrm{H}}_{4}$, ${\mathrm{BH}}_{4}^{\phantom{\rule{0ex}{0ex}}\ensuremath{-}}$, ${\mathrm{NH}}_{4}^{\phantom{\rule{0ex}{0ex}}+}$, and C${\mathrm{H}}_{3}$F, and the results are successfully compared with the full configuration interaction results. The convergence is fairly good, and the calculated second-order RDM's almost satisfy the necessary conditions of the N representability, the P, Q, and G conditions, and the first-order RDM's are exactly N representable. These results show that the present method is very promising.