Parametrization of the Two-Electron Reduced Density Matrix for its Direct Calculation without the Many-Electron Wave Function

Parametrization of a molecular two-electron reduced density matrix (2-RDM) enables energies and properties to be directly computed at a highly efficient computational cost. In this Letter an improved 2-RDM parametrization yields energies and properties that are markedly better than those calculated with a similar computational scaling by traditional ab initio methods. Computed 2-RDMs very nearly satisfy well-known $N$-representability conditions. Applications are made to ground-state energies of several molecules and equilibrium bond distances and harmonic frequencies of HF, ${\mathrm{F}}_2$, and CO. The method for single-bond breaking in HF and ${\mathrm{CH}}_4$ yields similar accuracy at equilibrium and nonequilibrium geometries.

Figure 1

Potential energy curves of (a) dissociating HF (b) abstracting a hydrogen from ${\mathrm{CH}}_4$ are shown from the parametric 2-RDM methods with $K$ and $M$ topological factors as well as several traditional wave function methods.