Molecule-optimized Basis Sets and Hamiltonians for Accelerated Electronic Structure Calculations of Atoms and Molecules

摘要

Molecule-optimized basis sets, based on approximate natural orbitals, aredeveloped for accelerating the convergence of quantum calculations withstrongly correlated (multi-referenced) electrons. We use a low-cost approximatesolution of the anti-Hermitian contracted Schr{\"o}dinger equation (ACSE) forthe one- and two-electron reduced density matrices (RDMs) to generate anapproximate set of natural orbitals for strongly correlated quantum systems.The natural-orbital basis set is truncated to generate a molecule-optimizedbasis set whose rank matches that of a standard correlation-consistent basisset optimized for the atoms. We show that basis-set truncation by approximatenatural orbitals can be viewed as a one-electron unitary transformation of theHamiltonian operator and suggest an extension of approximate natural-orbitaltruncations through two-electron unitary transformations of the Hamiltonianoperator, such as those employed in the solution of the ACSE. Themolecule-optimized basis set from the ACSE improves the accuracy of theequivalent standard atom-optimized basis set at little additional computationalcost. We illustrate the method with the potential energy curves of hydrogenfluoride and diatomic nitrogen. Relative to the hydrogen fluoride potentialenergy curve from the ACSE in a polarized triple-zeta basis set, the ACSE curvein a molecule-optimized basis set, equivalent in size to a polarizeddouble-zeta basis, has a nonparallelity error of 0.0154 a.u. which issignificantly better than the nonparallelity error of 0.0252 a.u. from thepolarized double-zeta basis set.