Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field

To reduce the basis set incompleteness of the complete-active-space self-consistent field (CASSCF) wave function and energy we develop a second-order perturbation correction due to single excitations to complete set of unoccupied states. Other than the one-and two-electron integrals, only one- and two-particle reduced density matrices are required to compute the correction, denoted as [2](S). Benchmark calculations on prototypical ground-state bond-breaking problems show that only the aug-cc-pVXZ basis is needed with the [2](S) correction to match the accuracy of CASSCF energies of the aug-cc-pV(X+1)Z quality. (C) 2010 American Institute of Physics. [doi:10.1063/1.3499600]