N-electron Valence State Perturbation Theory - Properties

Properties

NEVPT is blessed with many important properties, making the approach very solid and reliable. These properties arise both from the theoretical approach used and on the Dyall's Hamiltonian particular structure:

• Size consistency: NEVPT is size consistent (strict separable). Briefly, if A and B are two non-interacting systems, the energy of the supersystem A-B is equal to the sum of the energy of A plus the energy of B taken by themselves . This property is of particular importance to obtain correctly behaving dissociation curves.

• Absence of intruder states: in perturbation theory, divergencies can occur if the energy of some perturber happens to be nearly equal to the energy of the zero-order wavefunction. This situation, which is due to the presence of an energy difference at the denominator, can be avoided if the energies associated to the perturbers are guaranteed to be never nearly equal to the zero-order energy. NEVPT satisfies this requirement.

• Invariance under active orbital rotation: The NEVPT results are stable if an intraclass active-active orbital mixing occurs. This arises both from the structure of the Dyall Hamiltonian and the properties of a CASSCF wavefunction. This property has been also extended to the intraclass core-core and virtual-virtual mixing, thanks to the Non Canonical NEVPT approach, allowing to apply a NEVPT evaluation without performing an orbital canonization (which is required, as we saw previously)

• Spin purity is guaranteed: The resulting wavefunctions are guaranteed to be spin pure, due to the spin-free formalism.

• Efficiency: although not a formal theoretical property, computational efficiency is highly important for the evaluation on medium-size molecular systems. The current limit of the NEVPT application is largely dependent on the feasibility of the previous CASSCF evaluation, which scales factorially with respect to the active space size. The NEVPT implementation using the Dyall's Hamiltonian involves the evaluation of Koopmans' matrices and density matrices up to the four-particle density matrix spanning only active orbitals. This is particularly convenient, given the small size of currently used active spaces.

• Partitioning into additive classes: The perturbative correction to the energy is additive on eight different contributions. Although the evaluation of each contribution has a different computational cost, this fact can be used to improve performance, by parallelizing each contribution to a different processor.