A formulation of the n-electron valence state perturbation theory ͑NEVPT͒ at the third order of perturbation is presented. The present implementation concerns the so-called strongly contracted variant of NEVPT, where only a subspace of the first-order interacting space is taken into account. The resulting strongly contracted NEVPT3 approach is discussed in three test cases: ͑a͒ the energy difference between the 3 B 1 and 1 A 1 states of the methylene molecule, ͑b͒ the potential-energy curve of the N 2 molecule ground state, and ͑c͒ the chromium dimer ͑Cr 2 ͒ ground-state potential-energy profile. Particular attention is devoted to the last case where large basis sets comprising also h orbitals are adopted and where remarkable differences between the second-and third-order results show up.

The potential energy curves of the ground state and of some excited states of the manganese dimer have been calculated over a wide range of internuclear distances using the second order n-electron valence state perturbation theory applied to a complete active space self-consistent field reference wave function. The ground state of Mn(2), for which also the third order NEVPT has been used, is calculated to be a singlet belonging to the Sigma(g) (+) symmetry, characterized by a large equilibrium internuclear distance R(e) of 3.7-3.8 A, by a low dissociation energy D(e) of 0.07-0.08 eV, and by a small harmonic frequency omega(e) of 43 cm(-1). The experimental evidence that Mn(2) is a van der Waals molecule is thus confirmed. Among the excited states, (11)Pi(u), which is usually indicated as the ground state by density functional theory studies, appears as a low-lying state with R(e)=2.50 A, D(e)=1.35 eV, and omega(e)=246 cm(-1).

The potential energy curves of the molecules Mo(2), W(2), and CrMo have been studied ab initio using large basis sets and the "n-electron valence state perturbation theory" up to the third order in the energy. The third order results for Mo(2) and W(2) reproduce the equilibrium distances r(e) and the harmonic frequencies omega(e) in fairly good accordance with the experimental values but tend to underestimate the dissociation energy. The CrMo molecule, for which experimental dissociation energy data do not exist yet, is predicted to have a value for D(e) of approximately 2.5 eV.

ABSTRACT:A short summary of the n-electron valence state perturbation theory (NEVPT) is provided, and the defects inherent in cases of quasi-degeneration are underscored. A new version of the theory, called QD-NEVPT, based on quasidegenerate perturbation theory, is presented. The new theory introduces an effective interaction among the zero-order wave functions and overcomes the difficulties of statespecific NEVPT. An application concerning the interaction among the 3 * and Rydberg singlets of formaldehyde is presented.