General considerations

NEVPT2 is a form of second-order multireference perturbation theory which can be applied to CAS-SCF wavefunctions or, more generally, to CAS-CI wavefunctions. The term NEVPT is an acronym for ``n-electron valence state perturbation theory''. While we refer the reader to the pertinent literature [104,105,106,107], we limit ourselves to recalling here that the most relevant feature of NEVPT2 consists in that the first order correction to the wave function is expanded over a set of properly chosen multireference functions which correctly take into consideration the two-electron interactions occurring among the active electrons. Among the properties ensured by NEVPT2 we quote:

• Strict separability (size consistence): the energy of a collection of non-interacting systems equals the sum of the energies of the isolated systems
• Absence of intruder states: the zero-order energies associated to the functions of the outer space are well separated from the zero-order energy of the state being studied, thus avoiding divergences in the perturbation summation
• The first order correction to the wavefunction is an eigenfunction of the spin operators $S^2$ and $S_z$
• Electronically excited states are dealt with at the same level of accuracy as the ground state
• NEVPT2 energies are invariant under a unitary transformation of the active orbitals. Furthermore, the choice of canonical orbitals for the core and virtual orbitals (the default choice) ensure that the results coincide with those of an enlarged version of the theory fully invariant under rotations in the core and virtual orbital spaces, respectively [107]
• NEVPT2 coincides with MP2 in the case of a HF wave function

NEVPT2 has been implemented in two variants both of which are present in DALTON, these are the strongly contracted (SC) and the partially contracted (PC) variants. The two variants differ by the number of perturber functions employed in the perturbation summation. The PC-NEVPT2 uses a richer function space and is in general more accurate than the SC-NEVPT2. The results of SC-NEVPT2 and PC-NEVPT2 are anyway usually very close to one another.