  We present a formulation and implementation of second-order quasidegenerate
N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and
accurate description of spin-orbit coupling and dynamic correlation effects in
multiconfigurational electronic states. In our approach, the energies and
wavefunctions of electronic states are computed by treating electron repulsion
and spin-orbit coupling operators as equal perturbations to the
non-relativistic complete active-space wavefunctions and their contributions
are incorporated fully up to the second order. The spin-orbit effects are
described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess
(DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting
second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating
spin-orbit coupling effects in nearly degenerate electronic states by
diagonalizing an effective Hamiltonian expanded in a compact non-relativistic
basis. For a variety of atoms and small molecules across the entire periodic
table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with
variational two-component relativistic theories. BP2-QDNEVPT2 shows high
accuracy for the second- and third-period elements, but its performance
deteriorates for heavier atoms and molecules. We also consider the first-order
spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which
DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and
DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure
methods for treating electron correlation and spin-orbit coupling in a variety
of applications.
