Novel zero-field splitting (ZFS) formula is developed to calculate the spin-orbit contribution (D-SO) to the ZFS tensor by using finite-perturbation theory, i.e., two-component self-consistent-field procedures with second-order Douglas-Kroll-Hess Hamiltonian. The ZFS formula is extended to second-order generalized unrestricted Moller-Plesset perturbation theory. For triplet diatomic molecules, several fundamental contributions to the D-SO tensor are investigated. The electron-correlation effects were relatively large (more than 23%) and were very significant (more than 56%) especially for SeS, Se-2, and Te-2. (C) 2011 Elsevier B.V. All rights reserved.