Different powerful approaches and program packages for precise correlation calculations of heavy-atom systems are developed to-date.
Among them one can emphasize two ``ultimate'' approaches, the Relativistic Coupled Cluster (RCC) and Spin-Orbit Configuration Interaction (SOCI) methods.
The nonrelativistic CC formulation was developed by \v{C}izek in 1966 whereas the RCC method was first implemented by Kaldor \& Eliav in 1992.
In turn, the nonrelativistic MultiReference single- and Double-excitation table CI (MRD-CI) method with configuration selection and perturbative energy corrections (to approximate full-CI energies) was developed by Buenker and Peyerimhoff in 1974-1975.
Systematic SOCI calculations (with Relativistic Effective Core Potentials or RECPs) of heavy-atom molecules were started by K.Pitzer with coworkers since 1979.
Many combined approaches of the Multi-Configurational SCF (MCSCF), Perturbation Theory (PT), RCC and SOCI approaches were also developed and successfully applied to studying many-electron systems.
The RCC and SOCI approaches have demonstrated their high efficiency in many calculations of heavy atoms and their compounds.
They adjoin well to each other in the sense of the fields of their optimal applicability.
In general, the RCC method allows one to describe the dynamic (core-core and core-valence) correlations by the best manner.
In turn, the SOCI approaches are usually most optimal (accurate) in describing nondynamic correlations (between valence electrons) which are first required for successful treatment of avoided crossings of electronic terms, open shells, etc.
In opposite to the Density Functional Theory (DFT) that is naturally applied to very large systems and to Quantum Mechanics -- Molecular Dynamics (QM/MD) problems, the RCC and SOCI approaches can be used in accurate calculation of excited electronic states in a given symmetry.
The RCC and SOCI methods are often used as a basis for constructing combined approaches, in which PT and MCSCF (including Restricted/Complete Active Space SCF or RASSCF/CASSCF) are also involved. RASSCF is often used at the stage of preparation of optimal orbitals for further large-scale RCC and SOCI calculations.
In turn, PT (mainly second-order PT or PT2) is usually used for configuration selection and approximate accounting for the configurations giving relatively small contributions together with RCC and SOCI.
In the report, Correlated RECPs, RCC and SOCI techniques as well as their combinations applicable to calculation of properties of different types are discussed.
Accurate calculations of heavy-atom systems with these methods mainly performed by our group are presented.
The present work is supported by the RFBR grant 03-03-32335.