Relativistic GAS Coupled Cluster of General Excitation Rank

For the most efficient treatment of dynamic electron correlation, a relativistic quasi-MRCC approach of general excitation rank has been developed. The non-relativistic precursor program was introduced by Olsen (J. Chem. Phys. 113,17 (2000) 7140-7148) which uses higher excitations defined by the Generalized Active Space (GAS) concept to simulate multi-reference model spaces (see image). For electronic ground states

both a determinant-based (CI expansion based) version (see ref. Theo. Chem. Acc. 2007) and a commutator-based version (see ref. J. Chem. Phys. 2011), the latter with a correct computational scaling as conventional CC approaches (see Z Phys Chem 2010) have been devised. These implementations assume a basis of Kramers-paired spinors, but do not yet fully exploit time-reversal symmetry at the many-particle level (see Phys Rev A 2008). The Dirac-Coulomb Hamiltonian or approximations to it, such as Dyall's spin-free Hamiltonian, may be employed for rigorously determining effects of spin-orbit interaction. The method is currently capable of treating general, but small, closed- and open-shell molecules and dissociation processes of heavy-element systems at high accuracy. The CI-based version can be applied roughly up to 12 correlated electrons whereas the correctly scaling commutator-based version has been applied with more than 20 correlated electrons. Both the CI-based and commutator-based implementations have been extended to the treatment of electronically excited states by diagonalising the CC Jacobian. The approach corresponds to earlier implementations of CC response theory (e.g. by Christiansen, Joergensen, and Koch) and to Equation-Of-Motion (EOM-CC) approaches (e.g. by Bartlett and co-workers), however here with a four-component relativistic Hamiltonian.
Much of current work deals with improving the new implementations both with respect to efficiency and applicability.