Excitation energies with spin-orbit couplings using equation-of-motion coupled-cluster singles and doubles eigenvectors.

A method of calculation of excited states with spin-orbit couplings, which utilizes left and right eigenvectors of equation-of-motion coupled-cluster singles and doubles model has been formulated and implemented. The spin-orbit interactions are introduced by using the spin-orbit mean field approximation of the Briet-Pauli Hamiltonian. In order to evaluate all the necessary matrix elements, a scheme based on the diagrammatic representation of the second-quantized form of the spin-orbit interaction operator and the standard rules of second-quantized algebra is presented. We posit that this scheme is general and much simpler to use than the often used rules derived for the configuration state functions by using the Wigner-Eckart theorem. We show that the spin-orbit coupled states (i.e., target relativistic states) must satisfy specific conditions in order to classify them according to the double group symmetry. This interrelation between the structure of the target relativistic states and its double group symmetry is discussed in detail. An algorithm to classify the target states according to the irreducible representation of the double group symmetry is offered and implemented. Numerical tests for several atoms and molecules show good agreement of predicted and experimental spin-orbit splittings of the target excited states.