Coupled-cluster open-shell analytic gradients: Implementation of the direct product decomposition approach in energy gradient calculations

Analytic energy gradients for the coupled-cluster singles and doubles (CCSD) method have been implemented for closed-shell systems using restricted Hartree–Fock (RHF) and open-shell systems using unrestricted Hartree–Fock (UHF) reference functions. To achieve maximum computational efficiency, the basic theory has been reformulated in terms of intermediates, thus reducing the number of required floating-point operations, and all computational steps are given in terms of matrix products in order to exploit the vector capabilities of modern supercomputers. Furthermore, the implementation has been designed to take full advantage of Abelian symmetry operations. To illustrate the computational efficiency of our implementation and in particular to demonstrate the possible savings due to the exploitation of symmetry, computer timings and hardware requirements are given for several representative chemical systems. In addition, the newly developed analytic CCSD gradient methods are applied to calculate the equilibrium geometry and energy splitting of the lowest singlet and triplet states of the C4O2 molecule.