Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

An efficient implementation of time-dependent linear-response theory for strongly orthogonal geminal wave function models

We present an implementation of time-dependent linear-response equations for strongly orthogonal geminal wave function models: the generalized valence bond perfect-pairing theory (TD-GVB) and the antisymmetrized product of strongly orthogonal geminals (TD-APSG). The geminal wave functions are optimized using a restricted-step second-order algorithm suitable for handling many geminals, and the linear-response equations are solved in an efficient way using a direct iterative approach. The wave function optimization algorithm features an original scheme to create initial orbitals for the geminal functions in a black-box fashion. The implementation is employed to examine the accuracy of the geminal linear response for singlet excitation energies of small and medium-sized molecules. In systems dominated by dynamic correlation, geminal models constitute only a minor improvement with respect to time-dependent Hartree-Fock. Compared to linear-response complete active space self-consistent field (LR-CASSCF), TD-GVB either misses or gives large errors for states dominated by double excitations.

Describing Strong Correlation with Block-Correlated Coupled Cluster Theory

A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide satisfactory descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single C-C bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all C-C bonds.

Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew-Zunger Self-Interaction Corrected Density Functional Theory Calculations

Implentation of seminumerical stability analysis for calculations using the Perdew-Zunger self-interaction correction is described. It is shown that real-valued solutions of the Perdew-Zunger equations for gas phase atoms are unstable with respect to imaginary orbital rotations, confirming that a proper implementation of the correction requires complex-valued orbitals. The orbital density dependence of the self-interaction corrected functional is found to lead to multiple local minima in the case of the acrylic acid, H6, and benzene molecules. In the case of benzene, symmetry breaking that results in incorrect ground state geometry is found to occur, erroneously leading to alternating bond lengths in the molecule.