A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions.

We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate, for example, transition and spin-orbit coupling matrix elements between arbitrary electronic states, provided that they share the same one-electron basis functions and size of the active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation, by exploiting a sequence of nonunitary transformations, following a proposal by Malmqvist [Int. J. Quantum Chem. 1986, 30, 479]. This is well-known for traditional wave function parametrizations but has not yet been exploited for MPS wave functions.