Minimal Matrix Product States and Generalizations of Mean-Field and Geminal Wave Functions

Simple wave functions of low computational cost but which can achieve qualitative accuracy across the whole potential energy surface (PES) are of relevance to many areas of electronic structure theory as well as to applications to dynamics. Here, we explore a class of simple wave functions, the minimal matrix product state (MMPS), that generalizes many simple wave functions in common use, such as projected mean-field wave functions, geminal wave functions, and generalized valence bond states. By examining the performance of MMPSs for PESs of some prototypical systems, we find that they yield good qualitative behavior across the whole PES, often significantly improving on the aforementioned ansätze.