Curl condition: Existence of sub‐Hilbert space for molecular species or chemical processes

Abstract

The "accuracy" of diabatic Hamiltonian matrix elements solely depends on the level of ab initio calculation and on the included set of coupled electronic manifold forming a "true" sub-Hilbert space (SHS). If ab initio calculations are performed with enough accuracy, existence of SHS can be validated only when the Curl Condition attains zero within numerical precision. For the first time, we depict a theoretical and algorithmic formulation on the calculation of Curl Condition to demonstrate the existence of SHS on molecular processes or chemical reactions.