A density fitting scheme for the fast evaluation of molecular electrostatic potential

Molecular electrostatic potential (MEP) is a significant and crucial physical quantity that can be applied to a large number of scenarios, such as the prediction of nucleophilic or electrophilic attacks, fitting atomic charges, σ-hole, and so forth. The computational cost for the MEP has an O(N² ) scaling with the increase of atoms, which is intractable and laborious for macromolecules. Herein, a density fitting molecular electrostatic potential (DF-MEP) is used to reduce the computational costs for the macromolecular MEP. It is found that the accuracy of DF-MEP is almost identical to the conventional molecular electrostatic potential (Conv-MEP), while the computational costs can be reduced to an O(N) scaling, for example, the computational time of 699,200 grids for the Trp-cage molecule (304 atoms) only takes 16.6 s at the B3LYP-D3(BJ)/def2-SVP level of theory with 16 CPU cores compared with 3060.2 s for the Conv-MEP method.