Minimally corrected partial atomic charges for non-covalent electrostatic interactions

ABSTRACT

We develop a new scheme for determining molecular partial atomic charges (PACs) with external electrostatic potential (ESP) closely mimicking that of the molecule. The PACs are the ‘minimal corrections’ to a reference set of PACs necessary for reproducing exactly the tensor components of the Cartesian zero-, first- and second- molecular electrostatic multipoles. We evaluate the quality of ESP reproduction when ‘minimally correcting’ (MC) Mulliken, Hirshfeld or iterative-Hirshfeld reference PACs. In all these cases, the MC-PACs significantly improve the ESP while preserving the reference PACs’ invariance under the molecular symmetry operations. When iterative-Hirshfeld PACs are used as reference, the MC-PACs yield ESPs of comparable quality to those of the ChElPG charge fitting method.

KEYWORDS:

• Partial atomic charges
• force fields
• non-covalent electrostatic interactions
• molecular charge moments

Acknowledgments

Authors express special thanks to Dr Yihan Shao from Q-CHEM Inc. for his advice and critical assistance in performing the iHPA calculations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. When defining the moments, it is customary to take the origin in the centre of the positive charge distribution.

2. See [8]; we use the Einstein convention by which repeated Cartesian indices are summed over.

3. Note that the expression in Equation (5(5) ) cannot become singular due to this requirement.

4. Since the matrix is dominated by zeros, one can formulate the linear equation in a more concise way. However, this form is straightforward to derive and manipulate when there are instabilities, discussed later.

5. Minimally corrected PACs that reproduce only the dipole moment are designated mcD and those that reproduce the components of the dipole and the quadrupole ESMs are designated mcDQ.

6. We cannot rule out possible issues if the matrix S of Equation (9(9) ) becomes rank deficient. However, we believe this is an unlikely or quite rare event.

Additional information

Funding

The study was supported by the Israel Science Foundation [grant number 189/14].