Date of Award

Spring 2016

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Timerghazin, Qadir K.

Second Advisor

Babikov, Dmitri

Third Advisor

Gardinier, James


Atom-centered point charge model of the molecular electrostatics remains a major workhorse in the atomistic biomolecular simulations. However, this approximation fails to reproduce anisotropic features of the molecular electrostatic potential (MEP), and the existing methods of the charge derivation are often associated with the numerical instabilities. This work provides an in-depth analysis of these limitations and offers a novel approach to describe electrostatic interactions that paves the way toward efficient next-generation force fields. By analyzing the charge fitting problem from first principles, as an example of the mathematical inverse problem, we show that the numerical instabilities of the charge-fitting problem arise due to the decreasing contribution from the higher multipole moments to the overall MEP. This insight suggests that if the point charges are arranged over the sphere using Lebedev quadrature, the resulting point charge model is able to exactly reproduce multipoles up to a given rank. At the same time, point charge values can be derived without fitting to the MEP, avoiding numerically unstable method of the charge derivation. This approach provides a systematic way to reproduce multipole moments up to any rank within the point charge approximation, which makes this model a computationally efficient analog of the multipolar expansion. Moreover, the proposed charged sphere model can be also used in the multi-site expansions with the expansion centers located at each atom in a molecule. This provides a natural approach to expand the traditional atom-centered point charge approximation to include higher-rank atomic multipoles and to account for the anisotropy of the MEP. We applied the proposed charged sphere model to S-nitrosothiols (RSNOs)—a class of biomolecules that serves to store and transmit nitric oxide, a biologically important signaling molecule. We showed that when the atom-centered charged spheres are optimized together with the Lennard-Jones parameters, the resulting force field can accurately reproduce the anisotropic features of the intermolecular interactions that play a crucial role in the biological regulation of RSNO chemistry. Overall, the developed charge model is a promising approach that can be used in the biomolecular simulations and beyond, e.g. in the multipolar force fields for atomistic and coarse-grained simulations.