The exact multicenter multipolar part of a molecular charge distribution and its simplified representations

Abstract

We study the problem of representing the molecular charge distribution in a convenient way for practical applications and we propose, instead of a single representation, a flexible procedure for building approximations with an arbitrary level of accuracy as concerns the long-range part of the electrostatic potential. We first discuss the splitting of the total electrostatic potential into a multipolar part (long-range) and a penetration part (shortrange) in connection with the usual one-center multipole expansion: at large enough distances, this expansion precisely converges towards the multipolar part. However, this representation is not practically efficient as soon as the molecule departs from a spherical shape, and we therefore consider a so-called multicenter multipole representation. In the MO-LCAO framework, the use of a basis of Gaussian atomic orbitals {χα} generates such a representation in a natural way: indeed, each elementary distribution χ*αχβ then reduces to a one-center distribution with a finite number of multipoles, hence an exact multipolar representation (corresponding to the approximate MO-LCGO wave function) involving a finite (albeit large, in general) number of centers, each one bearing a finite (small) number of multipoles. From this representation used as a reference, we then generate simplified multicenter multipole representations through a systematic procedure of reduction of the number of centers (having chosen a reduced set of new centers, we represent the multipoles of each suppressed old center through suitable new multipoles located on a few new centers closest to the old one under consideration). The number and locations of the new centers are arbitrary, hence the great flexibility of the method. We checked the accuracy of this procedure for molecules of different polarity (water, benzene, adenine), and we noticeably found that a representation involved as centers, the atoms plus one point per chemical bond exhibited quite a satisfactory accuracy. In the conclusion, we briefly discuss the possibility of extending the method to other kinds of basis functions (e.g., Slater orbitals), in connection with the problem of representing the charge distribution associated with the exact molecular wave function, we also discuss the choice of the number centers according to the desired accuracy and we briefly describe a way of applying the method to the problem of representing a large molecule in terms of molecular fragments.

Electrostatic properties in the catalytic site of papain: A possible regulatory mechanism for the reactivity of the ion pair

“…The use of multicentered multipolar expansions, instead of classical force field or potential derived atom charges, is a more theoretical grounded and precise way to compute molecular electrostatic properties 61,62 with a reasonable computational cost even in biological macromolecules. 30,[63][64][65] Moreover, previous studies indicate that in protein electrostatic investigations the OME reassociation method is the best choice in order to achieve a better and more homogeneous description of both the electrostatic potential and the intensity and direction of the electric field.…”

Towards a force field based on density fitting

“…Such a procedure was originally demonstrated to provide a very good approximation of the true multipolar energy. 4 The values of the multipolar Coulomb energy were computed using the SIBFA package.…”

“…1 For example, the value of the true intermolecular Coulomb energy (the intermolecular electrostatic contribution) cannot be matched in the bonding area by traditional classical approaches using long range approximations such as fitted point charges 2 or even with more advanced distributed multipole representations. [3][4][5][6] Indeed, short range quantum effects related to the overlap of electron clouds (penetration energy) are missing from current force fields and are a non-negligible source of error. In other words, if the goal is to reach "chemical accuracy" it is not enough for a model energy function to perform well outside the molecular van der Waals envelope; it is also important to be able to reproduce energies even when electronic densities overlap (especially in molecular dynamics simulations where close contacts are frequently generated).…”

Intermolecular electrostatic energies using density fitting

“…15 The original molecular-centered expansion has been largely superseded by a distributed multipole expansion in terms of specific atomic or site contributions, due to its better convergence properties. 14,16,17 In order to employ this expression, the atomic or site-specific multipolar moments need to be determined by partitioning the wave function or the electronic density. A disadvantage of the multipolar expansion is that this approximation neglects the charge penetration effects which may be substantial at short range.…”