Atom-centered electric multipole moments dynamically generated from QM/MM MD simulations

TL;DR

Problem: atom-centered multipoles are useful but not uniquely defined, complicating their use in simulations. Approach: extend D-RESP to xDRESP to dynamically generate multipoles up to order $\Lambda$ from QM/MM MD ESP fits on MM SR sites, with restraints to reference charges and optional QM moment constraints within the MiMiC framework. Contributions: validation across Ace, AlaGly, Gua, CREB-APAP, Ph-Br, and SN2 shows xDRESP accurately reproduces $V^{\mathrm{QM \to MM}}$ and molecular multipoles, with instantaneous charges performing best and higher-order multipoles offering ESP improvements in halogenated systems (requiring appropriate restraints). Significance: provides a practical, extensible route to system-specific electrostatics and on-the-fly polarization analysis, with implications for force-field parameterization, polarizable embeddings, and reaction-density tracking in QM/MM contexts.

Abstract

Atom-centered electric multipole moments can be extremely useful in chemistry as they enable the systematic mapping of a complex electrostatic problem to a simpler model. However, since they do not correspond to physical observables, there is no unique way to define them. In this work, we present an extension of the dynamically generated RESP charges (D-RESP) method, referred to as xDRESP, where atom-centered multipoles are computed from mixed quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations. We compare the ability of xDRESP charges to reproduce the electrostatic potential, as well as molecular multipoles, against the performance of fixed point-charge models commonly used in force fields. Moreover, we highlight cases where DRESP atomic multipoles can provide valuable information about chemical systems, such as indicating when polarization plays a significant role, and chemical reactions, in which xDRESP atomic multipoles can be used as an on-the-fly analysis tool to track changes in electron density.

Figures (31)

• Figure 1: Systems for which the QM/MM MD simulations with xDRESP analysis have been performed. Here, only the QM region is represented, but all systems are solvated in water, except for the S$_\mathrm{N}$2 reaction, which has been performed in acetone instead. For the CREB--APAP system, the protein target (CREB) is also present in the simulation.
• Figure 2: Distribution of xDRESP charges for the Ace sytem during 1ps QM/MM MD with different restraint weights $w_\textrm{R}$ to the Hirshfeld charges. In the bottom panel, the reference Hirshfeld charges from the QM external program (CPMD) are reported for comparison.
• Figure 3: Different metrics used to assess the accuracy of the xDRESP point charge set obtained with $w_\mathrm{R}$ = e-3 for the Ace system. The total potential, $V^{\mathrm{QM \to MM}}$, and molecular multipoles are computed during the dynamics for the electrostatic QM/MM coupling, and have been used as reference.
• Figure 4: Comparison of the resulting molecular multipole moments (dipole and quadrupole) from xDRESP charges and from different atomic charge schemes and point-charge models in commonly used classical FFs. Averaged xDRESP charges ($\langle\text{xDRESP}\rangle$) and Hirshfeld charges (instantaneous and averaged) are also shown. For three different systems, AlaGly, Gua, and CREB--APAP, we report the data from a 1ps QM/MM MD as a distribution of the difference in the molecular dipole/quadrupole calculated from the point charge model with respect to the one calculated from the QM charge distribution. The values are calculated as the Euclidean norm for the difference in the dipole and the Frobenius norm for the difference in the quadrupole. Note that the ranges of the axes change among the different plots.
• Figure 5: xDRESP charges for the Phe--Br molecule during 1ps QM/MM MD with a restraint to the Hirshfeld charges $w_\textrm{R}$=e-3, fitting atomic charges (left) and comparison of the ability in reproducing the potential, $V^{\mathrm{QM \to MM}}$, with xDRESP, the fixed point-charge variant $\langle\text{xDRESP}\rangle$ and a simultaneous xDRESP fit of atomic charges and dipoles xDRESP{$q$, $\mu$} (right).