Origin and control of superlinear polarizability scaling in chemical potential equalization methods

Abstract

Many common chemical potential equalization ͑ Eq͒ methods are known to suffer from a superlinear scaling of the polarizability with increasing molecular size that interferes with model transferability and prevents the straightforward application of these methods to large, biochemically relevant molecules. In the present work, we systematically investigate the origins of this scaling and the mechanisms whereby some existing methods successfully temper the scaling. We demonstrate several types of topological charge constraints distinct from the usual single molecular charge constraint that can successfully achieve linear polarizability scaling in atomic charge based equilibration models. We find the use of recently employed charge conservation constraints tied to small molecular units to be an effective and practical approach for modulating the polarizability scaling in atomic Eq schemes. We also analyze the scaling behavior of several Eq schemes in the bond representation and derive closed-form expressions for the polarizability scaling in a linear atomic chain model; for a single molecular charge constraint these expressions demonstrate a cubic dependence of the polarizability on molecular size compared with linear scaling obtainable in the case of the atom-atom charge transfer ͑AACT͒ and split-charge equilibration ͑SQE͒ schemes. Application of our results to the trans N-alkane series reveals that in certain situations, the AACT and SQE schemes can become unstable due to an indefinite Hessian matrix. Consequently, we discuss sufficient criteria for ensuring stability within these schemes.

The ReaxFF reactive force-field: development, applications and future directions

“…A polarisable charge calculation method is essential for a transferable reactive force-field method. ReaxFF typically employs the electronegativity equalisation method (EEM) developed by Mortier et al 129 Unfortunately, EEM has a few drawbacks, [130][131][132][133][134] the worst being its inability to restrain longrange charge-transfer, even between molecular fragments that are well separated. This issue is especially apparent in low-density gas phase simulations, where EEM-ReaxFF predicts small, but certainly nonzero, charges on isolated molecular species, which significantly affects accommodation coefficients.…”

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…First, EEM predicts that the dipole polarizability of a chain molecule grows cubically with the chain length, while one expects a linear trend in the macroscopic limit for dielectric molecules. 56,57 Second, one obtains fractional charges when a molecule dissociates, 58,59 while one expects integer-charged fragments. 60,62 These errors limit the applicability of EEM to isolated small molecules where an incorrect polarizability is acceptable.…”

“…The first problem is that EEM always predicts a cubic scaling of the dipole polarizability with system size, while dielectric systems exhibit a linear scaling in the macroscopic limit. 56,57 The second problem is that EEM yields, in general, fractional molecular charges for a system with two or more molecules, even when these molecules are well separated. 58,59 For such systems, one expects integercharged molecules because the energy of an isolated molecule is a piece-wise linear function of the molecular population with derivative discontinuities at integer populations.…”

“…These terms guarantee a linear scaling of the dipole polarizability. 56,57 It is common to associate split charges only with pairs of atoms that are covalently bonded, which disables intermolecular charge transfer. Later, Nistor et al proposed the split-charge equilibration (SQE), 66 which has EEM and AACT as limiting cases.…”

“…Several ad hoc approaches were proposed to solve both EEM problems, e.g., with artificial constraints on molecular charges 20,57 or with harmonic restraints on molecular dipoles. 47 One can also suppress the impact of electronegativity differences at long distances.…”