An Iterative Fragment Scheme for the ACKS2 Electronic Polarization Model: Application to Molecular Dimers and Chains

Abstract

The treatment of electrostatic interactions is a key ingredient in the force-field based simulation of condensed phase systems. Most approaches used fixed, site-specific point charges. Yet, it is now clear that many applications of force fields (FFs) demand more sophisticated treatments, prompting the implementation of charge equilibration methods in polarizable FFs to allow the redistribution of charge within the system. One approach allowing both, charge redistribution and site specific polarization, while at the same time solving methodological shortcomings of earlier methods, is the firstprinciples-derived atom condensed Kohn-Sham density functional theory method approximated to second order (ACKS2). In this work we present two fragment approaches to ACKS2, termed f-ACKS2 and a self-consistent version, scf-ACKS, that treat condensed phase systems as a collection of electronically polarizable molecular fragments.The fragmentation approach to ACKS2 not only leads to a more transferable and less system specific collection of electronic response parameters, but also opens up the method to large condensed phase systems. We validate the accuracies of f-ACKS2 and scf-ACKS2 by comparing polarization energies and induced dipole moments for a number of charged hydrocarbon dimers against DFT reference calculations. Finally, we also apply both fragmented ACKS2 variants to calculate the polarization energy for electron-hole pair separation along a chain of anthracene molecules and find excellent agreement with reference DFT calculations.

Treating Polarization Effects in Charged and Polar Bio-Molecules Through Variable Electrostatic Parameters

“…An alternative strategy is provided by atom-condensed Kohn−Sham density functional theory approximated to second order (ACKS2) 71,72 and its extensions, such as fragment approaches to ACKS2 (f-ACKS2) and self-consistent one (scf-ACKS2). 73,74 Among these methods, implementation of ACKS2 is quite similar to EEM without consuming much more computational cost. The Drude oscillator model 50 is the origin of the shell method proposed by Dick and Overhauser 51 and further referred as the charge-on-spring method.…”

“…In addition, for small hydrocarbons, superlinear scaling of the dipole polarizability instead of dielectric systems for n -alkanes was predicted and the size extensivity was broken. , Additional fictitious sites such as the ABEEM-7P FQ model for water were often introduced to remedy this shortcoming, but further computational cost was incurred. An alternative strategy is provided by atom-condensed Kohn–Sham density functional theory approximated to second order (ACKS2) , and its extensions, such as fragment approaches to ACKS2 (f-ACKS2) and self-consistent one (scf-ACKS2). , Among these methods, implementation of ACKS2 is quite similar to EEM without consuming much more computational cost.…”

Unifying Charge-Flow Polarization Models

“…The energy was originally given in terms of changes in atomic charges relative to a set of reference charges, Δ , but for comparison with the other models, the Q form will be used (Supporting Information), and E ACKS2 can, with the notation from the CRK section, be written as in eq . The E ACKS2 can be considered as including the FQ and CRK expressions in eqs and . In the original ACKS2 paper and in subsequent work, − the operational equations are derived by making the Lagrange function in eq stationary, where two Lagrange multipliers λ Q and λ V are introduced to ensure Q and V conservation, and this results in the four coupled equations in eq . The singular nature of the K matrix, however, makes λ V equal 0 (Supporting Information), and the second equation becomes eq . This is identical to the CRK expression in eq , but without a partitioning into internal and external components for K and V . The remaining ACKS2 equations can be solved explicitly (Supporting Information), with the result for Q given in eq . The 1 t K = 0 condition ensures that eq always provides the correct molecular charge, and λ Q is thus redundant and can be omitted. Equation with λ Q = 0 can be rewritten to eq (Supporting Information), showing the equivalence to the CRK expression in eq with a redefinition of the reference charges Q 0 . Using eq allows the last two terms in eq to be condensed into one, as shown in eq . Analogous to the CRK case in eq , E ACKS2 c...…”

A new framework for frequency-dependent polarizable force fields

“…Later, they proposed two ACKS2 variants, f-ACKS2 and scf-ACKS2, to handle condensed phases by dividing them into molecular fragments, which are coupled by Coulomb interactions. 46 This work extends ACKS2 to the time-and frequency-dependent domain to compute the dynamical response properties of finite molecules, e.g., frequency-dependent polarizabilities, C 6 dispersion coefficients, and molecular absorption spectra. The resulting ACKS2ω model, through its use of atomic multipole expansions, allows one to investigate the contribution of charge-flow effects on dynamic response properties, which is a topic of ongoing research.…”