A new framework for frequency-dependent polarizable force fields

Abstract

A frequency-dependent extension of the polarizable force field “Atom-Condensed Kohn–Sham density functional theory approximated to the second-order” (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2 ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2 ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C6 dispersion coefficients, ACKS2 ω closely reproduces its TDDFT reference. When parameters for ACKS2 ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2 ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.

Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

“…The α 00 , α 01 , α 10 , and α 11 contributions to the molecular polarizability (eqs 2 and 3) are examples of properties that can be calculated with standard linear response theory. 69 Morita and Kato have pioneered this for calculating α 00 , denoted the charge response kernel, with atomic charges defined by fitting to the electrostatic potential. 70,71 This charge definition, however, is prone to numerical instabilities, and indeed their calculated α 00 values are sensitive to details in the fitting procedure.…”

“…Since the molecular dipole moment is exactly reproduced by the atomic charges and dipoles in eq , the polarizability is also exactly reproduced by the atomic charge flow and induced dipole terms. The α 00 , α 01 , α 10 , and α 11 contributions to the molecular polarizability (eqs and ) are examples of properties that can be calculated with standard linear response theory . Morita and Kato have pioneered this for calculating α 00 , denoted the charge response kernel, with atomic charges defined by fitting to the electrostatic potential. , This charge definition, however, is prone to numerical instabilities, and indeed their calculated α 00 values are sensitive to details in the fitting procedure. − We have implemented the α kl response quantities with the MBIS definition of AIM, with details that will be reported elsewhere.…”

Unifying Charge-Flow Polarization Models

“…The ACKS2 model has been extended to include intermolecular polarization by including an intermolecular Coulombic interaction. , This has no influence on the above analysis as the J ̃ matrix implicitly accommodates this. The ACKS2 model has been generalized to frequency-dependent polarization, and thereby also modeling dispersion, by making K frequency-dependent and including a frequency-dependent perturbation corresponding to χ …”

“…The ACKS2 model has been generalized to frequency-dependent polarization, and thereby also modeling dispersion, by making K frequency-dependent and including a frequency-dependent perturbation corresponding to χ. 125 Bond Capacity Model. Analysis of the H 2 molecule suggests 126 that the bond capacity (bond softness) may be expressed in terms of atomic charges, and the LoProp formalism for assigning charge polarizability 127 implies that the ability of a bond to conduct charge is correlated with the bond order (and goes to zero for long distances 126 ), and inversely correlated with the difference in atom electronegativities, or somewhat equivalent, depends on the (inverse) HOMO−LUMO energy difference.…”

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

“…Three classes of semiempirical models have been proposed for simulating optical spectra in recent decades. In the first class, molecular mechanics force fields were extended to contain frequency-dependent polarization, which allows for the definition of absorption spectra through the imaginary part of the dynamic polarizability. − …”