Describing Molecular Polarizability by a Bond Capacity Model

Abstract

We propose a bond capacity model for describing molecular polarization in force field energy functions at the charge-only level. Atomic charges are calculated by allowing charge to flow between atom pairs according to a bond capacity and a difference in electrostatic potential. The bond capacity is closely related to the bond order and decays to zero as the bond distance is increased. The electrostatic potential is composed of an intrinsic potential, identified as the electronegativity, and a screened Coulomb potential from all other charges. The bond capacity model leads to integer fragment charges upon bond dissociation and displays linear scaling of the polarizability with system size. Bond capacity parameters can be derived from reference molecular polarizabilities, while electronegativity parameters can be derived from reference atomic charges or a reference molecular electrostatic potential. Out-of-plane polarization for planar systems is modeled by off-nuclei charge sites. The model is shown to be able to reproduce anisotropic reference molecular polarizabilities with an accuracy of ∼10% using a limited set of bond capacity parameters and can describe both inter- and intramolecular polarization.

Including implicit solvation in the bond capacity polarization model

“…The BC model is built upon the assumption that the charge transferred between an atom pair is proportional to a bond capacity times an electrostatic potential difference between the involved pair in analogy with classical capacitors. 33 The bond capacity is closely related to the bond order and contains an attenuation function that decays to zero as the bond length is elongated. The atomic electrostatic potential consists of an intrinsic potential (an atomic electronegativity), a screened Coulomb potential from all other charges, and a Coulomb self-interaction term (an atomic hardness).…”

“…As derived in detail in Ref. 33, the set of N atomic charges Q can be obtained from the following equation:…”

“…2, where ξ 0 ij represents the bond capacity parameter for the ij pair of atoms at equilibrium distance and g(Rij) is an attenuation function that takes a value of one at equilibrium bond length and decays exponentially to zero as Rij increases. This ensures that charge transfer can only take place between atom pairs within wave function overlap, and the structure of the C matrix automatically ensures charge conservation, 33 Cij…”

“…24,[30][31][32] We have recently proposed a Bond Capacity (BC) polarization model, where the anisotropic molecular polarizability is represented by (only) atomic charges that are allowed to respond to changes in the electrostatic potential. 33 Off-nuclei sites are included for modeling out-of-plane polarization. While similar in spirit to the fluctuating charge model, 34 the BC model is free from artificial long range charge transfer and nonlinear scaling of the polarizability with system size.…”

The FFLUX Water Model: Flexible, Polarizable and with a Multipolar Description of Electrostatics

“…However, it would be possible to use kriging models to reproduce polarizations based on charge-only models. [52] In FFLUX, atomic multipole moments are described as spherical harmonics of rank l, where l = 0 corresponds to the atomic charge, l = 1 corresponds to the dipole (consisting of three moments), l = 2 corresponds to the quadrupole (five moments), and so on. This formalism is more compact than the Cartesian one, which introduces redundancies.…”