Accurate Molecular Polarizabilities Based on Continuum Electrostatics

Geometrical, electrical, and energetic parameters of hetero-disubstituted cumulenes and polyynes in the presence and absence of the external electric field

Cumulenes and polyynes have the potential to be applied as linear, sp-hybridized, one-dimensional all-carbon nanowires in molecular electronics and optoelectronics. The delocalization and conductivity descriptors of the two π-conjugated systems, heterodisubstituted with the NO2, CN, NH2, and OH groups, were studied using the B3LYP, B3LYP/D3, CAM-B3LYP, and ωB97XD DFT functionals, combined with the aug-cc-pVTZ basis set. Three independent types of molecular descriptors, based on geometry (the HOMA index), electrical properties (trace of the polarizability tensor), and energetic (the HOMO-LUMO energy gap) were shown to be mutually correlated and provided concordant indication that communication through the cumulene chain was considerably better than through the polyyne one. The communication can be tuned by using substituents of significantly different π-electron donor-acceptor properties as well as by the external electric field directed along the carbon chain.

Toward Automated Benchmarking of Atomistic Force Fields: Neat Liquid Densities and Static Dielectric Constants from the ThermoML Data Archive

Atomistic molecular simulations are a powerful way to make quantitative predictions, but the accuracy of these predictions depends entirely on the quality of the force field employed. Although experimental measurements of fundamental physical properties offer a straightforward approach for evaluating force field quality, the bulk of this information has been tied up in formats that are not machine-readable. Compiling benchmark data sets of physical properties from non-machine-readable sources requires substantial human effort and is prone to the accumulation of human errors, hindering the development of reproducible benchmarks of force-field accuracy. Here, we examine the feasibility of benchmarking atomistic force fields against the NIST ThermoML data archive of physicochemical measurements, which aggregates thousands of experimental measurements in a portable, machine-readable, self-annotating IUPAC-standard format. As a proof of concept, we present a detailed benchmark of the generalized Amber small-molecule force field (GAFF) using the AM1-BCC charge model against experimental measurements (specifically, bulk liquid densities and static dielectric constants at ambient pressure) automatically extracted from the archive and discuss the extent of data available for use in larger scale (or continuously performed) benchmarks. The results of even this limited initial benchmark highlight a general problem with fixed-charge force fields in the representation low-dielectric environments, such as those seen in binding cavities or biological membranes.

Numerical study on the partitioning of the molecular polarizability into fluctuating charge and induced atomic dipole contributions

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Löwdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

A finite field method for calculating spherical tensor molecular polarizability tensors α(lm;l'm') = ∂Δ(lm)/∂ϕ(l'm')* by numerical derivatives of induced molecular multipole Δ(lm) with respect to gradients of electrostatic potential ϕ(l'm')* is described for arbitrary multipole ranks l and l'. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water using the following ab initio methods: Hartree-Fock (HF), Becke three-parameter Lee-Yang-Parr exchange-correlation functional (B3LYP), Møller-Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields.

Using electronic polarization from the internal continuum (EPIC) for intermolecular interactions

Recently, the vacuum-phase molecular polarizability tensor of various molecules has been accurately modeled (Truchon et al., J Chem Theory Comput 2008, 4, 1480) with an intramolecular continuum dielectric model. This preliminary study showed that electronic polarization can be accurately modeled when combined with appropriate dielectric constants and atomic radii. In this article, using the parameters developed to reproduce ab initio quantum mechanical (QM) molecular polarizability tensors, we extend the application of the "electronic polarization from internal continuu" (EPIC) approach to intermolecular interactions. We first derive a dielectric-adapted least-square-fit procedure similar to RESP, called DRESP, to generate atomic partial charges based on a fit to a QM abinitio electrostatic potential (ESP). We also outline a procedure to adapt any existing charge model to EPIC. The ability of this to reproduce local polarization, as opposed to uniform polarization, is also examined leading to an induced ESP relative root mean square deviation of 1%, relative to ab initio, when averaged over 37 molecules including aromatics and alkanes. The advantage of using a continuum model as opposed to an atom-centered polarizable potential is illustrated with a symmetrically perturbed atom and benzene. We apply EPIC to a cation-pi binding system formed by an atomic cation and benzene and show that the EPIC approach can accurately account for the induction energy. Finally, this article shows that the ab initio electrostatic component in the difficult case of the H-bonded 4-pyridone dimer, a highly polar and polarized interaction, is well reproduced without adjusting the vacuum-phase parameters.

Polarization effects in molecular mechanical force fields

The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations.

Polarization and polarizability assessed by protein amide acidity

Hydroxide-catalyzed exchange rate constants were determined for those amides of FK506-binding protein (FKBP12), ubiquitin, and chymotrypsin inhibitor 2 (CI2) that are solvent-accessible in the high-resolution X-ray structures. When combined with previous hydrogen exchange results for the rubredoxin from Pyrococcus furiosus, the acidity of these amides was calculated by continuum dielectric methods as a function of the nonpolarizable electrostatic parameter set, internal dielectric, and the charge distribution of the peptide anion. The CHARMM22 parameter set with an internal dielectric value of 3 and an ab initio-derived anion charge distribution yielded an rmsd value of 7 for the 56 amide exchange rate constants ranging from 10(0.67) to 10(9.0) M(-1) s(-1). The OPLS-AA parameter set yielded comparably robust predictions, while that of PARSE, AMBER parm99, and AMBER ff03 performed more poorly. The small value for the optimal internal dielectric, combined with the brief lifetime of the peptide anion intermediate and the uniformity of the correlation between predicted and observed amide acidities, is consistent with electronic polarizability providing the dominant contribution to dielectric shielding. By construction, nonpolarizable force fields do not model electric field attenuation by electronic polarizability. Accurate prediction of the total electrostatic energy by such force fields necessitates the hyperpolarization of the atomic charge values in order to match the average electric field energy density (1/2)epsilon(tau)E(2)(tau) when epsilon(tau) is set to the in vacuo dielectric value of 1. The resulting predictions of the experimental hydrogen exchange data demonstrate the substantial systematic errors in the predicted electrostatic potential that can arise when dielectric shielding due to electronic polarizability is neglected.