Accuracy of typical approximations in classical models of intermolecular polarization

Assessing many-body contributions to intermolecular interactions of the AMOEBA force field using energy decomposition analysis of electronic structure calculations

In this work, we evaluate the accuracy of the classical AMOEBA model for representing many-body interactions, such as polarization, charge transfer, and Pauli repulsion and dispersion, through comparison against an energy decomposition method based on absolutely localized molecular orbitals (ALMO-EDA) for the water trimer and a variety of ion-water systems. When the 2- and 3-body contributions according to the many-body expansion are analyzed for the ion-water trimer systems examined here, the 3-body contributions to Pauli repulsion and dispersion are found to be negligible under ALMO-EDA, thereby supporting the validity of the pairwise-additive approximation in AMOEBA's 14-7 van der Waals term. However AMOEBA shows imperfect cancellation of errors for the missing effects of charge transfer and incorrectness in the distance dependence for polarization when compared with the corresponding ALMO-EDA terms. We trace the larger 2-body followed by 3-body polarization errors to the Thole damping scheme used in AMOEBA, and although the width parameter in Thole damping can be changed to improve agreement with the ALMO-EDA polarization for points about equilibrium, the correct profile of polarization as a function of intermolecular distance cannot be reproduced. The results suggest that there is a need for re-examining the damping and polarization model used in the AMOEBA force field and provide further insights into the formulations of polarizable force fields in general.

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 comparison between QM/MM and QM/QM based fitting of condensed-phase atomic polarizabilities

Recently we reported a combined QM/MM approach to estimate condensed-phase values of atomic polarizabilities for use in (bio)molecular simulation. The setup relies on a MM treatment of the solvent when determining atomic polarizabilities to describe the response of a QM described solute to its external electric field. In this work, we study the effect of using alternative descriptions of the solvent molecules when evaluating atomic polarizabilities of a methanol solute. In a first step, we show that solute polarizabilities are not significantly affected upon substantially increasing the MM dipole moments towards values that are typically reported in literature for water solvent molecules. Subsequently, solute polarization is evaluated in the presence of a QM described solvent (using the frozen-density embedding method). In the latter case, lower oxygen polarizabilities were obtained than when using MM point charges to describe the solvent, due to introduction of Pauli-repulsion effects.

Induced fit docking, and the use of QM/MM methods in docking

Docking methods are popular computational techniques in drug discovery to identify new active molecules that bind to a given biological target. Although widely used, the predictive reliability of docking methods is often limited by the inability to accurately and efficiently model protein flexibility and quantify binding strength. We highlight several emerging concepts that address those methodological issues including a discussion on the incorporation of QM/MM methodologies in the scoring process.

The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Development of the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and side chain torsional parameters were determined by comparing to gas-phase QM (RI-TRIM MP2/CBS) conformational energies of dipeptides and to statistical distributions from the Protein Data Bank. Molecular dynamics simulations are reported for short peptides in explicit water to examine their conformational properties in solution. Overall the calculated conformational free energies and J-coupling constants are consistent with PDB statistics and experimental NMR results, respectively. In addition, the experimental crystal structures of a number of proteins are well maintained during molecular dynamics (MD) simulation. While further calculations are necessary to fully validate the force field, initial results suggest the AMOEBA polarizable multipole force field is able to describe the structure and energetics of peptides and proteins, in both gas-phase and solution environments.

The polarizable point dipoles method with electrostatic damping: implementation on a model system

Recently, the use of polarizable force fields in Molecular Dynamics simulations has been gaining importance, since they allow a better description of heterogeneous systems compared to simple point charges force fields. Among the various techniques developed in the last years the one based on polarizable point dipoles represents one of the most used. In this paper, we review the basic technical issues of the method, illustrating the way to implement intramolecular and intermolecular damping of the electrostatic interactions, either with and without the Ewald summation method. We also show how to reduce the computational overhead for evaluating the dipoles, introducing to the state-of-the-art methods: the extended Lagrangian method and the always stable predictor corrector method. Finally we discuss the importance of screening the electrostatic interactions at short range, defending this technique against simpler approximations usually made. We compare results of density functional theory and classical force field-based Molecular Dynamics simulations of chloride in water.

A NEMO potential that includes the dipole-quadrupole and quadrupole-quadrupole polarizability

To increase the accuracy of molecular force fields a systematical and balanced improvement of the various terms included is needed. In this work, we have followed this strategy to improve the quality of the NEMO potential for the formaldehyde dimer by introducing local quadrupole moments and higher-order polarizabilities. It is found that inclusion of the quadrupole moment significantly improves the interaction potential. Furthermore, the inclusion of higher-order polarizabilities up to quadrupole-quadrupole polarizability is shown to give a better description of the intermolecular interaction. In addition, it is demonstrated that localized properties based on MP2 densities reproduces the BSSE corrected MP2 interaction energy at large intermolecular separations. This is not the case for HF-SCF based properties.

How accurate can a force field become? A polarizable multipole model combined with fragment-wise quantum-mechanical calculations

A new method to accurately estimate the interaction energy between a large molecule and a smaller ligand is presented. The method approximates the electrostatic and induction contributions classically by multipole and polarizability expansions, but uses explicit quantum-mechanical fragment calculations for the remaining (nonclassical) contributions, mainly dispersion and exchange repulsion. Thus, it represents a limit of how accurate a force field can ever become for interaction energies if pairwise additivity of the nonclassical term is assumed (e.g., all general-purpose force fields). The accuracy is tested by considering protein-ligand model systems for which the true MP2/6-31G* interaction energies can be computed. The method is shown to be more accurate than related fragmentation approaches. The remaining error (2-5 and approximately10 kJ/mol for neutral and charged ligands, respectively) can be decreased by including the polarizing effect from surrounding fragments in the quantum-mechanical calculations.

Inclusion of the quadrupole moment when describing polarization. The effect of the dipole-quadrupole polarizability

A method to compute distributed dipole-quadrupole polarizabilities is suggested. The method is based on numerical differentiation of distributed quadrupole moments, using finite field perturbation calculations. It is tested using two different multicenter multipole expansions, and compared with results using polarizabilities obtained via the uncoupled Hartree-Fock approximation. The accuracy of these dipole-quadrupole polarizabilities are tested for different molecules and basis sets, by comparing the induced electrostatic potential of the Hartree-Fock density with the induced electrostatic potential of the polarization models. This is done by perturbing the molecules with an external homogeneous field and with an external dipole. It is found that inclusion of the dipole-quadrupole polarizability significantly improves the accuracy of the response of the molecule to these external perturbations. This suggests that inclusion of higher-order induced moments can be of importance when improving the description of intermolecular interactions using force fields.