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Register a new userA novel formulation of nonlocal electrostatics
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Added by
Andreas Hildebrandt
Publication date
2004
fields
Physics
and research's language is
English
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The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel formulation allowing for numerical solutions for the nontrivial molecular geometries arising in the applications mentioned before. Our approach is based on the introduction of a secondary field, $psi$, which acts as the potential for the rotation free part of the dielectric displacement field ${bf D}$. For many relevant models, the dielectric function of the medium can be expressed as the Greens function of a local differential operator. In this case, the resulting coupled Poisson (-Boltzmann) equations for $psi$ and the electrostatic potential $phi$ reduce to a system of coupled PDEs. The approach is illustrated by its application to simple geometries.
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Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atoms multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atoms covalent bonding directions. The new local frame allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the PME implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that, to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration.
A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent.
By using fundamental units c, h, G as conversion factors one can easily transform the dimensions of all observables. In particular one can make them all ``geometrical, or dimensionless. However this has no impact on the fact that there are three fundamental units, G being one of them. Only experiment can tell us whether G is basically fundamental.
We present a new class of electrostatics problems that are exactly solvable by adding finitely many image charges. Given a charge at some location inside a cavity bounded by up to four conducting grounded segments of spheres: if the spheres have a symmetry derived via a stereographic projection from a 4D finite reflection group, then this is a solvable generalization of the familiar problem of a charge inside a spherical cavity. There are 19 three-parametric families of finite groups formed by
Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii in a consistent way. We test our approach on simple ions and small molecules for which both experimental results and other theoretical descriptions are available for quantitative comparison. We conclude that our approach is both physically transparent and quantitatively reliable.
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