Publisher Summary The chapter focuses on a general description of the force fields that are most commonly used at present, and it gives an indication of the directions of current research that may yield better functions in the near future. After a brief survey of current models, mostly generated during the 1990s, the focus of the chapter is on the general directions the field is taking in developing new models. The most commonly used protein force fields incorporate a relatively simple potential energy function: The emphasis is on the use of continuum methods to model the electrostatic effects of hydration and the introduction of polarizability to model the electronic response to changes in the environment. Some of the history and performance of widely used protein force fields based on an equation on simplest potential energy function or closely related equations are reviewed. The chapter outlines some promising developments that go beyond this, primarily by altering the way electrostatic interactions are treated. The use of atomic multipoles and off-center charge distributions, as well as attempts to incorporate electronic polarizability, are also discussed in the chapter.

https://dasher.wustl.edu/ponder/papers/advprotchem-66-27-03.pdf

Force fields for protein simulations

A new molecular dynamics model in which the point charges on atomic sites are allowed to fluctuate in response to the environment is developed and applied to water. The idea for treating charges as variables is based on the concept of electronegativity equalization according to which: (a) the electronegativity of an atomic site is dependent on the atom’s type and charge and is perturbed by the electrostatic potential it experiences from its neighbors and (b) charge is transferred between atomic sites in such a way that electronegativities are equalized. The charges are treated as dynamical variables using an extended Lagrangian method in which the charges are given a fictitious mass, velocities, and kinetic energy and then propagated according to Newtonian mechanics along with the atomic degrees of freedom. Models for water with fluctuating charges are developed using the geometries of two common fixed‐charge water potentials: the simple point charge (SPC) and the four‐point transferable intermolecular po...

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Dynamical fluctuating charge force fields: Application to liquid water

This paper briefly reviews the current status of the most popular methods for combined quantum mechanical/molecular mechanical (QM/MM) calculations, including their advantages and disadvantages There is a special emphasis on very general link-atom methods and various ways to treat the charge near the boundary Mechanical and electric embedding are contrasted We consider methods applicable to gas-phase organic chemistry, liquid-phase organic and organometallic chemistry, biochemistry, and solid-state chemistry Then we review some recent tests of QM/MM methods and summarize what we learn about QM/MM from these studies We also discuss some available software Finally, we present a few comments about future directions of research in this exciting area, where we focus on more intimate blends of QM with MM

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QM/MM: what have we learned, where are we, and where do we go from here?

A reappraisal of what we have learnt during three decades of computer simulations on water

Over the last forty years many computer simulations of water have been performed using rigid non-polarizable models. Since these models describe water interactions in an approximate way it is evident that they cannot reproduce all of the properties of water. By now many properties for these kinds of models have been determined and it seems useful to compile some of these results and provide a critical view of the successes and failures. In this paper a test is proposed in which 17 properties of water, from the vapour and liquid to the solid phases, are taken into account to evaluate the performance of a water model. A certain number of points between zero (bad agreement) and ten (good agreement) are given for the predictions of each model and property. We applied the test to five rigid non-polarizable models, TIP3P, TIP5P, TIP4P, SPC/E and TIP4P/2005, obtaining an average score of 2.7, 3.7, 4.7, 5.1, and 7.2 respectively. Thus although no model reproduces all properties, some models perform better than others. It is clear that there are limitations for rigid non-polarizable models. Neglecting polarizability prevents an accurate description of virial coefficients, vapour pressures, critical pressure and dielectric constant. Neglecting nuclear quantum effects prevents an accurate description of the structure, the properties of water below 120 K and the heat capacity. It is likely that for rigid non-polarizable models it may not be possible to increase the score in the test proposed here beyond 7.6. To get closer to experiment, incorporating polarization and nuclear quantum effects is absolutely required even though a substantial increase in computer time should be expected. The test proposed here, being quantitative and selecting properties from all phases of water can be useful in the future to identify progress in the modelling of water.

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Simulating water with rigid non-polarizable models: a general perspective

In order to achieve a simple description of aggregates of deformable water molecules, a new model has been constructed which treats H+ and O2− particles as the basic dynamical and structural elements. The H+ units are bare protons, while the O2− units possess a form of nonlocal polarizability consistent with their electronic structure. The model yields water molecules which have the correct geometry and dipole moment, and which engage in hydrogen bonding to one another. Minimum‐energy structures have been determined for the water dimer and trimer and for small hydrate clusters of H+ and OH−; comparison with relevant experiments and quantum–mechanical calculations is satisfactory.

Polarization model for water and its ionic dissociation products

A geometry search was carried out to locate the global energy minimum for (H2O)8, in its full 66 dimensional space of relative configurations. The ’’polarization model’’ was used to represent interactions. The optimal structure uncovered has nine nearly linear hydrogen bonds, and amounts to an aqueous analog of the saturated hydrocarbon bicyclo[2.2.2] octane. This structure is recognizable as a fragment of the hexagonal ice crystal, and thus may be important as a prenucleation cluster for that phase. The zwitterionic form of the octamer was found to have no region of local stability.

Study of the water octamer using the polarization model of molecular interactions

The polarization model, previously introduced to approximate both intramolecular and intermolecular interactions in water, has been extended to include pentavalent phosphorus. The extension appears to be successful in representing structures of simple compounds of P5+ with O2− and H+. The model has been applied to statistical mechanical study of liquid phospheric acid at 200 C, using the Monte Carlo method of computer simulation for 216‐atom systems. Two versions of the simulation have been implemented corresponding to stoichiometrically equivalent but experimentally distinguishable materials: (a) 27 orthophosphoric acid molecules, and (b) a mixture of water and polyphosphoric acid. Pair correlation functions for all types of atom pairs, as well as details of acid dissociation statistics, have been computed for both materials.

Application of the polarization model to the study of phosphoric acid media

The photodetachment curves of Cl—, Br—, and I— have been examined in their threshold regions by absorption spectroscopy of shock‐heated alkali halide vapors. The chloride curve appears smooth and normal in terms of threshold laws, but the bromide and iodide curves show maxima about 500 cm−1 above the thresholds, with widths of about 200 cm−1 at half‐height. The threshold positions are not affected by changes in conditions. The anomalously large absorption or resonances seem to be due to the halide ions, but to be influenced to some degree by the alkali atoms or ions. Three explanations, none entirely satisfactory, are put forth for the maxima; these are (1) near‐resonant transfer of energy from X+e— to M, giving X—+M*; (2) metastable autodetaching states of the halides; and (3) mixing of vacant alkali ion orbitals with continua of the halides. The third is considered most plausible.

Threshold Shapes and Resonances in the Photodetachment Cross Sections of Chloride, Bromide, and Iodide

The thermodynamic energy of the octomer of ice is computed using standard Monte CArlo methods as a function of temperature. The bond distribution function for a low temperature Monte Carlo run (24 °K) and a high temperature run (400 °K) is plotted as a function of temperature. (AIP)

Carl W. David

Papers

Polarization model for water and its ionic dissociation products

Study of the water octamer using the polarization model of molecular interactions

Application of the polarization model to the study of phosphoric acid media

Threshold Shapes and Resonances in the Photodetachment Cross Sections of Chloride, Bromide, and Iodide

Phase transition in octomers of ice