A combined quantum mechanical (QM) and molecular mechanical (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mechanical calculations semiempirical methods of the MNDO and AM1 type are used, while the molecular mechanics part is treated with the CHARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodology is applied to parts of the same molecule or to different molecules are considered. The details of the method and a range of test calculations, including comparisons with ab initio and experimental results, are given. It is found that in many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodology are discussed.

A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations

New atom- and group-based spherical-cutoff methods have been developed for the treatment of nonbonded interactions in molecular dynamics (MD) simulation. A new atom-based method, force switching, leaves short-range forces unaltered by adding a constant to the potential energy, switching forces smoothly to zero over a specified range. A simple improvement to group-based cutoffs is presented: Switched group-shifting shifts the group–group potential energy by a constant before being switched smoothly to zero. Also introduced are generalizations of atom-based force shifting, which adds a constant to the Coulomb force between two charges. These new approaches are compared to existing methods by evaluating the energy of a model hydrogen-bonding system consisting of two N-methyl acetamide molecules and by full MD simulation. Thirty-five 150 ps simulations of carboxymyoglobin (MbCO) hydrated by 350 water molecules indicate that the new methods and atom-based shifting are each able to approximate no-cutoff results when a cutoff at or beyond 12 A is used. However, atom-based potential-energy switching and truncation unacceptably contaminate group–group electrostatic interactions. Group-based potential truncation should not be used in the presence of explicit water or other mobile electrostatic dipoles because energy is not a state function with this method, resulting in severe heating (about 4 K/ps in the simulations of hydrated MbCO). The distance-dependent dielectric (ϵ ∝ r) is found to alter the temperature dependence of protein dynamics, suppressing anharmonic motion at high temperatures. Force switching and force shifting are the best atom-based spherical cutoffs, whereas switched group-shifting is the preferred group-based method. To achieve realistic simulations, increasing the cutoff distance from 7.5 to 12 A or beyond is much more important than the differences among the three best cutoff methods. © 1994 by John Wiley & Sons, Inc.11

New spherical-cutoff methods for long-range forces in macromolecular simulation

We have performed long molecular dynamics simulations of water using four popular water models, namely simple point charge (SPC), extended simple point charge (SPC/E), and the three point (TIP3P) and four point (TIP4P) transferable intermolecular potentials. System sizes of 216 and 820 molecules were used to study the dependence of properties on the system size. All systems were simulated at 300 K with and without reaction fields and with two different cutoff radii, in order to study the impact of the cutoff treatment on density, energy, dynamic, and dielectric properties. Furthermore we generated two special-purpose water models based on the SPC and TIP4P models, for use with a reaction field. The atomic charges and the Lennard-Jones C12 parameter were optimized to reproduce the correct energy and pressure using the weak coupling algorithm for parameters. Indeed, in simulations without parameter coupling of both new models the density and potential energy were found to be close to the experimental values...

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A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field

The fundamental equation of electrostatics, i.e. the integral equation for the polarization of a macroscopic dielectric in an arbitrary external field, is written in a form that allows explicit inclusion of the toroidal boundary conditions as well as the cutoff of dipolar interactions often used in the computer simulation of polar systems. The toroidal boundary conditions are accounted for in a natural way if the integral equation is formulated (and solved) in Fourier space. Rigorous expressions for the polarization induced by a homogeneous field as well as for the equilibrium dipole moment fluctuations, both as a function of the dielectric constant, are then easily derived for general systems in two and three dimensions. The equations obtained for spherical cutoff geometry with reaction field are identical to those valid for an infinite periodic system (Ewald sum plus reaction field). When applied to the case of a highly polar Stockmayer system (μ*2=3·0, θ*=0·822, T*=1·15) the formulas lead to a consiste...

Dipole moment fluctuation formulas in computer simulations of polar systems

We investigate pairwise electrostatic interaction methods and show that there are viable computationally efficient (O(N)) alternatives to the Ewald summation for typical modern molecular simulations. These methods are extended from the damped and cutoff-neutralized Coulombic sum originally proposed by Wolf et al. [J. Chem. Phys. 110, 8255 (1999)]. One of these, the damped shifted force method, shows a remarkable ability to reproduce the energetic and dynamic characteristics exhibited by simulations employing lattice summation techniques. Comparisons were performed with this and other pairwise methods against the smooth particle-mesh Ewald summation to see how well they reproduce the energetics and dynamics of a variety of molecular simulations.

https://sourceforge.net/p/lammps/mailman/attachment/051901cbd5e9%244b777f90%24e2667eb0%24%40zips.uakron.edu/2/

Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics

Truncation of the interaction between dipoles in the computer simulation of polar fluids is responsible for an upward drift in the total energy of the system. Methods of avoiding this are discussed. A series of simulations has been made for 108 dipoles interacting through the Stockmayer potential with μ* = 1·0, ρ* = 0·8. A variety of summation methods has been used; all lead to closely similar thermodynamic properties and diffusion coefficients but the autocorrelation function of the dipole moment of a spherical region varies considerably according to the summation method used.

Eveline M. Adams

Papers

The computer simulation of polar liquids