The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within t...

Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

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

This is an overview of some of the important, challenging, and problematic issues in contemporary electron transfer research. After a qualitative discussion of electron transfer, its time and distance scales, energy curves, and basic parabolic energy models are introduced to define the electron transfer process. Application of transition state theory leads to the standard Marcus formulation of electron transfer rate constants. Electron transfer in solution is coupled to solvent polarization effects, and relaxation processes can contribute to and even control electron transfer. The inverted region, in which electron transfer rate constants decrease with increasing exoergicity, is one of the most striking phenomena in electron transfer chemistry. It is predicted by both semiclassical and quantum mechanical models, with the latter appropriate if there are coupled high- or medium-frequency vibrations. The intramolecular reorganizational energy has different contributions from different vibrational modes, whic...

Contemporary Issues in Electron Transfer Research

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

Ewald summation for systems with slab geometry

The hydrated electron: quantum simulation of structure, spectroscopy, and dynamics

A new algorithm for the quantum dynamical simulation of a mixed classical-quantum system that rigorously includes nonadiabatic quantum transitions is applied to the problem of the solvation dynamics of an initially energetic excess electron in liquid water. Computed results reveal a major channel associated with the appearance of a relatively long-lived solvated excited state postulated earlier; this state is identified as a distorted form of the equilibrium first excited state. The transient spectra evaluated directly from the simulation compare well with experimental data.

Solvation dynamics of the hydrated electron: A nonadiabatic quantum simulation.

An excess electron in a sample of classical water molecules at room temperature has been simulated using path integral techniques. The electron–water interaction is modeled by a pseudopotential with effective core repulsion and further terms for the Coulomb interaction and polarization effects. Various discretizations of the electron path, up to 1000 points, are examined. The charge distribution of the electron is found to be compact and to occupy a cavity in the water, in agreement with the conventional picture. The solvation shell structure is similar to that of relatively large solvated atomic anions, but the radial electron‐solvent correlations are largely smeared out due to fluctuations of the electronic density distribution. In parts of the simulation the structure of the first solvation shell corresponds on the average to the structure proposed for hydrated electrons by Kevan. The computed solvation energy and the estimated energy of the first optical excitation agree reasonably well with experimental data.

Quantum simulation study of the hydrated electron

A simple electron–molecule pseudopotential is obtained that describes the interaction between an excess electron and a rigid water molecule in the electronic ground state. The potential is completely local and involves only spherically symmetric terms with respect to the three molecular nuclei (interaction site model). The potential is thus suitable for large‐scale computer simulations, as well as more analytical theories. A description is given of the contributions included in this potential, as well as the ramifications of alternative choices.

An electron–water pseudopotential for condensed phase simulation

The optical-absorption spectrum of an excess electron solvated in a molecular sample of liquid water at 300 K has been calculated with use of solvent configurations generated via path-integral simulation and subsequent solution of the excess-electronic eigenvalue problem. Electronic transitions from an s-like ground state to three bound-localized, p-like excited states dominate the broad asymmetric spectrum with excitations into an apparent continuum following at higher energy. Asymmetric distortions and radial fluctuations of the solvent cavities contribute comparably to the spectral broadening.

Jurgen Schnitker

Papers

The hydrated electron: quantum simulation of structure, spectroscopy, and dynamics

Solvation dynamics of the hydrated electron: A nonadiabatic quantum simulation.

Quantum simulation study of the hydrated electron

An electron–water pseudopotential for condensed phase simulation

A priori calculation of the optical absorption spectrum of the hydrated electron.