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A general theoretical framework for treating the kinetics of diffusion-influenced bimolecular reactions in solution is presented. It is based on a hierachy of phenomenological kinetic equations for the reduced distribution functions of reactant molecules. With this formalism, a perturbation series expression for the rate coefficient for irreversible reactions involving a long-ranged sink function is derived. For a delta-function sink, it reduces to that obtained previously by Northrup and Hynes

A major problem in virtual screening concerns the accuracy of the binding free energy between a target protein and a putative ligand. Here we report an example supporting the outperformance of the AutoDock scoring function in virtual screening in comparison to the other popular docking programs. The original AutoDock program is in itself inefficient to be used in virtual screening because the grids of interaction energy have to be calculated for each putative ligand in chemical database. However

A solution reaction path Hamiltonian (SRPH) is constructed for heavy particle charge transfer reactions in a nondissipative polar solvent. This formulation includes anharmonicities arising from, e.g., potential anharmonicity and reaction path curvature. The SRPH is used in conjunction with variational transition state theory (VTST) to obtain an expression for the reaction rate constant. This expression generalizes the van der Zwan–Hynes rate theory to include the influence of anharmonic effects

This paper presents a predictive tool that uses safety factors to estimate accident risk for processes commonly employed on construction sites. The tool is demonstrated in the context of the utility-trenching process. Based on expert surveys, preplanning, supervision, and training are identified as critical safety factors needed to predict accident risk when evaluating safety performance related to trenching operations. Preplanning has a greater impact on excavation tasks than supervision and tr

The solution reaction path Hamiltonian (SRPH) developed in the previous paper is applied to model SN2 and ionic dissociation reactions in water solvent. The solution reaction paths are determined and show marked deviations from a standard equilibrium solvation picture. The impact of potential anharmonicities, reaction path curvature, and varying solvent mass on the rate constant is calculated via the variational transition state theory approach of I, and the deviations from harmonic van der Zwan

The formalism presented in the preceding paper is applied to investigate the combined effects of gating modes and orientation-dependent reactivity on the rate of diffusion-influenced bimolecular reactions. A general expression for the rate coefficient is derived for reactions involving a sink function that is highly localized along the orientational and gating coordinates. For reactions involving spherical molecules, of which one species has a diffusive gating coordinate, the expression for the

Abstract The dynamic aspects of protein folding are described by a series of diffusion‐collision steps involving structural units (microdomains) of various sizes that combine to form the protein in its native state. A method is introduced for obtaining the rate constants for the basic diffusion‐collision step by use of Brownian dynamics. The method is applied to an investigation of the folding dynamics of two α‐helices connected by a flexible (random‐coil) polypeptide chain. The results of this

The failure of the electron gas model calculation of the Ar–N2 interaction potential at large intermolecular separations [J. Chem. Phys. 68, 5001 (1978)] is remedied by using a model developed earlier by one of the present authors and Gordon. The results give predictions of the Ar–N2 interaction potential for the entire portion of physically interesting region of the potential surface. The spherically averaged potential is compared with the available experimental potentials and shows the improve

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Exact expressions for the statistical errors arising from the replacement of the ensemble average by a finite time average in diffusive Brownian dynamics simulations are derived for the displacement correlation function and the orientational correlation function. The results are illustrated by analyzing Brownian dynamics simulations of some oligomeric molecules. These include flexible and rigid dimers and models for the α helix. Flexibility is found to have a significant effect on rotational dif

We introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction. We test the accuracy of the propagator expression by calculating the diffusion-controlled geminate