Intermolecular interactions with the direct reaction field method

The direct reaction field (DRF ) method, developed to incorporate the effects of a (large) semiclassical environment into the Hamiltonian of a quantum mechanical system, is briefly reviewed. It is shown that the DRF method behaves—at least—like a supermolecule SCF calculation. With the water dimer as an example, the similarity with the SCF procedure is demonstrated, and an application to the interaction between the active site of papain and the remaining 3000 or so atoms of this protein shows the inadequacy of dielectric constant models and the necessity of including atomic polarizabilities in model force fields.     

A boundary element method for molecular electrostatics with electrolyte effects

A boundary element method is developed to compute the electrostatic potential inside and around molecules in an electrolyte solution. A set of boundary integral equations are derived based on the integral formulations of the Poisson equation and the linearized Poisson-Boltzmann equation. The boundary integral equations are then solved numerically after discretizing the molecular surface into a number of flat triangular elements. The method is applied to a spherical molecule for which analytical solutions are available. Use is made of both constant and linearly varying unknowns over the boundary elements, and the method is tested for various values of parameters such as the dielectric constant of the molecule, ionic strength, and the location of the interior point charge. The use of the boundary integral method incorporating the nonlinear Poisson-Boltzmann equation is also briefly discussed.     

Modelling mass analyzer performance with fields determined using the boundary element method

Computer modelling is widely used in the design of mass analysers to evaluate proposed designs and determine the effects of manufacturing imperfections. For quadrupole mass filters and ion traps, the models require accurate values of the electric field throughout the regions of the analyser in which ions travel. Most published results using models to predict mass analyser behaviour use electric fields computed with finite element (FE) or finite difference (FD) method. However, the boundary element method (BEM) is capable of achieving the same, or higher, accuracy with both computation times and memory requirements that are at least an order of magnitude less than those required by FE and FD methods. In this paper, electric field evaluation is performed using the BEM formulated in a manner described by previous workers; modifications to their method are described, which lead to higher accuracy field values. Simultaneous equation solution techniques are incorporated, which avoid solutions that are physically not realistic. The performance of linear quadrupole mass spectrometers with hyperbolic, circular and planar section electrodes has been determined using fields computed using these methods and compared with previous results obtained by alternative field computation techniques and with experiment. Behaviour of an ion trap mass spectrometer with circular symmetry has also been investigated. The results demonstrate that in each case using the BEM to determine the fields produces the observed behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

The reaction path intrinsic reaction coordinate method and the Hamilton-Jacobi theory

The definition and location of an intrinsic reaction coordinate path is of crucial importance in many areas of theoretical chemistry. Differential equations used to define the path hitherto are complemented in this study with a variational principle of Fermat type, as Fukui [Int. J. Quantum Chem., Quantum Chem. Symp. 15, 633 (1981)] reported in a more general form some time ago. This definition is more suitable for problems where initial and final points are given. The variational definition can naturally be recast into a Hamilton-Jacobi equation. The character of the variational solution is studied via the Weierstrass necessary and sufficient conditions. The characterization of the local minima character of the intrinsic reaction coordinate is proved. Such result leads to a numerical algorithm to find intrinsic reaction coordinate paths based on the successive minimizations of the Weierstrass E-function evaluated on a guess curve connecting the initial and final points of the desired path.     

Modeling steady-state experiments with a scanning electrochemical microscope involving several independent diffusing species using the boundary element method

The BEM algorithm developed earlier for steady-state experiments in the scanning electrochemical microscopy (SECM) feedback mode has been expanded to allow for the treatment of more than one independently diffusing species. This allows the treatment of substrate-generation/tip-collection SECM experiments. The simulations revealed the interrelation of sample layout, local kinetics, imaging conditions, and the quality of the obtained SECM images. Resolution in the SECM SG/TC images has been evaluated, and it depends on several factors. For most practical situations, the resolution is limited by the diffusion profiles of the sample. When a dissolved compound is converted at the sample (e.g., oxygen reduction or enzymatic reaction at the sample), the working distance should be significantly larger than in SECM feedback experiments (ca. 3 r(T) for RG = 5) in order to avoid diffusional shielding of the active regions on the sample by the UME body. The resolution ability also depends on the kinetics of the active regions. The best resolution can be expected if all the active regions cause the same flux. In one simulated example, which might mimic a possible scenario of a low-density protein array, considerable compromises in the resolving power, were noted when the flux from two neighboring spots differs by more than a factor of 2.     

The boundary element method: chronoamperometric simulations at microelectrodes

The application of the boundary element method (BEM) as an efficient and powerful method for the analysis of the time-dependent electrochemical processes at multiple electrode configurations is presented. The paper describes the theory and numerical details required for developing one-, two- and three-dimensional transient diffusion models for chronoampermetric simulations under diffusion control. The benefits of the BEM approach are discussed, including the reduction in dimensionality brought about by the formulation procedure and complete elimination of the need for domain discretisation with the time-domain convolution approach. The versatility and efficiency of the numerical procedures are examined with respect to a number of electrode geometries. Results are presented for chronoamperometric simulations at microband, microhemishpere, microcylinder and microdisc electrodes compared to appropriate analytical theory. The three-dimensional simulations focus on the modelling of double-electrode configurations (microdisc and microhemisphere) operating in a generator–collector mode. The influence of electrode separation on the transient current response is presented and normalised working curves currently unavailable via analytical methods are provided.     

A robust negative flash based on a parameterization of the tie-line field

We propose a novel approach to flash calculation, with particular application to negative flash. The basis of the method is a parameterization of the tie-line field. Rather than solving the Rachford–Rice equation (or any of its variants) we solve directly for the parameters defining the tie line. For an N  -component system, our approach leads to a system of N−2$N-2$quadratic equations, which we solve efficiently using a Newton method. The iterative method is very robust: unlike other negative flash procedures, the solution displays continuous dependence on the overall composition, even in the transition to negative concentrations. We illustrate the properties and behavior of the proposed approach on three-component and four-component systems, and we then generalize the method to systems of N components. From the global triangular structure of the system with constant K-values, it follows that the system of N⁻² quadratic equations can only have two roots. For the important case of three components, the flash calculation is explicit.     

A precise boundary element method for macromolecular transport properties

A very precise boundary element numerical solution of the exact formulation of the hydrodynamic resistance problem with stick boundary conditions is presented. BEST, the Fortran 77 program developed for this purpose, computes the full transport tensors in the center of resistance or the center of diffusion for an arbitrarily shaped rigid body, including rotation-translation coupling. The input for this program is a triangulation of the solvent-defined surface of the molecule of interest, given by Connolly's MSROLL or other suitable triangulator. The triangulation is prepared for BEST by COALESCE, a program that allows user control over the quality and number of triangles to describe the surface. High numerical precision is assured by effectively exact integration of the Oseen tensor over triangular surface elements, and by scaling the hydrodynamic computation to the precise surface area of the molecule. Efficiency of computation is achieved by the use of public domain LAPACK routines that call BLAS Level 3 hardware-optimized subroutines available for most processors. A protein computation can be done in less than 10 min of CPU time in a modern Pentium IV processor. The present work includes a complete analysis of the sources of error in the numerical work and techniques to eliminate these errors. The operation of BEST is illustrated with applications to ellipsoids of revolution, and Lysozyme, a small protein. The typical numerical accuracy achieved is 0.05% compared to analytical theory. The numerical precision for a protein is better than 1%, much better than experimental errors in these quantities, and more than 10 times better than traditional bead-based methods.     

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

Although most of the work concerned with reaction kinetics concentrates on empirical findings, stochastic models, and differential equations, a growing number of researchers is exploring other methods to elucidate reaction kinetics. In this work, the parameterization of an utter discrete spatio-temporal model, more specifically, a cellular automaton (CA), describing the reaction of HCl with CaCO(3) , is suggested. Furthermore, a system of partial differential equations (PDE), deduced from a set of CA rules, is implemented to compare both modeling paradigms. In this article, the experimental setup to acquire time series of data is explained, a stochastic CA-based model and a continuous PDE-based model capable of describing the reaction are proposed, the models are parameterized using the experimental data and, finally, the relationship between a discrete time step of the CA-based model and the physical time is studied. Essentially, the parameterization of both models can be traced back to the quest for a solution of the inverse problem in which a (set of) rule(s), respectively a system of PDE, is deduced starting from the observed data. It is demonstrated that the proposed CA- and PDE-based models are capable of describing the considered chemical reaction with a high accuracy, which is confirmed by a root mean squared error between the simulated and observed data of 0.388 and 0.869 g CO(2) , respectively. Further, it is shown that an exponential or linear relationship can be used to link the physical time to a discrete time step of the CA-based model.     

Pairwise interaction method in crystal field theory

We describe a new variant of crystal field theory — the pairwise interaction method. The pairwise interaction method is a superposition variant of crystal field theory in which as the parameters we use the shifts in the one-electron orbital energy levels of the innerZ-electron under the action of the perturbation caused by a single ligand. We establish a relationship between the pairwise interaction method parameters and parameters of the angular overlap model and classifical crystal field theory. We present tables allowing us to consider (in the weak crystal field approximation) the complexes ML₆, ML₈(Oh), and ML₄(Td) with integral and half-integral values of J for the central atom (6), and also the octahedral complex in the case of an intermediate crystal field for integral J6.Translated from Teoretieheskaya i Éksperimental naya Khimiya, Vol. 21, No. 4, pp. 450–459, July–August, 1985.     

General theory of photochemical reaction kinetics. I. Quantum-statistical description

By methods of statistical mechanics a consistent derivation of photochemical kinetic equations has been carried out. The method of density matrix and projection operator formalism was used. A self-consistent set of kinetic equations describing the combined behaviour of field and medium under the conditions (1) interaction of field with optically active scribing the combined behavior of field and medium under the conditions of (I) interaction of field with optically active molecule transition, (2) chemical reaction in the medium, and (3) effects of relaxation processes caused by collisions has been obtained. These equations, unlike the balance equations widely used in photochemistry, correctly take into account the role of medium polarization in a photochemical process.     

A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent

A fast multigrid boundary element (MBE) method for solving the Poisson equation for macromolecular electrostatic calculations in a solvent is developed. To convert the integral equation of the BE method into a numerical linear equation of low dimensions, the MBE method uses an adaptive tesselation of the molecular surface by BEs with nonregular size. The size of the BEs increases in three successive levels as the uniformity of the electrostatic field on the molecular surface increases. The MBE method provides a high degree of consistency, good accuracy, and stability when the sizes of the BEs are varied. The computational complexity of the unrestricted MBE method scales as O(N_at), where N_at is the number of atoms in the macromolecule. The MBE method is ideally suited for parallel computations and for an integrated algorithm for calculations of solvation free energy and free energy of ionization, which are coupled with the conformation of a solute molecule. The current version of the 3-level MBE method is used to calculate the free energy of transfer from a vacuum to an aqueous solution and the free energy of the equilibrium state of ionization of a 17-residue peptide in a given conformation at a given pH in ∼ 400 s of CPU time on one node of the IBM SP2 supercomputer. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 569–583, 1997     

Rapid parameterization of small molecules using the force field toolkit

The inability to rapidly generate accurate and robust parameters for novel chemical matter continues to severely limit the application of molecular dynamics simulations to many biological systems of interest, especially in fields such as drug discovery. Although the release of generalized versions of common classical force fields, for example, General Amber Force Field and CHARMM General Force Field, have posited guidelines for parameterization of small molecules, many technical challenges remain that have hampered their wide‐scale extension. The Force Field Toolkit (ffTK), described herein, minimizes common barriers to ligand parameterization through algorithm and method development, automation of tedious and error‐prone tasks, and graphical user interface design. Distributed as a VMD plugin, ffTK facilitates the traversal of a clear and organized workflow resulting in a complete set of CHARMM‐compatible parameters. A variety of tools are provided to generate quantum mechanical target data, setup multidimensional optimization routines, and analyze parameter performance. Parameters developed for a small test set of molecules using ffTK were comparable to existing CGenFF parameters in their ability to reproduce experimentally measured values for pure‐solvent properties (<15% error from experiment) and free energy of solvation (±0.5 kcal/mol from experiment). © 2013 Wiley Periodicals, Inc.     

Computation of electrostatic forces between solvated molecules determined by the Poisson-Boltzmann equation using a boundary element method

A rigorous approach is proposed to calculate the electrostatic forces among an arbitrary number of solvated molecules in ionic solution determined by the linearized Poisson-Boltzmann equation. The variational principle is used and implemented in the frame of a boundary element method (BEM). This approach does not require the calculation of the Maxwell stress tensor on the molecular surface, therefore it totally avoids the hypersingularity problem in the direct BEM whenever one needs to calculate the gradient of the surface potential or the stress tensor. This method provides an accurate and efficient way to calculate the full intermolecular electrostatic interaction energy and force, which could potentially be used in Brownian dynamics simulation of biomolecular association. The method has been tested on some simple cases to demonstrate its reliability and efficiency, and parts of the results are compared with analytical results and with those obtained by some known methods such as adaptive Poisson-Boltzmann solver.     

Comparison of the boundary theory with the contact rule of phase regions and Gupta’s method

The phase boundary theory and the contact rule of phase regions are compared, and some weaknesses of the latter are manifested. The comparison between the Gupta’s method and the boundary theory method for constructing multicomponent isobaric sections is also presented.     

A density functional theory formulation of the reaction field model of solvent effects

It is possible to reformulate the reaction field (RF ) model of continuum solvent effects, by considering an approximate expression describing the energy changes from one ground state to another, in the frame of density functional theory (DFT ). The energy functional for an arbitrary electronic system coupled to a spin-independent electrostatic external perturbation is used to derive the well-known Born expression giving the electrostatic component of the solvation energy of an atomic ion. The approximate RF –DFT model is illustrated for a series of representative singly positive and negatively charged atomic ions. A Kohn–Sham (KS )-like formalism is then proposed to compute solvation energies within a self-consistent field scheme. The extension of the RF -DFT model to molecular systems is also outlined. © 1995 John Wiley & Sons, Inc.