Biomedical subjects

Richard Dawes

Publications and source records attributed to Richard Dawes.

7 recordsLinked to original sources

PubMed2006

A nested molecule-independent neural network approach for high-quality potential fits.

It is shown that neural networks (NNs) are efficient and effective tools for fitting potential energy surfaces. For H2O, a simple NN approach works very well. To fit surfaces for HOOH and H2CO, we develop a nested neural network technique in which we first fit an approximate NN potential and then use another NN to fit the difference of the true potential and the approximate potential. The root-mean-square error (RMSE) of the H2O surface is 1 cm(-1). For the 6-D HOOH and H2CO surfaces, the nested approach does almost as well attaining a RMSE of 2 cm(-1). The quality of the NN surfaces is verified by calculating vibrational spectra. For all three molecules, most of the low-lying levels are within 1 cm(-1) of the exact results. On the basis of these results, we propose that the nested NN approach be considered a method of choice for both simple potentials, for which it is relatively easy to guess a good fitting function, and complicated (e.g., double well) potentials for which it is much harder to deduce an appropriate fitting function. The number of fitting parameters is only moderately larger for the 6-D than for the 3-D potentials, and for all three molecules, decreasing the desired RMSE increases only slightly the number of required fitting parameters (nodes). NN methods, and in particular the nested approach we propose, should be good universal potential fitting tools.

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PubMed2006

Using simultaneous diagonalization and trace minimization to make an efficient and simple multidimensional basis for solving the vibrational Schrodinger equation.

In this paper we improve the product simultaneous diagonalization (SD) basis method we previously proposed [J. Chem. Phys. 122, 134101 (2005)] and applied to solve the Schrodinger equation for the motion of nuclei on a potential surface. The improved method is tested using coupled complicated Hamiltonians with as many as 16 coordinates for which we can easily find numerically exact solutions. In a basis of sorted products of one-dimensional (1D) SD functions the Hamiltonian matrix is nearly diagonal. The localization of the 1D SD functions for coordinate qc depends on a parameter we denote alphac. In this paper we present a trace minimization scheme for choosing alphac to nearly block diagonalize the Hamiltonian matrix. Near-block diagonality makes it possible to truncate the matrix without degrading the accuracy of the lowest energy levels. We show that in the sorted product SD basis perturbation theory works extremely well. The trace minimization scheme is general and easy to implement.

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PubMed2005

How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates.

In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. The one-dimensional (1D) functions from which we build the direct product basis are chosen to satisfy two conditions: (1) they nearly diagonalize the full Hamiltonian matrix; (2) they minimize off-diagonal matrix elements that couple basis functions with diagonal elements close to those of the energy levels we wish to compute. By imposing these conditions we increase the number of product functions that can be removed from the multidimensional basis without degrading the accuracy of computed energy levels. Two basic types of 1D basis functions are in common use: eigenfunctions of 1D Hamiltonians and discrete variable representation (DVR) functions. Both have advantages and disadvantages. The 1D functions we propose are intermediate between the 1D eigenfunction functions and the DVR functions. If the coupling is very weak, they are very nearly 1D eigenfunction functions. As the strength of the coupling is increased they resemble more closely DVR functions. We assess the usefulness of our basis by applying it to model 6D, 8D, and 16D Hamiltonians with various coupling strengths. We find approximately linear scaling.

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PubMed2005

An ab initio study of S(N)2 reactivity at C6 in hexopyranose derivatives. I. Influence of dipole-dipole interactions in the transition structure.

It is widely accepted that dipole-dipole interactions in the S(N)2 transition structure can play a dominant role in determining reaction rates. A model of this type was proposed some years ago to explain the remarkably low reactivity of galactopyranose-6-O-sulfonates toward S(N)2 displacement, and similar arguments have recently been restated in the context of gas-phase reactions. In this paper, we present ab initio calculations (B3LYP/6-31+G(d,p)) on model structures and an analysis of charge densities using the theory of atoms in molecules. We find that the maximum possible impact of local dipole-dipole interactions is insufficient to account for the observed reactivity differences.

Carbohydrates↗

PubMed2005

An ab initio study of S(N)2 reactivity at C6 in hexopyranose derivatives. II. Role of populations, barriers, and reaction path curvature.

This paper continues our investigation into a simple dipole-dipole interaction model proposed to explain the dramatically reduced S(N)2 reactivity at the primary C6 position of galacto-configured pyranose systems relative to their gluco isomers. We present ab initio calculations (B3LYP/6-31+G(d,p)) on six model structures that show that this effect is not a major influence. Reactant rotameric equilibria as well as free-energy reaction barriers and reaction path curvature were evaluated. Results point to a number of other factors that could account for the observed reactivity differences. Our results cast doubt on the general relevance of transition structure dipole-dipole repulsions to S(N)2 reactivity.

Carbohydrates↗

PubMed2004

Absolute intensities of Raman trace scattering from bicyclo-[1.1.1]-pentane.

Our previous theoretical studies have identified the Raman intensity parameter for the bridgehead C-H stretch in bicyclo-[1.1.1]-pentane as the largest for any saturated hydrocarbon yet considered, while the methylene C-H parameter is predicted to be ordinary. Theoretical methods including self-consistent field, static and time dependent density functional theory, and coupled cluster, all predict a large bridgehead intensity parameter, but differ widely in the actual value. We have synthesized bicyclo-[1.1.1]-pentane and recorded the absolute intensity Raman trace scattering spectra. The recorded intensity of a resonance polyad in the C-H stretching region has been resolved and distributed onto the fundamental modes through an anharmonic resonance analysis from a computed quartic force field. The experimental internal coordinate intensity parameters have been obtained and compared with those computed. Although the static and dynamic density functional values overestimate the parameter by 10%-18%, the values predicted at the coupled-cluster level are found to be correct to within experimental error.

Journal Article↗

PubMed2004

A multidimensional discrete variable representation basis obtained by simultaneous diagonalization.

Direct product basis functions are frequently used in quantum dynamics calculations, but they are poor in the sense that many such functions are required to converge a spectrum, compute a rate constant, etc. Much better, contracted, basis functions, that account for coupling between coordinates, can be obtained by diagonalizing reduced dimension Hamiltonians. If a direct product basis is used, it is advantageous to use discrete variable representation (DVR) basis functions because matrix representations of functions of coordinates are diagonal in the DVR. By diagonalizing matrices representing coordinates it is straightforward to obtain the DVR that corresponds to any direct product basis. Because contracted basis functions are eigenfunctions of reduced dimension Hamiltonians that include coupling terms they are not direct product functions. The advantages of contracted basis functions and the advantages of the DVR therefore appear to be mutually exclusive. A DVR that corresponds to contracted functions is unknown. In this paper we propose such a DVR. It spans the same space as a contracted basis, but in it matrix representations of coordinates are diagonal. The DVR basis functions are chosen to achieve maximal diagonality of coordinate matrices. We assess the accuracy of this DVR by applying it to model four-dimensional problems.

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