Published on Brock University (http://www.brocku.ca)
We have a general interest in quantum chemistry and in computational chemistry and physics. Our current research has the following thrusts:
1) developing new algorithms for the so-called quantum Monte Carlo computer simulation method to solve electronic structure problems;
2) elucidating protein structure using simulation methods, such as Monte Carlo and molecular dynamics, coupled with powerful statistical analysis techniques.
These efforts have a strong interdisciplinary flavour. Professor Rothstein has a cross appointment in the Department of Physics.He can supervise students in either chemistry or physics.
QUANTUM MONTE CARLO METHOD
The Schroedinger equation has locally singular potentials which have to be canceled by the kinetic energy (electron-nuclear and electron-electron cusps). Also, by virtue of the repulsion of like charges, each electron influences the locations of all the others (electron correlation). These effects must be reflected in the wave function, and it simply isn't efficient to do this by taking combinations of Slater determinants with a finite set of one-electron basis functions, as in the traditional approaches. Furthermore, the traditional methods make huge computational demands for systems containing a large number of electrons, necessitating approximations or practical limits on the scale of the calculations.
Facilitated by the speed of modern computers, quantum Monte Carlo methods have been developed to complement the traditional methods. One statistically samples from a pre-specified, explicitly correlated wave function (depends explicitly upon the inter-electronic distances) and thereby treats the various electron correlation effects explicitly. Other features of the exact wave function, such as the electron-electron and electron-nuclear cusps are also treated in a direct manner.
Our current Monte Carlo research is focused on the accurate estimation of physical properties other than the energy.
QUANTUM MONTE CARLO DETERMINATION OF PROPERTIES OTHER THAN THE ENERGY
Traditionally there is a strong interest in energy-related physical properties, such as the force constant and other spectroscopic constants. For example, we showed how to estimated these using quantum Monte Carlo methods for a transition metal containing molecule: CuH [Ref. 50] .
It is a challenge to estimate physical properties other than the energy, because the electron distribution obtained in quantum Monte Carlo is not sufficiently accurate for these properties. In principle, the exact electron distribution is required, the square of the exact wavefunction.
Although we do not have an analytic form for the exact wavefunction, we developed a quantum Monte Carlo algorithm, practical for properties represented by non-differential operators, where indeed we can sample from the "exact" electron distribution [Ref. 63].
Our goal now is to derive within the framework of quantum Monte Carlo a systemized methodology to estimate the non-trivial electrical properties of atoms and molecules, such as high order polarizabilities and hyperpolarizabilities. We are building on previous work in our laboratory [Refs. 60, 63], promising higher accuracy for these properties. Polarizabilities are potentially fundamental in determining the molecular geometry of products of chemical reactions.
Thanks to the speed of high performance computers at the University of Alberta made available through Westgrid, we have been able develop methodologies to estimate polarizabilities to fourth order in the external field perturbation. Details appropriate for spherically symmetric systems, such as atoms, has been published [Ref. 60].
TOWARDS THE COMPLETE CLASSIFICATION OF PROTEIN NATIVE STATE CONFORMATIONAL DIVERSITY
The traditional objective in the computational investigation of protein structure is to locate a single conformation at the global minimum in the potential energy. It was commonly believed that the native state of a protein lies at that position on the energy surface. In recent developments it is now believed to be necessary to characterize the distribution of conformations of a protein active site, not just the single conformation at the global minimum.
A further difficulty is the inefficiency of the widely used simulated annealing method when employed to optimize the structures of proteins, especially those which exhibit a frustrated energy landscape. An exhaustive search of parameter space in such systems is unfeasible, so it is typical for only a handful of runs to be performed on a reasonably sized protein. Even allowing for advances in high performance computer technology and for the development of more efficient Monte Carlo optimization algorithms, it is likely that the problem of incomplete energy distributions and qualitative characterization of low-energy conformations will persist for the foreseeable future.
Recently we published a pattern recognition technique, “histogram filtering” [Ref. 56] with which to optimize parameters in wave functions for use in quantum Monte Carlo simulations. We adapted histogram filtering to cluster the high-dimensional data that arise in the analysis of protein simulation data. to a) characterize the low-energy local minimum energy structures, and b) to arrive at a complete description of the distribution of conformations for proteins, without having to take recourse to a very large number of simulated annealing runs [Ref. 62].
PHYSICALLY SIGNIFICANT MOTIONS OF A BIOPOLYMER
To glean information inherent in molecular dynamics (MD) trajectories by visualization and cluster analysis is a challenging area of current research in computational science.
Recently we described an application of histogram filtering to extract from MD trajectories phsycally significant motions of a biopolymer [Ref. 74], summarized as follows:
We investigated an all-atom model of the response regulator protein Bacillus subtilis, 124 amino acid residues. A sample of a-carbon interatomic distances drawn from independent MD snapshots were subjected to histogram filtering. Two clusters were uncovered, continuous with respect to the trajectory time-line, representative of the protein's motion within two sampled low-energy basins on the potential energy surface.
We performated a principal component analysis (PCA) of the data subset that includes every snapshot within the time-range defined by a cluster membership. Squared-loadings of the varimax-rotated PCA vectors isolated significant variation in the inter-residue distances, and, in turn, these were associated with concerted motions of entire mobile secondary structure elements.
These, so-called "collective coordinates" were consistent with the location of the protein's known active sites and its experimentally-determined mobile regions.