Donald J. Kouri - US grants

The Theoretical and Computational Chemistry Program is supporting Professor D. Kouri of the University of Houston. In this next grant period he we will continue to pursue computational implementation and testing of the Time-Independent Wavepacket Divide-and-Conquer (TIWDC) approach. The immediate objectives are: a) Testing the DC-procedure whereby the initial arrangement is also uncoupled from the strong interaction region. b) Testing the DC strategy for uncoupling the vibrational-rotational, pure rotational, and elastic final state interaction regions so that the maximum benefit of the approach can be realized. c) Applying the DC procedure to H+O2 -> OH+O in order to try and carry out the first ever completely ab initio calculation of state-to-state reaction cross sections for the system as a function of energy. He also will carry out the first full 3D tests of the TIWDC method for photodissociation of HOD, with emphasis on a comparison with experiment when the HOD is vibrationally hot. Secondly, he will continue development of the distributed approximating functionals (DAFs), including the exploration of a new class of DAFs that are related to various interpolation schemes. These investigations will also study the fitting of multidimensional potential energy surfaces using finite amounts of ab initio input data, with particular emphasis on electronically non-adiabatic systems. Third, he will continue studies of a new method being developed for diagonalizing extremely large matrices with very dense eigenspectra. Finally, he will begin work on developing and testing new approximation methods for solving the quantum equations for reactions involving more than 4 atoms in order to simulate more complex chemical systems. The research supported here focuses on developing robust, efficient, and highly stable methods for solving the partial differential equations which are used to describe fundamental chemical reaction processes. Because of the enormous complexity of the equations, solutions are feasible only by using the most powerful, high-speed, large-memory computers. However, the development of a detailed understanding of the elementary chemical reaction process can open up the possibilities of controlling chemical reactions in order to maximize desired products. These studies are also used in simulating numerically fundamental processes that occur in the earth's atmosphere, in order to understand and better deal with pollution. Such studies also find application in modeling the detailed chemistry of combustion in order to develop pollution-free propulsion systems. In addition, some of the techniques being developed can also be used to solve other, enormously important partial differential equations. Thus, the techniques being developed show great promise for making it possible to solve equations ranging from long term weather forecasting, to other equations used to model combustion.

The Theoretical and Computational Chemistry Program in the Chemistry Division is supporting research by Prof. Donald Kouri at the University of Houston on a new approach to quantum dynamics calculations. This is a collaborative project with Prof. David Hoffman of Iowa State University whose effort is also being supported by the Division. The Feynman path integral method is used to replace the customary calculation of matrix products, eigenvalues, and inverses which scale very rapidly with system size. Gaussian importance sampling is used to produce a manageable variance in the Monte Carlo integral. The goal is to make possible fully quantum mechanical treatment of scattering systems of a larger size than previously possible. %%% Numerically exact quantum mechanical methods of analyzing chemical reactions have in the past been limited to systems containing no more than three atoms, at least one of which must be hydrogen. This project is testing a new computational technique which offers promise of permitting such calculations on larger systems and, more generally, can be used in studying other quantum mechanical collisional processes.

This award from the Academic Research Infrastructure Program will help the Department of Chemistry at the University of Houston acquire a new departmental computer system. The areas of chemical research that the acquisition will impact are the following: 1. Theoretical/computational approach to problems in peptide mimetic design and antiviral nucleic acid oligomers. 2. Development and application of powerful new methods for time-evolving wavepackets describing multiparticle systems. 3. The refinement of crystallographically determined structures using XPLOR and studies of protein dynamics on aspartate transcarbamylase. 4. Reaction dynamics in organometallic, solid-state and biological areas of chemistry. 5. Exploration of several problems in the areas of molecular recognition, binding and reactivity. %%% The use of mini-supercomputers provides theoreticians with computing performance equal to that of large mainframe computers. Theoretical chemistry computations give a quantitative description of the energetics and rates of elementary chemical reactions and also provide a qualitative understanding of the fundamental factors governing chemical changes. Most of these studies would not have been possible before the acquisition of the mini-supercomputer because the cost of mainframe computers or the computer time required would have been prohibitive.

9310235 Kouri The implementation of newly developed theoretical formalism, Distributed Approximating Functions (DAF), is proposed for studying large scale quantum dynamics on massively parallel machines. The formalism has been tested successfully in various 1 D, 2 D and 3 D scattering problems in the frame of time dependent Schrodinger equation (TDSE) by the methods of the real time Feynman path integral and matrix vector multiplication. The real time Feynman which is made practically useful by the DAF, will make the calculation of many body, high dimension quantum scattering systems more feasible.

Don Kouri of the University of Houston is supported by the Theoretical and Computational Chemistry Program for formal and computational studies focusing on the time-independent wave packet reactant-product decoupling (TIW-RPD) approach to reactive scattering and on the exploration of the use of distributed approximating functionals (DAFs). TIW-RPD methods will be used to develop and test approximations for enlarging the range of reactive systems for which reliable cross sections can be computed. DAFs will be explored for use in multi-resolution analysis with likely applications in digital signal processing. Development and applications of an algorithm for constructing sufficiently accurate quantum potentials to enable the direct solution of the Bohmian dynamics equations will be pursued, with the goal of enabling the method to be applied to three-dimensional reactive atom-diatom scattering calculations.

The development and application of new mathematical and computational methods for formulating and solving fundamental quantum mechanical equations is relevant to molecular collision dynamics, and consequently to all chemical reactions. Research in such a highly specialized area can lead to more general impacts. For example, data compression arises in all areas of science, engineering, and medicine. It is especially important in chemical problems such as reducing the amount of data needed to fit potential energy surfaces, and reducing the number of grid points needed to solve differential equations. Tools developed for treating reactive scattering are now showing promise for medical and geophysical imaging, and digitization in communications.

This proposal addresses the fundamental challenge of creating a theory
that gives rise to directionally unbiased, fast processing of images
and multidimensional data structures. The proposed Isotropic Multiresolution
Analysis (IMRA) enables decompositions of data structures without
orientational preference that parallel the numerical efficiency of one
dimensional MRA-wavelet constructions. A crucial ingredient of this new theory
is an MRA of radial functions based on an innovative concept of radial
translations. Together with a suitable angular resolution, this allows to
replicate all the beneficial characteristics of classical one-dimensional
MRA-wavelets in higher dimensions. Therefore, IMRA-wavelets are expected to
parallel the success of their one-dimensional predecessors in isolating edges
and separating textures. Compared to previous attempts of MRA-construtions
in higher dimensions, IMRAs combine symmetry properties, smoothness, and
compactness of support of scaling functions and wavelets to an unprecedented
degree. The proposed theory is anticipated to have a significant impact on all
areas of digital signal processing in two or more dimensions, especially in
biomedical image processing.

To date, digital image processing systems commonly handle data in a row
and column fashion. Although this pixelized approach is natural for digital
machines, it is much less natural if the objective is to extract information
from natural images or more general multidimensional data structures. In this
proposal, we create a mathematical theory that mimicks features of retinal
processing by mammalian visual systems. Retinal processing is known to detect
edges and textures at different scales of spatial and temporal resolution,
regardless of their orientation and of the topology of their boundary contours.
The proposed theory of Isotropic Multiresolution Analysis (IMRA) offers a way
of digitizing analog signals and of synthesizing analog signals from digital
data in a manner that is more compatible with the "digitization" of natural
images performed by our retina. One particular component of IMRAs is the use of
radial translations, inspired by the evolving wave pattern created when a rock
falls in a pond of calm water. To ensure fast numerical processing
capabilities, we use concepts similar to those in the framework of wavelets,
which have proved computationally efficient in the processing of one-
dimensional signals, e.g. audio. The intellectual merit of this work is that it
delivers directionally unbiased, fast processing capabilities to all areas of
digital signal processing of two or more dimensions, in particular to
biomedical image processing. The Fast Isotropic Wavelet Algorithms resulting
from our theory will be applied to anonymized medical patient data provided to
us by the world renowned Texas Heart Institute (THI) in a joint effort for the
accurate and early detection of the formation of vulnerable plaque in coronary
arteries. The goal of this effort is an accurate non-invasive initial screening
test to assess the risk of mycardial infarcts using CT-scans of the heart.