Development and application of computational methods: from quantum statistical mechanics calculations to data processing in Fourier transform spectroscopy

University Of California-Irvine, Irvine CA

Investigators

Abstract

In this project funded by the Chemical Theory, Models and Computational Methods program of the Chemistry Division, Professor Vladimir Mandelshtam of the University of California, Irvine, is conducting research in the area of theoretical chemistry. He is developing new computational methods that take advantage of advances in high performance computers. These methods are being applied in the study of important and interesting properties of clusters of molecules at the atomic level. Another major component of Professor Mandelshtam's research is the development and application of computational methods designed to process data from Magnetic Resonance experiments. These new methods are providing ways to process the signals, reducing the time required for experiments and making new experiments possible. These methods could also be applied to other experimental studies. The development of new numerical techniques and distribution of software allows a broader research community to conduct their studies. The software resulting from this project is being made available free of charge to the scientific community. Professor Mandelshtam's research in Quantum Statistical Mechanics is concerned with the development of the Self-Consistent Phonons (SCP) method. SCP was introduced several decades ago in solid-state physics. While potentially very powerful, until recently SCP was essentially limited to systems with simple pairwise interactions. The breakthrough algorithmic improvements introduced in Professor Mandelshtam's group made it possible to reduce the computational times by several orders of magnitude, thus, making SCP practical for general systems. Further algorithmic improvements are being pursued that should make SCP even more efficient, such as an algorithm that would replace an iterative self-consistent solution of coupled non-linear equations by a deterministic minimization procedure. SCP is being applied to compute the spectra and other equilibrium properties of water and ion-water clusters. Diffusion Monte Carlo (DMC) is also being used to complement these studies and to help assess the accuracy of SCP. The major focus associated with the development of the Filter Diagonalization Method (FDM) is its implementation for 3D Diffusion Ordered SpectroscopY (DOSY), which is a unique and potentially very powerful Nuclear Magnetic Resonance experiment designed to characterize mixtures in solutions. DOSY is currently limited in its applications due to the lack of an adequate inversion algorithm associated with the solution of the inverse Laplace transform problem. The advantage of FDM is due to its multidimensional nature that allows one to avoid the unfavorable factorization of the 3-dimensional inversion problem to 1-dimensional problems.