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

在这个由化学系化学理论、模型和计算方法计划资助的项目中，加州大学欧文分校的弗拉基米尔·曼德尔什塔姆教授正在进行理论化学领域的研究。他正在开发新的计算方法，以利用高性能计算机的进步。这些方法正被用于在原子水平上研究分子团簇的重要和有趣的性质。曼德尔施塔姆教授研究的另一个主要组成部分是开发和应用旨在处理磁共振实验数据的计算方法。这些新方法提供了处理信号的方法，减少了实验所需的时间，并使新的实验成为可能。这些方法也可应用于其他实验研究。新的数值技术的发展和软件的分发使更广泛的研究界能够进行他们的研究。该项目产生的软件正在向科学界免费提供。曼德尔施塔姆教授在量子统计力学方面的研究与自洽声子(SCP)方法的发展有关。SCP是几十年前在固态物理学中引入的。尽管SCP可能非常强大，但直到最近，SCP基本上还局限于具有简单的成对交互的系统。Mandelshtam教授的小组引入的突破性算法改进使计算时间减少了几个数量级，从而使SCP适用于一般系统。正在寻求进一步的算法改进，以使SCP甚至更有效率，例如，一种算法将用确定性最小化程序取代耦合非线性方程的迭代自洽解。SCP被用来计算水和离子-水团簇的光谱和其他平衡性质。扩散蒙特卡罗(DMC)也被用来补充这些研究，并帮助评估SCP的准确性。与过滤器对角化方法(FDM)的发展相关的主要焦点是其在3D扩散有序谱(DOSY)中的实现，这是一种独特且潜在非常强大的核磁共振实验，旨在表征溶液中的混合物。目前DOSY的应用受到限制，这是由于缺乏与拉普拉斯逆变换问题的解相关的适当的反演算法。有限差分法的优点在于它的多维性，可以避免将三维逆问题分解为一维问题的不利因素。

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.