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Clusters hold the key to our understanding of intermolecular forces and how these affect the physical properties of bulk condensed matter. They can be found in a multitude of important applications, including novel fuel materials, atmospheric chemistry, semiconductors, nanotechnology, and computational biology. Focusing on the class of weakly bound substances known as van derWaals clusters or complexes,
The book develops finite temperature statistical simulation tools and real-time algorithms for the exact solution of the Schrödinger equation. It draws on potential energy models to gain insight into the behavior of minima and transition states. Using Monte Carlo methods as well as ground state variational and diffusion Monte Carlo (DMC) simulations, the author explains how to obtain temperature and quantum effects. He also shows how the path integral approach enables the study of quantum effects at finite temperatures.
To overcome timescale problems, this book supplies efficient and accurate methods, such as diagonalization techniques, differential geometry, the path integral method in statistical mechanics, and the DMC approach. Gleaning valuable information from recent research in this area, it presents special techniques for accelerating the convergence of quantum Monte Carlo methods [
Features [ Covers a broad scope of quantum simulation aspects, from FORTRAN programming through the classical physical laws and the algorithms for their integration to the fundamentals of statistical mechanics. Applies linear algebra, Lie algebra, and differential geometry to computations Explains how to perform state-of-the-art vector space quantum mechanics calculations, such as the discrete variable representation coupled with the Lanczos algorithm Introduces real and imaginary time evolution methods in quantum mechanics Presents applications to atomic clusters Shows how to carry out DMC and path integral simulations in curved spaces, which have proven crucial for simulating molecular clusters. Provides simulations in nonrelativistic wave mechanics and statistical thermodynamics
Table of Contents [ Fundamentals
FORTRAN Essentials Basics of Classical Dynamics Basics of Stochastic Computations Vector Spaces, Groups and Algebras Matrix Quantum Mechanics Time Evolution in Quantum Mechanics The Path Integral in Euclidean Spaces Atomic Clusters
Characterization of the Potential of Ar7 Classical and Quantum Simulations of Ar7 Methods in Curved Space Introduction to Differential Geometry Simulations in Curved Manifolds Applications to Molecular Systems
Clusters of Rigid Tops
The website for this book is
Curotto, E.