Second Quantization-Based Methods in Quantum Chemistry


Book Description

Second Quantization-Based Methods in Quantum Chemistry presents several modern quantum chemical tools that are being applied to electronic states of atoms and molecules. Organized into six chapters, the book emphasizes the quantum chemical methods whose developments and implementations have been presented in the language of second quantization. The opening chapter of the book examines the representation of the electronic Hamiltonian, other quantum-mechanical operators, and state vectors in the second-quantization language. This chapter also describes the unitary transformations among orthonormal orbitals in an especially convenient manner. In subsequent chapters, various tools of second quantization are used to describe many approximation techniques, such as Hartree-Fock, perturbation theory, configuration interaction, multiconfigurational Hartree-Fock, cluster methods, and Green's function. This book is an invaluable source for researchers in quantum chemistry and for graduate-level students who have already taken introductory courses that cover the fundamentals of quantum mechanics through the Hartree-Fock method as applied to atoms and molecules.




Second Quantized Approach to Quantum Chemistry


Book Description

The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi~ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.




Lecture Notes in Quantum Chemistry


Book Description

"Quantum Chemistry" is the course material of a European Summer School in Quantum Chemistry, organized by Bj|rn O. Roos. It consists of lectures by outstanding scientists who participate in the education of students and young scientists. The book has a wider appeal as additional reading for University courses. Contents: P.-A. Malmquist: Mathematical Tools in Quantum Chemistry J. Olsen: The Method of Second Quantization P.R. Taylor: Molecular Symmetry and Quantum Chemistry B.O. Roos: The Multiconfigurational (MC) Self-Consistent Field (SCF) Theory P.E.M. Siegbahn: The Configuration Interaction Method T. Helgaker: Optimization of Minima and Saddle Points P.R. Taylor: Accurate Calculations and Calibration U. Wahlgren: Effective Core Potential Method




The Method of Second Quantization


Book Description

The Method of Second Quantization deals with the method of second quantization and its use to solve problems of quantum mechanics involving an indefinite number of particles, mainly in field theory and quantum statistics. Topics covered include operations on generating functionals; linear canonical transformations; quadratic operators; and Thirring's four-fermion model. State spaces and the simplest operators are also described. This book is comprised of four chapters and begins with an overview of the method of second quantization and the relevant notations. The first chapter focuses on the connections between vectors and functionals and between operators and functionals, together with fundamental rules for operating on functionals. The reader is then introduced to the so-called quadratic operators and the linear canonical transformations closely connected with them. Quadratic operators reduced and not reduced to normal form are considered. The final chapter discusses the Thirring model, the simplest relativistically invariant model in quantum field theory, and explains why it includes infinities. This monograph will be of value to students and practitioners of mathematical physics.




Modern Quantum Chemistry


Book Description

This graduate-level text explains the modern in-depth approaches to the calculation of electronic structure and the properties of molecules. Largely self-contained, it features more than 150 exercises. 1989 edition.




Brillouin-Wigner Methods for Many-Body Systems


Book Description

Brillouin-Wigner Methods for Many-Body Systems gives an introduction to many-body methods in electronic structure theory for the graduate student and post-doctoral researcher. It provides researchers in many-body physics and theoretical chemistry with an account of Brillouin-Wigner methodology as it has been developed in recent years to handle the multireference correlation problem. Moreover, the frontiers of this research field are defined. This volume is of interest to atomic and molecular physicists, physical chemists and chemical physicists, quantum chemists and condensed matter theorists, computational chemists and applied mathematicians.




Simple Theorems, Proofs, and Derivations in Quantum Chemistry


Book Description

Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in prepara tion of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.




Computational Methods In Quantum Chemistry, Volume 2: Quantum Chemistry


Book Description

This book provides a comprehensive account, from first principles, of the methods of numerical quantum mechanics, beginning with formulations and fundamental postulates. The development continues with that of the Hamiltonian and angular momentum operators, and with methods of approximating the solutions of the Schroedinger equation with variational and perturbation methods.Chapter 3 is a description of the Hartree-Fock self-consistent field method, which is developed systematically for atoms. The Born-Oppenheimer approximation is introduced, and the numerical methods presented one by one thereafter in a logically consistent way that should be accessible to undergraduates. These include LCAO, Hartree-Fock-SCF method for molecules, Roothaan LCAO-MO-SCF method, and electron correlation energy.Chapter 4 is devoted to the more sophisticated computational methods in quantum chemistry, with an introduction to topics that include: the zero differential overlap approximation; Huckel MO theory of conjugated molecules; Pariser-Parr-Pople MO method; extended Huckel theory; neglect of differential overlap methods; invariance in space requirements; CNDO; INDO; NDDO; MINDO; MNDO; AM1; MNDO-PM3; SAM1; SINDO1; CNDO/S; PCILO,Xα; and ab initio methods.This is followed by an introduction to Moller-Plesset perturbation theory of many electrons, and coupled perturbed Hartree Fock theory, with a description of the coupled cluster method. Finally Chapter 5 applies these methods to problems of contemporary interest.The book is designed to be a junior/senior level text in computational quantum mechanics, suitable for undergraduates and graduates in chemistry, physics, computer science, and associated disciplines.




Reviews in Computational Chemistry


Book Description

THIS VOLUME, WHICH IS DESIGNED FOR STAND-ALONE USE IN TEACHING AND RESEARCH, FOCUSES ON QUANTUM CHEMISTRY, AN AREA OF SCIENCE THAT MANY CONSIDER TO BE THE CENTRAL CORE OF COMPUTATIONAL CHEMISTRY. TUTORIALS AND REVIEWS COVER * HOW TO OBTAIN SIMPLE CHEMICAL INSIGHT AND CONCEPTS FROM DENSITY FUNCTIONAL THEORY CALCULATIONS, * HOW TO MODEL PHOTOCHEMICAL REACTIONS AND EXCITED STATES, AND * HOW TO COMPUTE ENTHALPIES OF FORMATION OF MOLECULES. * A FOURTH CHAPTER TRACES CANADIAN RESEARCH IN THE EVOLUTION OF COMPUTATIONAL CHEMISTRY. * ALSO INCLUDED WITH THIS VOLUME IS A SPECIAL TRIBUTE TO QCPE. FROM REVIEWS OF THE SERIES "Reviews in Computational Chemistry proves itself an invaluable resource to the computational chemist. This series has a place in every computational chemist's library."-JOURNAL OF THE AMERICAN CHEMICAL SOCIETY




Many-Body Methods in Quantum Chemistry


Book Description

The present volume contains the text of the invited lectures presented at the Symposium on Many Body Methods in Quantum Chemistry, held on the campus of Tel Aviv University in August 1988. The Symposium was a satellite meeting of the Sixth International Congress on Quantum Chemistry held in Jerusalem. The development and application of many-body methods in Quantum chemistry have been on the rise for a number of years. This is therefore a good time for an interim report on the state of the field. It is hoped that such a report is hereby provided, though it may not be complete. The Symposium was held under the auspices of Tel Aviv University, Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry. Other sponsors were the Israeli Academy of Sciences and Humanities, and the Israeli Ministry of Science and Development. Many thanks go to all of them. Finally, I would like to thank all the speakers and participants for making the meeting the enjoyable and (I hope) profitable experience it was. Tel Aviv, Israel Uzi Kaldor TESTS AND APPLICATIONS OF COMPLETE MODEL SPACE QUASIDEGENERATE MANY-BODY PERTURBATION THEORY FOR MOLECULES Karl F. Freed The James Franck Institute and Department of Chemistry The University of Chicago, Chicago, DUnois 60637 U.S.A.