# The Basics of Theoretical and Computational Chemistry

1. Edition January 2007

X, 185 Pages, Hardcover

37 Pictures (31 Colored Figures)

8 tables*Textbook*

**978-3-527-31773-8**

### Short Description

This textbook does away with the classic, unimaginative approach and comes straight to the point with a bare minimum of mathematics. It nonetheless covers all important aspects, at the point where computational chemistry becomes exciting.

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This textbook does away with the classic, unimaginative approach and comes straight to the point with a bare minimum of mathematics -- emphasizing the understanding of concepts rather than presenting endless strings of formulae. It nonetheless covers all important aspects of computational chemistry, such as

- vector space theory

- quantum mechanics

- approximation methods

- theoretical models

- and computational methods.

Throughout the chapters, mathematics are differentiated by necessity for understanding - fundamental formulae, and all the others. All formulae are explained step by step without omission, but the non-vital ones are marked and can be skipped by those who do not relish complex mathematics.

The reader will find the text a lucid and innovative introduction to theoretical and computational chemistry, with food for thought given at the end of each chapter in the shape of several questions that help develop understanding of the concepts.

What the reader will not find in this book are condescending sentences such as, 'From (formula A) and (formula M) it is obvious that (formula Z).'

Theory and Models - Interpretation of Experimental Data

Notations

Vector Space and Function Space

Dual Space and Hilbert Space

The Probability Function

Operators

BASIC CONCEPTS OF VECTOR SPACE THEORY OF MATTER

The Wave Equation as Probability Function

Postulates of Quantum Mechanics

The Schrödinger Equation

Hermicity

Exact Measurability and Eigenvalue Problems

Eigenvalue Problems of Hermitian Operator

The Eigenvalue Equation of the Hamiltonian

Eigenvalue Spectrum

CONCEQUENCES OF QUANTUM MECHANICS

Geometrical Interpretation of Eigenvalue Equations in Vector Space

Commutators and Uncertainty Relations

Virtual Particles and Forces in Nature

CHEMISTRY AND QUANTUM MECHANICS

Eigenvalue Problem of Angular Momentum and 'Orbital' Concept

Molecular Orbital and Valence Bond Models

Spin - Antisymmetry Principle

Virial Theorem

Chemical Bond

APPROXIMATION FOR MANY-ELECTRON SYSTEMS

Non-relativistic Stationary Systems

Adiabatic / Born-Oppenheimer Approximation

Independent Particle Approximation

Spin Orbitals and Slater Determinants

Atomic and Molecular Orbitals: The LCAO-MO Approach

Quantitative Molecular Orbital Calculations

Canonical and Localised Orbitals and Chemical Model Concepts

PERTURBATION THEORY IN QUANTUM CHEMISTRY

Projections and Projectors

Principles of Perturbation Theory

Rayleigh-Schrödinger Perturbation Theory

Application Examples

GROUP THEORY IN THEORETICAL CHEMISTRY

Definition of a Group

Symmetry Groups

Application Examples in Quantum Chemistry

Applications in Spectroscopy

METHODS IN COMPUTATIONAL QUANTUM CHEMISTRY

ab initio Methods

Semiempirical MO Methods

Density Functional Methods

FORCE FIELD METHODS AND MOLECULAR MODELLING

Empirical Force Fields

Molecular Modelling Programs

Docking

QSAR - Quantitative Activity - Structure Relationships

STATISTICAL SIMULATIONS: MONTE CARLO AND MOLECULAR DYNAMICS METHODS

Common Features

Monte Carlo Simulations

Molecular Dynamics Simulations

Evaluation and Visualisation of Simulation Results

Quantum Mechanical Simulations

Thomas S. Hofer has graduated from a college of technology and obtained his M.Sc. degree in chemistry at the University of Innsbruck. Since 2005, he has been working as assistant professor in theoretical chemistry at the University of Innsbruck and will obtain his Ph.D. degree in this field in 2006. He has published 16 scientific articles, including two review articles. He has been awarded the Austrian nation-wide prize for outstanding studies.

Michael Kugler obtained his secondary education in Tyrol and Upper Austria and is at present a graduate student of physics and chemistry at the University of Innsbruck.