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E-raamat: Computational Quantum Chemistry: Molecular Structure and Properties In Silico

(University of Manchester, UK)
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Metabolomics is an emerging field and this is the first book to present chromatographic techniques in metabolomics in a fundamental way. Sample preparation and quality control are crucial aspects which are described in detail. Uniquely, guidelines for the selection of appropriate methodology are also provided. The book covers the chromatographic techniques, such as liquid chromatography, gas chromatography, comprehensive two-dimensional gas chromatography and electrochromatographic techniques utilised in metabolomics.The book presents computational electronic structure theory as practised in terms of ab initio wavefunction methods and density functional approaches. A significant part of the book is devoted to the evaluation of a wide range of molecular properties and includes relativistic effects.

Principal sections give an overview of the stages involved in carrying out computational studies and the theoretical background required to perform such studies. Each principal section will be followed by several subsections which will give much greater detail about the theoretical background. Thus, the book is of value to final year undergraduates, who could use the principal sections to obtain a workable introduction to the various topics and understand the components of a computational undergraduate project. By contrast a researcher may wish to go directly to the detail.

Arvustused

In the past few decades, computational resources have become more powerful every year and in addition methodology development has led to much more effi- cient techniques through parallelization of the calculations and the advent of den- sity functional theory. These reasons make it possible for computational quantum chemists to work on relatively large chem- ical systems with a total number of atoms well over 100 nowadays. As a result of this, interest in applications of computational quantum chemistry has considerably widened and opened up research opportu- nities in novel areas. In particular, applica- tions of realistic quantum chemical sys- tems have become possible and as such it is starting to become common practise in fields of, e.g., bioinorganic chemistry and biochemistry, to do experimental studies side-by-side with computational model- ing. This means that computational quan- tum chemistry does not operate in virtual worlds and settings anymore on small atomic systems, but can address major chemical problems. These combined experimental/computational studies gen- erally give a broader perspective of a chemical problem and look into it from different angles and perspectives than stand-alone experimental studies. Thus, the computational studies give important additional information alongside exper- iment and assist in the interpretation of the experimental data. Furthermore, with computational quantum chemistry short- lived catalytic intermediates and their reactivity patterns can be investigated, which coupled to experimental work can explain product distributions and reac- tion rates. In addition, the computationalwork can make predictions that encourage future experimental studies. This symbio- sis of experiment and theory has led to a large field of research, where theoreticians and experimentalists work together. As a result of that it is not uncommon any- more that PhD students and postdoctoral researchers do a combination of experi- ment and computation for a single mul- tidisciplinary project. However, although many experimentally based groups are starting to use computational chemistry methods, almost at a routine basis, nowa- days there are some serious caveats with the methods and techniques and often these computational studies cannot be done through black-box-procedures but require expert supervision. Although there is an increased popularity of computational quantum chemistry mainly through the use of computational quantum chemistry meth- ods by experimentalists, this does not mean these methods and techniques are routinely done with little or no prior knowledge of the theories and back- grounds. To highlight the difficulties in doing computational quantum chem- istry research on experimentally relevant chemical systems, McDouall has written a monograph on the chemical procedures and techniques behind the computational chemistry software packages and the many pitfalls the user should be aware of. The book, therefore, tries to address questions for beginners in doing computational chemistry research, including: 1. What does computational quantum chemistry offer? 2. Where do you start? 3. How do you select a theoretical model? 4. What useful output do I generate and how do I relate this to my experiment? The book is subdivided into five chap- ters covering the basics of computational quantum chemistry, electronic structure methods, computation of molecular prop- erties, molecular orbitals, spin densities and relativistic effects. These are the key methods and techniques necessary for computational quantum chemistry in col- laboration with experiment and a descrip- tion of the essential components of the output that can be linked to experiment. Each chapter has a logic set-up that first gives a laymans explanation of the reasons and the background of the basic theories with clear figures. Of course, a quantum chemistry book cannot be complete with- out equations and there are quite a lot of those in this book. However, these are well explained andMcDouall puts them in a broad context and clearly defines their variables and uses. As such I do not feel that the equations scare off the reader here, but are illustrative of the background. There are plenty of examples in the text that explain the theories in better detail. The book is very well written and is aimed at starters in the field of compu- tational quantum chemistry, such as new Master and PhD students. This book, how- ever, is not like normal quantum chem- istry books, where the reader gets drowned in very difficult to understand equations that require a high level of Mathematics knowledge. Instead, the author has cho- sen a selective set of equations and explains in detail what the equation means in chemical terms, what you can do with it and how you can solve the equations. As such, it makes the book highly read- able even for starters in the field that not necessarily have a thorough previous background in computational quantum chemistry. It may even be worthwhile for experimentalists who collaborate with computational quantum chemist to read this book and get understanding of what computational quantum chemistry can offer. What I found particularly useful was the section on converting quantum chem- ical energies into free energies through thermodynamic state functions and thereby gives experimentally measurable variables. The book is illustrated with a large number of drawings and figures that highlight what is explained in the text. In summary, the book on Computational Quantum Chemistry by McDouall is highly recommended literature for anyone working in the field, collaborating with computational chemists or interested in moving into the field of computational quantum chemistry. The work is very accessi- ble to the lay-reader and should help and assist with getting started in the field.

Received:12August2013;accepted:13August2013; published online:03September2013. Citation:deVisserSP(2013)Gettingstartedincom- putationalquantumchemistry.Front.Chem. 1:14. doi: 10.3389/fchem.2013.00014 This articlewassubmittedtoTheoreticaland ComputationalChemistry,asectionofthejournal FrontiersinChemistry. Copyright©2013deVisser.Thisisanopen-access articledistributedunderthetermsoftheCreative CommonsAttributionLicense(CCBY).Theuse,dis- tributionorreproductioninotherforumsisper- mitted, providedtheoriginalauthor(s)orlicensor arecreditedandthattheoriginalpublicationin this journaliscited,inaccordancewithaccepted academicpractice.Nouse,distributionorrepro- ductionispermittedwhichdoesnotcomplywith theseterms. -- Sam P de. Visser * doi: 10.3389/fchem.2013.00014 *

Chapter 1 Computational Quantum Chemistry
1.1 What Does Computational Quantum Chemistry Offer?
1(2)
1.2 The Model: Quantum Mechanics
3(12)
1.2.1 The Schrodinger Equation and the Born-Oppenheimer Approximation
5(6)
1.2.2 Electronic Wavefunctions and the Antisymmetry Principle
11(2)
1.2.3 Molecular Orbitals and Basis Set Expansions
13(2)
1.3 Chemistry in Silico: Where Do You Start?
15(12)
1.3.1 Potential Energy Curves, Forces and Force Constants
15(2)
1.3.2 Potential Energy Surfaces, Stationary Points and Reactivity
17(6)
1.3.3 Linking the Electronic Energy with Thermodynamic State Functions
23(4)
1.4 Standard Models of Electronic Structure
27(20)
1.4.1 The Hartree-Fock Model and Electron Correlation
28(7)
1.4.2 Configuration Interaction Methods
35(2)
1.4.3 Perturbation Theory Methods
37(2)
1.4.4 Coupled-Cluster Methods
39(2)
1.4.5 Multiconfigurational and Multireference Methods
41(5)
1.4.6 Density Functional Methods
46(1)
1.5 How Do You Select a Theoretical Model?
47(1)
1.6 The. Apparatus: Hardware and Software
48(15)
Appendix 1A Physical Constants, Atomic Units and Conversion Factors
52(1)
Appendix 1B Elementary Properties of Determinants
53(3)
Appendix 1C Diagonalisation of Matrices
56(4)
Appendix 1D Moments of Inertia and the Inertia Tensor
60(2)
References
62(1)
Chapter 2 Computational Electronic Structure Theory
2.1 A Few Essential Notions and Requirements
63(11)
2.1.1 Matrix Elements and Integrals
65(4)
2.1.2 Permutational Symmetry of One-and Two - Electron Integrals
69(1)
2.1.3 Spin Symmetry
70(2)
2.1.4 The Variation Theorem
72(2)
2.2 Hartree-Fock Theory
74(13)
2.2.1 Minimisation of the Hartree-Fock Energy
77(3)
2.2.2 The Canonical Hartree-Fock Equations
80(1)
2.2.3 Understanding Solutions to the Hartree-Fock Equations: Canonical Molecular Orbitals
81(1)
2.2.4 Understanding Solutions to the Hartree-Fock Equations: Orbital Energies
82(1)
2.2.5 The Total Hartree-Fock Energy
83(2)
2.2.6 Ionisation Energies: Koopmans' Theorem
85(2)
2.3 Open-Shell Systems in Hartree-Fock Theory
87(7)
2.3.1 The Restricted Open-Shell Hartree-Fock (ROHF) Method
87(1)
2.3.2 The Unrestricted Hartree-Fock (UHF) Method
88(3)
2.3.3 UHF Method for S = 0 and the Dissociation Problem
91(1)
2.3.4 Spin Polarisation
92(2)
2.4 Computational Realisation of the Hartree-Fock Theory
94(12)
2.4.1 The Roothaan-Hall Equations and Basis Set Expansions
94(5)
2.4.2 Orbital Optimisation: The Self-Consistent Field (SCF) Procedure for Closed Shells
99(1)
2.4.3 Basis Set Expansions in the UHF Method
99(3)
2.4.4 Convergence of the SCF Process
102(2)
2.4.5 The Direct SCF Method
104(2)
2.5 Molecular Basis Sets
106(12)
2.5.1 Gaussian Type Functions
106(7)
2.5.2 Types of Contracted Basis Sets
113(3)
2.5.3 Basis Set Superposition Error: Non-Covalent Interactions
116(2)
2.6 Electron Correlation: Background to Post Hartree-Fock Methods
118(20)
2.6.1 Brillouin's Theorem
121(1)
2.6.2 Spin Eigenfunctions/Configuration State Functions
122(5)
2.6.3 Integral Approximations: Density Fitting Configuration Interaction Methods
127(5)
2.7.1 Density Matrices and Natural Orbitals
132(1)
2.7.2 Truncated Configuration Interaction Methods
133(4)
2.7.3 The Frozen Core Approximation
137(1)
2.8 Perturbation Methods
138(10)
2.8.1 Maller-Plesset Perturbation Theory
143(4)
2.8.2 Improvements in Low-Order Perturbation Theory: Spin Component Scaling and Orbital Optimisation
147(1)
2.9 Coupled-Cluster Methods
148(5)
2.9.1 The Coupled-Cluster Doubles Equations
149(3)
2.9.2 Higher Order Methods
152(1)
2.10 Localised Orbital Formulations of Post Hartree-Fock Techniques
153(4)
2.11 Non-Dynamic Electron Correlation and Multi-configurational Reference Wavefunctions
157(11)
2.11.1 The MCSCF Method and Associated Optimisation Problems
160(5)
2.11.2 Electron Correlation Methods Based on a CASSCF Reference Wavefunction
165(3)
2.12 Density Functional Theory
168(23)
2.12.1 The Hohenberg-Kohn Theorems
170(2)
2.12.2 The Kohn-Sham Method
172(3)
2.12.3 The Local Density Approximation
175(1)
2.12.4 Generalised Gradient Approximation
176(2)
2.12.5 Meta-Generalised Gradient Approximation
178(1)
2.12.6 Adiabatic Connection: Hybrid Functional
178(1)
2.12.7 Double Hybrid Functionals
179(1)
2.12.8 Non-Covalent Interactions
180(1)
2.12.9 Ionisation Energies in Density Functional Theory
181(2)
Appendix 2A The Method of Lagrange Multipliers
183(1)
Appendix 2B Orthogonalisation Methods
184(3)
Appendix 2C Computing Eigenvalues and Eigenvectors of Large Matrices
187(1)
References
188(3)
Chapter 3 The Computation of Molecular Properties
3.1 Molecular Properties as Derivatives of the Potential Energy
191(3)
3.2 Analytic Differentiation of the Energy Expression
194(4)
3.2.1 Variational Wavefunctions
195(2)
3.2.2 Non-Variational Wavefunctions
197(1)
3.3 First Derivative with Respect to Geometric Coordinates: Variational Case
198(3)
3.4 Second Derivative with Respect to Geometric Coordinates: Variational Case
201(3)
3.5 Application of Energy Derivatives with Respect to Geometric Coordinates: Geometry Optimisation
204(4)
3.6 Electric and Magnetic Field Perturbations
208(9)
3.6.1 External Electric Fields
208(1)
3.6.2 External Magnetic Fields and Internal Magnetic Moments
209(8)
3.7 Time-Dependent Linear Response Methods: Excited States
217(4)
3.8 Continuum Methods of Solvation
221(7)
References
225(3)
Chapter 4 Understanding Molecular Wavefunctions, Orbitals and Densities
4.1 Isosurface Representations
228(2)
4.2 Canonical Orbitals, Density Matrices and Natural Orbitals
230(3)
4.3 Natural Bond Orbitals
233(1)
4.4 Localised Molecular Orbitals
234(3)
4.5 Natural Transition Orbitals
237(2)
4.6 Electronic Population Analysis
239(3)
4.7 Mayer Bond Orders and Valencies
242(1)
4.8 Electrostatic Potential
242(2)
4.9 Energy Decomposition Analysis
244(5)
References
248(1)
Chapter 5 Relativistic Effects and Electronic Structure Theory
5.1 Relativistic Effects and Chemistry
249(3)
5.2 Special Relativity and the Dirac Equation
252(5)
5.3 Elimination of the Small Component: The Pauli Approximation
257(3)
5.4 Elimination of the Small Component: Regular Approximations
260(3)
5.5 Elimination of the Small Component: Unitary Decoupling of the Dirac Equation
263(3)
5.6 Elimination of the Small Component: The Picture Change Transformation of Operators
266(1)
5.7 Spin-Orbit Coupling
267(3)
5.8 Summary
270(2)
References
270(2)
Subject Index 272
Walter Thiel studied chemistry at the University of Marburg (West Germany) from 1966 to 1971, where he subsequently obtained his doctorate with A. Schweig in 1973. After a post-doctoral stint at the University of Texas at Austin with M. J. S. Dewar (19731975), he obtained his habilitation from the University of Marburg in 1981. He was appointed Professor of Theoretical Chemistry at the University of Wuppertal (West Germany) in 1983 and Professor of Chemistry at the University of Zurich (Switzerland) in 1992. In 1987 he was a visiting professor at the University of California at Berkeley. Since 1999, he is a director at the Max Planck Institute for Coal Research in Mülheim an der Ruhr (Germany) and an honorary professor at the neighbouring University of Düsseldorf (Germany) since 2001.