Computational Chemistry

Transcription

1 Computational Chemistry

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3 Errol G. Lewars Computational Chemistry Introduction to the Theory and Applications of Molecular and Quantum Mechanics Third Edition 2016

4 Errol G. Lewars Trent University Peterborough, ON, Canada ISBN ISBN (ebook) DOI / Library of Congress Control Number: st edition: Kluwer Academic Publishers nd edition: Springer Science+Business Media B.V Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland

5 To Anne and John, who know what their contributions were

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7 Preface Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry-an aberration which is happily almost impossible-it would occasion a rapid and widespread degeneration of that science. Augustus Compte, French philosopher, ; in Philosophie Positive, A dissenting view: The more progress the physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility to which it may be submitted to calculation. Adolphe Quetelet, French astronomer, mathematician, statistician, and sociologist, , writing in This third edition differs from the second in these ways: 1. The typographical errors that were found in the first edition have been (I hope) corrected. 2. Sentences and paragraphs have on occasion been altered to clarify an explanation. 3. The biographical footnotes have been updated as necessary. 4. Significant developments since 2010 (the year of the latest references in the second edition), up to the end of 2015, have been added and referenced in the relevant places. As might be inferred from the word Introduction, the purpose of this book, like that of previous editions, is to teach the basics of the core concepts and methods of computational chemistry. This is a textbook, and no attempt has been made to please every reviewer by dealing with esoteric advanced topics. Some fundamental concepts are the idea of a potential energy surface, the mechanical picture of a molecule as used in molecular mechanics, and the Schr odinger equation and its elegant taming with matrix methods to give energy levels and molecular orbitals. All the needed matrix algebra is explained before it is used. The fundamental vii

8 viii Preface techniques of computational chemistry are molecular mechanics, ab initio, semiempirical, and density functional methods. Molecular dynamics and Monte Carlo methods are only mentioned; while these are important, they utilize several fundamental concepts and methods explained here, and if presented at the level of the topics treated here would require a book of their own. I wrote the first edition (2003) because there seemed to be no text quite right for an introductory course in computational chemistry for a fairly general chemical audience, and the second (2011) edition was issued in the same belief; although there are several good books on quantum chemistry and on its disciplinary associate ( handmaiden might seem somewhat disparaging) computational chemistry, this edition is submitted in the same spirit as the first two. I hope it will be useful to anyone who wants to learn enough about the subject to start reading the literature and to start doing computational chemistry. As implied above, there are excellent books on the field, but evidently none that seeks to familiarize the general student of chemistry with computational chemistry in quite the same sense that standard textbooks of those subjects make organic or physical chemistry accessible. To that end the mathematics has been held on a leash; no attempt is made to prove that molecular orbitals are vectors in Hilbert space, or that a finite-dimensional inner-product space must have an orthonormal basis, and the only sections that the nonspecialist may justifiably view with some trepidation are the (outlined) derivation of the Hartree-Fock and Kohn-Sham equations. These sections should be read, if only to get the flavor of the procedures, but should not stop anyone from getting on with the rest of the book. Computational chemistry has become a tool used in much the same spirit as infrared or NMR spectroscopy, and to use it sensibly it is no more necessary to be able to write your own programs than the fruitful use of infrared or NMR spectroscopy requires you to be able to build your own spectrometer. I have tried to give enough theory to provide a reasonably good idea of how standard procedures in the programs work. In this regard, the concept of constructing and diagonalizing a Fock matrix is introduced early, and there is little talk of computationally less relevant secular determinants (except for historical reasons in connection with the simple Hückel method). Many results of actual computations, some done specifically for this book, are given. Almost all the assertions in these pages are accompanied by literature references, which should make the text useful to researchers who need to track down methods or results, and to anyone who may wish to delve deeper. It would be clearly inappropriate, if not impossible, to exhaustively reference each topic discussed. The choice of references has been oriented toward (besides justifying a particular assertion) reviews, and publications illustrating a topic in a general way, rather than some specialized aspect of it. In this age of the Internet once one is aware of the existence of some subject, it is usually not hard to obtain more information about it. The material should be suitable for senior undergraduates, graduate students, and novice researchers in computational chemistry. A knowledge of the shapes of molecules, covalent and ionic bonds, spectroscopy, and some familiarity with thermodynamics at about the second- or third-year

9 Preface ix undergraduate level is assumed. Some readers may wish to review basic concepts from physical and organic chemistry. The reader, then, should be able to acquire the basic theory of, and a fair idea of the kinds of results to be obtained from, common computational chemistry techniques. You will learn how one can calculate the geometry of (some may quibble and say a geometry for ) a molecule, its IR and UV spectra and its thermodynamic and kinetic stability, and other information needed to make a plausible guess at its chemistry. Computational chemistry is more accessible than ever. Hardware has become cheaper than it was even a few years ago, and powerful programs once available only for expensive workstations have been adapted to run on inexpensive personal computers. The actual use of a program is best explained by its manuals and by books written for a specific program, and the directions for setting up the various computations are not given here. Information on various programs is provided in Chap. 9. Read the book, get some programs, and go out and do computational chemistry. You may make mistakes, but they are unlikely to put you in the same kind of danger that a mistake in a wet lab might. For the first and second editions, it is a pleasure to acknowledge the help of: Professor Imre Csizmadia of the University of Toronto, who gave unstintingly of his time and experience; The knowledgeable people who subscribe to CCL, the computational chemistry list, an exceedingly helpful forum anyone seriously interested in the subject; My editor for the first edition at Kluwer, Dr Emma Roberts, who was always most helpful and encouraging; My very helpful editors for the second edition at Springer, Ms Claudia Culierat and Dr Sonia Ojo; For guidance with the third edition, Ms Karin de Bie at Springer; Professor Roald Hoffmann of Cornell University, who has insight and knowledge on matters that were at times somewhat arcane; Dr Andreas Klamt of COSMOlogic GmbH & Co., for sharing his expertise on solvation calculations; Professor Joel Liebman of the University of Maryland, Baltimore County for stimulating discussions; Professor Matthew Thompson of Trent University, for stimulating discussions. For the third edition, it is a pleasure to acknowledge the help of: Springer Senior Publishing Editor, Chemistry, Dr Sonia Ojo; Springer Production Editor Books, Ms Karin de Bie; Professor Robert Stairs of the department of Chemistry, Trent University, for his insight in fruitful discussions;

10 x Preface and finally, since this edition is not fully de novo, all those whom I thank, above, for the first and second editions. No doubt some names have been unjustly and inadvertently omitted, for which I tender my apologies. Peterborough, ON, Canada January 2016 Errol G. Lewars

11 Contents 1 An Outline of What Computational Chemistry Is All About What You Can Do with Computational Chemistry The Tools of Computational Chemistry Putting it All Together The Philosophy of Computational Chemistry Summary Easier Questions... 6 Harder Questions References The Concept of the Potential Energy Surface Perspective Stationary Points The Born-Oppenheimer Approximation Geometry Optimization Stationary Points and Normal-Mode Vibrations. Zero Point Energy Symmetry Summary Easier Questions Harder Questions References Molecular Mechanics Perspective The Basic Principles of Molecular Mechanics Developing a Forcefield Parameterizing a Forcefield A Calculation Using our Forcefield xi

12 xii Contents 3.3 Examples of the Use of Molecular Mechanics To Obtain Reasonable Input Geometries for Lengthier (ab Initio, Semiempirical or Density Functional) Kinds of Calculations To Obtain (Often Excellent) Geometries To Obtain (Sometimes Excellent) Relative Energies To Generate the Potential Energy Function Under Which Molecules Move, for Molecular Dynamics or Monte Carlo Calculations As a (Usually Quick) Guide to the Feasibility of, or Likely Outcome of, Reactions in Organic Synthesis Frequencies and Vibrational Spectra Calculated by MM Strengths and Weaknesses of Molecular Mechanics Strengths Weaknesses Summary Easier Questions Harder Questions References Introduction to Quantum Mechanics in Computational Chemistry Perspective The Development of Quantum Mechanics. The Schr odinger Equation The Origins of Quantum Theory: Blackbody Radiation and the Photoelectric Effect Radioactivity Relativity The Nuclear Atom The Bohr Atom The Wave Mechanical Atom and the Schr odinger Equation The Application of the Schr odinger Equation to Chemistry by Hückel Introduction Hybridization Matrices and Determinants The Simple Hückel Method Theory The Simple Hückel Method Applications Strengths and Weaknesses of the Simple Hückel Method The Determinant Method of Calculating the Hückel c s and Energy Levels

13 Contents xiii 4.4 The Extended Hückel Method Theory An Illustration of the EHM: The Protonated Helium Molecule The Extended Hückel Method Applications Strengths and Weaknesses of the Extended Hückel Method Summary Easier Questions Harder Questions References Ab initio Calculations Perspective The Basic Principles of the Ab initio Method Preliminaries The Hartree SCF Method The Hartree-Fock Equations Basis Sets Introduction Gaussian Functions; Basis Set Preliminaries; Direct SCF Types of Basis Sets and Their Uses Post-Hartree-Fock Calculations: Electron Correlation Electron Correlation The Møller-Plesset Approach to Electron Correlation The Configuration Interaction Approach to Electron Correlation. The Coupled Cluster Method Applications of The Ab initio Method Geometries Energies Frequencies and Vibrational (IR) Spectra Properties Arising from Electron Distribution: Dipole Moments, Charges, Bond Orders, Electrostatic Potentials, Atoms-in-Molecules Miscellaneous Properties UV and NMR Spectra, Ionization Energies, and Electron Affinities Visualization Strengths and Weaknesses of Ab initio Calculations Strengths Weaknesses Summary Easier Questions Harder Questions References

14 xiv Contents 6 Semiempirical Calculations Perspective The Basic Principles of SCF Semiempirical Methods Preliminaries The Pariser-Parr-Pople (PPP) method The Complete Neglect of Differential Overlap (CNDO) Method The Intermediate Neglect of Differential Overlap (INDO) Method The Neglect of Diatomic Differential Overlap (NDDO) Methods Applications of Semiempirical Methods Geometries Energies Frequencies and Vibrational Spectra Properties Arising from Electron Distribution: Dipole Moments, Charges, Bond Orders Miscellaneous Properties UV Spectra, Ionization Energies, and Electron Affinities Visualization Some General Remarks Strengths and Weaknesses of Semiempirical Methods Strengths Weaknesses Summary Easier Questions Harder Questions References Density Functional Calculations Perspective The Basic Principles of Density Functional Theory Preliminaries Forerunners to Current DFT Methods Current DFT Methods: The Kohn-Sham Approach Applications of Density Functional Theory Geometries Energies Frequencies and Vibrational Spectra Properties Arising from Electron Distribution Dipole Moments, Charges, Bond Orders, Atoms-in-Molecules Miscellaneous Properties UV and NMR Spectra, Ionization Energies and Electron Affinities, Electronegativity, Hardness, Softness and the Fukui Function Visualization

15 Contents xv 7.4 Strengths and Weaknesses of DFT Strengths Weaknesses Summary Easier Questions Harder Questions References Some Special Topics: (Section 8.1) Solvation, (Section 8.2) Singlet Diradicals, (Section 8.3) A Note on Heavy Atoms and Transition Metals Solvation Perspective Ways of Treating Solvation Singlet Diradicals Perspective Problems with Singlet Diradicals and Model Chemistries Singlet Diradicals, Beyond Model Chemistries A Note on Heavy Atoms and Transition Metals Perspective Heavy Atoms and Relativistic Corrections Some Heavy Atom Calculations Transition Metals Summary Solvation Easier Questions Harder Questions Singlet Diradicals Easier Questions Harder Questions Heavy Atoms and Transition Metals Easier Questions Harder Questions References Selected Literature Highlights, Books, Websites, Software and Hardware From the Literature Molecules Mechanisms Concepts To the Literature Books Websites for Computational Chemistry in General

16 xvi Contents 9.3 Software and Hardware Software Hardware Postscript References Answers Index