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A Guide to Molecular Mechanics and Quantum Chemical Calculations A Guide to Molecular Mechanics and Quantum Chemical Calculations Warren J. Hehre WAVEFUNCTION Wavefunction, Inc. 18401 Von Karman Ave., Suite 370 Irvine, CA 92612 first page 1 3/21/03, 10:52 AM Copyright © 2003 by Wavefunction, Inc. All rights reserved in all countries. No part of this book may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems without permission in writing from the publisher, except by a reviewer who may quote brief passages in a review. ISBN 1-890661-18-X Printed in the United States of America first page 2 3/21/03, 10:52 AM Acknowledgements This book derives from materials and experience accumulated at Wavefunction and Q-Chem over the past several years. Philip Klunzinger and Jurgen Schnitker at Wavefunction and Martin Head- Gordon and Peter Gill at Q-Chem warrant special mention, but the book owes much to members of both companies, both past and present. Special thanks goes to Pamela Ohsan and Philip Keck for turning a “sloppy manuscript” into a finished book. first page 3 3/21/03, 10:52 AM first page 4 3/21/03, 10:52 AM To the memory of Edward James Hehre 1912-2002 mentor and loving father. first page 5 3/21/03, 10:52 AM first page 6 3/21/03, 10:52 AM Preface Over the span of two decades, molecular modeling has emerged as a viable and powerful approach to chemistry. Molecular mechanics calculations coupled with computer graphics are now widely used in lieu of “tactile models” to visualize molecular shape and quantify steric demands. Quantum chemical calculations, once a mere novelty, continue to play an ever increasing role in chemical research and teaching. They offer the real promise of being able to complement experiment as a means to uncover and explore new chemistry. There are fundamental reasons behind the increased use of calculations, in particular quantum chemical calculations, among chemists. Most important, the theories underlying calculations have now evolved to a stage where a variety of important quantities, among them molecular equilibrium geometry and reaction energetics, may be obtained with sufficient accuracy to actually be of use. Closely related are the spectacular advances in computer hardware over the past decade. Taken together, this means that “good theories” may now be routinely applied to “real systems”. Also, computer software has now reached a point where it can be easily used by chemists with little if any special training. Finally, molecular modeling has become a legitimate and indispensable part of the core chemistry curriculum. Just like NMR spectroscopy several decades ago, this will facilitate if not guarantee its widespread use among future generations of chemists. There are, however, significant obstacles in the way of continued progress. For one, the chemist is confronted with “too many choices” to make, and “too few guidelines” on which to base these choices. The fundamental problem is, of course, that the mathematical equations which arise from the application of quantum mechanics to chemistry and which ultimately govern molecular structure and properties cannot be solved. Approximations need to be made in order to realize equations that can actually be solved. “Severe” approximations may lead to methods which can be widely applied i Preface 1 3/21/03, 10:54 AM but may not yield accurate information. Less severe approximations may lead to methods which are more accurate but which are too costly to be routinely applied. In short, no one method of calculation is likely to be ideal for all applications, and the ultimate choice of specific methods rests on a balance between accuracy and cost. This guide attempts to help chemists find that proper balance. It focuses on the underpinnings of molecular mechanics and quantum chemical methods, their relationship with “chemical observables”, their performance in reproducing known quantities and on the application of practical models to the investigation of molecular structure and stability and chemical reactivity and selectivity. Chapter 1 introduces Potential Energy Surfaces as the connection between structure and energetics, and shows how molecular equilibrium and transition-state geometry as well as thermodynamic and kinetic information follow from interpretation of potential energy surfaces. Following this, the guide is divided into four sections: Section I. Theoretical Models (Chapters 2 to 4) Chapters 2 and 3 introduce Quantum Chemical Models and Molecular Mechanics Models as a means of evaluating energy as a function of geometry. Specific models are defined. The discussion is to some extent “superficial”, insofar as it lacks both mathematical rigor and algorithmic details, although it does provide the essential framework on which practical models are constructed. Graphical Models are introduced and illustrated in Chapter 4. Among other quantities, these include models for presentation and interpretation of electron distributions and electrostatic potentials as well as for the molecular orbitals themselves. Property maps, which typically combine the electron density (representing overall molecular size and shape) with the electrostatic potential, the local ionization potential, the spin density, or with the value of a particular molecular orbital (representing a property or a reactivity index where it can be accessed) are introduced and illustrated. ii Preface 2 3/21/03, 10:54 AM Section II. Choosing a Model (Chapters 5 to 11) This is the longest section of the guide. Individual chapters focus on the performance of theoretical models to account for observable quantities: Equilibrium Geometries (Chapter 5), Reaction Energies (Chapter 6), Vibrational Frequencies and Thermodynamic Quantities (Chapter 7), Equilibrium Conformations (Chapter 8), Transition- State Geometries and Activation Energies (Chapter 9) and Dipole Moments (Chapter 10). Specific examples illustrate each topic, performance statistics and graphical summaries provided and, based on all these, recommendations given. The number of examples provided in the individual chapters is actually fairly small (so as not to completely overwhelm the reader), but additional data are provided as Appendix A to this guide. Concluding this section, Overview of Performance and Cost (Chapter 11), is material which estimates computation times for a number of “practical models” applied to “real molecules”, and provides broad recommendations for model selection. Section III. Doing Calculations (Chapters 12 to 16) Because each model has its individual strengths and weaknesses, as well as its limitations, the best “strategies” for approaching “real problems” may involve not a single molecular mechanics or quantum chemical model, but rather a combination of models. For example, simpler (less costly) models may be able to provide equilibrium conformations and geometries for later energy and property calculations using higher-level (more costly) models, without seriously affecting the overall quality of results. Practical aspects or “strategies” are described in this section: Obtaining and Using Equilibrium Geometries (Chapter 12), Using Energies for Thermochemical and Kinetic Comparisons (Chapter 13), Dealing with Flexible Molecules (Chapter 14), Obtaining and Using Transition-State Geometries (Chapter 15) and Obtaining and Interpreting Atomic Charges (Chapter 16). iii Preface 3 3/21/03, 10:54 AM Section IV. Case Studies (Chapters 17 to 19) The best way to illustrate how molecular modeling may actually be of value in the investigation of chemistry is by way of “real” examples. The first two chapters in this section illustrate situations where “numerical data” from calculations may be of value. Specific examples included have been drawn exclusively from organic chemistry, and have been divided broadly according to category: Stabilizing “Unstable” Molecules (Chapter 17), and Kinetically- Controlled Reactions (Chapter 18). Concluding this section is Applications of Graphical Models (Chapter 19). This illustrates the use of graphical models, in particular, property maps, to characterize molecular properties and chemical reactivities. In addition to Appendix A providing Supplementary Data in support of several chapters in Section II, Appendix B provides a glossary of Common Terms and Acronyms associated with molecular mechanics and quantum chemical models. At first glance, this guide might appear to be a sequel to an earlier book “Ab Initio Molecular Orbital Theory”*, written in collaboration with Leo Radom, Paul Schleyer and John Pople nearly 20 years ago. While there are similarities, there are also major differences. Specifically, the present guide is much broader in its coverage, focusing on an entire range of computational models and not, as in the previous book, almost exclusively on Hartree-Fock models. In a sense, this simply reflects the progress which has been made in developing and assessing new computational methods. It is also a consequence of the fact that more and more “mainstream chemists” have now embraced computation. With this has come an increasing diversity of problems and increased realization that no single method is ideal, or even applicable, to all problems. The coverage is also more broad in terms of “chemistry”. For the most part, “Ab Initio Molecular Orbital Theory” focused on the structures and properties of organic molecules, accessible at that time * W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1985. iv Preface 4 3/21/03,
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