HANDBOOK OF COMPUTATIONAL CHEMISTRY RESEARCH No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services HANDBOOK OF COMPUTATIONAL CHEMISTRY RESEARCH CHARLES T COLLETT AND CHRISTOPHER D ROBSON EDITORS Nova Science Publishers, Inc New York Copyright © 2010 by Nova Science Publishers, Inc All rights reserved No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, 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advice or recommendations contained in this book In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services If legal or any other expert assistance is required, the services of a competent person should be sought FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Available upon request ISBN 978-1-61122-680-5 (eBook) Published by Nova Science Publishers, Inc New York CONTENTS Preface vii Chapter Recent Progress in ‘Algebraic Chemistry’ Cynthia Kolb Whitney Chapter ONIOM and ONIOM-Molecular Dynamics Methods: Principles and Applications Toshiaki Matsubara 69 Chapter Constraining Optimized Exchange Marcel Swart, Miquel Solà and F Matthias Bickelhaupt 97 Chapter Temperature Integral and Its Approximations Junmeng Cai 127 Chapter Determination of Protein Coarse-Grain Charges from Smoothed Electron Density Distribution Functions and Molecular Electrostatic Potentials Laurence Leherte and Daniel P Vercauteren 153 Chapter The Effect of Molecular Structure on Confinement inside the β-Cyclodextrin Cavity E Alvira 193 Chapter Use of Error Theory in the Computational Methods Devised for Kinematic Viscosity - Temperature Correlations in Undefined Petroleum Fractions José Alberto Maroto Centeno and Manuel Quesada-Pérez 215 Chapter Improvement to Conventional Potential Functions by Means of Adjustable Interatomic Parameters Teik-Cheng Lim 229 vi Contents Chapter Orbital Signatures as a Descriptor of Chemical Reactivity: A New Look at the Origin of the Highest-Occupied Molecular Orbital Driven Reactions Teodorico C Ramalho, Douglas H Pereira, Rodrigo R da Silva and Elaine F.F da Cunha 259 Chapter 10 Wavelet Based Approaches and High Resolution Methods for Complex Process Models Hongmei Yao, Tonghua Zhang, Moses O Tadé and Yu-Chu Tian 273 Chapter 11 The Stability and Antiaromaticity of Heterophosphetes and Phosphole Oxides Zoltán Mucsi and György Keglevich 303 Chapter 12 A Modern Tool to Evaluate the Solvent Effect on Organic Systems Boaz Galdino de Oliveira 321 Chapter 13 A Morphological Approach to the Offset Curve Problem Antomio Jimenno 337 Chapter 14 A New Computational Chemistry and Complex Networks Approach to Structure-Function and Similarity Relationships in Protein Enzymes Riccardo Concu, Gianni Podda, Eugenio Uriarte, Francisco J Prado-Prado, Miguel A del Río Vazquez, and Humberto González-Díaz 387 Chapter 15 A New Density Functional Method for Electronic Structure Calculation of Atoms and Molecules Amlan K Roy 409 Chapter 16 Addition Theorems for Multi-center Integrals over Exponential Type Functions Rachid Ghomari, Abdelati Rebabti, Ahmed Bouferguene and Hassan Safouhi 435 Chapter 17 On the Zero Point Energy Difficulty of Quasiclassical Trajectory Simulations Song Ling and Robert Q Topper 467 Chapter 18 Dynamical Systems Approach for the Chapman-Crutzen Mechanism F.J Uribe and R.M Velasco 477 Index 493 PREFACE This book presents ways in which computers can be used to solve chemical problems One approach develops synoptic algebraic scaling laws to use in place of the case-by-case numerical integrations prescribed by traditional quantum chemistry The ONIUM hybrid method combines a quantum mechanical method with the molecular mechanical method One study includes placing functional constraints and testing the performance of the resulting constrained functionals for several chemical properties A review of the known approximations for the temperature integral is included Some of the other areas of research discussed include protein coarse-grain models, a specific application of spherical harmonics, use of the FERMO concept to better explain reactions that are HOMO driven, wavelet based approaches and high resolution methods with successful application to a fixed-bed adsorption column model There is a discussion of stability and thermodynamics, as well as kinetic properties of heterophosphetes and phosphole oxides A model is proposed that applies methods and concepts in mathematical morphology paradigms to solve the problem of offset curves as well as a description of the solvent effects through the in silico procedures by the use of continuum and discrete models A simulation method attempts to relate the microscopic details of a system to macroscopic properties of experimental interest Techniques to retain the use of simple potential functions are also discussed, but with the possibility of allowing them to readjust their properties to fit the potential energy curves of the more complex functions The Chapman-Cruzen mechanism is also studied using the ideas of the theory of dynamical systems Chapter reprises and extends the development of a new approach to fundamental problems in chemistry, now known as ‘Algebraic Chemistry’ It collects and summarizes all results so far produced Problems addressed here include 1) the nominal pattern of singleelectron state filling across all of the elements, 2) the exceptions to that pattern that occur for about 20% of elements; 3) the numerical patterns in the experimental data about ionization potentials of all elements and all orders, and 4) plausible reasons for the existence of chemical periodicity and 5) some insights on the possible nature of chemical bonds The approach develops synoptic algebraic scaling laws to use in place of the case-by-case numerical integrations prescribed by traditional Quantum Chemistry The development of Algebraic Chemistry requires an initial re-examination of two pillars of twentieth century physics: not just Quantum Mechanics (QM), but also Special Relativity Theory (SRT) The reader is asked to entertain an ‘Expanded SRT’, in which an additional ‘speed’ concept appears, and several additional mathematical relationships among speed concepts appear This Expanded SRT viii Charles T Collett and Christopher D Robson allows an ‘Expanded QM’, in which the main actors are not the modern, and very abstract, probability-amplitude waves, but the old-fashioned, and very concrete, point particles Although the hundred years elapsed since SRT and QM were first introduced may make this sort of re-work seem troublesome, the practical utility of the results produced makes the effort clearly worthwhile The ONIOM hybrid method, which combines a quantum mechanical (QM) method with the molecular mechanical (MM) method, is one of the powerful methods that allow to calculate large molecular systems with the high accuracy afforded for smaller molecular systems The notable feature of this method is that it can include the environmental effects into the high level QM calculation through a simple extrapolation procedure This is a significant difference from the conventional QM/MM methods The definition of the layer is simple, and also the layer is easily extended to the multiple-layers Contrary to this, the traditional QM/MM method that adopts the sophisticated link between the QM and MM regions makes the handling difficult The ONIOM method is thus more flexible and versatile than the conventional QM/MM method, and is therefore increasingly adopted as an efficient approach beneficial to many areas of chemistry Recently, the ONIOM-molecular dynamics (MD) method has been developed to analyze the more complicated large molecular system where the thermal fluctuations of the environment play an important role For example, when the target is a biomolecule, such as an enzyme, the property of the entire system is strongly affected by its dynamical behavior In such case, the ONIOM method is not satisfactory The coupling of the ONIOM method with the molecular dynamics (MD) method is necessary to account for the thermal fluctuations of the environment Newly developed ONIOM-MD method has made it possible to characterize the function of enzyme etc in a realistic simulation of the thermal motion, retaining the concept embodied in the ONIOM method In Chapter 2, the basic concept of the ONIOM and ONIOM-MD methods we developed and their applications to typical cases are introduced Several recent studies (J Phys Chem A 2004, 108, 5479; J Comput Chem 2007, 28, 2431) have shown impressive results when replacing the non-empirical PBE density functional by the empirical OPBE or OLYP functionals, i.e replacing the PBE exchange functional by Handy and Cohen’s OPTX functional To investigate the origin of the improvements, we have placed constraints from the non-empirical PBE exchange functional on the empirical OPTX exchange functional, and tested the performance of the resulting constrained functionals for several characteristic chemical properties.in Chapter 3, the performance of the new functionals is tested for a number of standard benchmark tests, such as the atomization energies of the G2 set, accuracy of geometries for small molecules, atomic exchange energies, and proton affinities of anionic and neutral molecules Furthermore, the new functionals are tested against a benchmark set of nucleophilic substitution SN2 reactions, for which we have recently compared DFT with high-level coupled cluster CCSD(T) data (J Comput Chem 2007, 28, 1551) Our study makes clear that the performance depends critically on the number of constraints, and on the reference data to which the constrained functionals are optimized For each of these properties studied, there is at least one functional that performs very well Although a new promising functional (MLffOLYP) emerged from the set of constrained functionals that approaches coupled-cluster accuracy for geometries and performs very well for the energy profile of SN2 reactions, there is no one of the newly constructed functionals that performs equally well for all properties Preface ix The temperature integral, which frequently occurs in the kinetic analysis of solid-state reactions, does not have an exact analytical solution Instead of performing the numerical integration, most of the researchers prefer to circumvent the problem by using approximate expressions The main aim of Chapter is to carry out a review of the known approximations for the temperature integral, to establish a ranking of those temperature integral approximations and to present some applications of the temperature integral approximations The design of protein coarse-grain (CG) models and their corresponding interaction potentials is an active field of research, especially for solving problems such as protein folding, docking… Among the essential parameters involved in CG potentials, electrostatic interactions are of crucial importance since they govern local and global properties, e.g., their stability, their flexibility… Following our development of an original approach to hierarchically decompose a protein structure into fragments from its electron density (ED) distribution, the method is applied in Chapter to molecular electrostatic potential (MEP) functions, calculated from point charges as implemented in well-known force fields (FF) To follow the pattern of local maxima (and minima) in an ED or a MEP distribution, as a function of the degree of smoothing, we adopted the following strategy First, each atom of a molecule is considered as a starting point (a peak, or a pit for negative potentials in a MEP analysis) As the smoothing degree increases, each point moves along a path to reach a location where the ED or MEP gradient value vanishes Convergences of trajectories lead to a reduction of the number of points, which can be associated with molecular fragments Practically, to determine the protein backbone representations, we analyzed CG models obtained for an extended strand of polyglycine The influence of the different amino acid side chains was then studied for different rotamers by substituting the central glycine residue Regarding the determination of charges, we adopted two procedures First, the net charge of a fragment was calculated as the summation over the charges of its constituting atoms Second, a fitting algorithm was used to assign charges to the obtained local maxima/minima Applications to a literature case, a 12-residue β-hairpin peptide, are also presented It is observed that classical CG models are more similar to ED-based models, while MEP-based descriptions lead to different CG motifs that better fit the MEP distributions A simulation method attempts to relate the microscopic details of a system (atomic masses, interactions between them, molecular geometry, etc.) to macroscopic properties of experimental interest (equation of state, structural parameters, etc.) The first step in performing a molecular simulation requires knowledge of the potential energy of interaction between the particles of the system, and one of the simplest methods used to obtain this treats the intermolecular energy as the sum of pairwise additive potentials (as in the force-field method) The model presented in Chapter does not consider the molecules as formed by rigid spherical particles (atoms or assemblies of atoms) but as continuum distributions of matter (without electrical charge), and this has two effects: it can be applied to many kinds of systems and extends the information on the system, relating a microscopic property (such as the interaction energy) with macroscopic properties (such as the structural parameters of the molecules) To simulate the interaction energy between β−cyclodextrin (β−CD) and molecules with different structure (cyclic, spherical and linear geometry), a model was constructed from a simple pairwise-additive Lennard-Jones potential combined with a continuum description of the cyclodextrin cavity and the guest molecule This model INDEX A absorption, 35, 39 accelerator, 2, 459, 460 access, 374 accessibility, 406 accidental, 41 accommodation, xi, 273 accounting, x, 46, 215, 216, 468 accuracy, viii, x, xi, xiii, 50, 69, 70, 71, 73, 77, 93, 97, 98, 99, 100, 102, 106, 112, 114, 115, 120, 122, 134, 151, 215, 216, 220, 221, 222, 223, 224, 226, 229, 230, 231, 256, 274, 278, 286, 291, 299, 339, 360, 362, 363, 387, 388, 389, 394, 395, 406, 410, 411, 414, 415, 416, 417, 436, 437, 449, 486 acetate, 32 acid, ix, 37, 71, 78, 79, 80, 81, 82, 83, 94, 108, 153, 154, 188, 259, 261, 263, 265, 267, 268, 270, 271, 328, 334, 390, 392, 404, 405 acidity, 270, 328, 330, 331, 334 ACM, 300 acrylonitrile, 203 activation, 79, 128, 134, 144, 145, 146, 147, 148, 150, 151, 152, 309, 318 activation energy, 128, 144, 145, 146, 147, 148, 150, 151 activation parameters, 318 active site, 71, 78, 79, 80, 81, 82, 84, 85, 86, 94 acylation, 305, 306 Adams, xiv, 477, 486, 487 adaptation, 302, 343 adjustment, 222 adsorption, vii, xi, 194, 196, 273, 274, 275, 278, 284, 294, 300, 301 advection-diffusion, 278 age, 187 AGOA, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 334 aid, 411 air, 31, 479, 491 air pollution, 491 Alabama, 65 Albert Einstein, 66 Alberta, 435 Alchemy, 465 alcohol, 261, 267, 268, 270, 328, 331 alcohols, x, 259, 260, 261, 262, 267, 268, 270, 271, 328, 330, 331 Algeria, 435 algorithm, ix, xii, 153, 154, 155, 156, 157, 161, 162, 163, 164, 166, 167, 168, 170, 171, 173, 175, 179, 180, 181, 183, 185, 186, 188, 231, 276, 298, 322, 323, 337, 339, 342, 355, 356, 359, 360, 361, 362, 364, 369, 373, 374, 375, 376, 377, 378, 380, 383, 385, 393, 405, 406, 408, 442, 452, 454, 456, 459, 460, 461 alkanes, 328 ALL, 23, 26 alternative, xiii, 40, 61, 230, 238, 275, 322, 359, 363, 369, 388, 409, 411, 412, 425, 439 alternatives, 39, 355, 369 amide, 154, 169 amines, x, 259, 334 amino, ix, 71, 78, 80, 81, 82, 83, 94, 153, 154, 160, 188, 189, 389, 390, 391, 392, 394, 404, 405 amino acid, ix, 71, 78, 80, 81, 82, 83, 94, 153, 154, 160, 188, 189, 389, 390, 391, 392, 394, 404, 405 amino acids, 160, 189, 389, 390, 391, 392, 394 ammonia, 79, 108 ammonium, 332 amplitude, 1, 4, 5, 6, 7, 8, 11, 38, 154, 174, 205, 474, 475 Amsterdam, 65, 97, 109, 124, 125, 431, 465 analog, 58, 59, 60 angular momentum, 2, 15, 27, 417, 418 angular velocity, 199 annealing, 160, 406 annotation, 388, 389, 403 anomalous, 29, 44 anthropogenic, 477 antibacterial, 400 antibiotic, xiii, 387, 402 antibiotics, 402 anticancer, 79, 94, 407 anticancer drug, 79, 94 API, 217, 227 494 Index appendix, 480, 481, 486, 490 application, vii, xii, xiv, 34, 63, 70, 71, 75, 79, 145, 155, 160, 162, 181, 188, 216, 218, 224, 226, 227, 233, 270, 278, 280, 284, 296, 321, 337, 342, 346, 347, 348, 349, 350, 351, 353, 355, 356, 361, 363, 365, 369, 373, 382, 393, 400, 404, 407, 435, 451, 470, 477 applied mathematics, 300 aqueous solution, 260, 328 argument, 270, 332 arithmetic, 246, 330 Arrhenius equation, 127 Arrhenius parameters, 128 ART, 146 articulation, 32 artistic, 420 assessment, x, 22, 39, 105, 215, 216, 222 assignment, 155 assumptions, x, 129, 150, 193, 295 ASTM, x, 215, 216, 219, 220, 221, 222, 223, 224, 225, 226, 227 asymptotic, 260, 427, 442, 445, 446, 448, 449, 450, 451, 459 asymptotically, 436, 444, 445, 459 atmosphere, 430, 477, 481, 488 atmospheric pressure, x, 75, 215, 216, 218 atomic distances, 314 atomic orbitals, 417, 446 atomic positions, 159 atoms, ix, xiii, xiv, 2, 9, 10, 22, 24, 25, 28, 29, 31, 32, 33, 35, 36, 47, 50, 58, 61, 62, 63, 64, 70, 74, 76, 80, 81, 82, 83, 85, 86, 99, 106, 122, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 165, 166, 169, 172, 174, 179, 181, 185, 188, 189, 193, 194, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 211, 212, 213, 261, 266, 305, 313, 314, 318, 321, 322, 323, 330, 331, 332, 392, 409, 410, 411, 412, 413, 421, 424, 426, 427, 428, 458, 479 attacks, 79, 87 attribution, 64 Australia, 273 Australian Research Council, 300 autocorrelation, 299, 405, 473, 474 automata, 404 availability, 436 avoidance, 341, 475 B background information, xii, 337 bacteria, 402 bacterial, 402, 404, 408 barium, 253 barrier, 76, 80, 82, 88, 89, 90, 92, 93, 102, 117, 310 barriers, 101, 103, 117, 120, 122 base case, 377 basis set, xiii, 101, 102, 106, 107, 108, 109, 113, 114, 117, 118, 157, 261, 322, 409, 412, 414, 416, 417, 418, 419, 420, 421, 423, 425, 428, 429, 437 Bayesian, 105, 120, 407 BEE, 105, 112, 113, 116, 118, 120, 121 behavior, viii, xi, 7, 8, 9, 12, 22, 29, 38, 41, 52, 61, 62, 69, 78, 81, 101, 104, 111, 189, 259, 260, 262, 263, 265, 267, 270, 271, 328, 329, 331, 403, 427, 437, 470, 474, 478, 481, 482, 488 behaviours, 274 Belgium, 153, 190 benchmark, viii, 97, 99, 100, 101, 102, 106, 107, 113, 114, 120, 122 benchmarks, 120, 122, 459 bending, 410 benzene, 155, 311, 312, 313 Bessel, 440, 465 binding, x, 102, 194, 199, 334, 389, 404, 405, 413, 418 bioinformatics, 388, 406 biological systems, 70, 331, 392, 407 biomolecular, 78 biomolecule, viii, 69, 78 biomolecules, 71 biopolymer, 389 birth, 411 blocks, 27 blurring, 156 boiling, 217, 218, 219, 220, 222 bonding, 30, 31, 32, 36, 106, 116, 330 bonds, 1, 33, 80, 84, 86, 119, 240 Boston, 383 bottleneck, 339 boundary conditions, 4, 278, 279, 280, 281, 284, 285, 295, 296 bounds, 111, 442, 445, 462 Brazil, 259, 321, 335 Brazilian, 271 breakdown, 354 building blocks, 445 burns, 33 bypass, 423 C CAD, xii, xiii, 337, 338, 372, 380, 384 caffeic acid, 405 calculus, 448 CAM, xii, xiii, 337, 338, 372, 380, 384 Canada, 435, 462 cancer, 79 candidates, xi, 274, 299, 414, 425, 438 capacity, 389 capillary, 224 carbon, 30, 33, 34, 185, 270 carbonyl groups, 162 carrier, 84 Cartesian coordinates, 469 Index case study, 294 cast, 40, 376, 415, 449 catalysis, 94 catalyst, 31 catalytic activity, 94 catalytic properties, 411 cation, 334, 335 CCC, 295 cell, 79, 393, 400 cell surface, 400 CH4, 33, 107 channels, 400 charge density, 415, 417 charged particle, 10 chemical bonds, vii, 1, 3, 31 chemical engineering, 277, 278, 302 chemical interaction, 70 chemical kinetics, 478 chemical modeling, 436 chemical properties, vii, viii, xii, 15, 29, 30, 97, 122, 303, 410, 418, 436, 437 chemical reactions, 70, 270, 478, 484, 489, 490 chemical reactivity, 263, 269, 270, 271 chemicals, 406, 407 China, 127 chiral, 210 chloride, 101, 102 chromatography, 274, 275, 284, 286, 302 circulation, 44 cis, 71, 75, 76, 77, 85, 86, 87, 88, 89, 90, 93, 94, 187, 304 citizens, 32 classes, 98, 157, 260, 404, 408 classical, ix, x, xiv, 45, 58, 59, 63, 154, 193, 194, 199, 233, 251, 252, 293, 340, 341, 342, 364, 372, 373, 376, 380, 412, 413, 414, 416, 418, 421, 422, 424, 467, 468, 470, 472, 473, 474, 475 classical mechanics, 468, 474 classification, 276, 394, 402, 404 classroom, 444 climate change, 489, 491 cluster model, 327 clustering, 56, 155, 156, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 173, 175, 179, 180, 181, 183, 185, 186, 188, 422 clusters, 3, 9, 10, 35, 36, 37, 56, 58, 61, 62, 63, 67, 189, 307, 322, 324, 325, 329, 330, 331, 332, 333, 410, 415, 417, 429, 468 CO2, 32, 33, 34, 107 cocaine, 405 codes, 487 coding, 405, 406 coherence, 108 collisions, 381 colorectal cancer, 79 Committee on Standards, 227 communication, 371, 372, 422 community, 415 comparative advantage, 233, 237, 244 495 compensation, 341, 376 competitiveness, 278 complement, 260, 486 complementarity, 155, 189 complexity, 5, 98, 225, 231, 275, 356, 359, 360, 362, 373, 382, 424 complications, 29, 48, 360, 427 components, x, 38, 49, 55, 117, 119, 160, 215, 216, 274, 275, 276, 343, 344, 346, 389, 412, 415, 420, 422, 423, 424, 425, 426, 427 composition, x, 194, 197, 199, 200, 201, 202, 203, 208, 209, 210, 211, 213, 215, 216, 221, 223, 261, 265, 267, 268, 269, 270, 382, 404, 405 compounds, x, xi, xii, 100, 101, 120, 259, 260, 261, 262, 263, 266, 269, 271, 303, 305, 306, 312, 313, 314, 324, 328, 407 computation, xi, xii, xiii, xiv, 145, 231, 256, 273, 274, 276, 293, 299, 337, 338, 339, 355, 356, 357, 358, 360, 361, 362, 363, 364, 368, 374, 377, 382, 384, 416, 420, 435, 437, 441 computer science, 384 computer technology, 411 computing, xi, 273, 275, 291, 298, 299, 365, 369, 373, 383, 467 concentrates, 82, 84, 89 concentration, 275, 276, 278, 284, 285, 286, 287, 292, 293, 296, 297, 299, 300, 478, 479, 480, 482, 483 conceptual model, 61, 342 concordance, 328, 330 concrete, viii, 1, 348 condensed matter, 233, 412, 422 conditioning, 365 conductive, 16, 17, 18, 19, 20, 21 conductor, 261 confidence, 418 configuration, 30, 35, 72, 78, 197, 198, 199, 201, 202, 204, 205, 207, 208, 209, 212, 274, 294, 411, 418, 437 confinement, 10, 11, 15, 16, 21, 29, 195, 203, 211, 212 conflict, 39 conformational stability, 405, 406 confusion, 43, 447 Congress, 383 conjugation, 310, 311, 313, 314, 316 connectivity, 165, 407 consensus, 82, 420 conservation, xiv, 7, 44, 154, 477, 479, 480, 488 constraints, vii, viii, xii, xiii, 4, 97, 99, 103, 104, 105, 110, 111, 115, 116, 117, 119, 122, 169, 172, 179, 337, 380, 419, 440 construction, 7, 45, 120, 280, 413, 416, 422 consumption, 64 continuity, 198, 370, 371 contracts, control, 39, 40, 222, 260, 275, 276, 339, 354, 377, 402 496 Index convergence, xiv, 34, 101, 156, 279, 298, 325, 339, 415, 422, 423, 425, 435, 439, 441, 442, 443, 444, 445, 451, 452, 459, 460, 461 conversion, 57, 79, 127, 129, 144, 145, 240, 256, 347 convex, 339 Cooper pair, 11, 28, 35 correlation, x, xi, 36, 71, 76, 99, 103, 104, 105, 110, 112, 115, 120, 155, 189, 215, 216, 217, 218, 219, 221, 222, 242, 259, 260, 263, 265, 267, 268, 270, 312, 317, 393, 399, 411, 414, 415, 423, 425, 428 correlation coefficient, 267, 270 correlation function, 99, 103, 112, 120, 425 correlations, x, xi, 215, 216, 217, 221, 222, 223, 226, 227, 259, 262, 263, 265, 267, 268 corridors, 341 cosine, 51 costs, 371, 382 Coulomb, 9, 38, 39, 43, 44, 45, 56, 110, 155, 161, 322, 415, 416, 418, 419, 421, 438, 442, 443, 444, 447 Coulomb interaction, 421 coumarins, 407 couples, 478 coupling, viii, 69, 71, 78, 405, 470, 472 covalent, 72, 74, 233, 234, 239, 251, 252 covalent bond, 74, 233, 234, 239, 252 covering, 35, 43, 47, 226, 412 CPU, 292 CRC, 190 critical points, xiv, 477, 480, 481, 482, 483, 485, 486, 488, 490 crude oil, x, 215, 216, 222 crystal structure, 79, 80, 81 crystal structures, 79 crystallization, 278, 302 curiosity, 44 cycles, 87, 296, 478, 488 cyclodextrin, ix, 193, 194 cyclopentadiene, 203 cytosine, 71, 80, 107, 108, 115 D data mining, 23 data set, xiii, 387 database, 2, 22, 147, 221, 388, 394, 399, 400, 405, 407, 408 decay, 64 decomposition, xiii, 161, 162, 169, 188, 389, 409, 410, 420, 422, 481, 488, 490 defense, 436 definition, viii, 37, 41, 42, 69, 70, 72, 74, 77, 100, 236, 276, 340, 341, 342, 343, 344, 346, 351, 352, 353, 357, 362, 365, 366, 371, 372, 373, 375, 378, 380, 381, 383, 438, 442, 445, 446, 447, 449, 459, 486 degrees of freedom, 154 delocalization, 205 Delphi, 157 demand, xi, 98, 273, 274, 291, 322, 332 density, viii, ix, x, xiii, 35, 63, 71, 80, 97, 98, 103, 104, 105, 110, 153, 155, 157, 188, 195, 197, 199, 205, 206, 207, 208, 209, 211, 217, 219, 259, 260, 322, 328, 382, 393, 400, 409, 411, 412, 413, 414, 416, 419, 421, 423, 424, 425, 428, 429, 442 density functional theory, viii, x, xiii, xiv, 80, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 115, 119, 259, 260, 261, 262, 263, 264, 265, 266, 270, 271, 409, 411, 412, 413, 414, 418, 419, 420, 421, 422, 423, 427, 428, 429, 431, 446 dependent variable, 49, 275 derivatives, 74, 98, 155, 209, 231, 287, 315, 405, 410, 439 destruction, 4, 25, 477, 478 detection, 340 determinism, 382 deviation, x, 82, 89, 90, 93, 99, 100, 102, 108, 111, 112, 113, 114, 115, 117, 119, 159, 215, 216, 218, 221, 234, 316, 423, 426, 427, 428, 472 diamond, 489 diamonds, 182 diatoms, 241, 242 differential equations, xiv, 5, 8, 279, 301, 302, 414, 477, 478, 486, 488 differentiation, xiv, 34, 477 diffraction, 4, 5, diffusion, 128, 129, 157, 158, 301 dilation, 342, 345, 346, 351, 352, 353, 354, 355, 364, 365, 366, 367, 368, 373, 376, 382 dimer, 62, 107, 108, 115, 315, 334, 406 dimerization, 318 dipeptides, 155 dipole, 57, 58, 60, 159, 160, 165, 172, 180, 188, 189, 260, 322, 323, 410 dipole moment, 159, 160, 165, 172, 188, 189, 260, 322, 323 dipole moments, 260 Dirac delta function, Dirac equation, 248 directionality, 9, 22, 38 Dirichlet boundary conditions, 279, 281 discipline, 8, 410 discontinuity, 28, 373, 374 Discovery, 300, 405 discretization, 275, 277, 278, 284, 285, 287, 288, 291, 292, 296, 298, 301, 338, 374, 381, 383 discrimination, 393, 406 discriminatory, 393 diseases, 402 dispersion, 4, 103, 278, 299 displacement, 15, 82, 83, 158 disposition, 417 dissociation, 84, 232, 236, 256, 410, 411 distortions, 347 distribution, ix, xiv, 8, 153, 155, 156, 157, 160, 161, 163, 164, 165, 168, 169, 179, 180, 181, 188, 189, Index 194, 197, 237, 238, 290, 291, 297, 322, 323, 328, 435, 446, 447, 474 distribution function, 155, 161, 163, 164, 168, 169, 179, 180, 188 divergence, 408 diversity, 181 division, 420 DNA, 102, 103, 106, 108, 116, 190, 388, 400, 405, 406 doped, 411 Doppler, 65 drug design, 400 drugs, 388, 389, 390, 394, 400, 402, 404, 406 duality, 354 duration, 285 dynamic viscosity, 217 dynamical system, vii, xiv, 300, 477, 478, 480, 481, 483, 485, 488, 489 dynamical systems, vii, xiv, 300, 477, 480, 489 E Education, 409 eigenvector, 416 elaboration, 160 electric charge, 154 electromagnetic, 5, 34, 37, 38, 44, 47 electromagnetism, 44 electron, vii, ix, xiii, xiv, 2, 3, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 29, 30, 31, 32, 33, 35, 36, 37, 43, 44, 45, 47, 48, 49, 50, 52, 57, 58, 61, 63, 64, 70, 71, 75, 76, 77, 78, 87, 88, 98, 104, 153, 155, 188, 234, 260, 270, 307, 310, 316, 318, 409, 410, 411, 412, 414, 416, 417, 419, 421, 423, 424, 427, 435, 439, 446 electron charge, 417 electron density, ix, xiii, 98, 153, 155, 188, 260, 409, 411, 412, 416, 419, 421, 423 electron gas, 98, 104, 417 electron pairs, 307 electron state, vii, 2, 64 electronegativity, 328 electronic structure, xiii, 260, 303, 310, 312, 409, 410, 411, 412, 422 electrons, 2, 10, 11, 12, 13, 14, 17, 18, 19, 21, 22, 23, 24, 25, 29, 30, 32, 33, 34, 35, 36, 56, 59, 61, 62, 64, 65, 99, 104, 389, 410, 412, 418, 419, 422, 429, 436 electrostatic force, 36 electrostatic interactions, 154, 155 element 118, 12 emission, 35, 39, 40, 61 enantiomer, 210 enantiomers, xi, 274, 296, 299, 301 endothermic, 76, 307, 309 energy, vii, viii, ix, x, xii, xiii, xiv, 4, 5, 7, 8, 9, 11, 12, 16, 25, 29, 34, 35, 37, 39, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 497 64, 65, 70, 71, 72, 73, 74, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 97, 98, 101, 102, 103, 104, 105, 106, 107, 108, 109, 112, 116, 117, 119, 120, 122, 145, 146, 154, 161, 193, 194, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 207, 208, 210, 211, 212, 213, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 260, 261, 262, 263, 265, 267, 268, 270, 303, 305, 307, 309, 310, 311, 312, 317, 318, 322, 323, 325, 326, 327, 331, 332, 334, 389, 390, 406, 409, 410, 411, 412, 413, 414, 415, 416, 418, 423, 424, 425, 426, 427, 428, 429, 436, 467, 468, 469, 472, 473, 474, 475 energy consumption, 64 energy density, 4, 5, 98, 428 energy transfer, England, 65, 66 environment, viii, 69, 71, 76, 78, 82, 83, 85, 93, 94, 155, 328, 364, 365 environmental effects, viii, 69, 71, 72, 78, 80, 82, 86, 90, 93, 94 enzymatic, 94, 388, 393, 399, 407 enzymes, xiii, 71, 78, 79, 82, 86, 387, 388, 389, 393, 394, 400, 401, 402, 403, 404 equality, 55, 352 equating, 46, 48, 256 equilibrium, 202, 231, 232, 234, 236, 238, 256, 275, 284, 285, 286, 294, 299, 304, 305, 306, 328, 334, 411, 418 equol, 210 erosion, 342, 345, 346, 348, 352, 353, 354, 355, 364, 368, 373, 376 ethanol, 261, 328, 331, 332 ethylene, 74 Euclidean space, 345, 349, 357, 359, 364 European Union, 122 evolution, 3, 9, 78, 129, 204, 207, 208, 470, 473, 478 excitation, 61, 62 execution, x, 229, 346, 381 exercise, 36, 38, 46, 60, 179, 410 expansions, xiv, 130, 155, 368, 391, 435, 438, 439, 441, 459, 461 experimental condition, 224 extrapolation, viii, 69, 72, 74, 221 eyes, 23 F fabrication, 328 factorial, 440 failure, xii, 4, 100, 101, 115, 116, 303, 328 family, xii, 51, 52, 54, 189, 303, 305, 344, 345, 346, 348, 350, 404 FDA, 400 feedback, 5, 23 FEM, 275 Fermi-Dirac, 412 498 Index Feynman, 474, 475 FFT, 421, 422 film, 299 financial support, 122, 213, 300, 462 finite differences, 276 finite volume, 4, 275 first principles, 410 flavors, 419 flexibility, ix, 111, 153, 154, 229, 231, 332, 357 flight, flow, 216, 224, 274, 295, 300, 468, 478, 491 flow behaviour, 224 flow rate, 295, 300 fluctuations, viii, 69, 78, 82, 87, 88, 89, 90, 92, 94, 205 fluid, 216, 220, 221, 222, 274, 299 fluoride, 102 focusing, 104, 442 folding, ix, 153, 154, 389 force constants, 248, 252, 410 formamide, 108 Fortran, 199 Fourier, xiii, 6, 7, 8, 34, 65, 155, 189, 278, 409, 421, 422, 428, 439, 459, 473 Fox, 256, 300 free energy, 389 freedom, 91, 154 fulfillment, 122, 252 fullerene, 411 funding, 2, 271, 403 fusion, 10 G GAMESS, 423 gas, 12, 13, 14, 31, 32, 33, 61, 104, 128, 318, 412, 468 gas phase, 318 gases, 213 Gaussian, xiv, 8, 37, 66, 155, 156, 157, 159, 261, 272, 412, 416, 417, 418, 420, 421, 436, 439, 467, 468, 469, 470, 472, 473, 474, 475 Gaussian equation, 66 gel, 294 gene, 404, 408 generalization, 340, 373, 388, 404, 460 generation, 189, 301, 322, 331, 338, 340, 374, 385, 427, 487 genome, 403, 407 genomics, 389, 405, 407 geometrical parameters, 315, 455 Germany, 67, 407 Gibbs, 277, 309, 321 gift, glass, 224 glutamic acid, 79, 80 glycine, ix, 153, 165, 169 gold, 67, 99, 114 gold standard, 114 GPO, 273 grain, 188 grains, 181 grammar rules, 11, 12 graph, 203, 331, 332, 406, 446, 447 gravity, 217, 218, 219, 220, 224 grids, 159, 165, 167, 168, 169, 172, 175, 181, 183, 276, 301, 329, 330, 415, 421, 422, 423, 425 groups, 61, 70, 71, 72, 81, 101, 115, 154, 162, 165, 169, 220, 262, 263, 267, 268, 270, 271, 305, 307, 308, 313, 328, 331, 334, 391 growth, xii, 128, 129, 321, 328, 354, 388, 410 guidance, 468 H halogens, 307 Hamiltonian, 410, 413, 415, 416, 418, 469, 472, 474 handling, viii, 69, 72, 225 hardness, 37, 231 harmonics, vii, xiv, 435, 439, 444 H-bonding, 103 heart, 8, 29 heat, 468 heating, 129, 144, 151 heating rate, 129, 144, 151 height, 377, 481 Heisenberg, 7, helix, 162, 406 heme, 279 Hessian matrix, 410 high resolution, vii, xi, 273, 274, 275, 278, 279, 280, 284, 287, 289, 290, 291, 292, 293, 296, 298, 299, 302, 369 high-level, viii, 70, 97, 100 high-speed, 54 highways, 26 Hilbert, 232, 438 Hilbert space, 232, 438 Hiroshima, 69 histidine, 80 HIV-1, 406 holistic, 36 Holland, 465 HOMO, vii, xi, 259, 260, 262, 263, 265, 266, 267, 268, 269, 270, 312, 317, 429 homogeneity, 160 homogenous, 346, 347, 348, 349, 352, 353, 354, 356, 370 homology, 388 homomorphism, 344 hormone, 400 host, 209, 210, 410, 418, 424 human, 79, 156, 405, 408 Hungary, 303 hybrid, vii, viii, 69, 93, 98, 99, 100, 102, 112, 360, 402, 425, 446, 447, 451, 455, 459, 461 Index hybridization, 313 hydration, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 334 hydrides, 107, 115 hydro, x, 215, 216 hydrocarbon, 32, 219 hydrocarbons, x, 215, 216 hydrogen, xii, 70, 74, 79, 83, 116, 154, 189, 199, 321, 322, 323, 325, 328, 330, 331, 332, 334, 392, 436 hydrogen atoms, 70, 189, 322, 330, 332 hydrogen bonds, xii, 199, 321 hydrogenation, 313, 316 hydrolases, 408 hydrophobic, xiii, 265, 328, 387, 388, 389 hydrophobic interactions, xiii, 387 hydroxide, 32 hydroxyl, 79, 174, 266, 268, 270, 328 hyperbolic, xiv, 477, 480, 484, 485, 488 hypothesis, 357 I IBM, 190, 191, 384 idealization, identification, 159, 165, 169, 216, 408 identity, 423 images, 10, 156, 344, 363, 364, 369, 382, 385, 404 implementation, xii, 216, 277, 299, 301, 321, 322, 382, 414, 419, 452, 486 in vitro, 408 inclusion, x, 42, 98, 100, 101, 193, 194, 198, 199, 202, 204, 205, 206, 208, 209, 210, 211, 212, 213, 354 independence, 271, 367, 371 independent variable, 42, 49, 480 India, 409, 430 Indian, 409 Indiana, 190 indices, 245, 246, 252, 256, 388, 396, 397, 406, 407 indirect measure, 224 indole, 324, 327 induction, 5, 6, 7, industrial, xi, 273, 279, 284, 299 industry, 216, 222, 275 inequality, 55 inert, 418, 468 inertia, 341 infinite, xiv, 34, 52, 63, 286, 435, 438, 439, 441, 445, 446, 448, 451, 452, 459, 460, 461 Information Technology, 273 inherited, 343, 354 inhibition, 400 inhibitors, 407, 408 injection, 285, 286 insertion, xii, 223, 225, 321 insight, 16, 52, 86, 486 instability, 50, 52, 315, 316 499 integration, ix, 34, 35, 62, 127, 130, 146, 197, 204, 275, 414, 419, 420, 421, 422, 423, 426, 438, 447, 448, 449, 468, 474 Intel, 291, 292 interaction, ix, 70, 72, 76, 83, 88, 103, 115, 153, 154, 155, 188, 193, 194, 195, 197, 198, 199, 200, 201, 202, 203, 205, 208, 210, 211, 212, 213, 230, 233, 234, 235, 239, 305, 311, 322, 323, 325, 326, 327, 330, 331, 388, 389, 390, 406, 410, 411, 413, 418, 442 interaction effect, 188 interaction effects, 188 interactions, ix, xii, xiii, 10, 25, 70, 76, 88, 102, 103, 106, 108, 114, 115, 116, 117, 120, 122, 153, 154, 155, 161, 193, 194, 229, 230, 231, 321, 322, 327, 328, 329, 334, 387, 389, 390, 394, 406, 409, 411, 422, 423, 429, 436, 437 interface, 129, 299, 300, 389 interference, 4, 160, 468, 474, 475 Intergovernmental Panel on Climate Change, 491 intermolecular, ix, 103, 193, 194, 198, 204, 212, 229, 322, 411 internal consistency, 489 Internet, 223, 225, 257 interpretation, 64, 270, 353, 366, 485 interstitial, 296, 300, 421 interval, 51, 57, 198, 225, 280, 296, 352, 353, 354, 449 intrinsic, 335, 448 investigative, ion channels, 400 ionic, 262, 305, 418 ionization, vii, xiii, 1, 3, 22, 23, 25, 28, 29, 30, 33, 36, 47, 63, 65, 260, 263, 265, 270, 271, 409, 427, 428 ionization potentials, 1, 3, 22, 23, 29, 30, 33, 36, 47, 63, 65, 260, 263 ions, x, 34, 70, 75, 157, 263, 267, 270, 321, 328, 354, 392 iron, 100, 101, 105, 109, 120, 253 island, 377 isolation, 310, 405 isomerization, 75 isomers, 274, 304, 324 isothermal, 129, 150, 151, 322 isotherms, 275, 294 isotope, 63 isotropic, 158 Italy, 387 iteration, 283, 298, 415 iterative solution, 415 J Jacobian, xiv, 74, 477, 484, 485 Jacobian matrix, xiv, 74, 484 Japan, 69 Japanese, 305 500 Index Jordan, 408 judge, 421 Jung, 384 justification, 2, 222 K kernel, 350, 421, 422, 459 kinase, 407 Kinases, 407 kinetic energy, 83, 84, 85, 98, 412, 413, 414, 415, 416 kinetic equations, 478, 479, 483 kinetic model, 150 kinetic parameters, 145, 146, 151, 152 kinetics, 151, 152, 284, 294, 303, 436, 478, 479, 480, 481 Korean, 95 L labeling, 110 labor, 486 lactams, 311 lactones, 311 Lagrangian, 276 landscapes, 101, 102, 106, 108, 109 language, 43, 147, 157 large-scale, 411, 415, 422 laser, 427 law, 284, 322 laws, vii, 1, 26, 35, 49 lead, ix, xi, 29, 86, 112, 153, 154, 169, 208, 243, 246, 248, 256, 259, 270, 271, 349, 357, 427, 452, 468, 488 learning, 404 lifetime, ligand, 75, 76, 77, 101, 155 ligands, 70, 71, 75, 77, 87, 89, 90, 94, 101 limitation, 4, 56, 78, 321 limitations, xi, xii, 260, 273, 321, 322, 415, 436 linear, ix, xi, xiii, 2, 3, 4, 11, 24, 30, 34, 37, 63, 99, 104, 129, 144, 151, 193, 194, 197, 198, 199, 201, 202, 203, 204, 207, 208, 209, 210, 211, 212, 260, 261, 262, 263, 265, 266, 268, 270, 274, 278, 279, 285, 286, 298, 313, 345, 357, 359, 387, 393, 394, 415, 416, 417, 442, 443, 447, 451, 455, 456, 457, 459, 460, 474 linear model, xi, xiii, 261, 262, 263, 270, 274, 298, 387, 394 linear molecules, 197, 198, 199, 201, 203, 204, 208, 209, 210, 211, 212 linear regression, 260 linear systems, 359, 459 linkage, 72 lipid, 404 liquid chromatography, 301 liquid phase, 275 liquids, x, 213, 215, 216, 220, 224 Lithium, 24 localization, 7, 265, 269 location, ix, 5, 21, 153, 156, 157, 161, 185, 186, 187, 189, 224, 404, 436, 437, 439 locus, 338, 340 London, 66, 256, 385, 430, 434, 491 Los Angeles, 430 low-temperature, 10 luminal, 10, 56 LUMO, 264, 265, 269, 317 lysine, 394, 402 lysozyme, 405 M machine learning, 388, 404 machines, 404, 406 magnetic, 4, 10, 11, 12, 15, 16, 29, 37, 39, 44, 45, 410, 437 magnetic effect, 10, 29 magnetic field, 10, 11 magnetic moment, 44, 45 magnets, 10 mandates, 4, 48 manifold, 485, 488 manifolds, 485 manipulation, 416 manufacturer, 222 manufacturing, 342, 382 mapping, 413, 420 Markov, xiii, 387, 388, 389, 390, 406 Markovian, 406, 407 mass transfer, 216, 275, 294, 299 Massachusetts, 383 materials science, 411 Mathematical Methods, 464 mathematicians, 485, 490 mathematics, xiv, 35, 37, 38, 55, 346, 384, 435, 452 matrix, xiv, 74, 346, 347, 367, 390, 393, 394, 410, 415, 416, 419, 421, 422, 425, 452, 459, 470, 472, 473, 474, 477, 484 Maxwell equations, measurement, 218, 222, 224 measures, 399, 400 media, 330, 335 mediation, 80 melting, 468 membership, 354 memory, 437 Mendeleev, 3, 29 metal ions, 392 metals, 10, 101 metaphor, 30 metastatic, 79 methane, 33 methanol, 155, 328, 331, 332 Index mica, 154 microorganisms, 402 Microsoft, 393, 408 migration, 83 mining, 23 Minnesota, 101 misinterpretation, 43 mobility, x, 193, 194, 207, 212, 276 model system, 70, 74, 76, 80, 470 modeling, x, 9, 46, 229, 300, 405, 411, 421, 436 models, vii, ix, xi, xii, xiii, 74, 153, 154, 155, 160, 169, 174, 181, 182, 185, 187, 188, 189, 222, 262, 270, 273, 274, 278, 284, 296, 298, 321, 322, 324, 327, 338, 365, 367, 368, 369, 372, 387, 389, 393, 394, 395, 396, 398, 400, 403, 436, 489 modules, 408 moieties, 303 mole, 76, 427 molecular dynamics, viii, x, xiv, 69, 71, 78, 93, 154, 194, 199, 210, 212 molecular orbitals, xi, 259, 312, 317, 412, 417 molecular orientation, 198, 199, 207 molecular oxygen, 482 molecular structure, x, 156, 158, 160, 161, 165, 174, 188, 193, 194, 331, 446 molecular weight, 215, 216, 219, 223, 224, 225, 226, 227 molecules, viii, ix, x, xiii, xiv, 31, 32, 33, 34, 36, 37, 50, 62, 70, 72, 80, 97, 99, 100, 106, 107, 109, 114, 115, 120, 122, 155, 189, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 239, 240, 241, 260, 265, 268, 269, 270, 303, 321, 322, 323, 324, 325, 326, 327, 328, 330, 332, 388, 392, 394, 409, 410, 411, 412, 417, 421, 423, 424, 425, 426, 427, 428, 429, 467, 468, 475 molybdenum, 237, 243, 244, 253 momentum, 2, 6, 7, 8, 15, 27, 42, 44, 154, 216, 410, 417, 418, 467, 468, 469, 470, 473, 474, 475 money, 32 monoclonal, 405 monoclonal antibodies, 405 monomers, 31 Monte Carlo, 154, 160, 321, 389 Moon, 39, 66 morphological, xiii, 337, 338, 342, 343, 344, 345, 346, 347, 348, 351, 352, 353, 354, 355, 356, 359, 361, 363, 364, 365, 366, 367, 368, 369, 372, 373, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385 morphology, vii, xii, xiii, 337, 343, 344, 345, 346, 348, 351, 352, 354, 360, 363, 364, 365, 369, 371, 372, 382, 383, 384 motion, viii, x, xiv, 9, 11, 38, 39, 69, 71, 78, 82, 83, 84, 85, 86, 89, 90, 93, 94, 194, 199, 204, 343, 467, 468, 470, 471, 473, 474, 475, 477, 479, 480, 488 motivation, 419 mouse, 408 movement, 274, 276, 346, 352, 354, 376, 389 501 MRA, 279 multidimensional, 301, 470 multiples, 42, 57 multiplication, 436 multiplicity, 28 mutants, 405, 406, 407 N NaCl, 31, 32, 240, 241, 242 National Academy of Sciences, 67 natural, 8, 9, 25, 35, 188, 260, 263, 269, 274, 390, 417, 477, 484 natural evolution, 477 neck, 383 neglect, 245 neighbourhoods, 280 Netherlands, 65, 97, 122, 430 network, 154, 389, 393, 397, 399, 400 network density, 400 neutrons, 47 New York, 65, 66, 122, 191, 213, 227, 319, 320, 384, 408, 430, 431, 462, 464, 465, 475 Newton, 78, 283, 296, 460 Newton iteration, 296 Newtonian, 39, 44, 224, 321 Nielsen, 190 NIST, 262, 433, 434 nitrogen, xiv, 325, 477, 478, 481, 482, 483, 488 nitrogen oxides, xiv, 477, 478, 481, 482, 483, 488 nodes, 99, 276, 277, 295, 393, 397, 399, 400 noise, 64, 188 non-enzymatic, 393 nonlinear, xiii, 152, 278, 300, 301, 302, 387, 388, 416, 429, 457 non-native, 406 non-uniform, 276, 277 normal, 25, 34, 64, 74, 82, 84, 88, 89, 338, 340 normalization, 6, 7, 417, 419, 472 normalization constant, 417 nuclear, 12, 22, 23, 24, 27, 63, 74, 102, 322, 400, 410, 412, 437, 444, 445, 448, 456, 457, 458, 459, 461 nuclear charge, 22, 23, 24, 27, 63 nuclear magnetic resonance, 102, 306, 319, 410, 437 nucleation, 129 nuclei, 47, 78, 129, 414, 420, 437, 444, 459 nucleic acid, 390 nucleotides, 390 nucleus, xiv, 10, 11, 12, 29, 35, 36, 61, 62, 63, 102, 415, 418, 435, 436, 437 numerical analysis, 460 O observations, 188, 478 octane, 99 502 Index oil, x, 215, 216, 219, 225 oils, x, 215, 216, 223, 224, 225, 226, 227 old-fashioned, viii, one dimension, 276 on-line, 276 operator, 34, 275, 279, 280, 372, 374, 414, 415, 461, 469 Opioid, 407 optical, optics, optimization, 70, 74, 185, 187, 189, 261, 276, 322, 325, 326, 327, 383, 400 oral, 79 orbit, 10, 11, 44, 52, 54, 55, 56, 58, 60, 62, 64, 391, 394 ordinary differential equations, xi, xiv, 273, 275, 468, 474, 477, 488 organ, 70, 71, 75, 77, 85, 94, 101 organic, x, 70, 99, 155, 189, 259, 260, 271 organic compounds, 260 organometallic, 70, 71, 75, 77, 85, 94, 101 orientation, 194, 197, 198, 199, 202, 323, 324, 332, 341, 354, 355, 373, 382 oscillation, 6, 83, 84, 88, 282, 298, 478 oscillations, 205, 478 oscillator, 410, 472, 473 oxidation, 101, 315, 318 oxidative, 70, 75, 77, 86 oxide, 315, 316, 317, 318 oxides, vii, xii, 303, 305, 315, 316, 317, 483 oxygen, 33, 34, 81, 83, 154, 169, 185, 263, 265, 266, 267, 269, 270, 323, 328, 332, 478, 480, 482, 488 ozone, xiv, 102, 477, 478, 480, 482, 483, 488, 489, 491 P packaging, 406 paper, 2, 3, 8, 9, 10, 22, 29, 35, 37, 38, 39, 40, 47, 52, 62, 65, 100, 106, 108, 109, 147, 265, 271, 291, 303, 342, 345, 383, 442, 468, 472, 474 parabolic, 275 paradox, 38 paradoxical, 43 parallel computation, 355 parallel implementation, 414 parallelism, 355, 371 parameter, xi, 2, 3, 27, 30, 34, 111, 112, 130, 146, 156, 158, 194, 200, 201, 205, 208, 218, 221, 222, 224, 225, 231, 233, 236, 241, 242, 244, 245, 246, 253, 254, 256, 273, 275, 277, 284, 328, 338, 340, 347, 348, 351, 353, 367, 370, 373, 396, 438, 440, 468, 472 partial differential equations, xi, 273, 275, 276, 277, 278, 279, 281, 282, 291, 293, 296, 298, 299, 300, 301, 302 particle density, 414 particles, viii, ix, x, 1, 10, 41, 47, 55, 129, 193, 194, 410 partition, 72, 86, 91, 274 pathogens, 408 pathways, 102, 410, 411 PCM, xii, 155, 261, 263, 265, 266, 321 Peclet number, xi, 274, 286, 287, 293, 296, 298, 300 pedagogical, 63 penalty, 34, 276 peptide, ix, 154, 160, 162, 165, 169, 172, 179, 180, 181, 182, 183, 185, 186, 188, 411 peptide chain, 160 peptides, 160, 169, 189 perception, 134 performance, vii, viii, 97, 98, 100, 101, 106, 108, 111, 112, 114, 115, 116, 117, 119, 120, 122, 275, 277, 285, 287, 291, 293, 294, 298, 301, 343, 421, 424, 425, 429 periodic, 160, 417 Periodic Table, 3, 36, 63, 65 periodicity, vii, 1, 3, 26, 29, 30, 36 permeability, 37, 39 permit, 224, 225, 342, 343, 351, 354, 355, 361, 362, 363, 365, 369, 382 permittivity, 37, 39 personal, 291, 292 Perth, 273 perturbation, 50, 55, 82, 411 perturbation theory, 411 perturbations, 10 petroleum, x, 215, 216, 217, 219, 221, 222, 223, 224, 225, 226, 227, 300 petroleum products, 224 phage, 394, 402, 408 pharmaceutical, 79, 411 phase space, 467, 468, 473, 474, 480 phenol, 209, 261, 262, 265, 267, 268, 270 Philadelphia, 227, 433 phosphorous, 317 photochemical, 477, 479 photoelectron spectroscopy, 410 photoemission, 427 photoionization, 427 photolysis, 481 photon, 4, 34, 35, 64, 65 photons, 38, 61, 62, 64, 65 phylogeny, 405 physical properties, 220, 410 physical sciences, 452 physicists, 2, 62 physicochemical, 411, 416 physicochemical properties, 411, 416 physics, vii, xiv, 1, 2, 9, 11, 34, 37, 56, 98, 224, 233, 328, 407, 413, 422, 435, 438, 439, 484, 490 planar, 129, 310, 313 plane waves, 475 planning, 216 plasma, 33, 50, 64 platforms, 355, 382 Index platinum, 75 plausibility, 428 play, viii, 4, 30, 57, 69, 75, 81, 94, 418, 477, 481 Poisson, 421 Poisson equation, 421 polar coordinates, 420 polarization, 105, 109, 314, 322 police, 33 pollution, 491 polygons, 357, 360 polynomial, xi, 130, 230, 231, 273, 296, 338, 421, 439, 459, 480, 481, 486, 490 polynomial functions, 130 polynomials, 278, 293, 439, 448, 459 pond, 455 poor, 119, 122, 260, 262, 270, 427 poor performance, 119, 122 population, 11, 25, 32, 63, 270, 278, 301, 302, 330, 406 porosity, 300 ports, 274 positive feedback, 23 positron, 57 potential energy, vii, ix, x, xiii, 70, 84, 85, 86, 154, 161, 193, 194, 198, 200, 201, 202, 203, 210, 212, 229, 230, 231, 234, 236, 237, 238, 240, 242, 243, 244, 246, 249, 250, 251, 253, 254, 255, 256, 270, 322, 409, 411, 412, 423, 424, 429 power, xi, 45, 46, 49, 70, 273, 275, 298, 393, 436, 473 powers, 390, 455, 456, 457, 469 prediction, xi, xiii, 216, 217, 218, 274, 288, 289, 293, 298, 299, 387, 388, 389, 400, 402, 405, 406, 409, 411 preference, 62 present value, 455 pressure, x, 63, 75, 215, 216, 218, 300, 478, 479 primitives, xiii, 337, 338, 342, 343, 346, 352, 354, 359, 363, 369, 382, 417 prior knowledge, 299 probability, x, 1, 7, 8, 35, 84, 90, 171, 172, 194, 199, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 395, 396, 400, 401, 402, 403, 468, 474, 475 probability distribution, 8, 474 probe, xiii, 338 process control, xi, 273 production, 25, 328, 478, 482 profits, 216, 222 program, x, 26, 49, 77, 109, 122, 129, 147, 157, 158, 160, 167, 181, 189, 199, 210, 215, 216, 223, 225, 227, 322, 331, 399, 403, 423, 425, 486 programming, 147, 157 proliferation, 411 promote, 71, 94 propagation, 4, 5, 34, 39, 40, 47, 278, 286, 296, 390, 468, 472, 473 property, viii, ix, 34, 41, 69, 78, 102, 113, 115, 117, 118, 159, 193, 220, 280, 339, 428, 436, 447, 449, 483 503 proportionality, 64 proposition, 31 protein, vii, ix, xiii, 99, 153, 154, 155, 159, 160, 162, 169, 173, 181, 185, 188, 189, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 399, 403, 404, 405, 406, 407, 408 protein folding, 153, 154 protein function, 388, 389, 404, 408 protein sequence, 154, 189, 388, 404, 405, 406 protein structure, xiii, 99, 154, 155, 160, 188, 189, 387, 389, 390, 394, 404, 405, 406, 407 proteins, xiii, 155, 158, 189, 190, 191,387, 388, 389, 393, 394, 396, 399, 402, 403, 404, 405, 406, 407 protocol, 305, 393, 457, 458 protons, 24, 61, 62 prototype, 9, 75, 94 proxy, 42 pseudo, 373, 377, 404, 405 PTO, 363 pulse, 5, 7, 8, 38, 40, 285, 286 pulses, pyrrole, 316, 317 Q QED, 38 QSAR, 388, 389, 393, 397, 398, 399, 400, 403, 405, 406, 407 quadratic curve, 339 quadrupole, 57, 58, 60, 410 quantization, 61 quantum, vii, viii, xiii, xiv, 1, 2, 3, 11, 15, 27, 28, 52, 62, 63, 65, 69, 84, 86, 155, 189, 259, 260, 334, 409, 410, 413, 415, 417, 423, 424, 428, 435, 436, 438, 439, 442, 462, 464, 467, 468, 472, 473, 474, 475 quantum chemistry, vii, xiii, xiv, 409, 410, 413, 415, 417, 423, 428, 435, 436, 462 quantum mechanics, 1, 438, 439, 467, 468 quantum state, 15 quantum theory, 65, 189 quasiclassical, 468, 474 query, 388 question mark, 12 questioning, 39 R radiation, 4, 8, 9, 35, 38, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 478, 479 radical, 479, 488 radio, 360 radius, 4, 11, 49, 50, 51, 54, 55, 58, 59, 60, 61, 62, 159, 195, 201, 202, 339, 340, 341, 362, 365, 366, 367, 372, 373, 374, 375, 376, 378, 379 random, 188, 332, 393, 394, 399, 472 random configuration, 332 504 Index range, xi, 49, 54, 102, 103, 106, 107, 117, 130, 134, 198, 205, 217, 219, 220, 222, 223, 226, 231, 232, 233, 235, 236, 237, 238, 240, 245, 246, 247, 249, 250, 251, 253, 254, 255, 256, 274, 275, 279, 284, 298, 318, 334, 340, 370, 371, 373, 375, 382, 400, 411, 415, 423, 424, 426, 459 reactant, 101, 119 reactants, 76, 101, 119 reaction mechanism, 79, 94, 260 reaction rate, 127, 128, 488, 490 reactivity, 75, 76, 82, 85, 86, 89, 90, 92, 94, 103, 263, 269, 270, 271 reading, 406 real numbers, 65 real time, 369 reality, 43, 363 recall, 442, 481 recalling, 404 receptors, 400, 405 recognition, 407 reconcile, reconstruction, 25, 342, 383 recovery, 39, 394 recursion, 377, 422 redevelopment, 43, 47 redistribution, 32, 276 reduction, ix, 102, 111, 119, 153, 162, 222, 371, 416, 443, 478, 483 reference system, 199, 413 refining, reflection, 222 regression, 152, 260, 263 regression analysis, 260 regression method, 152 regressions, 3, 263 regular, 162, 185, 338 relationship, 7, 42, 53, 64, 104, 115, 119, 152, 216, 217, 233, 260, 284, 325, 334, 389, 392, 405 relationships, vii, xiii, 1, 8, 41, 42, 43, 227, 237, 245, 260, 387, 388, 390, 405 relaxation, 48, 210, 325 relevance, 412, 452, 477 reliability, 101, 221, 222, 424 repressor, 407 reproduction, 180, 478 research, vii, ix, xi, xiii, 65, 99, 153, 154, 189, 274, 275, 363, 389, 393, 394, 403, 407, 409, 427, 436 Research and Development, 384 researchers, ix, xiv, 35, 39, 127, 288, 388, 435, 439, 477 residues, 71, 78, 80, 81, 82, 83, 94, 154, 160, 162, 163, 165, 166, 169, 172, 173, 174, 175, 179, 180, 181, 185, 188, 189 resistance, 299 resolution, vii, x, xi, 22, 154, 159, 188, 189, 193, 194, 273, 274, 275, 278, 279, 280, 284, 287, 289, 290, 291, 292, 293, 296, 298, 299, 301, 302, 321, 357, 369, 415, 423, 474 resources, 32, 410 retardation, 56 returns, 65, 369, 374, 377 revenue, 222 ribose, 80, 81, 83 rigidity, x, 193, 486 rings, 2, 3, 4, 9, 10, 11, 12, 29, 33, 35, 36, 61, 311 RNA, 102, 389, 404 robot navigation, xii, 337, 338, 341 robotics, 338 room temperature, 75 rotation transformation, 357 rotations, 318, 346, 347, 373 routines, 216, 422 RTS, 118 rubidium, 237, 243, 244, 253 S sacrifice, 35 sample, 94, 224, 381, 437 sampling, 406 sand, 197 satellite, scalability, 415 scalar, 4, 7, 22, 37 scaling, vii, 1, 23, 25, 26, 34, 35, 47, 49, 58, 60, 62, 63, 99, 105, 156, 196, 200, 205, 208, 231, 238, 239, 246, 278, 299 scaling law, vii, 1, 26, 35 scattering, 439 Schrödinger equation, 260 scientists, 36, 216, 436 SCN, 303, 307, 308, 313 scores, 393 search, xiii, 156, 244, 322, 356, 357, 387, 388, 394, 402, 468 searching, 399 security, 341, 377 seed, segmentation, 371 selectivity, 75 Self, 437 semiconductor, 411 semi-empirical methods, 410 sensitivity, 62 separation, xi, xiv, 45, 62, 120, 274, 275, 276, 286, 294, 296, 298, 299, 300, 301, 360, 362, 435 sequencing, 343, 346 series, xiii, xiv, 8, 28, 29, 30, 45, 63, 66, 100, 101, 107, 130, 157, 213, 224, 256, 274, 282, 296, 339, 369, 384, 394, 400, 402, 409, 421, 425, 435, 438, 439, 441, 442, 443, 445, 446, 448, 451, 452, 454, 456, 459, 460, 462 set theory, 372 Shanghai, 127 shape, xii, 4, 7, 8, 129, 179, 201, 231, 265, 267, 269, 270, 286, 290, 312, 317, 331, 337, 341, 342, 372, Index 373, 374, 375, 376, 377, 378, 379, 380, 381, 383, 417 shear, 224 shear rates, 224 Shell, 157 shock, 277, 301 short-range, 391, 394, 422 short-term, 390 sign, 8, 9, 28, 41, 42, 51, 57, 61, 165, 288, 481 signals, 41 significance level, 394 silica, 294 silicon, 234, 235, 328 similarity, 8, 23, 26, 30, 62, 157, 242, 252, 388, 404, 408 simulation, vii, viii, ix, x, xi, 69, 71, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 94, 154, 155, 193, 194, 199, 205, 207, 208, 209, 210, 211, 212, 213, 273, 293, 294, 299, 300, 321, 324, 332 simulations, 80, 85, 86, 89, 94, 154, 287, 291, 296, 474 sine, 379 Singapore, 229, 430, 431 singular, 239, 250, 373 sites, 154, 265, 323, 408 Slater determinants, 413 Slater Type Orbitals, 440 smoothing, ix, 153, 155, 156, 158, 162, 165, 188, 189, 276 smoothness, 250 Sobolev space, 438 sodium, 31 software, x, 134, 146, 147, 229, 230, 277, 392, 393 solar, 478 solid phase, 275, 299 solid-state, ix, 11, 127, 128, 129, 145, 146, 147, 150, 151, 152, 229 solubility, 328 solutions, xi, xii, 4, 8, 9, 41, 42, 51, 52, 54, 55, 57, 58, 59, 60, 61, 70, 274, 275, 278, 284, 288, 289, 290, 291, 298, 337, 363, 415, 436, 468, 480, 484, 487, 488 solvation, 107, 321, 328, 332, 334, 406 solvent, vii, x, xi, xii, 80, 81, 82, 83, 84, 85, 154, 155, 193, 259, 261, 265, 268, 321, 322, 323, 324, 325, 326, 328, 329, 330, 332, 335, 406 solvent molecules, 321, 326 sounds, 222 Spain, 97, 193, 215, 337, 387, 403 spatial, 4, 5, 8, 35, 275, 276, 277, 279, 282, 284, 287, 291, 296, 298, 330, 355, 360, 363, 388, 410, 422 special relativity, Special Relativity Theory (SRT), vii, viii, 1, 2, 9, 22, 34, 35, 38, 39, 40, 41, 42, 43, 59, 66 specialisation, 343, 382 species, xii, 303, 314, 318, 330, 334, 407, 412, 426, 428, 478, 479, 480 specific gravity, 217, 218, 219, 220 specific heat, 91 505 specificity, 160 spectroscopic methods, 410 spectroscopy, 2, 9, 29, 52, 62, 63, 65, 306, 410 spectrum, 9, 62, 64, 473, 478 speed, vii, 1, 4, 5, 6, 35, 37, 39, 40, 41, 42, 43, 50, 55, 56, 59, 60, 231, 256, 341, 437, 460 speed limit, 59 speed of light, 35 spheres, xii, 154, 164, 182, 186, 321, 421, 487, 488 spin, 2, 10, 11, 28, 35, 100, 101, 104, 105, 120, 410, 411, 436 stability, vii, ix, xi, xii, 32, 33, 52, 153, 154, 274, 282, 283, 299, 301, 303, 307, 310, 315, 328, 405, 406, 407, 410, 411, 423, 424, 441, 478, 480, 483 stabilization, xii, 208, 303, 326, 331, 332, 334 stabilize, 307, 308 standard deviation, 82, 90, 92, 93, 145 statistical analysis, 322 statistical mechanics, 464 statistics, 468, 474, 475 STD, 395, 396, 398 steady state, xi, 274, 284, 296, 297, 298, 299, 301 steric, 70, 71, 72, 73, 75, 76, 77, 82, 83, 85, 87, 90, 94, 318 stimulus, 410 STO, 101, 417, 440, 441 stochastic, 390, 394, 406, 407 strain, 310 strategies, 189, 403, 405 stratosphere, 479, 481, 482, 488 strength, 22, 81, 199, 201, 205, 211, 212, 330, 472 streptococci, 404 stress, 224, 486 stretching, 230, 242, 245, 251, 252, 255, 256, 410 strong interaction, 270 STRUCTURE, 193, 409 structuring, 342, 344, 345, 348, 349, 350, 351, 352, 353, 354, 355, 356, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 382, 385 students, 39 substances, 328 substitution, viii, 97, 101, 102, 107, 230 substrates, 79 sulfur, 188 Sun, 248, 257, 476 superconductor, 10, 61, 411 superiority, 428 superposition, 155, 475 supervision, 403 surface layer, 411 swarm, 468, 473, 474, 475 switching, 231, 238, 239, 274, 284, 295, 296, 297, 298, 300 symbolic, xiv, 435 symbols, 390, 394, 397 symmetry, xiv, 53, 260, 261, 312, 313, 317, 410, 435 synthesis, xii, 303, 305, 307, 407 506 Index systems, viii, ix, x, xi, xii, xiii, 9, 39, 44, 52, 69, 70, 71, 76, 77, 92, 102, 104, 108, 120, 122, 189, 193, 197, 198, 215, 216, 229, 260, 273, 276, 299, 300, 302, 321, 325, 334, 338, 380, 406, 409, 410, 411, 415, 417, 419, 421, 424, 427, 429, 436, 457, 459, 468, 469, 470, 474, 486 T targets, 71, 75, 78, 400 Taylor expansion, 468 technology, 10, 275, 467 temperature, vii, ix, x, 61, 80, 84, 90, 92, 127, 129, 130, 134, 135, 138, 144, 145, 150, 151, 152, 161, 193, 194, 199, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 220, 222, 224, 305, 318, 478, 481 temperature dependence, 481 temporal, xii, 5, 275, 277, 292, 337, 342, 355, 357, 360, 362, 367, 382 Texas, 465 textbooks, 411, 436, 448 textile, 341 TGA, 151 theory, vii, x, xiv, 1, 7, 9, 22, 23, 25, 34, 35, 39, 43, 44, 47, 71, 78, 80, 86, 103, 122, 124, 213, 215, 216, 222, 223, 224, 227, 260, 271, 308, 311, 312, 313, 314, 317, 318, 321, 328, 389, 390, 400, 410, 411, 412, 413, 414, 415, 420, 427, 430, 446, 477, 480 therapy, 79, 408 thermal analysis, 151 thermal energy, 85 thermodynamic, xii, 303, 307, 329, 406 thermodynamic stability, 307 thermodynamics, vii, 63, 307, 322 thermogravimetric, 150, 151 thinking, 4, 6, 10, 30, 35, 36, 37 three-dimensional, 30, 156, 323, 411 threshold, 443 time, x, xi, xii, xiii, 2, 3, 4, 5, 6, 7, 8, 16, 17, 34, 37, 40, 41, 66, 70, 73, 76, 78, 83, 84, 86, 87, 93, 103, 112, 117, 120, 127, 154, 158, 161, 199, 205, 206, 208, 209, 210, 211, 212, 213, 224, 229, 260, 274, 275, 276, 277, 280, 282, 283, 285, 287, 291, 292, 296, 298, 299, 300, 301, 302, 303, 307, 340, 359, 360, 366, 367, 368, 369, 374, 375, 380, 381, 387, 389, 390, 393, 409, 410, 417, 419, 436, 439, 442, 445, 462, 468, 469, 470, 472, 473, 474, 475, 478, 480, 486, 487, 489 time consuming, 439, 486 TIPS, 324 tolerance, 338, 339, 486, 487 toluene, 75 topological, 340, 344, 345, 382, 391, 394, 399, 400 topology, 37, 307, 340, 345, 399, 406 torque, 43, 44, 45, 46, 49, 51, 52, 57, 60, 61, 199 total energy, 4, 5, 52, 64, 72, 73, 74, 417, 424, 426, 427, 429, 472 tracking, 277, 301 trade-off, 410 tradition, 36 training, 393, 394, 403 trajectory, 156, 199, 204, 207, 208, 209, 210, 213, 341, 342, 343, 346, 351, 352, 353, 354, 356, 359, 364, 367, 369, 370, 371, 372, 373, 376, 380, 382, 383, 467, 468, 470, 472, 473, 474, 475 trans, 75, 171, 175, 304, 356, 359, 421 transfer, 8, 70, 84, 88, 216 transformation, 276, 278, 285, 304, 307, 309, 310, 318, 339, 346, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 395, 452, 459, 460 transformation matrix, 347 transformations, 309, 346, 347, 348, 356, 370, 373, 385, 439 transition, xii, 65, 70, 76, 77, 84, 101, 102, 119, 303, 307, 318, 411 transitions, 62, 64, 276, 410 translation, 318, 330, 349, 354, 446 translational, 199 transmembrane, 406 transparent, 224 transport, x, 215, 216, 284, 411, 479 transport phenomena, 479 transpose, 484 travel, 5, 6, 41 traveling waves, trees, 30 trend, 116, 117, 234, 307 trial, 413 tripeptide, 189, 391 tritium, 63 Trp, 172, 177, 179, 181, 185 tumor, 79 tunneling, 468 twins, 38 two-dimensional, 470 U ubiquitous, uncertainty, xiv, 226, 467, 475 Uncertainty Principle, 7, 8, 230 unification, 271 uniform, 4, 34, 98, 104, 105, 197, 277, 415, 421 United States, 400 universal gas constant, 128 uridine, 80 Utah, 191 V vacuum, 327 valence, 30, 304, 322, 412, 418, 423 Index Valencia, 403 validation, 102, 105, 107, 115, 382, 394, 450 validity, 225, 240, 241, 246, 249, 270, 378, 449 values, xi, 3, 35, 47, 82, 88, 89, 102, 104, 106, 107, 112, 113, 114, 115, 116, 117, 119, 120, 130, 134, 137, 146, 155, 158, 159, 160, 161, 165, 169, 172, 174, 180, 181, 185, 188, 197, 198, 200, 201, 203, 205, 207, 211, 212, 217, 220, 221, 223, 225, 226, 259, 260, 261, 262, 263, 266, 267, 268, 270, 271, 283, 307, 308, 309, 312, 313, 316, 317, 318, 322, 325, 330, 331, 332, 333, 334, 335, 346, 347, 351, 352, 354, 359, 360, 370, 371, 373, 390, 393, 395, 396, 397, 398, 410, 422, 423, 426, 427, 428, 429, 443, 445, 446, 448, 449, 455, 456, 457, 459, 468, 469, 470, 472, 473, 475, 478, 479, 480, 481, 484, 485, 488 van der Waals, 210, 230, 233, 239, 331, 334, 388, 389, 390, 394, 395, 397, 399, 406, 407 variability, 28, 165, 330 variable, xiv, 7, 25, 42, 49, 146, 224, 282, 328, 341, 346, 347, 351, 352, 353, 355, 372, 373, 375, 382, 393, 395, 396, 399, 402, 413, 435, 438, 439, 440, 447 variables, 22, 35, 224, 346, 382, 393, 395, 396, 397, 398, 399, 438, 485, 486 variance, 90, 91 variation, 4, 5, 198, 201, 203, 212, 222, 270, 276, 307, 355, 365, 367, 368, 413, 419 vector, 4, 5, 34, 37, 38, 39, 43, 47, 59, 156, 322, 338, 348, 349, 350, 356, 357, 359, 361, 369, 370, 374, 388, 390, 404, 406, 436, 437, 438, 439, 457, 472, 484 velocity, 37, 38, 39, 52, 60, 61, 66, 78, 199, 204, 296, 300 vibration, 390, 410 virus, 402 viscosity, x, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 278 visible, 55, 413 507 vision, 25, 156, 369 visual images, 10 visualization, 12, 16 vocabulary, 10, 11, 12 W water, 31, 32, 34, 72, 79, 80, 81, 82, 83, 84, 85, 108, 155, 261, 322, 323, 324, 325, 326, 327, 328, 330, 332, 392 wave number, 4, 6, 7, 8, 105 wave packet, 4, 8, 39 wave propagation, xi, 273, 298 wavelengths, 63 wavelet, vii, xi, 273, 274, 275, 278, 279, 280, 287, 288, 289, 290, 293, 296, 298, 299, 300, 301, 302 wavelets, 4, 277, 278, 287, 300, 301, 302, 414 wavepacket, xiv, 467, 468, 469, 470, 474, 475 weak interaction, 102, 103, 106, 114, 115, 116, 120, 122, 411 Weak Interactions, 115 weakness, 388, 423 wealth, 2, 32, 427 web, 147, 394 workers, 418, 419 worry, 290 X X-ray analysis, 306 Y yeast, 406, 407 yield, 210, 305, 307, 325 ... more global picture of the orbits than that provided by the local analysis consisting in analyzing the nature of the critical points In: Handbook of Computational Chemistry Research Editors: C.T... functions are indispensable in computational chemistry as a result of their ease of execution With over eight decades of interatomic potential functions since the days of Lennard-Jones, numerous.. .HANDBOOK OF COMPUTATIONAL CHEMISTRY RESEARCH No part of this digital document may be reproduced, stored in a retrieval system