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computational chemistry vol 19 Reviews in computational chemistry vol 19 lipkowitz boyd Reviews in computational chemistry vol 19 lipkowitz boyd Reviews in computational chemistry vol 19 lipkowitz boyd Reviews in computational chemistry vol 19 lipkowitz boyd Reviews in computational chemistry vol 19 lipkowitz boyd Reviews in computational chemistry vol 19 lipkowitz boyd
Reviews in Computational Chemistry Volume 19 Reviews in Computational Chemistry Volume 19 Edited by Kenny B Lipkowitz, Raima Larter, and Thomas R Cundari Editor Emeritus Donald B Boyd Kenny B Lipkowitz Department of Chemistry Ladd Hall 104 North Dakota State University Fargo, North Dakota 58105-5516, USA kenny.lipkowitz@chem.ndsu.nodak.edu Raima Larter Division of Chemistry National Science Foundation 4201 Wilson Boulevard Arlington, Virginia 22230, USA rlarter@nsf.gov Thomas R Cundari Department of Chemistry University of North Texas Box 305070, Denton, Texas 76203-5070, USA tomc@unt.edu Donald B Boyd Department of Chemistry Indiana University–Purdue University at Indianapolis 402 North Blackford Street Indianapolis, Indiana 46202-3274, USA boyd@chem.iupui.edu Copyright # 2003 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail: permreq@wiley.com Limit of Liability/Disclaimer of Warranty: While the publisher and authors have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services please contact our Customer Care Department within the U.S at 877-762-2974, outside the U.S at 317-572-3993 or fax 317-572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print, however, may not be available in electronic format ISBN 0-471-23585-7 ISSN 1069-3599 Printed in the United States of America 10 Preface Ed Koch, former mayor of New York City, was fond of saying ‘‘How am I doing?’’ That’s a question we asked ourselves recently We have published over 100 chapters in this book series to date, and although we are confident that the material has been used heavily by the computational chemistry community at large, we have not been able to address Koch’s question in a quantifiable way (other than from sales records) We can now answer the question of how we’re doing; we’re doing very well One indicator that can be used to assess the value of a book or journal is the impact factor of the Institute for Scientific Information Inc (ISI) In a SciBytes listing, journals were ranked by impact (http://in-cites.com/research/ 2002/august 19 2002-2.html) Three rankings were presented; they are tabulated below: Rank 10 2001 Chemical Reviews Accounts of Chemical Research Chemical Society Reviews Angewandte Chemie International Edition Journal of the American Chemical Society Topics in Current Chemistry Chemistry—a European Journal Journal of Physical and Chemical Reference Data Journal of Combinatorial Chemistry Reviews in Computational Chemistry 1997–2001 Chemical Reviews Accounts of Chemical Research Chemical Society Reviews Journal of the American Chemical Society Angewandte Chemie International Edition in English Topics in Current Chemistry Chemische BerichteRecueil Chemistry—a European Journal Reviews in Computational Chemistry Chemical Research in Toxicology 1981–2001 Chemical Reviews Accounts of Chemical Research Chemical Society Reviews Journal of the American Chemical Society Journal of Computational Chemistry Topics in Current Chemistry Chemistry International Journal of the Chemical Society, Chemical Communications Marine Chemistry Reviews of Chemical Intermediates v vi Preface In this table the citation impact of journals in a given field (in this case listed by Sci-Bytes as ‘‘general’’) are compared over three different time spans The leftmost column ranks journals according to their ‘‘impact factors,’’ as enumerated in the current edition of the ISI Journal Citation Reports The 2001 impact factor was calculated by taking the number of all current citations to source items published in a journal over the previous years and dividing it by the number of articles published in the journal during the same period This is simply a ratio between citations and citable items published The next two columns show impact over longer timespans of and 21 years These results were based on figures from the ISI Journal Performance Indicators To generate the citations-per-paper impact scores, the total number of citations to a journal’s published papers were divided by the total number of papers published in that particular journal Reviews in Computational Chemistry is ranked highly in the category of ‘‘general’’ journals, now making it among the top 10 We are pleased that the quality of the chapters has been high and that the community values these chapters enough to cite them as frequently as they have been Our goal over the years has been to provide tutorial-like reviews covering all aspects of computational chemistry In this, our nineteenth volume, we present four chapters covering a range of topics that have as a theme macroscopic modeling In Chapter 1, Professors Robert Q Topper and David L Freeman provide a short tutorial on Monte Carlo simulation techniques with their students Denise Bergin and Keirnan R LaMarche The emphasis of this tutorial is on calculating thermodynamic properties of systems at the atomic level They begin their tutorial with the Metropolis method, the generalized Metropolis algorithm, and the Barker–Watts algorithm for molecular rotations They provide insights along the way about random-number generation and practical matters concerning equilibration, error estimation, and heat capacities Then they introduce the problem we all encounter: the inability to reach every possible state on the potential surface from every possible initial state This, in turn, leads to quasiergodicity Quasiergodic systems are insidious in that they usually appear to be ergodic The authors point out this pitfall and in the next section of their tutorial describe methods available for overcoming quasiergodicity Magnifying step sizes in a Metropolis walk (mag-walking), using the Shew–Mills subspace sampling method or the related ‘‘jump between wells’’ method of Still, can help overcome the ergodic problem, as can implementing umbrella sampling strategies and histogram methods Another class of generally applicable Monte Carlo (MC) methods used to address quasiergodicity allows Metropolis walkers at different temperatures to exchange configurations with one another J-walking, parallel tempering, and the use of Tsallis statistics are introduced and described The authors end their tutorial by describing another class of methods used to remove sampling difficulties that is based on multicanonical ensembles Throughout the chapter the strengths and weaknesses of methods used for Preface vii Monte Carlo simulations are delineated and pitfalls to avoid them are highlighted In Chapter 2, Professors David E Smith and Tony Haymet provide a tutorial on computing hydrophobicity The authors promulgate the opinion that one must seek to explain the set of verifiable experimental observations to fully understand hydrophobicity Accordingly, rather than covering everything on this topic that has appeared in the literature, the authors treat only methods for which full details have been published They begin their tutorial by explaining the basic simulation methods needed and point out, surprisingly, that hydrophobicity is relatively insensitive to the water potential used An emphasis is placed on particle insertion methods, free-energy perturbation (FEP), and thermodynamic integration (TI) strategies The authors explain that entropies of hydration and association are considered to be one of the primary signatures of hydrophobicity Hydrophobic hydration is described in the next section of their review Details about hydration structure, hydration free energy, entropy, and heat capacity are brought into sharp focus The chapter ends with a description of computational techniques used to compute hydrophobic interactions, specifically, solvent-induced interactions between nonpolar solutes in water A clear, concise expose´ describing what is right and what is not right in the extant literature is presented in this chapter In Chapter 3, Lipeng Sun and Bill Hase review techniques for carrying out classical trajectory simulations within the Born–Oppenheimer (BO) approximation They begin their chapter with a review of the basic theory in which equations of motion for the atoms involved in a chemical reaction are defined on a potential energy surface Traditionally, this surface has been defined analytically, but with the increasing speed and computational power now available, it has become possible to use electronic structure theory directly in carrying out classical trajectory simulations with the equations of motion Sun and Hase review the theoretical basis of the BO direct dynamics approach This is followed by a discussion of integration techniques for the classical equations of motion and of algorithms for choosing initial conditions for ensembles of trajectories They continue with a critique of the adequacy of classical mechanics in describing chemical processes that are, in reality, quantum-mechanical in nature The importance of possible quantum effects is discussed They conclude their chapter by giving several examples of application of the BO direct dynamics method of actual problems: cyclopropane stereomutation, Cl À þ CH3Cl barrier dynamics, OH À þ CH3F exit channel dynamics, and, finally, protonated glycine surface-induced dissociation The final chapter thoroughly discusses the theoretical underpinnings of the widely used Poisson–Boltzmann (PB) equation During the 1990s there was a dramatic increase in the use of the PB equation that can be attributed to advances in computers, needs in biological chemistry, and a renewed interest in colloidal systems Many computational chemists use the PB equation routinely in their research But in spite of this usage, they are often completely viii Preface unaware of the theoretical underpinnings associated with the method Dr Gene Lamm presents us with a complete tutorial on the PB equation that covers and even extends the basic theoretical background This chapter is not meant for the novice molecular modeler as are most chapters in this series, but instead it is directed toward the seasoned professional The tutorial is divided into four parts, the first of which is a brief history of the PB equation and its derivation In the second part the PB equation is applied to several model systems for which exact or approximate analytical solutions can be found The author brings together in this, the largest part of the chapter, many examples for planar and curved systems scattered throughout the literature to demonstrate for the reader a coherence of purpose and application within the field In the third part of the tutorial, numerical methods commonly used in applying the PB equation to systems more complicated than onedimensional representations are provided Most readers of this book series will be interested in this section of the chapter and are encouraged to skip to this section once they read about the Gouy–Chapman model Here a brief description of finite-difference/finite element PB algorithms used in popular programs such as UHBD, DelPhi, APBS, and MEAD are explained The fourth and final part of the chapter introduces topics of more advanced nature This chapter sets the groundwork for a forthcoming chapter we intend to publish in a subsequent volume that will have as its focus the many uses and applications of the PB equation We invite our readers to visit the Reviews in Computational Chemistry Website at http://chem.iupui.edu/rcc/rcc/html It includes the author and subject indexes, color graphics, errata, and other materials supplementing the chapters We are delighted to report that the Google search engine (http:// www.google.com/) ranks our Website among the top hits in a search on the term ‘‘computational chemistry.’’ This search engine is becoming popular because it ranks hits in terms of their relevance and frequency of visits Google also is very fast and appears to provide a quite complete and up-to-date picture of what information is available on the World Wide Web We are also pleased to note that our publisher plans to make our most recent volumes available in an online form through Wiley Interscience Please check the Web (http://www.interscience.wiley.com/onlinebooks) or contact reference@wiley.com for the latest information For readers who appreciate the permanence and convenience of bound books, these will, of course, continue We thank the authors of this and previous volumes for their excellent chapters Kenny B Lipkowitz and Raima Larter Indianapolis, Indiana Thomas R Cundari Denton, Texas January 2003 Contents Computational Techniques and Strategies for Monte Carlo Thermodynamic Calculations, with Applications to Nanoclusters Robert Q Topper, David L Freeman, Denise Bergin, and Keirnan R LaMarche Introduction Metropolis Monte Carlo Random-Number Generation: A Few Notes The Generalized Metropolis Monte Carlo Algorithm Metropolis Monte Carlo: The ‘‘Classic’’ Algorithm The Barker–Watts Algorithm for Molecular Rotations Equilibration: Why Wait? Error Estimation Quasi-ergodicity: An Insidious Problem Overcoming Quasi-ergodicity Mag-Walking Subspace Sampling Jump-Between-Wells Method Atom-Exchange Method Histogram Methods Umbrella Sampling J-Walking, Parallel Tempering, and Related Methods J-Walking Parallel Tempering Jumping to Tsallis Distributions Applications to Microcanonical Simulations Multicanonical Ensemble/Entropy Sampling Conclusions Acknowledgments References 11 11 13 18 23 23 23 24 24 24 25 26 27 30 32 33 34 36 37 37 ix Author Index Shimizu, A., 144 Shimizu, S., 76, 77 Shing, K S., 74 Shirts, R B., 143 Shklovskii, B I., 349 Shumaker, J B., 356 Siegbahn, P E M., 137 Siepmann, J I., 38, 39, 140, 362 Sigal, V L., 340 Sigga, E D., 343 Silver, R N., 138 Silverstein, K A T., 74 Simonson, T., 76, 353, 358 Sinden, R R., 357 Singh, D J., 138 Singh, R K., 336 Singh, S., 38, 39 Singh, U C., 139 Sitkoff, D., 356 Sjostrom, L., 361 Skerjanc, J., 341, 345 Skipper, N T., 75 Sklenar, H., 356 Skodje, R T., 142 Skolnick, J., 349 Slivnik, T., 360 Sloane, C S., 136, 141 Smit, B., 37, 74, 142 Smit, J A M., 342, 343, 348 Smith, A C., 360 Smith, D E., 75 Smith, E B., 39 Smith, E R., 138 Smith, G R., 361 Smith, P E., 359 Soelvason, D., 138 Sommer, M S., 358 Song, K., 142, 143, 145 Sorensen, C M., 74 Soto, J., 143 Soumpasis, D M., 344, 348 Southall, N T., 75, 76 Sparnaay, M J., 346 Spencer, H G., 345 Spencer, N D., 142 Sperb, R., 359 Sridharan, S., 354 Srinivasan, A., 38 Srinivasan, J., 358 Stahlberg, J., 351 Stam, A J., 39 Stankovich, J., 348, 350, 351 Stark, K., 136, 142 Stasiak, A., 348 Stasiak, A Z., 348 Stefanov, B B., 145 Stegun, I A., 342 Steinfeld, J I., 41 Steinhauser, O., 77 Steitz, T A., 345 Stern, O., 333 Sternberg, M J E., 352, 355 Stevens, M J., 348, 349 Stevens, W J., 140 Stewart, J J P., 137 Sticher, H., 349 Stigter, D., 342, 365 Still, W C., 39, 356 Stillinger, F H., 76, 363 Stokes, A N., 340 Stoll, S., 348 Stoton, J A G., 351 Straatsma, T P., 39, 75, 76 Strain, M C., 145 Stratmann, R E., 145 Stratt, R M., 140 Straub, J E., 40, 41 Strauss, U P., 344 Strozak, M A., 40 Stumpf, M., 136 Styles, M L., 145 Subramaniam, S., 355, 357 Suddaby, A., 338 Sumpter, B G., 140 Sun, L., 145, 145 Sun, N., 349 Swamy, K N., 136, 142 Swedsen, R H., 39, 40, 41 Sweeney, P., 39 Swope, W C., 76 Szabo, A., 363 Szulejko, J E., 142 Tabatabaian, Z., 343 Tachikawa, H., 143, 144 Taira, K., 346 Tamashiro, M N., 337, 363 Tamor, M A., 146 Tanaka, Y., 346 Tanelian, D L., 334 Tanford, C., 334, 357 Tavan, P., 139 Taylor, D., 137 Taylor, J D., 346 Taylor, J R., 39 Tejerina, F., 343 379 380 Author Index Teller, A H., 37, 358 Teller, E., 37, 358 Tempczyk, A., 356 Tennant, L., 357 Tesi, M C., 41 Teso, A., 336 Teukolsky, S A., 38, 352 Thery, V., 139 Thiel, W., 137, 140 Thirumalai, D., 38, 346 Thomas, H M., 334 Thompson, D L., 135 Thompson, E A., 41 Thompson, M A., 139, 140 Tildesley, D J., 37, 74, 142, 362 Tironi, I G., 359 Tobias, I., 348 Tomac, S., 363 Tomasi, J., 145 Toma´ s-Oliveira, I., 76 Tonner, D S., 144 Topaler, M., 141 Topper, R Q., 38, 39, 40 Torrie, G M., 37, 75, 334, 338, 361 Tracy, C A., 341 Tralli, N., 349 Tran, V T., 354 Trizac, E., 339, 340, 344 Troe, J., 136 Trucks, G W., 145 Truhlar, D G., 39, 137, 139, 140, 141, 142, 145, 146, 362 Truong, T N., 137 Tsai, C J., 40 Tsai, N.-H., 39 Tsallis, C., 41 Tsao, H.-K., 342, 348, 349, 350 Tseng, M.-T., 339, 350 Tsui, V., 359 Tucker, S C., 145 Tully, J C., 146 Turq, P., 341 Uggerud, E., 140 Ugolini, R., 358, 360 Ullmann, G M., 357 Ushakov, V G., 136 Usui, S., 347 Uzer, T., 140 Valleau, J P., 37, 40, 75, 337, 338, 361, 362 Van Aken, G A., 340 van Beek, L K H., 354 Van Belle, D., 354 van der Maarel, J R C., 361, 362 van der Vaart, A., 359 van Eijck, B P., 40 van Gunsteren, W F., 40, 353, 359 Van Keulen, H., 342, 343 van Roij, R., 364 Vande Linde, S R., 136, 145 Varandas, A., 136 Varandas, A J C., 38, 136 Varnek, A 355 Vasilyev, V., 361 Vasquez, M., 353 Va´ zquez, S A., 143 Verlet, L., 140 Verma, C S., 358 Verwey, E J W., 334 Vetterling, W T., 38, 352 Viadiu, H., 346 Viggiano, A A., 144 Viglino, P., 340, 360 Vijayakumar, M., 358 Vila, J A., 358 Vipond, I B., 346 Vlachy, V., 333, 343, 361, 362, 363 Vogel, H J., 357 Voityuk, A A., 137 Volkov, A G., 334 Vologodskii, A., 348 von Gruă nberg, H H., 336, 350, 351 Vorobjev, Y N., 358 Vosko, S J., 138 Voter, A F., 39, 40, 138 Voth, G A., 38 Vriend, G., 357 Wade, R C., 334, 357, 358, 360 Wagner, K., 349 Wales, D J., 39 Walker, G W., 341 Wallqvist, A., 75, 76 Walz, J Y., 349 Wang, A H J., 346 Wang, C X., 353 Wang, F., 335 Wang, H., 136, 140, 142, 144, 145 Wang, I S Y., 136 Wang, J S., 41 Wang, W., 38 Wang, Y., 145 Wang, Z.-W., 341 Warshel, A., 136, 137, 139, 353 Warwicker, J., 353, 357 Author Index Watanabe, K., 76 Watson, H C., 353 Watson, G N., 342 Watts, R O., 39 Weber, H J., 341 Weeks, J D., 74 Weinberger, H F., 354 Weiner, R B., 143 Weisbuch, G., 340, 364 Welge, K H., 136 Wells, B H., 39 Wennerstroă m, H., 335, 336, 343 Werner, H., 136, 144 Werner, H.-J., 136, 137, 138, 142 Westcott, T P., 348 Whetten, R L., 40, 41 White, L R., 338, 347 Whitehead, R., 342 Whitlock, P A., 37 Whittington, S G., 37, 41, 362 Widom, B., 74 Widom, H., 341 Wiersma, P H., 340 Wieser, G R., 347 Wilcock, R J., 74 Wilde, R W., 38, 39 Wilhelm, E., 74 Wilk, L., 138 Williams, D J A., 352 Williams, D R M., 338 Williams, Jr., J C., 352 Wilson, Jr., E B., 136, 141 Wilson, R W., 344, 345 Wilson, W D., 359 Windemuth, A., 354 Winlove, C P., 343 Witteman, M., 344 Wodak, S J., 76, 354 Wolf, R J., 136, 141 Wolfe, S., 144 Wolfes, H., 346 Won, Y S., 355 Wong, L., 342, 352, 353, 357, 361, 364 Wong, M W., 145 Woodbury, Jr., C P., 340, 365 Wooding, R A., 339 Woods, C J., 356 Woodson, S., 346 Wrede, E., 136 Wright, P E., 357 Wu, I., 144 Wyatt, R E., 141, 143 Xu, X., 41, 353 Yamaguchi, Y., 139 Yamazaki, K., 346 Yan, Q., 41 Yan, T.-Y., 142 Yang, A S., 334, 355, 358 Yang, G., 344 Yang, W., 138, 139 Yeomans, L., 343 Yethiraj, A., 364 Yi, X.-Z., 341 Yinhu, X., 354 Yoon, B J., 350, 354, 355 York, D M., 138 You, T J., 352, 357 Yuet, P K., 350 Yun, W., 338 Yunyu, S., 354 Zacharias, M., 76, 356, 359 Zakharova, S S., 362 Zakrzewski, V G., 145 Zaloj, V., 355 Zara, S J., 337 Zauhar, R J., 354, 355 Zerner, M C., 137 Zewail, A H., 142 Zhang, L., 75 Zhang, Y., 139 Zhexin, X., 354 Zholkovskji, E K., 344 Zhou, H.-X., 349, 354, 358, 359 Zhou, R., 40 Zhou, S., 347 Zhou, S J., 139 Zhou, Z., 353 Zhu, C., 145 Zhu, L., 136, 145 Zichi, D A., 76 Zielenkiewicz, P., 361, 363 Ziman, J M., 341 Zimm, B H., 340, 364, 365 Zoebisch, E G., 137 Zuccato, P., 340 Zukoski, C F., 349 Zuzic, M., 334 Zydney, A., 350 381 Subject Index Computer programs are denoted in boldface; databases and journals are in italics a-chymotripsin, 314 Ab initio direct dynamics, 86 Ab initio electronic structure theory, 88 Ab initio multiple spawning (AIMS) method, 134 Ab initio potential energies, 80 Acceptance probability, Active space, 89 Activity coefficient, 317, 320 Actual charge density, 267 Adaptive finite-element gridding, 292 Adaptive meshes, 292 Additive GC expression, 197 Adsorption bandwidth, 116 Alanine dipeptide, 30 Alternatives to the PB equation, 325 AM1, 86, 87, 88, 119, 129, 131 AM1-SRP, 87, 119 AMBER, 131 Amino acid side chains, 307 Analytical potential energy surface, 80, 122 Angular momentum, 99, 100 Anharmonic systems, 102 APBS, 150 Apparent charge, 261 Apparent charge density, 215, 222, 267 Apparent charge for micelles, 260 Apparent Debye-Huăckel (ADH), 167, 183, 197, 240 Apparent Gouy-Chapman length, 212, 215, 240, 264 Apparent linear charge density, 240, 241, 243, 254 Apparent surface charge density, 182, 240, 259, 264 Approximate cell model, 181 Approximate microcanonical ensemble, 102 Approximate PB expression, 197, 323 Aqueous methane, 73 Aqueous solutions, 46 Ar solutes, 65 Arabinose proteins, 305 Artificial bias potential, 25 Aspartyl-tRNA synthetase, 315 Atom-exchange method, 24 Atomic solvation parameter, 306 Average concentration, 180 Average counterion concentration, 229, 250 Average Debye screening constant, 250 Average dielectric coefficient, 293, 295 Average protonation state, 311, 312 Average reaction probability, 108 Average solute-solvent energy, 57 b-lactamase, 314 b-lactoglobulin, 314 B3/ACM, 90 BLYP, 90 B3LYP, 88, 129 B88, 90 Bacteriorhodopsin, 314 Barker-Watts algorithm, 11 Barker-Watts move, 9, 11, 23 Barnase, 315 Barnase-barstar, 316 Barrier recrossings, 122 Reviews in Computational Chemistry, Volume 19 edited by Kenny B Lipkowitz, Raima Larter, and Thomas R Cundari ISBN 0-471-23585-7 Copyright ß 2003 Wiley-VCH, John Wiley & Sons, Inc 383 384 Subject Index Basis functions, 84 Basis Sets aug-cc-pVTZ, 125 3-21ỵG(d), 119 3-21ỵG*, 90 3-21G(d), 119 6-31ỵ ỵG*, 129 6-31ỵG(d), 119 6-31ỵG**, 129 6-31ỵG*, 90, 129 6-31G(d), 119 6-31G(d,p), 119 6-31G**, 87, 89, 90 6-31G*, 90, 122, 124 6-311ỵG(2df,2pd), 125, 130 6-311ỵG**, 90 6-311G(d,p), 119 B-DNA, 165, 227, 235, 282, 287 Bending of long cylinders, 253 Bimolecular reactions, 106, 114 Binding energy, 302 Biomolecular interior, 293 Biomolecular surface, 291 Biomolecules, Biopolyelectrolytes, 165, 175 Bjerrum length, 159 Blocking, 15 Boltzmann constant, Boltzmann distribution, 3, 106 Boltzmann probability, 11 Boltzmann test, 10 Bond energies, 82 Born’s solvation energy formula, 305 Born-Oppenheimer (BO) direct dynamics, 84, 85, 118 Born-Oppenheimer approximation, 91 Boundary conditions, 155, 168, 173, 178, 187, 198, 200, 210, 220, 250, 254, 273, 280, 314, 325 Boundary element method, 301 Boundary QM atoms, 93 BPTI, 34, 315 Brownian dynamics, 301, 316 Bulk dielectric value, 296 Bulk electrolyte, 151, 154, 161, 232, 234, 291 Bulk limits, Bulk water, 59 B-Z transition in DNA, 254, 305 Calbindin, 314 Calcium binding protein, 314 Canonical ensemble, 3, 47 Canonical TST, 110 Capillaries, 249 Caricain, 314 Car-Parrinello (CP) direct dynamics, 84 Cartesian coordinates, 95 Cartesian displacements, 96 Catalytic hydrolysis, 255 Cauchy condition, 155 CCSD(T), 87, 122, 125 CDF formula, 104, 108 Cell boundary screening constant, 180 Cell model, 177, 179 Central barrier, 123 Central force model (CF1), 63 Central-barrier dynamics, 121 Centrifugal barrier, 114 Characteristic lengths, 159 Charge density, 168 Charge regulation, 200 Charge transfer, 315 Charged capillaries, 253 Charged cylinder, 245, 249, 264, 278, 329 Charged cylindrical pores, 253 Charged planar surfaces, 186 Charged sphere, 262 Charged surface, 232 Chemical activation, 103 Chemical potential, 51 Chemical reaction, 80 Chymotrypsin-ovomucoid docking, 305 Classical equations of motion, 95 Classical mechanics, 114 Classical trajectory simulations, vii, 79, 84 Clathrate-hydrate cage structures, 59 CNDO, 85 Coion, 152, 164, 181, 296 Colligative properties, 329 Collision impact parameter, 107 Colloidal particle, 254 Colloidal solutions, 149 Combined MD-PB, 315 Complete active space self-consistent field (CASSCF) method, 88, 89, 118 Computational chemistry, vi, viii Concentric cylindrical surfaces, 252 Condensation radius, 244 Condensed phase, 1, 91 Conditional probability, Conditional transition probabilities, 31 Configuration integral, Configuration interaction (CI), 88 Configurational energy, 48 Configurational partition function (ZN), 48 Configurations, Subject Index Conjugate gradient method, 295 Conjugate momenta, 80 Constant charge density, 198, 252, 277 Constant dielectric coefficient, 152, 319 Constant surface charge density, 200 Constant surface potential, 252, 277 Constraints, 93 Constrained entropy, 179 Constraining potential, Continuum solvent, 318 Correlation effects, 328 Correlation energy, 88 Correlation hole, 323 Correlation length, 14, 15 Coulomb potential, 152 Counterions, 152, 164, 181 Counterion concentration, 250 Counterion condensation, 185, 205, 232, 240, 243, 253 Counterion condensation theory, 151, 230, 260, 329 Coupled-cluster (CC) method, 89 Coupling parameter, 53, 54, 68 Couplings between vibrational modes, 117 Covariance, 14, 17 Critical coordinates, 84 Critical point, 51, 65 Cumulative distribution function, 110, 112 Curved cylinder, 253 Curved double layers, 204 Curved surfaces, 200, 272 CV, constant volume heat capacity, Cyclopropane stereomutation, 118 Cylinder stiffness, 284 Cylinder surface, 231 Cylinders, 200 Cylindrical capillary, 250, 252 Cylindrical charged rods, 232 Cylindrical disks, 253 Cylindrical DNA models, 150 Cylindrical PB equation, 253 Cylindrical polyelectrolytes, 226, 227, 245, 329 Cylindrical pores, 253 Debye length, 159, 227, 272 Debye screening constant, 159, 164, 168, 172, 278, 285, 326 Debye-Gouy-Chapman length, 162, 172, 176, 183, 205, 237, 261 Debye-Huă ckel additivity, 278 bulk model, 324 385 cell model, 259 equation, 154, 197, 210, 236, 294 potential, 163, 182, 238, 239 profiles, 166 screening constant, 161, 179 solution, 250 theory, 167, 186, 308 Degree of hydrogen bonding, 44 DelPhi, 150 Deletion process, 51 Denaturation of proteins, 2, 72 Density fluctuations, 51 Density functional theory (DFT), 84, 89, 315 Density of states, 33, 102 Derjaguin approximation, 254, 272 Derjaguin theory, 290 Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, 186, 189 Detailed balance, 6, 29, 30 DHX approximation, 181 Diamond {111} surface, 129 Dielectric coefficient, 295, 293, 313, 320 Dielectric continuum, 314 Dielectric saturation, 319 Diffusion, 316 Diffusion-controlled bimolecular association, 316 Dipole moments, 86 Direct dynamics simulations, 84, 85 Dirichlet boundary conditions, 155, 224 Discrete charge effects, 253 Discrete solvent effects, 319, 323 Discrete surface charge, 200, 323 Discretization, 292 Dissociation pathways, 128 Distance of closest approach, 292 Distribution functions, 80 Divalent counterions, 200, 253, 254 DNA duplexes, 315 DNA, 200, 226, 245, 253, 284, 286, 295, 307, 320 DNA-ligand complexes, 305 DNA-protein recognition, 254, 319 Docking of macromolecules, 288 Docking schemes, 315 Donnan coefficient, 253 Donnan exclusion coefficients, 253 Dressed-ion theory (DIT), 277, 327 Drug-induced DNA unwinding, 305 Dusty plasmas, 149 Dynamically modified windows, 53 Eccentric cell model, 288 386 Subject Index Effective Born radii, 306 Effective fragment potential (EFP), 94 Efficient microcanonical sampling (EMS), 99 Einstein-Brillouin-Keller (EBK) semiclassical quantization condition, 106 Elasticity of curved membranes, 204 Electric double layer, 147, 165, 318, 326 Electric field stress tensor, 189 Electrokinetic flow, 252 Electron correlation, 85 Electron transfer reorganization in proteins, 305 Electronic Hamiltonian, 92 Electronic structure theory, 1, 84 Electrons and nuclei dynamics (END), 135 Electrostatic fields, 299 Electrostatic free energy, 163, 188, 200, 216, 255, 273, 275, 302, 304, 309, 314 Electrostatic peristence length, 284, 286 Electrostatic potential, 148, 158, 301, 302 Electrostatic pressure, 160, 163 Electroviscous flow, 253 Embedded titratable sites, 307 Empirical potential, 80 End effects, 249, 253, 282 Endonucleases, 254 Energy barriers, 20 Energy conservation, 95, 99 Energy fluctuations, 95 Energy of association, 71 Energy transfer, 129 Enhanced recrossing, 124 Ensemble of trajectories, 80 Ensembles, 10, 33, 34, 49, 97, 98, 101 Enthalpy of hydration, 64 Enthalpy, 49 Entropy, 45, 48, 55, 57 Entropy changes, 53 Entropy of association, 71 Entropy of hydration, 55, 58 Entropy sampling methods, 34, 35 Equations of motion, 79, 94, 95 Equilibration of a walker, 12 Equilibration period, 12 Equilibration, 11 Equilibrium distribution of ions, 153 Equilibrium geometries, 82 Equipartition theorem, 3, 17, 20 Ergodic, 97 Ergodic random walk, 18 Ergodic sampling, 19, 27 Ergodic walk, Ermak-McCammon algorithm, 316 Error estimation, 13, 15, 206 Euler’s angles, 109, 112 Exact sampling, 98 Excess chemical potential, 45, 49, 52 Excess Helmholtz free energy, 49 Exchange correlation energy, 90 Excluded volume, 280, 319 Exit-channel dynamics, 109, 124 Experimental data, 44, 82 Experimental nonrandom sampling, 103 Explicit solvent molecules, 314, 328 Extended NLDH approximation, 252 Fab-antigen complexes, 316 Fast adaptive multipole algorithm, 287 Fast multipole moment (FMM), 90 Femtochemistry, 124 FEP method, 68 Fictitious electronic degrees of freedom, 84 Field-dependent dielectric coefficient, 295 Finite-difference algorithm, 291, 298 Finite-difference/finite-element (FDFE) approach, 302 Finite-element algorithm, 291 Finite-length cylinders, 253 Fixed charge density, 156 Fixed surface potential, 156 FK506 binding protein, 315 Flow of zero-point energy, 115 Fluctuations, 12, 17, 56, 186 Fluctuation corrections, 326 Fluctuations of calculated properties, 20 Fluctuation potential, 321 Fock operator, 89 Force constants, 82 Force field, 314 Fragmentation pathways, 128 Franck-Condon factor, 104 Free energy of association, 68 Free energy, 55, 148 Free energy of binding, 302 Free energy of solvation, 44 Free-energy decomposition, 56 Free-energy differences, 54 Free-energy perturbation (FEP), 51, 52, 68 Free-energy surface, 63 Freezing transition, Freezing-point depression, 152 Frozen Gaussian approximation, 134 Frozen-core approximation, 130 Full CI, 89 Full Poisson-Boltzmann equation, 154 Functionals, 87, 90 Subject Index Gamma function, 33 Gas solubility, 44 Gas-surface collisions, 112 Gauss’ law, 157, 206, 244, 300 Gaussian distribution, 6, 14 Gaussian wavepacket dynamics (GWD) algorithm, 134 GAUSSIAN98, 122, 126 Gauss-Seidel iteration, 295 Generalized gradient approximations (GGA), 90 Generalized hybrid orbital (GHO), 94 Generalized Metropolis Monte Carlo (gMCC), Genomes, 148 Gibbs ensemble, 10 Gibbs free energy, 163, 304 Globular protein, 254, 255 Gouy-Chapman (GC) theory, 156, 164, 167 Gouy-Chapman equation, 201, 288, 320 Gouy-Chapman length, 159, 162, 168, 183, 261, 328 Gouy-Chapman profile, 161, 166, 174 Grahame’s equation, 161, 168, 203, 214, 255 Grand canonical ensemble, 10 Hamilton’s equations of motion, 95 Hamiltonian operator, 91 Hard sphere (HS) potential, 47 Hard sphere ionic solutions, 232 Hard-sphere exclusion volume, 322 Hard-sphere solutes, 51 Harmonic approximation, 96 Harmonic oscillator, 99 Harmonic oscillator/rigid rotor model, 103 Harmonic systems, 102 Hartree-Fock calculation, 86 Hartree-Fock wavefunction, 88 He solutes, 65 Heat capacity, 3, 17, 20, 44, 45, 49, 57, 58 Heat capacity of association, 72 Heat capacity of solvation, 59, 66 Heats of formation, 86 Heaviside (step) function, 33 Helical charge symmetry, 253 Helmholtz free energy, 48, 49, 163, 302 Henderson-Hasselbach titration curve, 311 High ionic strength solution, 286 High surface charge density, 169 Highly charged cylinder, 234 Highly charged macromolecules, 305 Highly charged polyelectrolytes, 319 Highly charged sphere, 256 387 Highly charged surface, 173, 200 Highly concentrated ionic solutions, 319 Highly selective initial excitation, 105 High-temperature walk, 27, 30 Histogram sampling methods, 24, 34 HIV protease binding, 305 HIV-1 reverse transcriptase inhibitors, 305 Hogg-Healy-Furstenau (HHF) method, 269 Hohenberg-Kohn theorem, 89 Hoogsteen pairing, 307 Hopping trajectories, 134 Hybrid PB-DH cell model, 254 Hydration, 45 energy, 64 entropy, 49, 64 free energy, 61, 66 heat capacity, 66 of biomolecules, 301 of krypton, 56 shell, 58 structure, 59 Hydrogen bond network, 65 Hydrogen bond strengths, 59 Hydrogen bonding in water, 66 Hydrogen bonding structure of water, 67 Hydrogen bonding, 44, 86 Hydrophobic effects, 57 Hydrophobic forces, 314 Hydrophobic hydration, 51, 58, 66 Hydrophobic interaction, 68 Hydrophobic repulsion, 69 Hydrophobicity, vii, 43, 72 Hypernetted chain (HNC), 326, 327 Hysteresis, 53, 55 Iceberg hypothesis, 57, 58, 68 Image charges, 289 Impact factors, vi Impact parameter, 107 Importance sampling method, Induced charge density, 301 Inertia tensor, 101 Infinite charged cylinder, 278 Infinitely long cylinder, 226 Information theory (IT), 51, 66 Inhomogeneous Neumann condition, 157 Initial condition, 79, 97, 102, 103, 105, 114, 130 Initial configuration, Inner Helmholtz layer, 152, 166 Instantaneous deviation of solvent energy, 57 Instantaneous normal-mode coordinates, 96 Institute for Scientific Information (ISI), v 388 Subject Index Interacting cylinders, 220 Interacting spheres, 220 Interaction between two protonated sites, 312 Interfaces, 53, 59, 64 Internal conversion, 103, 104, 105 Internal coordinates, 95 Internal energy, Internal protein dielectric coefficient, 313 Intramolecular dynamics, 97, 115 Intramolecular vibrational (energy) redistribution (IVR), 98, 104, 111, 126, 127 Intrinsic non-RRKM behavior, 98 Intrinsic pKa, 311 Intrinsic reaction coordinate (IRC), 125, 126 Ion channel pore, 320 Ion correlation, 320 Ion distributions, 302 Ion-dipole complex, 116, 121 Ion-displaced solvent molecules, 319 Ion-exchange chromatography, 290 Ionic conductivity, 152 Ionic radial distribution function, 318 Ionic strength effects, 315 Ionic strength, 159, 248, 288 Ion-ion correlation, 321 Ionizable sites, 228, 255, 301 Ionization potentials, 86 Ion-penetrable membrane, 200, 299 Irregular dielectric boundaries, 315 Isothermal compressibility, 56 Isothermal-isobaric ensemble, 10 Isotropic dielectric coefficient, 319 Jacobi iteration, 295 Jump-Between-Wells (JBW) method, 24 Jump-walking, 27 Kr solutes, 65 Krypton hydration free energies, 63 Krypton, 67 l repressor, 315 lcI repressor-DNA complex, 305 Large solute size, 53, 64 Large spherical macroion, 326 Large-scale simulations, 94 Lennard-Jones (LJ) potential, 12, 47 Lennard-Jones cluster, 30 Lennard-Jones oscillator, 12, 17 Lifetime distribution, 98 Lifetime of vibrationally excited molecule, 80 Linear colloidal particles, 245 Linear DH equation, 208 Linear Poisson-Boltzmann (LPB) equation, 151, 155 Linear polyelectrolyte, 227 Linear scaling, 90 Linear superposition approximation, 190, 193, 269 Link atom, 93 Liquid water, 11 Liquid-vapor coexistence curve, 58 Local charge density, 316, 326 density approximation (LDA), 90 density fluctuations, 50 dielectric coefficient, 153 dipole moment density, 316 electric polarization, 316 electrostatic potential, 152, 307 force, 166 Hamiltonians, 90 mode state, 106 polarization, 319 self-consistent field (LSCF), 94 solvent polarization, 328 surface curvature, 170 Localized orbitals, 90 Local-mode excitation, 103, 105 Local-mode overtone state, 116 Local-mode sampling, 105 London-Eyring-Polanyi-Sato function, 80 Long-time quantum dynamics, 116 Low polyelectrolyte concentrations, 259 Low surface charge density, 169 Low-energy insertions, 50 Lysozyme, 314, 315 Macroion, 157 Macromolecular solvation energy, 305 Macromolecular surface, 301 Macroscopic modeling, vi Magnified stepsize, 22, 23 Mag-walking, 22, 23 Manning radius, 231 Manning’s counterion condensation theory, 243 Many-body solute-solute effects, 70 Markov chain, 5, 10, 24 Markov process, 14 Markov walk, 12 Maximal entropy, 44 Maxwell stress tensor, 160, 302 Maxwell’s equation, 316 Maxwell’s law, 153 Subject Index Maxwell-Boltzmann distribution, 114 McMillan-Mayer theory, 314, 318, 328 MEAD, 150 Mean charge density, 153 Mean electrostatic potential, 153, 320, 321 Mean spherical approximation (MSA), 327 Mean-field Boltzmann approximation, 317 Mean-squared fluctuations, 17 Mechanical persistence length, 284 Melting transitions, 19 Membrane model, 200 Membrane, 156 Mercedes Benz (MB) model of water, 59, 66 Methane molecules in water, 54 Methane, 61, 65, 69 Methane-methane PMF, 70, 71, 72 Metropolis method, 46 Metropolis Monte Carlo (MMC), 3, 5, 14, 314, 315, 328 Metropolis Monte Carlo walk, 20 Metropolis Monte Carlo, generalized (gMMC), Metropolis sampling, Metropolis walk, 23 Metropolis walkers, different temperatures, 26 Micelles, 148, 165, 200, 254, 299, 305 Microcanonical ensemble, 33, 97, 98, 101 Micropores, 148 Microscopic reversibility, Mixed electrolyte solutions, 156, 171, 256 MNDO, 86, 87 MNDO/d, 86, 87 MNDO97, 87 Mobility of water, 59 Mode specificity, 105 Model respresentations of DNA, 201 Moderately charged cylinder, 236, 257 Moderately charged sphere, 257 Moderately charged surface, 175 Modified HHF (mHHF) expression, 274 Modified Poisson-Boltzmann (MPB) theory, 151, 321, 326 Molecular clusters, Molecular dynamics (MD), 14, 18, 37, 46, 112, 148, 234, 280, 301, 314, 315 Molecular geometries, 86 Molecular mechanical force fields, 91 Molecular mechanics, Molecular rotation, 11 Molecular surface area, 306 Molecule-surface collisions, 113 Møller-Plesset (MP) perturbation theory, 89 Mono-valent counterions, 200, 251, 253, 254 389 Mono-valent electrolyte, 296 Monte Carlo (MC), vi, 2, 46, 79, 80, 108, 112, 148, 151, 232, 252, 262, 280, 289, 301, 314, 321, 322, 326 Monte Carlo thermodynamic calculations, Monte Carlo, path-integral methods, Monte Carlo, quantum effects, Monte Carlo, thermodynamic scaling, 26 MOPAC, 130 Morse function, 84, 106 Move strategy, 8, 10 MP2 direct dynamics trajectory, 122 MP2, 89, 122, 125, 129 MP3, 89 MP4, 89 MPB equation, 326 Multicanonical ensemble, 34 Multicanonical sampling, 35 Multiconfiguration self-consistent field (MCSCF) method, 89 Multigrid method, 295, 326 Multiple histograms, 25 Multiple minima, 20 Multireference configuration interaction (MRCI), 89 Multivalent counterion effects, 25 Myoglobin, 314 Nanoclusters, Nanopores, 249 NDDO parameters, 87 NDDO-SRP, 87 Ne solutes, 65 Neglect of diatomic differential overlap (NDDO) model, 86 Neumann condition, 155, 224 Neuraminidase inhibitors, 305 Newton’s equations of motion, 95 Newtonian mechanics, 314 Noble gases, 65 Nonadiabatic transition region, 134 Noncritical coordinates, 84 Non-IRC path, 126 Nonlinear Boltzmann expression, 181 Nonlinear Debye-Huă ckel (NLDH) approximation, 193, 204, 210, 236, 245, 269, 263 Nonlinear Gouy-Chapman solution, 259 Nonlinear PB equation, 155, 208, 255, 294, 325 Nonpolar gases, 45 Nonpolar molecules, 49 Nonpolar solute, 53, 55, 59, 66, 68 390 Subject Index Nonrandom excitation, 103, 116 Nonrandom sampling, 105 Non-RRKM dynamics, 121, 124 Nonstatistical effects, 121 Nonstatistical fragmentation dynamics, 133 Nonsymplectic schemes, 95 Non-TST dynamics, 124 Nonuniformly charged sphere, 290 Normal modes, 95, 101, 103 Normal mode momenta, 96 Normal modes of vibration, 112 Normal-mode displacements, 96 Normal-mode/rigid-rotor Hamiltonian, 99, 101 Normal-mode/rigid-rotor quasiclassical model, 110 Normalized Debye-Huă ckel solution, 215 Normalized probability density function, Nucleic acids, 254, 305, 307 Numerical integration algorithms, 46 OM1, 87 OM2, 87 One-dimensional solutions of PB equation, 165 One-electron integrals, 86 Orbital angular momentum, 114 Order parameters, 12 Order-disorder transition, 23 Orthant sampling, 101 Osmotic pressure, 152, 160, 189, 232, 253, 318 Ostwald solubility coefficient, 44 Outer Helmholtz layer, 152, 158, 166 Overlapping distribution method, 51 Overlapping windows, 55 Overtone line-widths, 105 Overtone state, 105, 116 Ovomucoid third domain, 315 Pairs of nonpolar solutes, 68 Pairwise hydrophobic interactions, 68, 71 Papain, 314 Parallel charged surfaces, 186 Parallel computing, 292 Parallel cylinders, 254 Parallel tempering, 30 Partial molar volume, 56 Particle deletion, 61 Particle insertion methods, 49, 61 Partition function, 47, 103, 110 PB-DFT theory, 315 Peptide ion fragmentation, 128 Periodically spaced charged cylinders, 253 Persistence length, 148, 278, 283, 284 Perturbation methods, 52 Perturbation theory, 89 Perturbed Gouy-Chapman, 201, 241, 261 PGC approximation, 263 pH, 248 Phase equilibrium studies, 10 Phase space, 52, 53, 97, 101 Phase space shell, 102 Phase space structure, 116 Phase space volume, 95 Phase transitions, 2, 17 Phonon spectrum, 130 Phosphoglycerate mutase, 295 Photoisomerization, 86 Physical boundaries, 292 pKa, 148, 254, 255, 288, 301, 307, 310 Planar membranes, 150, 163 Planar PB equation, 177 Plasmid of DNA, 283 PM3, 86, 87 PM3-SRP, 119 Point mobile ions, 320 Poisson-Boltzmann cell (PBC) model, 177, 178, 229, 234, 253, 324 Poisson-Boltzmann (PB) equation, vii, 153, 173, 290, 302, 304, 307 Polarized continuum models, 315 Polyelectrolyte, 157 Polyelectrolyte solutions, 148 Polyelectrolyte surface, 323 Polyelectrolyte-counterion interaction, 253 Pooling of zero-point energy, 118 Potential energy surface (PES), 20, 23, 26, 82, 87, 88, 92, 96, 121, 125, 134 Potential energy, 4, 80 Potential of mean force (PMF), 50, 52, 54, 68, 277, 317, 320 Predictor-corrector algorithms, 95, 122, 295 Pressure dependence of hydrophobic interactions, 72 Pressure, 247 Probability distribution function, 2, 4, 5, 25, 51, 112 Protein folding, 319 protein G, 314 Protein ionization sites, 254 Protein-membrane interactions, 319 Proteins, 301, 307 Proteomics, 148 Protonated glycine, 128 Pseudobond method, 94 Pseudorandom number, Subject Index Pure water, 44, 49 PW91, 90 QCISD(T), 129 QM/MM boundary, 93, 94 QM/MM Hamiltonian operator, 93 QM/MM links, 94 QM/MM methods, 91 QMỵMM, 93, 130 Quadratic configuration interaction (QCI), 89 Quantum dynamics simulations, 114 Quantum effects, 114 Quantum mechanical calculations, 148 Quantum-mechanical tunneling, 114 Quasiclassical model, 108 Quasiclassical normal-mode method, 130 Quasiclassical normal-mode sampling, 112, 123 Quasiequilibrium, 55 Quasi-ergodic sampling, 18 Quasi-ergodicity, 18, 26 Radial distribution functions (RDFs), 50, 55, 59, 61 Radial Manning parameter (RMP), 230 Radius of curvature, 264 Raman spectroscopy, 44 Random number, 2, 4, 10 Random sampling, 4, 103 Random values, 108 Random walk, 2, Randomness, 14 Rate constant, 113 Reaction coordinate, 111 Reaction cross section, 106, 108, 113 Reaction intermediates, 115 Reaction probability, 108, 113 Reactive trajectories, 113 Recursive bisection method (RBM), 91 Reduced potential, 159 Reduced-site approximation, 313 Reference determinant, 88 Regulated charge, 252 Rejection techniques, 99 Resonance states, 124 Ribonuclease A, 314 Ribonuclease T1, 314 Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant, 97, 98 Rigid rotor, 99 Rippled sphere, 287 RNA, 315 RNA hairpins, 315 391 RNA-protein binding, 315 Rolling-sphere algorithm, 292 Root mean square (RMS) fluctuations, 17 Rotational move, 11 Rotational quantum numbers, 100, 103, 107 RRKM theory, 97, 103, 111, 116, 123 Runge-Kutta procedure, 291 Running averages, 121 Running estimate, 12 Saddle point, 87, 120 Salt bridges, 307 Salt-induced conformational changes, 253 Sampling, 101 Sampling errors, 20 Sampling problems, 30, 34 Scaled apparent charge density, 248, 249 Scaled potential, 159 Scaled surface charge density, 245 Scaled-position link atom method (SPLAM), 93 Schottky junctions, 149 Schroă dinger equation, 134 Sci-Bytes, v Screening constant, 256 Semiempirical direct dynamics, 119 Semiempirical electronic structure theory, 86 Simplified theoretical models, 91 Simulated annealing-optimal histogram method, 25 Simulation methods, 46 Single histogram method, 24 Single-particle move, 10, 11 Single-particle NLDH potential, 211 Size-consistency, 89 Skewed cylinders, 249 Slater determinants, 88 Slow growth TI method, 55 Small local electric field, 319 Small size hypothesis, 67 Small solute molecules, 50, 59, 64, 66 Small surface charge densities, 196 Smart darting, 30 Smart walking, 30 Smoluchowski equation, 316 SN2 nucleophilic substitution reaction, 82, 86, 89, 121 Solubility data, 44 Solute aggregation, 69 Solute concentrations, 55 Solute molecules, 49 Solute-sized cavities, 50 Solute-water attractions, 64 Solution properties, 50 392 Subject Index Solvation, 94 Solvation energies, 65, 148, 305, 315 Solvation entropy, 65 Solvent, 50, 314 Solvent accessible surface area, 69 Solvent cavity, 306 Solvent packing, 187 Solvent reorganization, 57, 64 Solvent separated methane, 73 Solvent-induced conformational changes, 315 Solvent-induced oscillations, 329 Solvent-mediated ion-surface interactions, 319 Spatially dependent dielectric coefficient, 164 Spatially inhomogeneous systems, 52 Spatially varying dielectric continuum, 153 Spawned wavefunctions, 134 Spheres, 200 Sphere-plane interactions, 288, 289 Sphere-sphere interactions, 289 Spherical micelle, 150, 256 Spin orbitals, 88 Spin-orbit coupling, 91 Spurious angular momentum, 101 Specific Reaction Parameters (SRPs), 119 Stability of colloidal solutions, 269 Staged FEP, 61 Staged insertion, 52 Statistical mechanics, 47, 147 Stepsize, 22 Steric packing of large counterions, 200 Stern layer, 166 Stratified sampling, Strict cell model, 181 Structural transformations, Structure, 55 Subspace sampling, 23 Subtilisin-chymotrypsin inhibitor, 305 Successive overrelaxation, 295 Sulfate-binding proteins, 305 Supercoiled DNA, 280 Supercooled water, 44, 66 Superoxide dismutase, 316 Surface, 112 charge density, 161, 166, 181, 216, 219, 228, 250, 254, 255, 296, 299, 307 constant curvature, 151 counterion concentration, 298 curvature, 201, 213, 264, 274 elements, 301 -induced dissociation (SID), 128 models, 112 potential, 168, 215, 216, 255, 273, 296 roughness, 200 small radius of curvature, 218 SVWN, 90 Symmetric-top polyatomic molecule, 103 Symmetric-top rigid rotor, 99 Symplectic integrators, 95 Systematic errors, 29 Tandem J-walking, 27 Tanford-Kirkwood model, 312 Tanford-Roxby mean-field approximation, 313 Test particle method, 49, 61, 68 Thermal expansion coefficient, 56 Thermal rate constant, 106 Thermodynamic average, 3, 4, 14 Thermodynamic cycle, 305, 307, 310 Thermodynamic integration (TI), 51, 53, 68 Thermodynamic properties, 3, 17, 20, 44, 47, 328 Thermodynamic-scaling Monte Carlo method, 26 Third-domain ovomucoid, 314 Three-body hydrophobic interactions, 69 Time-dependent nuclear wavefunctions, 134 Time-independent Schroă dinger equation, 93 Timescales for intramolecular motions, 127 TIPS3P water, 65 Titratable site, 307 Tobacco mosaic virus, 245 Trajectory initial conditions, 97 Trajectory surface hopping (TSH) model, 133 Trajectory, 80 Transition rate, Transition state (TS), 109, 110 Transition state theory (TST), 110, 122 Translational energy, 101 Trapping of trajectories, 122 Trial configuration, 8, 10 Trial move, Trial probability, 7, 28 Trimethylene biradical, 118 Trimethylene unimolecular dynamics, 121 Triple helical nucleic acid structures, 315 Triple-stranded DNA, 313, 315 Tsallis distributions, 32 Tsallis statistics, 32 Tunneling, 114 Tunneling effect, 134 Tunneling probabilities, 115 Two particle NLDH potential, 219 Two-dimensional hard-sphere fluid, Two-electron integrals, 86 Two-electron one-center integrals, 86 Subject Index UHBD, 150, 326 Umbrella potential, 25 Umbrella sampling, 25, 35, 55, 71 Uncertainties, 13 Unexcited ground-state, 104 Uniform dielectric coefficient, 156 Uniform distribution, 5, 6, 100 Uniform sampling of phase-space, 99 Unimolecular rate constant, 97, 117 Unimolecular rate theory, 97 Unimolecular reactions, 97, 103, 115 Unphysical atom, 93 Unphysical effect, 115 Unphysical results, 116 Valence force field potentials, 84 Variable dielectric coefficient, 317, 320, 328 Variable grid spacing, 292 Variable local dielectric coefficient, 296 Variance, 14 Variational calculation, 89 Variational principle, 223 Variational transition state theory, 110 VENUS, 80, 126, 130 VENUS96, 122 Verlet algorithm, 95 Vesicle, 299 Vibrational electronegativities, 93 energies, 93 393 frequency, 93, 100 modes, 80 period, 100 -rotational coupling, 101 -rotational excitation, 97 -rotational levels, 110, 111 -rotational state, 103, 105 quantum numbers, 106 Vibrationally adiabatic barrier, 114 Vibrationally excited ground-state, 104 Vibrationally excited molecules, 104 Vibrationally-rotationally cold, 105 Virial coefficient, 70 Virial theorem, 102 Virtual spin orbitals, 88 Von Neumann rejection method, 99, 103 Walden inversion mechanism, 121 Water, 44, 58 Water mimics, 67 Water models, 47 Weak-field Debye-Huă ckel solution, 255 Weakly charged proteins, 307 Weeks-Chandler-Andersen (WCA) potential, 47 Wigner-Seitz cell, 229 Xe solutes, 65 Zero-point energy, 105, 114, 117, 122 Zero-point energy motions, 124 .. .Reviews in Computational Chemistry Volume 19 Reviews in Computational Chemistry Volume 19 Edited by Kenny B Lipkowitz, Raima Larter, and Thomas R Cundari Editor Emeritus Donald B Boyd Kenny... Chemie International Edition in English Topics in Current Chemistry Chemische BerichteRecueil Chemistry a European Journal Reviews in Computational Chemistry Chemical Research in Toxicology 198 1–2001... tutorial-like reviews covering all aspects of computational chemistry In this, our nineteenth volume, we present four chapters covering a range of topics that have as a theme macroscopic modeling In Chapter