146 Polarizability <strong>in</strong> Computer Simulations 236. E. J. Dodson, G. J. Davis, V. S. Lamz<strong>in</strong>, G. N. Murshudov, and K. S. Wilson, Structure, 6, 685–690 (1998). Validation Tools: Can They Indicate the Information Content of Macromolecular Crystal Structures? 237. P. Hobza and J. S˘poner, Chem. Rev., 99, 3247–3276 (1999). Structure, Energics, and Dynamics of the Nucleic Acid Base Pairs: Nonempirical Ab Initio Calculations. 238. J. N. Wilson and R. M. Curtis, J. Phys. Chem., 74, <strong>18</strong>7–196 (1970). Dipole Polarizabilities of Ions <strong>in</strong> Alkali Halide Crystals. 239. G. D. Mahan, Solid State Ionics, 1, 29–45 (1980). Polarizability of Ions <strong>in</strong> Crystals. 240. P. W. Fowler and P. A. Madden, Phys. Rev. B: Condens. Matter, 29, 1035–1042 (1984). In-crystal Polarizabilities of Alkali and Halide Ions. 241. J. K. Badenhoop and F. We<strong>in</strong>hold, J. Chem. Phys., 107, 5422–5432 (1997). Natural Steric Analysis: Ab Initio van der Waals Radii of Atoms and Ions. 242. A. Warshel and R. M. Weiss, J. Am. Chem. Soc., 102, 62<strong>18</strong>–6226 (1980). An Emprical Valence Bond Approach for Compar<strong>in</strong>g Reactions <strong>in</strong> Solutions and <strong>in</strong> Enzymes. 243. M. J. L. Sangster, Solid State Commun., 15, 471–474 (1974). Properties of Diatomic Molecules from Dynamical Models for Alkali Halide Crystals. 244. L. Greengard, and V. Rokhl<strong>in</strong>, J. Comput. Phys., 73, 325–348 (1987). A Fast Algorithm for Particle Simulations. 245. H.-Q. D<strong>in</strong>g, N. Karasawa, and W. A. Goddard III, J. Chem. Phys., 97, 4309–4315 (1992). Atom Level Simulations of a Million Particles: The Cell Multipole Method for Coulomb and London Nonbond Interactions. 246. R. W. Hockney and J. W. Eastwood, Computer Simulation Us<strong>in</strong>g Particles, Institute of Physics Publish<strong>in</strong>g, Bristol, UK, 1988. 247. T. Darden, D. York, and L. Pedersen, J. Chem. Phys., 93, 10089–10092 (1993). Particle Mesh Ewald: An N log(N) Method for Ewald Sums <strong>in</strong> Large Systems. 248. P. Ewald, Ann. Phys., 64, 253–287 (1921). Die Berechnung optischer und elektrostatischer Gitterpotentiale. 249. D. M. Heyes, J. Chem. Phys., 74, 1924–1929 (1981). Electrostatic Potentials and Fields <strong>in</strong> Inf<strong>in</strong>ite Po<strong>in</strong>t Charge Lattices. 250. M. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys., 97, 1990–2001 (1992). Reversible Multiple Time Scale Molecular Dynamics. 251. S. J. Stuart, R. Zhou, and B. J. Berne, J. Chem. Phys., 105, 1426–1436 (1996). Molecular Dynamics with Multiple Timescales: The Selection of Efficient Reference System Propagators. 252. P. Kaatz, E. A. Donley, and D. P. Shelton, J. Chem. Phys., <strong>18</strong>0, 849–856 (1998). A Comparison of Molecular Hyperpolarizabilities from Gas and Liquid Phase Measurements. 253. G. Maroulis, J. Chem. Phys., 94, 1<strong>18</strong>2–1190 (1991). Hyperpolarizability of H2O. 254. The l<strong>in</strong>ear <strong>in</strong>crease <strong>in</strong> polarization with molecule size assumes that the characteristic polarizability a is small compared to the characteristic volume per polarizable unit: a r3 . See Eqs. [15] and [16]. In cases where this approximation does not hold, the polarizability will <strong>in</strong>crease faster than l<strong>in</strong>early with system size, lead<strong>in</strong>g to a polarization catastrophe. 255. B. L. Bush, C. I. Bayly, and T. A. Halgren, J. Comput. Chem., 20, 1495–1516 (1999). Consensus Bond-Charge Increments Fitted to Electrostatic Potential or Field of Many Compounds: Application to MMFF94 Tra<strong>in</strong><strong>in</strong>g Set.
CHAPTER 4 New Developments <strong>in</strong> the Theoretical Description of Charge-Transfer Reactions <strong>in</strong> Condensed Phases Dmitry V. Matyushov* and Gregory A. Voth y * Department of <strong>Chemistry</strong> and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, and y Department of <strong>Chemistry</strong> and Henry Eyr<strong>in</strong>g Center for Theoretical <strong>Chemistry</strong>, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112 INTRODUCTION <strong>Reviews</strong> <strong>in</strong> <strong>Computational</strong> <strong>Chemistry</strong>, <strong>Volume</strong> <strong>18</strong> Edited by Kenny B. Lipkowitz and Donald B. Boyd Copyr ight © 2002 John Wiley & Sons, I nc. ISBN: 0-471-21576-7 Nearly half a century of <strong>in</strong>tense research <strong>in</strong> the field of electron transfer (ET) reactions <strong>in</strong> condensed phases has produced remarkable progress <strong>in</strong> the experimental and theoretical understand<strong>in</strong>g of the key factors <strong>in</strong>fluenc<strong>in</strong>g the k<strong>in</strong>etics and thermodynamics of these reactions. The field evolved <strong>in</strong> order to describe many important processes <strong>in</strong> chemistry and is actively expand<strong>in</strong>g <strong>in</strong>to biological and materials science applications. 1 Due to its significant experimental background and relative simplicity of the reaction mechanism, the problem of electron transitions <strong>in</strong> condensed solvents turned out to be a benchmark for test<strong>in</strong>g fundamental theoretical approaches to chemical activation. A number of excellent reviews deal<strong>in</strong>g with various aspects of the field have been written. Two volumes of Advances <strong>in</strong> Chemical Physics (Vols. 106 and 107, 1999) covered much of the progress <strong>in</strong> the field achieved <strong>in</strong> recent decades. Therefore, the aim of this chapter is not to replicate these 147
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CHAPTER 3 Potentials and Algorithms
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Vn (1 + cos(nω + γ)) 2 K θ (θ
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are modified by their environment w
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References 209 59. R. Kubo and Y. T