Ciarlet Essential Computational Modeling in Chemistry

1. Auflage 2010
ISBN: 978-0-444-53761-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 400 Seiten

Essential Computational Modeling in Chemistry presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling in Chemistry Vol. 10(2005). Computational Modeling is an active field of scientific computing at the crossroads between Physics, Chemistry, Applied Mathematics and Computer Science. Sophisticated mathematical models are increasingly complex and extensive computer simulations are on the rise. Numerical Analysis and scientific software have emerged as essential steps for validating mathematical models and simulations based on these models. This guide provides a quick reference of computational methods for use in understanding chemical reactions and how to control them. By demonstrating various computational methods in research, scientists can predict such things as molecular properties. The reference offers a number of techniques and the numerical analysis needed to perform rigorously founded computations. Various viewpoints of methods and applications are available for researchers to chose and experiment with; Numerical analysis and open problems is useful for experimentation; Most commonly used models and techniques for the molecular case is quickly accessible

Autoren/Hrsg.

Ciarlet, Philippe G.

Inhaltsverzeichnis

1;Front Cover;1
2;Essential Computational Modeling in Chemistry;4
3;Copyright;5
4;General Preface;6
5;Contributors;8
6;Contents;12
7;Chapter 1: The Modeling and Simulation of the Liquid Phase;14
7.1;1. Physical approaches to the study of liquids;19
7.2;2. Chemical approaches to the study of liquids;24
7.3;3. The energy of the system and the solvation energy;33
7.4;4. Computation of the electrostatic contribution;39
7.5;5. Geometry optimization;46
7.6;6. Molecular surface meshing;47
7.7;7. Monte Carlo methods;65
7.8;8. Molecular Dynamics;68
7.9;9. Quantum mechanics/molecular mechanics (QM/MM);71
7.10;10. Layered methods: ONIOM;73
7.11;11. The effective fragment potential (EFP) method;74
7.12;12. Car-Parrinello ab initio molecular dynamics: AIMD;75
7.13;13. Liquids;78
7.14;14. Molecules in solution;84
7.15;15. Continuum solvation approaches;104
7.16;References;108
8;Chapter 2: Computational Approaches of Relativistic Models in Quantum Chemistry;114
8.1;1. Introduction;115
8.2;2. Linear Dirac equations;119
8.3;3. The MCDF method for atoms;130
8.4;4. Numerical relativistic methods for molecules;138
8.5;References;141
9;Chapter 3: Quantum Monte Carlo Methods for the Solution of the Schrödinger Equation for Molecular Systems;144
9.1;Preface;144
9.2;Part I. Introduction;145
9.3;1. Numerical solution of the Schrödinger equation;146
9.4;2. Properties of the exact wave function;147
9.5;Part II. Algorithms;149
9.6;3. Variational Monte Carlo;149
9.7;4. Wave function optimization;157
9.8;5. Projector methods;158
9.9;Part III. Special topics;174
9.10;6. Fermion nodes;174
9.11;7. Treatment of heavy elements;176
9.12;8. Other properties;177
9.13;Acknowledgments;184
9.14;References;185
10;Chapter 4: Finite Difference Methods for Ab Initio Electronic Structure and Quantum Transport Calculations of Nanostructures;192
10.1;1. Introduction;192
10.2;2. Electronic structure calculation by finite differences;196
10.3;3. Quantum transport;215
10.4;4. Applications: conductivity from ab initio local orbital Hamiltonian;221
10.5;Acknowledgments;226
10.6;References;227
11;Chapter 5: Simulating Chemical Reactions in Complex Systems;232
11.1;1. Introduction;232
11.2;2. Classical theories of reaction rates;233
11.3;3. Calculating condensed-phase potential energy surfaces;239
11.4;4. Simulation methods for investigating chemical reactions;248
11.5;5. Quantum algorithms;255
11.6;6. Challenges and perspectives;257
11.7;Acknowledgments;257
11.8;References;258
12;Chapter 6: Biomolecular Conformations Can Be Identified as Metastable Sets of Molecular Dynamics;262
12.1;1. Introduction;262
12.2;2. Conceptual preliminaries;264
12.3;3. Description of dynamical behavior;267
12.4;4. Metastability;273
12.5;5. Transfer operators;277
12.6;6. Numerical realization;288
12.7;7. Illustrative numerical experiments;293
12.8;8. Application to biomolecular systems;296
12.9;9. Appendix;298
12.10;References;303
13;Chapter 7: Numerical Methods for Molecular Time-Dependent Schrödinger Equations - Bridging the Perturbative to Nonperturbativ;306
13.1;1. Introduction;306
13.2;2. Gauges and representations;309
13.3;3. Numerical schemes;313
13.4;4. Boundary conditions and energy spectra;321
13.5;5. Beyond the dipole approximation;326
13.6;6. Conclusion;331
13.7;Acknowledgment;332
13.8;References;333
14;Chapter 8: Control of Quantum Dynamics;336
14.1;1. Introduction;336
14.2;2. Basic principles;338
14.3;3. Controllability of quantum mechanical systems;343
14.4;4. Quantum control algorithms;356
14.5;5. Challenges for the future;374
14.6;6. Conclusion;382
14.7;Acknowledgments;382
14.8;References;383
15;Subject Index;390

Leseproben

Chapter II Continuum Models As said above, continuum models tend to simplify the problem by introducing solvent response functions describing its interaction with the focused model (we shall call it for brevity the “solute”). The main advantage of this approach consists in a very large reduction of the internal degrees of freedom of the system one has to consider. In passing from the whole solution to the solute + continuum model, a detailed monitoring of all the degrees of freedom of the solvent molecules is no more necessary. The solvent response functions are specific for the various types of interactions occurring in liquids. Among them, that carrying more information is the electrostatic response. For several years also modern continuum methods were limited to the electrostatic interactions only. We shall consider now the origin and evolution of this electrostatic model starting from the seminal paper by ONSAGER [1936] in which he presented several concepts that are the basis of modern continuum methods. The model used in Onsager’s paper was quite simple. A solute, reduced to a point dipole, µ, but provided of polarizability a, is placed into a spherical cavity of appropriate radius; the solvent, placed out of the cavity is described as a continuous isotropic dielectric. The solute charge distribution induces a polarization of the dielectric, and in turns, this polarized medium polarizes the solute charge distribution, via an electric field, called by Onsager the solvent reaction field R. As a consequence the solute dipole changes from µ to µ*, this last depending on µ, its polarizability a, the dielectric constant e, and the radius a of the cavity. The elaboration of this formula, quite simple, was done on the basis of classical electrostatics. We have anticipate that this simple model introduces some basic concepts, among them we first quote the cavity. Onsager’s definition of cavity is a physical entity: it corresponds to a portion of the physical space in which the solvent is not allowed, because already occupied by the solute molecule. Kirkwood, another eminent figure in the study of liquid systems, remarked a short time after that this was an epochmaking innovation: all the cavities used before (e.g., Maxwell and Lorentz cavities, BÖTTCHER [1973], BÖTTCHER and BORDEWIJK [1978]) were just mathematical devices. Onsager was well aware of it. In its quoted papers he paid attention to the shape of the cavity, to its dependence on the thermally induced volume changes, to the problems related to the possible occurrence of hydrogen bonds. These are problems amply treated in the more recent versions of continuum models. The second concept introduced by Onsager is that of the reaction field. He spoke of the reaction field because its solute model was a dipole, now we are speaking more generally of a reaction potential. Here again he paid attention to the physical content of this concept: he analyzed some aspects of the nonideal behavior the homogeneous continuum dielectric may have in real systems, like the phenomena of nonlinearity that can be phenomenologically related to dielectric saturation and to electrostriction effects. Onsager also introduced a third concept, that of the cavity field G, occurring when the liquid sample is subjected to an external electric field E. G is related to E and to the geometrical factors defining size and shape of the cavity. The field R is the father of the electrostatic solute–solvent interaction potentials we are using in QM continuum models, G plays an important role in the very recent extensions of the continuum model to compute molecular properties. The development of these basic ideas will be discussed in the following pages. Here we remark that the original Onsager model continues to be amply employed, especially to get a rationale of experimentally observed trends in chemical properties. Some modifications of this models introduced new concepts. We quote its application to the description of solvent shifts in electronic spectra. An important development was the translation of this model in a QM language. In the models called Onsager–SCRF (or simply SCRF, were the acronym stays for self-consistent reaction field) the solute is described at the QM level, put in a spherical cavity and subjected to the action of a R field having as its origin the dipolar contribution of the charge distribution of the solute. This model is quite simple to implement and to use when a code for the calculation of QM molecular wavefunctions is available. For this reason the first implementation of the Onsager–SCRF model (TAPIA and GOSCINSKI [1975]) was done forty years after the original Onsager paper. Actually few years before (1973) a proposal was made by Rivail’s group in Nancy to introduce in the model other terms of the multipole expansion of the solute charge distribution. The proposal was expressed in a better way and documented by results in RIVAIL and RINALDI [1976]. This innovation eliminates at a good extent a defect of the too simple description of the electrostatic terms given in the original version: the use of the dipole only may produce serious deformations in the description of the solvent effects for molecules with a complex shape. A typical example is that of solutes having two or more identical polar groups, which are spatially arranged in the molecule to give a net value of the total dipole equal to zero: in this case the Onsager–SCRF model gives zero solvent effects. The original SCRF model has been continuously refined: we quote here the extension to ellipsoidal cavities and to cavities with a molecular shape. SCRF models are easy to implement and to use when the cavity has a constant curvature (sphere, ellipsoid). At present, they may also be used for more realistic cavities with a shape modeled on that of the molecule, but the elaboration of the model and in particular its use is a bit more delicate. The multipole expansion still presents some limits for complex molecules, that could be partially eliminated by using segmental local expansions, with expansion centers placed at opportune sites of the molecule. There exists programs able to do it, but they are rarely employed. The SCRF method has been further generalized to high-level QM approaches (like MCSCF and Coupled-Cluster) by MIKKELSEN, CESAR, ÅGREN and JENSEN [1995] who implemented the spherical version of the SCRF model in the Dalton QM code (HELGAKER ET AL. [2001]). An alternative approach to SCRF-like continuum models was proposed by our group. The first paper is of MIERTUŠ, SCROCCO and TOMASI [1981]. In this approach the multipole expansion used in all the previous models was replaced by another way of solving the electrostatic problem posed by the model. The solution of the Laplace and Poisson equations requested by the model was expressed in term of an apparent charge distribution, defined by applying theorems of classical electrostatics, and spread on the cavity surface. The solvent reaction potential was expressed in terms of this apparent charge properly discretized into point charges and introduced in the Hamiltonian of the solute as a solute–solvent interaction potential. In such a way the multipole expansions of both the molecular and the reaction potentials, rather cumbersome in the case of cavities of molecular shape, was avoided. The method was presented within a QM formalism for computing molecular wavefunctions of ab initio type (the previously quoted SCRF methods were at that time all at the semi-empirical level, probably because it was not easy to compute high multipole integrals with ab initio codes). The procedure we devised was the application to a QM problem of the boundary element method (BEM). We realized it later; actually at that time the name was not yet diffused in the literature. Afterwards it was called Polarizable Continuum Model (PCM) and it continues to keep this name even if many important improvements have been introduced in the years with respect to the original version (CAMMI and TOMASI [1995b], CANCÈS and MENNUCCI [1998b], CANCÈS, MENNUCCI and TOMASI [1997], MENNUCCI, CANCÈS and TOMASI [1997]). We shall consider later more details and extensions of PCM. Other methods sharing some similarity with PCM appeared in the nineties: among them we quote the socalled COSMO model and the methods making explicit use of other mathematical techniques, as the Finite Element method (FEM) and the finite difference (FD) approach. In the last two cases the solvent response function is obtained by sampling the solvent electric potential at a relatively large number of points inside the bulk dielectric. One among these methods has gained wide popularity in a semi-classical version (the solute charge distributions is reduced to a set of point charges on the nuclei) to study large biomolecules (CHEN and HONIG [1997]). In the method known with the acronym COSMO, the model is different as the screening effects in the dielectric are replaced by the screening effects in a conductor (KLAMT and SCHÜÜRMANN [1993], TRUONG and STEFANOVICH [1995]). In other words, COSMO method is a solution of the Poisson equation designed for the case of very high e, and it takes advantage of the analytic solution for the limit case of a conductor...