Information Theory of Molecular Systems (eBook)

Roman F Nalewajski (Autor)

eBook Download: PDF | EPUB

2006 | 1. Auflage
462 Seiten
Elsevier Science (Verlag)
978-0-08-045974-5 (ISBN)

Infos

As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information distance (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity.

The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT), followed by an outline of the main ideas and techniques of IT, including several illustrative applications to molecular systems. Coverage includes information origins of the chemical bond, unbiased definition of molecular fragments, adequate entropic measures of their internal (intra-fragment) and external (inter-fragment) bond-orders and valence-numbers, descriptors of their chemical reactivity, and information criteria of their similarity and independence.

Information Theory of Molecular Systems is recommended to graduate students and researchers interested in fresh ideas in the theory of electronic structure and chemical reactivity.

?Provides powerful tools for tackling both classical and new problems in the theory of the molecular electronic structure and chemical reactivity
?Introduces basic concepts of the modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT)
?Outlines main ideas and techniques of Information Theory

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As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information "e;distance"e; (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT), followed by an outline of the main ideas and techniques of IT, including several illustrative applications to molecular systems. Coverage includes information origins of the chemical bond, unbiased definition of molecular fragments, adequate entropic measures of their internal (intra-fragment) and external (inter-fragment) bond-orders and valence-numbers, descriptors of their chemical reactivity, and information criteria of their similarity and independence. Information Theory of Molecular Systems is recommended to graduate students and researchers interested in fresh ideas in the theory of electronic structure and chemical reactivity.*Provides powerful tools for tackling both classical and new problems in the theory of the molecular electronic structure and chemical reactivity*Introduces basic concepts of the modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT)*Outlines main ideas and techniques of Information Theory

Inhalt

Cover 1
copyright 5
Preface 6
front matter 6
CONTENTS 12
Acronyms 18
INTRODUCTION 20
General Outlook 21
A Need for the Conceptual Approach 24
Chemical Understanding of Molecular Processes 28
Taylor Expansions of the Electronic Energy for Molecules and Reactants 33
Electron Wave-Function and Density Theories 38
Horizontal and Vertical Displacements of Molecular Electronic Structure 43
body 47
ALTERNATIVE PERSPECTIVES AND REPRESENTATIONS 47
Energy and Entropy Principles in Thermodynamics 48
Legendre Transformations 49
The Chemical Softness Representation 53
Closed (TV-Controlled) Systems 54
Open (mu-Controlled) Systems 57
The Chemical Hardness Representation 64
Closed (N-Controlled) Systems 65
Open (mu-Controlled) Systems 71
Transformations between Perturbations and Responses 73
ENTROPY, INFORMATION AND COMMUNICATION CHANNELS 75
Entropy and Information 76
Properties of Shannon Entropy 78
Entropy Deficiency 82
Fisher Information 84
Dependent Probability Distributions 89
Grouping/Combination Rules 93
Communication Channels 100
Principle of the Extreme Physical Information 105
PROBING THE MOLECULAR ELECTRON DISTRIBUTIONS 110
Entropy-Deficiency Descriptors of Molecular Electron Densities 111
Approximate Relations in Terms of the Density Difference Function 115
Displacements of Molecular Shannon Entropy 119
Illustrative Application to Propellanes 124
Electron Localization Function as Information Measure 128
ATOMS-IN-MOLECULES FROM THE INFORMATION THEORY 137
Introduction 138
One-Electron Stockholder Principle 142
Information-Theoretic Justification 146
Illustrative Two-Reference Problems 148
Many-Electron Stockholder Principle 151
Stockholder Partition of Two-Electron Distributions in Diatomics 155
Electron Distributions of One- and Two-Electron Stockholder Atoms 159
Vertical Effects of Electron Correlation 161
Horizontal Density Displacements due to Coulomb Correlation 167
Near-Dissociation Bond Elongation 171
Cluster Components of Two-Electron Stockholder AIM in Diatomics 177
Conclusion 185
OTHER PROPERTIES OF STOCKHOLDER SUBSYSTEMS 188
Local Entropy/Information Equalization Rules 189
Additivity of Information Distances 192
Entropy Displacements of Bonded Atoms 194
Vertical and Horizontal Density Displacements 203
Chemical Potential Equalization and Effective v-Representability 204
Charge Sensitivities 212
Conclusion 218
COMMUNICATION THEORY OF THE CHEMICAL BOND 220
Introduction 221
Molecules as "Communication" Systems 223
Atomic Discretization of Electron Distributions 223
Molecular Communication Channels 226
Example: Communication Channels of VB-Struetures in H2 230
Ground-State Indices of Chemical Bonds 238
Variational Principles 242
Two-Orbital Model of the Chemical Bond 243
Orbital Channel 245
Spin Channel 254
Multiplicities of n Bonds 256
Conclusion 260
ENTROPY/INFORMATION INDICES OF MOLECULAR FRAGMENTS 263
Introduction 264
Renormalized Channels of Separate Diatomics-in-Molecules 265
Communication Channels of the Mutually Separate Groups of AIM. 268
Combining Subsystem Indices into Global Information Descriptors 273
Additive Decomposition of Molecular Bond Indices 279
Illustrative Partial Channels of Molecular Fragments 285
Atomic Resolution of Global Entropy/Information Bond Indices 293
Bond-Entropy Concept 296
Reduced Channels of Molecular Fragments 298
Input and Output Reductions of Molecular Channels 298
Reduced pi Channels in Butadiene 303
General Combination Rules for Reduced Channels 305
Illustrative Results for Benzene 308
Conclusion 310
REACTIVE SYSTEMS 312
Charge Affinities of Stockholder Reactants 313
Simple Orbital Model of a Symmetric Transition-State Complex 318
Three-Orbital Model 318
Global Bond Descriptors from MO Theory 320
Overall Bond Multiplicities from Communication Theory 323
Separate Diatomic Channels 326
Partial Channels 327
Reduced Channels 335
Information-Distance Approach to Hammond Postulate 338
Conclusion 344
ELEMENTS OF THE INFORMATION-DISTANCE THERMODYNAMICS 346
Introduction 347
"Horizontal" Processes in Molecules 348
"Thermodynamic" Principle in Energy Representation 349
Illustrative Example: Hydrogen-Like Atom 353
"Thermodynamic"Principle for Non-Equilibrium Density 354
Variational Principles in Entropy-Deficiency Representation 355
Vertical Processes in Molecular Fragments 357
Equilibrium Distributions of Molecular Subsystems: "Thermodynamic" Interpretation 359
Instantaneous Processes 366
Conclusion 376
back matter 378
APPENDICES 378
APPENDIX A: Functional Derivatives 379
APPENDIX B: Geometric Interpretation of Density Displacements and Charge Sensitivities 383
Hilbert Space of Independent Density Displacement Modes 383
Density-Potential Relations 389
Geometric Decomposition of the Fukui Function 394
Geometric Decomposition of Density-Potential Kernels 395
APPENDIX C: The Kohn-Sham Method 398
APPENDIX D: Constrained Equilibria in Molecular Subsystems 403
State-Parameters in the Subsystem Description 404
Legendre-Transformed Representations 405
Charge Sensitivities 406
Additive and Non-Additive Components of Hardness and Softness Kernels 408
APPENDIX E: The Molecular Channels: Elaboration 410
"Phase" Problem in Excited Configurations of 2-AO Model 411
Singly-Excited Configurations 411
Doubly-Excited Configuration 417
The Partial "Forward" and "Reverse" Flows of Entropy/Information 418
Singly-Excited Configurations: Reappraisal 421
Local Hirshfeld Channel 423
APPENDIX F: Atomic Resolution of Bond Descriptors in the Two-Orbital Model 428
Row-Channels 428
Column-Channels 431
Atomic Bond-Indices and Valence-Numbers from MO Theory 433
APPENDIX G: Elements of Thermodynamic Description of Instantaneous Processes in Continuous Systems 435
Distributions of Instantaneous State-Variables 436
Elements of Hydrodynamic Description 437
REFERENCES 440
INDEX 453

Textauszug

1

Introduction

Abstract

A brief survey of modern concepts and principles of the electronic structure and chemical reactivity is presented with an emphasis on the importance of chemical concepts for understanding the molecular behavior. The specificity of the chemical interpretation of molecular processes, in terms of AIM, chemical bonds, functional groups, reactants, etc., is commented upon. The classical structural and reactivity rules are reviewed. The quadratic Taylor expansion of the electronic energy of molecular systems in powers of displacements (perturbations) of the system state-parameters is introduced. It is defined by the generalized response quantities: “potentials”, the first partials of the energy, and charge sensitivities, the second partials of the energy with respect to the system parameters of state. This series constitutes an adequate framework for describing reactant subsystems in a bimolecular reactive system. The role of the electronic density as the source and carrier of the complete information about the system ground-state equilibrium and all its physical and chemical properties is stressed. Basic elements of the electron wave-function and density-functional theories of electronic structure are summarized and the conceptual advantages of DFT over the standard wave-function approach are emphasized. The Euler equation for the ground-state density, the DFT equivalent of the Schrödinger equation of the wave-function theory, is discussed in some detail. It embodies the crucial ground-state relation between the equilibrium distribution of electrons and the external potential due to the system nuclei. This equation is shown to imply the chemical potential (electronegativity) equalization throughout the physical space. A distinction is made between transitions from one ground-state density to another, called here the “horizontal” displacements of the system electronic structure, and those corresponding to flows of electrons between molecular subsystems, for the fixed density of the molecule as a whole, called the “vertical” displacements.

1.1. General Outlook   2

1.2. A Need for the Conceptual Approach   5

1.3. Chemical Understanding of Molecular Processes   9

1.4. Taylor Expansions of the Electronic Energy for Molecules and Reactants   14

1.5. Electron Wave-Function and Density Theories   19

1.6. Horizontal and Vertical Displacements of Molecular Electronic Structure   24

1.1 GENERAL OUTLOOK

The prediction of chemical reactivity presents a constant challenge to chemists, who desire to define the optimum conditions for performing specific reactions. The basic aim of the so called reactivity “theories” is to predict reactivity trends or to find an explanation, in chemical terms, of the experimentally or computationally determined course of a reaction. Such theories have to provide means of systematization, recognition of regularities and rationalization of the myriads of established experimental and computational facts, to disclose the fundamental causes governing the reactivity phenomena. The most general of them are formulated in terms of the appropriate variational principles or the most favorable “matching” rules for the crucial physical properties of reactants (global or regional), which uncover the decisive factors responsible for the preferred direction of a given chemical process.

Investigations into the primary sources of the observed chemical behaviour of molecules cover both the thermodynamic/statistical and quantum-mechanical laws of chemical change. For example, the concept of an activation energy in a bimolecular reaction is statistical in character, but the actual value of this critical energy of reactants, which is required for the reactive outcome of their collision, cannot be understood without the quantum-mechanical description of changes in the electronic structure of reacting species.

The ultimate goal of theoretical chemistry is to predict and understand the electronic structure of chemical compounds and their reactions using concepts and techniques of both the static and dynamical approaches. The basic objective of the dynamical treatment is to calculate the rates of chemical reactions from the first principles. Given the interaction potential for the nuclear motion in the specified system of reactants, one should in general be able to determine the probabilities, cross-sections, and rate constants for fundamental elementary reaction processes by solving the quantum-mechanical equation of motion for the system. This dynamical goal, however, has so far been realized only for very simple reactions involving only three or four atoms, due to the computationally immense task in the theoretic determination of the complete electronically adiabatic, Born–Oppenheimer (BO) Potential Energy Surface (PES), and in solving the Schrödinger equation for nuclear motions.

Therefore, much of the present understanding of the chemical reaction dynamics at the molecular level has come about by using limited information about the multidimensional PES. For example, the model (analytical) PES, reproducing a network of selected ab initio points, or approximate methods, e.g., the classical trajectories, have been used to probe the dynamics of elementary reactive collisions. Another familiar example is the statistical Transition-State (TS) theory, in which only the data on the geometry and frequencies of the separated reactants and the TS complex are required to convert this limited information about the interaction between reactants into measurable rate quantities. The DFT rooted molecular charge sensitivities (CS) constitute attractive (static) concepts, in terms of which the truly two-reactant reactivity criteria can be defined within CSA, for both the externally (or mutually) closed or open subsystems (see: Ayers and Parr, 2000, 2001; Baekelandt et al., 1993; Cohen, 1996; Chattaraj and Parr, 1993; Gázquez, 1993; Gázquez et al., Geerlings et al., 2003; Nalewajski, 1993, 1995a,b, 1997a,b, 1999, 2000a, 2002d, 2003a; Nalewajski and Korchowiec, 1997; Nalewajski et al., 1996).

Recently, the familiar HK variational principle of DFT, which determines the electron ground-state density, has been interpreted (Nalewajski, 2005d) as that for the extremum of the electronic energy subject to the information entropy constraint, in close analogy to the familiar criterion of the thermodynamical equilibrium of macroscopic systems in the energy-representation (Callen, 1962). The equivalent extremum rule for the molecular entropy deficiency, subject to the constraint of a constant electronic energy, has also been given, again paralleling the familiar entropy-representation principle of classical thermodynamics. In this development the electronic chemical potential (negative electronegativity) of DFT (see Parr and Yang, 1989) appears as the system global information “temperature”. The associated local chemical potential gives rise to a similar “thermodynamic”-like description of the non-equilibrium electron densities of molecular systems in terms of the local information temperature. Of similar character is the application of the Extreme Physical (Fisher) Information (EPI) principle of Frieden (2000) to derive the Kohn-Sham (KS) (1965) equations of DFT (Nalewajski, 2003c), and to explore the entropic principles in Daudel’s Loge Theory (Aslangul et al., 1972; Daudel, 1969, 1974) of the molecular electronic structure (Nalewajski, 2003d).

It will be demonstrated in the book that the combined DFT/IT approach allows one to treat objectively both the “horizontal” and “vertical” displacements of the molecular electronic structure in a thermodynamic-like fashion. The “vertical” problem is vital for extracting the chemical interpretation from the known molecular electron density, in terms of such chemical concepts as bonded atoms, functional groups, reactants, lone electron pairs, and bonds, which connect the constituent subsystems in the molecule. For example, it has recently been demonstrated (Nalewajski and Parr, 2000, 2001; Nalewajski, 2002a, 2003c) that IT can be successfully used to tackle the definition of AIM, by searching for atomic densities, which reproduce the density of the system as a whole and exhibit the least information distance relative to the corresponding free atoms of the “promolecule”. These effective information-theoretic distributions of electrons in chemical atoms can be monitored at different stages of their reconstruction in a molecular environment, e.g., the optimum polarization (P) of the mutually closed atoms and after the charge-transfer (CT) between the system constituent atoms. Such information-theoretic AIM were shown to be identical with the familiar “stockholder” atoms of structural chemistry (Hirshfeld, 1977).

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Produkt-Details

• Erscheint lt. Verlag: 31.3.2006
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Chemie ► Organische Chemie
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik
• ISBN-10: 0-08-045974-9 / 0080459749
• ISBN-13: 978-0-08-045974-5 / 9780080459745