Keywords:
Molecules -- Models.
;
Chemical models.
;
Electronic books.
Description / Table of Contents:
Reflecting the growing volume of published work in this field, researchers will find this book an invaluable source of information on current methods and applications.
Type of Medium:
Online Resource
Pages:
1 online resource (525 pages)
Edition:
1st ed.
ISBN:
9781847553317
Series Statement:
Issn Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=1185320
DDC:
541.22015118
Language:
English
Note:
Chemical Modelling -- Contents -- Chapter 1 Electric Multipoles, Polarizabilities and Hyperpolarizabilities -- 1 Introduction -- 2 Perturbation of Molecules by Static Electric Fields: General Theory -- 2.1 Analytic Derivatives of the Energy -- 3 Frequency-Dependent Polarizabilities: General Theory -- 3.1 Time-Dependent Perturbation Theory: The Sum over States Method -- 3.1.1 Second Order Effects -- 3.1.2 Third Order Effects -- 3.2 Measurement of the Dynamic Hyperpolarizabilities -- 4 Methods of Calculation: Development from 1970 to 1998 -- 4.1 Permanent Multipoles -- 4.2 Static Polarizabilities and Hyperpolarizabilities -- 4.3 Dynamic Response Functions -- 4.4 The First Hyperpolarizability of Organic Donor/Acceptor Molecules -- 4.5 Calculations of the Second Hyperpolarizability -- 5 Review of Literature: 1998-May 1999 -- 5.1 Dipole and Quadrupole Moments -- 5.2 Polarizabilities and Hyperpolarizabilities of Small Molecules -- 5.2.1 Diatomic Molecules -- 5.2.2 Butadiene -- 5.2.3 Static Polarizabilities and Hyperpolarizabilities by ab initio Methods -- 5.2.4 Dynamic Polarizabilities and Hyperpolarizabilities by ab initio Methods -- 5.2.5 Density Functional Calculations -- 5.2.6 Clusters and Small Homologous Series -- 5.2.7 Excited State Polarizabilities -- 5.3 Polarizabilities and Hyperpolarizabilities of Larger Molecules -- 5.3.1 Ab initio Calculations -- 5.3.2 Semi-Empirical Methods -- 5.3.3 Linear Conjugated Chains -- 5.3.4 Vibrational Polarization -- 5.3.5 Fullerenes -- 5.3.6 Solvent Effects, Crystal Fields -- 5.3.7 New Theoretical Developments -- References -- Chapter 2 Atomic Structure Computations -- 1 Introduction -- 2 Methods with Coefficients Dependent on the Frequency of the Problem -- 2.1 Exponential Multistep Methods -- 2.1.1 The Derivation of Exponentially-Fitted Methods for General Problems -- 2.1.2 Exponentially-Fitted Methods.
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2.1.3 Linear Multistep Methods -- 2.1.4 Predictor-Corrector Methods -- 2.1.5 New Insights in Exponentially-Fitted Methods -- 2.1.6 A New Tenth Algebraic Order Exponentially-Fitted Method -- 2.1.7 Open Problems in Exponentially Fitting -- 2.2 Bessel and Neumann Fitted Methods -- 2.3 Phase Fitted Methods -- 2.3.1 A New Phase Fitted Method -- 2.4 Numerical Illustrations for Exponentially-Fitted Methods and Phase Fitted Methods -- 2.4.1 The Resonance Problem: Woods-Saxon Potential -- 2.4.2 Modified Woods-Saxon Potential: Coulombian Potential -- 2.4.3 The Bound-States Problem -- 2.4.4 Remarks and Conclusion -- 3 Theory for Constructing Methods with Constant Coefficients for the Numerical Solution of Schrödinger Type Equations -- 3.1 Phase-lag Analysis for Symmetric Two-Step Methods -- 3.2 Phase-lag Analysis of General Symmetric 2k-Step, k ε N Methods -- 3.3 Phase-lag Analysis of Dissipative (Non-Symmetric) Two-Step Methods -- 3.4 Phase-lag Analysis of the Runga-Kutta Methods -- 3.5 Phase-lag Analysis of the Runga-Kutta-Nyström Methods -- 4 Methods with Constant Coefficients -- 4.1 Implicit Methods -- 4.1.1 P-Stable Methods -- 4.1.2 Methods with Non-Empty Interval of Periodicity -- 4.2 Explicit Methods -- 4.2.1 Fourth Algebraic Order Methods -- 4.2.2 Sixth Algebraic Order Methods -- 4.2.3 Eighth Algebraic Order Methods -- 5 Variable-Step Methods -- 6 P-Stable Methods of High Exponential Order -- 7 Matrix Methods for the One-Dimensional Eigenvalue Schrödinger Equation -- 7.1 Methods of Discretization -- 7.1.1 Methods Which Lead to a Tridiagonal Form of the Matrix A -- 7.1.2 Methods Which Lead to a Pentadiagonal Form of the Matrix A -- 7.1.3 Methods Which Lead to a Heptadiagonal Form of the Matrix A -- 7.1.4 Numerov Discretization -- 7.1.5 Extended Numerov Form -- 7.1.6 An Improved Four-Step Method -- 7.1.7 An Improved Three-Step Method.
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7.1.8 An Improved Hybrid Four-Step Method -- 7.2 Discussion -- 8 Runga-Kutta and Runga-Kutta-Nyström Methods for Specific Schrödinger Equations -- 9 Two Dimensional Eigenvalue Schrödinger Equation -- 10 Numerical Illustrations for the Methods with Constant Coefficients and the Variable-Step Methods -- 10.1 Methods with Constant Coefficients -- 10.1.1 Remarks and Conclusion -- 10.2 Variable-Step Methods -- 10.2.1 Error Estimation -- 10.2.2 Coupled Differential Equations -- 10.3 Remarks and Conclusion -- Appendix -- References -- Chapter 3 Atoms in Molecules -- 1 Introduction -- 1.1 What Is AIM? -- 1.2 Scope -- 1.3 The Roots of AIM -- 1.4 The Development of AIM -- 1.5 Software -- 2 Theoretical -- 2.1 Open Systems -- 2.2 Molecular Similarity and QSAR -- 2.3 Electron Correlation -- 2.4 Transferability -- 2.5 Multipoles -- 2.6 Molecular Dynamics -- 2.7 Partitioning -- 3 The Laplacian -- 3.1 Alternative Wave Functions -- 3.2 Relation to Bohm Quantum Potential -- 3.3 Protonation -- 4 Electron Densities from High-resolution X-ray Diffraction -- 4.1 State of the Art -- 4.2 Comparison between Experimental and Theoretical Densities -- 4.3 Hydrogen Bonding -- 4.4 Organic Compounds -- 4.5 Transition Metal Compounds -- 4.6 Minerals -- 5 Chemical Bonding -- 5.1 Theory -- 5.2 Ligand Close Packing (LCP) Model -- 5.3 Hypervalency -- 5.4 Organic Compounds -- 5.5 Transition Metal Compounds -- 5.6 Minerals -- 5.7 Solid State -- 5.8 Compounds of Atmospheric Interest -- 5.9 Van der Waals Complexes -- 6 Hydrogen Bonding -- 6.1 Review -- 6.2 Relationships -- 6.3 Cooperative Effect -- 6.4 Bifurcated Hydrogen Bonds -- 6.5 Low-barrier Hydrogen Bonds -- 6.6 Dihydrogen Bonds -- 6.7 Very Strong Hydrogen Bonds -- 6.8 Organic Compounds -- 6.9 Biochemical Compounds -- 6.10 Compounds of Atmospheric Importance -- 7 Reactions -- 7.1 Organic Compounds -- 7.2 Inorganic Compounds.
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8 Conclusion -- 9 Disclaimer -- References -- Chapter 4 Modelling Biological Systems -- 1 Introduction -- 2 G-Protein Coupled Receptors -- 3 Protein-Protein Docking -- 3.1 Traditional Docking Approaches -- 3.2 Sequence-based Approaches to Docking -- 4 Simulations on the Early Stages of Protein Folding -- 5 Simulations on DNA -- 5.1 Particle Mesh Ewald -- 6 Free Energy Calculations -- 6.1 Free Energy Calculations from a Single Reference Simulation -- 6.2 Multimolecule Free Energy Methods -- 6.3 Linear Response Method -- 6.4 Free Energy Perturbation Methods with Quantum Energies -- 6.5 Force Fields -- 7 Continuum Methods -- 7.1 Parameter Dependence -- 7.2 pKa Calculations -- 7.3 Binding Studies -- 7.4 Protein Folding and Stability -- 7.5 Solvation and Conformational Energies -- 7.6 Redox Studies -- 7.7 Additional Studies -- 8 Hybrid QM/MM Calculations -- 8.1 Methodology Developments -- 8.2 The Models -- 8.3 The Link Atom Problem -- 8.4 Miscellaneous Improvements -- 8.5 The "Onion" Approach -- 8.6 Applications -- 8.6.1 Nickel-Iron Hydrogenase -- 8.6.2 β-Lactam Hydrolysis -- 8.6.3 Bacteriorhodopsin -- 8.6.4 The Bacterial Photosynthetic Reaction Centre -- 8.6.5 Other Studies -- 9 Car-Parrinello Calculations -- Acknowledgement -- References -- Chapter 5 Relativistic Pseudopotential Calculations, 1993-June 1999 -- 1 Methods -- 1.1 Introduction -- 1.2 Model Potentials -- 1.3 Shape-Consistent Pseudopotentials -- 1.4 DFT-Based Pseudopotentials -- 1.5 Soft-Core Pseudopotentials and Separability -- 1.6 Energy-Consistent Pseudopotentials -- 1.7 Core-Polarization Pseudopotentials -- 1.8 Concluding Remarks -- 2 Applications by Element -- 3 Some Applications by Subject -- 3.1 New Species -- 3.2 Metal-Ligand Interactions -- 3.3 Closed-Shell Interactions -- 3.4 Chemical Reactions and Homogeneous Catalysis -- 3.5 Chemisorption and Heterogeneous Catalysis -- 3.6 Other.
,
Acknowledgements -- References -- Chapter 6 Density-Functional Theory -- 1 Introduction -- 2 Fundamentals -- 2.1 Wavefunction-based Methods -- 2.2 Approximating the Schrödinger Equation -- 2.3 Density-functional Theory -- 2.4 Hybrid Methods -- 3 Structural Properties -- 3.1 Structure Optimization -- 3.2 Examples of Structure Optimizations -- 4 Vibrations -- 5 Relative Energies -- 5.1 Dissociation Energies -- 5.2 Comparing Isomers -- 6 Chemical Reactions -- 6.1 Transition States -- 6.2 Hardness, Softness and Other Descriptors -- 7 Weak Bonds -- 7.1 van der Waals Bonds -- 7.2 Hydrogen Bonds -- 8 The Total Electron Density -- 9 The Orbitals -- 10 Excitations -- 11 Spin Properties -- 11.1 NMR Chemical Shifts -- 11.2 Electron Spin -- 11.3 Electronic Spin-Spin Couplings -- 11.4 Nuclear Spin-Spin Couplings -- 12 Electrostatic Fields -- 13 Solvation -- 13.1 Dielectric Continuum -- 13.2 Point Charges -- 14 Solids -- 14.1 Band Structures -- 14.2 Applications -- 15 Liquids -- 16 Surfaces as Catalysts -- 17 Intermediate-sized Systems -- 18 Conclusions -- Acknowledgements -- References -- Chapter 7 Many-body Perturbation Theory and Its Application to the Molecular Electronic Structure Problem -- 1 Introduction -- 1.1 A Personal Note -- 2 Theoretical Apparatus and Practical Algorithms -- 2.1 Quantum Electrodynamics and Many-body Perturbation Theory -- 2.1.1 The N-Dependence of Perturbation Expansions -- 2.1.2 The Linked Diagram Theorem -- 2.2 Many-body Perturbation Theory -- 2.2.1 Closed-shell Molecules -- 2.2.2 Open-shell Molecules -- 2.3 Relativistic Many-body Perturbation Theory -- 2.3.1 The Dirac Spectrum in the Algebraic Expansion -- 2.3.2 Many-electron Relativistic Hamiltonians -- 2.3.3 The 'No Virtual Pair' Approximation -- 2.3.4 Quantum Electrodynamics and Virtual Pair Creation Processes -- 2.4 The Algebraic Approximation.
,
2.4.1 Gaussian Basis Sets and Finite Nuclei.
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