Modern Techniques in Computational Chemistry: Motecc-91

ISBN-13: 9789072199102 / Angielski / Twarda / 1991 / 1268 str.

Clementi, E.

Spis treści

1. Introduction to MOTECC-91.- Evolution of Computers and Simulations.- Global Simulation.- MOTECC-91: An “Assembly Line” to Produce Chemical Information.- An Example of Global Simulation: From 3 Nuclei and 10 Electrons to a Million Molecules.- Conclusions 20.- References 20.- 2. Independent Electron Models: Hartree-Fock for Many-Electron Atoms.- and Chapter Organization.- The Analytic Hartree-Fock Method.- Open Shell Methods and Roothaan Vector Coupling Coefficients.- Basis Sets for Atomic Computations.- Optimization of Orbital Exponents.- Contraction Coefficients.- Geometrical Basis Sets.- Matrix Elements, Spherical Symmetry and Integrals.- The Correlation and Pair Correlation Energies.- Density Functionals for Atomic Computations.- Configuration and Momentum Expectation Values.- The Finite Element Method (FEM).- Appendix 2A. Two-Electron Integrals.- Appendix 2B. Pseudopotentials.- References.- 3. Non-Relativistic Configuration Interaction Calculations for Many-Electron Atoms: ATOMCI.- Tensor Operator.- Recoupling Transformation.- Complete Set of Shell States.- Shell Creation Tensor Operators in LS-scheme.- Complete Shell States in LSQ-scheme.- Generation of Shell States in ATOMCI.- Matrix Elements.- Orthonormal Tensors for Many Shells.- Hamiltonian Operator.- Reduction Formulas for Matrix Elements.- Appendix 3A. Simply Reducible Group.- Integer Representation and Half Integer Representation.- Even and Odd Representation.- Three-j Symbols.- Six-j Symbol and Nine-j Symbol.- Appendix 3B. Rotation Group.- References.- 4. Kinetically Balanced Geometric Gaussian Basis Set Calculations for Relativistic Many-Electron Atoms.- Relativistic Hamiltonians and Relativistic Orbitals.- Matrix Elements of the Hamiltonian.- Choice of Basis Sets.- Relativistic Hartree-Fock-Roothaan Equation.- Angular Coefficients.- Evaluation of Radial Integrals.- Finite Nucleus Approximation.- Open-Shell Calculations.- Vector Coupling Coefficients.- Dirac-Fock Calculations.- Dirac-Fock-Breit Calculations.- Conclusions.- References.- 5. A Relativistic Multiconfiguration Self-Consistent-Field Method for Atoms.- Relativistic Hamiltonians.- Relativistic Wavefunctions.- The Hamiltonian Matrix.- Approximate Atomic Energies.- The Energy Functional.- Relativistic Basis Set Methods.- Relativistic Gaussian Basis Sets.- Analytical Expressions for One Electron Integrals.- Analytical Expressions for Two Electron Integrals.- The Method of Rotations.- Conclusion.- References.- 6. ALCHEMY II: A Research Tool for Molecular Electronic Structure and Interactions.- ALCHEMY II Program Modules.- Weak Molecular Interactions.- The He — H2O Interaction.- Approximate ICF Configuration Spaces.- Appendix 6A. The MOLECULE Integral Generator.- Appendix 6B. Algorithm for Large Scale Second Order MCSCF Calculations.- Overview of the MCSCF Method.- Second Order MCSCF Equation.- Orbital Gradient.- CI Gradient.- Orbitai Hessian.- CI-Orbital Coupling.- CI Hessian.- Large CI Expansions.- Matrix Formulation of Orbital Hessian.- Orbital Hessian.- Integral Transformation.- Iterative Solution of MCSCF Equations.- Iterative Solution of a System of Linear Equations.- Convergence Threshold.- The CI Portion of VX.- The Prototype CI Method.- Overview.- Prototype Configurations.- Prototype Matrices.- Prototype Diagonal Matrices.- Prototype Singles Matrices.- Prototype Doubles Matrices.- Discussion.- References.- 7. Quantum Molecular Dynamics with Gaussian Basis Set.- Combined DFT-MD Approach.- DFT with LCAO-Contracted Gaussians as a Basis Set.- Solutions to the Kohn-Sham Equations.- Energy Gradients and Molecular Dynamics.- Geometry Optimization.- Molecular Dynamics.- Example Calculation.- Summary.- References.- 8. Molecular Interactions and Large Molecules with KGNMOL.- Computation of Carbon Clusters.- Basis Sets: Gaussian Type Functions.- The Hydrogen Molecule and the Water Dimer.- Basis Set Superposition Error (BSSE).- Special Options for Adding Fragments or Molecules: ADD Option.- The MP2 Option.- Density Functionals for Molecules.- Clementi-Chakravorty Electron-Pair Functional.- Topology of Molecular Charge Distributions.- One-Electron Integral Formulae.- Incomplete and Complete Gamma Function.- Product of Gaussian Type Functions.- Normalization of Gaussian Type Functions.- Two-Electron Integral Formulae.- General Analytical Formulae.- Special Formulas for Integrals Involving s- and p-Type Functions.- Two-Electron Integrals with Explicit Factorization of One-Electron Dependent Terms.- Geometrical Basis Sets and Their Use.- Effective Core Potentials.- Packing and Unpacking Routines for Storing Two-Electron Integrals and Indices.- Appendix 8A. The Gaussian Product Theorem.- Appendix 8B. Integrals Related to the Gamma Function.- References.- 9. MELD: A Many Electron Description.- Integrals.- One-Electron Integrals, Closed Form.- Other One-Electron Integrals.- Two-Electron Integrals.- Auxiliary Functions.- Charge Distributions.- Pseudo Potentials.- Symmetrized Integrals.- Self Consistent Field.- Integral Transformation.- Configuration Interaction.- Eigenvalue Program.- Molecular Properties.- Appendix 9A. Evaluation of CI Matrix Elements.- References.- 10. MOLCAS: A General Purpose Quantum Chemistry Program System for Correlated Wavefunctions.- Program Descriptions.- Integral Evaluation and Handling.- The Two-Electron Transformation Program MOTRA.- The Self Consistent Field (SCF) Program.- The Restricted Active Space (RAS) SCF Program.- The RAS State Interaction (RASSI) Program.- The Configuration Interaction Programs.- Many Body Perturbation Theory (MBPT) Programs.- The Molecular Properties Program.- A Timing Example, The Pyrimidine Molecule.- Concluding Remarks.- References.- 11. AMPAC: A General Program for Chemical Calculations Using Procedures Developed by the Dewar Group.- Theory.- Applications of AMPAC.- Accuracy.- MOPAC and PM3.- References.- 12. HONDO: A General Atomic and Molecular Electronic Structure System.- Wavefunctions and Energies.- Closed Shell Hartree-Fock (SCF) Wavefunction.- Spin Unrestricted Open Shell Hartree-Fock (UHF) Wavefunction.- High Spin Restricted Open Shell Hartree-Fock (ROHF) Wavefunction.- General Restricted Open Shell Hartree-Fock and.- Valence Bond Wavefunctions (ROHF-GVB).- Configuration Interaction (CI) Wavefunction.- Multiconfiguration Hartree-Fock (MCSCF) Wavefunction.- Moller-Plesset Perturbation (MP2, MP3, MP4).- Electronic Properties.- Dipole Polarizability and Hyperpolarizabilities.- Molecular Structure Options.- Equilibrium Structure Determination.- Transition State Determination.- Force Constant Calculation.- Infrared and Raman Intensities Calculation.- Reaction Pathway Determination.- Potential Surface Scan.- Crossing Seam Minimum Energy Point Determination.- Non-Gradient Optimization.- Other Options.- Electron Transfer Reactions.- Effective Core Potentials.- Representation of An External Field.- Miscellaneous Features.- Integrals and Derivatives.- Point Group Symmetry.- Illustrative Examples.- References.- 13. HYCOIN: Hylleraas Configuration Interaction Method Using Gaussian Functions.- HCI Theory.- Applications and Specific Examples.- Two-electron Systems.- Verification of the Three-Electron Theory.- Two-electron Integrals in Gaussian Cartesian Functions.- The S Integral.- The K Integral.- The N Integral.- Three-electron Integrals in Gaussian Cartesian Functions.- The S Integral.- The T Integral.- The K Integral.- The N Integral.- Four-electron Integrals in Gaussian Cartesian Functions.- The S Integral.- The T Integral.- The U Integral.- Many-electron Integrals in Gaussian Lobe Functions.- Two-electron Integral Formulas.- The K Integral.- The S Integral.- The N Integral.- Three-electron Integral Formulas.- The K Integral.- The S Integrals.- The T Integral.- The N Integral.- Numerical Examples and Discussion.- Many-electron Integrals with Exponential-type Correlation Factor.- The SE Integral.- The EE Integral.- The KE Integral.- The NE Integral.- Appendix 13A. The R(ij) Operator.- References.- 14. SIRIUS: A General Purpose Direct Second Order MCSCF Program.- Outline of Program Features.- Theory.- Orbital Based Quantum Chemistry: The Hamiltonian.- Parameterization of the MCSCF Wave Functions.- Restricted-step. Second-order MCSCF Optimization.- The Direct Iterative NEO Algorithm.- Implementation.- Gradient Evaluation.- The Macro Iterations, Step Calculation, and Step Control.- The Micro Iterations, the Dynamical Update of the Damping Factor, and the Direct MCSCF Step.- Integral Transformations.- Step-Control Algorithm.- Direct Configuration Interaction Theory.- RAS-CI Expansions in a CSF Basis.- Slater Determinants and Strings.- Direct CI for RAS Expansions.- Construction of Density Matrices.- Counter Rotations of CI Coefficients.- Auxiliary Optimization Algorithms.- Split Configuration and Orbital Trial Vectors.- Optimal Orbital Trial Vectors.- Convergence of Solution Vectors in Direct NEO and NR Algorithms.- Transformation to Natural and Fock Type Orbitals.- Intermediate Optimization of Orbitals for Fixed Configuration Coefficients.- Initial Guess and Optimization of Core Hole States.- References.- 15. Dirac-Fock Self-Consistent Field Calculations for Closed Shell Molecules with Kinetic Balance and Finite Nuclear Size.- Preliminary.- Choice of Basis Spinors.- Evaluation of One-Electron and Two-Electron Matrix Elements.- Evaluation of Small-Component Matrix Elements.- Evaluation of Primitive Integrals in Cartesian Form.- Numerical Considerations and Preliminary Results.- Concluding Remarks.- Appendix 15A. Finite Nuclear Size Corrections.- Appendix 15B. Eulerian Angles and Rotation Matrix Elements.- References.- 16. Continuum by L2 Methods: Molecular Photoionization Cross Section.- Molecular States in the Electronic Continuum.- The K-Matrix Technique.- The Partial Wave Channels.- The L2 Basis Set Approximation.- RPA Matrix Elements in the Continuum.- One- and Two-Photons Transition Matrix Elements.- One-Photon Transitions.- Two-Photon Transitions.- Integral Cross Section by L2 Methods.- Stieltjes Imaging.- Generalization of the Stieltjes Imaging.- Computational Aspects.- The Basis Set.- One Photon Ionization.- Two Photon Ionization.- Appendix 16A. Rotationally Averaged Differential Cross Sections.- References.- 17. RMPROP: A Computer Program for Quantum Mechanical Close Coupling Calculations for Inelastic Collisions.- Close Coupling Theory.- Coupled Channels Equations.- Asymptotic Boundary Conditions.- R Matrix Propagation Algorithm.- Sector Adiabatic Basis Functions.- Sector Propagation Matrix.- Stepsize Determination.- Propagation Across Sector Boundaries.- Reduction of the Number of Closed Channels Propagated in the Larger Region.- Asymptotic Reordering of Channels.- Single and Multiple Energy Runs.- Program Structure.- Segmentation of Program and Flow Chart.- Restart Options.- Vectorization.- Concluding Remarks.- References.- 18. BNDPKG2: A Linear Combination of Gaussian Orbitals (LCGO) Band Structure Program for Cubic Crystals with One Atom per Unit Cell.- The LCGO Method for Energy Band Calculations.- BNDPKG 2.- Sample BNDPKG 2 Calculations.- References.- 19. LCAO Ab Initio Band Structure Calculations for Polymers.- The Periodic Model of a Polymer Chain.- Principles of LCAO Band Structure Calculations on Polymers.- The Electrostatic Balance between the Nucleus- and Electron-Electron Interactions.- Multipole Expansion for Long-Range Coulomb Interactions.- The Short- or Long-Rangeness Character of the Exchange Contribution.- Use of Screw Symmetry in Polymer Calculations.- A Simulated Ab Initio Technique: The Valence Effective Hamiltonian (VEH).- Particular Aspects of Computer Implementation.- Band Structure Calculations.- Summation over Polymeric States and Integrations over First Brillouin Zones.- Basis Set Linear Dependence.- Band Indexing Difficulty.- Density of States Calculations.- Graphics Interface: BandDos.- Applications.- Appendix 19A. Tables of VEH Parameters.- Single-Zeta Potentials.- Double-Zeta Potentials.- References.- 20. First Principles Molecular Dynamics.- The Interatomic Potential within DF Theory.- A Dynamical Approach to Energy Functional Minimization.- Molecular Dynamics in the Coupled Electron-Ion Parameter Space.- Conclusions.- References.- 21. Molecular Dynamics Simulations with ab initio Interaction Potentials.- Interaction Potentials.- Ab initio Force Field for Biomolecules.- Classification of Atoms.- The Molecular Dynamics Method.- Numerical Integration for the Equations of Motion.- Calculation of Properties.- Properties Related to Neutron Scattering Experiments.- Periodic Boundary Conditions and Long Range Forces.- Free Energy Calculations.- Energy Minimization.- Gradient Methods.- Minimization Applications.- Applications and Examples.- Liquid Water with the Flexible ab initio Potential.- BPTI Simulations in Vacuo and in Solution.- Neutron Scattering Properties.- Examples Using the ab initio Force Field.- ?-Helix Stability of C-peptide.- Conformational Analysis of Cyclolinopeptide A.- Interaction of Spermine with Oligonucleotide.- References.- 22. Langevin Dynamics Simulations of Biomolecules.- Computational Algorithm for Langevin Dynamics Simulations.- Langevin Dynamics Simulation of the BPTI Protein.- Discussion.- References.- 23. Molecular Dynamics Simulations of Fluid Flows.- Computational Algorithm for a Large Scale Molecular Dynamics Simulation.- Applications and a Discussion of Results.- References.- 24. Brownian Dynamics Simulations of a Complex Fluid System.- Brownian Dynamics Simulation: Basic Concepts.- Fokker-Planck Description.- Langevin Description.- The Simulation Program “BROWNIAN”: An Overview.- The Nonlinear Rheology of the Colloidal Suspension.- Discussion.- Shear Induced Phase Transition in a Colloidal Suspension.- Generalized Brownian Dynamics Techniques.- References.- 25. Protein Structure Prediction and Neural Networks.- Neural Networks.- Neural Networks in Globular Protein Secondary Structure Predictions.- Neural Networks in Globular Protein Tertiary Structure Predictions.- Methods.- Tools.- Testing the Proposal: BPTI as an Example.- Discussion and Future Development.- References.- 26. Cellular Automata.- Cellular Automata.- Two-Dimensional Lattice-Gas Automata.- Simulation of 2D Fluid Flows.- Three-Dimensional Lattice-Gas Automata.- Results of 3D Simulations.- References.- 27. Microscopic and Mesoscopic Simulations of Complex Flows with Cellular Automata and Related Techniques.- Review of Boolean Lattice Gas.- From Microscopic to Mesoscopic: The Lattice Boltzmann Equation.- LBE with Enhanced Collisions.- Subgrid Modelling of Fluid Turbulence.- Applications of LBE.- Three-dimensional Laminar Flows in Complex Geometries.- Bifurcations of a Two-dimensional Poiseuille Flow.- Fully Developed Two-dimensional Forced Turbulence.- Performance Considerations.- What Next?.- Quantum Automata.- Conclusion.- References.- 28. The Equations of Fluid Flow and Their Solution by Numerical Methods.- The Equations of Fluid Flow.- Derivation of the Navier Stokes Equations.- Reduction to Various Specific Forms.- The Finite Element Method.- The Method of Weighted Residuals.- The H-Version of the Finite Element Method.- The P-Version of the Finite Element Method.- Solution Techniques.- Direct Solution Methods.- Iterative Methods.- Overview of Preconditioning Techniques.- Multilevel Solution Method.- Computational Solution of the Navier Stokes Equations.- Parallel Implementation of the Solution Scheme.- Turbulent Flow.- Reynolds Equations.- Empirical Relations for the Reynolds Stress Tensor.- Direct Numerical Simulation of Isotropic Turbulent Flows.- Dealiasing.- Time Stepping Scheme.- Parallel Implementation of the Numerical Scheme.- Results.- Application of the Finite Element Method in Quantum Chemistry.- References.- 29. The Equations of Elasticity and Their Solution by Finite Element Methods.- The Equations of Elasticity.- Computational Techniques for Linear Static Analysis.- Solution of Large 3-D Problems with Finite Elements.- Iterative Solution with the Conjugate Gradient Method.- Rapid Operator Application.- Utility of Rapid Operator Application.- Parallel Implementation of Iterative Schemes.- References.- 30. Numerical Modeling of Axisymmetric Laminar Flames.- Problem Formulation.- Method of Solution.- Serial Implementation.- Parallel Implementation.- References.- 31. Modeling of Atmospheric Pollutant Transport in Shorelines.- Model Development and Governing Equations.- Equations for the Mesoscale Variables.- Equations for the Synoptic Scale Variables.- Boundary Layer Parameterization.- Diffusivities in the Surface Layer.- Diffusivities in the Planetary Boundary Layer.- Numerical Methods.- Initial and Boundary Conditions.- Summertime Flow over a Lake.- Summary and Conclusions.- References.- 32. Interactive Visualization Techniques for Chemistry: KGNGRAF, XWIB and REMOTE.- The graPHIGS Application Programming Interface (API).- to KGNGRAF.- The User Interface.- Display of Molecular Models.- Display of Electron Densities and Molecular Orbitals.- Creation and Manipulation of Molecules.- Superposition of Molecular Structures.- Molecule Building from Templates.- Protein Building from Templates.- Inquiry of Geometrical Parameters.- Display of Molecular Vibrations and Molecular Spectra.- Display of Molecular Energy Diagrams.- Interactive Animations.- Files Manipulation.- Windows Oriented Interfaces for Input Specification.- XWIB: An X Window Interface Builder.- Format Checking.- Dependency Handling Mechanisms.- Help Messages.- On-Line Documentation.- Other Utility Functions.- REMOTE: Remote File Transfer and Execution.- Summary.- References.- 33. LCAP: Loosely Coupled Array of Processors Parallel Processing Systems.- The LCAP-3090 Experimental System.- Early LCAP Systems.- LCAP Parallel Processing Software and Performance Issues.- LCAP Design Philosophy.- LCAP Features for Effective Parallelism.- Conclusions.- Author Index.