Modern Techniques in Computational Chemistry: MOTECC-91 Edited by Enrico Ciementi International Business Machines Corporation Kingston, New York 12401, U.S.A. ESCOM Leiden 1991
Modern Techniquesin
Computational Chemistry:MOTECC-91
Edited by
Enrico Ciementi
International Business Machines Corporation
Kingston, New York 12401, U.S.A.
ESCOM
Leiden 1991
Contents
Foreword to MOTECC-91 v
Foreword to MOTECC-90 vii
Foreword to MOTECC-89 xi
Chapter 1. Introduction to MOTECC-91
E. Ciementi
IBM Corporation, Dept. 48BJ428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 1
Evolution of Computers and Simulations 2
Global Simulation 9
MOTECC-91: An "Assembly Line" to Produce Chemical Information....
12
An Example of Global Simulation: From 3 Nuclei and 10 Electrons
to a Million Molecules 17
Conclusions 20
References 20
Chapter 2. Independent Electron Models: Hartree-Fock for
Many-Electron Atoms
E. Ciementi, S.J. Chakravorty, G. Corongiu, J.R. Flores
and V. Sonnad
IBM Corporation, Dept. 48BJ428, Neighborhood Road
Kingston, NY 12401, USA
Introduction and Chapter Organization 23
The Analytic Hartree-Fock Method 26
Open Shell Methods and Roothaan Vector Coupling Coefficients 31
Basis Sets for Atomic Computations 34
Optimization of Orbital Exponents 43
Contraction Coefficients 44
Geometrical Basis Sets 46
Matrix Elements, Spherical Symmetry and Integrals 61
xv
xvj Contents
The Correlation and Pair Correlation Energies 67
Density Functional for Atomic Computations 79
Configuration and Momentum Expectation Values 90
The Finite Element Method (FEM) 93
Appendix 2A. Two-Electron Integrals 107
Appendix 2B. Pseudopotentials 109
References 110
Chapter 3. Non-Relativistic Configuration Interaction Calculations
for Many-Electron Atoms: ATOMCI
F. Sasaki, M. Sekiya, T. Noro, K. Ohtsuki and Y. Osanai
Department of Chemistry, Faculty of Science, Hokkaido University
Sapporo 060, Japan
Introduction 115
Tensor Operator 117
Recoupling Transformation 121
Complete Set of Shell States 125
Shell Creation Tensor Operators in LS-scheme 126
Complete Shell States in LSQ-scheme 131
Generation of Shell States in ATOMCI 138
Matrix Elements 138
Orthonormal Tensors for Many Shells 138
Hamiltonian Operator 141
Reduction Formulas for Matrix Elements 142
Appendix 3A. Simply Reducible Group 146
Integer Representation and Half Integer Representation 147
Even and Odd Representation 150
Three-j Symbols 153
Six-j Symbol and Nine-j Symbol 159
Appendix 3B. Rotation Group 164
References 166
Chapter 4. Kinetically Balanced Geometric Gaussian Basis Set Calculations
for Relativistic Many-Electron Atoms
A.K. Mohanty, F.A. Parpia and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 167
Relativistic Hamiltonians and Relativistic Orbitals 169
Matrix Elements of the Hamiltonian 171
Choice of Basis Sets 174Relativistic Hartree-Fock-Roothaan Equation 175Angular Coefficients 177
Contents xvii
Evaluation of Radial Integrals 180
Finite Nucleus Approximation 182
Open-Shell Calculations 184
Vector Coupling Coefficients 189
Dirac-Fock Calculations 193
Dirac-Fock-Breit Calculations 200
Conclusions 204
References 206
Chapter 5. A Relativistic Mulriconflguration Self-Consistent-Field
Method for Atoms
F.A. Parpia and A.K. MohantyIBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 211
Relativistic Hamiltonians 212
Relativistic Wavefunctions 213
The Hamiltonian Matrix 216
Approximate Atomic Energies 217
The Energy Functional 218
Relativistic Basis Set Methods 218
Relativistic Gaussian Basis Sets 222
Analytical Expressions for One Electron Integrals 223
Analytical Expressions for Two Electron Integrals 226
The Method of Rotations 227
Conclusion 229
References 229
Chapter 6. ALCHEMY II: A Research Tool for Molecular Electronic
Structure and Interactions
A.D. McLean, M.Yoshimine, B.H. Lengsfield,P.S. Bagus and B. Liu
IBM Research Division, Almaden Research Center
650 Harry Road, San Jose, CA 95120-6099, USA
Introduction 233
ALCHEMY II Program Modules 234
Weak Molecular Interactions 236
The He - H20 Interaction 241
Approximate ICF Configuration Spaces 249
xvj;jContents
Appendix 6A. The MOLECULE Integral Generator254
J. Almlbf
Dept. of Chemistry, University of Minnesota
Minneapolis, MN 55455, USA
P.R. TaylorFLORET Institute, Palo Alto, CA 94303, USA
NASA Ames Research Center, Moffet Field, CA 94035, USA
Appendix 6B. Algorithm for Large Scale Second Order
MCSCF Calculations 256
B. Liu and B.H. LengsfieldIBM Research Division, Almaden Research Center,
650 Harry Road, San Jose, CA 95120-6099, USA
Introduction 256
Overview of the MCSCF Method 257
Second Order MCSCF Equation 258
Orbital Gradient 259
CI Gradient 259
Orbital Hessian 260
CI-Orbital Coupling 261
CI Hessian 261
Large CI Expansions 261
Matrix Formulation of Orbital Hessian 263
Orbital Hessian 263
Integral Transformation 265
Iterative Solution of MCSCF Equations 266
Iterative Solution of a System of Linear Equations 267
Convergence Threshold 268
The CI Portion of VX 269
The Prototype CI Method 269
Overview 269
Prototype Configurations 270
Prototype Matrices 272
Prototype Diagonal Matrices 273
Prototype Singles Matrices 274
Prototype Doubles Matrices 274
Discussion 275
References 276
Chapter 7. Quantum Molecular Dynamics with Gaussian Basis Set
B. Feuston, C. Lee and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Contents xix
Introduction 279
Combined DFT-MD Approach 280
DFT with LCAO-Contracted Gaussians as a Basis Set 283
Solutions to the Kohn-Sham Equations 286
Energy Gradients and Molecular Dynamics 289
Geometry Optimization 289
Molecular Dynamics 290
Example Calculation 291
Summary 292
References 293
Chapter 8. Molecular Interactions and Large Molecules with KGNMOL
E. Ciementi, G. Corongiu and O.G. Stradella
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 295
Computation of Carbon Clusters 297
Basis Sets: Gaussian Type Functions 307
The Hydrogen Molecule and the Water Dirner 310
Basis Set Superposition Error (BSSE) 316
Special Options for Adding Fragments or Molecules: ADD Option 317
The MP2 Option 319
Density Functionals for Molecules 321
Clementi-Chakravorty Electron-Pair Functional 334
Topology of Molecular Charge Distributions 339
One-Electron Integral Formulae 341
Incomplete and Complete Gamma Function 341
Product of Gaussian Type Functions 345
Normalization of Gaussian Type Functions 346
Two-Electron Integral Formulae 349
General Analytical Formulae 349
Special Formulas for Integrals Involving s- and p-Type Functions 352
Two-Electron Integrals with Explicit Factorization of the
One-Electron Dependent Terms 356
Geometrical Basis Sets and Their Use 358
Effective Core Potentials 366
Packing and Unpacking Routines for Storing Two-Electron Integralsand Indices 367
Appendix 8A. The Gaussian Product Theorem 370
Appendix 8B. Integrals Related to the Gamma Function 372
References 374
xxContents
Chapter 9. MELD: A Many Electron Description
E.R. Davidson
Department of Chemistry, Indiana University
Bloomington, IN 47405, USA
Introduction 381
Integrals382
One-Electron Integrals, Closed Form 386
Other One-Electron Integrals 387
Two-Electron Integrals389
Auxiliary Functions 391
Charge Distributions 394
Pseudo Potentials 394
Symmetrized Integrals 405
Self Consistent Field 408
Integral Transformation 412
Configuration Interaction 413
Eigenvalue Program 415
Molecular Properties 418
Appendix 9A. Evaluation of CI Matrix Elements 419
References 433
Chapter 10. MOLCAS: A General Purpose Quantum Chemistry Program
System for Correlated Wavefunctions
B.O. Roos, G. Karlstrom, P.-A. Malmqvist, A.J. Sadlej
Department of Theoretical Chemistry, Chemical Centre
P.O.B. 124, S-221 00 Lund, Sweden
P.-O. Widmark
S&TC Group, ACIS, IBM Sweden
Introduction 435
Program Descriptions 437
Integral Evaluation and Handling 437
The Two-Electron Transformation Program MOTRA 439
The Self Consistent Field (SCF) Program 440
The Restricted Active Space (RAS) SCF Program 441
The RAS State Interaction (RASSI) Program 444
The Configuration Interaction Programs 446
Many Body Perturbation Theory (MBPT) Programs 448
The Molecular Properties Program 449
A Timing Example, The Pyrimidine Molecule 450
Concluding Remarks 452
References 453
Contents xxi
Chapter 11. AMPAC: A General Program for Chemical Calculations UsingProcedures Developed by the Dewar Group
Michael J.S. Dewar
Department of Chemistry, The University of Florida
Gainesville, FL 32611, USA
Introduction 455
Theory 458
Applications of AMPAC 461
Accuracy 463
MOPAC and PM3 464
References 466
Chapter 12. HONDO: A General Atomic and Molecular Electronic
Structure System
M. Dupuis and S.A. Maluendes
IBM Corporation, Dept. 41PA/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 469
Wavefunctions and Energies 470
Closed Shell Hartree-Fock (SCF) Wavefunction 470
Spin Unrestricted Open Shell Hartree-Fock (UHF) Wavefunction 477
High Spin Restricted Open Shell Hartree-Fock (ROHF)Wavefunction 478
General Restricted Open Shell Hartree-Fock and Generalized
Valence Bond Wavefunctions (ROHF-GVB) 479
Configuration Interaction (CI) Wavefunction 480
Multiconfiguration Hartree-Fock (MCSCF) Wavefunction 481
Moller-Plesset Perturbation (MP2, MP3, MP4) 486
Electronic Properties 506
Dipole Polarizability and Hyperpolarizabilities 507
Molecular Structure Options 512
Equilibrium Structure Determination 512
Transition State Determination 513
Force Constant Calculation 513
Infrared and Raman Intensities Calculation 513
Reaction Pathway Determination 514
Potential Surface Scan 515
Crossing Seam Minimum Energy Point Determination 515
Non-Gradient Optimization 516
Other Options 516
Electron Transfer Reactions 516
Effective Core Potentials 521
Representation of An External Field 521
Miscellaneous Features 521
xx;j Contents
Integrals and Derivatives 521
Point Group Symmetry -524
Illustrative Examples 528
References -531
Chapter 13. HYCOIN: Hylleraas Configuration Interaction Method UsingGaussian Functions
A. Preiskorn, D. Frye, G.C. Lie and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 535
HCI Theory 538
Applications and Specific Examples 542
Two-electron Systems 542
Verification of the Three-Electron Theory 544
Two-electron Integrals in Gaussian Cartesian Functions 546
The S Integral 547
The K Integral 548
The N Integral 549
Three-electron Integrals in Gaussian Cartesian Functions 551
The S Integral 552
The T Integral 554
The K Integral 557
The N Integral 557
Four-electron Integrals in Gaussian Cartesian Functions 560
The S Integral 561
The T Integral 564
The U Integral 565
Many-electron Integrals in Gaussian Lobe Functions 567
Two-electron Integral Formulas 569The K Integral 570The S Integral 571The N Integral 571
Three-electron Integral Formulas 572
The K Integral 572
The S Integrals 573
The T Integral 578The N Integral 580
Numerical Examples and Discussion 587
Many-electron Integrals with Exponential-type Correlation Factor 588
The SE Integral 589
The EE Integral 590
The KE Integral 591
The NE Integral 592
Contents xxjjj
Appendix 13A. The R(rj) Operator 594
References 595
Chapter 14. SIRIUS: A General Purpose Direct Second Order MCSCF
Program
H.J.Aa. Jensen
Department of Chemistry, University of Aarhus
DK-8000 Aarhus C, Denmark
H. AgrenInstitute of Quantum Chemistry, University of UppsalaBox 518, S-751 20 Uppsala, Sweden
J. Olsen
Theoretical Chemistry, Chemistry Center, University ofLund
Box 124, S-221 00 Lund, Sweden
Introduction 599
Outline of Program Features 600
Theory 603
Orbital Based Quantum Chemistry: The Hamiltonian 603
Parameterization of the MCSCF Wave Functions 604
Restricted-step, Second-order MCSCF Optimization 608
The Direct Iterative NEO Algorithm 611
Implementation 615
Gradient Evaluation 617
The Macro Iterations, Step Calculation, and Step Control 619
The Micro Iterations, the Dynamical Update of the Damping Factor,and the Direct MCSCF Step 621
Integral Transformations 622
Step-Control Algorithm 623
Direct Configuration Interaction Theory 624
RAS-CI Expansions in a CSF Basis 624
Slater Determinants and Strings 628
Direct CI for RAS Expansions 631
Construction of Density Matrices 634
Counter Rotations of CI Coefficients 636
Auxiliary Optimization Algorithms 636
Split Configuration and Orbital Trial Vectors 636
Optimal Orbital Trial Vectors 638
Convergence of Solution Vectors in Direct NEO and NR Algorithms . . .639
Transformation to Natural and Fock Type Orbitals 641
Intermediate Optimization of Orbitals for Fixed ConfigurationCoefficients 641
Initial Guess and Optimization of Core Hole States 643
References 644
xxjvContents
Chapter 15. Dirac-Fock Self-Consistent Field Calculations for Closed
Shell Molecules with Kinetic Balance and Finite Nuclear Size
A. Mohanty, S. Panigrahy and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction647
Preliminary650
Choice of Basis Spinors656
Evaluation of One-Electron and Two-Electron Matrix Elements 660
Evaluation of Small-Component Matrix Elements 664
Evaluation of Primitive Integrals in Cartesian Form 673
Numerical Considerations and Preliminary Results 678
Concluding Remarks 682
Appendix 15A. Finite Nuclear Size Corrections 683
Appendix 15B. Eulerian Angles and Rotation Matrix Elements 688
References 691
Chapter 16. Continuum by L2 Methods: Molecular Photoionization
Cross Section
/. Cacelli
Scuola Normale Superiore, Piazza dei Cavalieri, 56126 Pisa, Italy
V. Carravetta and A. Rizzo
I. C. Q. E. M. del CNR, Via Risorgimento 35, 56126 Pisa, Italy
R. Moccia
Dipartimento di Chimica e Chimica Industriale, Universita di Pisa
Via Risorgimento 35, 56126 Pisa, Italy
Introduction 695
Molecular States in the Electronic Continuum 697
The K-Matrix Technique 700
The Partial Wave Channels 700
The L2 Basis Set Approximation 705
RPA Matrix Elements in the Continuum 708
One- and Two-Photons Transition Matrix Elements 710
One-Photon Transitions 710
Two-Photon Transitions 712
Integral Cross Section by L2 Methods 717
Stieltjes Imaging 718
Generalization of the Stieltjes Imaging 721
Computational Aspects 723
The Basis Set 723
One Photon Ionization 731
Two Photon Ionization 736
Contents xxv
Appendix 16A. Rotationally Averaged Differential Cross Sections 741
References 745
Chapter 17. RMPROP: A Computer Program for Quantum Mechanical Close
Coupling Calculations for Inelastic Collisions
M.J. Unekis, D.W. Schwenke*, N. Mullaney Harvey,and D.G. Truhlar
Dept. of Chemistry, Chemical Physics Program, and
Supercomputer Institute, University of Minnesota
Minneapolis, MN 55455-0431, USA
* University of Minnesota and NASA Ames Research Center
Moffett Field, CA 94035, USA
Introduction 749
Close Coupling Theory 751
Coupled Channels Equations 751
Asymptotic Boundary Conditions 754
R Matrix Propagation Algorithm 756
Sector Adiabatic Basis Functions 756
Sector Propagation Matrix 757
Stepsize Determination 760
Propagation Across Sector Boundaries 761
Reduction of the Number of Closed Channels Propagated in the
Large-r Region 762
Asymptotic Reordering of Channels 764
Single and Multiple Energy Runs 767
Program Structure 768
Segmentation of Program and Flow Chart 768
Restart Options 769
Vectorization 771
Concluding Remarks 771
References 772
Chapter 18. BNDPKG2: A Linear Combination of Gaussian Orbitals (LCGO)
Band Structure Program for Cubic Crystals with One Atom
per Unit Cell
N.E. Brener and J. CallawayDepartment of Physics and Astronomy
Louisiana State University, Baton Rouge, LA 70803, USA
J.M. Tyler
Department of Computer Science
Louisiana State University, Baton Rouge, LA 70803, USA
Introduction 773
The LCGO Method for Energy Band Calculations 775
xxvj Contents
BNDPKG 2 779
Sample BNDPKG 2 Calculations 785
References 790
Chapter 19. LCAO Ab Initio Band Structure Calculations for Polymers
J.M. Andre, J.L. Bredas, J. Delhalle and J.G. Fripiat
Laboratoire de Chimie Theorique Appliquee
Facultes Universitaires Notre-Dame de la Paix, 61 rue de Bruxelles
B-5000 Namur, Belgium
D.J. Vanderveken and D.P. Vercauteren
Laboratoire de Chimie Moleculaire Structurale
Facultes Universitaires Notre-Dame de la Paix, 61 rue de Bruxelles
B-5000 Namur, Belgium
Introduction 793
The Periodic Model of a Polymer Chain 794
Principles of LCAO Band Structure Calculations on Polymers 797
The Electrostatic Balance between the Nucleus- and
Electron-Electron Interactions 803
Multipole Expansion for Long-Range Coulomb Interactions 807
The Short- or Long-Rangeness Character of the ExchangeContribution 809
Use of Screw Symmetry in Polymer Calculations 811
A Simulated Ab Initio Technique: The Valence Effective
Hamiltonian (VEH) 813
Particular Aspects of Computer Implementation 816
Band Structure Calculations 816
Summation over Polymeric States and Integrations over
First Brillouin Zones 816
Basis Set Linear Dependence 817
Band Indexing Difficulty 819
Density of States Calculations 821
Graphics Interface: BandDos 822
Applications 826
Appendix 19A. Tables of VEH Parameters 826
Single-Zeta Potentials 826
Double-Zeta Potentials 826
References 828
Chapter 20. First Principles Molecular Dynamics
M. Parrinello
IBM Research Division, Zurich Research LaboratoryCH-8803 Ruschlikon, Switzerland
Introduction 833
The Interatomic Potential within DF Theory 835
A Dynamical Approach to Energy Functional Minimization 837
Molecular Dynamics in the Coupled Electron-Ion Parameter Space 840
Conclusions 844
References 845
Chapter 21. Molecular Dynamics Simulations with ab initio
Interaction Potentials
G. Corongiu, M. Aida, M.F. Pas, and E. Ciementi
IBM Corporation, Dept. 48B\428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 847
Interaction Potentials 848
Ab initio Force Field for Biomolecules 850
Classification of Atoms 851
The Molecular Dynamics Method 857
Numerical Integration for the Equations ofMotion 859
Calculation of Properties 862
Properties Related to Neutron Scattering Experiments 868
Periodic Boundary Conditions and Long Range Forces 876
Free Energy Calculations 878
Energy Minimization 882
Gradient Methods 883
Minimization Applications 885
Applications and Examples 889
Liquid Water with the Flexible ab initio Potential 889
BPTI Simulations in Vacuo and in Solution 902
Neutron Scattering Properties 905
Examples Using the ab initio Force Field 908
a-Helix Stability of C-peptide 908
Conformational Analysis of Cyclolinopeptide A 910
Interaction of Spermine with Oligonucleotide 913
References
xxviii Contents
Chapter 22. Langevin Dynamics Simulations of Biomolecules
D.K. Bhattacharya, W. Xue and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 921
Computational Algorithm for Langevin Dynamics Simulations 922
Langevin Dynamics Simulation of the BPTI Protein 927
Discussion 935
References 937
Chapter 23. Molecular Dynamics Simulations of Fluid Flows
D.K. Bhattacharya, G. C. Lie and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 939
Computational Algorithm for a Large Scale Molecular DynamicsSimulation 942
Applications and a Discussion of Results 946
References 968
Chapter 24. Brownian Dynamics Simulations of a Complex Fluid System
D.K. Bhattacharya and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 971
Brownian Dynamics Simulation: Basic Concepts 973
Fokker-Planck Description 973
Langevin Description 975
The Simulation Program "BROWNIAN": An Overview 979
The Nonlinear Rheology of the Colloidal Suspension 980
Discussion 983
Shear Induced Phase Transition in a Colloidal Suspension 984
Generalized Brownian Dynamics Techniques 986
References 987
Chapter 25. Protein Structure Prediction and Neural Networks
/. Vanhala and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 991
Neural Networks 993
Contents xxix
Neural Networks in Globular Protein Secondary Structure
Predictions 997
Neural Networks in Globular Protein Tertiary Structure
Predictions 999
Methods 999
Tools 1002
Testing the Proposal: BPTI as an Example 1006
Discussion and Future Development 1009
References 1011
Chapter 26. Cellular Automata
R. Panda, V. Sonnad and E. Ciementi
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Cellular Automata 1017
Two-Dimensional Lattice-Gas Automata 1017
Simulation of 2D Fluid Flows 1021
Three-Dimensional Lattice-Gas Automata 1025
Results of 3D Simulations 1028
References 1029
Chapter 27. Microscopic and Mesoscopic Simulations of Complex Flows
with Cellular Automata and Related Techniques
S. Sued
IBM European Center for Scientific and Engineering ComputingVia Giorgione 159, 00147 Rome, Italy
R. Benzi
Dept. of Physics, Universitd di Roma II, Tor Vergata
Via O. Raimondo, 00173 Rome, Italy
A. Cancelliere
Dept. of Hydraulic Engineering, Universitd di Catania
Via A. Doria, Catania, Italy
F. Higuera
Dept. of Fluid Mechanics, School of Aeronautics
P.za Cardenal Cisneros, 28040 Madrid, Spain
M. VergassolaDept. of Physics, Universitd di Roma I, La SapienzaP.le Aldo Mow, 00185 Rome, Italy
Introduction 1031
Review of Boolean Lattice Gas 1032
From Microscopic to Mesoscopic: The Lattice Boltzmann Equation 1037
LBE with Enhanced Collisions 1038
xxx Contents
Subgrid Modelling of Fluid Turbulence 1042
Applications of LBE 1043
Three-dimensional Laminar Flows in Complex Geometries 1043
Bifurcations of a Two-dimensional Poiseuille Flow 1045
Fully Developed Two-dimensional Forced Turbulence 1046
Performance Considerations 1049
What Next? 1050
Quantum Automata 1051
Conclusion 1052
References 1053
Chapter 28. The Equations of Fluid Flow and Their Solution by
Numerical Methods
V. Sonnad, R. Panda, B. Jiang, H. Murakami,
S. Hassanzadeh and S. Foresti
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
The Equations of Fluid Flow 1055
Derivation of the Navier Stokes Equations 1055
Reduction to Various Specific Forms 1062
The Finite Element Method 1066
The Method of Weighted Residuals 1067
The H-Version of the Finite Element Method 1068
The P-Version of the Finite Element Method 1069
Solution Techniques 1070
Direct Solution Methods 1070
Iterative Methods 1071
Overview of Preconditioning Techniques 1072
Multilevel Solution Method 1073
Computational Solution of the Navier Stokes Equations 1075
Parallel Implementation of the Solution Scheme 1077
Turbulent Flow 1079
Reynolds Equations 1079
Empirical Relations for the Reynolds Stress Tensor 1081
Direct Numerical Simulation of Isotropic Turbulent Flows 1082
Dealiasing 1084
Time Stepping Scheme 1084
Parallel Implementation of the Numerical Scheme 1084
Results 1085
Application of the Finite Element Method in QuantumChemistry 1087
References 1088
Contents xxxi
Chapter 29. The Equations of Elasticity and Their Solution byFinite Element Methods
V. Sonnad, H. Murakami, S. Foresti, S. Hassanzadeh and B. JiangIBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
The Equations of Elasticity 1091
Computational Techniques for Linear Static Analysis 1096
Solution of Large 3-D Problems with Finite Elements 1096
Iterative Solution with the Conjugate Gradient Method 1097
Rapid Operator Application 1098
Utility of Rapid Operator Application 1104
Parallel Implementation of Iterative Schemes 1104
References 1106
Chapter 30. Numerical Modeling of Axisymmetric Laminar Flames
M.D. Smooke
Dept. of Mechanical Engineering, Yale UniversityNew Haven, CT 06510, USA
Introduction 1109
Problem Formulation 1110
Method of Solution 1114
Serial Implementation 1114
Parallel Implementation 1115
References 1117
Chapter 31. Modeling of Atmospheric Pollutant Transport in Shorelines
Z.D. Christidis
IBM Research, T.J. Watson Research Center
Yorktown Heights, NY 10598, USA
P.J. Samson
Dept. of Atmospheric, Oceanic and Space Sciences
University of Michigan, Ann Arbor, MI 48109, USA
Introduction 1119
Model Development and Governing Equations 1120
Equations for the Mesoscale Variables 1122
Equations for the Synoptic Scale Variables 1123
Boundary Layer Parameterization 1124
Diffusivities in the Surface Layer 1124
Diffusivities in the Planetary Boundary Layer 1126
Numerical Methods 1127
Initial and Boundary Conditions 1128
Summertime Flow over a Lake 1131
xxxii Contents
Summary and Conclusions 1135
References 1137
Chapter 32. Interactive Visualization Techniques for Chemistry:
KGNGRAF, XWIB and REMOTE
S. Chin, M. Martins-Costa, R. Tagliavini, S.B. Rondeau
and J.P. Prost
IBM Corporation, Dept. 48BJ428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 1139
The graPHIGS Application Programming Interface (API) 1140
Introduction to KGNGRAF 1143
The User Interface 1145
Display of Molecular Models 1146
Display of Electron Densities and Molecular Orbitals 1153
Creation and Manipulation of Molecules 1158
Superposition of Molecular Structures 1163
Molecule Building from Templates 1165
Protein Building from Templates 1166
Inquiry of Geometrical Parameters 1168
Display of Molecular Vibrations and Molecular Spectra 1168
Display of Molecular Energy Diagrams 1169
Interactive Animations 1169
Files Manipulation 1173
Windows Oriented Interfaces for Input Specification 1173
XWIB: An X Window Interface Builder 1178
Format Checking 1178
Dependency Handling Mechanisms 1178
Help Messages 1183
On-Line Documentation 1183
Other Utility Functions 1183
REMOTE: Remote File Transfer and Execution 1186
Summary '. 1188
References 1188
Contents xxxiii
Chapter 33. LCAP: Loosely Coupled Array of Processors Parallel
Processing Systems
E. Ciementi and S. Chin, G. Corongiu, J. Detrich, M. Dupuis,L.J. Evans, D. Folsom, D. Frye, G.C. Lie, D. Logan,D. Meek, V. Sonnad
IBM Corporation, Dept. 48B/428, Neighborhood Road
Kingston, NY 12401, USA
Introduction 1191
The LCAP-3090 Experimental System 1193
Early LCAP Systems 1198
LCAP Parallel Processing Software and Performance Issues 1204
LCAP Design Philosophy 1207
LCAP Features for Effective Parallelism 1211
Conclusions 1219
Bibliography 1220
Author Index 1227
Subject Index 1251
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