Table Of ContentLecture Notes in Chemistry 75
Edited by:
Prof. Dr. Gaston Berthier
Universite de Paris
Prof. Dr. Hanns Fischer
UniversiUit ZUrich
Prof. Dr. Kenichi Fukui
Kyoto University
Prof. Dr. George G. Hall
University of Nottingham
Prof. Dr. JUrgen Hinze
Universitat Bielefeld
Prof. Dr. Joshua Jortner
Tel-Aviv University
Prof. Dr. Werner Kutzelnigg
UniversiUH Bochum
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Iowa State University
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Universita di Pisa
Springer-Verlag Berlin Heidelberg GmbH
A. Lagana A. Riganelli (Eds.)
Reaction and
Molecular Dynamics
Proceedings of the European School on
Computational Chemistry,
Perugia, Italy, July (1999)
Springer
Editors
Prof. Antonio Lagana Antonio Riganelli
Dipartimento di Chimica Departamento de Quimica
Universita di Perugia Universidade de Coimbra
Via Bice di Sotto 8 3049 Coimbra, Portugal
Perugia, Italy
E-mail: [email protected]
E-mail: [email protected]
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek -CIP-Einheitsaufuahme
Lagana, Antonio:
Reaction and molecular dynamics : from small systems and rogorous
methods to large systemsand approximate methods I A. Laganâ ; A.
Riganelli. -Berlin; Heidelberg ; New York; Barcelona ; Hong Kong ;
London ; Milan ; Paris; Singapore; Tokyo: Springer, 2000
(Lecture notes in chemistry ; 75)
ISSN 0342-4901
ISBN 978-3-540-41202-1 ISBN 978-3-642-57051-3 (eBook)
DOI 10.1007/978-3-642-57051-3
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Table of Contents
Computational Reaction and Molecular Dynamics: from Simple
Systems and Rigorous Methods to Large Systems and
Approximate Methods
Antonio Lagana. and Antonio lliganelli. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1. Introduction.................................................... 1
2. Potential energy surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Quantum nuclear dynamics ...................................... 4
4. Approximate Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5. Quantum Mechanics Molecular Dynamics methods. . . . . . . . . . . . . . . . . . 8
6. Advanced Computing for Chemical Reactivity Calculations. . . . . . . . . .. 10
Part I. Lectures
Fitting Potential Energy Surfaces
George C. Schatz .................................................. 15
1. Introduction.................................................... 15
2. Representing Potential Energy Surfaces: General Considerations ...... 18
3. Fitting and Interpolation Methods .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
3.1 Global Methods. .. . . . . .. . . . . . . . . . . . .. ... . .. . . . . . . . . . . . . . . .. 20
3.2 Local Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26
4. Conclusion..................................................... 30
Multivalued Potential Energy Surfaces for Dynamics Studies
Antonio J.C. Varandas ............................................. 33
1. Introduction.................................................... 33
2. The hierarchy of approximations. . . .. . . .. . ... .. . .. . . . . .. . . . . .. .. .. 35
2.1 Born-Huang expansion .. '" . . . .. . . .. . .. . ... .. . . . . .. . . . . .. . . .. 36
2.2 The solution of the electronic problem. . . . . . . . . . . . . . . . . . . . . . . .. 39
3. Ab initio potential energy surfaces ................................ 39
3.1 Correlation energy partitioning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
3.2 Semiempirical correction of ab initio energies . . . . . . . . . . . . . . . . . .. 41
4. Semiempirical global potential energy surfaces . . . . . . . . . . . . . . . . . . . . .. 42
4.1 Diatomics-in-molecules theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
VI Table of Contents
4.2 The double many-body expansion method. . . . . . . . . . . . . . . . . . . . .. 44
4.3 Energy-switching scheme for spectroscopically accurate functions.. 46
5. Applications.................................................... 47
5.1 H3 and Li3: two well studied systems..... ......... .. ... ....... 47
5.2 Other systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53
6. Concluding remarks ........................................... " 53
Distributed Approximating Functionals: a Robust, New
Approach to Computational Chemistry and Physics
David K. Hoffman and Donald J. Kouri.. . .. .... . ..... . .. . ............ 57
1. Introduction.................................................... 57
2. Derivation and Construction of Various DAFs . . . . . . . . . . . . . . . . . . . . .. 60
2.1 Variational Derivation of DAFs ............................. " 60
2.2 Dirac Delta Sequence Derivation of DAFs . . . . . . . . . . . . . . . . . . . . .. 64
2.3 Gaussian Weighted Interpolating Shells . . . . . . . . . . . . . . . . . . . . . . .. 70
3. Gauss-Hermite DAFs ............................................ 71
Time Dependent Quantum Approaches to Chemical Reactivity
Gabriel G. Balint-Kurti.......... ...... ................... .... ...... 74
1. Wavepa.ck.et propagation. Solving the time-dependent Schrodinger equa-
tion ........................................................... 74
2. Expansion of the propagator ..................................... 75
3. Energy resolution and energy range of a wavepa.cket. ................ 76
4. The wavefunction and the wavepa.cket. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
5. The Hamiltonian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
5.1 The radial Kinetic Energy Terms: Radial Grids and Fourier 'Irans-
forms ...................................................... 78
5.2 The angular Kinetic Energy Terms. ........................... 79
6. Preparation of the initial wavepa.cket.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80
7. Analysis of product states. Calculation of S matrix. . . . . . . . . . . . . . . . .. 80
8. Reactant and Product coordinate systems. ......................... 81
9. Calculations for J > 0, centrifugal coupling and helicity decoupling. . .. 82
10. Angular basis functions and angular grids. ......................... 83
11. Cross sections and reaction probabilities.. . . . . . . . . . . . . . . . . . . . . . . . . .. 84
12. Fourier transforms: Absorbing the wavepacket at grid edge. .......... 84
13. Forms of Complex absorbing potential. ............................ 85
14. J-shifting and capture models for estimating cross sections. .......... 86
15. New Developments and Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86
Quantum Reactive Scattering for Three Particle Systems using
Hyperspherical Coordinates
Gregory A. Parker, Stefano Crocchianti, and Mark Keil. .... ..... . .. .... 88
1. Introduction.................................................... 88
2. The system of coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 90
Table of Contents VII
2.1 Jacobi Coordinates ........................................ " 90
2.2 APH Coordinates ........................................... 92
2.3 Delves Hyperspherical and Tangent Sphere Coordinates ........ " 93
3. The computational percourse ................................... " 94
4. S matrix and experimental observables ........................... " 96
5. Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
Approximate Time Independent Methods for Polyatomic
Reactions
Joel M. Bowman ................................................... 101
1. Introduction .................................................... 101
2. The Cumulative Reaction Probability ............................. 102
3. Energy-shift approximations ...................................... 105
4. Adiabatic approximations ........................................ 106
5. J-shifting for complex-forming reactions ............................ 111
6. Summary and conclusions ........................................ 113
Quantum-Classical Methods
Gert D. Billing .................................................... 115
1. Introduction .................................................... 115
2. Theory ...._ ................................................... 116
2.1 One-dimensional hamiltonian ................................. 116
2.2 An example ................................................ 120
3. Two-dimensional case ........................................... 122
3.1 Simple quantum-classical theories ............................. 125
4. Second quantization approach .................................... 126
5. Discussion ..................................................... 128
Direct Calculation of Reaction Rates
Uwe Manthe ...................................................... 130
1. Introduction.................................................... 130
2. General theory ................................................. 131
2.1 Reactive scattering: state-selected and cumulative properties ..... 131
2.2 Rate constants in scattering theory ............................ 131
2.3 Flux correlation functions .................................... 132
2.4 Classical mechanics ......................................... 134
2.5 Transition state theory ...................................... 135
2.6 Quantum transition state theory .............................. 136
3. Quantum calculations ........................................... 137
3.1 Accurate evaluation of flux correlation functions ................ 137
3.2 The thermal flux operator .................................... 138
3.3 N(E)-calculation ............................................ 141
3.4 Rotational motion ......................... , ................ 143
3.5 Special methods ............................................ 144
VIII Table of Contents
4. Exatnples ..................................................... 144
+ +
4.1 The H2 OH -+ H H20 reaction ............................ 144
+ +
4.2 The H2 CN -+ H HCN reaction ........................... 145
4.3 The 0 + HCI -+ OH + CI reaction ............................. 146
+ +
4.4 The H2 CI -+ H HCI reaction ............................. 147
CAS-SCF and MM-VB Dynamics: Applications to Organic
Photochemistry
Michael A. Robb and Marco Garavelli ................................ 150
1. Introduction .................................................... 150
2. Non-Adiabatic Transitions: Trajectory-Surface-Hop versus Mixed-State
Approach ...................................................... 150
3. The MM-VB Approach to Dynatnics .............................. 152
4. Conclusions .................................................... 153
Ab-Initio MD Calculations on Dynamics and Reactivity in
Confined and Disordered Systems
Aldo Gatnba ...................................................... 156
1. Introduction .................................................... 156
2. Computational Methods: a view ... " .......... , .................. 157
3. Car-Parrinello method ................................. '" ....... 157
4. Applications .................................................... 158
4.1 Static and Vibrational properties ............................. 159
4.2 Reactivity and catalysis ...................................... 162
4.3 Host-Guest Interactions ...................................... 164
Parallel Paradigms for Scientific Computing
Marco Vanneschi ................................................... 168
1. Introduction .................................................... 168
2. Parallel programming environments ............................... 169
2.1 Issues and perspectives ...................................... 169
2.2 SkIE: a structured environment for HPC ....................... 170
3. Paradigms for structured parallel programming ..................... 172
3.1 Skeletons and SkiE-cl ........................................ 172
3.2 A simple exatnple: designing a ray tracer ....................... 173
3.3 A data mining application ................................... 175
3.4 Design of a parallel visualization environment .................. 177
4. Memory problem and shared objects .............................. 179
5. Related work and conclusion ..................................... 180
Networking and Hypermedia in Chemistry
Osvaldo Gervasi ................................................... 182
1. Introduction .................................................... 182
2. Internet technologies ............................................ 183
Table of Contents IX
3. High Speed Network Technologies ................................. 184
3.1 Ethernet Switching Technologies .............................. 184
3.2 ATM Technology ........................................... 186
3.3 The xDSL Technology ....................................... 187
3.4 Satellite Technologies ........................................ 187
3.5 Mobile networks ............................................ 187
4. Impact of Hypermedia in Chemistry ............................... 188
4.1 SIMBEX ................................................... 188
4.2 DASP ..................................................... 189
5. Conclusions .................................................... 189
Part II. Tutorials
Tutorial on Fitting of Potential Energy Surfaces
Guillermo Ochoa de Aspuru and Maria Luz Hernandez ................ 193
1. Introduction .................................................... 193
2. Potential energy surfaces by interpolation .......................... 194
3. Semiempirical models: the LEPS function .......................... 196
4. The many-body expansion ....................................... 199
5. The bond order cordinates and the many-process expansion .......... 202
A. Appendix ...................................................... 206
Time-Dependent Techniques
Marlies Hankel and Valentina Piermarini .............................. 209
1. Introduction.................................................... 209
2. The computational approach ..................................... 209
2.1 The initial conditions ........................................ 210
2.2 Grid representation ......................................... 210
2.3 The time propagation ....................................... 211
2.4 The asymptotic analysis ..................................... 213
3. The computational procedure ..................................... 213
3.1 The propagation program .................................... 214
3.2 The analysis program ........................................ 214
4. The work plan of the tutorial ..................................... 215
4.1 The collinear H + H2 -+ H2 + H ............................. 216
4.2 The isotopic variant D + H2 -+ DH + H ....................... 217
4.3 The three dimensional case: (J=O) D + H2 -+ HD + H .......... 219
4.4 Results .................................................... 219
The exact Computation of Reactive Cross Sections for
Atom-Diatom Systems. The Hyperspherical Propagative
Approach
Alessandro Bolloni, Fermin Huarte-Larrafiaga, and Xavier Gimenez ...... 222
1. Introduction .................................................... 222
x Table of Contents
2. The formulation of the scattering problem within the hyperspherical
propagative approach ............................................ 224
3. Reference frame and coordinate system ............................ 226
4. The solution of the internal problem ............................... 229
5. Propagation of the coupled set of differential equations .............. 232
6. From reaction probabilities to integral cross sections ................. 235
7. Concluding remarks ............................................. 239
A Quasiclassical Trajectory Study of Atom Diatom Reactions
Ernesto Garcia .................................................... 242
1. Introduction.................................................... 242
2. Quasiclassical 'Irajectory Method ................................. 242
3. Quasiclassical 'Irajectory Computational Codes ..................... 244
4. The Li + HF -+ LiF + H reaction ................................. 246
5. Exercises ...................................................... 248
5.1 Accuracy of QCT calculations ... " .......... , ........... , .... 248
5.2 Properties of a trajectory .................................... 250
5.3 QCT estimates of reactive properties .......................... 253
Quantum-Classical Methods: a Quantum-Classical Approach to
Diatom-Diatom Reactive Scattering and VV Energy Transfer
Cecilia Coletti and Gert D. Billing ................................... 257
1. Introduction .................................................... 257
2. Method ........................................................ 258
3. Cross sections and numerical results ............................... 262
4. Conclusions .................................................... 269
Part III. Contributed papers
+ Ht +
Resonance Characterization for the Ne -+ NeH+ H
System: Time Delays and Argand Diagrams
Fermin Huarte-Larraiiaga ..................... " ... , . " ........ , .... 273
1. Introduction .................................................... 273
2. Outline of the calculations ........................................ 274
3. Analysis of a particular resonant peale Results and Discussion. . ...... 275
4. Conclusions .................................................... 278
Quasiclassical Trajectory Study of the
+ +
OeD) H20 -+ 20H,H H02 Reactions
Ramon Sayos, Carolina Oliva, and Miguel Gonzalez .................... 279
1. Introduction .................................................... 279
2. Results ........................................................ 280
3. Conclusions .................................................... 283
