95 332 density functional theory the valence electron

95
3.3.2 Density Functional Theory Methods
. . . . . . . . . . . . . . . . .
96
3.3.3 The Valence Electron Method
. . . . . . . . . . . . . . . . . . . . .
97
3.3.4 Dropping Multicenter Integrals
. . . . . . . . . . . . . . . . . . . . .
98
3.4 Full Range Process Potentials
. . . . . . . . . . . . . . . . . . . . . . . . . . .
99
3.4.1 The Three-Body Internuclear Coordinates
. . . . . . . . . . . . .
99
3.4.2 Global Formulation of the Potential Energy Surface
. . . . .
100
3.4.3 Local and Mobile Methods
. . . . . . . . . . . . . . . . . . . . . . . .
102
3.4.4 Process-Driven Local and Mobile Fitting Methods
. . . . . . .
104
xiv Contents

3.5 Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
3.5.1 Qualitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
3.5.2 Quantitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . .
108
4 The Treatment of Few-Body Reactions
. . . . . . . . . . . . . . . . . . . . . . .
111
4.1 The Combined Dynamics of Electrons and Nuclei
. . . . . . . . . . . .
111
4.1.1 The N-Body Dynamical Equations
. . . . . . . . . . . . . . . . . .
111
4.1.2 A Direct Integration of the General Equations
. . . . . . . . . .
113
4.1.3 The Born – Oppenheimer Approximation
. . . . . . . . . . . . . .
114
4.2 Three-Atom Systems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
4.2.1 Three-Body Orthogonal Coordinates
. . . . . . . . . . . . . . . . .
116
4.2.2 Atom – Diatom Reactive Scattering Jacobi Method
. . . . . . .
119
4.2.3 Atom – Diatom Time-Independent APH Method
. . . . . . . . .
121
4.2.4 The Atom – Diatom Time-Dependent APH Method
. . . . . . .
127
4.3 Beyond Full Quantum Calculations
. . . . . . . . . . . . . . . . . . . . . . .
128
4.3.1 Reduced Dimensionality Quantum Treatments
. . . . . . . . . .
128
4.3.2 Leveraging on Classical Mechanics
. . . . . . . . . . . . . . . . .
130
4.3.3 Semiclassical Treatments
. . . . . . . . . . . . . . . . . . . . . . . . .
132
4.4 Basic Features of Atom – Diatom Reactions
. . . . . . . . . . . . . . . . . .
136
4.4.1 Energy Dependence of the Detailed Probabilities
. . . . . . . .
136
4.4.2 Quantum Effects
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
4.4.3 Experimental Observables
. . . . . . . . . . . . . . . . . . . . . . . .
142
4.4.4 Periodic Orbits and Statistical Considerations
. . . . . . . . . .
144
4.4.5 The Last Mile to the Experiment
. . . . . . . . . . . . . . . . . . .
147
4.5 Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
148
4.5.1 Qualitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
148
4.5.2 Quantitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . .
149
5 Complex Reactive Applications: A Forward Look to Open
Science
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
151
5.1 Toward More Complex Systems
. . . . . . . . . . . . . . . . . . . . . . . . .
151
5.1.1 Full Range Ab Initio PESs for Many-Body Systems
. . . . .
151
5.1.2 Fitting PESs for Reactive and Nonreactive Channels
. . . . .
153
5.1.3 Four-Atom Many-Process Expansion
. . . . . . . . . . . . . . . .
156
5.1.4 Four-Atom Quantum and Quantum-Classical Dynamics
. . .
158
5.1.5 Last Mile Calculations for Crossed Beam Experiments
. . .
161
5.2 Large Systems Studies Using Classical Dynamics
. . . . . . . . . . . .
165
5.2.1 Trajectory Studies for Many-Body Systems
. . . . . . . . . . . .
165
5.2.2 Some Popular Molecular Dynamics Codes
. . . . . . . . . . . .
166
5.2.3 Force Fields
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
169
5.2.4 Toward Multiscale Treatments
. . . . . . . . . . . . . . . . . . . . .
172
5.3 Supercomputing and Distributed Computing Infrastructures
. . . . . .
173
5.3.1 High-Performance Versus High-Throughput Computing
. . .
173
Contents xv

5.3.2 Networked Computing and Virtual Communities
. . . . . . . .
175
5.3.3 The Collaborative Grid Empowered Molecular
Simulator
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
178
5.4 Toward an Open Molecular Science
. . . . . . . . . . . . . . . . . . . . . .
180
5.4.1 A Research Infrastructure for Open Molecular Science
. . .
180
5.4.2 Foundations and Stakeholders for the Molecular Open
Science RI
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
181
5.4.3 Compute Resources and Data Management for Molecular
Open Science
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
5.4.4 Molecular Open Science Use-Cases
. . . . . . . . . . . . . . . . .
184
5.5 The Innovativity of the Open Science Design
. . . . . . . . . . . . . . . .
186
5.5.1 Service Layers and Data Storage
. . . . . . . . . . . . . . . . . . .
186
5.5.2 Multidisciplinarity, Societal Challenges, Impact
and Dissemination
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188
5.5.3 User and Service Quality Evaluation
. . . . . . . . . . . . . . . . .
192
5.5.4 A Credit Economy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
193
5.6 Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
5.6.1 Qualitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
5.6.2 Quantitative Problems
. . . . . . . . . . . . . . . . . . . . . . . . . . .
195
Appendix
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
197
References
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .