95 332 Density Functional Theory The Valence Electron Method 97

95 332 density functional theory the valence electron

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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
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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
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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