Solving the Schrödinger equation [[electronic resource] ] : has everything been tried? / / editor, Paul Popelier

• Record Nr.: UNINA9910778827903321
• Pubbl/distr/stampa: London, : Imperial College Press, c2011
• ISBN: 1-283-43320-6; 9786613433206; 1-84816-725-3
• Descrizione fisica: 1 online resource (375 p.)
• Altri autori (Persone): PopelierPaul L. A
• Disciplina: 530.12/4
• Soggetti: Schrödinger equation; Wave functions; Wave mechanics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents; Bibliography; Preface; 1. Intracule Functional Theory Deborah L. Crittenden and Peter M.W. Gill; 1.1 Introduction; 1.2 Intracules; 1.3 Electron Correlation Models; 1.4 Dynamic and Static Correlation; 1.5 Dispersion Energies; 1.6 Future Prospects; Bibliography; 2. Explicitly Correlated Electronic Structure Theory Frederick R. Manby; 2.1 Introduction; 2.1.1 Basis-set expansions; 2.2 F12 Theory; 2.2.1 MP2-F12; 2.2.2 Explicitly correlated coupled-cluster theory; 2.3 Five Thoughts for F12 Theory; 2.3.1 Thought 1: Do we need (products of) virtuals?; 2.3.2 Thought 2: Are there better two-electron basis sets?2.3.3 Thought 3: Do we need the resolution of the identity?; 2.3.4 Thought 4: Could we have explicit correlation for higher excitations?; 2.3.5 Thought 5: Can we avoid three-electron errors in two-electron systems?; 2.4 Conclusions; Acknowledgments; Bibliography; 3. Solving Problems with Strong Correlation Using the Density Matrix Renormalization Group (DMRG) Garnet Kin-Lic Chan and Sandeep Sharma; 3.1 The Problem of Strong Correlation; 3.2 The Density Matrix Renormalization Group Wavefunction; 3.3 Locality and Entanglement in the DMRG; 3.4 Other Properties of the DMRG3.5 Relation to the Renormalization Group; 3.6 Dynamic Correlation - the Role of Canonical Transformations; 3.7 What Can the DMRG Do? A Brief History; 3.8 The Future: Higher Dimensional Analogues; Bibliography; 4. Reduced-Density-Matrix Theory for Many-electron Correlation David A. Mazziotti; 4.1 Introduction; 4.2 Variational 2-RDM Method; 4.2.1 Energy as a 2-RDM functional; 4.2.2 Positivity conditions; 4.2.2.1. Two-positivity; 4.2.2.2. Three-positivity; 4.2.3 Semidefinite programming; 4.2.4 Applications; 4.2.4.1. Dissociation of the N molecule; 4.2.4.2. Metal to insulator transition in the H lattice4.2.4.3. Polyradical character of the acene chains; 4.3 Contracted Schr dinger Theory; 4.3.1 ACSE and cumulant reconstruction; 4.3.2 Solving the ACSE for ground and excited states; 4.3.3 Applications; 4.3.3.1. Energy barriers of bicyclobutane's transition states; 4.3.3.2. Conical intersections in CH 's triplet excited states; 4.4 Parametric 2-RDM Method; 4.4.1 Parametrization of the 2-RDM; 4.4.2 Applications; 4.4.2.1. Correlation energies at equilibrium geometries; 4.4.2.2. Dissociation of the HF molecule; 4.4.2.3. Isomerization of nitrosomethane4.5 Looking Ahead; Acknowledgments; 5. Finite Size Scaling for Criticality of the Schr dinger Equation Sabre Kais; 5.1 Introduction; 5.2 Criticality for Large-dimensional Models; 5.3 Finite Size Scaling: A Brief History; 5.4 Finite Size Scaling for the Schr dinger Equation; 5.5 The Hulthen Potential; 5.5.1 Analytical solution; 5.5.2 Basis set expansion; 5.5.3 Finite element method; 5.5.4 Finite size scaling results; 5.6 Finite Size Scaling and Criticality of M-electron Atoms; 5.7 Conclusions; Acknowledgments; Bibliography; 6. The Generalized Sturmian Method James Avery and John Avery
• Sommario/riassunto: The Schrödinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrödinger equation. Each method is based on a set of core ideas and this volume aims to expla