Quantum Crystallography

Quantum crystallography (QCr) is a novel scientific discipline combining quantum chemistry methods and crystal structure determination. Written by leading experts in the field, this book describes original quantum-mechanical approaches to obtain crystallographic data of enhanced value and explains how they correlate with real diffraction and scattering experiments. In particular, the book covers quantum N-representability, Clinton equations, kernel energy method (KEM), and quantum theory of atoms in molecules (QTAIM) methods and their applications in crystallographic studies. Readers will be interested in the Foreword written by Nobel Laureate Ada Yonath and the Epilogue by noted science philosopher Olimpia Lombardi. * Outlines the latest achievements and developments of this novel area of research. * Written by the leading scientists of the field. * Bridges together theoretical methods and experimental studies. Cover Half Title Also of interest Quantum Crystallography Copyright Dedication Acknowledgements Preface Reference Foreword Contents About the authors Introduction References 1. Some basic concepts of crystallography 1.1 Introductory remarks 1.2 Elastic scattering and Bragg’s law 1.3 Structure factors 1.4 The electron density 1.5 Conclusion References 2. Some basic concepts of quantum chemistry 2.1 Introduction 2.2 The Schrödinger equation 2.3 Atomic units (au) 2.4 The molecular Hamiltonian 2.5 The variational principle 2.6 The Pauli exclusion principle 2.7 The Hartree–Fock method 2.8 Some essentials of density functional theory (DFT) 2.9 Level of theory in molecular calculations References 3. Quantum crystallography: an introduction 3.1 N-representability 3.2 Derivation of the Clinton equations 3.3 Conclusion References 4. Example applications of the Clinton equations 4.1 First application: the beryllium crystal 4.2 Second application: maleic anhydride crystal 4.3 Conclusion References 5. The kernel energy method: a computational approach to large systems 5.1 The computational scaling bottleneck of quantum calculations 5.2 The KEM method as a solution to the computational scaling bottleneck 5.3 The lead-up to the KEM formalism 5.4 The kernel energy method 5.5 The scaling of the KEM 5.6 Closing remarks References 6. The kernel energy method: accurate and fast calculations on large systems by example 6.1 An approach to quantum calculations on large systems: the kernel energy method 6.2 The kernel energy method applied to large biomolecules 6.3 The kernel energy method and the calculation of response properties 6.4 The kernel energy method and the calculation of properties of at atoms in molecules 6.5 Closing remarks References 7. The quantum theory of atoms in molecules 7.1 From topography to topology 7.2 Critical points in the electron density 7.3 The zero-flux surface bounding proper open quantum systems 7.4 Coincidence of the topological atom and the quantum atom 7.5 The atomic statement of the virial theorem 7.6 The Laplacian of the electron density 7.7 Examples of bond properties 7.7.1 The electron density at the BCP (ρb) 7.7.2 The Laplacian of the electron density at the BCP (∇2ρb) 7.7.3 The bond ellipticity (ε) 7.7.4 Energy densities at the BCP 7.8 Atomic contributions to molecular properties 7.9 Examples of atomic properties 7.9.1 Atomic population [N(Ω)] and charge [q(Ω)] 7.9.2 Kinetic energy [T(Ω)] 7.9.3 The atomic integrated Laplacian [L(Ω)] 7.9.4 The (virial) atomic energy [E(Ω)] 7.10 Back to experiment 7.11 Conclusion References 8. The quantum theory of atoms in molecules and quantum crystallography: a symbiosis 8.1 QTAIM charges for large molecules from KEM 8.2 Interacting quantum atoms energy components from from KEM 8.3 The Clinton iterative melding of assembled electron densities and of molecular aggregates 8.4 The density (matrix) in momentum space 8.5 The total energy 8.6 Atomic virial energies 8.7 Excited-state electron densities from X-ray diffraction experiments 8.8 Conclusions References 9. The calculation of the energy 9.1 The case of N-representable ρ2-det extracted from KEM ρ1-det 9.2 The energy from X-ray quantum crystallographic density? 9.3 Discussion and conclusion References Epilogue Appendix 1. Historical note: N-representability References Appendix 2. Comments regarding new discussions of quantum crystallography References Appendix 3. Publications on quantum crystallography by the authors 1. Edited special journal issues on quantum crystallography 2. Journal articles and chapters in books on quantum crystallography Index