Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.

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Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.

The ground-state energy of the two-dimensional uniform electron gas has been calculated with a fixed-node diffusion Monte Carlo method, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits our simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first-order polarization transition occurs shortly before Wigner crystallization as the density is lowered.

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Correlation energy and spin polarization in the 2D electron gas.

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wavefunctions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well suited to implementation on petascale computers, and the computational cost scales as a polynomial in the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimization of wavefunctions, performing calculations under periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

https://iopscience.iop.org/article/10.1088/0953-8984/22/2/023201/pdf

Continuum variational and diffusion quantum Monte Carlo calculations.

The uniform electron gas at warm dense matter conditions

Finite-Size Effects and Coulomb Interactions in Quantum Monte Carlo Calculations for Homogeneous Systems with Periodic Boundary Conditions

A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method.

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Elimination of Coulomb finite-size effects in quantum many-body simulations

Wave functions for the homogeneous electron gas, a germanium pseudosolid, and a germanium pseudoatom are optimized using the method of variance minimization. Forms for the Jastrow factor which are convenient to optimize and may be evaluated rapidly are devised and tested and we stress the advantages of using expressions which are linear in the variable parameters. For each system studied we have performed variational and diffusion quantum Monte Carlo calculations to test the accuracy of the optimized wave functions. The results of our study are very promising for future applications of quantum Monte Carlo methods to real materials.

L. M. Fraser

Papers

Finite-Size Effects and Coulomb Interactions in Quantum Monte Carlo Calculations for Homogeneous Systems with Periodic Boundary Conditions

Elimination of Coulomb finite-size effects in quantum many-body simulations

Optimized wave functions for quantum Monte Carlo studies of atoms and solids.