It will typically include two types of activities : (1) lectures on theory, algorithms and implementations in the morning sessions and (2) hands-on exercises in the afternoon sessions. The lectures and exercises will be synchronized in such a way as to have the practical applications of the morning classes investigated in detail with the developers support in the afternoons.
Electronic Structure: Basic Theory and Practical Methods: Basic Theory and Practical Density Functio
- density functional theory (DFT) and density functional perturbation theory (DFTP) in both the standard planewave-pseudopotential and projector-augmented wavefunctions (PAW) formulations,- phonon band structures and thermodynamical properties- response functions and couplings with electric field, magnetic field, and strain- response in finite electric field- Raman and electro-optic responses- electron-phonon coupling
The goals Richard Martin's research are to develop theoretical and computational methods for condensed matter starting from the fundamental many-body equations for the electrons. The primary methods used are density functional methods, which can be applied to diverse solids and liquids, and quantum Monte Carlo simulations, which can find exact properties of many-body systems. This is combined with fundamental theory of many-body systems, for example the distinction between metals and insulators in terms of the ground state wavefunction and quantitative measures of polarization and localization in an insulator.
Theoretically, how does the time to do a density functional theory (DFT) calculation scale with the number of electrons? I'm interested in "typical" DFT implementations such as VASP, ABINIT, etc., not O(N) codes.
The basic theory that describes the chemical bond - and practically all observable phenomena around us - is quantum mechanics. What is appealing about quantum mechanics is that this theory is truly free of any materials-specific parameter. It provides a mathematical recipe that is, in principle, capable of predicting the properties of any material by purely computational means. Ideally, the basic properties that are determined at the atomic scale can then enter larger-scale, phenomenological but validated models. Examples include materials parameters of simple metallic solids such as elasticity, thermal expansion, etc., electronic properties of semiconductor nanostructures, their optical properties, etc.
The primary workhorse theory of the field today is density functional theory (DFT), often used at the level of so-called "semilocal" or (more expensive) hybrid functionals. Beyond that, many-body approaches can give a more accurate description of ground- and excited state properties of "difficult" materials. The quantum nature of nuclei is most often incorporated by the so-called "Born-Oppenheimer" approximation - treat the electrons first, and then use the result to look at the "motion" (vibrations, phonons, ab initio molecular dynamics, statistical mechanics) of the nuclei. In practice, this usually works very well - where it does not, schemes to incorporate electron-nuclear coupling beyond "Born-Oppenheimer" for "real" (large and complex) systems are an active frontier of the field.
This development happens in close collaboration with other groups in Berlin, Munich, Helsinki, London and elsewhere around the world. This work is happening at a rapid pace - see our publications page for details. Recent milestone publications include a detailed spin-orbit coupling benchmark, hybrid functional calculations for periodic solids beyond 1,000 atoms or the stress tensor for numeric atom-centered orbital density-functional theory:
We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a computational complexity much lower than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI are modest. This even makes it possible to perform Kohn-Sham DFT calculations for 10 000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8, 0) boron nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of the accuracy required in a practical DFT calculation. 2ff7e9595c
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