AngstromCube

AngstromCube is an experimental all-electron DFT application.
It is based on a various representations:
    real-space grids,
    plane waves and
    factorizable local orbitals.
Furthermore, the Green functions formalism, near-sightedness
for linear-scaling and the projector augmented wave method (PAW), 
in particular the revised PAW method (see Paul F. Baumeister and Shigeru Tsukamoto,
  proceedings of PASC'19, https://dl.acm.org/doi/10.1145/3324989.3325717)

Name The name refers to a cube with edge length 1 Angstrom which is abbreviated \AA in TeX code. This is because always 4x4x4 real-space grid points are grouped for performance which corresponds to roughly one \AA^3

Principles The idea is to have a code that

• is highly parallel
• can make use of GPUs
• does not require more input than the atomic coordinates
• can scale linearly

Current Status

• These features are planned but have so far not been addressed:
  • different versions of LDA, GGA, meta-GGA (currently only LDA implemented)
  • efficient eigensolver for the grid Hamiltonian (currently inefficient subspace rotation method)
  • MPI parallelization (currently none)
  • OpenMP parallelization (currently none)
  • GPU acceleration (currently none)
  • fancy boundary conditions (currently only periodic and isolated)
  • forces (currently none)
  • self-consistency convergence criteria (currently we set the number of iterations)
  • magnetism, collinear and non-collinear (currently none)
• These features are ready:
  • total energy
  • complex wave functions, k-points
  • potential generation (currently only non-magnetic)
  • multigrid Poisson solver for the electrostatics (currently only serial)
  • SHO-projector PAW with all-electron atoms (currently only non-magnetic)
• Some features are build in only for development purposes:
  • a stable FFT Poisson solver for the electrostatic problem
  • plane wave basis set using a dense matrix eigensolver (LAPACK) or iterative (in development)
  • dense eigensolver for the real-space grid Hamiltonian
• These features are not intended to be implemented ever:
  • strain calculation
  • exact exchange
  • phonons

Directories The root folder of this repository contains the following directories:

Directory	Purpose
bin	you can move your compiled executabales/libraries here but please do not git-add them
data	matrix element files for CHO and SHO transforms between radial and Cartesian bases
doc	documentation
external	put third party libraries here
green	source folder for the Green function executable ./green
src	source folder for the generator executabale ./a43
include	source folder for header files
julia	experimental modules in the Julia programming language
ref	reference output of certain unit tests
test	test scripts for certain modules

Abbreviations

Abbr.	Explanation
DFT	Density Functional Theory
LDA	Local Density Approximation
GGA	Generalized Gradient Approximation
PAW	Projector Augmented Wave
CPU	Central Processing Unit
GPU	Graphical Processing Unit
SHO	Spherical Harmonic Oscillator
CHO	Circular Harmonic Oscillator
MPI	Message Passing Interface
FFT	Fast Fourier Transform
OpenMP	Open Multi-Processing
TeX	typesetting