Plane wave density functional theory using Julia programming language
PWDFT.jl
is a package to solve
electronic structure problems
based on
density functional theory
(DFT)
and Kohn-Sham equations.
It is written in Julia programming language.
The Kohn-Sham orbitals are expanded using plane wave basis. This basis set is very popular within solid-state community and is also used in several electronic structure package such as Quantum ESPRESSO, ABINIT, VASP, etc.
Libxc.jl
)Clone the repository to your computer or download the zip file and extract it.
Start Julia and navigate to the downloaded or extracted PWDFT.jl directory. This
directory should contain Project.toml
file. Then activate the project
using Pkg
Pkg.activate(".")
Pkg.instantiate()
This process will install the required packages.
To run the examples move to the example directory (for example
using shell mode or cd
function)
and simply include the run.jl
file.
cd("examples/Si_fcc")
include("run.jl")
FFTW
SpecialFunctions
Libxc
(a wrapper to Libxc)LightXML
(for parsing UPF file)OffsetArrays
(currently used for some convenientThese packages are registered so they can be installed by using Julia's package manager.
using Pkg
Pkg.add("FFTW")
Pkg.add("SpecialFunctions")
Pkg.add("Libxc")
Pkg.add("LightXML")
Pkg.add("OffsetArrays")
These packages should be automatically installed PWDFT.jl
is installed as
local package (see below).
Currently, this package is not yet registered. So, Pkg.add("PWDFT")
will not work (yet).
We have several alternatives:
Pkg.add(PackageSpec(url="https://github.com/f-fathurrahman/PWDFT.jl"))
$HOME/.julia/dev
for this.$HOME/.julia/dev
directory, we need to modify the Julia'sLOAD_PATH
variable. Add the following line in your$HOME/.julia/config/startup.jl
.push!(LOAD_PATH, expanduser("~/.julia/dev"))
After this has been set, you can download the the package as zip file (using Github) or clone this repository to your computer.
If you download the zip file, extract the zip file under
$HOME/.julia/dev
. You need to rename the extracted directory
to PWDFT
(with no .jl
extension).
Alternatively, create symlink under $HOME/.julia/dev
to point to you cloned (or extracted) PWDFT.jl
directory.
The link name should may not
contain the .jl
part. For example:
ln -fs /path/to/PWDFT.jl $HOME/.julia/dev/PWDFT
]
,activate .
.Install the PWDFT.jl package in this environment:
(PWDFT) pkg> develop <path/to/PWDFT.jl>
To make sure that the package is installed correctly, you can load the package and verify that there are no error messages during precompilation step. You can do this by typing the following in the Julia console.
using PWDFT
Change directory to examples/Si_fcc
and run the following in the terminal.
julia run.jl
The above command will calculate total energy of hydrogen atom by SCF method.
The script will calculate total energy per unit cell of silicon crystal using self-consistent field iteration and direct energy minimization.
PWDFT.jl
internally uses Hartree atomic units (energy in Hartree and length in bohr).
Atoms
:atoms = Atoms(xyz_file="CH4.xyz", LatVecs=gen_lattice_sc(16.0))
Hamiltonian
:ecutwfc = 15.0 # in Hartree
pspfiles = ["../pseudopotentials/pade_gth/C-q4.gth",
"../pseudopotentials/pade_gth/H-q1.gth"]
Ham = Hamiltonian( atoms, pspfiles, ecutwfc )
KS_solve_SCF!( Ham, betamix=0.2 ) # using SCF (self-consistent field) method
# or
KS_solve_Emin_PCG!( Ham ) # direct minimization using preconditioned conjugate gradient
Atoms
GaAs crystal (primitive unit cell), using keyword xyz_string_frac
:
# Atoms
atoms = Atoms( xyz_string_frac=
"""
2
Ga 0.0 0.0 0.0
As 0.25 0.25 0.25
""",
in_bohr=true,
LatVecs = gen_lattice_fcc(10.6839444516)
)
Hydrazine molecule in extended xyz file
atoms = Atoms(ext_xyz_file="N2H4.xyz")
with the following N2H4.xyz
file (generated using ASE):
6
Lattice="11.896428 0.0 0.0 0.0 12.185504 0.0 0.0 0.0 11.151965" Properties=species:S:1:pos:R:3:Z:I:1 pbc="T T T"
N 5.94821400 6.81171100 5.22639100 7
N 5.94821400 5.37379300 5.22639100 7
H 6.15929600 7.18550400 6.15196500 1
H 5.00000000 7.09777800 5.00000000 1
H 5.73713200 5.00000000 6.15196500 1
H 6.89642800 5.08772600 5.00000000 1
Lattice vectors information is taken from the xyz file.
Hamiltonian
Using 3x3x3 Monkhorst-Pack kpoint grid (usually used for crystalline systems):
Ham = Hamiltonian( atoms, pspfiles, ecutwfc, meshk=[3,3,3] )
Include 4 extra states:
Ham = Hamiltonian( atoms, pspfiles, ecutwfc, meshk=[3,3,3], extra_states=4 )
Using spin-polarized (Nspin=2
):
Ham = Hamiltonian( atoms, pspfiles, ecutwfc, meshk=[3,3,3],
Nspin=2, extra_states=4 )
NOTES: Currently spin-polarized calculations are only supported by
specifying calculations with smearing scheme (no fixed magnetization yet),
so extra_states
should also be specified.
Using PBE exchange-correlation functional:
Ham = Hamiltonian( atoms, pspfiles, ecutwfc, meshk=[3,3,3],
Nspin=2, extra_states=4, xcfunc="PBE" )
Currently, only two XC functional is supported, namely xcfunc="VWN"
(default) and
xcfunc="PBE"
. Future developments should support all functionals included in LibXC.
Several solvers are available:
KS_solve_SCF!
: SCF algorithm with density mixing
KS_solve_SCF_potmix!
: SCF algorithm with XC and Hartree potential mixing
KS_solve_Emin_PCG!
: using direct total energy minimization by preconditioned conjugate
gradient method (proposed by Prof. Arias, et al.). Only
the version which works with systems with band gap is implemented.
Stopping criteria is based on difference in total energy.
The following example will use Emin_PCG
.
It will stop if the difference in total energy is less than
etot_conv_thr
and it occurs twice in a row.
KS_solve_Emin_PCG!( Ham, etot_conv_thr=1e-6, NiterMax=150 )
Using SCF with betamix
(mixing parameter) 0.1:
KS_solve_SCF!( Ham, betamix=0.1 )
Smaller betamix
usually will lead to slower convergence but more stable.
Larger betamix
will give faster convergence but might result in unstable
SCF.
Several mixing methods are available in KS_solve_SCF!
:
simple
or linear mixing
linear_adaptive
anderson
broyden
pulay
ppulay
: periodic Pulay mixing
rpulay
: restarted Pulay mixing
For metallic system, we use Fermi smearing scheme for occupation numbers of electrons.
This is activated by setting use_smearing=true
and specifying a small smearing parameter kT
(in Hartree, default kT=0.001
).
KS_solve_SCF!( Ham, mix_method="rpulay", use_smearing=true, kT=0.001 )
Please see this as an example of how this can be obtained.
Articles:
M. Bockstedte, A. Kley, J. Neugebauer and M. Scheffler. Density-functional theory calculations for polyatomic systems:Electronic structure, static and elastic properties and ab initio molecular dynamics. Comp. Phys. Commun. 107, 187 (1997).
Sohrab Ismail-Beigi and T.A. Arias. New algebraic formulation of density functional calculation. Comp. Phys. Comm. 128, 1-45 (2000)
C. Yang, J. C. Meza, B. Lee, L.-W. Wang, KSSOLV - a MATLAB toolbox for solving the Kohn-Sham equations, ACM Trans. Math. Softw. 36, 135 (2009)
Books:
Richard Milton Martin. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press, 2004.
Jorge Kohanoff. Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods. Cambridge University Press, 2006.
Dominik Marx and Jrg Hutter. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods. Cambridge University Press, 2009.