PWDFT.jl
PWDFT.jl
is a package to solve
electronic structure problems
based on
density functional theory
(DFT)
and KohnSham equations.
It is written in Julia programming language.
The KohnSham orbitals are expanded using plane wave basis. This basis set is very popular within solidstate community and is also used in several electronic structure package such as Quantum ESPRESSO, ABINIT, VASP, etc.
Features
 Total energy calculation of molecules, surfaces, and crystalline system within periodic unit cell (however, no corrections are implemented for nonperiodic systems yet).
 SCF with electron density mixing (for semiconducting and metallic systems)
 Direct minimization method using conjugate gradient (for semiconducting systems)
 GTH pseudopotentials (included in the repository)
 LDAVWN and GGAPBE functionals (via
Libxc.jl
)
Requirements
 Julia version >= 0.7, with the following packages installed:
These 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("LibSymspg")
These packages should be automatically installed PWDFT.jl
is installed as
local package (see below).
Many thanks to @unkcpz for providing Libxc
and LibSymspg
.
Installation
Currently, this package is not yet registered. So, Pkg.add("PWDFT")
will not work (yet).
We have several alternatives:
 Using Julia's package manager to install directly from the repository URL:
Pkg.add(PackageSpec(url="https://github.com/ffathurrahman/PWDFT.jl"))
 Using Julia development directory. We will use
$HOME/.julia/dev
for this. To enable$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 not
contain the .jl
part. For example:
ln fs /path/to/PWDFT.jl $HOME/.julia/dev/PWDFT
 Install PWDFT.jl as local package. Firstly, get into Pkg's REPL mode by tapping
]
, and activate a independent environmentactivate .
.
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 selfconsistent field iteration and direct energy minimization.
Units
PWDFT.jl
internally uses Hartree atomic units (energy in Hartree and length in bohr).
A simple work flow
 create an instance of
Atoms
:
atoms = Atoms(xyz_file="CH4.xyz", LatVecs=gen_lattice_sc(16.0))
 create an instance of
Hamiltonian
:
ecutwfc = 15.0 # in Hartree
pspfiles = ["../pseudopotentials/pade_gth/Cq4.gth",
"../pseudopotentials/pade_gth/Hq1.gth"]
Ham = Hamiltonian( atoms, pspfiles, ecutwfc )
 solve the KohnSham problem
KS_solve_SCF!( Ham, betamix=0.2 ) # using SCF (selfconsistent field) method
# or
KS_solve_Emin_PCG!( Ham ) # direct minimization using preconditioned conjugate gradient
Atoms
More examples on creating an instance of 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
More examples on creating an instance of Using 3x3x3 MonkhorstPack 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 spinpolarized (Nspin=2
):
Ham = Hamiltonian( atoms, pspfiles, ecutwfc, meshk=[3,3,3],
Nspin=2, extra_states=4 )
NOTES: Currently spinpolarized calculations are only supported by
specifying calculations with smearing scheme (no fixed magnetization yet),
so extra_states
should also be specified.
Using PBE exchangecorrelation 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.
More examples on solving the KohnSham problem
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=1e6, 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 )
Band structure calculations
Please see this as an example of how this can be obtained.
Citation
 Fadjar Fathurrahman, Mohammad Kemal Agusta, Adhitya Gandaryus Saputro, Hermawan Kresno Dipojono PWDFT.jl : A Julia package for electronic structure calculation using density functional theory and plane wave basis. Comp. Phys. Comm. 256 107372 (2020).
Some references
Articles:

M. Bockstedte, A. Kley, J. Neugebauer and M. Scheffler. Densityfunctional theory calculations for polyatomic systems:Electronic structure, static and elastic properties and ab initio molecular dynamics. Comp. Phys. Commun. 107, 187 (1997).

Sohrab IsmailBeigi and T.A. Arias. New algebraic formulation of density functional calculation. Comp. Phys. Comm. 128, 145 (2000)

C. Yang, J. C. Meza, B. Lee, L.W. Wang, KSSOLV  a MATLAB toolbox for solving the KohnSham equations, ACM Trans. Math. Softw. 36, 1–35 (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 Jürg Hutter. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods. Cambridge University Press, 2009.