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  #1  
27th March 2017, 02:57 PM
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Gpaw dtu

Hi I would like to know what GPAW is as well as the details about the functions and also the density of states?
  #2  
27th March 2017, 03:17 PM
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Join Date: Mar 2013
Re: Gpaw dtu

GPAW is a density-functional theory (DFT) Python code based on the projector-augmented wave (PAW) method as well as the atomic simulation environment (ASE).
The wave functions can be described as:

• Plane-waves (pw)
• Real-space uniform grids, multigrid methods and the finite-difference approximation (fd)
• Atom-centered basis-functions (lcao)

>>> # H2-molecule example:
>>> from ase import Atoms
>>> from gpaw import GPAW, PW
>>> h2 = Atoms('H2', [(0, 0, 0), (0, 0, 0.74)])
>>> h2.center(vacuum=2.5)
>>> h2.cell
array([[ 5. , 0. , 0. ],
[ 0. , 5. , 0. ],
[ 0. , 0. , 5.74]])
>>> h2.positions
array([[ 2.5 , 2.5 , 2.5 ],
[ 2.5 , 2.5 , 3.24]])
>>> h2.set_calculator(GPAW(xc='PBE', mode=PW(300), txt='h2.txt'))
>>> h2.get_potential_energy()
-6.6237575005960494
>>> h2.get_forces()
array([[ 9.37566400e-14, 4.40256983e-14, -6.44750360e-01],
[ -9.98454736e-14, 4.37862132e-14, 6.44750360e-01]])

Density of States

The density of states is defined by
ρ(ε)=∑n⟨ψn|ψn⟩δ(ε−εn),

where εn
is the eigenvalue of the eigenstate |ψn⟩

.Inserting a complete orthonormal basis, this can be rewritten as
ρ(ε)ρ(ε)=∑iρi(ε),=∫drρ(r,ε),ρi(ε)ρ(r,ε)=∑n⟨ψn|i⟩⟨i |ψn⟩δ(ε−εn)=∑n⟨ψn|r⟩⟨r|ψn⟩δ(ε−εn)

using that 1=∑i|i⟩⟨i|
and 1=∫dr|r⟩⟨r|.

Last edited by Rajkumar Agarwal; 27th March 2017 at 03:41 PM.


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