#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?
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#2
27th March 2017, 03:17 PM
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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. |