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RMGDFT / rmgdft

RMG is an Open Source code for electronic structure calculations and modeling of materials and molecules. It is based on density functional theory and uses a real space basis and pseudopotentials.
GNU General Public License v2.0
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Why is k-point needed for Real-space basis #78

Closed DeeliN221 closed 1 year ago

DeeliN221 commented 2 years ago

Hi, I am not familiar with the underlying formula of DFT codes, and got confused in some conceptions.

I know wavefunction can be expressed on the real-space basis, plane-wave, or LCAO basis. The plane-wave code represents wavefunction in k-space though Fourier transform, thus the k-point is needed. But why does the real-space basis code still need k-space? Is it just for computational efficiency or is it a natural requirement of ALL DFT code?

Many Thanks.

elbriggs commented 2 years ago

This is a conseqence of the periodic nature of the wavefunctions in a crystal. Plane waves provide a convenient way of expressing this but the concept is more fundamental than that.

DeeliN221 commented 1 year ago

This is a conseqence of the periodic nature of the wavefunctions in a crystal. Plane waves provide a convenient way of expressing this but the concept is more fundamental than that.

Thanks, I reviewed the textbook of solid physics and agree with you. Still, I am wondering is it possible to solve the KS equation without K-point? For example, in a non-periodic system.