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48 lines
1.3 KiB
Markdown
48 lines
1.3 KiB
Markdown
# Gaussian Plane Wave
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The primary basis in CP2K consists of Gaussian Type Orbital (GTO) functions. To take advantage of
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the efficient FFT algorithm for solving the Poisson equation, the electronic density must first be
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transferred from the GTO representation to a regular grid. This is referred to as _collocation_.
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After solving the Poisson equation the obtained electrostatic potential has to be transferred back
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into the GTO basis, which is referred to as _integration_. This ”opportunistic” switching between a
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Gaussian and a plane wave representation is the core idea of the Gaussian and Plane Waves (GPW)
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method. Its high-level operations are illustrated in the following flowchart:
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```mermaid
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block-beta
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columns 5
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a["el. Density\n(Gaussian Basis)"]
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space
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b["el. Density\n(Regular Grid)"]
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space
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c["el. Density\n(Plane Waves)"]
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space space space space space
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f["el. Potenial\n(Gaussian Basis)"]
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space
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e["el. Potenial\n(Regular Grid)"]
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space
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d["el. Potenial\n(Plane Waves)"]
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a -- "Collocate" --> b
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b -- "FFT" --> c
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c -- "Poisson Solver" --> d
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d -- "FFT<sup>-1</sup>" --> e
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e -- "Integrate" --> f
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```
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## See also
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- <https://www.cp2k.org/gpw>
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- <https://www.cp2k.org/quickstep>
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- [](#Lippert1997)
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- [](#K%C3%BChne2020)
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```{youtube} v2vnZbhNEpw
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---
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url_parameters: ?start=2
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align: center
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privacy_mode:
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---
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```
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