gpw
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gpw [2016/10/18 12:53] – 134.147.125.236 | gpw [2024/10/01 05:27] (current) – [Cutoff] tkuehne | ||
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$n$ and $\tilde n$ are not equal, and this introduces an error in the calculation. $\tilde n$ converges toward $n$ when the cutoff (that controls the grid spacing) goes to infinity (and gridspacing to 0). Which cutoff is sufficient to represent a density depends on how sharp is the gaussian basis set (or that of the potential, but it is always broader). | $n$ and $\tilde n$ are not equal, and this introduces an error in the calculation. $\tilde n$ converges toward $n$ when the cutoff (that controls the grid spacing) goes to infinity (and gridspacing to 0). Which cutoff is sufficient to represent a density depends on how sharp is the gaussian basis set (or that of the potential, but it is always broader). | ||
- | For historical reasons the density of the grid is given as the energy (in Ry) of the highest reciprocal vector that can be represented | + | For historical reasons the density of the grid is given as the energy (in Ry) of the highest reciprocal vector that can be represented on the grid. This can be roughly given as $0.5(\pi/ |
- | It turns out that if one wants to put the whole density on the grid, the core electrons of even the simplest atoms cannot be represented, | + | It turns out that if one wants to put the whole density on the grid, the core electrons of even the simplest atoms cannot be represented, |
===== Smoothing ===== | ===== Smoothing ===== | ||
$\tilde n$ is optimized for the electrostatic part, but is used also to calculate the exchange and correlation potential. Because of this, and because the [[GTH pseudopotential]] goes almost to 0 close to the core of the atom, the xc potential, especially for gradient corrected functionals, | $\tilde n$ is optimized for the electrostatic part, but is used also to calculate the exchange and correlation potential. Because of this, and because the [[GTH pseudopotential]] goes almost to 0 close to the core of the atom, the xc potential, especially for gradient corrected functionals, | ||
- | For MD of water using a cutoff of 280 Ry '' | + | For MD of water using a cutoff of 280 Ry '' |
Methods that do not redefine the total energy are '' | Methods that do not redefine the total energy are '' |
gpw.1476795232.txt.gz · Last modified: 2020/08/21 10:15 (external edit)