events:2016_summer_school:gpw
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events:2016_summer_school:gpw [2018/05/29 21:48] – [Gaussians and Plane Wave method (GPW)] mwatkins | events:2016_summer_school:gpw [2020/08/21 10:15] (current) – external edit 127.0.0.1 | ||
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But, like in Hartree-Fock theory, we have to ensure that the electron orbitals are orthonormal to prevent the system imploding. | But, like in Hartree-Fock theory, we have to ensure that the electron orbitals are orthonormal to prevent the system imploding. | ||
- | **Orthogonality constraint** | + | === Orthogonality constraint |
$$ | $$ | ||
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$$ | $$ | ||
- | **Variational search in the space of the orbitals** | + | === Variational search in the space of the orbitals |
We correct the non-interacting electron model by adding in an (in principle unknown) XC potential that accounts for **all** quantum mechanical many-body interactions (electron-electron repulsion) | We correct the non-interacting electron model by adding in an (in principle unknown) XC potential that accounts for **all** quantum mechanical many-body interactions (electron-electron repulsion) | ||
- | **Classical election-electron repulsion** | + | === Classical election-electron repulsion |
$$ | $$ | ||
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$$ | $$ | ||
- | **Kohn-Sham functional** | + | === Kohn-Sham functional |
$$ | $$ | ||
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The exact functional form for the electron-electron repulsion is not known, but various levels of approximation are available (Jacob' | The exact functional form for the electron-electron repulsion is not known, but various levels of approximation are available (Jacob' | ||
- | The existence of this functional is guarenteed | + | The existence of this functional is guaranteed |
This maps mathematically onto the familiar Hartree-Fock model of electronic structure. | This maps mathematically onto the familiar Hartree-Fock model of electronic structure. | ||
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$$ | $$ | ||
- | You can scan through potentials available at [[http://cp2k.web.psi.ch/ | + | You can scan through potentials available at [[https://www.cp2k.org/static/ |
Original papers: | Original papers: | ||
- | [[Goedeker, Teter, Hutter, PRB 54 (1996), 1703]http:// | + | [[https:// |
- | [[Hartwigsen, Goedeker, Hutter, PRB 58 (1998) 3641]http:// | + | [[https:// |
==== Electrostatics ==== | ==== Electrostatics ==== | ||
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\sum_{\alpha \beta} P_{\alpha \beta} \bar{\phi}_{\alpha \beta} (\mathbf{r}) = n(\mathbf{R}) | \sum_{\alpha \beta} P_{\alpha \beta} \bar{\phi}_{\alpha \beta} (\mathbf{r}) = n(\mathbf{R}) | ||
$$ | $$ | ||
- | where $n(\mathbf{R})$ is the density at grid points in the cell, and $\bar{\phi}_{\alpha \beta}$ are the products of two basis functions | + | where $n(\mathbf{R})$ is the density at grid points in the cell, and $\bar{\phi}_{\alpha \beta}$ are the products of two basis functions. |
- | {{materials/ | + | |
* numerical approximation of the gradient $n(\mathbf{R}) \rightarrow \nabla n(\mathbf{R})$ | * numerical approximation of the gradient $n(\mathbf{R}) \rightarrow \nabla n(\mathbf{R})$ | ||
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{{http:// | {{http:// | ||
- | GTH pseudos have small density at the core - graph of density and $v_{XC}$ through a water molecule. These spikes can cause ripples in the energy as atoms move relative to the grid. | + | GTH pseudos have small density at the core - graph of density and $v_{XC}$ through a water molecule. These spikes can cause ripples in the energy as atoms move relative to the grid. These can be very problematic when trying to calculate vibrational frequencies. |
- | There are smoothing routines `& | + | |
+ | There are smoothing routines `& | ||
{{http:// | {{http:// | ||
- | avoid with higher cutoff, or GAPW methodology. | + | Avoid ripples |
+ | |||
+ | Whatever you do don't change settings between simulations you want to compare. | ||
- | These can be very problematic when trying to calculate vibrational frequencies. | ||
==== Multigrids ==== | ==== Multigrids ==== | ||
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NGRIDS 5 | NGRIDS 5 | ||
&END MGRID | &END MGRID | ||
- | < | + | </code> |
you can see in the output | you can see in the output |
events/2016_summer_school/gpw.1527630513.txt.gz · Last modified: 2020/08/21 10:14 (external edit)