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events:2016_summer_school:gpw [2018/05/29 21:48] – [Gaussians and Plane Wave method (GPW)] mwatkinsevents: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's Ladder).  The exact functional form for the electron-electron repulsion is not known, but various levels of approximation are available (Jacob's Ladder). 
  
-The existence of this functional is guarenteed by the 1st Hohenberg-Kohn Theroem.+The existence of this functional is guaranteed by the 1st Hohenberg-Kohn Theroem.
  
 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/potentials/|Matthias Krack's website]]+You can scan through potentials available at [[https://www.cp2k.org/static/potentials/|here]]
  
 Original papers:   Original papers:  
-[[Goedeker, Teter, Hutter, PRB 54 (1996), 1703]http://journals.aps.org/prb/abstract/10.1103/PhysRevB.54.1703]   +[[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.54.1703| Goedeker, Teter, Hutter, PRB 54 (1996), 1703]] and   
-[[Hartwigsen, Goedeker, Hutter, PRB 58 (1998) 3641]http://journals.aps.org/prb/abstract/10.1103/PhysRevB.58.3641]+[[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.58.3641| Hartwigsen, Goedeker, Hutter, PRB 58 (1998) 3641]]
  
 ==== 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/collocate.bmp}}+
  
   * 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://ars.els-cdn.com/content/image/1-s2.0-S0010465505000615-gr002.gif}} {{http://ars.els-cdn.com/content/image/1-s2.0-S0010465505000615-gr002.gif}}
  
-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 `&XC_GRID / XC_DERIV`, but probably best to stick with the defaults ... whatever you do don't change settings between simulations you want to compare.+ 
 +There are smoothing routines `&XC_GRID / XC_DERIV`, see the exercise [[events:2018_summer_school:converging_cutoff]].
  
 {{http://ars.els-cdn.com/content/image/1-s2.0-S0010465505000615-gr003.gif}} {{http://ars.els-cdn.com/content/image/1-s2.0-S0010465505000615-gr003.gif}}
  
-avoid with higher cutoff, or GAPW methodology.+Avoid ripples with higher a cutoff, or GAPW methodology.  
 + 
 +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>+</code>
  
 you can see in the output you can see in the output
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