ENCUTGWSOFT: Difference between revisions

Latest revision as of 05:42, 29 August 2024

Default: ENCUTGWSOFT	= ENCUTGW $\times 0.8$	for ALGO=ACFDT
	= ENCUTGW $\times 0.8$	as of VASP.6.3
	= ENCUTGW	else

Important: For vasp.6.3 and later releases ENCUTGWSOFT always defaults to ENCUTGW

\times 0.8

.

Descprition: The flag ENCUTGWSOFT sets the energy cutoff for the response function, such that it allows to truncate the Coulomb kernel slowly between the energy specified by ENCUTGWSOFT and ENCUTGW using a cosine window function.

RPA/ACFDT correlation energies converge very slowly with respect to $\mathbf{G}_{\rm max }$ . Thus VASP automatically extrapolates to the infinite basis set limit using a linear regression to the equation: ^[1]^[2]^[3]

$E_{\mathrm{c}}({\mathbf{G}})=E_{\mathrm{c}}(\infty)+\frac{A}{{\mathbf{G}}^3}$ .

This usually leads to much smoother energy-volume curves in ACFDT calculations and MP2 calculations. The modified Coulomb kernel is in this case: ${\displaystyle v_{G} = \frac{4 \pi e^2} {G^2} \frac{1}{2} \left( 1 + \cos \left( \pi \, \frac{ \frac{\hbar^{2} G^2 }{2 m_e} - \mathrm{ ENCUTGWSOFT} }{ \mathrm{ENCUTGW} - \mathrm{ENCUTGWSOFT}} \right) \right) \qquad \mbox{for} \quad \frac{\hbar^2 G^2 }{2 m_e} > \mathrm{ENCUTGWSOFT}}$

If LSCK is set to .TRUE., the squeezed Coulomb kernel is used instead of the cosine window:^[4]

${\displaystyle v_{G} = 4 \pi e^2 \frac{ (G_{max}-G_{min})(G_{max}-G) }{ (G_{min}^2 - G(2G_{min}-G_{max}))^2 } \qquad \mbox{for} \quad \mathrm{ENCUTGWSOFT}=\frac{\hbar^2G_{min}^2}{2m_e}<\frac{\hbar^2 G^2}{2m_e}<\frac{\hbar^2G_{max}^2}{2m_e}=\mathrm{ENCUTGW}}$

This kernel squeezes contributions from large wave vectors $G>G_{max}$ into the window given by ENCUTGWSOFT. For GW type calculations the squeezed Coulomb kernel was the default (when ENCUTGWSOFT was set in the INCAR file) before version vasp.6.3, but in newer releases the code always defaults to a smoothed Coulomb kernel (both for GW and RPA type calculations). If one desires to recover the behavior of vasp.6.2 and older versions, LSCK=.TRUE. must be set in the INCAR file for GW type calculations if ENCUTGWSOFT is set in the INCAR file.

Mind: The infinite basis set limit extrapolation for RPA/ACFDT is described in more detail here.

@@ Line 1: / Line 1: @@
-{{TAGDEF|ENCUTGWSOFT|[real] (energy cutoff for response function)}}
+{{TAGDEF|ENCUTGWSOFT|[real]}}
-{{DEF|ENCUTGWSOFT|{{TAG|ENCUTGW}}<math>\times 0.8</math>| for {{TAG|ALGO}}{{=}}''ACFDT''|{{TAG|ENCUTGW}}|else}}
+{{DEF|ENCUTGWSOFT|{{TAG|ENCUTGW}}<math>\times 0.8</math>| for {{TAG|ALGO}}{{=}}''ACFDT''|{{TAG|ENCUTGW}}<math>\times 0.8</math>| as of VASP.6.3 | {{TAG|ENCUTGW}}|else}}
+{{NB|important|For vasp.6.3 and later releases {{TAG|ENCUTGWSOFT}} always defaults to {{TAG|ENCUTGW}}<math>\times 0.8</math>.}}
+Descprition: The flag {{TAG|ENCUTGWSOFT}} sets the energy cutoff for the response function, such that it allows to truncate the Coulomb kernel slowly between the energy
+specified by {{TAG|ENCUTGWSOFT}} and {{TAG|ENCUTGW}} using a cosine window function.
+----
+RPA/ACFDT correlation energies converge very slowly with respect to <math>\mathbf{G}_{\rm max }</math>.
+Thus VASP automatically extrapolates to the infinite basis set limit using a linear regression to the equation: {{cite|harl:2008}}{{cite|harl:2010}}{{cite|klimes:2014}}
+<math>E_{\mathrm{c}}({\mathbf{G}})=E_{\mathrm{c}}(\infty)+\frac{A}{{\mathbf{G}}^3}</math>.
+This  usually leads to much smoother energy-volume curves in {{TAG|ACFDT calculations}} and {{TAG|MP2 calculations}}.
+The modified Coulomb kernel is in this case:
+<math>v_{G} = \frac{4 \pi e^2} {G^2} \frac{1}{2} \left( 1 + \cos \left( \pi \, \frac{ \frac{\hbar^{2} G^2 }{2 m_e} - \mathrm{ ENCUTGWSOFT} }{ \mathrm{ENCUTGW} -  \mathrm{ENCUTGWSOFT}} \right) \right)
+\qquad \mbox{for} \quad  \frac{\hbar^2 G^2 }{2 m_e} >  \mathrm{ENCUTGWSOFT}</math>
+If {{TAG|LSCK}} is set to .TRUE., the squeezed Coulomb kernel is used instead of the cosine window:{{cite|riemelmoser:jcp:2020}}
+<math>v_{G} = 4 \pi e^2 \frac{
+(G_{max}-G_{min})(G_{max}-G)
+}{
+(G_{min}^2 - G(2G_{min}-G_{max}))^2
+}
+\qquad \mbox{for} \quad  \mathrm{ENCUTGWSOFT}=\frac{\hbar^2G_{min}^2}{2m_e}<\frac{\hbar^2 G^2}{2m_e}<\frac{\hbar^2G_{max}^2}{2m_e}=\mathrm{ENCUTGW}</math>
-The flag allows to truncate the Coulomb kernel slowly between the energy
+This kernel ''squeezes'' contributions from large wave vectors <math>G>G_{max}</math> into the window given by {{TAGBL|ENCUTGWSOFT}}.
-specified by {{TAG|ENCUTGWSOFT}} and {{TAG|ENCUTGW}}.
+For GW type calculations the squeezed Coulomb kernel was the default (when {{TAGBL|ENCUTGWSOFT}} was set in the INCAR file) before version vasp.6.3, but
-This  usually leads to much smoother energy-volume curves in AC-FDT and MP2 calculations.
+in newer releases the code always defaults to a smoothed Coulomb kernel (both for GW and RPA type calculations). If one desires to recover the behavior
-The modified Coulomb kernel is in this case:
+of vasp.6.2 and older versions, {{TAG|LSCK}}=.TRUE. must be set in the INCAR file for GW type calculations if {{TAGBL|ENCUTGWSOFT}} is set in the INCAR file.
-<math>v_{\bf G} = \frac{4 \pi e^2} {| \bf G|^2} \frac{1}{2} \left( 1 + {\rm cos} \left( \pi \, \frac{ \frac{\hbar^2 |\bf G|^2 }{2 m_e} - {{TAG|ENCUTGWSOFT}}}{ {{TAG|ENCUTGW}} -  {{TAG|ENCUTGWSOFT}}} \right) \right)
-\qquad \mbox{for} \quad  \frac{\hbar^2 |\bf G|^2 }{2 m_e} >  {{TAG|ENCUTGWSOFT}}</math>
-== Related Tags and Sections ==
+{{NB|mind|The infinite basis set limit extrapolation for RPA/ACFDT is described in more detail [[ACFDT/RPA_calculations#Basis_set_convergence|here]].}}
+== Related tags and articles ==
 {{TAG|PRECFOCK}},
 {{TAG|ENCUT}},
 {{TAG|ENCUTGW}},
-{{TAG|GW calculations}}
+{{TAG|GW calculations}},
+{{TAG|LSCK}},
+[[ACFDT/RPA_calculations#Basis_set_convergence|RPA/ACFDT basis set convergence]],
+{{sc|ENCUTGWSOFT|Examples|Examples that use this tag}}
 ----
-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]][[Category:GW]]
+[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]]