Density Functional
The starting point for the xc functional is usually the result for the homogeneous electron gas, after which so called nonlocal or generalized gradient corrections (GGA: Generalized Gradient Approximation) are added.
XC functionals
The density functional approximation is controlled by the XC key.
XC (block-type)
Three classes of exchange-correlation functionals are supported: LDA, GGA, and meta-GGA. There is also the option to add an empirical dispersion correction. The only ingredient of the LDA energy density is the (local) density, the GGA depends additionally on the gradient of the density, and the meta GGA has an extra dependency on the kinetic energy density.
In principle you may specify different functionals to be used for the potential, which determines the self-consistent charge density, and for the energy expression that is used to evaluate the (XC part of the) energy of the charge density. This is not so important for a single point calculation as BAND prints the bonding energies of a set of common functionals, but the energy functional is used for the nuclear gradients (geometry optimization). To be consistent, one should generally apply the same functional to evaluate the potential and energy respectively. Two reasons, however, may lead one to do otherwise:
- The evaluation of the GGA part (especially for Meta GGAs) in the potential is rather time-consuming. The effect of the GGA term in the potential on the self-consistent charge density is often not very large. From the point of view of computational efficiency it may, therefore, be attractive to solve the SCF equations at the LDA level (i.e. not including GGA terms in the potential), and to apply the full expression, including GGA terms, to the energy evaluation a posteriori: post-SCF.
- A particular XC functional may have only an implementation for the potential, but not for the energy (or vice versa). This is a rather special case, intended primarily for fundamental research of Density Functional Theory, rather than for run-of-the-mill production runs.
All subkeys of
XC are optional and may occur twice in the data block: if one wants to specify different functionals for potential and energy evaluations respectively, see above.XC
{LDA {Apply} LDA {Stoll}}
{GGA {Apply} GGA}
{DiracGGA GGA}
{MetaGGA {Apply} GGA}
{Dispersion {s6scaling} {RSCALE=r0scaling} {Grimme3} {BJDAMP} {PAR1=par1} {PAR2=par2} {PAR3=par3} {PAR4=par4}}
{Model [LB94|TB-mBJ|KTB-mBJ|JTS-MTB-MBJ|GLLB-SC]}
{SpinOrbitMagnetization [None|NonCollinear|CollinearX|CollinearY|CollinearZ]}
{LibXC {Functional}}
End
The common use is to specify either an LDA or a (meta)GGA line. (Technically it is possible to have an LDA line and a GGA line, in which case the LDA part of the GGA functional (if applicable) is replaced by what is specified by the LDA line.)
Apply- States whether the functional defined on the pertaining line will be used self-consistently (in the SCF-potential), or only post-SCF, i.e. to evaluate the XC energy corresponding to the charge density. The value of apply must be SCF or POSTSCF. (default=SCF)
LDA/GGA/metaGGA
LDA- Defines the LDA part of the XC functional and can be any of the following:Xonly: The pure-exchange electron gas formula. Technically this is identical to the Xalpha form with a value 2/3 for the X-alpha parameter.Xalpha: the scaled (parameterized) exchange-only formula. When this option is used you may (optionally) specify the X-alpha parameter by typing a numerical value after the string Xalpha (Default: 0.7).VWN: the parameterization of electron gas data given by Vosko, Wilk and Nusair (ref [1], formula version V). Among the available LDA options this is the more advanced one, including correlation effects to a fair extent.Stoll: For the VWN or GL variety of the LDA form you may include Stoll’s correction [2] by typing Stoll on the same line, after the main LDA specification. You must not use Stoll’s correction in combination with the Xonly or the Xalpha form for the Local Density functional.
GGA- Specifies the GGA part of the XC Functional, in earlier times often called the ‘non-local’ correction to the LDA part of the density functional. It uses derivatives (gradients) of the charge density. Separate choices can be made for the GGA exchange correction and the GGA correlation correction respectively. Both specifications must be typed (if at all) on the same line, after the GGA subkey.For the exchange part the options are:
- Becke: the gradient correction proposed in 1988 by Becke [3]
- PW86x: the correction advocated in 1986 by Perdew-Wang [4]
- PW91x: the exchange correction proposed in 1991 by Perdew-Wang [5]
- mPWx: the modified PW91 exchange correction proposed in 1998 by Adamo-Barone [27]
- PBEx: the exchange correction proposed in 1996 by Perdew-Burke-Ernzerhof [12]
- HTBSx: the HTBS exchange functional [43]
- RPBEx: the revised PBE exchange correction proposed in 1999 by Hammer-Hansen-Norskov [13]
- revPBEx: the revised PBE exchange correction proposed in 1998 by Zhang-Wang [28]
- mPBEx: the modified PBE exchange correction proposed in 2002 by Adamo-Barone [29]
- OPTX: the OPTX exchange correction proposed in 2001 by Handy-Cohen [30]
For the correlation part the options are:- Perdew: the correlation term presented in 1986 by Perdew [6]
- PBEc: the correlation term presented in 1996 by Perdew-Burke-Ernzerhof [12]
- PW91c: the correlation correction of Perdew-Wang (1991), see [5], [8], [9]
- LYP: the Lee-Yang-Parr 1988 correlation correction [7]
Some GGA options define the exchange and correlation parts in one stroke. These are:- BP86: this is equivalent to Becke + Perdew together
- PW91: this is equivalent to pw91x + pw91c together
- mPW: this is equivalent to mPWx + pw91c together
- PBE: this is equivalent to PBEx + PBEc together
- HTBS: this is equivalent to HTBSx + PBEc together
- RPBE: this is equivalent to RPBEx + PBEc together
- revPBE: this is equivalent to revPBEx + PBEc together
- mPBE: this is equivalent to mPBEx + PBEc together
- BLYP: this is equivalent to Becke (exchange) + LYP (correlation)
- OLYP: this is equivalent to OPTX (exchange) + LYP (correlation)
- OPBE: this is equivalent to OPTX (exchange) + PBEc (correlation) [31]
DiracGGA- (Expert option!) This key handles which XC functional is used during the Dirac calculations of the reference atoms. A string is expected which is not restricted to names of GGAs but can be LDA-like functionals, too.Note: In some cases using a GGA functional leads to slow convergence of matrix elements of the kinetic energy operator w. r. t. the
Accuracyparameter. Then one can use the LDA potential for the calculation of the reference atom instead.
MetaGGA- Key to select the evaluation of a meta GGA. A byproduct of this option is that the bonding energies of all known functionals are printed (using the same density). Meta GGA calculations can be quite a bit more time consuming, especially when active during the SCF.Self consistency of the meta GGA is implemented as suggested by Neuman, Nobes, and Handy.[11]The available functionals of this type are:
0 Comments