The density functional approximation is controlled by the XC key.
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:
1. 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.
2. 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.
The key that controls the Density Functional is xc,
with sub keys LDA
and (meta)GGA to define the LDA
and
(meta)GGA parts of the functional. All subkeys are optional (need not be
used) 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}}
End
The common use is to specify either an LDA, line 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.
For each record separately the default (if no
Apply value is given in that record) is
SCF.
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 (see next) 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 (separated by a blank). If omitted this parameter takes the default value 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.
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]
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].
LYP: the
Lee-Yang-Parr 1988 correlation correction [7-9].
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
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].
(Expert option.) Sometimes it is better to use the LDA potential for the Numerical atoms, when the exact solutions are too wild. We found this to be the case for the PBE functional (and its variations). In that case the matrix elements of the Kinetic energy operator converged very slowly with the Accuracy parameter.
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:
M06L: The Meta GGA as developed by the
Minesota group [16]
TPSS: The 2003 Meta GGA [15]
revTPSS: (only postscf) The 2009 revised Meta GGA [26]
If the DISPERSION keyword is present a dispersion
correction by Grimme [32]
will be added to the total bonding energy, where applicable. The term is added to the bonding energies of all printed functionals, standard the LDA and a couple of GGAs.
The global scaling
factor with which the correction is added depends on the exchange-correlation functional used at SCF
but it can be modified using the s6scaling parameter. The following scaling factors are used
(with the XC functional in parantheses):
1.20 (BLYP), 1.05 (BP), 0.75 (PBE), 1.05 (B3LYP). In all other cases a factor 1.0 is used unless modified
via the s6scaling parameter.
The van der Waals radii used in this implementation are hardcoded.
However, it is possible to modify the global scaling parameter for them using the RSCALE=r0scaling
argument. The default value is 1.1 as proposed by Grimme
[32].
Defaults and special cases
