The approximants to the kinetic energy dependent component of the embedding potential are described here.
FDE
{approximants to the kinetic energy dependent
component of the embedding potential}
{CJCORR [rho_cutoff]}
{GGAPOTXFD exchange approximant}
{GGAPOTCFD correlation approximant}
end
approximants to the kinetic energy dependent component of the embedding potential
Several approximants to the kinetic-energy-dependent component of the
effective potential given in Eq. (21) of [Ref. 184] are available.
None of them is applicable if the embedded system is covalently bound to its environment.
The user is recommended to look at the numerical value of the TSNAD(LDA) parameter which is given in the units of energy and
can be considered as a measure of the overlap. The following rule of thumb should be applied:
if this parameter is smaller than the estimated interaction energy between the embedded subsystem and the environment, then
the available approximants are most probably adequate. If it exceeds this limit, the results can be less reliable.
Printing TSNAD(LDA) is not done by default, as it can be quite time-consuming. Its printing is switched on
by including "EXTPRINTENERGY", and "PRINTRHO2", and "FULLGRID" in the FDE input block.
If no kinetic energy approximant is specified, by default the
local-density approximation (Thomas-Fermi approximant) is used.
For an assessment of approximants for weakly overlapping pairs of densities see Refs. [238,
239,
188,
241].
Based on these studies, the use of PW91k (= GGA97) is recommended.
APPROXIMANTS TO BE USED IN NORMAL APPLICATIONS
THOMASFERMI (default)
Local-density-approximation form of vt[rhoA,rhoB] [237] derived from Thomas-Fermi expression for Ts[rho] [194, 195].
GGA97 (or PW91K)
Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the Lembarki-Chermette [197] approximant to Ts[rho]. This approximant is currently the recommended one based on the numerical analysis of its accuracy [188,239] and the fact that the used enhancement factor disappears at large reduced density gradients, i.e. where the second-order gradient-expansion approximation fails [238, 241].
NDSD
Similarly to GGA97, the NDSD approximant is constructed by taking into account the asymptotic behavior of the functional vt[rhoA,rhoB] at small density gradients. In the construction of NDSD, the exact property of vt[rhoA,rhoB] at rho_A → 0$ and for ∫ rhoB = 2 given in Eq. A6 of Ref. [279] is also taken into account. The analysis of the accuracy of this potential [279] shows that NDSD is of the same or superior quality as GGA97. NDSD is, therefore, recommended as the successor of GGA97 to be used anywhere where the quality of the results depends directly on the accuracy of the potential vt[rhoA,rhoB], i.e., for obtaining electronic-structure-dependent properties. The analytical form of the corresponding approximant to the functional Tsnad [\rho_A,\rho_B]$ exists (Eq. 23 in Ref. [279]). It is not possible, however, to obtain the analytical form of the corresponding parent functional for the kinetic energy Ts[rho]. To reflect this and the fact that, similarly to the GGA approximants to vt[rhoA,rhoB], the numerical values of only first- and second derivatives of density are needed, the label NDSD (Non-Decomposable Second Derivatives) is used.
OBSOLETE APPROXIMANTS (can be used but GGA97 leads usually to a better embedding potential see [238,239])
LLP91
Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from Lee-Lee-Parr [Ref. 198] approximant to Ts[rho].
PW86k
Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from the Fuentealba-Reyes approximant to Ts[rho] [242].
THAKKAR92
Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the Thakkar approximant to Ts[rho] [201].
APPROXIMANTS WHICH MIGHT BE USEFUL ONLY FOR THEORY DEVELOPMENT
The accuracy of some of these approximants was investigated in detail [239, 238, 188, 241]. Each of them was shown to lead to a qualitatively incorrect embedding potential. They shouldn't be used in practical applications.
COULOMB
Neglecting completely vt[rhoA,rhoB] (vt[rhoA,rhoB] equals zero) together with the exchange-correlation component of the embedding potential introduced by Wesolowski and Warshel.
TF9W
The approximant to vt[rhoA,rhoB] [184] derived from the second-order gradient expansion [242]] for Ts[rho].
WEIZ
The approximant to vt[rhoA,rhoB] [241] derived from the von Weizsäcker approximant to Ts[rho] [186].
OL91A
Generalized-gradient-approximation form of vt[rhoA,rhoB] [238] derived from the first Ou-Yang and Levy approximant to Ts[rho] [200].
OL91B
Generalized-gradient-approximation form of vt[rhoA,rhoB] [239] derived from the second Ou-Yang and Levy approximant to Ts[rho] [200].
E00
Generalized-gradient-approximation form of vt[rhoA,rhoB] [263] derived from a kinetic energy functional by Ernzerhof [264] which represents the gradient expansion approximation up to the fourth order.
P92
Generalized-gradient-approximation form of vt[rhoA,rhoB] [263] derived from a kinetic energy functional by Perdew [265] which represents the gradient expansion approximation up to the sixth order.
LONG DISTANCE CORRECTIONS TO THE EFFECTIVE POTENTIAL
CJCORR
Option to switch on a long-distance correction. By default this option is not used. As was shown in Ref. [220], with the available approximate kinetic-energy approximants, the embedding potential has the wrong form in the limit of a large separation of the subsystems. In particular, it was shown that this can have serious consequences in the case of "supermolecular expansion of electron density of each subsystem" calculations (USEBASIS option). In Ref. [220], a correction is proposed that enforces the correct long-distance limit. (See also this reference for limitations of this correction.)
CJCORR [rho_cutoff]
This option switches on the long-distance correction. This option has to be used in combination with one of the above kinetic-energy approximants. By default, a density cut-off of 0.1 is employed.
NONADDITIVE EXCHANGE-CORRELATION APPROXIMANT
GGAPOTXFD
GGAPOTCFD
Option to specify the nonadditive exchange-correlation approximant. By default, in the construction of the effective embedding potential the exchange-correlation approximant that was specified in the XC block is used. It is possible to specify a different approximant with the GGAPOTXFD and GGAPOTCFD options. This is particularly useful in combination with the use of model potentials like SAOP, that can not be used in the embedding potential because of their orbital dependence. (For a discussion, see Ref. [189].)
GGAPOTXFD exchange approximant
The exchange approximant is used in the construction of the embedding potential. The same exchange approximants as in the XC key are available.
GGAPOTCFD correlation approximant
The correlation approximant is used in the construction of the embedding potential. The same correlation approximants as in the XC key are available.
