11.7 Frozen-Density Embedding Theory

11.7.2 FDE-Man Job Control

(June 30, 2021)

The FDE-Man job control with respect to embedding parameters is accomplished via options in the $fde input section. The format of the $fde section requires key and value pairs separated by a space character:

$fde
   <Keyword>  <parameter>
$end

Note:  The following job control variables belong only in the $fde section. Do not place them in the $rem section.

The supermolecular expansion (SE) uses the full basis set of the supersystem for calculations on each fragment. Because of the computational cost this option should only be used for small to medium sized supersystems. Note that for visualization of orbitals or densities SE only supports the generation of volumetric data via MAKE_CUBE_FILES (MolDen files are not supported, i.e. MOLDEN_FORMAT should be avoided). On the other hand, the monomer expansion (ME) only uses the basis set of each individual fragment. This choice of basis expansion is recommended for daily basis embedding calculations.

Analogous to a regular DFT calculation in Q-Chem (by using METHOD) the exchange-correlation functional combination can either be selected with one keyword XC_Func,or by defining X_Func and C_Func (similar to EXCHANGE and CORRELATION). To include only the electrostatic terms in the embedding potential one can set all the functional keywords to None.

It is recommended to employ the same level of approximation for the non-additive kinetic and exchange-correlation functional, for instance TF/SVWN or PW91k/PW91.

The minimal specifications required to successfully run a FDET calculation are:

  • Functionals for embedding potential: T_Func, XC_Func (or X_Func and C_Func),

  • Basis expansion: Expansion,

  • Method for environment density: rhoB_method

T_Func
       Kinetic energy functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       TF Use Thomas-Fermi kinetic energy functional. PW91k / LC94 Use kinetic energy functional based on PW91. None Do not include any kinetic energy functional.
RECOMMENDATION:
       Use the same level of approximation as for the non-additive exchange-correlation energy functional.

XC_Func
       Exchange-Correlation functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA exchange-correlation functionals available in Q-Chem. None Do not include any exchange-correlation energy functional.
RECOMMENDATION:
       Only use LDA or GGA-type functionals.

X_Func
       Exchange functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA exchange functionals available in Q-Chem. None Do not include any exchange energy functional.
RECOMMENDATION:
       Only use LDA or GGA-type functionals. XC_Func and X_Func are mutually exclusive.

C_Func
       Exchange-Correlation functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA correlation functionals available in Q-Chem. None Do not include any exchange energy functional.
RECOMMENDATION:
       Only use LDA or GGA-type functionals. XC_Func and C_Func are mutually exclusive.

Expansion
       Specifies which basis set expansion should be used.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       SE/super/supermolecular Supermolecular basis is used for both System A and B. ME/mono/monomer Monomer expansion basis is used on each System A and B.
RECOMMENDATION:
       SE should be used for testing purposes only, since it is more expensive. Use the ME as standard choice, particularly for large systems.

rhoA_method
       Method to calculate reference density ρAref(𝐫) of the core fragment (A). If DFT is requested, the respective exchange-correlation functional is the same as defined for the embedding calculation, i.e. with the keywords XC_FUNC or X_FUNC and C_FUNC.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       HF
OPTIONS:
       HF Use Hartree-Fock method. DFT Use Density Functional Theory. MP Use Second-Order Møller-Plesset perturbation theory.
RECOMMENDATION:
       Use either HF or DFT.

rhoB_method
       Method to calculate the environment density (B). If DFT is requested, the respective exchange-correlation functional has to be defined using the keyword XC_FUNC_B or X_FUNC_B and C_FUNC_B.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       HF Use Hartree-Fock method. DFT Use Density Functional Theory. MP Use Second-Order Moller-Pleset method.
RECOMMENDATION:
       Use either HF or DFT.

XC_Func_B
       Exchange-Correlation functional used for the environment DFT calculation.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA/global-hybrid-GGA exchange-correlation functionals available in Q-Chem.
RECOMMENDATION:
       None

X_Func_B
       Exchange functional used for the environment DFT calculation.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA exchange functionals available in Q-Chem.
RECOMMENDATION:
       XC_Func_B and X_Func_B are mutually exclusive.

C_Func_B
       Correlation functional used for the environment DFT calculation.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       NAME NAME can be any of the LDA/GGA correlation functionals available in Q-Chem.
RECOMMENDATION:
       XC_Func_B and C_Func_B are mutually exclusive.

PrintLevel
       Print level for FDE-Man output.
INPUT SECTION: $fde
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 minimum print level 1 extended print level 2 maximum print level 3 maximum print level and additional text files (densities, etc.)
RECOMMENDATION:
       Use minimal print level.

11.7.2.1 Superposition of Molecular Densities

When the selected environment comprises many atoms and molecules, a sensible approximation is to construct the total environment density as the sum of the densities of the individual molecules. This can be done with the keywords Superposition_B or Import_Superposition_B. In the first case, the molecular densities are computed in the same calculation, and assembled into one single density matrix. The molecular densities and the superposed density matrices are saved into text files.

Superposition_B
       Compute the density of fragment B as a superposition of molecular densities.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Do a superposition of molecular densities to build the density of fragment B. FALSE Don’t do a superposition, use the whole fragment B.
RECOMMENDATION:
       The molecular densities are calculated with the method specified with the keyword: rhoB_method.

In the second case, the individual density matrices are expected to be already calculated independently and are required to be present in the same folder of the calculation.

Import_Superposition_B
       Assemble the density of fragment B from molecular densities.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Read and superpose the molecular densities to build the density of fragment B. FALSE Don’t do a superposition, use the whole fragment B.
RECOMMENDATION:
       The files with the molecular density matrices should be .txt files, numerated from 0, with the prefix SCF_Dens_B_Subfrag_.

Note:  No embedding calculation is performed if these functions are selected. In both cases, only the geometry of fragment B has to be given, and each molecule needs to be specified as independent fragment in the MOLECULE section.

When using the superposition options, the file of the superposed density matrix of the environment (B) is saved with the name Densmat_B.txt, and can be used with the import_rhoB option to subsequently perform an embedding calculation (see Sec. 11.7.2.2 below).

11.7.2.2 Import Densities

In FDE-Man the user has the option to import the density matrices used to generate the embedding potential. This alternative is particularly useful if the desired method to generate the densities for the embedding potential is not available in the current version, for instance, or when the superposition of densities is used to generate ρB(𝐫). The density matrices must be given in AO basis in a text file with the following format:

<nspin> <nbas> <nbas>
<value>
<value>
...

where <nspin> has two possible values (1 or 2) depending on the number of spin densities contained in the file. The first line should also contain the dimensions of the density matrix (<nbas>).

import_rhoA
       Import density of subsystem A used for the embedding potential. The file must be named Densmat_A.txt and located in the calculation folder.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Read the density for subsystem A from file. FALSE Do not use density from file.
RECOMMENDATION:
       None

import_rhoB
       Import density of subsystem B used for the embedding potential. The file must be named Densmat_B.txt and located in the calculation folder.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Read the environment density from file. FALSE Do not use density from file.
RECOMMENDATION:
       None

11.7.2.3 Pre-Polarization of the Environment Density

Formally the exactness of FDET equations requires the condition 𝐫(ρ0(𝐫)ρB(𝐫)) to be satisfied, whereby ρ0(𝐫) denotes the exact density of the supersystem. 1166 Wesolowski T. A., Warshel A.
J. Phys. Chem.
(1993), 97, pp. 8050.
Link
, 1167 Wesolowski T. A.
Phys. Rev. A
(2008), 77, pp. 012504.
Link
, 792 Neugebauer J.
Phys. Rep.
(2010), 489, pp. 1.
Link
This condition can, however, not be assured a priori. In practice, deficiencies with the initial choice of ρB(𝐫) can be cured to some extent by pre-polarizing the environment density. 933 Ricardi N. et al.
Phys. Chem. Chem. Phys.
(2018), 20, pp. 26053.
Link
Pre-polarization schemes available in FDE-Man can be turn on with the prepol keyword. The different pre-polarization options are described below.

prepol
       Pre-polarize ρB(𝐫) in the field of the embedded species represented by point charges or a charge density.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Turn on pre-polarization of ρB(𝐫). FALSE Do not pre-polarize the environment density.
RECOMMENDATION:
       See Ref. 933 for a review of FDET polarization schemes.

prepol_type
       Type of pre-polarization scheme.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       Mulliken
OPTIONS:
       Mulliken Use Mulliken charges of system A to pre-polarize ρB(𝐫). CHELPG Use ChElPG charges of system A to pre-polarize ρB(𝐫). elstat / Coulomb Use electrostatic embedding potential (using density and nuclear charges of A) to pre-polarize ρB(𝐫).
RECOMMENDATION:
       None

root_Aref
       Defines which electronic state is considered for ρAref(𝐫) in the pre-polarization scheme.
INPUT SECTION: $fde
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       n Use nth state of A for pre-polarization scheme (ground state = 0).
RECOMMENDATION:
       None

11.7.2.4 Miscellaneous Options

Debug
       Request additional printings as well as saving the separate components of the embedding potential (in AO basis) to disk.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Print extra options and save components to disk. FALSE Do not print extra info.
RECOMMENDATION:
       This option creates multiple files and additional details in the output. Use only for debugging purposes.

rhoB_basis
       Use a different basis set for fragment B than the one for the embedded system A, specified in the $rem section. Basis sets can be requested in the same way as in the BASIS section. However, contrary to the standard definition inside the input file, the user-defined basis and mixed basis must be defined without $basis and $end, in a text file called fde_genbasB and located in the calculation folder.
INPUT SECTION: $fde
TYPE:
       STRING
DEFAULT:
       None
OPTIONS:
       General, Gen User-defined. See Section 8.4. Symbol Use standard basis sets as in the tables in Section 8.3. Mixed Use a combination of different built-in basis sets (see Section 8.5).
RECOMMENDATION:
       Smaller basis for fragment B can be used to improve the performance of embedding calculations.

Note:  All basis used within the FDE-Man module use PURECART = 2111.

print_props
       Print molecular properties (multipole moments, Mulliken charges) associated with the reference fragment densities used to construct the embedding potential.
INPUT SECTION: $fde
TYPE:
       INTEGER
DEFAULT:
       1
OPTIONS:
       0 Do not print molecular properties. 1 Print molecular properties only for fragment A. 2 Print molecular properties for both fragments A and B.
RECOMMENDATION:
       None

If the user desires to only save the embedding potential without performing an embedding calculation, it can be done by setting to TRUE simultaneously the variables debug and Vemb_only. In this case, the individual components of the embedding potential are saved to disk into text files as mentioned above in the debug.

Vemb_only
       Only generate the embedding potential and save its components to disk.
INPUT SECTION: $fde
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Generate embedding potential and exit FDE-Man. FALSE Perform regular embedding calculation.
RECOMMENDATION:
       None