# *FDE¶

Frozen density embedding (FDE) directives.

General information on the FDE method can be found in recent reviews (e.g. [Jacob2013], [Gomes2012a]), whereas details concerning the Dirac implementation are found in [Gomes2008], [Hofener2012] and [Hofener2013].

## Data import¶

If Dirac is used to calculate the subsystem of interest, data from the subsystem(s) making up the environment must be fed into the program.

### .EMBPOT¶

Specifies the name of the file containing the embedding potential over an integration grid.

Default:

.EMBPOT
EMBPOT

### .FRDENS¶

Specifies the name of the file containing the “frozen” quantities (integration grid, electrostatic potential, electrostatic potential due to external fields (e.g. point charges), density and (x,y,z) components of the density gradient).

Default:

.FRDENS
FRZDNS

## Embedding potential¶

If the .EMBPOT option was selected, the program will simple compute matrix elements of the the AO basis used by the program, and add it to the one-electron Fock matrix. Because of that, this option can be used with any wavefunction in Dirac. The ground-state calculation in this case corresponds to the “fixed potential” scheme of [Gomes2008].

However, if .EMBPOT is not specified, the program implicitly selects the .UPDATE option, and assumes a frozen density has been provided (see .FRDENS).

### .UPDATE¶

This option requires that the embedding potential for the ground-state be calculated using the “frozen” quantities and those for the subsystem treated with Dirac. The non-additive contributions are calculted with the orbital-free kinetic energy and exchange-correlation density functionals specified under .NAKEF and .NAXCF, respectively.

Currently this option is only supported during the SCF procedure, so it does not have any effect for correlated wavefunctions (e.g. MP2, CI, CC).

The .EMBPOT and this option cannot be specified at the same time.

### .NAKEF¶

Specifies the orbital-free kinetic energy density functional used to calculate the non-additive kinetic energy contributions to the ground-state embedding potential (see .UPDATE) and/or response contributions (see .RSP or .RSPLDA)

Default:

.NAKEF
kin_tf

Which corresponds to the Thomas-Fermi kinetic energy functional. Other available functionals are: PW91k (kin_pw91).

### .NAXCF¶

Specifies the exchange-correlation density functional used to calculate the non-additive kinetic energy contributions to the ground-state embedding potential (see .UPDATE) and/or response contributions (see .RSP or .RSPLDA)

Default:

.NAXCF
lda

Where lda is equivalent to specifying “slaterx=1.0 vwnc=1.0” (without quotes). Other available functionals are: pbe (equivalent to “pbex=1.0 pbec=1.0”), blyp (equivalent to “beckex=1.0 lypc=1.0”), pp86 (equivalent to “pw86x=1.0 p86c=1.0”)

## Response contributions¶

For response-based approaches (TDHF, TDDFT), contributions from FDE to the active subsystem can be included through the keywords below (the default is to not include any). For correlated wavefunctions (e.g. MP2, CI, CC) these do not yet have any effect.

These options can be used together with either .UPDATE or .EMBPOT, but require that “frozen” quantities are present (see .FRDENS)

### .RSP¶

Specifies that FDE response contributions should be calculated employing the density functionals specified under .NAKEF and .NAXCF, if any.

### .RSPLDA¶

Specifies that the non-additive exchange-correlation and kinetic energy FDE response contributions should be calculated with the LDA and Thomas-Fermi functionals, respectively.

## Data export¶

Dirac can also provide ground-state data (density and density gradient, electrostatic potential etc) from the subsystem in question over a grid, so that these can be used by other programs.

### .GRIDOU¶

Warning

Development version only.

Specifies the grid over which the quantities will be calculated and exported, and enables the export. The input is a XYZW file, and the output is in XML format. The original file is overwritten.

Default:

.GRIDOU
GRIDOUT

### .LEVEL¶

Warning

Development version only.

Specifies which kind of wavefunction will be used to obtain the exported quantities

Default:

.LEVEL
DHF

which corresponds to SCF (Hartree-Fock, DFT) ones. Also supported: MP2.

### .EXONLY¶

Warning

Development version only.

This option forces the program to skip the calculation of any FDE contributions, and proceed to exporting the

Warning

Development version only.

## Magnetic properties with London atomic orbitals - FDE contributions to the property gradient¶

In calculations of magnetic properties with London atomic orbitals (LAOs), additional contributions from FDE to the active subsystem should be included in the property gradient (:cite: olejniczak2017).

$E_{[1],emb}^{[B]} = - \int v_{emb}^I \Omega_{ia}^{B,I} - \iint w_{emb}^{I,I} \Omega_{ia}^{I} \Omega_{jj}^{B,I} - \iint w_{emb}^{I,II} \Omega_{ia}^{I} \Omega_{jj}^{B,II}$

where $$\Omega_{pq}^{B}$$ is the first-order perturbed overlap distribution, which in a basis of London orbitals consists of two terms

$\Omega_{pq}^{B} = \frac{i}{2} (R_{MN} \times r) \Omega_{pq} + (T_{pt}^{B*} \Omega_{tq} + \Omega_{pt}T_{tq}^B)$

“direct” LAO term (the first term) and “reorthonormalization” term (two last terms in brackets).

FDE contributions to property gradient can be included by the keywords presented below.

### .LAO11¶

This keyword turns on the FDE-LAO contributions to the property gradient dependent on the embedding potential ($$v_{emb}^I$$) and the uncoupled embedding kernel ($$w_{emb}^{I,I}$$). This is the advised option. Other contributions to the property gradient can be included or excluded by using expert keywords (below).

### .LDPT¶

This keyword turns on the term dependent on the embedding potential ($$v_{emb}^I$$) only. Calculations with the .LDPT keyword are less demanding than calculations with the .LAO11 keyword, but may lead to inaccurate results, especially for heavy elements.

### .NOLDPT¶

This keyword turns off the term dependent on the embedding potential ($$v_{emb}^I$$).

### .L11KR¶

This keyword turns on the terms dependent on the uncoupled embedding kernel ($$w_{emb}^{I,I}$$).

### .NL11KR¶

This keyword turns off the terms dependent on the uncoupled embedding kernel ($$w_{emb}^{I,I}$$).

### .LDKR¶

This keyword corresponds to the term dependent on the uncoupled embedding kernel ($$w_{emb}^{I,I}$$), which involves only the “direct” LAO contribution.

### .NOLDKR¶

This keyword excludes the “direct” LAO contribution to the uncoupled embedding kernel ($$w_{emb}^{I,I}$$).

### .LRKR¶

This keyword corresponds to the term dependent on the uncoupled embedding kernel ($$w_{emb}^{I,I}$$), which involves only the “reorthonormalization” LAO contribution.

### .NOLRKR¶

This keyword excludes the “reorthonormalization” LAO contribution to the uncoupled embedding kernel ($$w_{emb}^{I,I}$$).

### .LAO12¶

This keyword turns on the FDE-LAO contributions to the property gradient dependent on the coupled embedding kernel ($$w_{emb}^{I,II}$$). This option includes both, the term dependent on the non-additive part of the coupled embedding kernel and the Coulomb term. Each of these terms can be turned on by separate keywords (below). If this keyword is employed, it is also necessary to import perturbed densities using the .PERTIM keyword.

### .LAOFRZ¶

This keyword corresponds to the term dependent on the non-additive part of embedding kernel involving the coupling between two subsystems ($$w_{emb}^{I,II}$$). In order to calculate this term, it is necessary also to use the keyword .PERTIM.

### .LFCOUL¶

This keyword corresponds to the term dependent on the Coulomb part of embedding kernel involving the coupling between two subsystems ($$w_{emb}^{I,II}$$). In order to calculate this term, it is necessary also to use the keyword .PERTIM.

### .PERTIM¶

This keyword should be used whenever .LAOFRZ keyword is present. It commands the program to read the contributions (“direct” LAO contribution and “reorthonormalization” contribution) to the perturbed density in LAO basis from files.

Default:

.PERTIM
pertden_direct_lao.FINAL
pertden_reorth_lao.FINAL

### .FRZNOS¶

This keyword means that no spin-density contributions to the perturbed density will be used in FDE calculations.

## Magnetizability with London atomic orbitals - FDE contributions to the expectation value of the magnetizability tensor¶

The FDE calculations of the magnetizability tensor with London atomic orbitals (LAOs), require the FDE-LAO contributions to the property gradient (presented above) and the FDE-LAO contributions to the expectation value of the magnetizability tensor. The latter involve the terms dependent on the embedding potential ($$v_{emb}^I$$), uncoupled embedding kernel ($$w_{emb}^{I,I}$$) and coupled embedding kernel ($$w_{emb}^{I,II}$$).

### .EMAFDE¶

This keyword turns on all FDE-LAO contributions to the expectation value part of the magnetizability tensor. This is the advised option. It is possible to exclude each contribution by using expert keywords (presented below).

### .MNOPOT¶

This keyword turns off the contribution to the expectation value part of the magnetizability tensor dependent on the embedding potential ($$v_{emb}^I$$).

### .MNOUKE¶

This keyword turns off the contribution to the expectation value part of the magnetizability tensor dependent on the uncoupled embedding kernel ($$w_{emb}^{I,I}$$).

### .MNONKE¶

This keyword turns off the contribution to the expectation value part of the magnetizability tensor dependent on the non-additive part of the coupled embedding kernel ($$w_{emb}^{I,II}$$).

## Debug/expert options¶

### .SKIPX¶

Specifies that the non-additive exchange-correlation contributions are not to be calculated.

### .SKIPK¶

Specifies that the non-additive kinetic energy contributions are not to be calculated.