FrozenDensity Embedding Theory (FDET) [498, 499] provides a formal framework in which the whole system is described by means of two independent quantities: the embedded wave function (interacting or not) and the density associated with the environment. The total energy equation in frozen density embedding theory for a wave function in state embedded in a environment density reads (for definitions see Table 11.7):
(11.86) 
The embedding operator , which is added to the Hamiltonian of subsystem A , is given in the form of a potential:
(11.87) 
The last term (nonelectrostatic component) in equation causes the embedding potential to be dependent, which in return induces an inconsistency between the potential and the energy. In the canonical form of FDET (conventional FDET) this inconsistency is addressed by performing macrocycles in which the embedding potential is repeatedly constructed using the current (embedded) density after each cycle until selfconsistency is reached.
In linearized FDET the nonadditive energy functionals (for abbreviation denoted as ) are each approximated by a functional which is linear in . The approximation is constructed as a Taylor expansion of the nonadditive energy functional at a reference density with the series being truncated after the linear term.
(11.88) 
In contrast to conventional FDET, the embedding potential then becomes independent and macrocycles are no longer necessary. Another consequence of the linearization is that orthogonality between states is maintained since the same potential is used for all states.
FDEADC [497] is a density embedding method based on the combination of the Algebraic Diagrammatic Construction scheme for the polarization propagator (ADC, Section 6.8) and FrozenDensity Embedding Theory (FDET). In this particular variant the subsystem A is represented by a wave function whereas subsystem B is described by a density. The FDEADC method uses the linearized FDET approximation [833].
The FDEADC job control is accomplished in two sections, $rem and $fde. Enabling FDEADC, specification of the ADC method and other ADC job control parameters (thresholds, max. iterations etc) should be set in the $rem section. FDEADC also supports the excited state analysis (STATE_ANALYSIS) carried out by the libwfa module.
The fragments are specified via the fragment descriptors (see Section 12) in the $molecule section, whereas the first fragment corresponds to the embedded species (A) while the second fragment represents the environment (B).
Note: The current implementation allows only for closed shell fragments.
FDE
Turns density embedding on.
TYPE:
BOOLEAN
DEFAULT:
False
OPTIONS:
True
Perform an FDEADC calculation.
False
Don’t perform FDEADC calculation.
RECOMMENDATION:
Set the $rem variable FDE to TRUE to start a FDEADC calculation.
METHOD
Determines which FDEADC method should be used if FDE = True.
TYPE:
STRING
DEFAULT:
None
OPTIONS:
adc(2)
Perform an FDEADC(2)s calculation.
adc(2)x
Perform an FDEADC(2)x calculation.
adc(3)
Perform an FDEADC(3) calculation (potential constructed with MP(2) density).
cvsadc(2)
Perform an FDEADC(2)s calculation of core excitations.
cvsadc(2)x
Perform an FDEADC(2)x calculation of core excitations.
cvsadc(3)
Perform an FDEADC(3) calculation of core excitations.
RECOMMENDATION:
None
The FDEADC 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).
The reassembling of density matrix (RADM) [497] option allows for calculations on larger systems by only including the basis functions of the embedded species for the ADC calculation. RADM introduces an approximation for the construction of the embedding potential by using an artificially (but cheaply) constructed density matrix for subsystem A. With RADM, all regular options for visualization are supported (MAKE_CUBE_FILES and MOLDEN_FORMAT). The RADM option is the recommended choice for an FDEADC calculation.
Analogous to a regular DFT calculation in QChem(by using METHOD) the exchangecorrelation functional combination can either be selected with one keyword XC_Func,or by defining X_Func and C_Func (similar to EXCHANGE and CORRELATION).
T_Func
Kinetic energy functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
TF
Use ThomasFermi kinetic energy functional.
RECOMMENDATION:
None
XC_Func
ExchangeCorrelation functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
All LDA/GGA exchangecorrelation functionals available in QChem.
RECOMMENDATION:
Only use LDA or GGAtype functionals.
X_Func
Exchange functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
All LDA/GGA exchange functionals available in QChem.
RECOMMENDATION:
Only use LDA or GGAtype functionals. XC_Func and X_Func are mutually exclusive.
C_Func
ExchangeCorrelation functional used for the construction of the embedding potential.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
All LDA/GGA correlation functionals available in QChem.
RECOMMENDATION:
Only use LDA or GGAtype 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.
RADM
Use RADM approximation (see above).
RECOMMENDATION:
SE should be used for testing purposes only since it is very expensive for large systems. Use the RADM approximation for larger systems.
rhoB_method
Method to calculate the environment density (B).
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
HF
Use HartreeFock method.
DFT
Use Density Functional Theory.
RECOMMENDATION:
If DFT is specified, the respective exchangecorrelation functional has to defined using the keyword XC_FUNC_B or X_FUNC_B and C_FUNC_B.
XC_Func_B
ExchangeCorrelation functional used for the environment DFT calculation.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
All LDA/GGA/globalhybridGGA exchangecorrelation functionals available in QChem.
RECOMMENDATION:
None
X_Func_B
Exchange functional used for the environment DFT calculation.
INPUT SECTION: $fde
TYPE:
STRING
DEFAULT:
None
OPTIONS:
All LDA/GGA exchange functionals available in QChem.
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:
All LDA/GGA correlation functionals available in QChem.
RECOMMENDATION:
XC_Func_B and C_Func_B are mutually exclusive.
PrintLevel
Print level for FDEADC output.
INPUT SECTION: $fde
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
minimum print level
1
extended print level
2
maximum print level
3
max. print level and additional text files (densities, etc.)
RECOMMENDATION:
None
Example 11.297 Input for a FDEADC(2)/ccpVDZ calculation in supermolecular expansion on CO embedded in one water molecule.
$rem SYM_IGNORE = true METHOD = adc(2) EE_STATES = 2 BASIS = ccpvdz FDE = true MEM_STATIC = 1024 MEM_TOTAL = 16000 ADC_DAVIDSON_MAXITER = 100 ADC_DAVIDSON_CONV = 5 $end $molecule 0 1  0 1 C 3.618090 1.376803 0.020795 O 4.735683 1.525556 0.115023  0 1 O 7.956372 1.485406 0.116792 H 6.992316 1.421133 0.177470 H 8.105846 2.442220 0.111599 $end $fde T_Func TF XC_Func PBE expansion super rhoB_method HF $end
In general the FDEADC output indicates all important stages of the FDEADC calculation, which are:
Generation of ,
Generation of ,
Construction of the embedding potential,
Start of FDEADC calculation and
Final FDEADC summary.
In the following table definitions of the terms printed to the output are collected. These quantities are printed for every state, i.e. for every . In addition, the nonelectrostatic interactions with respect to the reference density are printed at the top of the FDEADC summary.
Subsystem Energies 

Embedded system (A) 

Environment (B) 

Electrostatic Interactions 

rho_A <> rho_B 

rho_A <> Nuc_B 

rho_B <> Nuc_A 

Nuc_A <> Nuc_B 

NonElectrostatic Interactions 

nonadditive E_xc 

nonadditive T_s 

integrated v_xc nad 

integrated v_T nad 

Final FDEADC energies 

Delta_Lin 

Final Energy (A) 



Final Energy (A+B) 
