d8d9.ban

In case of a TT-BAN calculation for a d8-d9L initial state: 
 PRMULT 
 NCONF 2 2
 N2 1    
 def EG2 = 4.3 unity 
 def EF2 = 2.3 unity
 XMIX 2    2.0   -1.0
 2   1 1 2           2 1 2
 XHAM 2  1.0  1.66
 4   1 1   1 2   2 1   2 2
 TRAN  2    1 1    2 2
 TRIADS
    0+   1-   1- 0
    1+   1-   0- 0
    1+   1-   1- 0
    1+   1-   2- 0
    1+   1-  ^1- 0
    2+   1-   1- 0
    2+   1-  ^1- 0
   ^1+   1-   1- 0
   ^1+   1-   2- 0
   ^1+   1-  ^1- 0
   ^1+   1-  ^0- 0
   ^0+   1-  ^1- 0

PRMULT

This command should be used in octahedral symmetry. It indicates that when multiplying two irreps, an irrep may appear twice in the product.

NCONF [int1] [int2]

The number of configurations in the initial state (int1) and in the final state (int2).

N2 [int]

The number of copies of the ligand shell. In most cases N2 is set equals to 1
If N2 equals two or more, one can add the bandwidth as:
N2 [int] W [int2]
int2 gives the bandwidth in eV. As default the band is rectangular in shape.

def EG2 = [real] unity

This line defines the energy of the second configuration in the initial state.
The first configuration has an energy of 0.0

def EF2 = [real] unity

This line defines the energy of the second configuration in the final state.

If NCONF equals 3 there will be 3 configurations and the input must be repeated for EG3 and EF3.

In the present example:
 def EG2 = 4.3 unity 
 def EF2 = 2.3 unity
Thus the center-of-gravity of the 3d9L configuration is at an energy of 4.3 eV above the center-of-gravity of the 3d8 configuration.
Similarly the center-of-gravity of the 2p53d10L configuration is at an energy of 2.3 eV above the center-of-gravity of the 2p53d9 configuration.

NOTE that EG2 does not identify with DELTA!

DELTA (as used in the charge transfer models) is defined between the lowest configurations between 3d8 and 3d9L.
One can easily relate DELTA to EG2 by performing a calculation with the mixing terms set to zero, thereby defining the lowest energies of the pure 3d8 and 3d9L terms.

In case of x-ray absorption, EF2 is related to EG2 as: 

 EF2 = EG2 + U - Q =(approx) EG2 - 2.0
Using the fact that U is smaller than Q.

(U = 3d-3d electron correlation
Q = 2p-3d electron correlation)

XMIX [int] [real](i)

The integer defines the number of mixing coefficients.
The numbers following define the values of the coefficients.

Note that in octahedral symmetry the configuration mixing can be described with two parameters, corresponding to E and T2 mixing coefficients. 

2   1 1 2           2 1 2
This line specifies the action of the mixing operator.
The first number (2) implies that the mixing operator will act two times,
  • for (1 1 2), that is the initial state (1) between configuration 1 (3d8) and configuration 2 (3d9L).
  • for (2 1 2), that is the final state (2) between configuration 1 (2p53d9) and configuration 2 (2p53d10L).

    XHAM [int] [real](i)

    The integer defines the number of Hamiltonian matrices.
    The numbers following define the values of the matrices.

    The present example 1.0 1.66 implies:
  • The Atomic Hamiltonian is multiplied with 1.0 (which is used in all cases)
  • The Cubic Crystal Field is multiplied with 1.66 (given in electronVolts!)

    The sequence of Hamiltonian matrices must be defined in d8d9.rcg and d8d9.rac.

    XTRAN [int] (int int)[i]

    The integer defines the number of Transitions. The numbers following define the configurations in the initial and final states between which the transition occur.

    In the present example of d8d9.ban there are 2 transitions:
  • [1 1] between 3d8 and 2p53d9
  • [2 2] between 3d9(L) and 2p53d10(L)

    TRIADS

    The TRIADS given apply to systems with even number of 3d electrons in the initial state and to Oh symmetry.
     
    0+   1-   1- 0     ( Respectively given are:
    1+   1-   0- 0       initial state symmetry + parity (1+)
    1+   1-   1- 0       dipole transition      + parity (1-)
    1+   1-   2- 0       final state symmetry   + parity (2-)
    1+   1-  ^1- 0       counting number of the transition (0)
    2+   1-   1- 0       ALL possible symmetry combinations 
    2+   1-  ^1- 0       of the dipole transition are given )
   ^1+   1-   1- 0
   ^1+   1-   2- 0
   ^1+   1-  ^1- 0
   ^1+   1-  ^0- 0
   ^0+   1-  ^1- 0
    In case of an odd number of 3d electrons in Oh symmetry, the TRIADS are: 
     

  S0+   1-  S0- 0 
  S0+   1-  S1- 0  
  S1+   1-  S0- 0  
  S1+   1-  S1- 0  
  S1+   1-  S1- 1      (Note that the counting number is 1)
  S1+   1- ^S0- 0  
 ^S0+   1-  S1- 0 
 ^S0+   1- ^S0- 0