[DFTB-Plus-User] electronic coupling integral

Roozbeh Anvari roozbeh.anvari at research.uwa.edu.au
Sun May 21 17:22:33 CEST 2017

Dear All,

I am trying to calculate the electronic coupling integral (Hab) between the
surface oxygen of Ga2O3 electrode and the oxygen of water using the
fragment orbital approach.

      Fragment A           Fragment B
  O Ga O Ga O Ga
  Ga O Ga O Ga O         OH2  ...
  O Ga O Ga O Ga
 Ga O Ga O Ga `O -->OH2    ....
  O Ga O Ga O Ga             OH2     ...
  Ga O Ga O Ga O

fragment.A consists of 80 Ga (s ppp ddddd) and 120 O (s ppp)
and fragment.B consists of 49 O (s ppp) and 98 H(s)

I took the following steps to put the integral together :
I got the eigenvectors of the  isolated fragments i.e. Psi_A  & Psi_B
inspected band.out to determine the specific states that correspond to HOMO
and LUMO eigenvectors,
generated the Hamiltonian of the combined system,
and finally dissected the Hamiltonian to get the off-diagonal matrix
corresponding to electron hopping from the surface-oxygen of the oxide to
the neighboring oxygen of the water molecule

However now I wonder how I could deal with the integral itself , i.e.
Hab=<Psi_A| H_AB |Psi_B>,  because the length of PsiA vector is 1200*1, and
the length of PsiB vector is 294*1, while the size of the off-diagonal
section of the Hamiltonian is just 4*4.

Thank you for your help
Best regards
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