[DFTB-Plus-User] Dear dftb+ developers, possible to include 3-center integral in the current scheme ?

[Ben Hourahine]

Hello Peter,

The original DFTB papers by Seifert show that there is an error
cancellation when both the 3 and 4 centre integrals are neglected in
DFTB, leading to improved total energy for molecules. SCC-DFTB
empirically adds potentials from 3 and 4 centre charge densities, but is
non-symmetry breaking (being screened by the overlap matrix, so
retaining rotational invariance).

Adding explicit 3-centre terms is certainly mathematically possible
(s-symmetry crystal field potentials are almost identical in form to the
conventional Slater-Koster orbital transformations). But unless done
very carefully would disrupt this error cancellation, so could reduce
the energy accuracy. Additionally, it removes orthogonality between core
and valence orbitals on different sites, so requires either a) explicit
orthogonalisation, b) changing to a pseuodopotential instead of deriving
from all electron atoms, or c) being empirical and testing if ignoring
this causes problems.

There are (that I'm aware of) two different approaches under development
at the  moment to improve inclusion of atomic environment in the
SCC-DFTB (DFTB2) model, either by using multipole electrostatics, or by
including off-diagonal atomic terms within the Hamiltonian (in a
rotationally invariant form). Both of these should not remove the error
cancellation described above. There is also some evidence (see the PhD
thesis of Johannes Frenzel, Dresden 2006) that DFTB band structures can
become very close to DFT results when calculated in a SCF formalism
(i.e. the DFTB two centre matrix elements are re-evaluated from the
charge density instead of being pre-tabulated).

Regards

Ben

On 27/04/17 09:07, Peter Yen wrote:
> Dear DFTB+ developers
> I was wondering if it is possible to include the 3-center integral and
> crystal field effect in addition to the current dftb scheme? For
> example, a trigonal crystal might need to include a 3-center integral
> in order to calculate the total energy correctly.( the 3-center
> integral might become dominant in such case).  Is it possible to
> devise a dftb scheme which includes 3-center integral and crystal
> field effect ? Thanks! 
>
>
>                                                      With Best
> Regards, Peter
>
>
>
>
>
> -- 
> Postdoctoral fellow, Physics department,
> National Central University, Taiwan(R.O.C)
>
>
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-- 
      Dr. B. Hourahine, SUPA, Department of Physics,
    University of Strathclyde, John Anderson Building,
            107 Rottenrow, Glasgow G4 0NG, UK.
    +44 141 548 2325, benjamin.hourahine at strath.ac.uk

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