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

Peter Yen peter308 at gmail.com
Tue May 2 07:19:08 CEST 2017

Dear Mr. Hourahine
Thank you for your reply, it contains many useful information for me.
These days i have done some reading about the topics you mentioned.
I now learned that the potential at a third atom  will have
cancellation with the core-electron potential ( non-local peudopotential)
at this third atom. This is an ansatz that was assumed by the developers
of dftb in the early years. I was wondering, under any circumstances will
this ansatz breakdown and so this error cancellation will no longer be
valid ?
For example, a heavier material like gold will have more core electrons
 and this larger core orbital potential might not be able to have the same
error cancellation as in a lighter atom such as in Carbon atom. Or a
 lattice suggests that a 3-center interaction might be important in evaluating

the band structure energy. (From moments theorem, a electron hopping
back and forth contributes to second moment of the local density of state,
and a three loop hop or third moment will become dominant in a trigonal
lattice and therefore contribute significantly to the band structure energy,
 which indicates that three center integral is no longer negligible in such
case. Can you and others please provide some suggestion to me on this
issue? I was actually having some results of gold clusters that seems quite
strange to me. Thank you very much and i apologize for my late reply. I
was trying to understand the content you post in the mail these days.

                                                 With Best Regards, Peter

2017-04-27 19:08 GMT+08:00 Ben Hourahine <benjamin.hourahine at strath.ac.uk>:

> 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)
> _______________________________________________
> DFTB-Plus-User mailing listDFTB-Plus-User at mailman.zfn.uni-bremen.dehttps://mailman.zfn.uni-bremen.de/cgi-bin/mailman/listinfo/dftb-plus-user
> --
>       Dr. B. Hourahine, SUPA, Department of Physics,
>     University of Strathclyde, John Anderson Building,
>             107 Rottenrow, Glasgow G4 0NG, UK.
>     +44 141 548 2325 <+44%20141%20548%202325>, benjamin.hourahine at strath.ac.uk
> 2013/14 THE Awards Entrepreneurial University of the Year
>       2012/13 THE Awards UK University of the Year
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Postdoctoral fellow, Physics department,
National Central University, Taiwan(R.O.C)
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