[DFTB-Plus-User] Reliability of prediction on conduction band of silicon nano crystals

Ben Hourahine benjamin.hourahine at strath.ac.uk
Tue Feb 21 18:40:22 CET 2017

Hello ZhaoHui Huang,

Your TB code sounds very interesting, do you have plans to release it in
some form?

For quantum mechanical models, the total electronic energy (and as a
result the forces) requires functions of all the valence states, not
just those near to the band-edges. For DFTB there is also the
complication that this is a non-orthogonal basis, so requires
generalised eigenstates (i.e., orthogonal under the action of the
overlap matrix).

For empirical tight binding, what can be done is to relax geometries
with classical inter-atomic potentials, and then to solve for the band
edge states of the resulting structure (I believe this approach has been
previously used for quantum dots). In this case something like
bond-order potentials might potentially be a good choice to calculate
the forces. These are derived from tight-binding hopping elements so it
might be possible to make these more consistent with the electronic
structure hamiltonian.

Regarding the conduction bands, sp3d5s* should be able to reproduce the
lower conduction states well, depending on the parametrization. These
bands dominate the response properties, but as shown with the time
dependent DFTB energy and oscillator window methods, higher energy
states can also substantially contribute to response behaviour
(depending on the system).



On 21/02/17 14:33, ZHAOHUI HUANG wrote:
> Hello,
>     Sorry to bother you if not interested.
>     Last fall semester, I sent a message to DFTB+ list and ask if it is possible to solve large size TB Hamiltonian. the feedback said the largest possible size of H is roughly 60,000 for LAPACK routine. Since my silicon mesoscale crystal can easily run up to a few hundreds of thousand of atoms, like 100,000 silicon atoms, I cannot use DFTB+, so I write a MPI TB code with sp3d5s* basis to calculate, based on implicitly restarting arnoldi method (IRAM) as well as intel distributed LU factorization for sparse matrix. I aim at only achieving bands near band gap. Now it works. Here I want to ask DFTB+ community again,
>    What is the algorithm to relax the structure? see if I can embed my code into DFTB source, if DFTB relaxation is based on Lanczos method or its derivatives or whatever based on invariant space approach.
>    For the above basis, how reliable are prediction of conduction bands, except the lowest one? If I use TB conduction bands, a few thousands, is it possible to calculation response function for my mesoscale crystal? like epsilon, based on TB conduction bands. comments are welcome! thanks a lot 
> ZhaoHui Huang,
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