# [Pw_forum] About WanT calculation for large system

Nicola Marzari marzari at MIT.EDU
Fri Aug 25 00:35:57 CEST 2006

```
Dear Janiet,

your understanding is absolutely correct - we will email you a
copy of Young-Su Lee PhD, where these steps are spelt out
in greater detail (and you should look at the 1999 PRB of Marco
Buongiorno Nardelli, and at the 2004 PRB of Arrigo Calzolari et al).

Note that the procedure we use is slightly different from the WanT
approach (2004 PRB cited above), in that it deals with the
some subtleties of Gamma sampling, both in the disentanglement (the
disentangled space is complex, even if the kohn-sham orbitals are real),
and in the calculation of the matrix elements (you need to calculate
overlaps in real space, truncating the tails). This Gamma-specific
code is not yet in www.wannier.org, although it is making its way there.

> Since i donot catch the ideas of this step, I just guess that we can
> bulid the real-space hamiltonian of large system with  the real-space
> procedure. Would you please help me out ? Maybe it is trival , but it is
> really a big barrier  for me to "tunnel ".

First of all, your systems in PP-PW are always enormous - infinite.
Their unit cells can be large or small - you want unit cells, for this
problem, large enough so that the matrix elements of the Hamiltonian
in between MLWFs that sit more than a unit cell apart are zero (for
the nanotubes, unit cells of 100-200 atoms).

Now, think about the Hamiltonian of the very large system (maybe not
even periodic), expressed in a basis of Wannier functions. Now, most
matrix elements will be zero - whenever the distance of the centers is
large. So, the only non-zero elements will be between MLWFs that are
reasonably close to each other. What are those matrix elements ? Well,
you can just calculate them in a system whose unit cell is 100-200 atoms.

This is much better explained with a drwaing - that's why I'm sending
Y-S thesis - but I'm sure the general idea (that is a tight-binding
idea, if you think at it) is in Marco Nardelli paper (and many others).

nicola

--
---------------------------------------------------------------------
Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu

```