# [Wannier] question on hr_dat element for BaTiO3_example

Arash Mostofi a.mostofi at imperial.ac.uk
Mon Jun 3 23:53:32 CEST 2013

```Dear Wasim

know a little bit more about you.

In regard to your question, the matrix elements that are listed in the
*_hr.dat file are

H_{nm}(R) = <w_{n0}|H|w_{mR}>

where n and m are WF indices, and R is a lattice vector. The total
number of elements listed is equal to num_wann^2 for each lattice vector
R. This is explained in Sec 8.18 of the Wannier90 User Guide (v1.2).
There is a relationship between the periodicity of WFs in real space and
the k-point grid used to generate them - see, eg, Rev Mod Phys 84, 1419
(2012).

The on-site matrix elements are given by H_{nn}(0); the rest are
"hopping" matrix elements between WF sites.

The size of the matrix depends on what you are trying to study. In this
particular case you are considering the 9 oxygen p-orbitals of a BTO
primitive unit cell, hence you have a 9x9 matrix at each R.

Hope this helps,

Arash

--
Dr Arash A Mostofi
Departments of Materials and Physics
Deputy Director, CDT on Theory and Simulation of Materials
Imperial College London, London SW7 2AZ, UK
+44 (0)207 594 8154 | www.cmth.ph.ic.ac.uk/people/a.mostofi

On 03/06/2013 18:59, wasim mondal wrote:
> Dear wannier90 experts,
>   I am new user of wannier90. I have the following two questions:
>
> (1) I have constructed hr_dat file after running BaTiO3_example. I have
> got all the matrix element real and matrix dimension is 9*9.
>
>    Do the off-diagonal element of the matrix represent hoping ?
>    Do the diagonal element of the matrix represent orbital-energy?
>    Do the diagonal element of the matrix represent hopping and orbital
> energy both?
>      If yes , how can I get orbital energy ?
>
>
> (2)Now the size of the Hamiltonian is 9*9. Can I decrease the size of
> Hamiltonian matrix ?
>
>
> Regards
> wasim
>
>
> _______________________________________________
> Wannier mailing list
> Wannier at quantum-espresso.org
> http://www.democritos.it/mailman/listinfo/wannier
>

```