# [DFTB-Plus-User] DFTB+ about the process for calculating relaxed density

Ben Hourahine benjamin.hourahine at strath.ac.uk
Tue May 30 12:26:19 CEST 2017

Dear Seong Lee,

The ground state dipole is, as you mention, the derivative of energy
with respect to the field. This can be calculated using the
Hellmann-Feynman theorem through the derivative of the hamiltonian with
respect to the external field. This gives the same value as obtained
using the Mulliken charges and locations of atoms (this is due to the
use of Mulliken partitioning in constructing the contribution from an
external electric fields to the total energy).

When DFTB+ is compiled at DEBUG >= 2, it will evaluate dipole moments
for molecules using both of these methods.

The density matrix is written in the basis of the atomic orbitals used
for DFTB and it is these functions that are explicitly dependent on r,
not the density matrix itself. DFTB avoids evaluation of integrals
during the calculation by re-casting as much as possible in terms of the
overlap elements between atomic basis functions. So for example, the
contribution from an external field is

H_ij = 0.5 S_ij ( V_i + V_j)

where V_i is the external potential at the atom containing orbital i.
There is more detail in several of the articles listed at
http://www.dftb.org/about-dftb/references/

Are you instead asking about the oscillator strength for something else,
such as electronic or vibrational excitations?

Regards

Ben

On 30/05/17 10:33, 이인성 (화학과) wrote:
>
> Hello, DFTB+ developers
>
>
> I am a new user for dftb+ and I want to know about relaxed density matrix.
>
>
>
> To obtain the information about the oscillator strength, we have to
> know relaxed density matrix.
>
>
> And to obtain the relaxed density matrix, we have to know the dipole
> moment integrals.
>
>
> Differentiation of the total energy with respect to the field F gives
> the dipole moment.
>
>
> d_mu_nu = e * < chi_mu | r | chi_nu > = \partial(h_mu_nu) /
> \partial(field)
>
>
> where d_mu_nu is dipole moment integrals, chi is AO, e is electron
> charge, and r is the electron coordinate vector.
>
>
>
> I am sorry for low quality of upper equations.
>
>
> Thus, I want to know 1. the analytic formula for d_mu_nu and 2. the
> process how dftb+ calculate this dipole moment for oscillator strength.
>
>
> Thank you.
>
>
> In Seong Lee
>
>
>
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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

2013/14 THE Awards Entrepreneurial University of the Year
2012/13 THE Awards UK University of the Year

The University of Strathclyde is a charitable body,
registered in Scotland, number SC015263

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