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

Ben Hourahine benjamin.hourahine at strath.ac.uk
Tue Jun 6 20:12:16 CEST 2017

Hello Seong Lee,

In your expression, is r the vector between the atomic sites containing
the orbitals mu and nu? If so, then yes this is the moment integral in
the Mulliken approximation.

The calculation for the single particle transition dipole between the
Kohn-Sham like single particle states of DFTB, and the transformation of
these quantities into transition dipole moments between the ground and a
specified excited state are evaluated in the routines
calcTransitionDipoles, transitionDipole and transq which are included in
files inside lib_timedep/ directory.

Regards

Ben

On 31/05/17 08:16, 이인성 (화학과) wrote:
>
>
> I check the source code for dipole moment using Hellman-Feymann theorem.
>
>
> And I find the analytic form of dipole moment integral.
>
>
> d_mu_nu = e * r * S_mu_nu.
>
>
> If this is wrong, then please let me know about the form.
>
>
> Thanks.
>
>
> In Seong Lee.
>
> ________________________________
> 보낸 사람: Ben Hourahine <benjamin.hourahine at strath.ac.uk> 대신 DFTB-Plus-User <dftb-plus-user-bounces at mailman.zfn.uni-bremen.de>
> 보낸 날짜: 2017년 5월 30일 화요일 오후 7:26:19
> 받는 사람: dftb-plus-user at mailman.zfn.uni-bremen.de
> 제목: Re: [DFTB-Plus-User] DFTB+ about the process for calculating relaxed density
>
>
> 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<mailto: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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--

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