[DFTB-Plus-User] Calculating single atom (such as H, C, N, ...)

[Ben Hourahine]

Hello Yeonjoon,

in DFT, the energy (and ionization energy) of the hydrogen atom is also
not -0.5 hartree for usual functionals (mostly due to self interaction
error). See for example the NIST database for various functionals.

In the case of DFTB, the total energy for the isolated atom is not very
meaningful, as it omits double counting contributions that  full DFT
includes. The energy in DFTB (see review papers listed on
http://www.dftb.org/about-dftb/references/ ) consists of the band
structure energy plus the repulsive energy (and optional contributions
for charge self-consistency, spin polarization, etc.) For an isolated
atom, there is no repulsive contribution (and in the case of a H atom no
charge term contribution), so the energy is only the eigenvalue of the
single level in the system (only one s-type function present).  In the
DFTB method this is from the 1S single particle energy level of an
atomic Kohn-Sham DFT calculation, which, as mentioned above is incorrect
anyway in this case, but this is compounded by the lack of the
double-counting, so does not match the the DFT energy either.

DFTB is however intended to calculate relative energies between
structure which have bonded atoms. See the previous posts on the mailing
list about cohesive energy, which outlines exactly these issues of the
reference energy for the isolated atom being not very meaningful.

For the case of C and N atoms, it depends on what you want to calculate
and how accurate you need the numbers to be. As outlined above the total
energy will be wrong for isolated atoms anyway in DFTB as compared
against DFT. But even in Kohn-Sham DFT there is also the problem that
the ground state of an isolated atom often cannot be correctly
represented with usual methods. In the case of carbon, its ground state
is a triplet, which in this case can't be written as an eigenstate of
the angular momentum operator using just collinear up and down Kohn-Sham
states. The state can be constructed as fractionally occupied set of
spinor states (non-collinear) or equivalently as a multi-determinant
state, but this is not available to most DFT codes (and may not be the
ground state for the particular functional you are using).

If you just want to calculate these atoms without the precise details
being correct, then as a first approximation just set the unpaired
number of electrons as you suggest. If this is to calculate an
atomization energy, then its not going to be accurate. You would be
better off calculating the relative energy to a reference system
(graphite/diamond, N2 gas) etc. in that case.

Regards

Ben

On 25/03/16 06:49, 김연준 wrote:
>
> I have questions about how to calculate the energy of single atom
> using DFTB+.
>
>  
>
> Currently I'm using DFTB1.2.2 program with 3ob-3-1 parameter set.
>
>  
>
>  
>
> 1) The energy of the hydrogen atom is not -0.5 hartree(As I remember,
> around -0.2 hartree), and for proton, not 0 hartree(positive value).
>
>  
>
> Is it okay to accept those values?
>
>  
>
> 2) For carbon and nitrogen single atom, the spin-polarization option
> should be set.
>
>  
>
> Is it enough to just set the number of unpaired electrons?
>
>  
>
> I'm wondering which keywords should be used to obtain the most
> accurate results for single atoms.
>
>  
>
>  
>
> Thanks a lot!
>
>  
>
>  
>
> Sincerely,
>
>  
>
> Yeonjoon
>
>
>
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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

2013/4 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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