[Smeagol-discuss] Total Energy

[Ivan Rungger]

Hello Simon,

  I will first answer questions (a) and (c):

(a) yes.
(c) The energy output by a smeagol (EMTransport T) run is calculated
with the standard siesta routines. Therefore if the density matrix is
identical, also the resulting energy is equal between a smeagol and a
siesta run by construction (you can see this for example if you input
the same density matrix and look at the first output of the energies,
before the self-consistent cycle starts). The differences that you see
in the energy output are therefore due to the different density matrix
of smeagol and siesta. The main origin of the rather large difference is
that in smeagol the charge is not exactly conserved, and even a slight
change in the total charge usually leads to rather large changes in the
total energy. So whereas the individual eigenvalues are usually rather
similar between smeagol and siesta, the total energy differs more. In
general I would say that when comparing smeagol total energies between
themselves I would say that it is important to make sure that the
charging state of the different systems is very similar, in order to
obtain a meaningful quantity.

(b) I am not completely sure about this. I think that the energy of the
unit cell as it is calculated now is the correct energy for the
equilibrium situation, i.e. it should not be necessary to add any terms.
At equilibrium the NEGF formalism is just another equivalent way to
obtain the density matrix of the Kohn-Sham problem. Once the density
matrix is given, the energy can be calculated with the standard
equations. The only assumption also here I think is just that the
density matrix at the boundaries is converged to bulk.

Cheers,

 Ivan

Simon Dubois wrote:
> Dear Smeagol Users and Developpers,
>
> I have some questions related to the computation of the total energy in
> Siesta and Smeagol.
>
> (a) I know that, due to the presence of the self-energies, the effective
> SCF hamiltonian computed within smeagol is no more hermitian and that the
> eigenenergies are thus complex number. However, if I am not mistaking, the
> real part of these complex number still have the meaning of an energy
> while the complex part is related to the quasi-particle lifetime. Is that
> true ?
>
> (b) If the previous point is true, then, in order to compute the total
> energy of the open boundary system, we should simply add a term
> E_self = trace([rho]*[self_L + self_R])
> to the total energy computed by Siesta.
>
> (c) I have noticed the following differences between the enregy terms
> computed by Smeagol (left side) and Siesta (right side):
>
> siesta:-Eions   = -167171.565970       167171.565970
> siesta: Ena     =   14152.066946        14152.066948
> siesta: Ekin    =   82725.940493        82743.197427
> siesta: Enl     =  -29606.795074       -29621.564038
> siesta: DEna    =    1570.039623         1561.672622
> siesta: DUscf   =      73.434271           72.756367
> siesta: DUext   =       0.000000            0.000000
> siesta: Exc     =  -19114.634221       -19118.273918
> siesta: eta*DQ  =       0.000000            0.000000
> siesta: Emadel  =       0.000000            0.000000
> siesta: Ekinion =       0.000000            0.000000
> siesta: Eharris = -117371.513978      -117381.709241
> siesta: Etot    = -117371.513933      -117381.710563
> siesta: FreeEng = -117371.513933      -117381.742383
>
> Is it the NEGF density matrix which is used to compute these energies
> within Smeagol ? In this case, do these differences simply originate in
> the modification of the electronic density due to the presence of the
> self-energies?
>
> Any comments are welcome..... Thanks in advance!
>
> Best wishes,
>
> Simon
>
>   


-- 
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Ivan Rungger,

School of Physics and CRANN,  
Trinity College Dublin,  
Dublin 2,  IRELAND  
Phone: +353-1-8968454  
Email: runggeri at tcd.ie
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