[Smeagol-discuss] Total Energy

Tue Jan 20 10:48:32 GMT 2009

Hello Ivan,

thanks a lot  for your answers....

> (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).

I have performed the test you suggested: to compare the total energy
decomposition obtained by siesta and the one reported by smeagol after the
reading of the density matrix and before the SCF cycle. However, while the
density matrix are the same, the energies are different :

 SIESTA (converged) :          SMEAGOL (before SCF-cycle):
 --------------------          ---------------------------
 Eions   =    167171.565970    Eions   =    167171.565970
 Ena     =     14152.066948    Ena     =     14152.066946
 Ekin    =     82743.197427    Ekin    =     86831.485567
 Enl     =    -29621.564038    Enl     =    -31471.669646
 DEna    =      1561.672622    DEna    =         0.000000
 DUscf   =        72.756367    DUscf   =         0.000000
 DUext   =         0.000000    DUext   =         0.000000
 Exc     =    -19118.273918    Exc     =    -19614.673663
 eta*DQ  =         0.000000    eta*DQ  =         0.000000
 Emadel  =         0.000000    Emadel  =         0.000000
 Ekinion =         0.000000
 Eharris =   -117381.709241    Eharris =   -117507.895005
 Etot    =   -117381.710563    Etot    =   -117274.356766
 FreeEng =   -117381.742383    FreeEng =   -117274.356766

I have used the mixscf1=true, is it the reason of these differences ?
The same test with mixscf1=false is running....

> (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.

You are probably right, however, I find it strange to use a different
Hamiltonian for the SCF computation of the density matrix and for the
computation of the total energy.
Indeed, the effective hamiltonian used in the calculation of the NEGF is
H=[H_0 + Sigma_L +Sigma_R] so that I should expect the band-structure
energy
to be E_BS=Tr[H*rho] while what is computed is E_BS=Tr[H_0*rho]. What do
you think about that? Does the term E_self=Tr[(Sigma_L+Sigma_R)*rho]
nullify at equilibrium?

Thanks again,

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

-- 