[Smeagol-discuss] Total Energy

[Simon Dubois]

Hello Ivan,

thanks again for your (still relevant ;-) answers!

>  the smeagol energies should be identical to the siesta ones, in fact I
> checked it for some test system. Try starting both smeagol and siesta
> without initial density matrix, and see what you get. I think that maybe
> in your smeagol run you are using UsesaveDM false, because DEna, DUscf
> are 0, which I think is only the case if you use no initial density
> matrix.

Indeed, I made a mistake in the name of the .DM file, so that the file
wasn't red.


> The total energy is computed in the siesta part of the code for a
> periodic system, so that E_BS=Tr[H*rho] is used (not E_BS=Tr[H_0 *
> rho_0], where the matrices with index 0 span only over the unit cell,
> i.e. there are no connecting elements to the next cell). The main
> approximation involved therefore I think is about the fact that the
> boundary elements of H and rho (those overlapping to the next cell) are
> "bulk-like" (the boundary elements for rho are taken to be the bulk ones).

Ok. However, if the size of the cell is well converged (i.e. the bulk like
hartree potential is recovered in the last principal layer) it shouldn't
affect the result. Does it?

So, you are not puzzled by the absence of the self-energies in the total
energy calculation ? I am planning  to do some tests in order to see
whether the E_self term cancel or not....

Simon

>
> Cheers,
>
>  Ivan
>> 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
>>> =================================================
>>>
>>>
>>>
>>>
>>
>>
>>
>
>
> --
> =================================================
> 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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