[Smeagol-discuss] Total Energy

[Ivan Rungger]

Hello Simon,

 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.

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).

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
=================================================