[Pw_forum] Why the energies are different when two molecules are calculated together and separate?

Stefano de Gironcoli degironc at sissa.it
Wed Apr 12 23:59:02 CEST 2006

I think this argument is in general correct and that this effect would 
show up even more dramatically if you consider fragments that are open 
shell like E(H+F) compared with E(H)+E(F).

This effect came from the fact that the two fragments tend to align 
their chemical potential and you have some (small) charge transert.
With the *true* DFT funcional xc potentials and chemical potentials would 
have sudden jumps when crossing integer number of electrons so the
equal chemical potential condition is pinned at integer numbers but with
LDA, GGA etc this is not true and there is in general some charge 

In the present case, however, CO2 is a closed shell molecule so its LUMO 
is well separated from the HOMO and if the Hydrogen last eigenvalue is
higher than the CO2 HOMO but lover than CO2 LUMO then charge transfer 
should not occur.

In order to clarify what is happening one could calculate projected 
density of states in the two cases and see if there is indeed some charge 
transfer between the fragments..

Also, in order to remove possible source of spurious interaction between
the fragments, one should use large ecutrho (I guess you are using USPP 
for C and O) in order to avoid the augmentation charge to have small but 
not vanishing oscillating tails all around that could "mediate" the 

I assume you did the calculation using nspin=2 so as to allow H to be 

let us know what are the results of these tests.


On Wed, 12 Apr 2006, Nichols A. Romero wrote:

> Xunlei,
> I am not surprised that your two calculations:
> E(CO2) and E(H) separate supercells
> versus
> E(CO2+H) same supercell
> give different energies, even if they are well separated in a *huge* empty box.
> My former adviser, Richard Martin, tells me this is *famous* DFT problem.
> See,
> C. Almbladh and U. von Barth, "Exact results for the charge and spin
> densities, exchange-correlation potentials, and density-functional
> eigenvalues," Phys. Rev. B 31:3231, 1985.
> The *fundamental* problem is not with the basis set. "The general gist
> is that the exact functional must be discontinuous at integer
> occupations.  This shows the problems with any functional that does
> not have discontinuities -  like LDA and GGA!", my former adviser. So,
> I think if you have an asymptotically corrected functional, and I
> don't know of any publicly available code that have this available,
> you wouldn't have this problem.
> I tried a similar test in SIESTA not too long ago. And even with an
> LCAO basis set, you will see charge transfer in the combined systems
> that is well separated in a *huge* empty box. It will be a *very*
> small charge transfer but its there! Because of this small charge
> transfer, there will be an energy difference between the two
> calculations.
> Bests,
> On 4/12/06, Lucas Fernandez Seivane <quevedin at gmail.com> wrote:
>> I believe that this is more or less the case that Prof. Marzari states
>> as 1). It may due to an effect well known related to localized basis
>> (LCAO, gaussians) which has to do with the number of wavefunctions in
>> each one of your simulations: the  Basis Set Superposition Error.
>> Quoting from http://iqc.udg.es/~perico/bbopt.html:
>> "The theoretical study of molecular interactions under the
>> supermolecular approach with finite basis sets centered at the atomic
>> positions originates the so-called Basis Set Superposition Error
>> (BSSE) Within the LCAO-MO approach, each fragment can be expanded to
>> some extent in the basis set of the partner. Thus, BSSE is the
>> unphysical effect due to the improvement of the quantum mechanical
>> description of the fragments within the supermolecule. It has been
>> recognised for long time that this effect results in an increase of
>> the interaction energy."
>> Some ideas for dealing with it are seen for instance in
>> http://arxiv.org/PS_cache/physics/pdf/9908/9908022.pdf or in
>> http://dx.doi.org/10.1103/PhysRevB.72.075431
>> On 4/12/06, Nicola Marzari <marzari at mit.edu> wrote:
>>> My guess is that if you make your cell larger and larger the difference
>>> will, very slowly, disappear.
>>> You have two sources of error
>>> 1) the "covalent" interaction between CO2 and H. You do not see this
>>> in Gaussian because of the shortcomings of the basis set there -
>>> there are no states able to represent the weak overlap of wavefunctions
>>> midway between the molecule and the atom.
>>> 2) the dipole of the system, that interacts with itself periodically
>>> repeated. See e.g. Makov Payne PRB 1995, or cond-mat/0602599 and Refs.
>>> [14] in it.
>>> Let us know if 1) or 2) are to blame.
>>>                         nicola
>>> Xunlei Ding wrote:
>>>> Dear all,
>>>> In a supercell (15A^3), I calculated the energies of one CO2 molecule,
>>>> and a H atom, separately.
>>>> I got the energies E(CO2) and E(H). Then I calculated the system
>>>> contained both CO2 and H in the same supercell, and get the energy
>>>> E(CO2+H).
>>>> It is surprising to me that E(CO2+H) is lower than E(CO2)+E(H) by about
>>>> more than 0.1eV.
>>>> All calculations are used PBE functional and with Gamma point.
>>>> I have put the H atom from CO2 at different places and the distances are
>>>> tested for 6A and 9A. The cutoff are tested for 24Ry and 32Ry. The
>>>> supercell are tested for 15A^3 and 20A^3. All these tests give the
>>>> similar results and the energies differences are still more than 0.1eV.
>>>> Then with Gaussian03, both with PBC (period boundary conditions) and
>>>> without PBC (just free molecules), the results show that E(CO2+H) is
>>>> very close to E(CO2)+E(H).
>>>> It is found that the HOMO of H atom is also the HOMO of the system
>>>> H+CO2, but in PWSCF results, HOMO of (H+CO2) is lower than that in H
>>>> atom by ahout 0.1eV, while in Gaussian03 calculation, the HOMO is almost
>>>> the same in H+CO2 and H . This is the reason why the total energy of
>>>> H+CO2 is lower than E(H) + E(CO2).
>>>> I want to know the reason for this energy difference.
>>>> Thank you!
>>>> Yours sincerely,
>>>> Ding
>>>> _______________________________________________
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>>> --
>>> ---------------------------------------------------------------------
>>> Prof Nicola Marzari   Department of Materials Science and Engineering
>>> 13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
>>> tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu
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> --
> Nichols A. Romero, Ph.D.
> 1613 Denise Dr. Apt. D
> Forest Hill, MD 21050
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