[Pw_forum] kp

[Giovanni Cantele]

the correct statement is not that “there is no way” to calculate band structure for a molecule, but that 
a molecule has not a band structure. Band structure is a concept typical of solid state physics, and is related to
the occurrence, in crystals, of continuous energy intervals of allowed electronic levels separated by energy gaps
(where no electronic level can show up in an ideal crystal). The continuous distribution of levels in a band can be
described by assigning to each level a label, the k-vector, that represents the analogous of (but not the same as)
the momentum of the free electron when it moves in the free space instead of being subject to the periodic lattice
potential. The relation E(k) is just the energy dispersion and describes the band structure of the solid.

This is contrasted with discrete levels in molecules, where instead localised orbitals show up.

I want just to add that you can use plane waves to reproduce molecular orbitals, at the best level of approximation
allowed with the available exchange-correlation functionals. This means that if you calculate the molecular orbital of a molecule
within the GGA approximation, you get the same picture if you use plane wave packages, just as quantum-espresso, or other
packages based on localised basis sets. If using plane waves, you have just to take care of building appropriate super cells,
preventing the periodic replicas of the molecule form interacting with each other.

Giovanni

> On 29 Nov 2016, at 07:31, ashkan shekaari <shekaari at gmail.com> wrote:
> 
> Dear Giovanni,
> Thank you so much for your explanatory response. So, as I understood, there is no way to calculate band structure for a molecule and this is nonsensical. Is it true?
> 
> 
> On Nov 29, 2016 1:46 AM, <meisam.a63 at gmail.com <mailto:meisam.a63 at gmail.com>> wrote:
> Just to add that plain wave is not a good approximation to reproduce molecular orbitals.
> 
> Mortaza A
> 
> PhD of Physics 
> Ulm University, Germany 
> 
> On 28 Nov 2016, at 21:43, Giovanni Cantele <giovanni.cantele at spin.cnr.it <mailto:giovanni.cantele at spin.cnr.it>> wrote:
> 
>> if you try to ask the question: "what the k-point mesh is for?" you can easily understand
>> that a k-point mesh is for the Brillouin zone (BZ) sampling, that is, perform sums over k-points
>> that approximate, with a required level of accuracy, the integral over the whole BZ. This is
>> because in a crystal, the energy E(K) depends on the k vectors, and the same holds for the
>> wave functions. However, when you build for example a cubic supercell including vacuum to
>> simulate a molecule, you are actually dealing with a fictitious cubic crystal where the repeated
>> units are sufficiently far apart from each other to not interact.
>> 
>> Absence of interaction means flat (atomic-like) energy levels, that do not have dependence
>> on the k vector. That is, the E(K) dispersion that you get in the case of a molecule, provided
>> you include a sufficient vacuum space in your supercell, does not depend on k. If this is
>> the case, you can use only the gamma point (a larger grid means large but useless
>> computational time, because you are summing over eigenvalues at different k-points that 
>> are all the same!) for self consistency and BZ path is not needed, because if you select any
>> path you should get flat, k-independent bands
>> 
>> Giovanni
>> 
>> 
>>> On 28 Nov 2016, at 18:12, ashkan shekaari <shekaari at gmail.com <mailto:shekaari at gmail.com>> wrote:
>>> 
>>> Dear experts,
>>> 
>>> Is it necessary using kpoint mesh when we are dealing with molecules?
>>> 
>>> In the case of a molecule in cubic vacuum, what path in BZ should be selected?
>>> --
>>> Regards,
>>> Ashkan Shekaari
>>> Plasma Physics Research Center
>>> Science and Research Branch
>>> I A U, 14778-93855 Tehran, Iran.
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-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: http://people.na.infn.it/~cantele

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