It could well be that the predicted enhancement of the electron-phonon coupling discussed in

@article{PhysRevB.85.205453,

title = {Electron-phonon bound state in graphene},

author = {Badalyan, S. M. and Peeters, F. M.},

journal = {Phys. Rev. B},

volume = {85},

issue = {20},

pages = {205453},

numpages = {5},

year = {2012},

month = {May},

publisher = {American Physical Society},

doi = {10.1103/PhysRevB.85.205453},

url = {http://link.aps.org/doi/10.1103/PhysRevB.85.205453}

}

based on "singular vertex corrections beyond perturbation theory strongly increase the electron-phonon binding energy scale" in such way that the so-called "breakdown of the Born-Oppenheimer approximation" is explained.

For a discussion of other such systems see, e.g.

@article{PhysRevB.92.085137,

title = {Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure},

author = {Antonius, G. and Ponc\'e, S. and Lantagne-Hurtubise, E. and Auclair, G. and Gonze, X. and C\^ot\'e, M.},

journal = {Phys. Rev. B},

volume = {92},

issue = {8},

pages = {085137},

numpages = {9},

year = {2015},

month = {Aug},

publisher = {American Physical Society},

doi = {10.1103/PhysRevB.92.085137},

url = {http://link.aps.org/doi/10.1103/PhysRevB.92.085137}

}

See also

@article{PhysRevLett.115.176401,

title = {Fr\"ohlich Electron-Phonon Vertex from First Principles},

author = {Verdi, Carla and Giustino, Feliciano},

journal = {Phys. Rev. Lett.},

volume = {115},

issue = {17},

pages = {176401},

numpages = {5},

year = {2015},

month = {Oct},

publisher = {American Physical Society},

doi = {10.1103/PhysRevLett.115.176401},

url = {http://link.aps.org/doi/10.1103/PhysRevLett.115.176401}

}

 Dear Herbert

Thank you for your participation, Are there any other models that interpret the BOA breaking down?

Mr. Fadhil,

The answer to the question about the electronic transitions in graphene is associated with the electronic transitions in benzene where within the frame of D6h point group, a transition between ground state 1A1g and excited state 1B2u (low-lying) is one photon symmetry forbidden. Or are you shall describe benzene, coronene or an infinity condenzed structure ther approximations bring to the basic D6h unit in those cases. Please bear in mind that the experimental UV- spectra of both the graphene and coronene hav eshown UV-bands within 270-300 nm.

Generally, the removing of the fourfold degeneracy yields to a degenerated 1E1u state and two non-degenerated 1B1u (S1) and 1B2u (S2) states (attachment). Transitions leading to S1 (or 1B2u) which is realized between fi3 level (b2 local symmetry) to fi4 (also b2) is accompagnied with the change of the e-state (singlet-triplet) and thus this is a low - probable transition. In parallel at a level fi2 (b2), which has the same energy like fi3(b2) has also an e-allowing realization of an another transition to fi3 (a1) as well as the above mentioned electron from fi3 level (b2) can be involved into transition to fi5(a2). The last two transitions are transitions to S2 state. Both transitions are associated with change of the e-state as well as accounting for the fact that fi5(a2), fi4(b2) and fi4(a1) levels have the same energy. Along with another fact that the transitions to S2 are between orbitals with different symmetry (You can have 1B1 and 1B2). In other words the transitions S0-to-S1 and S0-to-S2 are low probable ones. However, S0-to-S2 transition has relatively higher probability than S0-to-S1 one.

Please pay attention to few fast computations of C6H6 shown as attachment as well. For 1A1g-to-1B1u and 1A1g-to-1B2u (S1) the oscillator strengths are shown as "0".

To evaluate the intensities of those transitions, you should take into consideration the vibrational contribution, obtaining relative intensity values, expressed in the shown example with "rel. f'" (attachment). About the vibrational contribution computations you could follow the discussion:

Your question, however, do not means that you cannot account for vibrational contribution using Herzberg-Teller theory (see the shown discussion-link above) within the frame of Born-Oppenheimer approximation.

Links to discussion above:

https://www.researchgate.net/post/Does_anyone_know_how_to_calculate_UV-VIS_spectrum_of_Q_bands_of_free_base_porphyrin

In  addition, in the attachment the states are as in  the text: 1B1u (S1) and 1B2u (S2) states  

Dear Prof. Ivanova

Thank you for your participation

I wonder if I have a model that doesn't adopt the BOA, is there is any software that can help to apply it on graphene or any other structure?

Thank you

I also wonder, Sadeem.

 Dear Sadeem,

The Born-Oppenheimer Approximation is mostly a wonderful approach in molecular physics, but it often breaks down, cf. the Jahn-Teller Mechanism, conical intersections and in condensed matter problems like superconductivity and strongly correlated systems, in addition to graphene.

In such systems one usually have two subsystems, (I) the fermionic system of light carriers and (II) the nuclear skeleton.  One can then use the mirror theorem for mappings between (I) and (II), see e.g. the discussion as well as references in the enclosed article below.

Erkki,

Sadeem and I want to know if software in this field (containing mirror theorem) exists.

Thank You in advance.

Follow-up,

If you are interested in superconductivity, you will find what you want in the paper I enclosed and references therein. Conical intersections is another hot topic, see e.g. Domcke-Yarkony, Ann. Rev. Phys. Chem 63:325 (2012).

The latter might be a future Nobel Prize Award, so the time invested in the Ann. Rev. Phys. Chem. might be well used!

Thank You for reference, Erkki. Unfortunately, it is not available for me. To my mind Sadeem (and I also) is interested mainly in software for quantum chemistry. Superconductivity, of course, is interesting, but it is somehow separate topic.

Thank you Erkki for your references and participation.

Yes dear Eugene you got my point.

Thank you

Eugene,

As being employed at a state university, most references should be available to you, if you are willing to do some search.

Ok, let's say it this way,  I have a new model that may solve the Graphene breakdown for the BOA I just need to prove it by applying it on Graphene, Is  any one interested to enter with me in a collaborative work, The model is there only I need to apply it through calculations

About availability. We here have different system, Erkki.

I want to know your model, Sadeem. Breakdown of BOA to my mind is the main problem in quantum chemistry. I, personally, don't know ways of it's solution.

Dear Eugene

Sure I will disseminate to you and to public when its ready, but still I need to confirm through calculations before anything.