Mr. Shekar,

There is needed statistical analysis per system. 

Dr. Ivanova, 

Thank you for your quick response. Can you please elaborate how it is done or any relevant articles which explains these effects in DFT.

Mr. Shekar,

You could pay attention to Refs. 1-13, for example. However, the objects are very simple as electronic structures, so there is unable to evaluate any kind of directional, toward molecular properties, effect.

Ref. 1.Y. SHIGETA, H. TAKAHASHI, S. YAMANAKA, M. MITANI, H. NAGAO, K. YAMAGUCHI, Density functional theory without the Born–Oppenheimer approximation and its application, Inc. Int J Quant Chem 70: 659–669, 1998

Ref. 2. Du, H., Yue, S., Wang, H., Wu, H., Hu, B. Reexamining the high-order harmonic generation of HD molecule in non-Born-Oppenheimer approximation (2016) J Chem Phys 144, art. no. 114308.

Ref. 3. Gidopoulos, N., Gross, E.Electronic non-adiabatic states: Towards a density functional theory beyond the Born-Oppenheimer approximation (2014) Philosophical Transactions of the Royal Society A 372 (2011), art. no. 20130059.

Ref. 4. Garrett, W.Non-Born-Oppenheimer approximation for very weakly bound states of molecular anions (2010) J Chem Phys 133, art. no. 224103

Ref. 5. Wodtke, A., Tully, J., Auerbach, D.Electronically non-adiabatic interactions of molecules at metal surfaces: Can we trust the Born-Oppenheimer approximation for surface chemistry?

Ref. 6. Craig, D., Thirunamachandran, T. Model calculations testing the adiabatic Born-Oppenheimer approximation and its non-adiabatic corrections (1994) Theor Chim Acta, 89, 123-136.

Ref. 7. Optics Commun. 383, 2017, 366-370, Interference minima effect of high-order harmonic generation from H2+ with different full width at half maximum, Pan, X., Zhang, J., Du, H., Liu, H., Zhang, H., Liu, X.

Ref. 8. J Physics B, 49, 2016, Art. 222001, Ion-momentum imaging of dissociative attachment of electrons to molecules, Slaughter, D., Belkacem, A., McCurdy, C., Rescigno, T., Haxton, D.

Ref. 10. ChemPhysChem, 2016, 2956-2961, The Importance of Vibronic Coupling for Efficient Reverse Intersystem Crossing in Thermally Activated Delayed Fluorescence Molecules, Gibson, J., Monkman, A., Penfold, T.

Ref. 11. Phys Review A 94, 2016, Art. 033415, Understanding molecular harmonic emission at relatively long intense laser pulses: Beyond the Born-Oppenheimer approximation, Ahmadi, H., Vafaee, M., Maghari, A.

Ref. 13. Phys Review A 93, 2016, Art. 053426, Theory of dissociative tunneling ionization, Svensmark, J., Tolstikhin, O., Madsen, L.

Dr. Ivanova,

Once again thank you for your reply. I'll go through them.