I want to know the simplest structures that BO model failed to descripe precisly.
May I suggest a system of three hydrogen atoms, any ideas about that?
Any one knows why the BO model failed to describe such simple systems
A relatively simple system displaying this failure, one which has theoretically been studied, is the hydrogen fluoride (HF) dimer. See the original wok by Ian M. Mills (J. Phys. Chem. 88, 532, (1984)) and the subsequent work by Edwin L. Silbert (J. Phys. Chem. 93, 5022 (1989)).
Dear Sadeem,
Although this is not my area, but I write in response to your message as below.
I know that Born-Oppenheimer approximation assumes that the nuclei are infinitely heavy compared to electrons. Also, the electronic wavefunction depends only on the positions of the nuclei. As a result, the nuclei can be assumed to be stationary objects while the electrons go freely. Mathematically this assumption allows us to write the full wavefunction (a function of the electronic positions and nuclear positions) in separable form.
This approximation fails in many known situations; for example when ground and excited electronic surfaces get very close, which happens more often in molecular systems. These cases have to be treated differently and more carefully, and these fall into the domain of what is known as 'non-adiabatic quantum dynamics'.
I hope this answer helps..
Dear Dr. Behnam and Dr. Mansour
Thank you for your answers and participation.
You are welcome Sadeem.
The interested may wish to consult the following text written by Mark Tuckerman for the Chemwiki of University of California, Davis. The worked-out example in this text, regarding the hydrogen molecule ion, is very instructive.
http://chemwiki.ucdavis.edu/Wikitexts/New_York_University/CHEM-UA_127%3A_Advanced_General_Chemistry_I/13%3A_The_Born-Oppenheimer_approximation_and_the_hydrogen_molecule_ion
Dear all;
How about Graphene? In your opinion is the BO model doing well in describing it?
As the name indicates, the Born-Oppenheimer approximation is an approximation, so that there must be aspects of its approximate nature to show up somewhere. However, all the electron-phonon calculations I have seen performed on graphene rely on the Eliashberg formalism, which relies on the Migdal theorem whose validity is equivalent to the validity of the Born-Oppenheimer approximation. So, the answer to your question is no, but you can make a literature search regarding electron-phonon calculations on graphene and see whether there are suggestions regarding possible non-adiabatic corrections to the theoretical results based on the neglect of these.
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