Hello
we know a nonlinear molecule has 3N degree of freedoms. 3 are translational, 3 are rotational and 3N-6 are vibrational degree of freedoms. but The molecule has another degree of freedoms to storing energy and it is electronic levels.
why we don't consider this degree of freedom?
Thank you
Hello,
First, some comments regarding previous postings in this thread:
To the question, yes, the electronic levels of a molecule can be regarded as degrees of freedom such as vibration and rotation, and it may make sense to do so, such as in the final stages of an isotope separation process. However, it is more often the case that the ro-vibrational energy range involved (eg, in the infrared for molecules) is very far from the electronic level energy range of the molecule, so as to make both possible and useful to not consider the electronic levels as a degree of freedom.
Further, the translation energy can also be regarded as a degree of freedom in a molecule, as in photodissociation and Doppler effects. For example of the later, the Doppler effect due to the random velocities of molecules in a gas causes a spectral line broadening that prevents a precise measurement of the line center for a molecule at rest. It can also obscure narrow splittings, for example caused by hyperfine effects, that provide information about the molecular wavefunction.
Cheers, Ed Gerck
Hi Abbas,
Energy storage means that you can store the energy in a stable mode. Trans, vibe and rot energy levels are stable unless interrupted by an external factor, such as collisions with other molecules. Energy "stored" in the electronic levels can be lost independently by the molecule without external influence. As such it is not a stable form of storage (although I agree with you that energy is indeed "kept within the molecule" as long as the electrons are excited.
Lastly, lasers are a good example of unstable or meta-stable forms of storing energy. The gas used in the laser system is kept at a highly populated electronic level. Even though energy is being "lost" from the gas in a form of photons escaping, new energy keeps being pumped into the gas molecules and one could claim that at any given moment the gas stores energy in a form that is not trans, vibe or rot. But the second you stop pumping energy into the gas it goes back into ground-populated state.
Hope this helps a bit.
- Dan Lev
Hello Abbas,
A molecule with N-nuclei and n-electrons can in general be considered as an (N+n)-body quantum system. It has 3(N+n) degrees of freedom (independent spatial coordinates). Strictly speaking one has to solve the time independent Schrodinger equation with 3(N+n) coordinates to find out the (stationary) energy levels of the molecule. This is done using approximate methods. The big difference in masses of nuclei and electrons is used in making a fist approximation; the Born-Oppenheimer approximation. Electrons are imagined to be moving much faster than nuclei so electronic energy levels can be evaluated assuming nuclei to be stationary (at a given geometrical distribution of nuclei). (The Schrodinger equation has only n dynamical coordinates, i.e. an n-body quantum system. Nuclear coordinates are considered as parameters with values specified by the specified geometry of the molecule. With this approximation you have assumed that the nuclei are classical particles) The electronic energy levels vary when the geometry of the molecule is changed. This varying electronic energy acts as potential for nuclear motion. (One can imagine calculating this potential energy by calculating electronic energy for all possible nuclear geometries.) Now calculating the possible energy levels associated with nuclear motion is imagined as an N-body quantum problem. It has 3N degrees of freedom. Further approximations are done by imagining nuclear motion as a combination of translation+rotation+vibration. So only the 3N nuclear degrees of freedom are broken down into translation+rotation+vibration.
The bottom line is that we have developed a model for describing the energy of a molecule where the electrons are treated strictly as quantum particles and treat nuclei semi-classically. The degree of freedom is retained only in describing the motion of semi-classical particles (nuclei).
For strong-field ionization of small atoms or molecules, people sometimes treat the full nuclear + electronic problem (not necessarily in all dimensions, though). The problem is that already for trivial molecules such as H2, this becomes rather challenging (partly due to the effect of strong laser fields, though).
As a consequence, almost everybody uses the Born-Huang description, where the electronic degrees of freedom only appear through the fact that you need one nuclear wave function per relevant electronic state. For more details, see a textbook on quantum dynamics. Starting with the original book by Born and Huang, which has a surprisingly modern and concise description of this
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