[Pw_forum] homo lumo

[Stefano Baroni]

On Dec 19, 2011, at 8:24 PM, yaldaa kh wrote:

> dear all
> how are determined the energy of homo and lumo for a molecule in gas
> and adsorbed states?

Dear Yaldaa,

it's a great pleasure to welcome a highschool teacher joining this community: WELCOME ON BOARD!

The two cases (gas phase and adsorbed states) are conceptually similar. What one has to do (either explicitly, if the complexity of the systems allows, or implicitly if it doesn't) is to calculate the lowest-lying "molecular orbitals" *of the entire system*. (I enclosed "molecular orbitals" in quotation marks because one has to treat the entire system - isolated molecule, if in the gas phase, or molecule+substrate if in the adsorbed state, as a unique big "molecule"). The number of calculated states must be no smaller than the number of electrons (the latter number is determined by the charge state of the overall system). Then, very simply, if you have N electrons, the N-th state will be the HOMO and the (N+1)-th the LUMO.

The only difference between the two cases is that, in the adsorbed state,  the "molecular orbitals" of the whole system (the only ones that have a mathematically and physically well defined meaning) will result from the hybridization of orbitals pertaining to the isolated molecule and the isolated substrate, much in the same way as molecular orbitals of an isolated molecule may be (approximately) expressed as linear combinations of atomic orbitals (LCAO). These hybridized orbitals will be strictly localized around the adsorbed molecule or delocalized all over the molecule+substrate system according to whether or not the corresponding energy is degenerate with some energy levels of the isolated substrate (two states are said "degenerate" if they have the same energy).

Hope to have been clear enough and of some help. If not, do not hesitate to revert to us, and I (we) will try to be clearer ...

Best wishes,
Stefano Baroni


> thanks in advance
> yaldaa k
> chemistry teacher
> dehkhoda highschool
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget

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