[Pw_forum] add or remove electron energy

[Stefano Baroni]

Ali: studying and reading is always a good idea. In this case, though, trying to figure out by yourself the "physical reason" could be even more instructive. Hint(s):

1) distinguish first the case of an open-shell atom/molecule from that of a closed-shell one. 

2) The simpler case is that of a closed shell. The ionization potential is the energy necessary to remove an electron from a system which has N of them, all paired into atomic/molecular orbitals. The electron affinity is the energy necessary to remove an electron from a system with the same external potential, but one electron more. In the independent-electron (or mean-field) approximation, the extra electron will necessarily be accomodated into an orbital of higher energy (all the available orbitals of equal or lower energy are occupied by the hypothesis of closed shells) ... can you complete the argument?

3) In the case of closed shells, the argument is a bit more sophisticated, because the independent-electron approximation would predict the electron affinity to be equal to the ionization potential. Can you tell why? If you can, then it should not be difficult to figure out how to refine the argument. Compare the effective potential (external-plus-electronic) of two systems with the same external potential, but differing in the number of electrons ... which one of the two is more attractive?

Give yourself 1-2 days of hard thinking, and if you fail to find an answer revert to us ...

Stefano B

On May 3, 2010, at 4:24 PM, Matteo Cococcioni wrote:

> 
> 
> Dear Ali,
> 
> I think this is a good reference on this topic:
> 
> J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev.
> Lett. 49, 1691 (1982)
> 
> Matteo
> 
> 
> 
> 
> kazempoor at ph.iut.ac.ir wrote:
>> Dear Stefano
>> 
>> I now that these are affinity and ionization, But I don't understand why ionization always is grater than affinity? I just want to know the physical reason.
>> 
>> 
>> 
>> Thanks a lot
>> 
>> 
>> 
>> 
>> Ali Kazempour
>> Physics Department, Isfahn University of Technology
>> 
>> ----- Original Message -----
>> From: "Stefano de Gironcoli" <degironc at sissa.it>
>> To: "PWSCF Forum" <pw_forum at pwscf.org>
>> Sent: Monday, May 3, 2010 6:10:25 PM
>> Subject: Re: [Pw_forum] add or remove electron energy
>> 
>> it is the difference between electron affinity and ionization potential.
>> stefano
>> 
>> kazempoor at ph.iut.ac.ir wrote:
>> 
>>> Dear All
>>> I add one electron to an isolated atom and the difference in E(n+1)-E(n)=-0.09 Ryd but when I remove an electron from this atom 
>>> I got E(n)-E(n-1)=-0.349 Ryd.
>>> what is the reason for this difference? I think that this behavior is same for every system.
>>> Thanks a lot 
>>> Ali Kazempour
>>> Physics Department, Isfahan University of Technology
>>> _______________________________________________
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>>> 
>> 
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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)

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