Subject: Is anion energy of every molecule MUST be LOWER than that of neutral one? Cation energy GREATER than neutral energy?

From: "Kiniu WONG Kin-Yiu" <[email-masked]>
Date: Mon, 25 Sep 2000 21:14:04 +0800

Hi all,

    I've learned we could estimate the value of HOMO eigen energy and LUMO
eigen energy by calculating the value of Ionization Energy (IE) and Electron
Affinity (EA) respectively. We could obtain HOMO = E(cation) - E(neutral)
and LUMO = E(neutral) - E(anion). So, I believe that E(cation) > E(neutral)
> E(anion).

    However, when I calculated IE and EA of molecule Alq3 (or Gaq3) by
Hartree-Fock (Gaussian 98), surprisingly the value of E(anion) > E(neutral)
with stabilised wavefunction of 6-31G(d). I don't know why. Is it just
because the upper bound of E(anion) is much higher than that of E(neutral),
so finally E(anion) > E(neutral)? Or any other reasons?

    Although, when I changed the basis function to be either 6-31+G(d)
(diffuse function special for anion) or LanL2DZ (ECP basis function) then
both give E(anion) < E(neutral), however, the computed LUMO ( E(neutral) -
E(anion) ) is much smaller than that of the experiment. How could I solve
this problem if I still use Hartree-Fock (HF) ? Any suggestions?

    Since we know HF gives us upper bound of the calculated energy, but we
don't know whether DFT gives us the upper bound or not, so my group still
prefers to use HF. Anyway, could this kind of problem be solved by DFT?
If so, why could DFT handle this kind of computation, but HF couldn't?

    Once you think details of Alq3 or Gaq3, such as their structures,
experimental or computational HOMO & LUMO, could help you answer my
question, I am very pleased to give you at once. Thanks for any help in
advance!

Regards,
Kiniu WONG Kin-Yiu
Undergraduate student
Department of Physics
The Chinese University of Hong Kong
Email: [email-masked]  or  [email-masked]

---

From: Christoph van Wüllen <[email-masked]>
Date: Mon, 25 Sep 2000 17:42:33 +0200

In principle, E(anion) must be lower then E(neutral), since otherwise
the extra electron might decide to go away: there is always the possibility
to describe the "anion" as

Neutral + electron at rest, far away

whose energy is E(neutral). (In other words, either the neutral binds another electron or it doesn't)

However, if you have localized basis functions, you cannot describe an electron far away, and hence E(anion) might be larger than E(neutral). If you enlarge the basis set, then E(anion) will either become identical to E(neutral) (in this case the neutral does not bind an electron), or E(anion) might become lower than E(neutral), in which case there is possibly an electron affinity.

Something similar holds for the cation vs. neutral energy, except that there 
is a large electrostatic term which makes it unlikely that E(cation) can be smaller than E(neutral), even in approximate calculations.

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