CCL: Homo-lumo gap significance

Dear all,

I agree, of course, that eigenvalues are not at all that best values to be used for gap calculations from the formal (and, frequently, also from the practical point of view), but, nevertheless, they DO provide SOME approximation. Eigenvalues, naturally, look like 'approximation for everything', as we are talking both about MO-to-MO transitions when considering UV-Vis spectra and about electron removal from some orbital / electron addition to some orbital, talking about ionization or electron capture. Of course, in reality one and the same quantity cannot describe both. However, it is well known that, for example, Koopmans' theorem often provides quite good results (okay, it's due to error compensation). Eigenvalue differences are also the first approximation in TD methods.
I want also to emphasize that the person asking was dealing with HOMO-LUMO gap in a TRANSITION STATE. From more physical point of view, Mr. van Sittert should compute ionization potential of electron donor in his reaction and electron affinity of the acceptor, according to Δ (or ΔSCF) methodology (energy difference). However, I do not know if this would be easy task to perform in transition state, correctly including the polarization of other molecules in the reaction center. Eigenvalues, on the contrary, are ready available from every optimization run; that's why I did not comment anything in my first answer.

We are now, actually, concerned with something similar, currently reconciling ourselves with Mulliken charges of surrounding molecules for the polarization field (but we are not dealing with the transition state). Is it correct enough to consider reactants as separate electronic systems in the transition state at all?

With best wishes,
Igors Mihailovs
Institute of Solid State Physics
University of Latvia


2015-02-09 23:58 GMT+02:00 Tymofii Nikolaienko tim_mail[A]ukr.net <owner-chemistry(_)ccl.net>:
Can I try to exaggerate this discussion a bit?

It is well known that a concept of 'orbital' has historically originated from Hartree-Fock approximation, and that in fact molecular orbital
is no more than a mathematical tool for building an approximate wavefunction.
Some authors have advocated the viewpoint that in reality orbitals simply do not exist! For example:
* Martín Labarca, Olimpia Lombardi "Why orbitals do not exist?" [Foundations of Chemistry, 2010, Volume 12, Issue 2, pp 149-157,  DOI 10.1007/s10698-010-9086-5 ]
* J. F. Ogilvie, "The nature of the chemical bond—1990: There are no such things as orbitals!" [J. Chem. Educ., 1990, 67 (4), p 280, DOI: 10.1021/ed067p280 ]

With that in mind, do HOMO and LUMO have any importance, - except for adding another 'beautiful picture' to some paper with HOMO and/or LUMO
isosurfaces and withOUT any discussion of what consequences does their shapes imply , -  for understanding physical properties and chemical reactivity ?

Similar doubts about an importance apply to the HOMO-LUMO gap, but here I'd like to recall that, ofr example, replacing ONE (filled) orbital (HOMO) in
a Slatter determinant with ONE unfilled orbital (e.g., LUMO) does NOT produce even approximate wavefunction of an excited state, since the
crudest approximation to that wavefunction comes with CIS method, where a linear combination of (many!) singly substituted determinants is used
in order to get (a not so good) wavefunction of an excited state. So, there seems to be no physical ground for associating the HOMO-LUMO gap with
characteristic wavelengths in a UV-Vis-like spectra.

So, why to care about HOMO / LUMO unless we are not dealing with solids ?...

Best regards,
Tymofii,
a physicist ;)







09.02.2015 20:49, Tom Albright talbright1234=-=gmail.com wrote:
The units are in Hartrees. HOWEVER, to categorically say that the HOMO-LUMO gap is a measure of thermodynamic or kinetic stability is not true. Let me take a simple example: cyclobutadiene (in its ground state) is very reactive and one can rightfully say that it is a consequence of a small HOMO-LUMO gap. On the other hand tetrakis(t-butyl)cyclobutadiene can be isolated, crystallized and stored indefinitely at room temperature and its HOMO-LUMO gap is similar to that in the parent molecule. You have three different transition states - should be done is to carefully compare the bonding in each. See, for example, Albright, Burdett and Whangbo, "Orbital Interactions in Chemistry, 2nd edition, J. Wiley 2013).
On Feb 9, 2015, at 11:50 AM, Igors Mihailovs igors.mihailovs0{}gmail.com wrote:

Dear Mr. van Sittert,

Which units are Your eigenvalues/gap values in? Possibly hartrees? You could possibly convert these gap values to joules and compare with k_B*T, as suggests, for instance, plain Arrhenius formula...
With best wishes,
Igors Mihailovs
Institute of Solid State Physics
University of Latvia


2015-02-09 14:16 GMT+02:00 Cornie Van Sittert Cornie.VanSittert^nwu.ac.za <owner-chemistry]*[ccl.net>:
Good afternoon,
 
I was wondering if anybody could help me.  I would like to ask you about the HOMO-LUMO energy gap.
 
I have three transition states to compare, TS1, TS2 and TS3. The HOMO-LUMO was calculated for each on the whole system, so I have my HOMO on my Nu- and my LUMO on my electrophile. For the HOMO-LUMO energy gap, I subtracted the LUMO energy from the HOMO energy and got the absolute value (column 2).  Column 3 is the HOMO-LUMO energy gap within the transition state structure.
 
In the table below I compare the HOMO-LUMO energy gaps, and it seems that at the transition state (TS, column 3), the N9 has the biggest energy gap, followed by N3, and then N7. I read that all transition states reach the most stable form, which is the TS with the largest HOMO-LUMO energy gap. This follows the trend in the lab where we made the N9>N3>>N7. The HOMO-LUMO energy gap of transition state minus the HOMO-LUMO energy gap of reactants (column 4) shows the N9<N3<N7 trend. Articles say that reactions will follow the one with the smallest gap, and this agrees with my experimental work.
From what I read in literature, the HOMO-LUMO energy gap for the transition state should be as big as possible so that the total HOMO-LUMO energy gap is small: (column 4)
E(total) gap = E(reactants) gap - E(transition state) gap
 

pathway

HOMO-LUMO gapR

HOMO-LUMO gapTS

HOMO-LUMO gap(TS-R)

N3

0.15009

0.12572

0.02439

N7

0.14983

0.12340

0.02643

N9

0.14973

0.12767

0.02206
 
 
The question that no one seems to answer is if these values (shown above) are significantly different from each other.
 
Is the difference on the 3rd decimal place in the eigenvalues for the TS significant? or would all the reactions occur?  When can the difference be taken as significant?
 
Kind regards,
Cornie van Sittert
 
 
 

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With Best Regards
Tom Albright