Subject: Delocalization. Let's do it.

From: YONG HUANG <[email-masked]>
Date: Sat, 22 Feb 1997 23:36:18 -0600 (CST)

Thanks to Lee, Alex and others for discussing the titled question I asked.
Still nobody has proposed a simple way to quantitate electronic delocalization.
One early morning a few days ago I couldn't sleep and I came up with some 
ideas. The following is my proposed formula:

DL = SQRT[SIGMA(BOcal-BOnom)^2] (1)
or DL = SQRT[SIGMA(AtCh)^2]     (2)

where	DL = a measure of electronic delocalization
	SQRT = square root of
	SIGMA = sum of
	BOcal = calculated bond order (in my case from CAChe MOPAC)
	BOnom = nominal bond order (1 for single bond, 2 for double bond...)
	AtCh = calculated charge at an atom, equal to nominal valence for the
	atom (1 for H, 2 for O, 4 for C... what do you call it?) minus
	calculated electron density at that atom

Based on chemical intuition, formula (1) seems to make more sense. Unfortunately
when I used my MOPAC data on gas phase amino acids, formula (2) seemed to be
better: Trp is very delocalized while Pro is very localized. But I have to say
I only tested (1) on 3 amino acids because MOPAC output file doesn't have a
good format for the small program I wrote like AtCh does which I just
copy&paste.

Comments: Lee's city-population interpretation of delocalization is a dynamic
one. I don't see any data contained in a simple calculation output file that is
associated with this "dynamics". What we have is static result from an output
file, e.g., bond order, charge, eigenvalue, eigenvector, etc.

To improve the method of formula (2), AtCh should not be measured in a way that
the distance covered in measuring the electron density around atom A and
that distance for B occupy the whole bond length, leaving no gap in between.
Instead, the distance should be rather small. See Figure.

     }  )(   {
 (A)-}--)(---{----(B)
     }  )(   {
     ^  ^^   ^
     1  23   4  <------position number for my text

I believe MOPAC and probably other programs measure electron density using
spheres of radii A-2 and 3-B. A better way is to use radii A-1 and 4-B. The
positions of 1 and 4 should be fixed a prior(i. By the way, how does MOPAC
determine positions 2 and 3 if A is not equal to B? (if A=B, 2 = 3 = middle
point)) Therefore, using formula (2) on delocalized cyclododecahexayne (C12,
despite of its nonexistence(?) in actuality) would give the same DL as on
strictly localized cyclododecahexayne if A-2 and 3-B radii are used, but
different DL if A-1 and 4-B are used.*

I'll say some of the above in my dissertation. I'm an experimental chemist. Any
comments from theoretical gurus like you are precious to me. And hope my
advisor won't say I'm pre-empting my data here again. I don't think I am.

Yong

------------------
*I don't want to use the example of benzene and cyclohexatriene because they
have hydrogens and so C-H bonds may have different electron density
distribution.