Subject: Alternant hydrocarbons and the film "My Fair Lady"

From: Henry Pang <[email-masked]>
Date: Thu, 13 Sep 2001 06:12:28 +0930

Hi CCL

I am interested to find out if my impression CC is a super reductionist
field is reasonable. The word "alternant" is found in CC books. Ira Levine
(1983), Quantum Chemistry says, "An alternant hydrocarbon is a planar
conjugated hydrocarbon in which the carbon atoms can be divided into a
starred set and an unstarred set."

My several general chemistry books do not mention alternant. I do not find
any entry for "alternant hydrocarbon" in the Cambridge International
Dictionary of English, Academic Press Dictionary of Science and Technology,
but the Concise Oxford Dictionary says, "alternant is alternating, of
alternating layers". I do not find any mention in books of cosmology,
astronomy, physics, archaeology, anthropology, history, language,
linguistics, law, medicine, surgery, politics, metal work, or mass media for
example.

I do have some idea; alternant is interesting in molecules such as
cyclobutadiene, naphthalene, benzyl radical, azulene, cyclopentadienyl
radical. I am looking for any discussion regarding what the word "alternant"
means in plain English, which other people in the university and community
might appreciate as human beings, even though not expert in CC.

Please understand I am not being disrespectful or even facetious. Do you
recall the award film "My Fair Lady"? Common flower girl Eliza Doolittle
asks phonetics expert Professor Higgins to teach her to speak like a lady.
Eliza becomes the belle of British society and the Prince takes her hand to
lead her to the dance floor at the great Ball. Higgins takes all the credit.
As he says, "I knew I could do it." He tells Eliza, but she replies in total
defiance, "I do not understand anything you are saying to me. I am too
ignorant!"

I am not CC, but just an Australian medical doctor. I am just curious about
CCL. Forgive me, but CCL seems like an intense activity looking the computer
measurements and bond strengths of the Lego blocks put together by my
children into interesting creations. CCL day in and day out, seems about
finding better ways of computing the minute details of my children's Lego
blocks?

Questions -
1.Have you any material, which explains "alternant" in plain English for my
children, so they might really understand what the animal is in real terms?
2.Have you ever heard of another word "Holism"? Could holism be of any
interest to the super reductionist field of CC? Does it really matter to the
world or our Universe in any case?

(I am disgusted and very sad about New York and the Pentagon)

Regards
Dr Henry Pang (medical) 
Australia

---

From: Rene Fournier <[email-masked]>
Date: Thu, 13 Sep 2001 10:43:52 -0400 (EDT)

Hello Dr Pang:

To answer your question:

>1.Have you any material, which explains "alternant" in plain English ...

   The word "alternant" shows up in matrix algebra.  The "alternant" may
be defined as the determinant of a Vandermonde matrix.  The 3x3 Vandermonde
matrices have this form:

 1    a    a^2
 1    b    b^2
 1    c    c^2

The determinant of this matrix, the ALTERNANT, is equal to
(a-b)(b-c)(c-a) = (b-a)(c-b)(c-a)

4x4 Vandermonde matrices have this form:

 1    a    a^2    a^3
 1    b    b^2    b^3
 1    c    c^2    c^3
 1    d    d^2    d^3

The alternant for this matrix is the product
(b-a)(c-a)(d-a)(c-b)(d-b)(d-c)

etc...

More generally, the product of all differences of a set of n numbers
y_1, y_2, y_3, ... y_n is equal to the determinant of the corresponding
n x n Vandermonde matrix (alternant) having elements y_1, y_2, y_3,
... y_n on the 2nd column.  So for the general n x n case, the alternant is

Product_for_all_pairs_i,j_(0<i<j<n+1)_of_(y_j-y_i)

See formula 14.311 in I S Gradshteyn and I M Ryzhik "Table of
integrals, series, and products", corrected and enlarged edition
prepared by Alan Jeffery (Academic Press, 1980, New York).

I guess one could, by extension, define "alternant" as follows:

the alternant associated with an ordered set of numbers is the product
of all the ordered differences that can be formed from these numbers.

It may not sound like plain English, but working out examples helps.
Here's some sets of numbers and the alternants associated with them:

{7, 4, 5}     the alternant is (4-7)*(5-7)*(5-4)= 6
{7, 5, 4}     the alternant is (5-7)*(4-7)*(4-5)=-6
{7, 5, 4, 1}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(1-5)*(1-4)= 432
{7, 5, 1, 4}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(1-5)*(4-1)=-432
{7, 1, 5, 4}  the alternant is (5-7)*(4-7)*(4-5)*(1-7)*(5-1)*(4-1)= 432

Rene Fournier.
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On Thu, 13 Sep 2001, Henry Pang wrote:

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From: "Graeme L. Nyberg" <[email-masked]>
Date: Fri, 14 Sep 2001 13:51:44 +1000

Henry,

You've received some responses, all of which are correct, but I have 
my doubts as to whether you're now much wiser. Here is a simple (I 
hope) explanation.

The word 'alternate' is derived from 'alternating'. Alternate 
hydrocarbons have alternating single and double bonds - eg 
CH2=CH-CH=CH-CH=CH2, hexa-tri-ene.
Note that you can 'star' alternate C's:  *      *     *

The term arose in the consideration of the electronic structure 
(bonding) of such molecules, which are all planar, and are termed 
'conjugated', meaning that the electrons of the double-bond system 
(referred-to as the pi-electrons) interact throughout the entire 
molecule. This results in their properties being quite different from 
those of even their closest non-conjugated relatives, eg 
CH2=CH-CH2-CH2-CH=CH2. Here the pi-electrons in the two double bonds 
don't interact, the molecule is not conjugated, and the concept of 
'alternate-ness' doesn't apply.

The more interesting class of conjugated (and 
alternate/non-alternate) molecules are the aromatic compounds, based 
on the benzene 6-membered ring (which is both fully conjugated and 
cyclic). The classical structural formula for this has alternating 
single and double bonds, but in fact no individual bond is either 
single or double; rather, they're all one-and-a-half. The concept of 
alternate- ness arose in the theory/model which was developed to 
properly account for this.

The commonly occurring aromatic molecules - eg naphthalene, 
anthracene,phenanthrene - can be thought of as being constructed from 
fused benzene rings, and are all alternates (since each ring has six 
carbons). Note that any even-membered ring will be an alternate, but 
that an odd-membered ring won't. Normal compounds with odd-membered 
rings won't, however, be fully conjugated [eg cyclo-penta-di-ene, 
(CH)4CH2, with an 'interrupting' CH2 group], so alternate-ness is not 
a concept which has been adopted into ordinary organic chemistry. 
Some of the related ions [eg the cyclopentadienyl anion, (CH)5-] are, 
though, fully conjugated, aromatic, and quite stable (and form 
complexes with metal cations).

It is at this point that the concept of 'starring' atoms becomes 
useful. In an even-membered ring, every 'starred' carbon will have 
two unstarred carbons as neighbours (and vise versa), whereas in an 
odd-membered ring there will be two adjacent carbons which are either 
both starred or both unstarred (and so be a non-alternate). Full 
conjugation is thus not synomymous with being alternate.

As well, there are a few compounds with fused odd-membered rings - eg 
azulene,which has fused five- and seven-membered rings. It is fully 
conjugated, with alternating single and double bonds (around the 
periphery), but is a non-alternate (because of the adjacent 
starred/unstarred carbons across the bridge). In contrast to 
naphthalene, its isomer, it isn't aromatic. Many of the properties of 
these molecules are thus accounted-for by their topologies.

The class of alternates can in fact be subdivided into odd-alternates 
(eg benzene = 'cyclo-hexa-triene') and even-alternates (eg 
cyclo-octa-tetrene). The former is aromatic, but the latter (though 
cyclic and nominally still fully conjugated) is not. (The neutral 
molecule is in fact non-planar.) The theory/model accounts for this.

Fascinating, isn't it?! Make you wish you'd carried on with chemistry 
instead of medicine??    ;-)

Cheers,
	Graeme Nyberg.