                          THE HMO PROGRAM (v1.0)

BASIC USE
HMO performs interactive Hckel theory calculations on planar conjugated
hydrocarbons.  HMO is invoked by entering hmo at the DOS prompt.  Input is
typed in response to the program's questions and the results are shown on
the monitor.

Try these simple examples and compare the results with your textbook.
Calculations on non-branched polyenes (chains) like ethene, butadiene,
hexatriene, etc. are simple.
EXAMPLE 1:  1,3-butadiene.
How many carbon atoms:              4
Chain, Ring or Other:               C
Neutral, Cation or Anion:           N

Calculations on monocyclic polyenes (rings) like cyclobutadiene, benzene,
etc. are also simple.
EXAMPLE 2: benzene.
How many carbon atoms:              6
Chain, Ring or Other:               R
Neutral, Cation or Anion:           N

Calculations on molecules that are neither simple chains nor rings require
a bit of planning.
1. Draw the carbon skeleton of the molecule.
2. Identify the largest chain or ring substructure that it contains.
3. Number the carbon atoms in the substructure first.  If the substructure
is a chain, number sequentially from left to right; if it is a ring, number
sequentially going around the ring.
4. Number the remaining carbon atoms.
5. Write down the link (bond) sequence(s) needed to build the molecule from
the substructure.  A link sequence consists of two or more carbon atom
numbers separated by blanks.  For example, the link sequence 1 4 links C1
to C4; the link sequence 1 4 7 9 links C1 to C4, C4 to C7, and C7 to C9.
To link C1 to C4 and C7 to C9 without linking C4 to C7, use two separate
link sequences:  1 4 and 7 9.

EXAMPLE 3: styrene. (total -electron energy of 8+10.424)
Phenylethene (styrene) has 8 carbon atoms and clearly contains a six-
membered ring (benzene-like) substructure.  The atoms in the ring are
numbered from 1 to 6 going around the ring, the carbon attached to the ring
can be numbered 7 and the terminal carbon can be numbered 8. To build
styrene from benzene, links are needed between carbon 6 and carbon 7, and
between carbon 7 and carbon 8. This means that either the single link
sequence 6 7 8 or two separate sequences 6 7 and 7 8 are required to build
styrene from the benzene substructure.  The input to the HMO program could
proceed as follows:

How many carbon atoms:                      8
Chain, Ring or Other:                       O
Substructure is Chain or Ring:              R
Carbons in substructure:                    6
Enter next link sequence:                   6 7 8
Enter next link sequence:                   Q
Is everything OK:                           Y
Neutral, Cation or Anion:                   N

EXAMPLE 4: styrene.
A little thought shows that styrene also contains a 8 carbon chain
(C1-C2-C3-C4-C5-C6-C7-C8) as a substructure.  The benzene ring can then be
formed by linking C1 to C6.  Thus, the HMO input could also be:
How many carbon atoms:                      8
Chain, Ring or Other:                       O
Substructure is Chain or Ring:              C
Carbons in substructure:                    8
Enter next link sequence:                   1 6
Enter next link sequence:                   Q
Is everything OK:                           Y
Neutral, Cation or Anion:                   N

EXAMPLE 5: napthalene (total -electron energy of 10+13.683)
One can build up napthalene from a benzene substructure but it is a lot
simpler to build it from a [10]-annulene (10 carbon ring) substructure.
How many carbon atoms:                      10
Chain, Ring or Other:                       O
Substructure is Chain or Ring:              R
Carbons in substructure:                    10
Enter next link sequence:                   1 6
Enter next link sequence:                   Q
Is everything OK:                           Y
Neutral, Cation or Anion:                   N

ADVANCED USE
Invoking the program with a /f or -f switch (hmo /f or hmo -f) will lead to
the results being placed in a file called hmo.tmp in your current directory
instead of being displayed on the monitor.

TERMINOLOGY
The charge receptivity is my name for  times what the HMO literature calls
the atom-atom self-polarizability.
The pi-count is the pi-electron population - often referred to as the
pi-electron density in the HMO literature.
The pi-order (p) is the (mobile) pi-bond order. The bond order is 1+p.

TECHNICAL NOTE
Bond lengths (R) are estimated from pi-bond orders (p) using Coulson's
formula:  R = s - (s-d)/[1+a(1-p)/p] in which s=154pm and d=134pm are
standard C-C and C=C bond lengths, and the dimensionless parameter a=0.765.

BIBLIOGRAPHY
The following references, in order of increasing mathematical difficulty,
treat Huckel theory in a manner that appeals to me.
1. K. Yates, Huckel Molecular Orbital Theory, Academic Press, NY, 1978
2. J.P. Lowe, Quantum Chemistry, Academic Press, NY, 1978, Chapter 8
3. F.L. Pilar, Elementary Quantum Chemistry, McGraw-Hill, NY, 1968,
   Chapter 18
