Simple Huckel Molecular Orbital (SHMO) Program
A talk presented at University of Osnabrueck as part of the seminar on
“ Software for Modelling and Data Analysis”
PhD program
Synthesis and Characterization of Surfaces and Interfaces assembled
from Clusters and Molecules
Tesfaye Hailu Degefa
Uinvesity of Osnabrueck
Institute for Chemistry
January 15, 2003

Introduction

What does SHMO program do?

Requirements?

How to access ?

How to do?

Applications

Introduction
SHMO program :
Orbiatl”
interactive program to perform electronic structure
calculations within the “ Simple Huckel Molecular
approximations

the simplest MO calculator available to Chemist
The theoretical basis for the method is described in:

Orbital Interaction Theory of Organic Chemistry, A. Raulk, Wiley
Interscience, 1994 (2001)

Advanced Organic Chemistry, Part A: Structure and Mechanisms,
3rd
Ed.,F.A.Carey and R.J. Sundberg, Plenum Pub. Coop.,
1993
Mathematically, the molecular orbital are treated as a linear combination of atomic
orbitals, so that the wave function, , is expressed as a sum of individual atomic
orbitals, ,multiplied by appropriate weighting factors (coefficients),c, :
 = c11 + c22 + ............. cnn
The coefficients indicate the contribution of each atomic orbital to the molecular
orbital.
In SHMO only the p- atomic orbitals are involved whereas in the semi-empirical
methods s-, p- and d- atomic orbitals are taken into account.
The coefficient corresponding to the contribution of atomic orbital of atom r to the
jth MO is given by:
Crj = (2/n+1)1/2 (sin rj/n+1)
The energy levels of the molecule are given by the expression:
E =  + mj
where:
a)
mj = 2cos(j/n+1) for j = 1, 2, ......................... n, for conjugated
chain system.
b)
mj = 2cos(2j/n) for j = 0,  1,  2, ..................
 n/2 for n even,
(n-1)/2 for n odd, for ring system.
n is the number of carbon atoms.
The a series of molecular orbiatls with energies expressed in
terms of the quantities  and  , which symbolize the Coulomb
integral and resonance integral, respectively.
The Coulomb integral,  , is related to the binding energy of an
electron in orbital, and is taken to be a constant for all carbon
atoms but will vary for heteroatoms as a result of the difference in
electronegativity.
The resonance integral,  , is related to the energy of an electron
in the field of two or more nuclei.
Examples:
Numerical operations for 1,3,5-Hexatriene and Calicen
gives the following results
Table1.

1
2
3
4
5
6
Energy Levels and Coefficients for 1,3,5-Hexatriene
mj
1.802
1.247
0.445
-0.445
-1.247
-1.802
C1
0.2319
0.4179
0.5211
0.5211
0.4179
0.2319
C2
0.4179
0.5211
0.2319
-0.2319
-0.5211
-0.4179
C3
0.5211
0.2319
-0.4179
-0.4179
0.2319
0.5211
C4
0.5211
-0.2319
-0.4179
0.4179
0.2319
-0.5211
C5
0.4179
-0.5211
0.2319
0.2319
-0.5211
0.4179
C6
0.2319
-0.4179
0.5211
-0.5211
0.4179
-0.2319
Table 2.

1
2
3
4
5
6
7
8
Energy Levels and Coefficients for Calicen
mj
2.359
1.816
0.677
0.618
-0.871
-1.0
-1.618
-1.98
C1
0.456
0.199
-0.586
0
0.125
0
0
0.628
C2
0.281
0.337
-0.155
-0.602
-0.371
0
0.372
-0.382
C3
0.207
0.413
0.481
-0.372
0.198
0
-0.602
0.128
C4
0.207
0.413
0.481
0.372
0.198
0
0.602
0.128
C5
0.281
0.337
-0.155
0.602
-0.371
0
-0.372
-0.382
C6
0.514
-0.313
-0.085
0
0.633
0
0
-0.48
C7
0.378
-0.384
0.264
0
-0.338
-0.707
0
-0.161
C8
0.378
-0.384
0.264
0
-0.338
0.707
0
0.161

What does SHMO program do?
SHMO program:

revels information how each molecular orbiatls are formed from
the
LCAO.

finds energies levels of the molecule and its corresponding
molecular orbitals, MO

predict  bond order and population net charge.

permits easy changes of orbital electronegativities (the Huckel
coulomb integrals,alpha) and intrinsic orbital interaction
values (the
Huckel resonance integrals, beta) to illustrate the effects
of
interacting orbital energies, orbital energy differences
and
overlaps on the resultant molecular orbital energies and
polarizations.

the success of SHMO in dealing with relative stabilities of cyclic
conjugated polyenes is impressive.

Requirements ?
Only organic, planar (2 dimensional) molecules with
delocalized electrons can work well with this theory.

How to access ?
SHMO program is licensed under the GNU General Public
License. It is always recommend to access its original site
(http://www.chem.ucalgary.ca/shmo) for most recent
version available.
SHMO is still a new program and may contain some bugs. If
you find a bug restart and document the sequence of
events that led you to the bug.
Email that information to Dr. Rauk (rauk@chem.ucalgary.ca)
and to Rich Cannings (rich@cannings.org) .

How to do?
1) Draw the structure
to draw structure click on "Add" icon and then click on the
main canvas to add atoms or drag the mouse from one atom to
another
to create bonds
2) Click on "Minimize" to adjust the structure to what it "normally”
resembles.
3) Click on "Find Energies" to initialize the graph. The graph shows
energies.
4) Click on the energies to view the MO's for that particular energy
level. "Find Energies” places the molecule into a matrix
representation and diagonalizes the matrix.
5) You can extract more information by clicking on “Show Data
Table” and “Show Orbital” icons .

Applications
1.
1,3,5-Hexatriene
2.
Calicene
3.
Cyclobutadiene
4.
Benzene