Transcript Simple Huckel Molecular Orbital Calculator
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)
1993 Advanced Organic Chemistry, Part A: Structure and Mechanisms, 3rd Ed.,F.A.Carey and R.J. Sundberg, Plenum Pub. Coop.,
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, :
= c 1
1 + c 2
2 + ............. c n
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 j th MO is given by: C rj = (2/n+1) 1/2 (sin rj
/n+1)
The energy levels of the molecule are given by the expression: E =
+ m j
where: a ) b ) m j = 2cos(j
/n+1) for j = 1, 2, ......................... n, for conjugated chain system.
m j = 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.
Energy Levels and Coefficients for 1,3,5-Hexatriene
1
2
3
4
5
6 m j 1.802
1.247
C 1 0.2319
0.4179
0.445
0.5211
-0.445 0.5211
-1.247 0.4179
-1.802 0.2319
C 2 0.4179
0.5211
0.2319
-0.2319
-0.5211
-0.4179
C 3 C 4 0.5211 0.5211
0.2319 -0.2319
-0.4179 -0.4179
-0.4179 0.4179
0.2319 0.2319
0.5211 -0.5211
C 5 0.4179
-0.5211
0.2319
0.2319
-0.5211
0.4179
C 6 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 m j C 1 C 2 C 3 C 4 C5 C6 C7 C8 2.359 0.456 0.281 0.207 0.207 0.281 0.514 0.378 0.378
1.816 0.199 0.337 0.413 0.413 0.337 -0.313 -0.384 -0.384
0.677 -0.586 -0.155 0.481 0.481 -0.155 -0.085 0.264 0.264
0.618 0 -0.602 -0.372 0.372 0.602 0 0 0 -0.871 0.125 -0.371 0.198 0.198 -0.371 0.633 -0.338 -0.338
-1.0
0 0 0 0 0 0 -0.707 0.707
-1.618 0 -1.98
0.372 -0.602 0.602 -0.372 0 0.628 -0.382 0.128 0.128 -0.382 -0.48
0 0 -0.161 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 of and Huckel resonance integrals, beta) to illustrate the effects interacting orbital energies, orbital energy differences 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 ([email protected]) and to Rich Cannings ([email protected]) .
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 another to create bonds one atom to 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