Theoretical
Quantum Mechanical Calculations on Styrene, Oxygen and
Hydrogen Sulphide Using Computer Software
By: Samuel Kougias & Alex Olig
Abstract:
Theoretical calculations to find electronic
structure were performed on diatomic oxygen, hydrogen sulfide, and
styrene. These calculations were performed and analyzed on
wxMacMolPlt, GamessQ, Jmol, and Igor Pro software. The electronic
structure calculations gave some close approximations for various
properties, including but not limited to: optimized geometry, HOMO
and LUMO orbitals, and electrostatic potential for the three
molecules.
Introduction:
Theoretical calculations can be a very useful
tool in chemistry. The ability to predict electronic structure
allows for the prediction of many properties of a molecule.
Molecular dipole moment, vibrational frequency, and the molecules
tendency to donate electrons are just a few of these useful
properties that can potentially be predicted by just knowing the
probable electronic structure.
A wave-function of an electron is known as its
molecular orbital. Exact values for the wave-functions
eigenfunction and eigenvalue can be found for single atom, single
electron structures. Estimations can be performed to find close
approximations of more complicated structures. These
approximations are possible due to the variation principle.
The variation principle states that: "If an
arbitrary wavefunction is used to calculate the energy, the value
calculated is never less than the true energy."1 This means that
it is possible to approximate true wave-functions as linear
combinations of trial wave-functions. These trial wave-functions
are not eigenfunctions of the Hamiltonian, so the expectation
value of the energy is calculated using:
<E> =
∫Ψ*ĤΨdτ/(∫Ψ*Ψdτ).
(1)
Plugging in larger basis set wave-functions, in general, give more
accurate predictions. Computers and advanced computer software can
do these calculations quite rapidly.
This experiment applies these theories and
calculations to diatomic oxygen, hydrogen sulfide, and styrene.
The basis sets used were a combination of MOPAC2 and
ab
initio methods. MOPAC2, a semi-emperical method, was applied using
the AM1 basis set. This basis set was the smallest set used for
calculations. The other three basis sets applied were
ab
initio methods. They were, in order from smallest to largest,
6-21G, 6-31G, and Double Valence Zeta (DZV). The computer software
used to study the theoretical properties of these molecules and
apply these methods were Jmol, WxMacMolPlt, GamessQ, and Igor Pro.
In general, calculations will be used to find geometry
optimizations, HOMO and LUMO orbitals, electrostatic potentials,
partial atomic charges, and dipole moments for these three
molecules. Other specific properties will be calculated for each
individual molecule.
Based on template by
A. Herráez as modified by J. Gutow
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