Intro

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.

Conclusion:

Various properties of diatomic oxygen, hydrogen sulfide, and styrene were calculated from computational software. Of the various basis sets used, the DZV basis set generally gave the closest approximations. These results were expected due to DZV being the largest basis set applied. The few exceptions to DZV having the closest approximations were random, thus meaning that to get good theoretical results, multiple basis sets should always be analyzed and compared to experimental data.

References:

1. Atkins, P. Paula, J. Physical Chemistry, 9th ed.; W.H. Freeman and Company: New

York, 2010; p 388.

2. Gutow, J. Molecular Orbital (MO) Calculations, handout for Chemistry 371. Spring

2013. UW Oshkosh.

Software used:

JMol, WxMacMolPlt, GamessQ, and Igor Pro

Diatomic Oxygen Styrene Hydrogen Sulfide

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