Quantum Calculations

Ross Wiese and Hannah Schoechert

Abstract

    Quantum Mechanics can be used to figure out molecular properties which are essential to knowing a molecules reactivity.  These properties are; vibrational frequency, molecular dipole moments, and polarizability.  Using numerous software packages such as Jmol, xmMacMolPlt, and Gamessq, all of these properties can be calculated to a very high degree of reliability which results in a very good understanding of how certain molecules will react to other known molecules.

Introduction

    A molecules electronic structure plays a huge role in its reactivity.  Knowing properties such as molecular dipole moments, vibrational frequencies, and polarizability are key to knowing a molecules reactivity.  All of these three properties are constantly being calculated by chemical physicists and physical chemists to ensure the most accurate literature values.  With the help of computers loaded with software packages, non-specialized individuals can do these calculations with relative ease.  Using this software geometry of structures can be optimized and energy calculations can be computed to predict whether reactions of certain compounds will work.  Not only do these programs generate useful data, they also generate 3-D models of molecular structures, showing molecular orbitals as well as vibrational movements for learning purposes.  A key thing to remember with these programs however is each level of theory produces different results.  The MOPAC uses empirical data as well as estimates the values for two, electron overlap integrals.  In MOPAC, PM3 and AM1 are used as Hamiltonians.  The best level of theory is ab initio.  In ab initio all integrals are calculated.  All three theories, AM1, PM3, and ab initio are capable of calculating optimized geometries, HOMO oribitals, dipole moments, and vibrational frequencies.  This web page will show how the best levels of theory was chose based upon calculated data for the molecular structures dinitrogen, formaldehyde, and ethyl benzene.


Di-Nitrogen


Formaldehyde


Ethyl Benzene



Conclusions

    In conclusion, computational results have great uses within the scientific world. These sorts of calculations can be used to more closely study the properties of molecules, especially new molecules, to understand and predict how they will interact with other substances. However, as much use these calculations have, there are weaknesses. These sorts of calculations can be considered too high for more simple systems and they may give heightened answers when higher basis sets are used. For situations like that, other calculations would be more appropriate. For example, taking in geometries that include unpaired electrons and removing the Huckel approximation will give better calculations as the system becomes more realistic.