Theoretical Calculations of Properties of m-Xylene

by Stacy Mundschau

Types of calculations performed

To generate the molecules shown below, three separate calculations involving the molecular orbitals and their associated electrons were performed by CAChe software. Due to the complexity involved in describing these shapes mathematically, assumptions concerning the extent to which these orbitals interact had to be made. Each set of assumptions, refered to as the Extended Huckel, MOPAC or ZINDO, varies in the treatment of these interacting, or overlapping, orbitals. While providing a simple method to generate molecular values, the Extended Huckel theory can not match the agreement that MOPAC and ZINDO calculations have with values determined in the laboratory. The degree to which each theory accounts for the overlap between molecules is a result of their dependence on a field of science known as quantum mechanics. Particles decribed by quantum mechanics exist at the atomic level (i.e electrons) and do not behave like the macroscale objects we encounter. The superior accuracy of the ZINDO and MOPAC models is thus a result of their reliance on quantum mechanical based modeling. the ZINDO and MOPAC models relied on empirical data gathered from spectroscopy studies.

Results of geometry optimization at various levels of theory

The following depictions of m-xylene are based on the types of molecular orbital calculations performed.

Extended Huckel 



While the figures above look very similar, the assumptions underlying each of the associated calculations can result in drastic differences in the molecule's structure. The Extended Huckel theory treats molecules as the familar balls linked to one another with sticks. The geometry the molecule is governed by the bonds between balls acting as stiff springs. ZINDO and MOPAC use the principles of quantum mechanics to determine the most likely shape of the model, based on the lowest calculated energy value. This results in a much more complete mathematical treatment of the molecule, and thus provides more accurate molecular property values and depictions.

The molecular orbitals that provide the primary bonding

Not all of the molecular orbitals calculated by each model contribute equally to the overall properties of m-xylene. Each theory's calculations essentially "weight" the significance of each orbital. The orbitals selected below are by no means all of the molecular orbitals that exist. However, their low energy provides a more stable environment for electrons to exist and interact with neighboring nuclei and electrons. Selected bonding orbitals of the aromatic ring found using ZINDO calculations are provided below.

The highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals

The identification of the HOMO and LUMO molecular orbitals are critical in understanding the manner in which a chemical reaction takes place. As these are the sites which contain the most energetically unstable electrons (HOMO) or are most willing to accept electrons (LUMO), It follows that these are the orbitals most involved in chemical reactions . A redox reaction can be used to illustrate the importance of HOMO and LUMO orbitals. Consider the process of rusting in which neutral iron loses electrons to oxygen. More specifically, the redistrubution of electrons from the HOMO orbital of iron atom to the LUMO orbtial of oxygen weakens the bonds between oxygen atoms. The decreased bond strength between oxygen atoms drives the cleavage of the oxygen molecule and the simultaneous oxidation of iron. In addition to explaining reactions, identifying HOMO and LUMO orbitals can be used to predict if a proposed reaction will occur.

Electron density/distribution maps

 In addition to determining the shape and energies of the molecular orbitals, each theory is able to model how the electrons will arrange themselves over the molecule. That is, these calculations will show where the electrons will most likely be in a concerted effort to lower the overall energy of the molecule. The left diagram of m-xylene shows the relative uniformity of electron density through out the aromatic ring. Recall that aromatic rings are molecules commonly represented by rings whose double bonds "flip" or resonate to alternating positions in the molecule. The diagram on the right shows the electron deficent regions on the methyl groups hydrogens. As electrons carry a negative charge, the increased probability that they will be found in a certain region results in a localized polarization of the molecule.
(this space contained an image of
Nitrobenzoic acid by mistake)

Image of m-xylene

Charge distribution maps

This tendency of electrons to polarize certain regions of the molecules allows for the intramolecular (inside of the molecule) charge to be depicted. It is important to mention that the prescece of negatively charged regions requires that equally postive charged regions must exist if the overall molecule is going to remain neutral.
So why does electron redistribution to certain regions of the molecule result in lower energies than in other arrangements? Essentially what accounts for this hoarding of electrons into specific regions is a property of individual atoms known as electronegativity. The tendency of electrons to gather near highly electronegative atoms is explained by the strength of attraction to its nucleus. Small molecules with few electrons "shielding" other electrons from its nucleus give rise to the most electronegative atoms. This pattern is reflected in the general increase of electronegativity moving up the periodic table and to the right (excluding the noble gases) The partial atomic charge, or the charge that each atom within a molecule experiences, is determined by the electronegativities of its neighbors. 
As m-xylene contains no atoms that are particularly electronegative compared to the neighbors, the partial atomic charge is relatively uniform throughout the molecule. This is shown by the continuous red cloud surrounding the xylene molecule.

Calculated dipole moments

By determing the molecular orbitals and regions of charge distribution through mathematical models, calculating overall the dipole moment of the molecule is possible. The dipole moment is a vector that shows how the charge is distributed in a molecule. It can be thought of as the net sum of the individual dipoles within the molecule. The following table lists the dipole moment values calculated by the type of model structure.
Ext.ended Huckel  0.711 
ZINDO  0.517 
MOPAC  0.254 
The Handbook of Chemistry and Physics lists ortho xylene's dipole moment as 0.640.