To generate the molecules you see below you, three separate calculations involving the molecular oribitals and their associated electrons had to be performed. 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 thoery accounts for the overlap between atomic orbitals 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.
The following depictions of nitrobenzoic acid are based on the types of molecular orbital calculations performed.
While the figures above look very similar, the assumptions
underlying each of the associated calculations can result in dramatic
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 (i.e. bonds angles) 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.
Not all of the molecular orbitals calculated by each model contribute equally to the overall properties of cyclohexane. 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 (listed by the molecular orbital number) provides a more stable environment for electrons to exist and interact with neighboring nuclei and
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The identification of the HOMO and LUMO molecular orbitals are critical in understanding the manner in which a reaction takes place. As these are the sites which contain the most energetically unstable electrons (HOMO) and most willing to accept electrons (LUMO), it follows that these are the orbitals most involved in chemical reactions . A common example of a chemical reaction which can be used to illustrate the importance of HOMO and LUMO orbitals is a redox reaction. Consider the process of rusting in which neutral iron atom loses electrons to oxygen. More specifically, the redistrubution of electrons from the HOMO orbital of iron atom to the LUMO orbital 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, the ability to identify HOMO and LUMO orbitals can be used to predict if a proposed reaction will occur. Below are molecular orbitals generated from the MOPAC model.
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.
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MOPAC |
The diagram of cyclohexane below at left provides an excellent example of this. As its electrons carry a negative charge, the increased probability that they will be found in a certain region of the molecule effectively polarizes the molecule. Due to the repulsion of like forces, electrons will naturally distrubute themselves to be as far away as possible from other electrons. Notice that in the diagram shown below, the electron density is the greatest at of the electron cloud. That is if the position of electrons were plotted over time, the most, frequently populated regions would be near the perimeter. Electron density decreases as the color grows lighter. Therefore the six blue regions (carbon atoms) correspond to areas of highest electron density. |
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 charge regions requires that equally postive charged regions must exist if the overall molecule is going to remain neutral. Notice that areas of expected high negative charge (the outer limits) are colored in blue. These areas are balanced by the electron defient regions left within the interior.
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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 concentrated regions is a property of individual atoms known as electronegativity. The tendency of electrons to gather near highly electronegative atoms is related to the strength of attraction to its nucleus. Small molecules with 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. Notice how uniform the atomic charge is over the cyclohexane molecule. This is a result of how symmetric the electronegative carbon atoms are arranged. |
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. The following table lists the dipole moment values calculated by the type of model structure by the model used to produce them.
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Extended Huckel |
0.002 |
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MOPAC |
0.002 |
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ZINDO |
0.000 |
MOPAC