Geometry Optimization Methods


The objective of this exercise is to compare the optimized molecular geometry predicted by various computational methods to the experimental molecular geometry.


Fill in the following table comparing the C-C bond length (in angstroms) predicted by various computational methods for several molecules.

Molecule Clean-up PM3 Ab Initio [HF/6-311G+(d,p)] Experiment
ethane 1.540 1.509 1.541 1.531
ethene 1.540 1.322 1.318 1.339
ethyne 1.540 1.190 1.183 1.203
1,3-butadiene C1-C2 1.540 1.331 1.323 1.345
1,3-butadiene C2-C3 1.540 1.456 1.467 1.483

Describe each method and comment on its accuracy.
Clean-up: Clean-up sets the bond lengths to standard values obtained using a bond length lookup table. Clean-up Makes no compensation for bond order nor for electron delocalization. This method is the least accurate in all but the most simple cases. However, due to its simplicity, it is also extremely fast. The purpose of clean-up is to yield a reasonable starting point for more detailed optimization methods.

PM3: PM3 uses semi-empirical quantum mechanical calculations to attain moderately accurate results. PM3 calculations are extremely fast because they refrain from evaluating complex integrals, in favor of substituting values from experiment. However, this shortcut introduces inherent error into any semi-empirical calculation. The surprising accuracy of PM3 calculations in these instances arises from the fact that PM3 was optimized for organic molecules.

Ab Initio: This method yielded good results, very comparable with the semi-empirical, PM3 calculations. Unlike semi-empirical calculations, ab initio methods calculate every quantity from first principles. This makes ab initio calculations significantly more time consuming than semi-empirical calculations, but potentially far more accurate. The accuracy of the results could have been obtained by using a higher level of theory, or a larger basis set.

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