Essentials of Computational Chemistry

162 5 SEMIEMPIRICAL IMPLEMENTATIONS OF MO THEORY
TS structures leading to different enantiomers, a %ee of 0 would result from equal TS
energies, a %ee of 82 from relative energies of 1.4 kcal mol −1 , and a %ee of 98 from
relative energies of 2.8 kcal mol −1 . Given this analysis, the near quantitative agreement
between PM3 and those experimental cases showing %ee values below 90 reflects startlingly
good accuracy for a semiempirical level of theory.
Armed with such solid agreement between theory and experiment, Goldfuss and Houk
go on to analyze the geometries of the various TS structures to identify exactly which interactions
lead to unfavorably high energies and can be used to enhance chiral discrimination.
They infer in particular that the optimal situation requires that the alkoxide carbon atom be
substituted by two groups of significantly different size, e.g., a hydrogen atom and a bulky
alkyl or aryl group. This work thus provides a nice example of how preliminary experimental
work can be used to validate an economical theoretical model that can then be used
to suggest future directions for further experimental optimization. However, it must not be
forgotten that the success of the model must derive in part from favorable cancellation of
errors – the theoretical model, after all, fails to account for solvent, thermal contributions
to free energies, and various other possibly important experimental conditions. As such,
application of the model in a predictive mode should be kept within reasonable limits,
e.g., results for new β-amino alcohol structures would be expected to be more secure than
results obtained for systems designed to use a substituted 1,2-diaminoethane ligand in place
of the β-amino alcohol.
Bibliography and Suggested Additional Reading
Clark, T. 2000. ‘Quo Vadis Semiempirical MO-theory?’ J. Mol. Struct. (Theochem), 530, 1.
Dewar, M. J. S. 1975. The PMO Theory of Organic Chemistry, Plenum: New York.
Famini, G. R. and Wilson, L. Y. 2002. ‘Linear Free Energy Relationships Using Quantum Mechanical
Descriptors’, in Reviews in Computational Chemistry, Vol. 18, Lipkowitz, K. B. and Boyd, D. B.,
Eds., Wiley-VCH: New York, 211.
Hall, M. B. 2000. ‘Perspective on “The Spectra and Electronic Structure of the Tetrahedral Ions
MnO4 − ,CrO4 2− ,andClO4 − ”’ Theor. Chem. Acc., 103, 221.
Hehre, W. J. 1995. Practical Strategies for Electronic Structure Calculations, Wavefunction: Irvine,
CA.
Jensen, F. 1999. Introduction to Computational Chemistry, Wiley: Chichester.
Levine, I. N. 2000. Quantum Chemistry, 5th Edn., Prentice Hall: New York.
Pople, J. A. and Beveridge, D. A. 1970. Approximate Molecular Orbital Theory, McGraw-Hill:
New York.
Repasky, M. P., Chandrasekhar, J., and Jorgensen, W. L. 2002. ‘PDDG/PM3 and PDDG/MNDO:
Improved Semiempirical Methods’, J. Comput. Chem., 23, 1601.
Stewart, J. J. P. 1990. ‘Semiempirical Molecular Orbital Methods’ in Reviews in Computational Chemistry,
Vol. 1, Lipkowitz, K. B. and Boyd, D. B., Eds., VCH: New York, 45.
Thiel, W. 1998. ‘Thermochemistry from Semiempirical Molecular Orbital Theory’ in Computational
Thermochemistry, ACS Symposium Series, Vol. 677, Irikura, K. K. and Frurip, D. J., Eds., American
Chemical Society: Washington, DC, 142.
Thiel, W. 2000. ‘Semiempirical Methods’ in Modern Methods and Algorithms of Quantum Chemistry,
Proceedings, 2nd Edn., Grotendorst, J., Ed., NIC Series, Vol. 3, John von Neumann Institute for
Computing: Jülich, 261.
Whangbo, M.-H. 2000. “Perspective on ‘An extended Hückel theory. I. Hydrocarbons”’ Theor. Chem.
Acc., 103, 252.