Computational Chemistry

Chapter 5

Ab initio Calculations

“I could have done it in a much more complicated way”, said the Red Queen,

immensely proud.

Attributed, probably apocryphally, to Lewis Carroll

AbstractAb initio calculations rest on solving the Schr€odinger equation; the
nature of the necessary approximations determines the level of the calculation. In
the simplest approach, the Hartree–Fock method, the total molecular wavefunction
Cis approximated as a Slater determinant composed of occupied spin orbitals. To
use these in practical calculations the spatial orbitals are approximated as a linear
combination (a weighted sum) of basis functions. Electron correlation methods are
also discussed. The main uses of the ab initio method are calculating molecular
geometries, energies, vibrational frequencies, spectra, ionization potentials and
electron affinities, and properties like dipole moments which are connected with
electron distribution. These calculations find theoretical and practical applications,
since, for example, enzyme–substrate interactions depend on shapes and charge
distributions, reaction equilibria and rates depend on energy differences, and
spectroscopy plays an important role in identifying and understanding novel mole-
cules. The visualization of calculated phenomena can be very important in inter-
preting results.

5.1 Perspective..............................................................

Chapter 4showed how quantum mechanics was first applied to molecules of
real chemical interest (pacechemical physics) by Erich H€uckel, and how the
extension of the simple H€uckel method by Hoffmann gave a technique of consider-
able usefulness and generality, the extended H€uckel method. The simple and the
extended H€uckel methods (SHM and EHM) are both based on the Schr€odinger
equation, and this makes them quantum mechanical methods. Both depend on

E.G. Lewars,Computational Chemistry,
DOI 10.1007/978-90-481-3862-3_5,#Springer ScienceþBusiness Media B.V. 2011

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