c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come
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QUANTUM MOLECULAR MODELING
With Slater determinants and the Hartree–Fock equations, one had everything neces-
sary to solve problems in molecular structure, energy, and dynamics. But the equa-
tions could not be solved. Quantum chemistry awaited two spectacular advances.
First, Roothaan derived a way to express its apparently insoluble integrodifferential
equations as equations in linear algebra. This was accompanied by an exponential
rise in power of the digital computer, which now routinely carries out trillions of
simple mathematical operations per second.
The total energy of a molecule is almost entirely that of its constituent atoms,
leaving only a fringe energy, which might otherwise be considered trivial, to hold
the molecule together. But it is thechemical bondthat dominates the world we see
around us with all its color, life, and diversity, and so it is the chemical bond that
we seek to calculate. We will be able to extend the atomic orbital concept to our
molecular calculations but, because chemical energies and energy differences are so
small, we must achieve a very high level of accuracy. Accurate programs now exist
that can be extended to all molecules (in principle at least). Finite computer speed
and memory place strict limitations on these grandiose plans, but barriers fall almost
every day in this active research field.20.1 THE MOLECULAR VARIATIONAL METHODThe variational method applies to molecules as well as to atoms. By it, we can
approach an optimized molecular energyE:E=〈|Hˆ|〉
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Concise Physical Chemistry,by Donald W. Rogers
Copyright©C2011 John Wiley & Sons, Inc.
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