Chemistry Reference
In-Depth Information
systems, convergent plane-wave expansions, and alternative statistical repre-
sentations such as the Thomas-Fermi theory for electron densities.
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It is inter-
esting that most of the recent real-space developments have come out of
academic physics groups and national laboratories around the world, with
the initial motivation often being the modeling of nanostructures. It is likely
that the real-space, localized orbital ideas will have growing influence in chem-
istry in the future since a great deal of modern chemical research is directed at
nanosystems and biological macromolecules. Sometimes it takes a decade or
more for a major shift to take hold.
Elimination of Molecular Orbitals?
As discussed above, wave functions and basis set expansions have had a
wide influence in chemistry. But long ago, Coulson suggested that quantum
chemical computations should focus instead on the one- and two-electron den-
sity matrices
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because these physical quantitites yield a much-reduced, yet
complete, description of the electronic structure. This goal has been pursued
off and on since Coulson's comments, and there continue to be developments
in this area.
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It is likely that this way of looking at electronic structure will
have a large impact in the future, perhaps coupled with ideas from quantum
Monte Carlo methods and stochastic differential equations.
254
An even more
aggressive step away from wave functions is the integral formulation of
DFT.
110,255,256
While there has been significant interest in this formal theory,
and some developments of orbital-free methods,
257,258
this appproach has not
reached its full potential in computational electronic structure. It is the one
approach to DFT that is truly in the spirit of the Hohenberg-Kohn theorem
because the only object that enters the theory is the physical electron density.
Larger Scale DFT, Electrostatics, and Transport
Ever-larger systems are being examined in biochemical and biophysical
research, as exemplified by studies on microtubules and the ribosome,
218
and
new algorithms and more powerful massively parallel machines will propagate
this trend. In terms of increased complexity, the author believes that more and
more biological phenomena will be shown to require a quantum treatment, at
least in a local region of space. An example discussed in this chapter is the solva-
tion of anions in ion channels and in water where the polarizability is an impor-
tant physical quantity linked to the pervasive Hofmeister series that continues to
crop up in a wide array of biological and colloid systems.
39
Quantum effects are
also important for studies of reaction dynamics where tunneling occurs as out-
lined by Truhlar et al. in a previous volume of this series.
259
It might seem that
ever-larger computers will lead the way, but the author predicts that novel algo-
rithms and new physical ideas will ''win out'' over hardware advances in how
we model complex chemical and biological phenomena. Of course, these
