Tractable Valence Space Models for Strong Electron Correlations

Tuesday, September 30, 2008 - 9:00am - 9:50am
EE/CS 3-180
Martin Head-Gordon (University of California, Berkeley)
Wave function-based quantum chemistry has two traditional lines of
development – one based on molecular orbitals (MO's), and the other on
valence bond (VB) theory. Both offer advantages and disadvantages for
the challenging problem of describing strong correlations, such as the
breaking of chemical bonds, or the low-spin (antiferromagnetic)
coupling of electrons on different centers.

Within MO methods, strong correlations can be viewed as those arising
within a valence orbital active space. One reasonable definition of
such a space is to supply one correlating orbital for each valence
occupied orbital. Exact solution of the Schrodinger equation in this
space is exponentially difficult with its size, and therefore
approximations are imperative. The most common workaround is to
truncate the number of orbitals defining the active space, and then
solve the truncated problem, as is done in CASSCF. An important
alternative is to systematically approximate the Schrödinger equation
in the full valence space, for example by using coupled cluster theory
ideas. I shall discuss progress in this direction.

Within spin-coupled VB theory, the target wave function consists of a
set of non-orthogonal orbitals, one for each valence electron, that
are spin-coupled together into a state of the desired overall
spin-multiplicity. The number of active orbitals is identical with
the valence space MO problem discussed above, though the problem is
not identical. Exact solution of the VB problem is exponentially
difficult with molecular size, and therefore approximations are
imperative. Again, the most common approach is to seek the exact
solution in a truncated valence orbital space, where other orbitals
are simply treated in mean-field. It is possible, however, to also
consider approximations that do not truncate the space, but rather
reduce the complexity. A new way of doing this will be introduced and
contrasted with the MO-based approaches.
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