Quantum Mechanical Insights into Biological Processes at the Electronic Level - Computational Modeling of Biological Systems - page 128

A slightly more elaborate multireference method is the Multiconfigurational
Self-Consistent Field (MCSCF), or its most commonly used variant the Complete
Active Space Self-Consistent Field (CASSCF) method [ 7 ]. It is similar to CI in
that the wave function is a linear combination of Slater determinants. However,
unlike in CI, in CASSCF the MOs inside of each determinant are also variationally
optimized. In this sense, CASSCF can be called multireference HF. The excited
state configurations are generated within the chosen active space. For example,
CASSCF(2,4) indicates that there are two active electrons that may be promoted
to higher MOs to form excited states, and the total number of MOs over which
these two electrons may be distributed is four (that includes the MOs initially
occupied by the two active electrons). Bigger active spaces typically mean higher
accuracy. If certain included excited states do not contribute to the wave function,
the coefficients in front of those determinants will be close to zero, but those
included determinants that appear to be important will have a chance to mix with
the reference configuration.
CI and CASSCF are methods that include static electron correlation, but are weak
in treating dynamic electron correlation. They can provide a hint for whether or not
a particular system has a multiconfigurational wave function, but cannot provide
very accurate results. Again, the simplest way to improve on a simpler solution is
to use the PT. Indeed, much like MP2 and MP3 improve the HF solution, CASPT2
and CASPT3 are used to improve the CASSCF solution [ 8 ]. These methods are the
second and third order, respectively, complete active space PT. They are known
to bring the results closer to the desired chemical accuracy, for species with
multiconfigurational wave functions. It is again important to remember that in order
for the PT to work, the reference CASSCF solution should be good enough, i.e.,
capture all the electronic configurations majorly contributing to the wave function.
In other words, the active space should be chosen carefully. Another known caveat
is that CASPT2 systematically overstabilizes states having more unpaired electrons,
and as a result the ground spectroscopic state may be determined incorrectly [ 9 ].
Most sophisticated variations that include much of static and dynamic correla-
tion for multireference methods are almost certainly prohibitively expensive for
biologically relevant calculations, at least until we learn to take a full advantage
of computing on GPU. However, it is worth mentioning that they exist. One
such method is multireference CI, MRCI, which forms a CI expansion, but the
components in the expansion are CASSCF wave functions, instead of single Slater
determinants [ 10 , 11 ]. Another method is multireference coupled cluster, MRCC
[ 12 , 13 ]. This is a young and promising method of exceptional accuracy, but it is
also exceptionally expensive computationally.
One thing to keep in mind about multireference calculations is that all of them
besides full-CI are not size consistent. This means that a particular truncated CI
active space does not provide equal amounts of electron correlation in calculations
of molecules of different sizes. As an implication, the dissociation limits of
molecules described by methods that are not size consistent will be slightly off.
What is often viewed as a sanctuary from the computational expense and
hardship of ab initio wave function methods, is a principally different approach