does not necessarily give better geometries and better relative (i.e. activation and
reaction) energies. Why is this so?
The calculated geometry is a local (sometimes the global) minimum on a
Born–Oppenheimer surface. At that point altering the geometry by a small amount
leads to an increase in energy (the situation is more complicated if the point is a
transition structure). There is no necessary requirement that the energy of the
minimum be in any sense “good”, although in practice, methods that give good
geometries do tend to give reasonably good relative energies (reaction energies, less
reliably, activation energies).
Chapter 5, Harder Questions, Answers
Q9
Why is size-consistency in an ab initio calculation considered more important than
variational behavior (MP2 is size-consistent but not variational)?
Size-consistency in a method enables one to use that method to compare the
energy of a species (a molecule or a complex like the water dimer or a van der
Waals cluster) with its components; for example, one can compute the stability of
the water dimer by comparing its energy with that of two separate water molecules,
allowing for basis set superposition error. Lack of size consistency means we
cannot use the method to compare the energy of a system with that of its compo-
nents, and so limits the versatility of the method. Variational behavior is desirable,
because it assures us that the true energy of a system is less than (in theory the same,
but this is unlikely) our calculated energy, giving a kind of reference point to
aim for in a series of calculations, for example with increasingly bigger basis
sets. However, in practice the lack of variational behavior does not limit much
the usefullness of a method: all the correlated methods including current DFT,
except full CI (and with certain reservations CASSCF, a partial CI method) are not
variational.
Chapter 5, Harder Questions, Answers
Q10
A common alternative to writing a HF wavefunction as an explicit Slater determi-
nant is to express it using apermutation operatorP^which permutes (switches)
electrons around in MOs. Examine the Slater determinant for a two-electron closed-
shell molecule, then try to rewrite the wavefunction usingP^.
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