straightforward closed-shell species, and is a linear combination of a few determi-
nants for open-shell species.
If you don’t understand the above equation and its exegesis, recall Eq. 5.169
(therecwas used fora, the weighting, when squared, of the CSF/determinant in
the total wavefunction). That equation shows how in configuration interaction
theory (CASSCF is a version of CI) each electronic state, ground, first excited,
etc., has a total wavefunctionCwhich is a linear combination of determinants
(or CSFs, for open-shell species). Within each D, for example the determinant of
Eq. 5.167, we have a number of MOsc.
- Why does an occupation number (see question 3) close to 0 or 2 (less than ca.
0.02 and more than ca. 1.98) indicate that an orbital does not belong in the active
space?
We want to shuffle electrons around in the active space, i.e. promote (“excite”)
them from formally occupied to formally unoccupied MOs. An MO that is
essentially full or empty has not participated in this shuffling, an incomplete
transfer process. - It has been said that there is no rigorous way to separate static and dynamic
electron correlation. Discuss.
First let us review static and dynamic electron correlation. Dynamic (dynamical)
electron correlation is easy to grasp, if not so easy to treat exhaustively. It is simply
the adjustment by each electron, at each moment, of its motion in accordance with
its interaction with each other electron in the system. Dynamic correlation and its
treatment with perturbation (Møller–Plesset), configuration interaction, and cou-
pled cluster methods was covered inSection 5.4.
Static (nondynamical) electron correlation refers to phenomena arising from the
presence in a molecule of two (or more) orbitals of the same or similar energy, each
formally half-filled.Section 5.4: “Static correlation energy is the energy a calcula-
tion (Hartree–Fock or otherwise) may not account for because it uses a single
determinant, or starts from a single determinant (is based on a single-determinant
reference –Section 5.4.3); this problem arises with singlet diradicals, for example,
where a closed-shell description of the electronic structure is qualitatively wrong”.
This phenomenon is “static” because it has no clear connection with motion, but it
is not clear why it should be regarded as acorrelationeffect; possibly just because
like dynamic correlation it is not properly handled by the Hartree–Fock method.
The treatment of static correlation by complete active space SCF is shown in some
detail inSection 8.2.
Is there no rigorous way to separate static and dynamic electron correlation?
Dynamic correlation is present in any system with two or more electrons, but static
correlation requires degenerate or near-degenerate partially-filled orbitals, a feature
absent in normal closed-shell molecules. So in this sense they are separate phenom-
ena. In another sense they are intertwined: methods that go beyond the Hartree–
Fock in invoking more than one determinant, namely CI and its coupled cluster
variant, improve the handling of both phenomena.
Answers 651