Computational Chemistry

3. What is the simplest singlet diradical hydrocarbon species?


4. Which MOs would be appropriate for CASSCF calculations on
   (1) the ring-opening of cyclobutene to 1,3-butadiene?
   (2) the Diels-Alder reaction?


5. How many CI configurations are used in
   (1) a CASSCF(2,2) calculation?
   (2) a CASSCF(2,3) calculation?

Harder Questions.........................................................

1. Is CASSCF size-consistent?


2. In one-determinant HF (i.e. SCF) theory, each MO has a unique energy (eigen-
   value), but this is not so for the active MOs of a CASSCF calculation. Why?


3. In doubtful cases, the orbitals really needed for a CASSCF calculation can
   sometimes be ascertained by examining theoccupation numbersof the active
   MOs. Look up this term for a CASSCF orbital.


4. Why does an occupation number (see question 3 above) close to 2 or 0 (more
   than ca. 1.98 and less than ca. 0.02) indicate that an orbital does not belong in the
   active space?


5. It has been said that there is no rigorous way to separate static and dynamic
   electron correlation. Discuss.

Heavy Atoms and Transition Metals........................................

Easier Questions..........................................................

1. Suggest a simple physical property of an atom for which a comparison of
   experiment with a calculated value might be used a test of whether the atom
   should be regarded as being “heavy” (hint: consider the energy of the valence
   electrons).


2. Suggest a simple property of a compound of elementXfor which a comparison
   of experiment with a calculated value might be used a test of whether elementX
   should be regarded as being “heavy”.


3. Dirac, the discoverer of the relativistic one-electron equation, thought that
   relativity would be unimportant in chemistry (P. A. M. Dirac, “Quantum
   Mechanics of Many-Electron Systems”, Proceedings of the Royal Society of
   London. Series A, Mathematical and Physical Sciences, 1929, 123 (792), 714).
   Why was he mistaken?


4. Of the first 100 elements, how many are transition metals?


5. Use the simple semiclassical Bohr equation for the velocityvof an electron in an
   atom (Eq. 4.12, to calculate a value ofvforZ¼100 and energy leveln¼1:

Heavy Atoms and Transition Metals 559