energy minimization, and LCAO. Using these, summarize the steps leading to
the Roothaan–Hall equationsFC¼SC«.- What are the similarities and the differences between the basis set of the
extended H€uckel method and the ab initio STO-3G basis set? - In the simple and extended H€uckel methods, the molecular orbitals are calcu-
lated and then filled from the bottom up with the available electrons. However,
in ab initio calculations the occupancy of the orbitals is taken into account as
they are being calculated. Explain.
Hint: look at the expression for the Fock matrix elements in terms of the density
matrix. - Isodesmic reactions have been used to investigate aromatic stabilization, but
there is not a unique isodesmic reaction for each problem. Write two isodesmic
reactions for the ring-opening of benzene, both of which have on each side of
the equation the same number of each kind of bond. Have you any reason to
prefer one of the equations to the other? - List the strengths and weaknesses of ab initio calculations compared to molec-
ular mechanics and extended H€uckel calculations. State the molecular features
that can be calculated by each method.
Harder Questions.............................................................
- Does the termab initioimply that such calculations are “exact”? In what sense
might ab initio calculations be said to be semiempirical – or at least not a
priori? - Can the Schr€odinger equation be solvedexactlyfor a species with two protons
and one electron? Why or why not? - The input for an ab initio calculation (or a semiempirical calculation of the type
discussed inChapter 6, or a DFT calculation –Chapter 7) on a molecule is
usually just the cartesian coordinates of the atoms (plus the charge and multi-
plicity). So how does the program know where the bonds are, i.e. what the
structural formula of the molecule is? - Why is it that (in the usual treatment) the calculation of the internuclear
repulsion energy term is easy, in contrast to the electronic energy term? - In an ab initio calculation on H 2 or HHeþ, one kind of interelectronic interac-
tion does not arise; what is it, and why? - Why are basis functions not necessarily the same as atomic orbitals?
- One desirable feature of a basis set is that it should be “balanced.” How might a
basis set be unbalanced? - In a Hartree–Fock calculation, you can always get a lower energy (a “better”
energy, in the sense that it is closer to the true energy) for a molecule by using a
bigger basis set, as long as the HF limit has not been reached. Yet a bigger basis
set does notnecessarilygive better geometries and better relative (i.e. activa-
tion and reaction) energies. Why is this so?
Harder Questions 389