Computational Chemistry

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

1. State the arguments for and against regarding DFT as being more a semiem-
   pirical than an ab initio-like theory.


2. What is the essential difference between wavefunction theory and DFT? What
   is it that, in principle anyway, makes DFT simpler than wavefunction theory?


3. Why can’t current DFT calculations be improved in a stepwise, systematic
   way, as can ab initio calculations?


4. Which of these prescriptions for dealing with a function are functionals: (1)
   square root off(x). (2) sinf(x). (3)

P^3

x¼ 1

fðxÞ. (4)

Ð

fðxÞdx. (5) exp(f(x)).

5. For which class(es) of functions is thenth derivative off(x) a functional?


6. Explain why a kind of molecular orbital is found in current DFT, although
   DFT is touted as an alternative to wavefunction theory.


7. What is fundamentally wrong with functionals that are not gradient-cor-
   rected?


8. The ionization energy of a molecule can be regarded as the energy required to
   remove an electron from its HOMO. How then would a pure density func-
   tional theory, with no orbitals, be able to calculate ionization energy?


9. Label these statements true or false: (1) For each molecular wavefunction there
   is an electron density function. (2) Since the electron density function has only
   x,y,zas its variables, DFT necessarily ignores spin. (3) DFT is good for
   transition metal compounds because it has been specifically parameterized to
   handle them. (4) In the limit of a sufficiently big basis set, a DFT calculation
   represents an exact solution of the Schr€odinger equation. (5) The use of very big
   basis sets is essential with DFT. (6) A major problem in density functional
   theory is the prescription for going from the molecular electron density function
   to the energy.


10. Explainin wordsthe meaning of the terms electronegativity, hardness, and the
    Fukui function.

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

1. It is sometimes said that electron density is physically more real than a
   wavefunction. Do you agree? Is something that is more easily grasped intui-
   tively necessarily more real?


2. A functional is a function of a function. Explore the concept of a function of a
   functional.


3. Why is it that the Hartree–Fock Slater determinant is an inexact representation
   of the wavefunction, but the DFT determinant for a system of noninteracting
   electrons is exact for this particular wavefunction?


4. Why do we expect the “unknown” term in the energy equation (EXC[r 0 ], in
   Eq.7.21) to be small?

518 7 Density Functional Calculations