Computational Chemistry

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

1. What do you understand by the term quantum mechanics?


2. Outline the experimental results that led to quantum mechanics.


3. What approximations are used in the simple H€uckel method?


4. How could the SHM Fock matrix for 1,3-butadiene be modified in an attempt to
   recognize the fact that the molecule has, formally anyway, two double bonds
   and one single bond?


5. What are the most important kinds of results that can be obtained from H€uckel
   calculations?


6. Write down the simple H€uckel Fock matrices (in each case usinga,band 0,
   and 0,"1 and 0) for: (1) the pentadienyl radical (2) the cyclopentadienyl
   radical (3) trimethylenemethane, C(CH2)3 (4) trimethylenecyclopropane (5)
   3-methylene-1,4-pentadiene.


7. The SHM predicts the propenyl cation, radical and anion to have the same
   resonance energy (stabilization energy). Actually, we expect the resonance
   energy to decrease as we addpelectrons; why should this be the case?


8. What molecular feature cannot be obtained at all from the simple H€uckel
   method? Why?


9. List the differences between the underlying theory of the simple H€uckel
   method and the extended H€uckel method.


10. A 400&400 matrix is easily diagonalized. How many carbons would an alkane
    have for its EHM Fock matrix to be 400&400 (or just under this size)? How
    many carbons would a (fully) conjugated polyene have if its SHM Fock matrix
    were 400&400?

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

1. Do you think it is reasonable to describe the Schr€odinger equation as a
   postulate of quantum mechanics? What is a postulate?


2. What is the probability of finding a particle at a point?


3. Suppose we tried to simplify the simple H€uckel method even further, by
   ignoring all interactions i, j; i 6 ¼j (ignoring adjacent instead interactions of
   setting them¼b). What effect would this have on energy levels? Can you see
   the answer without looking at a matrix or determinant?


4. How might the i,j-type interactions in the simple H€uckel Fock matrix be made
   to assume values other than just"1 and 0?


5. What is the result of using as a reference system for calculating the resonance
   energy of cyclobutadiene, not two ethene molecules, but 1,3-butadiene? What
   does this have to do with antiaromaticity? Is there any way to decide if one
   reference system is better than another?

172 4 Introduction to Quantum Mechanics in Computational Chemistry