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Chem 216 Please do not open this examination until the TA's say you may
do so. Please check that there are 3 questions in your exam.
Problems 1 and 2 are on two pages each. Problem 3 is on a
single sheet. The TA's have been told not to answer any
questions during the examination period. If you finish the
examination at least 15 minutes before the end of the exam you
may turn the exam in. Otherwise please wait at your desk for
your exam to be picked up by a TA. Please note this is a Chem 216 exam. F: i Name: Day of the
week your
lab meets: Question 1:
Question 2:
Question 3: TOTAL: s 18 eV while that of a carbon p
lecule below. In the answer box ta. (10 pts) The energy of an oxygen porbital i
se the indicated vectors in orbital is 12 eV. Consider the Icsystem oi the mo
' ' ' this ticsystem. Please u please write the Hamiltonian for
expressing your Hamiltonian as a matrix. Assume, as we did in class, that interactions between all b
interactions between unbonded atoms. O\C—‘_C/O
H/ \H equal to B and that there are no ;;;i;es_$ize;;t.s:e,.,..,,_,; ,t"§._A_‘_ : __ 1b. (18 pts) Let x and y be real positive numbers and assume x and y are not
equal to one another. Consider the n—molecular orbitals of the molecule illustrated in
Problem ‘la. As in the previous problem we define the individual atomic orbitals as follows: Whigh of the following can not be energy eigenvectors for any positive value of x
or y. 2a. ( 10 pts) Consider the n—molecular orbitals of the molecule illustrated below.
rfectly square shape. In class when we derived the Assume the molecule has a pa
'dered the two mutually perpendicular mirror MO diagram for this molecule we cons:
planes illustrated in the middle drawing. Please now use the alternate set of mutually perpendicular mirro r planes indicated on the drawing on the right. H H
\CMC/
M
/ \
H H s, draw the n—molecular orbital diagram in the With respect to these new mirror plane
electrons filling each orbital. box provided below. Please indicate the number of
ANSWER: ‘\: ":43: 5:21: ~  21:: '1 “:C'? at as r .q A r. us “is 7:
... 2b. (25 pts) Consider the trmolecuiar orbitals of the molecule illustrated below.
Assume the center ring oi the molecule has a perfectly square shape. Just as we
considered in class, consider the perturbation of the 0H o—bonding orbital
(illustrated on the right) on the n—MO diagram. in the box provided below draw this
perturbed rtMO diagram, indicating the number of electrons filling each orbital. 2c. (5 points) Based on your MO diagram, indicate the most probable site for
attack by H”. State succinctly your reasohing for this answer. 3. (32 pts) Consider the n~molecuiar orbitals of the molecule illustrated below. In
the box provided below please draw its n~M0 diagram, indicating the number of
. electrons filling each orbital. ENERGY 3b, ( 6 points) Based on your MO diagram, indicate the most probable site for attack by H“. State succinctly
ur reasoning for thi newer. ' «CW 1
art» ~~/ New Ace
wow as it“; .: :.‘._:.._:~¢_>Q:..a "1—53?" ::w.u.5..«h....~wuw...~ mm; “0:, d
it
p,
«1’
‘2 5. (25 pts) The rt—MO diagram for molecule a, illustrated below, is also shown
below. Energy An electron starts off in the orbital, 2 . If one measmes the energy compare the probability it is found to be in the states ‘1’1 , ‘1’2, “113, or ‘P4 ? If two probabilities are equal, please state that they are equal. ANSWER BOX: least probable most probable uare cyclobutadiene is shown below. An electron is initially in the state ‘1’. The energy is then measured. What are the
possible energies measured in this case? For each energy what are the
corresponding probablities? What is the average measured energy? 6. (25 pts) The n—MO diagram for sq ANSWER BOX: ...
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 Spring '08
 LEE, S

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