CHEM443 Physical Chemistry 1
Midterm Exam 1
October 7, 2011
Instructions: There are 5 questions for a total of 100 points. Please make sure to present your
solutions in a clear, logical, and legible m
two different (non-orthogonal) orbitals ( - x') and ( + x'). This picture is closely
related to the so-called generalized valence bond (GVB) model that W. A. Goddard and his
co-workers have developed
3
1
1
E
E(X) + E(Y)
1/2 [E(X) + E(Y) + E(Y) + E(X:)]
E(Y) + E(X:)
1
R
Configuration correlation diagram for a homonuclear case in which heterolytic bond
cleavage is energetically favored.
It is esse
The above strong CI mixing of 1 and 1* as R qualitatively alters the
configuration correlation diagrams shown above. Descriptions of the resulting valence
singlet and triplet states are given below fo
2
2
2
1e 2e
2
1
1e 1o
2
1
Even
1
Odd
2
1
1e 1o 2e
1
3
Odd
1
1e 2e 1o
1
Even
2
2
1e 1o
2
1e 2e
2
This SCD predicts that the thermal (i.e., on the ground electronic surface)
disrotatory rearrangement of
Section 3 Exercises, Problems, and Solutions
Review Exercises
1. For the given orbital occupations (configurations) of the following systems, determine
all possible states (all possible allowed combin
*
E
sY
sX
R
Re
Energies of the bonding and antibonding * orbitals as functions of internuclear distance.
Here, X is more electronegative than Y.
For the homonuclear case, as R approaches , the energie
1.
b. Forming SALC-AOs from the C and H atomic orbitals would generate the
following:
H
H
C
C
H
H
H1s + H1s = g = a1
H1s - H 1s = u = b2
H
H
H
H
C
C
H
H
C2s = a1
C
C
H
H
C2p = a1
C2p = b2
z
C2p = b1
y
1.
b. Remember that when coupling non-equivalent linear molecule angular momenta,
one simple adds the individual Lz values and vector couples the electron spin. So, in this
case (1 u12 u1), we have ML
7.
1
iv. 1D(ML=0,M S =0) = ( 2|p0p0| + |p 1p-1| + |p -1p1|)
6
Evaluating <1D(ML=0,M S =0)|H|1D(ML=0,M S =0)> we note that all the Slater Condon matrix
elements generated are the same as those evaluate
CHEM-443, Fall 2013, Section 010
Final Exam
Student Name_
December 9, 2013
Directions: Please answer each question to the best of your ability. Make sure your response is legible, precise,
includes re
CHEM-443, Fall 2013, Section 010
Quiz 1
Student Name_
August 30, 2013
Directions: Please answer each question to the best of your ability. Make sure your response is legible, precise,
includes relevan
In constructing the CCD, one must trace the energies of all four of the above CSFs
(actually there are more because the singlet and triplet excited CSFs must be treated
independently) along the propos
is the triplet CSF. In each case, the spin quantum number S, its z-axis projection MS , and
the quantum number are given in the conventional 2S+1 (MS) notation.
2. Orbital, CSF, and State Correlation
1. Orbitals, Configurations and States
The resultant family of six electronic states can be described in terms of the six
configuration state functions (CSFs) that arise when one occupies the pair of
Although, in principle, it is possible for some fraction of the events to follow the 1Odd
surface beyond this second intersection and to thus lead to 1Odd product molecules that
might fluoresce, quenc
to produce acetylene and 1D carbon is known to occur with an activation energy equal to
the reaction endothermicity. However, when triplet carbene decomposes to acetylene and
ground-state (triplet) ca
Even for the relatively simple two-electron, two-orbital single-bond interactions
between a pair of atoms or functional groups, the correlations among energy-ordered
molecular states and energy-ordere
1
E
1
3
E(Y) + E(X:)
1/2 [E(X) + E(Y) + E(Y) + E(X:)]
E(X) + E(Y)
1
R
Re
Configuration correlation diagram for homonuclear case in which homolytic bond cleavage
is energetically favored.
When hetero
III. Various Types of Configuration Mixing
A. Essential CI
The above examples of the use of CCD's show that, as motion takes place along the
proposed reaction path, geometries may be encountered at wh
1
E
3
1
E(X) + E(Y:)
E(X) + E(Y)
E(X:) + E(Y)
1
R
State correlation diagram for heteronuclear case in which heterolytic
bond cleavage to one product is energetically favored but homolytic
cleavage li
are substituted into the Slater determinant definitions of the CSFs. Here C and C* are the
normalization constants. The parameter z is 1.0 in the homonuclear case and deviates from
1.0 in relation to