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Chapter 5 Self-test questions
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Chapter 5 Self-test questions
Geometry Optimization
Quiz Content
*
not completed
.
One of the following reactions is unimolecular, while the others are bimolecular. Identify the unimolecular reaction.
C
_{6}
H
_{5}
SNa + C
_{2}
H
_{5}
Cl → C
_{6}
H
_{5}
SC
_{2}
H
_{5}
+ NaCl
correct
incorrect
NO
_{2}
^{+}
+ C
_{6}
H
_{6}
→ [C
_{6}
H
_{6}
-NO
_{2}
]
^{+}
correct
incorrect
CH
_{3}
-CH(BH
_{2}
)-CH
_{3}
→ CH
_{3}
-CH
_{2}
-CH
_{2}
-BH
_{2}
correct
incorrect
CH
_{3}
-CH=CH
_{2}
+ O
_{3}
→ ozonide
correct
incorrect
*
not completed
.
Which of the following reactions or processes would necessarily involve a potential energy barrier? (The others could involve uniformly attractive potential energy surfaces.)
Cr(CO)
_{5}
+ PPh
_{3}
→ (OC)
_{5}
Cr−PPh
_{3}
correct
incorrect
CH
_{3}
+ C
_{2}
H
_{5}
→ CH
_{3}
-CH
_{2}
-CH
_{3}
correct
incorrect
CH
_{3}
COOC
_{2}
H
_{5}
+ H
_{2}
O → CH
_{3}
COOH + C
_{2}
H
_{5}
OH
correct
incorrect
CH
_{3}
NH
_{3}
^{+}
+ CH
_{3}
OH → CH
_{3}
NH
_{3}
^{+}
…HOCH
_{3}
correct
incorrect
*
not completed
.
To characterize the potential energy surface for the rearrangement of hydrocyanic acid HCN to hydrogen isocyanide HNC,
ab initio
calculations are performed for different values of the H-C distance, the C-N distance, and the H-C-N angle. Assuming 5 different C-N distances, 15 different H-C distances, and 15 different angles are considered, how many calculations are needed in total?
1,125
correct
incorrect
35
correct
incorrect
90
correct
incorrect
232
correct
incorrect
*
not completed
.
Considering the steepest descent optimization algorithm and second-order methods such as that suggested by Broyden, Fletcher, Goldfard and Shanno (BFGS), which of the following statements is not correct?
Both the steepest descent and BFGS method require access to the energy and the gradient of the energy.
correct
incorrect
The BFGS method is so complicated that in most cases, it is easier just to use the steepest descent method despite the fact that it is less efficient.
correct
incorrect
The steepest descent method does not rapidly converge to a point very close to the minimum in most cases.
correct
incorrect
The steepest descent method is simpler and thereby easier to program.
correct
incorrect
*
not completed
.
Geometry optimization can be carried out using Cartesian coordinates, a minimal set of internal coordinates, or redundant internal coordinates. In the case of ethanol C
_{2}
H
_{5}
OH, what are the minimum number of coordinates needed to define the internal structure, the number of Cartesian coordinates, and the number of redundant internal coordinates, respectively?
21 internal coordinates, 27 Cartesian coordinates and 120 redundant internal coordinates, respectively.
correct
incorrect
27, 27 and 27.
correct
incorrect
21, 27 and 33.
correct
incorrect
21, 27 and 27.
correct
incorrect
*
not completed
.
For a non-linear molecule with
N
atoms, there are 3
N−
6 vibrational frequencies. At a transition state structure, one of these 'frequencies' corresponds to the reaction coordinate, so there is one fewer vibrational frequency. How many vibrational frequencies will there be for the TS of the Diels-Alder cycloaddition of ethene and 1,3-butadiene?
16
correct
incorrect
41
correct
incorrect
48
correct
incorrect
9
correct
incorrect
*
not completed
.
Which of the following is not a method to locate transition states structures?
Quasi-synchronous transit method
correct
incorrect
Relaxed scan method
correct
incorrect
Nudged elastic band method
correct
incorrect
Periodic boundary conditions
correct
incorrect
*
not completed
.
There are three different minima on the potential energy surface for
n
-butane, due to rotation around the central C
^{B}
-C
^{C}
bond (we neglect chemically identical conformers obtained by rotating around the C
^{A}
-C
^{B}
and C
^{C}
-C
^{D}
bonds). How many different conformers do you expect for hexane?
9
correct
incorrect
27
correct
incorrect
3
correct
incorrect
18
correct
incorrect
*
not completed
.
In order to locate transition state structures, a scan along some coordinates, as shown in Fig. 5.15, is frequently used. Consider the Cope rearrangement of 1,5-hexadiene H
_{2}
C
^{A}
=C
^{B}
H-C
^{C}
H
_{2}
-C
^{D}
H
_{2}
-HC
^{E}
=C
^{F}
H
_{2}
to an isomeric form H
_{2}
C
^{D}
=C
^{E}
H-C
^{F}
H
_{2}
-C
^{A}
H
_{2}
-HC
^{B}
=C
^{C}
H
_{2}
. Which of the following coordinates could be scanned in order to locate the region of the transition state?
The distance between C
^{A}
and C
^{B}
correct
incorrect
The distance between C
^{A}
and C
^{C}
correct
incorrect
The distance between C
^{A}
and C
^{E}
correct
incorrect
The distance between C
^{A}
and C
^{F}
correct
incorrect
*
not completed
.
Which of the following is not a property of transition state structures on a potential energy surface?
TSs are relatively low energy points separating one low-energy region on the surface from another region.
correct
incorrect
Multiple different transition state structures can exist separating two low-energy regions.
correct
incorrect
The curvature of the potential energy surface is positive in all directions at the TS structure.
correct
incorrect
The Hessian matrix has one negative eigenvalue at the TS structure.
correct
incorrect
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