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Chapter 2 Self-test questions
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Chapter 2 Self-test questions
Quantum Chemistry
Quiz Content
*
not completed
.
Consider a molecule of chlorobenzene, C
_{6}
H
_{5}
Cl. How many coordinates do you need in order to specify the absolute position in space of all of the
nuclei
making up this molecule?
12
correct
incorrect
3
correct
incorrect
30
correct
incorrect
36
correct
incorrect
*
not completed
.
Consider a molecule of chlorobenzene, C
_{6}
H
_{5}
Cl. How many coordinates do you need in order to specify the absolute position in space of all of the
electrons
making up this molecule?
174
correct
incorrect
58
correct
incorrect
17
correct
incorrect
212
correct
incorrect
*
not completed
.
The fundamental approximation that is made in Hartree-Fock theory is that:
The motion of each electron is in some sense independent of the motion of all the other electrons.
correct
incorrect
Electron-electron Coulomb interactions are not accounted for.
correct
incorrect
Electrons move at the speed of light so we can ignore their specific positions.
correct
incorrect
The spin of electrons is assumed to be described by either the α or the β spin state.
correct
incorrect
*
not completed
.
Which of the following methods is
not
used to improve the
convergence
behaviour when solving the Hartree-Fock equations?
Modifying the energy of the virtual orbitals when constructing the Fock operator, through level-shifting.
correct
incorrect
Combining the results of multiple steps to estimate the most accurate Fock operator matrix for the following step.
correct
incorrect
Carefully choosing the initial set of coefficients
c
_{ij}
within equation (2.11), so that this 'guess' for the wavefunction is as close as possible to the final Hartree-Fock wavefunction.
correct
incorrect
Re-calculating some of the two-electron integrals of eq. (2.13) at each step.
correct
incorrect
*
not completed
.
The Hartree-Fock energy calculated for chlorobenzene using the STO-3G family of basis sets is of −681.8957 hartree. Bearing in mind the approximate nature of the HF/STO-3G method, which of the following is true?
The heat of formation of chlorobenzene is roughly −681.8957 hartree.
correct
incorrect
The Hartree-Fock method is so inaccurate that we do not learn anything about the energy of chlorobenzene from this calculation.
correct
incorrect
Forming chlorobenzene from its separated nuclei and electrons releases roughly 1.8 million kJ mol
^{−1}
.
correct
incorrect
The energy required to split chlorobenzene up into six carbon atoms, five hydrogen atoms, and one chlorine atom is about 1.8 million kJ mol
^{−1}
.
correct
incorrect
*
not completed
.
Consider the bis(benzene)chromium complex Cr(η
^{6}
-C
_{6}
H
_{6}
)
_{2}
, which has a closed-shell electronic ground state. How many occupied spatial molecular orbitals will there be in the Hartree-Fock wavefunction for this species?
108
correct
incorrect
33
correct
incorrect
54
correct
incorrect
23
correct
incorrect
*
not completed
.
What is the total number of contracted basis functions (
s
,
p
_{x}
,
p
_{y}
and
p
_{z}
) used when carrying out a Hartree-Fock calculation on fluorobenzene C
_{6}
H
_{5}
F using the 6-31G basis set?
73
correct
incorrect
108
correct
incorrect
100
correct
incorrect
82
correct
incorrect
*
not completed
.
Which of the following gives the correct values for the expectation value of the
S
^{2}
operator for non spin-contaminated wavefunctions for singlet, doublet, triplet, quartet and quintet states?
0, 0.5, 1., 1.5, 2.
correct
incorrect
1, 2, 3, 4, 5
correct
incorrect
0, 0.75, 2., 3.75, 6.
correct
incorrect
0, 2, 6, 12, 20
correct
incorrect
*
not completed
.
Most modern electronic structure codes use
Gaussian
functions as basis functions with which to expand the molecular orbitals. Which of the following statements is
not
correct:
The commonly-used 'Slater-Type Orbital' family of basis sets uses Slater functions.
correct
incorrect
For a given number of basis functions, it would be more accurate to use Slater functions instead of Gaussian functions
correct
incorrect
The integrals over basis functions needed to carry out Hartree-Fock calculations are more difficult to evaluate for Slater functions than for Gaussian functions
correct
incorrect
Some combinations of multiple Gaussian functions are quite similar to Slater functions.
correct
incorrect
*
not completed
.
For the isovalue surface representation of the HOMO-1 of camphor shown in Fig. 2.3, which of the following statements is most correct?
The delocalized nature of the MO indicates that bonding is very delocalized also, due to participation by many resonance forms.
correct
incorrect
The black regions correspond to regions with positive charge, whereas those in lighter grey correspond to negatively charged regions.
correct
incorrect
The low amplitude near the C=O carbonyl group suggests that this is a very electron-deficient region of the molecule.
correct
incorrect
The HOMO-1 is rather delocalized across the molecule; this orbital has a number of nodal surfaces across which its sign changes.
correct
incorrect
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