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Unformatted text preview: artree-Fock models lead to unacceptable results for AH and AB bond
energies, irrespective of basis set. They should not be employed for this
The B3LYP/6-311+G** model yields similar AH bond energies (and a
similar mean absolute error) to that of the corresponding model with the ccpVQZ basis set. The MP2 model is more sensitive to basis set. The mean
absolute error in AH bond energies obtained from the MP2/6-311+G**
model is three times larger than that from the corresponding model with the
cc-pVQZ basis set. This result could have been anticipated by previously
noted differences between MP2 models with the cc-pVQZ and cc-pVTZ
basis sets (see Table P3-1). The 6-31G* basis set provides a much poorer
account of AH bond energies for both B3LYP and MP2 models.
In terms of mean absolute error, bond energies from the B3LYP model with
the 6-31G* and cc-pVQZ basis sets are comparable, while those obtained
using the 6-311+G** basis set are not as good.
21 Table P3-3: Summary of Deviations from G3(MP2) of Hartree-Fock, B3LYP and
MP2 AH and AB Bond Dissociation Energies (kJ/mol)
Basis Set AH AB B3LYP MP2 AH AB AH AB 6-31G* 20 15 54 20 6-311+G** 10 27 24 21 8 17 cc-pVTZ
cc-pVQZ 125 160 22 9 17 There are situations where the 6-311+G** basis set may not be adequate to provide an
accurate account of isomer energies. A particularly simple example is the identity of the
molecule resulting from dimerization of chlorine oxide, ClO. It is an important example
because the observed (high) concentration of ClO in the stratosphere above Antarctica as
a function of time of year corrlelates with the observed (low) concentrations of ozone, O3.
Current thinking involves a catalytic photochemical mechanism that starts with (ClO)
dimer formation and eventually loss of atomic chlorine. This in turn reacts with ozone
leading to molecular oxygen and chlorine oxide.
ClO + ClO (ClO)2
(ClO)2 + hυ Cl + ClOO
ClOO Cl + O2
Cl + O3 ClO + O2
The obvious choice for the structure of ClO dimer is chlorine peroxide, ClOOCl, but
“limiting” (cc-pVQZ basis set) B3LYP calculations show that chloryl chloride, ClClO2, is
only 19 kJ/mol higher in energy. The fact that analogous calculations with smaller basis
sets show progressively larger isomer differences (47 kJ/mol from the cc-pVTZ basis set
and 132 kJ/mol from the 6-311+G** basis set) strongly suggest that the separation is
even smaller (and perhaps actually favoring chlorine perchlorate. This would have
serious impact on the proposed ozone destruction mechanism.
Relative CH Bond Dissociation Energies in Hydrocarbons: CH bond energies in
acetylene, benzene and ethylene are known to be 113, 25 and 17 kJ/mol smaller than that
in ethane, whereas that in ethane is known to be 25 kJ/mol larger. Given this knowledge,
which bond in propyne is more likely to break, that on C1 (the alkyne) or on C3 (the
methyl group)? Which bond in propene is most likely to break, those on C1 or C2 (the
alkene) or on C3 (the methyl group)? Use calculations from the B3LYP/6-31G* model to
back up your answers.
Use the B3LYP/6-31G* model to obtain equilibrium geometries for allene, H2C=C=CH2,
and the radical resulting from CH bond dissociation. Calculate the bond dissociation
energy relative to that of methane (you will need to do calculations on methane and
methyl radical). Is this the result you expect based on the experimental result for bond
dissociation in ethylene? (You can confirm this result by performing calculations on
ethylene and vinyl radical.) If it is not, provide an explanation as to why not.
Chlorine Nitrate: Chlorine nitrate, ClONO2, may play an active role in the balance
ozone in the upper atmosphere. Specifically, the molecule may serve as a sink for NO2
and ClO free radicals that are known to react with ozone and destroy ozone.
ClO + NO2 ClONO2 23 Use the B3LYP/6-311+G** model to obtain equilibrium geometries for the two free
radicals as well as chlorine nitrate. Is radical recombination sufficiently exothermic to
make chlorine nitrate an effective radical sink? Elaborate.
Chlorine peroxynitrite (ClOONO) is a plausible isomer of chlorine nitrate. Were it in
equilibrium with chlorine nitrite, it might undergo cleavage of the OO bond leading back
to the initial radicals. Obtain the equilibrium geometry of chlorine peroxynitrite using the
B3LYP/6-311+G** model, and calculate the room-temperature Boltzmann distribution
between the two isomers. Is chlorine peroxynitrite likely to be involved? Elaborate.
Carbon-Fluorine Bond Stengths in Fluoromethanes: Carbon-fluorine bond lengths in
fluoromethanes, CFnH4-n (n=1-4), decrease with increasing number of fluorines, from
1.38Ǻ in fluoromethane to 1.32Ǻ in tetrafluoromethane. Does increase in the number of
fluorines also lead to increase in CF bond energies? Use the B3LYP/6-31G* model to
evaluate energies for each of the of the reactions below.
CH3F2 → CH3. + F.
CH2F2 → CH2F. + F.
CF3H → CHF2. + F.
CF4 → CF3. + F. Do CF bond energies in the fluoromethanes parallel CF bond distances?
Repeat your calculations and analysis for the analogous fluorosilanes, SiFnH4-n...
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- Spring '09