Unformatted text preview: -311+G** basis sets actually
yield slightly lower overall errors for this particular set of comparisons than
the corresponding models with larger “limiting” basis sets. Overall errors for
B3LYP models do not change significantly with basis set, while those for
MP2 models with the two smaller basis sets are larger than those for the
larger sets. Individual errors show wider deviations (see Excel spreadsheet).
The B3LYP/6-31G* and B3LYP/6-311+G** models show the best overall
performance, although those of the corresponding Hartree-Fock models are
quite similar. 26 Table P3-4:
Basis Set Summary of Deviations from G3 of Hartree-Fock, B3LYP and MP2
Energies of Structural Isomers (kJ/mol)
Hartree-Fock B3LYP MP2 6-31G* 9 8 17 6-311+G** 10 7 12 16 7 cc-pVTZ
cc-pVQZ 27 Acidity of Propyne: Loss of hydride anion from propyne can either occur from the sp
hybridized carbon or from the sp3 hybridized carbon. The former might be expected as
acetylene is a much stronger acid than ethane, while the latter might be expected as it
would lead to a delocalized anion. Which deprotonation is thermodynamically favored?
H3 C C C– H3C C CH H2C C C H2 – Use the B3LYP/6-311+G** model to obtain equilibrium geometries for the two anions.
Which is lower in energy? Is the less stable anion likely to be detectable in an equilibrium
mixture at room temperature? (Assume a threshold of 5%.)
Isomers of Carboranes: Carboranes are compounds of carbon, boron and hydrogen.
Depending on stoichiometry, they exhibit caged (closo), partially caged (nido from the
Latin word for nest) or open (arachno from the Greek word for spider) structures. are
B4C2H6 and B10C2H12 simple examples of closo structures. The former can exist in one of
two isomers, and the latter in one of three isomers. H
BH HB BH
H HB CH HB BH
H ChemDraw B10C2H12for isomers
Use the B3LYP/6-31G* model to obtain equilibrium geometries for the two isomers of
B4C2H6 and the three isomers of B10C2H12. Examine carbon-carbon bond lengths in the
appropriate isomer of each. Do these appear to be “normal” single bonds or are the
significantly shorter or longer? If the latter provide a rationalization? Identify the lowestenergy isomer for B4C2H6 and B10C2H12 and provide a rationale for the observed
Performance of Practical Models for Hydrogenation Reactions: A hydrogenation
reaction maintains overall bond count but does not maintain individual bond counts. For
example, the products of hydrogenation of ethane have the same number (eight) of σ
bonds as the reactants but two new CH bonds have replaced a C-C bond and H-H bond.
CH3-CH3 + H-H → 2CH4 Calculate hydrogenation energies for ethane, hydrazine, hydrogen peroxide and fluorine
using the Hartree-Fock, B3LYP and MP2 models with both the 6-31G* and 6-311+G** 28 basis sets (six models in total). Correct these for zero-point energy and finite temperature
using the data in Appendix X. Compare these to the results from the G3(MP2) recipe.
F- F -60 kJ/mol
-548 kJ/mol Which (if any) models yield hydrogenation energies that are within +/-12 kJ/mol of the
G3(MP2) values? Which model provides the best results overall?
Energy Content of Hydrazine Fuels: According to the B3LYP/6-31G* model, which
fuel delivers the greater energy on a per gram basis, hydrazine or tetramethylhydrazine?
The products of oxidation are N2 and water for hydrazine and N2, water and CO2 for
tetramethylhydrazine. Make certain to include the mass of the oxidizer (O2) in your
calculations. How does the better of the two fuels compare with molecular hydrogen on a
per gram basis?
Combustion of Hydrocarbons and Fluorocarbons: Hydrocarbons are commonly used
as fuels but fluorocarbons are not. Of course, fluorocarbons cannot be mined or drilled
from the earth, but is there also a fundamental reason? Use the B3LYP/6-31G* model to
calculate the energy of complete combustion of methane, ethane and propane (to CO2 and
water) and tetrafluoromethane, hexafluoroethane and decafluoropropane (to CO2 and
OF2). Point out differences between energies of combustion for the hydrocarbon and
analogous fluorocarbon and relate this to their use as fuels.
“Combustion” of Silanes: Silicon-oxygen polymers (“sand”) result from combustion (in
oxygen) of silanes and other silicon-containing compounds. This makes it difficult to
assign heats of formation. One clever solution is to “burn” such compounds in fluorine
(F2) rather than in oxygen. This leads only to gaseous products (SiF4 and HF) the amounts
of which may easily be determined, for example, combustion of silane.
SiH4 + 4F2 SiF4 + 4HF
Use the B3LYP/6-31G* model to determine energies of complete “combustion” (in F2) of
silane, disilane, trisilane, 2-silyltrisilane and 2,2-disilyltrisilane (resulting in only SiF4 and
HF as products). On a per gram basis, combustion of which of these produces the greates
amount of heat?
SiH4 H3 S i SiH3 H3 S i Si S i H2
H3 S i S i H3 SiH3 H3 S i SiH3
Si SiH3 H3 S i SiH3...
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