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Unformatted text preview: o 400 amu.
One possibility is the G3(MP2) method that we have used throughout this
chapter to supply reference data (in lieu of experimental data). In practice, it
is applicable only to very small molecules (with molecular weights below
150 amu). G3(MP2) heats of formation for several hundred small molecules
have been compared with experimental values contained in the NIST
thermochemical database. This leads to a mean absolute error of 6.2 kJ/mol
and an RMS error of 8.3 kJ/mol.
G3(MP2) actually involve a combination of several different quantum
chemical models, and perhaps is best referred to as a recipe. The first step is
to obtain an equilibrium geometry using the MP2/631G* model. Next, two
energy calculations are performed at this geometry, one an MP2 calculation
with the G3MP2large basis set an the other a QCISD(T) calculation with the
631G* basis set. The energy differences between the MP2 calculation with
the two basis sets and the QCISD(T) and MP2 calculations with the same
basis set are summed. This assumes that the changes in energy due to
increase in the size of the basis set from 631G* to the G3MP2large and
improvement in treatment of electron correlation from the MP2 to the
QCISD(T) are independent. This assumption is the reason that G3(MP2) is
as widely applicable as it is. Were it necessary to perform a QCISD(T)
calculation (which scales as the seventh power of the number of basis
functions) with the G3MP2large basis set, the procedure would be much
more limited. The fact that G3(MP2) heats of formation obtained are in
reasonable accord with experimental values validates the assumption. The
final step in the recipe involves a HF/631G* frequency calculation
(preceded by a HF/631G* geometry). This allows for calculation of the
zeropoint energy and for correction for finite temperature. 57 A new recipe, designated T1, has been formulated that requires significantly
less computation than G3(MP2), but yields heats of formation that are nearly
identical. Both the QCISD(T) and HartreeFock frequency calculations have
been eliminated and the MP2/G3MP2large calculation has been replaced by
a RIMP2 calculation in which the G3MP2large basis set is approximated
using socalled dual basis set techniques. A HF/631G* geometry replaces
the MP2/631G* geometry. Without further modification, these changes to
G3(MP2) result in heats of formation that are not sufficiently accurate to be
useful in thermochemical calculations. A successful recipe follows by
introducing a total of 66 linear regression parameters based on Mulliken
bond orders calculated from the HartreeFock wavefunction. These have
been determined using a training set of more than 1100 G3(MP2) heats of
formation. A plot of T1 vs. G3(MP2) heats of formation for this set is
provided in Figure P33.
Table P37 compares structural isomer energies obtained from T1 heats of
formation for a variety of simple systems with those obtained both from the
G3(MP2) recipe and with experimental heats. The mean absolute and rms
errors is 6.6 and 9.0 kJ/mol, roughly the same as those for the G3(MP2)
recipe.
As discussed earlier in this chapter, while the energy of a molecule is one of its most
fundamental properties, it is only rarely determined. This means that quantum chemical
models (or combinations of quantum chemical models) that were able to provide routine
and reliable energies (heats of formation) are of significant value. 58 Figure P33: Comparison of Heats of Formation Obtained from the T1 and
G3(MP2) Recipes (kJ/mol) 59 Table P37: Comparison of Energies of Structural Isomers from T1 and
G3(MP2) Recipes with Experimental Values (kJ/mol)
formula (reference) isomer T1 G3(MP2) expt. C2H3 N (acetonitrile) methyl isocyanide 102 100 88 C2H4 O (acetaldehyde) vinyl alcohol
oxirane 41
113 41
115 43
118 C2H4 O2 (acetic acid) methyl formate 68 70 75 C2H6 O (ethanol) dimethyl ether 49 50 51 C3H4 (propyne) allene
cyclopropene 3
91 1
100 7
93 C3H6 (propene) cyclopropane 36 38 29 C4H6 (1,3butadiene) 2butyne
cyclobutene
1,2butadiene
1butyne
methylenecyclopropane
bicyclo[1.1.0]butane 35
50
43
56
80
113 37
56
51
58
85
120 36
48
53
56
92
108 2methyl2propenal
cyclobutanone
2hydroxy1,3butadiene
2,3dihydrofuran
divinyl ether 7
4
25
48
35
96 6
3
23
38
35
97 5
9
23
38
43
102 C4H8 (2methylpropene) trans2butene
1butene
cyclobutane 4
15
46 6
16
47 7
17
46 C5H8 (cyclopentene) 2methyl1,3butadiene
methylenecyclobutane
1,4pentadiene
1,1dimethylallene
1,2pentadiene 42
89
69
86
98 37
87
67
90
101 40
86
70
93
105 5 4  C4H6 O (methyl vinyl ketone) trans2butenal mean absolute error 60 The version of Spartan provded with this textbook (Spartan Student) does not provide
for calculations using the T1 thermochemical recipe. However, the associated Spartan
Molecular Database includes T1 data for all the molecules required for the problems that
follow.
DoubleBond Disproportionation Reactions: A doublebond disproportionation
reaction relates the energy of a molecule incorporating a double bond with the average of
the energies of molecules incorporating the corresponding single and triple bonds. For
example, the doublebond disproportionation reaction for ethylene relates its energy to
the average of the energies of ethane and acetylene. Experimentally, this reaction is
endothermic by 38 kJ/mol, meaning that a CC double bond is weaker than the average of
carboncarbon single and triple bonds.
2 H2C=CH2 → H3CCH3 + HC≡CH Use the T1 recipe to calculate the energies of doublebond disproportionation reactions
for ethylene, methyleneimine (H2C=NH), formaldehyde (H2C=O) and thioformaldehyde
(H2C=S). (Build the molecules as you normally would and simply retrieve from the
Spartan Molecular Database.) Adjust your results for the last three to account for the
error in the reaction of ethylene. Note any significant differences among the four
disproportionation energies and try to rationalize them. 61 Calculation of Entropy and Gibbs Energy
The change in the Gibbs energy (ΔG) for a chemical reaction follows from
the change enthalpy (ΔH) by way of the usual thermodynamic relationship.
ΔG = ΔH  TΔS
T is the temperature in K and ΔS is the change in entropy. The entropy is a
sum of translational, rotational and vibrational parts.
S = Str + Srot + Svib
The translational part, which depends on the total molecular mass, M, and
pressure, P (n is the number of moles, and R and k are the gas and
Boltzmann constants), cancels in a massbalanced equation.
3 Str = nR 2 2!MkT + ln 3/ 2 2 nRT
P The rotational part depends on the principal moments of inertia, IA, IB and IC,
which in turn depend on the geometry. s is termed the symmetry number
which is usually unity.
3 Srot = nR 2 ( !vA vBvC )1/2 + ln s vA = h2/8!IA kT, vB = h2 /8!IB kT, vC = h2/8!IC kT The vibrational part depends on the frequencies. It is based on the linear
harmonic oscillator approximation, and incorrectly goes to ∞ and not ½ RT
as the frequency goes to 0. It needs to be adjusted to approach the proper
limit.
Svib = nR !
i (uieui – 1)–1 – ln (1 – e –ui ) µi = h!i/kT 62...
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