Chemistry 380.37
Fall 2015
Dr. Jean M. Standard
October 26, 2015
Better Computational Thermochemistry: Isogyric and Isodesmic Reactions
Bond Dissociation Reactions
We have previously seen that one of the cases where Hartree-Fock calculations perform poorly is in the calculation
of bond dissociation energies. This is because these calculations usually start with a molecule that has a closed shell
of electrons and the molecule breaks into two fragments that are open shell molecules. The energy difference
between closed and open shell molecules is very poorly described using Hartree-Fock methods as a result of the
difference in electron correlation in closed vs. open shell systems.
Table 1 reviews some results of molecular orbital calculations of the dissociation of the HF molecule into H and F
atoms. The Hartree-Fock result is very far off from the experimental dissociation energy. We see that methods that
include electron correlation, such as the others listed in the table (MP2, MP4, QCISD), are required in order to
properly treat the dissociation energy.
Table 1. Dissociation energies from molecular orbital calculations for the dissociation of the
HF molecule into H and F atoms using the 6-31+G(d) basis set.
Method
Dissociation Energy
% Diff.
(kcal/mol)
Hartree-Fock
84.8
37.7
MP2
122.8
9.8
MP4
120.2
11.7
QCISD
119.0
12.6
Experiment
136.2
Isogyric Reactions
In the dissociation of hydrogen fluoride, HF → H + F, the reaction has species on the reactant side in which all the
electrons are paired but it has species on the product side in which there are unpaired electrons. Therefore, in this
reaction, the electron correlation effects are not the same on both sides. This makes the reaction particularly
difficult to calculate directly with computational methods. Therefore, alternative routes to obtaining bond
dissociation energies often are sought.
Isogyric reactions are reactions in which the number of electron pairs in reactants and products is conserved. In the
direct bond dissociation reaction of HF, the number of electron pairs on the reactant side is 5 (one H-F single bond, a
1s core pair on F, and 3 lone pairs on F) but only 4 on the product side because of the bond breaking. So the
reaction HF → H + F is not an isogyric reaction. The HF → H + F reaction can be converted into a related
reaction that is isogyric by adding H atom to both sides,
HF + H → H2 + F .
(1)
In this reaction, there are 5 electron pairs and one unpaired electron on the both the reactant and product sides, so it
is an isogyric reaction.
2
There are many ways to construct isogyric reactions; for example, adding F atom to both sides leads to a different
isogyric reaction,
HF + F → H + F2 .
(2)
To use isogyric reactions to obtain improved bond dissociation enthalpies, the reactants and products are calculated
using molecular orbital methods. The calculated result for the enthalpy of reaction for an isogyric reaction like (1) is
expected to be more accurate than that of a directly calculated bond dissociation even using a low level of theory
because the electron correlation effects are very similar for both sides of the reaction.
To get the bond dissociation energy of HF using isogyric reaction (1), an accurate value from experiment or highlevel calculation is employed for the bond dissociation energy of H2. Thus, these types of isogyric reactions rely on
the determination of bond dissociation energies relative to one well-known result:
HF + H → H2 + F
H2 → H + H
(1)
(3)
Overall: HF → H + F
(4)
To obtain the bond dissociation enthalpy of HF, ΔH4, Hess' Law can be used,
ΔH4 = ΔH1 + ΔH3 .
Table 2 illustrates this process for calculations at the Hartree-Fock/6-31+G(d) level of theory. The isogyric results
were obtained using reaction (1) and a bond dissociation enthalpy for H2 from experiment of 104.21 kcal/mol.
Table 2. Bond dissociation enthalpy (kcal/mol) of HF at the Hartree-Fock/6-31+G(d) level.
Experiment
Direct
% Difference
Calculation
135.9
85.2
Isogyric
% Difference
Calculation
37
113.9
16
Notice that use of the isogyric reaction leads to a much improved, though still not perfect, computational value of
the bond dissociation enthalpy of hydrogen fluoride at the Hartree-Fock level of theory. The use of isogyric
reactions in general leads to much improved thermochemical predictions at this low level of theory.
Isodesmic Reactions
Another class of reactions that are frequently used in computations are isodesmic reactions. In isodesmic reactions,
the number and types of bonds are conserved on the reactant and product sides of the reaction. This again ensures a
very similar amount of electron correlation on both sides of the reaction and leads to more accurate thermochemical
values from even low-level computational methods.
An example isodesmic reaction is CH2F2 + CH4 → 2 CH3F. On the reactant side, there are two C-F single bonds
and six C-H single bonds. On the product side, there are the same number of C-F and C-H bonds as on the reactant
side.
Another example of an isodesmic reaction is NH3 + CH3NH3+ → NH4+ + CH3NH2. A reaction of this type could
be used to determine the proton affinity of nitrogen bases relative to ammonia.
3
To illustrate the use of isodesmic reactions, consider a comparison of ring strain in cyclopropane and ethylene oxide.
To explore this computationally, we might design an isodesmic reaction like the one shown below.
CH2
H2C
+
CH2
O
O
H3C
CH2
+
CH3
H2C
CH2
H3C
CH3
In this reaction, the three-membered ring on the reactant side is cyclopropane and on the product side it is ethylene
oxide. If the reaction is calculated to be exothermic, that would suggest that ethylene oxide is more stable (less
strained) than cyclopropane. If it is endothermic, then ethylene oxide is presumed to be less stable than
cyclopropane. The energies for the noncyclic molecules are assumed to include no ring strain. Since the reactant
and product sides both include two C-O bonds, three C-C bonds, and 12 C-H bonds, the energy difference is
expected to result primarily from differences in ring strain. Results for this reaction, calculated at the HartreeFock/6-31G(d) level of theory, are presented in Table 3.
Table 3. Hartree-Fock/6-31G(d) enthalpies
Species
Ee + Hcorr
(kcal/mol)
CH2
–73400.8
H2C
CH2
O
–96623.1
H3C
CH3
O
H2C
–95886.7
CH2
CH2
H3C
–74142.3
CH3
ΔHrx
–5.1
The reaction enthalpy is calculated to be exothermic, –5.1 kcal/mol. This implies that the product side is more
stable. In other words, this isodesmic reaction predicts that ethylene oxide has less ring strain than cyclopropane.