Computational Chemistry

DH¼’Sbond energiesðreactantsÞ#Sbond energiesðpdts=TSÞ

¼ð4C#HþC#CþC¼OÞ#ð3C#HþC¼CþC#OþO#HÞ

¼ð 4 ' 414 þ 347 þ 749 Þ#ð 3 ' 414 þ 611 þ 360 þ 464 ÞkJ mol#^1

¼ 2752 #2677 kJ mol#^1 ¼75 kJ mol#^1

The ethanal to ethenol (acetaldehyde to vinyl alcohol) reaction is predicted
to be endothermic by 75 kJ mol#^1 , i.e. neglecting entropy the enol is predicted to
lie 75 kJ mol#^1 above the aldehyde. Because these are only average bond energies,
the apparently remarkable agreement with the ab initio calculations in Fig.5.21
(71.6 kJ mol#^1 ; the connection betweenDHfrom calculations like this andDEfrom
ab initio calculations is discussed below) must be regarded as a coincidence. In any
case, the correct value is about 40 kJ mol#^1 [ 92 ]. Crude bond energy calculations
like this can be expected to be in error by 50 or more kJ mol#^1. More accurate bond
energy calculations can be done [ 142 ] using bond energies that refer to very specific
structural environments; for example, a C–H bond on a primary sp^3 carbon that is in
turn attached to another sp^3 carbon.
For a reaction taking place at 0 K the enthalpy change is simply the internal
energy change at 0 K:

DHð0KÞ¼DEtotal0K ð 5 : 181 Þ

Note that although the calculation ofEtotal0K values to getDEtotal0K demands fre-
quency jobs, which are relatively time-consuming (“expensive”), accurate relative
energy differences do require this, and we will regard the ZPE-uncorrected ab initio
energy differenceDEtotal, the difference in electronic energyþinternuclear repul-
sion, as only an approximation toDEtotal0K (see Section 5.2.3.6.4 andChapter 2,
Fig. 2.20). At temperatures other than 0 K,DHisDEtotal0K plus changes in the
increases in translational, rotational, vibrational and electronic energies on going
from 0 K to the higher temperatureT, plus the work done by the system in effecting
a pressure or volume change:

DHðTÞ¼DEtotal0K þDEtransþDErotþDEvibþDEelþDðPVÞð 5 : 182 Þ

One frequently chooses the standard temperature of 298.15 K, about room
temperature. From 0 K to room temperature the increase in electronic energy is
negligible and the increase in vibrational energy is small.
The entropy differenceDSfor a process is a measure of the disorder of the
products or the transition state, compared to the disorder of the reactants:

DS¼Sðpdts=TSÞ#SðreactantsÞ

¼disorderðpdts=TSÞ#disorderðreactantsÞ

(pdt or TS depending on whether we are considering reaction entropy or activation
entropy). Entropy is a sophisticated concept, and explaining it in terms of disorder

300 5 Ab initio Calculations