View source for Heat of formation group additivity

'''Heat of formation group additivity''' methods in [[thermochemistry]] enable the calculation and prediction of [[heat of formation]] of [[organic compound]]s based on [[Chemical additive|additivity]]. This method was pioneered by S. W. Benson.<ref>''Estimation of heats of formation of organic compounds by additivity methods'' N. Cohen, S. W. Benson [[Chem. Rev.]]; '''1993'''; 93(7); 2419-2438 {{doi|10.1021/cr00023a005}}</ref>

== Benson model ==
{{Main|Benson group increment theory}}
Starting with simple linear and branched [[alkane]]s and [[alkene]]s the method works by collecting a large number of experimental heat of formation data (see: [[Standard enthalpy change of formation (data table)|Heat of Formation table]]) and then divide each molecule up into distinct groups each consisting of a central atom with multiple ligands:

: X-(A)i(B)j(C)k(D)l

To each group is then assigned an empirical incremental value which is independent on its position inside the molecule and independent of the nature of its neighbors:

* P primary C-(C)(H)3 '''-10.00'''
* S secondary C-(C)2(H)2 '''-5.00'''
* T tertiary C-(C)3(H) '''-2.40'''
* Q quaternary C-(C)4 '''-0.10'''
* [[Gauche (stereochemistry)|gauche]] correction '''+0.80'''
* 1,5 [[pentane interference]] correction '''+1.60 '''
: in kcal/mol and 298 K

The following example illustrates how these values can be derived.

The experimental heat of formation of [[ethane]] is -20.03 kcal/mol and ethane consists of 2 P groups. Likewise [[propane]] (-25.02 kcal/mol) can be written as 2P+S, [[isobutane]] (-32.07) as 3P+T and [[neopentane]] (-40.18 kcal/mol) as 4P+Q. These four equations and 4 unknowns work out to estimations for P (-10.01 kcal/mol), S (-4.99 kcal/mol), T (-2.03 kcal/mol) and Q (-0.12 kcal/mol). Of course the accuracy will increase when the dataset increases.

the data allow the calculation of heat of formation for isomers. For example, the pentanes:
* n-pentane = 2P + 3S = -35 (exp. -35 kcal/mol)
* isopentane = 3P + S + T + 1 gauche correction = -36.6 (exp. -36.7 kcal/mol)
* neopentane = 4P + Q = 40.1 (exp. 40.1 kcal/mol)

The group additivities for alkenes are:
* Cd-(H2) '''+6.27'''
* Cd-(C)(D) '''+8.55'''
* Cd-(C)2 '''+10.19'''
* Cd-(Cd)(H) '''+6.78'''
* Cd-(Cd)(C) '''+8.76'''
* C-(Cd)(H)3 '''-10.00'''
* C-(Cd)(C)(H)2 '''-4.80'''
* C-(Cd)(C)2(H) '''-1.67'''
* C-(Cd)(C)3 '''+1.77'''
* C-(Cd)2(H)2 '''-4.30'''
* [[cis isomer|cis]] correction '''+1.10'''
* alkene gauche correction '''+0.80'''

In alkenes the cis isomer is always less stable than the trans isomer by 1.10 kcal/mol.

More group additivity tables exist for a wide range of functional groups.

==Gronert model==
An alternative model has been developed by S. Gronert based not on breaking molecules into fragments but based on 1,2 and 1,3 interactions <ref>''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(3) pp 1209 - 1219; [https://dx.doi.org/10.1021/jo052363t Abstract]</ref><ref>''An Alternative Interpretation of the C-H Bond Strengths of Alkanes'' Scott Gronert [[J. Org. Chem.]]; '''2006'''; 71(25) pp 9560 - 9560; (Addition/Correction) {{doi|10.1021/jo062078p}}.</ref>

The Gronert equation reads:
<math>\ \Delta H_f = -146.0*n_{C-C} -124.2*n_{C-H} - 66.2*n_{C=C} + 10.2*n_{C-C-C}   
+ 9.3*n_{C-C-H} + 6.6*n_{H-C-H} + f(C,H)</math>

<math>\ f(C,H) = (231.3*n_{C} + 52.1*n_{H})</math>

The pentanes are now calculated as:
* n-pentane  = 4CC + 12CH + 9HCH  + 18HCC + 3CCC + (5C + 12H) = - 35.1 kcal/mol
* isopentane = 4CC + 12CH + 10HCH + 16HCC + 4CCC + (5C + 12H) = - 36.7 kcal/mol
* neopentane = 4CC + 12CH + 12HCH + 12HCC + 6CCC + (5C + 12H) =  -40.1 kcal/mol

Key in this treatment is the introduction of 1,3-repulsive and destabilizing interactions and this type of [[steric hindrance]] should exist considering the [[molecular geometry]] of simple alkanes. In [[methane]] the distance between the hydrogen atoms is 1.8 [[angstrom]] but the combined [[Van der Waals radius|van der Waals radii]] of hydrogen are 2.4 angstrom implying steric hindrance. Also in propane the methyl to methyl distance is 2.5 angstrom whereas the combined van der Waals radii are much larger (4 angstrom).

In the Gronert model these repulsive 1,3 interactions account for trends in [[bond dissociation energy|bond dissociation energies]] which for example decrease going from methane to ethane to isopropane to neopentane. In this model the [[homolysis (chemistry)|homolysis]] of a C-H bond releases [[strain energy]] in the alkane. In traditional bonding models the driving force is the ability of alkyl groups to donate electrons to the newly formed [[free radical]] carbon.

== See also ==
* [[Joback method]]

== References ==
<references/>

[[Category:Thermochemistry]]
[[Category:Thermodynamic models]]