Group-contribution method

The simplest form of a group-contribution method is the determination of a component property by summing up the group contributions ${\displaystyle G_{i}}$:

${\displaystyle T_{\text{b}}[{\text{K}}]=198.2022567824111+\sum G_{i}.}$

This simple form assumes that the property (normal boiling point in the example) is strictly linearly dependent on the number of groups, and additionally no interaction between groups and molecules are assumed. This simple approach is used, for example, in the Joback method for some properties, and it works well in a limited range of components and property ranges, but leads to quite large errors if used outside the applicable ranges.

This technique uses the purely additive group contributions to correlate the wanted property with an easy accessible property. This is often done for the critical temperature, where the Guldberg rule implies that T_c is 3/2 of the normal boiling point, and the group contributions are used to give a more precise value:

${\displaystyle T_{\text{c}}=T_{\text{b}}\left[0.584+0.965\sum G_{i}-\left(\sum G_{i}\right)^{2}\right]^{-1}.}$

This approach often gives better results than pure additive equations because the relation with a known property introduces some knowledge about the molecule. Commonly used additional properties are the molecular weight, the number of atoms, chain length, and ring sizes and counts.

For the prediction of mixture properties it is in most cases not sufficient to use a purely additive method. Instead the property is determined from group-interaction parameters:

${\displaystyle P=f(G_{ij}),}$

where P stands for property, and G_ij for group-interaction value.

A typical group-contribution method using group-interaction values is the UNIFAC method, which estimates activity coefficients. A big disadvantage of the group-interaction model is the need for many more model parameters. Where a simple additive model only needs 10 parameters for 10 groups, a group-interaction model needs already 45 parameters. Therefore, a group-interaction model has normally not parameter for all possible combinations.

Some newer methods[2] introduce second-order groups. These can be super-groups containing several first-order (standard) groups. This allows the introduction of new parameters for the position of groups. Another possibility is to modify first-order group contributions if specific other groups are also present.[3]

If the majority of group-contribution methods give results in gas phase, recently, a new such method[4] was created for estimating the standard Gibbs free energy of formation (Δ_fG′°) and reaction (Δ_rG′°) in biochemical systems: aqueous solution, temperature of 25 °C and pH = 7 (biochemical conditions). This new aqueous-system method is based on the group-contribution method of Mavrovouniotis.[5][6]

A free-access tool of this new method in aqueous condition is available on the web.[7]

The Joback method was published in 1984 by Kevin G. Joback. It can be used to estimate critical temperature, critical pressure, critical volume, standard ideal gas enthalpy of formation, standard ideal gas Gibbs energy of formation, ideal gas heat capacity, enthalpy of vaporization, enthalpy of fusion, normal boiling point, freezing point, and liquid viscosity.[8] The Joback method is a first-order method, and does not account for molecular interactions.

The Ambrose method was published by Douglas Ambrose in 1978 and 1979. It can be used to estimate critical temperature, critical pressure, and critical volume. In addition to the molecular structure, it requires normal boiling point for estimating critical temperature and molecular weight for estimating critical pressure.[9][10]

The Nannoolal method was published by Yash Nannoolal et al in 2004. It can be used to estimate the normal boiling point. It includes first-order and second-order contributions.[11]