SMILES strings are used to identify the various groups of isomers based on their functional groups. For both straight-chain and branched species, we consider the following functional groups in the implementation:
hydroxy group, -OH (SMILES: O)
hydroxy radical, -O⋅(SMILES: [O])
carbonyl group, C=O (SMILES: C=O)
peroxy group, -OOH (SMILES: OO)
peroxy radical, -OO⋅(SMILES: O[O])
carbon radical, CH2/CH/C (SMILES: [CH2]/[CH]/[C])
Two species are considered to be candidates for isomers if they satisfy the following criteria:
They have the same number of each of the functional groups
Their main carbon chains (remaining after removing all functional groups), including all carbon branches, are identical
The locations of carbon-carbon double or triple bonds on the main chains are identical if they are unsaturated species (that is, alkenes)
For low-temperature kinetics, two additional rules are implemented based on the results of Ahmed et al. [12]:
The relative position of the C radical site to the OO group is identical between the species for the following conditions:
the C radical site is adjacent to the C site where OO group is attached
the C radical site is exactly at 2nd position from the C site where OO group is attached
the C radical site is exactly at 3rd position from the C site where OO group is attached
The relative position of the C sites where the OO/O[O] group is attached is identical between the species for the following conditions
the two C sites are adjacent to each other
there is exactly one C atom between the two C sites
there are exactly two C atoms between the two C sites
During our testing of the lumping rules mentioned above, we discovered that there could be significant difference in standard enthalpy of formation of species between isomers identified by molecular structure and functional groups. These differences can lead to large discrepancy in thermodynamic properties between the lumped species and the isomers. Such discrepancy will reduce the accuracy of the lumped mechanism. Therefore we implemented an additional lumping rule based on the values of standard enthalpy of formation of species so that a group of isomers will be divided into sub-groups if the maximum difference in standard enthalpy of formation among the isomers is beyond certain threshold value. As a result, any group of isomers will exhibit difference in standard enthalpy of formation within a pre-defined level and the discrepancy between the lumped species and isomers is minimized. Based on our testing, the optimal threshold for maximum allowed difference in standard enthalpy of formation among isomers is 5 kcal/mole in order to generate the smallest lumped mechanism while maintaining the highest level of accuracy.
Once isomers are identified based on species-lumping rules, the species in the isomer group are replaced by a single lumped species in the mechanism. This means that all thermodynamic and transport properties of isomers will be replaced by properties of the lumped species and all reactions involving those isomers must be modified such that the isomer species are replaced by the lumped species.
Because each lumped species replaces a group of isomers, the thermodynamic and transport properties of the lumped species are combinations of the corresponding properties of each isomer. We have implemented an approach similar to the constant ratio approach used by Lu and Law [13]. This approach tracks the intra-group mass fraction of isomers in each isomer group and uses the average mass fractions over all sampling points as the relative contribution of an isomer to the lumped species.