Vibrational Correction

For the calculation of the thermodynamics of radicals within the JTHERGAS system, the loss of vibrational states due to the loss of a hydrogen atom to form the radical is computed. The vibrational states lost are translated to corrections to the temperature dependent heat capacities.

The estimation of vibrational states is also based on a table of structures. A vibrational mode is identified by a given structure. Associated with the structure is a vibrational frequency (For example, see Table A.13 in Benson's book). This vibrational frequency is then translated to contributions to the entropies and the heat capacities as a function of temperature (see Table A.15 and A.17) in Benson's book.

Also associated with each vibrational structure is a numerical factor. This factor serves two purposes. The first is to take care of symmetries in the vibrational structure. For example, the bend structure, H-C-H, due to its symmetry, matches twice as many times. To ensure the counting, the number of matches has to be divided by two. The other purpose of the numerical factor is to determine whether the structure should be added (positive factor) or subtracted (negative factor). In counting the vibrational structures both matches in the parent molecule and the radical are made. The number of times a certain vibrational mode appears in the parent mode and the number of times a vibrational mode appears in the radical are subtracted. A positive numerical factor keeps this relationship and a negative numerical factor reverses this relationship. This was incorporated to give more flexibility in the definition of which modes should be counted.

Within JTHERGAS, the implementation goes beyond what is outlined in Table A.13 in Benson's book for carbon radicals. The loss of tetrahedral modes is calculated for loss of a hydrogen atom in primary, secondary and tertiary carbon configurations. This replaces the simple CCH and HCH bond bends listed in Benson's tables. In addition, corrections due to resonance are also included. For example, for the calculation of a carbon next to a double bond, i.e. a resonant structure, the structure ^.CH₂=C is matched. The associated frequencies are: 1300 (resonant stretch), two 1150 (twist and rock primary bends) and 1450 (primary bend). These frequencies are then translated to corrections in entropies and temperature dependent heat capacities.

Vibrational Detection: ch3/ch2/ch2(.)

Vibrational Detection for Radicals

Radical: ch2(#1)/ch(ch2(.))/ch2/ch(ch3)/ch2/ch(ch3)/1

Molecule: ch2(#1)/ch(ch3)/ch2/ch(ch3)/ch2/ch(ch3)/1