Gibbs free energy

  In our experiment, coniferyl alcohol (monolignols G) would become resonance structure after create a free radical, and two specific resonance structures would form a dimer (β-5, β-O-4, β-β).
It is changed into a dimer by the action of the enzyme and the addition of water. Because the method we used may not be the same as the literature, we decided to confirm the feasibility of the reaction through Gibbs free energy calculation.
(Calculation method using Spartan 16)

(1) From monomeric alcohol to carrying free radicals

Figure 1. Reaction diagram (Initial figure is from Reference [1])

Figure 2. Monolignol alcohol as the free energy benchmark (1 hartree ≈ 2625.5 kJ/mole), Resonance(left) is Figure 1. left resonance, Resonance(middle) is Figure 1. middle resonance, Resonance(right) is Figure 1. right resonance

In Figure 2, we found that the free energy of the process of creating free radicals is positive, so it is not spontaneous, so we need to make the reaction happen using enzymes and hydrogen peroxide.

(2) Free radical state to dimer formation

Figure 3. The green indicator is β-O-4; the blue indicator is β-β; the red indicator is β-5 (Initial figure is from Reference [1])

Figure 4. β-β free energy changes, (a) is the two resonant monolignols, (b) is the two resonant monolignol bonds, (c) is β-β formation (1 hartree ≈ 2625.5 kJ/mole)

Figure 5. β-5 free energy changes, (a) is the two resonant monolignols, (b) is the two resonant monolignol bonds, (c) is β-5 formation (1 hartree ≈ 2625.5 kJ/mole)

Figure 6. β-O-4 free energy change, (a) is two resonance monolignols, (b) is two resonance monolignol bonding, (c) is formed by β-O-4, and water is added to the reaction at 2 to 3 (1 hartree ≈ 2625.5 kJ/mole)

Boltzmann distribution is a probability distribution that gives the probability that a system will be in a certain state as a function of that state’s energy and the temperature of the system. [wiki]

From Boltzmann distribution we knew

If the system at constant pressure
1. We can use enthalpy (H) as the energy of state (ε).

2. We needed to multiply the number of different arrangement.

(From thermodynamic, (H - TS) = Gibbs free energy)

so Boltzmann distribution become

Used this form equation, we estimated that the probability of state is smaller if Gibbs free energy is larger.
Finally, we used this information to estimated that
three kinds dimer occurrence probabilities are β-5 > β-β >β-O-4 .