Bond Dissociation Free Energy

About

Bond Dissociation Free Energy (BDFE), also called Gibbs Free Energy of Bond Dissociation, is the thermodynamic quantity that measures the free energy required to break a specific chemical bond in a molecule, leading to the formation of two radicals, considering both enthalpic and entropic contributions under standard conditions.

While Bond Dissociation Energy (BDE) refers specifically to the energy required to break a bond (typically measured as the enthalpy change, $\Delta H$), BDFE accounts for the change in Gibbs free energy ($\Delta G$) and thus provides a more complete thermodynamic picture of bond dissociation by including the effects of entropy and temperature.

Key Concepts of Bond Dissociation Free Energy (BDFE):

1. Definition:

   • BDFE is the change in Gibbs free energy when a bond is homolytically broken into two radical species at a given temperature (often 298 K) and pressure (1 atm). It is expressed as: $\Delta G = \Delta H - T\Delta S$ where:

     • $\Delta G$ is the Gibbs free energy change (BDFE),

     • $\Delta H$ is the bond dissociation enthalpy (BDE),

     • $\Delta S$ is the change in entropy during bond dissociation,

     • $T$ is the absolute temperature (usually 298 K).

2. Homolytic Bond Dissociation:

   • As in BDE, BDFE is concerned with homolytic bond dissociation, where the bond breaks evenly and each atom receives one of the bonding electrons, forming two radicals: $\text{AB} \rightarrow \text{A}^{\bullet} + \text{B}^{\bullet}$

3. Difference Between BDFE and BDE:

   • BDE only accounts for the enthalpy (heat energy) required to break the bond, while BDFE includes the contribution of entropy.

   • Entropy (ΔS): During bond dissociation, entropy typically increases because two separate radical species are produced from a single molecule. This increase in entropy ( $\Delta S$) reduces the free energy required for dissociation, especially at higher temperatures.

   • As a result, BDFE is generally lower than BDE, especially for reactions with significant changes in entropy.

4. Factors Affecting BDFE:

   • Temperature: Since BDFE depends on the term $-T\Delta S$, the value of BDFE will decrease as temperature increases, because the entropic contribution becomes more significant.

   • Bond Strength: Stronger bonds have higher BDEs, which means their BDFEs are also generally higher. However, the impact of entropy can lower the free energy requirement for dissociation.

   • Radical Stability: The stability of the radicals formed after bond dissociation influences the BDFE. More stable radicals will result in lower BDFEs because the process is more thermodynamically favorable.

5. Measurement:

   • BDFE can be estimated from experimental data using thermodynamic measurements, or from theoretical calculations (e.g., using quantum chemistry methods such as Density Functional Theory (DFT)).

   • Experimentally, it may be inferred from reaction thermodynamics, such as equilibrium constants or rate constants, especially in radical-based reactions.

6. Applications:

   • Reaction Kinetics: BDFE is crucial for understanding reaction kinetics, especially in radical reactions like combustion, polymerization, and atmospheric chemistry, where bond breaking and radical formation are key steps.

   • Molecular Stability and Reactivity: BDFE helps in predicting which bonds in a molecule are likely to break under thermal or catalytic conditions.

   • Organic Chemistry: BDFE is used to analyze and design organic reactions, especially in areas involving free radicals (e.g., radical chain reactions, oxidation-reduction reactions).

   • Drug Design and Materials Science: Understanding the thermodynamics of bond dissociation helps in designing stable drugs or materials with specific degradation or reactivity profiles.

Example:

For the homolytic dissociation of a hydrogen molecule $\text{H}_2 \rightarrow 2\text{H}^{\bullet}$

• The BDE of the H-H bond is approximately 435 kJ/mol.

• The BDFE would be slightly lower, as the entropy term increases due to the formation of two H radicals, which increases the disorder of the system. If the entropy change $\Delta S$ is positive, the free energy required for bond dissociation decreases.

Summary:

Bond Dissociation Free Energy (BDFE) is a more comprehensive thermodynamic measure of bond strength than Bond Dissociation Energy (BDE) because it incorporates the effects of entropy and temperature. BDFE helps predict how easily bonds will break in various chemical processes, particularly in reactions that involve the formation of radical species. It is especially important in fields like catalysis, radical chemistry, and material science, where temperature and entropy play significant roles in determining reaction pathways.

Method

The BDE is predicted using the machine learning model BDE-db2:

SV SS, Kim Y, Kim S, John PC, Paton RS. Expansion of bond dissociation prediction with machine learning to medicinally and environmentally relevant chemical space. Digital Discovery. 2023;2(6):1900-10.

Find

The Bond Dissociation Free Energy is found under the Bond section in the property tree: