text: Statistical mechanics played a significant role in the development of TST. However, the application of statistical mechanics to TST was developed very slowly given the fact that in mid-19th century, James Clerk Maxwell, Ludwig Boltzmann, and Leopold Pfaundler published several papers discussing reaction equilibrium and rates in terms of molecular motions and the statistical distribution of molecular speeds.
  It was not until 1912 when the French chemist A. Berthoud used the Maxwell–Boltzmann distribution law to obtain an expression for the rate constant.
  where a and b are constants related to energy terms.
  Two years later, René Marcelin made an essential contribution by treating the progress of a chemical reaction as a motion of a point in phase space. He then applied Gibbs' statistical-mechanical procedures and obtained an expression similar to the one he had obtained earlier from thermodynamic consideration.
  In 1915, another important contribution came from British physicist James Rice. Based on his statistical analysis, he concluded that the rate constant is proportional to the "critical increment". His ideas were further developed by Richard Chace Tolman.  In 1919, Austrian physicist Karl Ferdinand Herzfeld applied statistical mechanics to the equilibrium constant and kinetic theory to the rate constant of the reverse reaction, k, for the reversible dissociation of a diatomic molecule.
  He obtained the following equation for the rate constant of the forward reaction
  where  is the dissociation energy at absolute zero, k is the Boltzmann constant, h is the Planck constant, T is thermodynamic temperature,  is vibrational frequency of the bond.
  This expression is very important since it is the first time that the factor kT/h, which is a critical component of TST, has appeared in a rate equation.
  In 1920, the American chemist Richard Chace Tolman further developed Rice's idea of the critical increment. He concluded that critical increment (now referred to as activation energy) of a reaction is equal to the average energy of all molecules undergoing reaction minus the average energy of all reactant molecules.