1. This is typically regarded as a purely empirical correction or fudge factor to make the model fit the data, but can have theoretical meaning, for example showing the presence of a range of activation energies or in special cases like the Mott variable range hopping. Theoretical interpretation of the equation Arrhenius's concept of activation energy Arrhenius argued that for reactants to transform into products, they must first acquire a minimum amount of energy, called the activation energy Ea. At an absolute temperature T, the fraction of molecules that have a kinetic energy greater than Ea can be calculated from statistical mechanics. The concept of activation energy explains the exponential nature of the relationship, and in one way or another, it is present in all kinetic theories. The calculations for reaction rate constants involve an energy averaging over a Maxwell–Boltzmann distribution with as lower bound and so are often of the type of incomplete gamma functions, which turn out to be proportional to . Collision theory One approach is the collision theory of chemical reactions, developed by Max Trautz and William Lewis in the years 1916–18. In this theory, molecules are supposed to react if they collide with a relative kinetic energy along their line of centers that exceeds Ea. The number of binary collisions between two unlike molecules per second per unit volume is found to be where NA is the Avogadro constant, dAB is the average diameter of A and B, T is the temperature which is multiplied by the Boltzmann constant kB to convert to energy units, and μAB is the reduced mass. The rate constant is then calculated as so that the collision theory predicts that the pre-exponential factor is equal to the collision number zAB. However for many reactions this agrees poorly with experiment, so the rate constant is written instead as . Here is an empirical steric factor, often much less than 1.00, which is interpreted as the fraction of sufficiently energetic collisions in which the two molecules have the correct mutual orientation to react. Transition state theory The Eyring equation, another Arrhenius-like expression, appears in the "transition state theory" of chemical reactions, formulated by Wigner, Eyring, Polanyi and Evans in the 1930s. The Eyring equation can be written: where is the Gibbs energy of activation, is the entropy of activation, is the enthalpy of activation, is the Boltzmann constant, and is Planck's constant.