Microstates coefficients

Transition strengths can be given in terms of Einstein rate coefficients. For a pair of states j > and k > it is shown in elementary texts that these are related in a simple way. If one assumes that, for any pair of microstates i and j, the rate from i to j is equal to the rate from j to i one has the principle of detailed balance). Then, the relation between the coefficients is consistent with thermodynamics (Planck s black-body radiation law). 

The coupling of the local microstates into the proper molecular states is provided by the diagonalisation of the spin Hamiltonian matrix. For the zero-field case the diagonalisation matrix represents an orthogonal transformation and its matrix elements relate to the combination of the Clebsch-Gordan coefficients. 

It can be shown that a trajectory generated by integrating the Langevin equation of motion (with at least one non-vanishing atomic friction coefficient y,) maps (at constant volume) a canonical distribution of microstates at temperature To. 

The identified sorption sites are separated by high-energy barrier surfaces therefore, penetrant diffusion can be seen as a series of infrequent transitions between adjacent microstates. In TST, to calculate the diffusion coefficient, the sorbates are displaced in the coarse-grained lattice over a large number of time steps and a large population of ghost walkers through a kinetic Monte Carlo (kMC) scheme. The diffusion coefficient is then calculated from the value of the mean square displacement (MSD) from the trajectories of all penetrant walkers... 

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