Multiple-well isomerization diffusion equation solutions with a shift and invert Lanczos algorithm

An RRKM/master equation model is constructed for the isomerization of cyclopropene. It is shown how the dense matrix of the master equation operator can be reduced to a banded form by a combination of diffusion equation approximation and equation rearrangement. The lowest eigenvalues and eigenvectors of the master equation, which are sufficient for simulation purposes, are rapidly found using shift and invert Lanczos based methods.