Multi-exponential unimolecular rate formulae

Eigenvalue Methods in Unimolecular Rate Calculations

“…The accuracy of the Nesbet algorithm was then tested extensively in a different manner. The matrix A can be transformed into another matrix M having the same set of eigenvalues, 9 but for which there exists an analytical solution 10 for the smallest eigenvalue and eigenvector of [M + D]. Over the complete range of pressures, the Nesbet eigenvalue agreed with the analytical solution to the number (7) of significant figures requested.…”

Eigenvalue Methods for Unimolecular Rate Calculations with Several Products

“…The present methods can still fail in extreme cases, , but solutions to eq 1, acceptable for approximate numerical modeling, may still be possible. As noted previously, given a relaxation matrix M having the same eigenvalues as A , the reaction matrix [ M + D ] can be solved analytically for the rate constant and eigenvector, and the shape of the falloff curve for [ M + D ] is very similar to that for [ A + D ], although the low-pressure limits are different , neither calculation of this eigenvalue nor those of A itself usually presents any problem.…”

“…The present methods can still fail in extreme cases, , but solutions to eq 1, acceptable for approximate numerical modeling, may still be possible. As noted previously, given a relaxation matrix M having the same eigenvalues as A , the reaction matrix [ M + D ] can be solved analytically for the rate constant and eigenvector, and the shape of the falloff curve for [ M + D ] is very similar to that for [ A + D ], although the low-pressure limits are different …”