The master equation for the multiple-well multiple-channel reactions can be represented as, where, The solver, diseig, solves the eigenvalue problem, by using LAPACK DSYEVR after symmetrizing the matrix.   According to the least-negative eigenvalue hypothesis, the rate coefficients are calculated from the eigenvector corresponding to the least-negative eigenvalue.

  For the multiple-well reactions, the steady-state dissociation described by eq (4) is not always the solution needed.   For the system with fairly high barrier between the isomers (wells), sometimes, the solution needed is rather represented by, This corresponds to the situation that the only one isomer (well-1) is dominantly produced in the reaction system, but the isomerization reactions are not so fast.   The solver, dislit, calculates the steady-state distribution, n_1,ss for eq (5) by iterative procedure, (6), starting from an initial guess, n₁⁽⁰⁾. The initial guess is the Boltzmann distribution for the highest pressure at one temperature, and the converged vector was used for the initial guess for the next pressure.   Thus the calculation is always done from higher pressure to lower pressure, and the choice of the starting pressure may affect the results in some cases.

  The dislit solver is also useful to obtain the steady-state solution (4).   At some condition, especially in the mutiple-well reactions, the least-negative eigenvalue is not always the solution needed.   This can be observed as the hop of the rate coefficients and distribution during the pressure scans.   For such cases, the iterative procedure, (7), can be used to obtain the distribution from an initial guess. In other words, the distribution thus obtained does not necessarily correspond to the least-negative eigenvalue.   The LAPACK DSYSV is used to solve the linear equations (6) or (7).

  The solver, carate, solves the master equation for chemically activated reaction, assuming the steady-state, by solving the linear equation system, The LAPACK DSYSV is used to solve the linear equation (9).

  The solver, catime, calculates the time-dependent solution to the master equation for chemically activated reaction, for constant flux condition: k_in = const. and n(t = 0) = 0; and for the initial value condition: k_in = 0 and n(t = 0) = r.   The LSODES in ODEPACK is used to solve (10).