University of MichiganAnn Arbor, MI 48109-2143

Climate and Space Sciences and Engineering

MultiWell Program Suite

J. R. Barker, T. L. Nguyen, J. F. Stanton, C. Aieta, M. Ceotto, F. Gabas, T. J. D. Kumar, C. G. L. Li, L. L. Lohr, A. Maranzana, N. F. Ortiz, J. M. Preses, J. M. Simmie, J. A. Sonk, and P. J. Stimac

About the Programs


Calculates time dependent concentrations, reaction yields, vibrational distributions, and rate constants as functions of temperature and pressure for multi-well, multi-channel unimolecular reactions systems that consist of stable species (wells) and multiple isomerization and/or dissociation reactions (channels). The stochastic method is used to solve the time-dependent Master Equation.

Users may supply sums of states and densities of states for RRKM theory, microcanonical unimolecular reaction rate constants calculated with some other code, or optionally use the Inverse Laplace Transform method to calculate k(E). One-dimensional tunneling corrections (unsymmetrical Eckart barrier) can be included. Provision is also made for treating non-RRKM effects.

Initial energy distributions include thermal, offset thermal, chemical activation, delta function, and user-supplied distributions. Users can select various models for energy transfer in weak collisions, including exponential, biexponential, generalized exponential, etc., and user-defined functions.

The code is intended to be relatively easy to use. It is designed so that both very complicated and very simple unimolecular reaction systems can be handled via the data file: no restructuring of the code or recompiling is necessary to handle even the most complex systems.


Exact counts of sums and densities of states via the Stein-Rabinovitch extension of the Beyer-Swinehart algorithm. Optionally, the Whitten-Rabinovitch approximation can be used. The current version includes harmonic oscillators, anharmonic oscillators, free rotors, hindered rotors, particle in a box, and translations.

bdens and paradensum

These codes are available for computing sums and densities of states for non-separable anharmonic vibrations. Program bdens is more appropriate for use with small molecules, while paradensum is more appropriate for large molecules, since it is a prallel code and can handle moleucles with >100 coupled vibrational degrees of freedom. Both bens and paradensum, like DenSum, produce output files that can be used directly as input files for the MultiWell master equatin code and for comuting thermochemical properties.


Calculates entropy, heat capacity, and H(T)-H(0) for individual species, based on vibrational frequencies, moments of inertia, internal rotation barriers, and electronic state properties. It includes all of the types of modes listed for DenSum. It calculates equilibrium constants, which are useful for obtaining recombination rate constants from the corresponding unimolecular decomposition rate constants. When provided with parameters for reactants and the transition state, it uses canonical transition state theory to calculate rate constants (including tunneling corrections based on the 1-D unsymmetrical Eckart barrier). By using input files generated by Programs 'adensum' and 'sctst' (see below), Thermo can include the effects of fully coupled anharmonic vibrations and/or compute thermal rate constants using the fully-coupled anharmonic semi-classical transition state theory formulated by W. H. Miller and coworkers.sition state theory rate constants.


Prinicipal moments of inertia of chemical species and reduced moments of inertia for internal rotors. Requires the cartesian coordinates for the atoms in the molecule. Such coordinates are obtainable from electronic structure programs.


Takes Cartesian coordinates, energies, and vibrational frequencies generated by GAUSSIAN (registered trademark of Gaussian, Inc.) and uses them to construct input data files for the MultiWell Program Suite.


Uses Cartesian coordinates along a path (obtained from electronic structure calculations) to compute the effective mass for large amplitude motions, such as internal hindered rotations, inversion vibrations, and multi-well potentials. For this purpose, lamm is a better choice than MomInert. A script, gauss2lamm, is provided to read GAUSSIAN (registered trademark of Gaussian, Inc.) output files and construct (in part) the data file needed for lamm.


This code is for using the semi-classical transition state theory (SCTST) formulated by W. H. Miller and coworkers to compute cumulative reaction probabilities (analogous to the sum of states for the transition state). The code also computes the partition function corresponding to the CRP at a set of temperatures from 50 K to 3400 K and generates a data file that can be used by program 'Thermo' to conveniently compute thermal rate constants using the SCTST of Miller and coworkers.


This code implements two varieties of Variational Transition State Theory (VTST): Canonical (i.e. thermal) and J-resolved Microcanonical (i.e. for fixed internal energies and angular momentum). From molecular vibration frequencies, moments of inertia, and potential energy provided at points along a reaction path to compute variationally optimized sums of states and J-resolved microcanonical rate constants (i.e. k(E,J)) for the reaction. These quantities can be used in 2-dimensional (i.e. depending on both E and J) master equations. By summing over J, it also gives microcanonical VTST rate constants (i.e. k(E) that can be used in 1-D (i.e. depending on E, alone) master equations. An important feature otf the code is that it automatically identifies cases where two or more bottlenecks occur along the same reaction path and then uses W. H. Miller's unified statistical theory27 to compute the over-all effective rae constant.


This code features a J-resolved steady-state master equation code that is solved by eigenvalue methods on large parallel computers. It utilizes the frozen-J approximation.