Fortran software for unimolecular reactions and energy transfer

Note: Most of these programs were developed by the author for use in a batch processing environment. Thus, most are not interactive (especially the time consuming programs). However it is hoped to convert these programs for interactive runtime use and/or interactive prreparation of datafiles for subsequent batch runs. Programs are intended to run on any computer with a Fortran 77 compiler and sufficient memory. As of present not all are available for public distribution. Conversion to Fortran 90 is planned.

RRK/RRKM theory

A#1 GRRK - generalised RRK theory

Calculates generalised RRK rate coefficients (k(w,T) and ka(E)) for reactant molecules including vibrational and/or rotational degrees of freedom (classical treatment).

A#2 QRRK - quantised RRK theory

Calculates predictions of unimolecular rate coefficients (k(w,T) and ka(E)) for reactant molecules including quantum vibrations (in an effective approximate form) and classical rotations. Demonstrates why RRK theory is often inadequate.
(H.W.Schranz, S.Nordholm, Int. J. Chem. Kin. 13(1981) 1051)

A#3 SSS - s-values

Calculates the effective number of oscillators s for a set of quantum harmonic vibrations for Ev, Cv and QRRK prescriptions. (see reference above)

A#4 RRKMF - SCA RRKM theory

Calculates RRKM rate coefficients (k(w,T) and ka(E)) for reactant molecules including harmonic quantum vibrations and classical rotations. The calculation is based on a microcanonical level of RRKM theory and there is a choice of active/inactive rotations, proportion of exact count and Whitten-Rabinovitch count. The traditional, normalised and exact predictions of k(w,T) in the strong collision assumption (SCA) level of theory are all calculated. Provides data for master equation solution.
(S. Nordholm, H. W. Schranz, Chem. Phys. 62(1981) 459)

Intermolecular energy transfer theories

B#1 IECT - impulsive ergodic collision theory

Calculates the average energy transferred per collision <DE> of a reactant and medium molecule according to impulsive ergodic collision theory. Both molecules are modelled as a set of harmonic vibrations and classical rotations. Quantum effects in the vibrations are approximately allowed for by calculating the effective s-value (number of oscillators or vibrations) from the quantum heat capacity while still maintaining the classical form of the main equation for <DE>.
(H.W.Schranz, S.Nordholm, I.J.C.K. 13(1981) 1051)

B#2 HSCT - hardsphere collision theory

Calculates the average energy transferred per collision and the rate of energy transfer for a polyatomic reactant and a monoatomic medium molecule. The collision event is modelled as a weighted average of individual hard sphere atom-atom collisions with each weight given as the collision frequency of the medium monatomic with the particular reactant atom.
(H.W.Schranz, chapter 5, Honours Thesis, Sydney University, 1979)

Master Equation solution

C#1 DME, EFBS, THERM - EFBS solution of thermal master equation

Using the Equilibrium Finite Basis Set (EFBS) method this program calculates the thermal unimolecular rate coefficient as a function of pressure as well as the corresponding high/low pressure limits for a given reactant molecule and for a given collisional transition probability model (e.g. SCA, stepladder, exponential, gaussian) at a specified temperature. The reactant molecule is specified by a given critical energy Eo, microscopic rate constant ka(E) and canonical probability density PT(E). The thermal unimolecular rate coefficient is obtained as the solution of the corresponding master equation (as the lowest (in absolute value) eigenvalue of the rate matrix).
(H.W.Schranz, S.Nordholm, Chem. Phys. 74(1983) 365)

C#2 DMC, EFBS, CHEM - traditional "sink" treatment of the chemically activated master equation

Using the EFBS method this program calculates the stabilization-/decomposition branching ratios as a function of pressure for a given reactant molecule and for a given transition probability model at a specified temperature. The treatment used assumes that molecules once stabilized can not be reactivated by collision (i.e. a sink). The reactant molecule is specified as in program C#1 above.
(H.W.Schranz, S.Nordholm, Chem. Phys. 87(1984) 163)

C#3. DMCIT, EFBS, CHEMIT - intermediate timescale treatment of the chemically activated master equation

As in program C#2 above, but the treatment used assumes a separation in timescales exist during which a steady state approximately exists.

C#4. DMCEX, EFBS, CHEMEX - exact treatment of the chemically activated master equation

As in program C#2 above, but the treatment used solves the master equation exactly to yield the time dependent stabilization/decomposition branching ratios.

C#5. DMBND, EFBND, THERBD - banded version of C#1

As in program C#1 above, but the rate matrix is constructed and stored in a banded manner which allows larger matrices to be used if fewer bands are employed for a given storage allocation.

Classical RRKM for linear polyatomic chains

D#1. NMRRKM - normal mode RRKM theory

This program calculates microscopic rate constants ka(E) from classical RRKM theory using the vibrational normal modes for the reactant and transition state configurations for linear polyatomic chains(nonrotating).
(H.W.Schranz, S.Nordholm,B.C.Freasier, Chem. Phys. 108(1986) 69,93,10)

D#2. NMODE - normal modes

This program calculates vibrational normal modes for linear polyatomic chains (nonrotating). See references above for details.

D#3. ELRRKM - classical RRKM theory

This program calculates microscopic rate constants ka(E) from classical RRKM theory using the specified bond potentials (Morse or harmonic) in the linear polyatomic chain. See ref. D#1 for details.

D#4. ELRKIB - classical RRKM theory-identical bonds

As for D#3 but this version is restricted to identical bonds only in the polyatomic chain which results in a faster runtime.

Simulation of dissociation of linear polyatomic chains

E#1. LSIM, SIM - single trajectory simulation

This program performs a single trajectory run from a specified initial state. If necessary, back integration is also performed from the forward integrated state to check trajectory accuracy and/or sensitivity to errors in the numerical integration.
(H.W.Schranz, S.Nordholm,B.C.Freasier, Chem. Phys. 108(1986) 69,93,105)

E#2. LTRAJ7, MCD6, MCP6, SNM, SIM, DPDIAG - multiple trajectory simulation

This program performs a multiple trajectory simulation given microcanonically selected initial states for specified polyatomic chain size, energy and bond cutoff. Integration is continued till dissociation or a time limit is reached. Selected statistics are output for each trajectory run. See ref. above.

E#3. Statistical Analysis Routines

Various routines are available which utilize output from E#1 or E#2 above to yield an estimation of the rate constant and errors (including bootstrap estimation), exponential fits of simulation data and correlation length estimation of the Markov chain used in the sampling.

Intermolecular energy transfer simulation (central force field potential surface)

F#1. ST1A3A - single trajectory simulation of monatomic medium and triatomic reactant

This program performs a single trajectory run from a specified initial state. Backward integration of the forward integrated state can also be performed as a check on trajectory accuracy and/or sensitivity to numerical integration errors.
(H.Hippler, H.W.Schranz, J.Troe, J.Phys.Chem. 90(1986) 6158
H.W.Schranz, J.Troe, J.Phys.Chem. 90(1986) 6168)

F#2. FC1A3A - multiple trajectory simulation of monatomic medium and triatomic reactant

This program performs multiple trajectories given an ensemble of initial states of the colliding triatomic-monatomic system. A sophisticated Markov chain sampling procedure allows the state of the triatomic molecule to be efficiently specified as chosen from a pure micro-canonical ensemble at constant molecular energy or the molecular angular momentum may be restricted to lie in a specified range as well. The medium-reactant degrees of freedom are sampled by a simple Monte Carlo procedure to yield a canonical ensemble of the specified medium temperature . Selected statistics are written off to a data file which can be statistically analyzed. See above references for details.

F#3. STET - single trajectory simulation of monatomic medium and triatomic reactant

This program is a version of F#1 that has been generalised to polyatomic reactants.

F#4. FCAN - statistical analysis of the output of FC1A3A

This program manipulates selected data records in the data file produced by a run of FC1A3A and calculates specified statistics. These can be output to another data file.

F#5. PLAN - plot analysis of the output of FC1A3A

This program is for the general purpose plotting of energy transfer results given in a user defined data file.

F#6. PLET - plot energy transfer results

This program is for the general purpose plotting of energy transfer results given in a user defined data file.

F#7. FLSQ - least squares analysis of the output of FC1A3A

This program performs a nonlinear least squares fit of selected output of FC1A3A to one or two dimensional exponential terms representing the collisional transition probability P(E,E') or P(Ev,EJ | Ev',EJ').

F#8. PWSPEC, PWSPC2 - FFT power spectra

These programs take a single trajectory as input and generate the corresponding power spectrum. The first program calls the IMSL power spectra routine FTFPS while the second program has an independent routine that calculates the power spectrum.

Low pressure Limit Diatomic Dissociation/Recombination Theory

G#1. MICRAT - mic-SCA/ISCA

This program calculates the mic-SCA and mic-ISCA low pressure dissociation/recombination rate constants. It also calculates the RRKM SCA fall-off calculation even though the high pressure regime is physically unattainable in the gas phase for a diatomic molecule.
(S.Nordholm, H.W.Schranz, B.C.Freasier, N.D.Homer, Chem. Phys. submitted 1987)

G#2. EJrat - EJ-SCA/ISCA

This program calculates the EJ-SCA and EJ-ISCA low pressure dissociation/recombination rate constants. This treatment allows for angular momentum conservation. See above references for details.

G#3. FRAT - correction factors

This program calculates collision cross section and quantum vibration correction factors for the dissociation/recombination rate constant.

Microcanonical ECT/RMC master equation solution

H#1. MICRAD - mic-SCA RRKM theory

This program calculates ka(E) and PT(E) for the diatomic reactant according to the usual microcanonical SCA RRKM theory. A date file containing ka(E) and PT(E) is output for input to the masterequation program DMD2 in H#3 below.

H#2. MICECD - ECT/RMC transition probability

This program calculates the ECT/RMC transition probability for collisions of a diatomic reactant with a monoatomic medium. The EFBS procedure is employed to create a grained rate matrix for input into the master equation program DMD2 in H#3 below.

H#3. DMD2, EFBD2, THERD2 - ECT/RMC master equation

This program is similar to program DME in C#1 The microscopic rate constant ka(E) and canonical probability density PT(E) and the grained rate matrix are input from programs MICRAD and MICECD in H#1 and H#2 above. The program allows output of k(w) and the high/low pressure limit rate constants.

Simulation of diatomic recombination

I#1. RECOMB - Multiple trajectory simulation of recombination.

This program performs multiple trajectory simulation of a canonical ensemble of ET (X2* + M) or RMC (XM + X) initial states. Backward integration is performed to check the identity of the initial states and forward integration is performed to identify those states that recombine. Successive collisions of new medium molecules M are performed with the newly formed bound X2 to check for redissociation (the nonequilibrium effect). The recombination flux is then calculated.

I#2. KEQRAT - ET equilibrium constant

This program calculates the ET equilibrium constant for the process X + X -> X2* in order to convert the ET recombination flux in program RECOMB in I#1.to a recombination rate constant.

I#3. KEQRMC - RMC equilibrium constant

This program calculates the RMC equilibrium constant for the process X + M -> MX in order to convert the RMC recombination flux in program RECOMB in I#1 to a recombination rate constant.

General Utilities

J#1. PLGEN - General Plotting Program

This program plots general 2D plots with an arbitrary number of curves (solid, dotted, dashed) with or without symbols (circle, square, triangle,...) and with or wihout error bars. The program calls PLOT79 routines and reads in a user defined data file.