BRIEF COMMUNICATION

POLYRATE-version 6.5, and MORATE-version 6.5/P6.5-M5.05.

Two Computer Programs for the Calculation of Chemical Reaction Rates

Wei-Ping Hu, Rozeanne Steckler,* Gillian C. Lynch, Yi-Ping Liu, Bruce C. Garrett, Alan D. Isaacson, Da-hong Lu, Vasilios Melissas, Ivan Rossi, James J. P. Stewart,
and Donald G. Truhlar**

*Corresponding author. Address: San Diego Supercomputer Center, P. O. Box 85608, San Diego, CA 92168-9784

**Corresponding author. Address: Department of Chemistry, University of Minnesota, 207 Pleasant Street S.E., Minneapolis, Minnesota 55455-0431, U.S.A.

POLYRATE and MORATE are computer programs for the calculation of chemical reaction rates for gas-phase reactions and reactions at gas-solid interfaces using variational transition state theory (VTST) and multidimensional semiclassical tunneling approximations. Both unimolecular and bimolecular reactions are included, and surface diffusion may be calculated as a special case of unimolecular reaction at a gas-solid interface.

The purpose of this communication is to briefly describe the history of both codes, with references to publications where the original equations, sample applications, and reviews may be found. We also summarize the licensing arrangements. It is our hope that these comments will be useful to potential users trying to decide if either of these codes would be suitable for their application needs.

Variational transition state theory has a long history.¹ In the formulation used in POLYRATE and MORATE, the rate constant for a canonical or microcanonical ensemble is numerically minimized with respect to a one-parameter sequence of trial generalized transitions states orthogonal to the minimum energy path in mass-scaled (i.e., isoinertial) coordinates; this approach dates back to a series of papers by two of the authors that were published in 1979.² The earliest applications^2,3 were to atom-diatom reactions, but a couple of years later a practical implementation for arbitrary polyatomic reactants was developed.⁴ The formalism was extended to unimolecular processes at gas-solid interfaces in 1985⁵ and to chemisorption reactions of gases with solids in 1989.⁶ Two early reviews⁷ include references for all applications up to 1987, and the basic theory has been discussed in two pedagogical articles.⁸

POLYRATE has developed in an unbroken line from our earliest⁴ polyatomic applications. Version 1.1 was published in 1987.⁹ The basic equations employed in POLYRATE are contained in a handbook-type article published in 1985.¹⁰ The original version of POLYRATE only applied to gas-phase reactions and only contained tunneling methods^4,10,11 suitable for systems with small reaction-path curvature. Further, the original small-curvature method^4,11 was valid only for systems with one nonzero component of the reaction-path curvature. Reactions at a gas-solid interface were added in version 1.5,¹² various aspects of large-curvature tunneling^10,13 were added in versions 2.0-3.0,¹⁴ and the current, generally applicable versions^15-17 of both small- and large-curvature tunneling approximations were added in versions 4.0-4.5. The current version of POLYRATE is 6.5.¹⁸

In the original mode of operation of POLYRATE, one supplies an analytic potential energy function as a subroutine that returns the energy and its derivatives as functions of atomic cartesian coordinates. Several sample potential functions are distributed with the code. Examples of applications employing analytic potentials are calculations on the reactions CH3 + H2 -> CH4 + H¹⁹ and Cl^- (H2O)n + CH3Cl' -> CH3Cl + Cl'^- (H2O)n²⁰ and calculations of the surface diffusion of H on the (100) crystal face of Cu.²¹

In 1989 we published a new way to employ POLYRATE, which is called "direct dynamics." In such calculations, the energy, gradient, and hessian at various points along the minimum energy path are directly input (as a data file) without fitting them to an analytic potential energy function.^22,23 This option was incorporated in version 1.5 of POLYRATE.¹² Any affordable level of electronic structure theory may be used to generate the energies, gradients, and hessians for the input file, but no electronic structure codes are supplied with POLYRATE. Examples of applications employing this option are a study of the reaction NH2 + H2 -> NH3 + H²⁴ and a study of carbene rearrangements.²⁵ POLYRATE-version 6.5 also supports a simpler way to use electronic structure data which is called zero-order interpolated VTST or IVTST-0; in this method electronic structure data is input for only three stationary points, and interpolation is used to generate intermediate data.²⁶ Version 6.6 will also support first-order interpolated VTST (IVTST-1),^26,27 which uses data for four stationary points.

The previous two paragraphs describe what may be called the single-level mode modes of operation. POLYRATE also supports dual-level direct dynamics, as explained below.

MORATE is a more self-contained package for direct dynamics employing semiempirical molecular orbital theory for the electronic structure calculations. It includes the dynamics capabilities of the POLYRATE package, and a set of interface routines to the MOPAC package^28-30 for electronic structure calculations (version 5.05mn of MOPAC is included as part of MORATE and need not be obtained separately). Using MORATE, one does not write an electronic structure input file for POLYRATE. Rather, every time MORATE needs an energy or a gradient it directly calls our interface routines to MOPAC. MORATE computes hessians by numerical first derivatives of the MOPAC gradients, and the user can choose whether this is done using POLYRATE routines or MOPAC routines. The current version of MORATE³¹ is 6.5/P6.5-M5.05 which denotes the version 6.5 package based on version 6.5 of POLYRATE and version 5.05mn of MOPAC. Version 6.5 supports electronic structure calculations at the MINDO/3,³² MNDO,³³ AM1,³⁴ PM3,³⁵ and NDDO-SRP^17,36,37 levels (where NDDO-SRP denotes neglect of diatomic differential overlap with specific reaction parameters, and the other abbreviations are standard). An example of a MORATE application employing AM1 and NDDO-SRP calculations is a treatment³⁶ of Cl^- (H2O)n + CH3Cl' -> CH3Cl + Cl'^- (H2O)n, for n = 1 and 2, which compared this treatment to the analytic potential energy function approach. An example applying MNDO, AM1, and PM3 to the same system is a treatment of the unimolecular rearrangement of deuterium-labeled cis-pentadiene.¹⁶ Another example of an NDDO-SRP application is the reaction of CF3 with CD3H.¹⁷

Our most recent enhancement of the capabilities of POLYRATE and MORATE is the incorporation of dual-level techniques.³⁸ In such calculations one combines two levels with a triple slash, e.g., CCSD(T)/cc-pVTZ///MP2/cc-pVDZ. Whereas the well known convention HL//LL denotes optimizing the geometry at lower level LL and calculating a single-point energy at higher level HL, the notation HL///LL denotes calculating the reaction path at lower level LL and adding corrections based on interpolation of a limited number of HL energies and optionally gradients and hessians. This dual-level approach is also called VTST-IC (variational transition state theory with interpolated corrections). The data for the higher level must be supplied in an external file by the user, and the data for the lower level is obtained by any of the methods available for single-level calculations. Thus POLYRATE can use an analytic potential energy function or data on an external file for the lower level, and MORATE can use semiempirical molecular orbital theory for the lower level. Two examples of dual-level calculations are given in a recent paper³⁹ on the reaction of OH with NH3. In particular the QCISD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ///MP2/6-31G* calculations in that paper were carried out with POLYRATE, and the QCISD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ///NDDO-SRP calculations were carried out with MORATE.

In addition to using POLYRATE and MORATE for full rate constant calculations, some authors may wish to use the codes for calculating certain quantities that occur in full calculations but are also of interest in their own right. For example, the codes contain several algorithms⁴⁰ for calculating minimum energy paths (MEPs) in mass-scaled coordinates;⁴¹ such paths are called intrinsic reaction coordinates (IRCs) by some workers. Examples of other quantities that may be of interest include fixed-energy tunneling probabilities⁴² and hindered internal rotator partition functions.⁴³

Great efforts have been made to insure probability. The current versions of POLYRATE and MORATE have been tested on several computers, including Cray supercomputers and IBM, Silicon Graphics, and Sun workstations. In all cases the test suites run properly and gives correct answers. Furthermore, the compiler options to detect non-ANSI FORTRAN77 code indicate only three types of non-ANSI code, all intentional; in particular we employ the INCLUDE and DO WHILE extensions, and we use lower case for subroutine names. The only machine-specific code is for date and time calls, and these are well documented and supplied in versions for several machines.

POLYRATE is distributed with a Postscript documentation file, and MORATE has two manuals in Postscript format and three in ASCII text format. These manuals explain, among other things, the installation, input and output, and the test suites.

Beginning with version 6.0, POLYRATE and MORATE have keyword input with carefully chosen defaults, making them much more convenient to use than earlier versions.

Future prospects include interfaces of POLYRATE with AMSOL, ACES II, and GAMESS.

POLYRATE and MORATE are each available with non-profit or commercial licenses. QCPE supplies the code with non-profit licenses only. There is no license fee for non-profit licenses, but the license must be signed. For ordering information and QCPE service charges see recent issues of this Bulletin or the QCPE internet server. Commercial licenses and the current fee schedule for commercial or proprietary applications are available from the principal investigator on this project (D.G.T., see address at beginning of this communication). Commercial license fees are placed in a University of Minnesota research account that supports further development. Neither non-profit nor commercial licenses allow redistribution in either original or modified form. Licenses do not include support or guarantees that the programs are bug-free. Inquires about special licenses for further development or redistribution should be directed to the principal investigator.

POLYRATE-version 6.5 and MORATE-version 6.5/P6.5-M5.05 were developed at the University of Minnesota with support by the U.S. Department of Energy, Office of Basic Energy Sciences and by Minnesota Supercomputing Institute and at San Diego Supercomputer Center with NSF support. Earlier versions of POLYRATE and MORATE were developed at the University of Minnesota (DOE, MSI), San Diego Supercomputer Center (NSF), Environmental Molecular Sciences Laboratory (DOE support), Chemical Dynamics Corporation (U.S. Army support), and Miami University. MOPAC-version 5.05mn was developed at the University of Minnesota. MOPAC-version 5 was developed at the Frank J. Seiler Research Laboratory of the U.S. Air Force Academy.

1. See, e.g., E. Wigner, J. Chem. Phys. 5, 720 (1937); J. Horiuti, Bull. Chem. Soc. Jpn. 13, 210 (1938); M. A. Eliason and J. O. Hirschfelder, J. Chem. Phys. 30, 1426 (1959); J. C. Keck, Adv. Chem. Phys. 13, 85 (1967).

2. B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 70, 1593 (1979), J. Phys. Chem. 83, 1052, 1079 (1979), 87, 4553(E) (1983), J. Amer. Chem. Soc. 101, 4534, 5207 (1979).

3. B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 72, 3460 (1980); B. C. Garrett, D. G. Truhlar, R. S. Grev, and A. W. Magnuson, J. Phys. Chem. 84, 1730 (1980).

4. A. D. Isaacson and D. G. Truhlar, J. Chem. Phys. 76, 1380 (1982); D. G. Truhlar, A. D. Isaacson, R. T. Skodje, and B. C. Garrett, J. Phys. Chem. 86, 2252 (1983).

5. J. G. Lauderdale and D. G. Truhlar, J. Amer. Chem. Soc. 107, 4590 (1985), Surf. Sci. 164, 558 (1985), J. Chem. Phys. 84, 1843 (1986).

6. T. N. Truong, G. C. Hancock, and D. G. Truhlar, Surf. Sci. 214, 523 (1989).

7. D. G. Truhlar and B. C. Garrett, Annu. Rev. Phys. Chem. 35, 159 (1984), Journal de Chimie Physique (in English) 84, 365 (1987).

8. M. M. Kreevoy and D. G. Truhlar, in Investigation of Rates and Mechanisms of Reactions, Part 1, edited by C. F. Bernasconi (Vol. 6 of the 4th edition of "Techniques of Chemistry,' edited by A. Weissberger, John Wiley & Sons, New York, 1986), p. 13; S. C. Tucker and D. G. Truhlar in New Theoretical Techniques for Understanding Organic Reactions (NATO ASI Series C, Vol 267), edited by J. Bertrán and I. G. Csizmadia (Kluwer Academic Publishers, Dordrecht, 1989), p. 291.

9. A. D. Isaacson, D. G. Truhlar, S. N. Rai, R. Steckler, G. C. Hancock, B. C. Garrett, and M. J. Redmon, Computer Phys. Commun. 47, 91 (1987).

10. D. G. Truhlar, A. D. Isaacson, and B. C. Garrett, in Theory of Chemical Reaction Dynamics, Vol 4, edited by M. Baer (CRC Press, Boca Raton, FL, 1985), p. 65.

11. R. J. Skodje, D. G. Truhlar, and B. C. Garrett, J. Phys. Chem. 85, 3019 (1981).

12. POLYRATE-version 1.5: A. D. Isaacson, D. G. Truhlar, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. N. Truong, T. Joseph, B. C. Garrett, and R. Steckler, University of Minnesota Supercomputing Institute Research Report 88/87, September 1988.

13. B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400 (1983); B. C. Garrett, N. Abusalbi, D. J. Kouri, and D. G. Truhlar, J. Chem. Phys. 83, 2212 (1985); M. M. Kreevoy, D. Ostovic, D. G. Truhlar, and B. C. Garrett, J. Phys. Chem. 90, 3766 (1986); B. C. Garrett, T. Joseph, T. N. Truong, and D. G. Truhlar, Chem. Phys. 136, 5302 (1989).

14. D.-h. Lu, T. N. Truong, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, V. S. Melissas, and D. G. Truhlar, POLYRATE-version 2.5, Quantum Chemistry Program Exchange program 601, QCPE Bulletin 11, 13 (1991).

15. D.-h. Lu, T. N. Truong, V. S. Melissas, G. C. Lynch, Y.-P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, and D. G. Truhlar, Computer Phys. Commun. 71, 235 (1992); T. N. Truong, D.-h. Lu, G. C. Lynch, Y.-P. Liu, V. S. Melissas, J. J. P. Stewart, R. Steckler, B. C. Garrett, A. D. Isaacson, A. Gonzalez-Lafont, S. N. Rai, G. C. Hancock, T. Joseph, and D. G. Truhlar, Computer Physics Communications 75, 143 (1993).

16. Y.-P. Liu, G. C. Lynch, T. N. Truong, D.- h. Lu, D. G. Truhlar, and B. C. Garrett, J. Amer. Chem. Soc. 115, 2408 (1993).

17. Y.-P. Liu, D.-h. Lu, A. Gonzalez-Lafont, D. G. Truhlar, and B. C. Garrett, J. Amer. Chem. Soc. 115, 7806 (1993).

18. R. Steckler, W.-P. Hu, Y.-P. Liu, G. C. Lynch, B. C. Garrett, A. D. Isaacson, D.- h. Lu, V. S. Melissas, T. N. Truong, S. N. Rai, G. C. Hancock, J. Lauderdale, T. Joseph, and D. G. Truhlar, POLYRATE-version 6.5, new version of QCPE program 601 (see new version announcement in this issue of QCPE Bulletin).

19. T. Joseph, R. Steckler, and D. G. Truhlar, J. Chem. Phys. 87, 7036 (1987); D.-h. Lu, D. Maurice, and D. G. Truhlar, J. Amer. Chem. Soc. 112, 6206 (1990).

20. S. C. Tucker and D. G. Truhlar, J. Amer. Chem. Soc. 112, 3347 (1990); X. G. Zhao, S. C. Tucker, and D. G. Truhlar, J. Amer. Chem. Soc. 113, 826 (1991); X. G. Zhao, D.-h. Lu, Y.-P. Liu, G. C. Lynch, and D. G. Truhlar, J. Chem. Phys. 97, 6369 (1992).

21. S. E. Wonchoba and D. G. Truhlar, J. Chem. Phys. 99, 9637 (1993).

22. K. Baldridge, M. S. Gordon, R. Steckler, and D. G. Truhlar, J. Phys. Chem. 93, 5107 (1989).

23. D. G. Truhlar and M. J. Gordon, Science 249, 491 (1990).

24. B. C. Garrett, M. L. Koszykowski, C. F. Melius, and M. Page, J. Phys. Chem. 94, 7096 (1990).

25. J. W. Storer and K. N. Houk, J. Amer. Chem. Soc. 115, 10426 (1993).

26. A. Gonzalez-Lafont, T. N. Truong, and D. G. Truhlar, J. Chem. Phys. 95, 8875 (1991).

27. V. S. Melissas and D. G. Truhlar, J. Chem. Phys. 98, 875 (1994).

28. J. J. P. Stewart, J. Computer-Aided Molecular Design 4, 1 (1990).

29. J. J. P. Stewart, MOPAC-version 6.0, Quantum Chemistry Program Exchange program 455-version 6.0, QCPE Bulletin 10, 86 (1990).

30. J. J. P. Stewart, I. Rossi, W.-P. Hu, G. C. Lynch, Y.-P. Liu, and D. G. Truhlar, MOPAC-version 5.05mn, University of Minnesota, Minneapolis, 1994.

31. W.-P. Hu, G. C. Lynch, Y.-P. Liu, I. Rossi, R. Steckler, B. C. Garrett, A. D. Isaacson, D.-h. Lu, V. S. Melissas, and D. G. Truhlar, MORATE-version 6.5/P6.5-M5.05 announced in this issue of Quantum Chemistry Program Exchange Bulletin.

32. R. C. Bingham, M. J. S. Dewar, and D. H. Lo, J. Amer. Chem. Soc. 97, 1294 (1975).

33. M. J. S. Dewar and W. Thiel, J. Amer. Chem. Soc. 99, 4899 (1977).

34. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. Amer. Chem. Soc. 107, 3902 (1985).

35. J. J. P. Stewart, J. Comp. Chem. 10, 221 (1989).

36. A. Gonzalez-Lafont, T. N. Truong, and D. G. Truhlar, J. Phys. Chem. 95, 4618 (1991).

37. I. Rossi and D. G. Truhlar, Chem. Phys. Lett. 223, 231 (1995).

38. W.-P. Hu, Y.-P. Liu, and D. G. Truhlar, J. Chem. Soc. Faraday Trans. 90, 1715 (1994).

39. J. C. Corchado, J. Espinosa-Garcia, W.-P. Hu, I. Rossi, and D. G. Truhlar, J. Phys. Chem. 99, 687 (1995).

40. M. Page and J. W. McIver, J. Chem. Phys. 88, 922 (1988); V. S. Melissas, D. G. Truhlar, and B. C. Garrett, J. Chem. Phys. 96, 5758 (1992).

41. I. Shavitt, J. Chem. Phys. 49, 4048 (1968); D. G. Truhlar and A. Kuppermann, J. Amer. Chem. Soc. 93, 1840 (1971).

42. F. B. Brown, S. C. Tucker, and D. G. Truhlar, J. Chem. Phys. 83, 4451 (1985).

43. D. G. Truhlar, J. Comp. Chem. 12, 266 (1991).