Skip to main content

Advertisement

Log in

A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies

  • Focus: Ion Activation
  • Published:
Journal of the American Society for Mass Spectrometry

Abstract

A new model for energy exchange between translational and internal degrees of freedom in atom-molecule collisions has been developed. It is suitable for both steady state conditions (e.g., a large number of collisions with thermal kinetic energies) and non-steady state conditions with an arbitrary distribution of collision energies (e.g., single high-energy collisions). In particular, it does not require that the collision energies be characterized by a quasi-thermal distribution, but nevertheless it is capable of producing a Boltzmann distribution of internal energies with the correct internal temperature under quasi-thermal conditions. The energy exchange is described by a transfer probability density that depends on the initial relative kinetic energy, the internal energy of the molecule, and the amount of energy transferred. The probability density for collisions that lead to excitation is assumed to decrease exponentially with the amount of transferred energy. The probability density for de-excitation is obtained from microscopic reversibility. The model has been implemented in the ion trap simulation program ITSIM and coupled with an Rice-Rampsberger-Kassel-Marcus (RRKM) algorithm to describe the unimolecular dissociation of populations of ions. Monte Carlo simulations of collisional energy transfer are presented. The model is validated for non-steady state conditions and for steady state conditions, and the effect of the kinetic energy dependence of the collision cross-section on internal temperature is discussed. Applications of the model to the problem of chemical mass shifts in RF ion trap mass spectrometry are shown.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Oxford: Backwell Scientific Publications, 1990.

    Google Scholar 

  2. Flynn, G. W. Collision-Induced Energy Flow between Vibrational Modes of Small Polyatomic Molecules. Acc. Chem. Rev. 1981, 14, 334–341.

    Article  CAS  Google Scholar 

  3. Krajnovich, D. J.; Parmenter, C. S.; Catlett, D. L. State-to-State Vibrational Transfer in Atom-Molecule Collisions. Beams versus Bulbs. Chem. Rev. 1987, 87, 237–288.

    Article  CAS  Google Scholar 

  4. Oref, I.; Tardy, D. C. Energy Transfer in Highly Excited Large Polyatomic Molecules. Chem. Rev. 1990, 90, 1407–1445.

    Article  CAS  Google Scholar 

  5. Nordholm, S.; Börjesson, L. E. B.; Ming, L.; Svedung, H. Progress on the Modeling of the Collisional Energy Transfer Mechanism in Unimolecular Reactions. Ber. Bunsenges. Phys. Chem. 1997, 101, 574–580.

    CAS  Google Scholar 

  6. Smith, S. C.; McEwan, M. J.; Giles, K.; Smith, D.; Adams, N. G. Unimolecular Decomposition of a Polyatomic Ion in a Variable-Temperature Selected-Ion-Flow-Drift Tube: Experiment and Theoretical Interpretation. Int. J. Mass Spectrom. Ion Processes 1990, 96, 77–96.

    Article  CAS  Google Scholar 

  7. Barker, J. R. A State-to-State Statistical-Dynamical Theory for Large Molecule Collisional Energy Transfer. Ber. Bunsenges. Phys. Chem. 1997, 101, 566–573.

    CAS  Google Scholar 

  8. Goeringer, D. E.; McLuckey, S. A. Relaxation of Internally Excited High-Mass Ions Simulated Under Typical Quadrupole Ion Trap Storage Xonditions. Int. J. Mass Spectrom. 1998, 177, 163–174.

    Article  CAS  Google Scholar 

  9. Plass, W. R. Ph.D. Thesis, Justus-Liebig-Universität Giessen, Germany, 2001 pp 43–78.

  10. Wells, J. M.; Plass, W. R.; Patterson, G. E.; Ouyang, Z.; Badman, E. R.; Cooks, R. G. Chemical Mass Shifts in Ion Trap Mass Spectrometry: Experiments and Simulations. Anal. Chem. 1999, 71, 3405–3415.

    Article  CAS  Google Scholar 

  11. Plass, W. R.; Li, H.; Cooks, R. G. Theory, Simulation, and Measurement of Chemical Mass Shifts in RF Quadrupole Ion Traps. Int. J. Mass Spectrom. 2003, 228, 237–267.

    Article  CAS  Google Scholar 

  12. March, R. E.; Londry, F. A. Theory of Quadrupole Mass Spectrometry. Practical Aspects of Ion Trap Mass Spectrometry, Vol. I; In March, R. E.; Todd, J. F. J., Eds.; CRC Press: Boca Raton, FL, 1995; pp 25–48.

    Google Scholar 

  13. Cooks, R. G.; Rockwood, A. L. The Thomson—A Suggested Unit for Mass Spectroscopists. Rapid Commun. Mass Spectrom. 1991, 5, 93.

    CAS  Google Scholar 

  14. Uggerud, E.; Derrick, P. J. Theory of Collisional Activation of Macromolecules. Impulsive Collisions of Organic Ions. J. Phys. Chem. 1991, 95, 1430–1436.

    Article  CAS  Google Scholar 

  15. Douglas, D. J. Applications of Collision Dynamics in Quadrupole Mass Spectrometry. J. Am. Soc. Mass Spectrom. 1998, 9, 101–113.

    Article  CAS  Google Scholar 

  16. Fujiwara, M.; Naito, Y. Simulation for Internal Energy Deposition in Sustained Off-Resonance Irradiation Collisional Activation Using a Monte Carlo Method. Rapid Commun. Mass Spectrom. 1999, 13, 1633–1638.

    Article  CAS  Google Scholar 

  17. Tardy, D. C.; Rabinovitch, B. S. Intermolecular Vibrational Energy Transfer in Thermal Unimolecular Systems. Chem. Rev. 1977, 77, 369–408.

    Article  CAS  Google Scholar 

  18. Barker, J. R. Monte Carlo Calculations on Unimolecular Reactions, Energy Transfer, and IR-Multiphoton Decomposition. Chem. Phys. 1983, 77, 301–318.

    Article  CAS  Google Scholar 

  19. Gilbert, R. G.; King, K. D. Gas/Gas and Gas/Wall Average Energy Transfer from Very Low-Pressure Pyrolysis. Chem. Phys. 1980, 49, 367–375.

    Article  CAS  Google Scholar 

  20. Miller, L. A.; Cook, C. D.; Barker, J. R. Temperature Effects in the Collisional Deactivation of Highly Vibrationally Excited Pyrazine by Unexcited Pyrazine. J. Chem. Phys. 1996, 105, 3012–3018.

    Article  CAS  Google Scholar 

  21. Goeringer, D. E.; McLuckey, S. A. Evolution of Ion Internal Energy During Collisional Excitation in the Paul Ion Trap: A Stochastic Approach. J. Chem. Phys. 1996, 104, 2214–2221.

    Article  CAS  Google Scholar 

  22. Landau, L. D.; Lifshitz, E. M. Quantum Mechanics; Pergamon: London, 1959, pp 432–435.

    Google Scholar 

  23. Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University Press: New York, 1987, 173–179.

    Google Scholar 

  24. Dunn, S. M.; Anderson, J. B. Direct Monte Carlo Simulation of Chemical Reaction Systems: Internal Energy Transfer and an Energy-Dependent Unimolecular Reaction. J. Chem. Phys. 1993, 99, 6607–6612.

    Article  CAS  Google Scholar 

  25. Porter, R. N.; Raff, L. M. Classical Trajectory Methods in Molecular Collisions. Dynamics of Molecular Collisions Part B; In Miller, W. H., Ed.; Plenum Press: New York, 1976; pp 1–52.

    Google Scholar 

  26. Drahos, D.; Vekey, K. Mass Kinetics: A Theoretical Model of Mass Spectra Incorporating Physical Processes, Reaction Kinetics, and Mathematical Descriptions. J. Mass Spectrom. 2001, 36, 237–263.

    Article  CAS  Google Scholar 

  27. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C; Cambridge University Press: Cambridge, 1992, pp 287–290, 359–362.

    Google Scholar 

  28. Julian, R. K.; Nappi, M.; Weil, C.; Cooks, R. G. Multi-Particle Simulation in the Ion Trap Mass Spectrometer: Resonant and Direct Current Pulse Excitation. J. Am. Soc. Mass Spectrom. 1995, 6, 57.

    Article  CAS  Google Scholar 

  29. Gioumousis, G.; Stevenson, D. P. Reactions of Gaseous Molecule Ions with Gaseous Molecules. V. Theory. J. Chem. Phys. 1958, 29, 294–299.

    Article  CAS  Google Scholar 

  30. Plass, W. R.; Gill, L. A.; Bui, H. A.; Cooks, R. G. Ion Mobility Measurements by DC Tomography in an RF Quadrupole Ion Trap. J. Phys. Chem. 2000, 104, 5059–5065.

    CAS  Google Scholar 

  31. Viehland, L. A.; Mason, E. A. Transport Properties of Gaseous Ions Over a Wide Energy Range. Part IV. At. Data Nucl. Data Tables 1995, 60, 37–95.

    Article  CAS  Google Scholar 

  32. Valentine, S. J.; Counterman, A. E.; Clemmer, D. E. A Database of 660 Peptide Ion Cross Sections: Use of Intrinsic Size Parameters for Bona Fide Predictions of Cross Sections. J. Am. Soc. Mass Spectrom. 1999, 10, 1188–1211.

    Article  CAS  Google Scholar 

  33. Henderson, S. C.; Li, J.; Counterman, A. E.; Clemmer, D. E. Intrinsic Size Parameters for Val, Ile, Leu, Gln, Thr, Phe, and Trp Residues from Ion Mobility Measurements of Polyamino Acid Ions. J. Phys. Chem. B 1999, 103, 8780–8785.

    Article  CAS  Google Scholar 

  34. Wysocki, V.; Kenttamaa, H. I.; Cooks, R. G. Internal Energy-Distributions of Isolated Ions After Activation by Various Methods. Int. J. Mass Spectrom Ion Processes 1987, 75, 181–208.

    Article  CAS  Google Scholar 

  35. Meroueh, O.; Hase, W. L. Energy Transfer Pathways in the Collisional Activation of Peptides. Int. J. Mass Spectrom. 2000, 201, 233–244.

    Article  CAS  Google Scholar 

  36. Rabrenovic, M.; Beynon, J. H.; Lee, S. H.; Kim, M. S. Collision-Induced Dissociation of keV Methane Molecular Ions. Analysis of the Pressure Dependence Using Probability Theory. Int. J. Mass Spectrom. Ion Processes 1985, 65, 197–210.

    Article  CAS  Google Scholar 

  37. Laskin, J.; Futrell, J. Internal Energy Distributions Resulting from Sustained Off-Resonance Excitation in Fourier Transform Resonance Mass Spectrometry. II. Fragmentation of the 1-Bromoaphthalene Radical Cation. J. Phys. Chem. 2000, 104, 5484–5494.

    CAS  Google Scholar 

  38. McLuckey, S. A. Principles of Collisional Activation in Analytical Mass Spectrometry. J. Am. Soc. Mass Spectrom. 1992, 3, 599–614.

    Article  CAS  Google Scholar 

  39. Goeringer, D. E.; Duckworth, D. C.; McLuckey, S. A. Collision-Induced Dissociation in Quadrupole Ion Traps: Application of a Thermal Model to Diatomic Ions. J. Phys. Chem. A 2001, 105, 1882–1889.

    Article  CAS  Google Scholar 

  40. Gillespie, D. T. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Chem. Phys. 1977, 81, 2340–2361.

    Article  CAS  Google Scholar 

  41. Baer, T.; Dutuit, O.; Mestdagh, H.; Rolando, C. Dissociation Dynamics of n-Butylbenzene Ions: The Competitive Production of m/z 91 and 92 Fragment Ions. J. Phys. Chem. 1988, 92, 5674–5679.

    Article  CAS  Google Scholar 

  42. Raznikov, V. V.; Kozlovsky, V. I.; Dodonov, A. F.; Raznikova, M. O. Heating of Ions Moving in a Gas Under the Influence of a Uniform and Constant Electric Field. Rapid Commun. Mass Spectrom. 1999, 13, 370–375.

    Article  CAS  Google Scholar 

  43. Laskin, J.; Byrd, M.; Futrell, J. Internal Energy Distributions Resulting from Sustained Off-Resonance Excitation in FTMS. I. Fragmentation of the Bromobenzene Radical Cation. Int. J. Mass Spectrom. 2000, 195/196, 285–302.

    Article  CAS  Google Scholar 

  44. Plomley, J. B.; Londry, F. A.; March, R. E. The Consecutive Fragmentation of n-Butylbenzene in a Quadrupole Ion Trap. Rapid Commun. Mass Spectrom. 1996, 10, 200–203.

    Article  CAS  Google Scholar 

  45. Syka, J. E. P. Commercialization of the Quadrupole Ion Trap. Practical Aspects of Ion Trap Mass Spectrometry, Vol. I; In March, R. E.; Todd, J. F. J., Eds.; CRC Press: Boca Raton, FL, 1995; p 169.

    Google Scholar 

  46. Nacson, S.; Harrison, A. G. Energy Transfer in Collisional Activation. Energy Dependence of the Fragmentation of n-Alkylbenzene Molecular Ions. Int. J. Mass Spectrom. Ion Processes 1985, 63, 325–337.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wolfgang R. Plass.

Additional information

Published online October 23, 2003

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plass, W.R., Cooks, R.G. A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies. J Am Soc Mass Spectrom 14, 1348–1359 (2003). https://doi.org/10.1016/j.jasms.2003.08.012

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1016/j.jasms.2003.08.012

Keywords

Navigation