In this paper , we studied the process of dissociation unimolecular of the evaporation of H + 2n+1 hydrogen clusters according to size, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The rate constants k(E) were determined with the use of statistical theory of unimolecular reactions using various approximations. In our work , we use d the products frequencies instead of transitions frequencies in the calculation of unimolecular dissociation rates obtained by three models RRKM. The agreement between the experimental cross section ratio and calculated rate ratio with direct count approximation seems to be reasonable.
W. Forst, “Theory of Unimolecular Reactions,” Academic Press, New York, 1973.
S. WEI, B. TZENG AND A. W. CASTLEMAN JR., “KINETIC ENERGY RELEASE MEASUREMENTS OF AMMONIA CLUSTER IONS DURING METASTABLE DECOMPOSITION AND DETERMINATION OF CLUSTER ION BINDING ENERGIES,” JOURNAL OF CHEMICAL PHYSICS, VOL. 92, NO. 1, 1990, P. 332. HTTP://DX.DOI.ORG/10.1063/1.458434
C. BRéCHIGNAC, PH. CAHUZAC, J. LEYGNIER AND J. WEINER, “DYNAMICS OF UNIMOLECULAR DISSOCIATION OF SODIUM CLUSTER IONS,” JOURNAL OF CHEMICAL PHYSICS, VOL. 90, NO. 3, 1989, P. 1492. HTTP://DX.DOI.ORG/10.1063/1.456675
C. BRéCHIGNAC, H. BUSH, PH. CAHUZAC AND J. LEYGNIER, “DISSOCIATION PATHWAYS AND BINDING ENERGIES OF LITHIUM CLUSTERS FROM EVAPORATION EXPERIMENTS,” JOURNAL OF CHEMICAL PHYSICS, VOL. 101, NO. 8, 1994, P. 6992. HTTP://DX.DOI.ORG/10.1063/1.468326
C. X. SU, D. A. HALES AND P. B. ARMENTROUT, “COLLISION INDUCED DISSOCIATION OF (N = 2 20) WITH XE: BOND ENERGIES, DISSOCIATION PATHWAYS, AND STRUCTURES,” JOURNAL OF CHEMICAL PHYSICS, VOL. 99, NO. 9, 1993, P. 6613. HTTP://DX.DOI.ORG/10.1063/1.465853
U. HILD, G. DIETRICH, S. KRüCKEBERG, M. LINDINGER, K. LüTZENKIRCHEN, L. SCHWEIKHARD, C. WALTHER AND J. SIEGLER, “TIME-RESOLVED PHOTOFRAGMENTATION OF STORED SILVER CLUSTERS (N = 8 21),” PHYSICAL REVIEW A, VOL. 57, NO. 4, 1998, PP. 2786-2793. HTTP://DX.DOI.ORG/10.1103/PHYSREVA.57.2786
U. Ray, M. F. Jarrold, J. E. Bower and J. S. Kraus, “Photodissociation Kinetics of Aluminum Cluster Ions: Determination of Cluster Dissociation Energies,” Journal of Chemical Physics, Vol. 91, No. 5, 1989, pp. 2912-2921. http://dx.doi.org/10.1063/1.456961
H. J. H wang, D. K. Sensharma and M. A. El Sayed, “Size and Temporal Dependence of the Average KineticEnergy Release during the Evaporation of Sputtered Clusters,” Physical Review Letters, Vol. 64, No. 7, 1990, pp. 808-811. http://dx.doi.org/10.1103/PhysRevLett.64.808
J. A. Smith, N. G. Grotts, J. F. Winkel, R. Hallett, A. J. Stace and B. J. Whitaker, “The Decay Dynamics of Photoexcited Argon Cluster Ions,” Journal of Chemical Physics, Vol. 97, No. 1, 1992, p. 397. http://dx.doi.org/10.1063/1.463584
M. Schmidt, R. Kusche, W. Kronmuller, B. Von Issendorff and H. Haberland, “Experimental Determination of the Melting Point and Heat Capacity for a Free Cluster of 139 Sodium Atoms,” Physical Review Letters, Vol. 79, No. 1, 1997, pp. 99-102. http://dx.doi.org/10.1103/PhysRevLett.79.99
W. de Herr, K. Selby, V. Kresin, J. Masui, M. Vollmer, A. Chatelain and W. D. Knight, “Collective Dipole Oscillations in Small Sodium Clusters,” Physical Review Letters, Vol. 59, No. 16, 1987, pp. 1805-1808. http://dx.doi.org/10.1103/PhysRevLett.59.1805
C. Bréchignac, Ph. Cahuzac, F. Carlier and J. Leygnier, “Collective Excitation in Closed-Shell Potassium Cluster Ions,” Chemical Physics Letters, Vol. 164, No. 4, 1989, pp. 433-437. http://dx.doi.org/10.1016/0009-2614(89)85233-9
C. Bréchignac, Ph. Cahuzac, N. Kébaili, J. Leygnier and A. Serfati, “Collective Resonance in Large Free Potassium Cluster Ions,” Physical Review Letters, Vol. 68, No. 26, 1992, pp. 3916-3919. http://dx.doi.org/10.1103/PhysRevLett.68.3916
F. Gulminelli and P. Chomaz, “Critical Behavior in the Coexistence Region of Finite Systems,” Physical Review Letters, Vol. 82, No. 7, 1999, pp. 1402-1405. http://dx.doi.org/10.1103/PhysRevLett.82.1402
M. D’Agostino, M. Bruno, F. Gulminelli, F. Cannata, Ph. Chomaz, G. Casini, E. Geraci, F. Gramegna, A. Moroni and G. Vannini, “Nuclear Liquid-Gas Phase Transition: Experimental Signals,” Nuclear Physics A, Vol. 749, 2005, pp. 55c-64c. http://dx.doi.org/10.1016/j.nuclphysa.2004.12.008
P. Chomaz and F. Gulminelli, “The Challenges of FiniteSystem Statistical Mechanics,” The European Physical Journal A, Vol. 30, No. 1, 2006, pp. 317-331. http://dx.doi.org/10.1140/epja/i2006-10126-5
A. Bonasera, M. Brano, C. O. Dorso and P. F. Mastinu, “Critical Phenomena in Nuclear Fragmentation,” Rivista Del Nuovo Cimento, Vol. 23, No. 2, 2000, pp. 1-102.
M. Belkacem, V. Latora and A. Bonasera, “Critical Evolution of a Finite System,” Physical Review C, Vol. 52, No. 1, 1995, pp. 271-285. http://dx.doi.org/10.1103/PhysRevC.52.271
B. Farizon, M. Farizon, M. J. Gaillard, F. Gobet, M. Carré, J. P. Buchet, P. Scheier and T. D. Mark, “Experimental Evidence of Critical Behavior in Cluster Fragmentation Using an Event-by-Event Data Analysis,” Physical Review Letters, Vol. 81, No. 19, 1998, pp. 4108-4111. http://dx.doi.org/10.1103/PhysRevLett.81.4108
B. Farizon, M. Farizon, M. J. Gaillard, R. Genre, S. Louc, J. Martin, J. P. Buchet, M. Carré, G. Senn, P. Scheier and T. D. Mark, “Mass Distribution and Multiple Fragmentation Events in High Energy Cluster—Cluster Collisions: Evidence for a Predicted Phase Transition,” International Journal of Mass Spectrometry and Ion Processes, Vol. 164, No. 3, 1997, pp. 225-230. http://dx.doi.org/10.1016/S0168-1176(97)00091-8
S. Yamabe, K. Hirao and K. Kitaura, “Theoretical Study on the Stability and the Structure,” Chemical Physics Letters, Vol. 56, No. 3, 1978, pp. 546-548. http://dx.doi.org/10.1016/0009-2614(78)89036-8
H. Huber, “Geometry Optimization in ab Initio SCF Calculations III. Floating Orbital Geometry Optimization (FOGO) with Floating Outer Shell Basis Functions,” Chemical Physics Letters, Vol. 70, 1980, p. 353. http://dx.doi.org/10.1016/0009-2614(80)85349-8
L. R. Wright and R. F. Borkman, “Ab Initio Studies on the Stabilities of Evenand Odd-Membered Clusters,” Journal of Chemical Physics, Vol. 77, No. 4, 1982, p. 1938. http://dx.doi.org/10.1063/1.444047
Y. Yamaguchi, J. F. Gaw and H. F. Schaefer III, “Molecular Clustering about a Positive Ion. Structures, Energetics, and Vibrational Frequencies of the Protonated Hydrogen Clusters , , , and ,” Journal of Chemical Physics, Vol. 78, No. 6, 1983, p. 4074. http://dx.doi.org/10.1063/1.445135
M. Farizon, B. Farizon-Mazuy, N. V. de Castro Faria and H. Chermette, “Ab Initio Structure Calculations of Hydrogen Ionic Clusters,” Chemical Physics Letters, Vol. 177, No. 4-5, 1991, pp. 451-457. http://dx.doi.org/10.1016/0009-2614(91)85082-8
M. Farizon, H. Chermette and B. Farizon-Mazuy, “Structure and Energetics of Hydrogen Clusters. Structures of and . Vibrational Frequencies and Infrared Intensities of the Clusters (n = 2 6),” Journal of Chemical Physics, Vol. 96, No. 2, 1992, p. 1325. http://dx.doi.org/10.1063/1.462168
U. Nagashima, K. Morokuma and H. Tanaka, “Ab Initio and Monte Carlo Study of the Structure and Stability of Hydrogen Clusters (n = 3 16),” Journal of Physical Chemistry, Vol. 96, No. 11, 1992, pp. 4294-4300. http://dx.doi.org/10.1021/j100190a036
T. Pang, “Properties of Ionic Hydrogen Clusters: A Quantum Monte Carlo Study,” Chemical Physics Letters, Vol. 228, No. 6, 1994, pp. 555-561. http://dx.doi.org/10.1016/0009-2614(94)01000-5
I. Stich, D. Marx, M. Parrinelo and K. Terakura, “ProtonInduced Plasticity in Hydrogen Clusters,” Physical Review Letters, Vol. 78, No. 19, 1997, pp. 3669-3672. http://dx.doi.org/10.1103/PhysRevLett.78.3669
E. W. Ignacio and S. Yamabe, “A Symmetric Structure of the Gas-Phase Cluster,” Chemical Physics Letters, Vol. 287, No. 5-6, 1998, pp. 563-569. http://dx.doi.org/10.1016/S0009-2614(98)00237-1
B. Farizon, M. Farizon, H. Razafinjanahary and H. Chermette, “Structure and Energetics of Hydrogen Clusters,” Physical Review B, Vol. 60, No. 6, 1999, pp. 3821-3828. http://dx.doi.org/10.1103/PhysRevB.60.3821
A. van Lumig and J. Reuss, “Collisions of Hydrogen Cluster Ions with a Gas Target, at 200 850 eV Energy,” International Journal of Mass Spectrometry and Ion Physics, Vol. 27, No. 2, 1978, pp. 197-208. http://dx.doi.org/10.1016/0020-7381(78)80039-4
M. Okumura, L. I. Yeh and Y. T. Lee, “Infrared Spectroscopy of the Cluster Ions ,” Journal of Chemical Physics, Vol. 88, No. 1, 1988, p. 79. http://dx.doi.org/10.1063/1.454488
K. Hiraoka and T. Mori, “Thermochemical Stabilities of with n = 1 10,” Chemical Physics Letters, Vol. 157, No. 5, 1989, pp. 467-471. http://dx.doi.org/10.1016/0009-2614(89)87282-3
S. Louc, B. Farizon, M. Farizon, M. J. Gaillard, N. Goncalves, H. Luna, G. Jalbert, N. V. de Castro Faria, M. C. Bacchus-Montabonel, J. P. Buchet and M. Carré, “Electron Capture in the Collision of Mass-Selected HydrogenCluster Ions with Helium Atoms,” Physical Review A, Vol. 58, No. 5, 1998, pp. 3802-3806. http://dx.doi.org/10.1103/PhysRevA.58.3802
O. K. Rice and H. C. Ramsperger, “Theories of Unimolecular Gas Reactions at Low Pressures. II,” Journal of the American Chemical Society, Vol. 50, No. 3, 1928, pp. 617-620. http://dx.doi.org/10.1021/ja01390a002
L. S. Kassel, “Kinetics of Homogeneous Gas Reactions,” Chemical Catalog Co., New York, 1932.
R. A. Marcus and O. K. Rice, “The Kinetics of the Recombination of Methyl Radicals and Iodine Atoms,” Journal of Physical and Colloid Chemistry, Vol. 55, No. 6, 1951, pp. 894-908. http://dx.doi.org/10.1021/j150489a013
T. Beyer and D. F. Swinehart, Comm. Ass. Com. Mach, Vol. 16, 1973, p. 379.
P. J. Robinson and K. A. Holbrook, “Unimolecular Reactions,” Wiley-Interscience, New York, 1972.
T. Baer and P. M. Mayer, “Statistical Rice-RamspergerKassel-Marcus Quasiequilibrium Theory Calculations in Mass Spectrometry,” Journal of the American Society for Mass Spectrometry, Vol. 8, No. 2, 1997, pp. 103-115. http://dx.doi.org/10.1016/S1044-0305(96)00212-7
G. Z. Whitten and B. S. Rabinovitch, “Approximation for Rotation—Vibration Energy Level Sums,” Journal of Chemical Physics, Vol. 41, No. 6, 1964, p. 1883. http://dx.doi.org/10.1063/1.1726175
M. E. Fisher, “The Theory of Equilibrium Critical Phenomena,” Reports on Progress in Physics, Vol. 30, 1967, p. 615. http://dx.doi.org/10.1088/0034-4885/30/2/306
S. Louc, “Mesure des Sections Efficaces des Différents Processus Intervenant dans la Fragmentation d’Agrégats d’Hydrogène (3 ≤ n ≤ 35) Induite par Collision à Haute Vitesse (60 keV/u) sur un Atome d’Hélium (60 keV/u) avec un Atome d’Hélium,” Ph. D. Thesis, Université Claude Bernard, Lyon, 1997.
B. Farizon, M. Farizon, M. J. Gaillard, E. Gerlic, S. Louc, N. V. de Castro Faria and G. Jalbert, “Direct Observation of Multi-Ionization and Multifragmentation in High Velocity Cluster Atom Collision,” Chemical Physics Letters, Vol. 252, 1996, p. 147.
B. Farizon, M. Farizon, M. J. Gaillard, F. Gobet, C. Guillermier, M. Carré, J. P. Buchet, P. Scheier and T. D. Mark, “Universal Behaviour in Fragmentation Phenomena? The Cluster Case,” European Physical Journal D, Vol. 5, No. 1, 1999, pp. 5-8. http://dx.doi.org/10.1007/s100530050222
B. Farizon, M. Farizon, M. J. Gaillard, F. Gobet, J. P. Buchet, M. Carre, P. Scheier and T. D. Mark, “Cooling and Heating of Channeled Ions and Corresponding Charge State Distributions,” Nuclear Instruments and Methods in Physics Research Section B, Vol. 209, 2003, pp. 9-18. http://dx.doi.org/10.1016/S0168-583X(02)02011-6
S. Eden, J. Tabet, K. Samraoui, S. Louc, B. Farizon, M. Farizon, S. Ouaskit and T. D. Mark, “Absolute Cross Sections for the Dissociation of Hydrogen Cluster Ions in High-Energy Collisions with Helium Atoms,” Physical Review A, Vol. 73, No. 2, 2006, Article ID: 023201. http://dx.doi.org/10.1103/PhysRevA.73.023201
E.-J. In, H.-I. Seo and S.-J. Kim, “The ab Initio Quantum Mechanical Investigation for the Weakly Bound (n = 1 6) Complexes,” Journal of the Korean Chemical Society, Vol. 45, No. 5, 2001.
K. Hiraoka and P. Kebarle, “A Determination of the Stabilities of , , , and from Measurement of the Gas Phase Ion Equilibria (n = 3, 5, 7, 9),” Journal of Chemical Physics, Vol. 62, No. 6, 1975, p. 2267. http://dx.doi.org/10.1063/1.430751
K. Hiraoka, “A Determination of the Stabilities of with n = 1-9 from Measurements of the Gas-Phase ion Equilibria ,” Journal of Chemical Physics, Vol. 87, 1987, p. 4048.
K. Hiraoka and T. Mori, “Thermochemical Stabilities of with n = 1 10,” Chemical Physics Letters, Vol. 157, No. 5, 1989, pp. 467-471. http://dx.doi.org/10.1016/0009-2614(89)87282-3
R. Prosmiti, P. Villarreal and G. Delgado-Barrio, “Structures and Energetics of Clusters (n = 5 11),” Journal of Physical Chemistry A, Vol. 107, No. 23, 2003, pp. 4768-4772. http://dx.doi.org/10.1021/jp0347318