Mass effects and internal space geometry in triatomic reaction dynamics (11 pages)

The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

[1]  Shane D. Ross,et al.  Theory and Computation of Non-RRKM Lifetime Distributions and Rates in Chemical Systems with Three or More Degrees of Freedom , 2005 .

[2]  Chun-Biu Li,et al.  Phase-space reaction network on a multisaddle energy landscape: HCN isomerization. , 2005, The Journal of chemical physics.

[3]  H. Teramoto,et al.  Dynamical and statistical effects of the intrinsic curvature of internal space of molecules. , 2005, The Journal of chemical physics.

[4]  K. Takatsuka,et al.  Effects of An Intrinsic Metric of Molecular Internal Space on Chemical Reaction Dynamics , 2005 .

[5]  C. Laperle,et al.  Three-body dissociation dynamics of the low-lying Rydberg states of H3 and D3. , 2004, Physical review letters.

[6]  A. Burbanks,et al.  Phase space conduits for reaction in multidimensional systems: HCN isomerization in three dimensions. , 2004, The Journal of chemical physics.

[7]  L. Lammich,et al.  Breakup dynamics and isotope effects in D2H+ and H2D +dissociative recombination , 2004 .

[8]  R. Schinke,et al.  Intra- and intermolecular energy transfer in highly excited ozone complexes. , 2004, The Journal of chemical physics.

[9]  K. Takatsuka,et al.  Kinematic effects associated with molecular frames in structural isomerization dynamics of clusters. , 2004, The Journal of chemical physics.

[10]  V. Aquilanti,et al.  Three-body problem in quantum mechanics: hyperspherical elliptic coordinates and harmonic basis sets. , 2004, The Journal of chemical physics.

[11]  Paul Fleurat-Lessard,et al.  van der Waals states in ozone and their influence on the threshold spectrum of O3(X1A1). I. Bound states. , 2003 .

[12]  K. Takatsuka,et al.  Collective coordinates and an accompanying metric force in structural isomerization dynamics of molecules , 2003 .

[13]  Robert B. Walker,et al.  Formation of ozone: Metastable states and anomalous isotope effect , 2003 .

[14]  I. Prigogine.  Chemical Kinetics and Dynamics , 2003, Annals of the New York Academy of Sciences.

[15]  Robert B. Walker,et al.  Metastable states of ozone calculated on an accurate potential energy surface , 2003 .

[16]  S. Wiggins,et al.  The geometry of reaction dynamics , 2002 .

[17]  Y. Gao,et al.  Strange and Unconventional Isotope Effects in Ozone Formation , 2001, Science.

[18]  Jerrold E. Marsden,et al.  Reduction theory and the Lagrange-Routh equations , 2000 .

[19]  Kazuo Takatsuka,et al.  Tunneling paths in multi-dimensional semiclassical dynamics , 1999 .

[20]  R. Marcus,et al.  An intramolecular theory of the mass-independent isotope effect for ozone. I , 1999 .

[21]  O. Kajimoto,et al.  ENERGY PARTITIONING IN TWO KINDS OF NO MOLECULES GENERATED FROM THE REACTION OF O(1D) WITH N2O : VIBRATIONAL STATE DISTRIBUTIONS OF NEW AND OLD NO 'S , 1999 .

[22]  O. Kajimoto,et al.  Nascent state distributions of NO(X 2Π) generated from the reaction of S(1D) with N2O: Intramolecular vibrational-energy redistribution in the reaction intermediate , 1999 .

[23]  Erbacher,et al.  Ozone isotope enrichment: isotopomer-specific rate coefficients , 1999, Science.

[24]  E. Yurtsever.  Angular-momentum-driven chaos in small clusters , 1998 .

[25]  K. Mitchell,et al.  Body frames and frame singularities for three-atom systems , 1998 .

[26]  A. Kuppermann.  Reactive Scattering with Row-Orthonormal Hyperspherical Coordinates. 2. Transformation Properties and Hamiltonian for Tetraatomic Systems , 1996 .

[27]  Sundström,et al.  Dissociative recombination of H2D+: Cross sections, branching fractions, and isotope effects. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[28]  Littlejohn,et al.  Internal or shape coordinates in the n-body problem. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[29]  C. Schlier,et al.  How accurate is the Rice–Ramsperger–Kassel–Marcus theory? The case of H+3 , 1994 .

[30]  R. Berry,et al.  Chaotic dynamics in small inert gas clusters: The influence of potential energy saddles , 1993 .

[31]  T. Iwai.  A representation of the Guichardet connection in the Aharonov-Anandan connection , 1992 .

[32]  Berry,et al.  Probability distributions of local Liapunov exponents for small clusters. , 1992, Physical review letters.

[33]  D. Wales,et al.  Chaos in small clusters of inert gas atoms , 1992 .

[34]  Chapuisat,et al.  Principal-axis hyperspherical description of N-particle systems: Classical treatment. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[35]  Robert Q Topper,et al.  Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory , 1991 .

[36]  Thomas L. Beck,et al.  Melting and phase space transitions in small clusters: Spectral characteristics, dimensions, and K entropy , 1988 .

[37]  G. A. Parker,et al.  Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory , 1987 .

[38]  T. Iwai.  A geometric setting for internal motions of the quantum three-body system , 1987 .

[39]  T. Iwai.  A gauge theory for the quantum planar three‐body problem , 1987 .

[40]  Tachibana,et al.  Complete molecular Hamiltonian based on the Born-Oppenheimer adiabatic approximation. , 1986, Physical review. A, General physics.

[41]  W. Miller.  Effect of reaction path curvature and dimensionality on the accuracy of classical transition state theory , 1982 .

[42]  Rudolph A. Marcus,et al.  Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates , 1968 .

[43]  Rudolph A. Marcus,et al.  On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions , 1966 .

[44]  F. T. Wall,et al.  Sensitivity of Exchange‐Reaction Probabilities to the Potential‐Energy Surface , 1963 .

[45]  F. Smith,et al.  A Symmetric Representation for Three‐Body Problems. I. Motion in a Plane , 1962 .

[46]  F. Smith.  Generalized Angular Momentum in Many-Body Collisions , 1960 .

[47]  Carl Eckart,et al.  Some Studies Concerning Rotating Axes and Polyatomic Molecules , 1935 .

[48]  Y. Gao,et al.  On the theory of the strange and unconventional isotopic effects in ozone formation , 2002 .

[49]  R. Littlejohn,et al.  Gauge fields in the separation of rotations and internal motions in the n-body problem , 1997 .

[50]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[51]  John E. Adams,et al.  Reaction path Hamiltonian for polyatomic molecules , 1980 .

[52]  W. Zickendraht,et al.  Configuration‐Space Approach to the Four‐Particle Problem , 1969 .