Kiyohiko Someda

Systematics of the average resonance widths in overlapping resonance-scattering and its connection with RRKM theory

Abstract Decay processes of densely distributed quasi-bound states are studied numerically by randomly generating the Hamiltonian matrices. The average decay rate obtained from the Feshbach theory of resonance scattering exhibits systematic behavior against the average density of states (ρ), the number of continua ( K ) and the average coupling strength to the continua (υ). The distribution of the decay rates bifurcates into long-lived and short-lived branches when ρ is larger than a certain critical value ρ c , which is found to be roughly equal to the inverse of the 0-th order partial width 〈γ part 〉. Thus one can clearly distinguish the isolated resonance regime in the region ρ c and overlapping resonance regime in the region ρ⪢ρ c . The states belonging to the short-lived branch exhibit a very broad energy spectrum and are recognized as background continua. They are not quasi-bound states in practice. The decay rates of the long-lived branch, on the other hand, systematically decrease with ρ at ρ ⪢ ρ c . The average of these decay rates is proportional to 〈γ part 〉 −1 K ρ −2 . When the short-lived branch is excluded, the average decay rate, 〈Γ/ℏ〉, roughly agrees with that of the RRKM rate in the region ρ ≈ ρ c , where the spectral profile becomes most diffuse. Outside the region of ρ ≈ ρ c , 〈Γ/ℏ〉 is always smaller than the RRKM rate. The above observation is confirmed also by a square-we potential model and ascertains the conventional belief that the RRKM theory holds only when resonances overlap and that it gives the upper bound. It is noteworthy that this RRKM regime corresponds to the critical overlap, ρ〈γ part. 〉 ≈ 1.

Dissociation dynamics of Na+n in collision with rare‐gas atoms

Dissociation dynamics of a sodium cluster ion, Na+n (n=2–9 and 11), in collision with a rare gas atom (He or Ne) was investigated by measuring the absolute cross sections for the production of fragmented ions by using a tandem mass‐spectrometer equipped with several octapole ion guides. The mass spectra of the fragmented ions show that release of Na and/or Na2 from Na+n occurs dominantly. The absolute total cross section for the dissociation of Na+n and the absolute partial cross sections for the Na and/or the Na2 release were determined at different collision energies and cluster sizes. The absolute total dissociation cross sections were calculated by a scheme that collisionally excited Na+n dissociates with leaving Na and Na2 unimolecularly. On the other hand, the partial cross sections for the Na and the Na2 release were successfully explained by the orbital correlation diagram for the dissociation system; the dissociation channel involving an adiabatic transition was found to be influenced significant...

He–He chemical bonding in high-frequency intense laser fields

On the basis of the Kramers–Henneberger (KH) high-frequency approximation, we carried out an ab initio molecular orbital calculation for He2 in intense laser fields. The potential energy curve is found to be attractive, indicating that a He–He chemical bond is formed. The formation of the He–He chemical bond is ascribable to changes in the nature of KH molecular orbitals. Intense laser fields cause a kind of sp hybridization of KH atomic orbitals. The degree of the hybridization depends on the internuclear distance, and reaches a maximum at around the equilibrium internuclear distance. This hybridization remarkably strengthens/weakens the bonding/anti-bonding character of the 1σg/1σu KH molecular orbitals, respectively.

SEPARATION OF COLLISIONAL AND VIBRATIONAL VARIABLES IN CHEMICAL REACTIONS : DECOUPLING SURFACE IN PHASE SPACE

A method for decoupling the collisional and vibrational variables in the collision process is developed. The present procedure of decoupling is based on a canonical transformation in phase space. The basic principle employed is the ‘‘maximal decoupling condition’’ [∂H/∂u]u=v=0=[∂H/∂v]u=v=0=0, where H is the Hamiltonian and u and v represent new vibrational coordinates and momenta. ‘‘Decoupling surface’’ is defined as the surface determined by u=v=0. The partial differential equation to be satisfied by this decoupling surface is derived. This partial differential equation can be solved easily by utilizing classical trajectories. Local vibrational frequencies along the decoupling surface are defined and their stability analysis is shown to provide the criterion for the separability. ‘‘Adiabatic approximation’’ which assumes the conservation of locally defined actions of the new vibrational variables leads to an ‘‘effective Hamiltonian’’ that describes the collision process under a given set of the initial v...

DERIVATIVE STATE ANALYSIS OF INTRAMOLECULAR VIBRATIONAL ENERGY REDISTRIBUTION OF ACETYLENE

The intramolecular vibrational energy redistribution (IVR) of acetylene in the electronically ground state is analyzed by a novel method called derivative state analysis [K. Someda, Bull. Chem. Soc. Jpn. 69, 3037 (1996)]. The derivative state analysis clarifies how the Hilbert space of quantum states are explored in IVR, and we are thereby able to classify the quantum states and to know their genealogy. The Hamiltonian presented by Temsamani and Herman [M. A. Temsamani and M. Herman, J. Chem. Phys. 102, 6371 (1995)] is adopted in the analysis. The IVR from three different types of initial vibrational states are analyzed: (1) The initial states excited in the trans-bending (ν4) mode undergo a rapid and instantaneous IVR when v4⩾10. (2) The IVR from the states with the CH antisymmetric stretch (ν3) excitation has an onset at v3=6 and is sequential. The vibrational energy is transmitted from the ν3 mode to the CC stretch (ν2) in the first stage and then to the trans- and cis-bending. (3) Simultaneous excitat...

A generalized langevin equation for wave functions. Intramolecular vibrational dephasing as a stochastic process

Abstract A generalized Langevin equation satisfied by time-evolving wave functions is derived by adapting the Mori formalism to the Schrodinger time dependent equation. The equation obtained describes both deterministic and stochastic time evolution of wave functions. Memory kernel of the ”delayed friction” term of the equation obtained consists of the temporal correlation function (in the quantum mechanical sense) among non-stationary wave function, i.e., wave packets. The memory is likely to decline rapidly essentially due to the dispersion of the wave packets, so that a “Markov” limit is justified. An ensemble of probability amplitudes of different quantum states is considered, and the probability distribution of these probability amplitudes is discussed. This probability distribution is connected with spectroscopic observables: It can be derived from excitation profiles of Raman scattering amplitudes with many different final states. By assuming the “random force” term of the Langevin equation to be Gaussian white noise, a Fokker-Planck equation is derived. The solution of this Fokker-Planck equation describes how “randomization” proceeds in intramolecular vibrational dephasing. As time goes to infinity, all the accessible states are equally populated on the average, but fluctuation around the “microcanonical equilibrium” remains.

COMPETITION BETWEEN INTRAMOLECULAR VIBRATIONAL ENERGY RE-DISTRIBUTION AND UNIMOLECULAR DISSOCIATION: A SCATTERING THEORETICAL POINT OF VIEW

Systematic behavior of decay rates of resonances above dissociation threshold is investigated by using the theory of resonance scattering. The condition for the Rice-Ramsperger-Kassel-Marcus (RRKM) rate formula to be valid is clarified by analyzing the random model of unimolecular dissociation. The decay rate averaged over many resonances agrees with the RRKM rate when the mean spacing and the mean width of the resonance states coincide with each other. On the other hand, auto- and mutual-correlation functions of the non-stationary wave functions indicate a rather paradoxical and intriguing phenomenon: In the RRKM regime, insufficient time is left for intramolecular vibrational energy redistribution (IVR) before dissociation.

Jahn-Teller deformation in potassium clusters and its manifestation in electron transfer from high-Rydberg Kr atoms

Abstract Potassium cluster anions produced from potassium clusters in collision with high-Rydberg Kr atoms were observed by mass spectrometry, and the relative cross-sections for collisional electron transfer were estimated. Even-odd magnitude alternation appearing in the cross-section versus cluster size-distribution was interpreted by Jahn-Teller distortion of the cluster anions in the framework of the shell model. The magnitude of the alternation was found to depend on the electron affinity of the parent neutral cluster and the number of bath modes related to the stabilization of the cluster anion formed.

A scattering theoretical examination of the statistical theory of chemical reactions: competition between direct and resonance scatterings

On the basis of the formal scattering theory, the reaction probability of the chemical reaction of the complex-formation mode is derived. The probability is expressed as the sum of the contributions from the direct and resonance scatterings. The contribution from the latter is shown to coincide with the reaction probability predicted by the conventional statistical theory of chemical reactions. The balance between the direct and resonance scatterings is governed by the parameter of the overlapping resonance, , where γ is the average partial width and ρ is the density of resonance states. It is shown that the prediction of the statistical theory is realized when the condition of the critical overlap of resonances, , is fulfilled. The setup and conclusion of the formal theory are illustrated by a numerical example of a simple model.

Nonadiabatic Dynamics of the Classical Hydrogen Molecular Ion H2

Classical dynamics of the hydrogen molecular ion H 2 + is investigated, and electron dynamics involved in nonadiabatic (non-Born–Oppenheimer) processes is clarified in the framework of nonlinear dy...