Transitions In Molecular Collisions Research Articles

Efficient computational methods for rovibrational transition rates in molecular collisions.

Astrophysical modeling of processes in environments that are not in local thermal equilibrium requires the knowledge of state-to-state rate coefficients of rovibrational transitions in molecular collisions. These rate coefficients can be obtained from coupled-channel (CC) quantum scattering calculations, which are very demanding, however. Here, we present various approximate but more efficient methods based on the coupled-states approximation (CSA), which neglects the off-diagonal Coriolis coupling in the scattering Hamiltonian in body-fixed coordinates. In particular, we investigated a method called NNCC (nearest-neighbor Coriolis coupling) [Yang et al., J. Chem. Phys. 148, 084101 (2018)] that includes Coriolis coupling to first order. The NNCC method is more demanding than the common CSA method but still much more efficient than full CC calculations, and it is substantially more accurate than CSA. All of this is illustrated by showing state-to-state cross sections and rate coefficients of rovibrational transitions induced in CO2 by collisions with He atoms. It is also shown that a further reduction of CPU time, practically without loss of accuracy, can be obtained by combining the NNCC method with the multi-channel distorted-wave Born approximation that we applied in full CC calculations in a previous paper.

Computational study of radiative transitions in molecular collisions induced by short laser pulses.

A theoretical study of radiative transitions in molecular collisions occurring in the presence of short laser pulses is carried out within the semiclassical two-state formalism. Transition probabilities are calculated by numerically integrating the Bloch equation for two model systems and the Na-Ar system. At high laser intensities where a short pulse is more effective in inducing transitions than cw radiation, the transition probability exhibits nonlinear character with respect to the pulse intensity. At such high intensities, noncollisional atomic transitions may also be present, which need to be eliminated for an observation of collisional transitions.

Vibrational transitions in the non-linearly driven oscillator: role of a time-varying frequency

An operator-algebraic approach is used to study the role of time-varying frequency in vibrational transitions in molecular collisions. The time-evolution operator is constructed in terms of the number, one-quantum, and direct two-quantum operators. The evolution of vibrational states in a homonuclear diatomic molecule forced by an incident particle of the same mass is presented. The effect of the time-dependent frequency on 0 → 1, O → 2, and 0 → 3 is found to be important over a wide range of collision energies. Two-quantum processes interfere destructively with one-quantum processes at lower energies but constructively at higher energies.

A self-consistent eikonal treatment of electronic transitions in molecular collisions

We develop an eikonal treatment of electronic transitions in many-atom collisions, in which classical nuclear trajectories are self-consistently coupled to quantal electronic transitions. The treatment starts with a discussion of the electronic representations required to assure that Hamiltonian matrices are Hermitian. The amplitudes of wave functions are found to satisfy coupled equations which are expanded in powers of a local de Broglie wavelength. Time-dependent equations are transformed to derive a Hamiltonian formalism that couples nuclear positions and momenta with electronic amplitudes. Cross sections are obtained from flux conservation and also from T-matrix elements.

Rotational and Vibrational Transitions in Molecular Collisions

Recent progress in understanding collision processes involving rotational and vibrational excitation in collisions of atoms (ions) with molecules in terms of simple models is illustrated for two systems. Rotational excitation of N2 in collision with He at 27 meV can be explained by an optical model. A more quantitative agreement is achieved by cross sections calculated exactly for the model potential of Tang and Toennies. Vibrational excitation probabilities for resolved single mode excitation of CF4 in small angle 10 eV ion collisions follow a Poisson distribution indicating a breathing sphere forced oscillator behaviour

Rotationally inelastic molecule–surface scattering in the sudden approximation

Rotational and reorientational transitions in molecular collisions with solid surfaces are investigated by a model based on a sudden approximation with respect to both the rotational and the diffraction states that play a role in the scattering. The approximation developed leads to computationally simple expressions and provides detailed insight into the physical properties of the processes involved. A detailed quantitative study is made of the rotational state distribution produced by the collision, the variation of rotational excitation probabilities with the scattering angle, and related questions. A number of factorizations, sum-rule, and scaling properties are predicted for ‖ Sjmj,00;j′m′j′,mn ‖2, the transition probability between the initial (jmj) and the final (j′m′j′) rotational states for scattering into the (mn) diffraction channel. The strongest sum rules and scaling laws are obtained using additional approximations beyond the sudden decoupling. Among the latter results: (1) The j,j′ dependence of ‖ Sj0,00;j’m’0,mn ‖2 is determined entirely by the difference variable Δj=j′−j. (2) The diffractive intensity distribution summed over all final rotational states is the same as that obtained for a mass-equivalent atom (with an interaction that is the orientation-averaged molecule–surface potential). (3) The rotational state distribution, summed over all diffraction states, equals that calculated from a corresponding flat surface. (4) All rotational transition probabilities for the (m,n) diffraction spot can be obtained from the diffraction–rotational transition probabilities in the (m,0) and (n,0) diffraction spots. The above and other properties are tested numerically in the framework of the full sudden approximation for a model of H2/LiF(001) in the energy range 0.5–0.9 eV. They are found to hold to excellent accuracy. Systematics of the results with regard to variation of the surface corrugation parameter are noted.

A new semiclassical decoupling scheme for electronic transitions in molecular collisions: Application to vibrational-to-electronic energy transfer

A new semiclassical decoupling scheme (the trajectory-based decoupling scheme) is introduced in a computational study of vibrational-to-electronic energy transfer for a simple model system that simulates collinear atom–diatom collisions. The probability of energy transfer (P) is calculated quasiclassically using the new scheme as well as quantum mechanically as a function of the atomic electronic-energy separation (λ), with overall good agreement between the two sets of results. Classical mechanics with the new decoupling scheme is found to be capable of predicting resonance behavior whereas an earlier decoupling scheme (the coordinate-based decoupling scheme) failed. Interference effects are not exhibited in P vs λ results.

Semiclassical theory of electronic transitions in molecular collisions: Combined effects of tunneling and energetically inaccessible electronic states

The semiclassical theory of collision-induced electronic transitions is extended to describe tunneling and the effect of energetically inaccessible states. The powerful technique of analytic continuation is utilized to yield very good agreement with exact quantum mechanical results on some model systems. The inaccessible states have a significant effect on transmission coefficients and thus can be important in semiclassical studies of molecular reactions.

Semiclassical treatment of electronic transitions in molecular collisions: Three-dimensional H + + D 2 → HD + + D

A semiclassical study is carried out for the three-dimensional reaction H + + D 2 → HD + + D, which involves an electronic transition from the ground to the first excited singlet state of the H 3 + system. The potential energy surfaces corresponding to the two singlet states exhibit an avoided intersection, and they are analytically continued into the complex nuclear coordinate plane. S-matrix elements in the classical limit are computed from complex-valued classical trajectories which propagate on the analytically continued surfaces and switch surfaces continuously at the complex intersection. These elements are computed for the transition from the ground rotational and vibrational states of D 2 to the ground rotational and first excited vibrational states of HD + for zero total angular momentum and for energies in the range from 4.0 eV to 5.0 eV relative to the bottom of the D 2 well on the lower surface.

Semiclassical treatment of electronic transitions in molecular collisions: Collinear H++D2→HD++D

A semiclassical treatment is presented for the dynamics of the collinear reaction H++D2→HD++D as occurring by transition from the ground to the first excited singlet electronic state of the HD2+ system. The potential energy surfaces corresponding to the two singlet states of the same symmetry have an avoided intersection for real values of nuclear coordinates, and the surfaces are analytically continued to the complex intersection. Complex-valued classical trajectories are integrated on the analytically continued surfaces, and an electronic transition is effected by a trajectory switching surfaces continuously at the complex intersection. From the complex action calculated along appropriate trajectories, the classical limit of S-matrix elements is calculated for transitions from the ground vibrational state of D2 to the ground and first excited vibrational states of HD+ for initial relative translational energies in the range 3–6 eV. These two vibrational states of HD+ differ in that the energy of the ground state lies below the asymptotic real intersection point of interest of the two surfaces while the first excited state lies above the real intersection point. Furthermore, transition points, which are points in time when a trajectory switches surfaces, occur close together in pairs for the transition to the ground vibrational state of HD+, whereas transition points are well separated for the transition to the first excited vibrational state of HD+. The differences of the transitions to these two vibrational states of HD+ result in different dynamical behavior of the trajectories leading to these transitions and require different expressions for the classical limit of the S-matrix elements.

Nonadjacent vibrational transitions in molecular collisions. Interference between one- and two-quantum excitation processes

Nonadjacent vibrational transitions in molecular collisions. Interference between one- and two-quantum excitation processes

Optical Potentials in Molecular Collisions

Inelastic transitions in molecular collisions are discussed in terms of optical (complex) potentials. Adiabatic and sudden approximations for molecular collisions are considered, as well as conditions for their validity. Numerical results obtained in an adiabatic approximation are presented for rotational and vibrational transitions in the H + H2 system, which include a study of the real and the imaginary parts of its optical potential. The relevance of optical potentials in the description of direct molecular reactions is also briefly considered.

General distorted-wave treatment of rotational transitions in molecular collisions

An iterative procedure is described for the determination of the cross-sections for rotational transitions in the collision of two diatomic molecules. The first iteration yields the familiar distorted-wave (d.w.) approximation, which has already been applied to the two principal transitions in parahydrogen. The iteration has now been carried a stage further, yielding what may be termed the second d.w. approximation; with the use of the same intermolecular potential function as gave reasonable agreement with experiment in the previous calculation, it is found that the cross-sections at thermal energies are decreased by about 8%. It is therefore concluded that the first d.w. approximation is adequate for the treatment of rotational relaxation in hydrogen at and below room temperatures.

Vibrational and Rotational Transitions in Molecular Collisions

Theoretical studies on the rotational and the vibrational transitions in molecular collisions are reviewed, with emphasis on the author's own work. Discussions in this article are mainly concerned with diatomic molecules. Part I begins with a brief historical introduction and a description of the scope of the present article. These are followed by introductory remarks on the relaxation times and the intermolecular interactions. In Part II, wave-mechanical formulation of the collision problem follows a brief description of the classical treatments. Then the rotational transitions in hydrogen molecules are discussed with the aid of the distorted wave method. Rotational transitions in other molecules present strong coupling problems, for which suggesting are made for approximate treatment. In Part III, the vibrational transitions in colinear collisions are discussed in detail. Then the present situation in the theory of three-dimensional collisions is summarized.

Vibrational and Rotational Transitions in Molecular Collisions

Theoretical studies on the rotational and vibrational transitions in molecular collisions are reviewed. Discussions are mainly concerned with diatomic molecules. A brief historical introduction and a description of the scope of the article are presented. These are followed by introductory remarks on the relaxation times and the intermolecular interactions. Wave-mechanical formulation of the collision problem follows a brief description of the classical treatments. The rotational transitions in hydrogen molecules are discussed with the aid of the distorted wave method. Rotational transitions in other molecules present strong coupling problems, for which suggestions are made for approximate treatment. The vibrational transitions in colinear collisions are discussed in detail. The present situation in the theory of three-dimensional collisions is summarized. 202 references. (auth)