Publisher Summary This chapter discusses the role that information–theoretic methods have played in dealing with the reactive molecular scattering. The information–theoretic approach has made possible the compaction of data in the fields of molecular beam kinetics, chemiluminescence, and chemical lasers. The surprisal analysis of vibrational population inversions often leads to a one-parameter description of the disequilibrium in fast exoergic elementary reactions. This is of importance in characterizing the gain in chemical lasers. Another practical application of the information–theoretic approach is to the evaluation of the entropy cycle involved in the operation of a maser or laser. However, the most fundamental practical application is the simplification in the description of severely non-Boltzmann state distributions. The key to the approach is the concept of the surprisal, the deviation from expectation on the basis of microcanonical equilibrium. Clearly the deviation is a less structured function of the classical energy variable than the populations themselves; hence the practical advantage of the present approach in the description of nonequilibrium processes, including state population distributions and product branching ratios.

Role of Energy in Reactive Molecular Scattering: An in Form a Tion-Theoretic Approach

Non-reactive heavy particle collision calculations

State‐to‐state differential cross sections for rotational transitions of Na2 in collisions with He are measured in the electronic and vibrational ground state at thermal collision energies using a new laser technique. Single rotational levels ji are labelled by modulation of their population via laser optical pumping using a dye laser. The modulation of the fluorescence induced by an Ar+ laser tuned to the level jf=28 is proportional to the cross section for collisional transfer ji→jf and is detected at the scattering angle ϑ. A single optical fiber and a fiber bundle provide a flexible connection between the detector and the laser and photomultiplier, respectively. Transitions as large as Δj=20 are observed. At small angles elastic scattering is dominant, but rotationally inelastic processes become increasingly important at larger scattering angles. Rotational rainbow structure causing a steep onset of the cross section with the scattering angle ϑ (at fixed Δj) or a sharp cutoff with Δj (at fixed ϑ) is f...

State‐to‐state differential cross sections for rotationally inelastic scattering of Na2 by He

Integral and differential cross sections for pure rotational and simultaneous rotational−vibrational excitation of H2 by Li+ impact have been computed following the coupled−channel formalism using two different SCF potential energy hypersurfaces and a CI hypersurface at 0.6 and 1.2 eV. Sensitivity of integral cross sections to (a) choice of ab initio potential energy surface and (b) expansion length of a Legendre polynomial representation of one of the energy surfaces is examined. It is seen that preparation of H2 in the v = 0, j = 2 state leads to four− and fivefold increases in excitation cross sections to the v′ = 1, j′ = i, i = 0,2,4 states relative to excitation of ground state (v = 0, j = 0) H2. Differential cross sections are reported at 1.2 eV for up to five quantum rotational and for vibrational transitions on one of the energy hypersurfaces. All angular distributions required for determining ratios (inelastic : elastic) of differential cross sections needed for comparison with recent time−of−fli...

Theoretical study of inelastic scattering of H2 by Li+ on SCF and CI potential energy surfaces

Three kinds of semiclassical theory are tested against quantum mechanical results for vibrational transition probabilities and average vibrational energy transfers in collinear collisions of atoms with harmonic and Morse vibrators for the He-H 2 mass combination. The interaction potential is assumed to be a repulsive exponential function with an exponential parameter which is realistic for He-H 2 collisions. The energy range studied is total energies of 2–8 in units of ħω e . The uniform semiclassical approximations of classical S matrix theory are tested only for classically allowed transitions, i.e., for transition probabilities greater than about 0.2. They are accurate quantitatively for both harmonic and Morse vibrators. The integral expressions of classical S matrix theory are found to be quantitatively accurate for classically allowed and weakly classically forbidden transitions, i.e., for transition probabilities greater than about 0.01–0.05, and to be unreliable for strongly classically forbidden transitions. Quasiclassical trajectory methods yield qualitatively accurate results only for classically allowed transitions but the phase-averaged energy transfer in quasiclassical collisions may be accurate even when classically forbidden transition probabilities are important for the calculation of the average energy transfer. Forced quantum oscillator methods using a classical path whose initial velocity is the average of the initial and final velocities corresponding to the transition of interest are accurate for transition probabilities as small as 4 × 10 −8 for harmonic vibrators but do not seem to accurately account for the effect of anharmonicity.

Tests of semiclassical treatments of vibrational-translational energy transfer collinear collisions of helium with hydrogen molecules

The coupled-channel formalism has been employed for He + H2 collisions including rotational (j = 0, 2) and vibrational (n = 0, 1) levels and making use of the Kraus-Mies potential energy surface. Integral and differential cross sections are obtained at the total energies 0.3884, 0.9, and 1.4116 eV for rotational and vibrational transitions separately, and for the combined processes. Considerable use has been made of the microscopic reversibility principle to extract cross sections from the S matrix for de-excitations as well as for excitations. Cross sections for vibrational excitation are found to decrease when accompanied by rotational excitation. For vibrational de-excitation, the effect of rotational excitation is to increase the cross sections. Defining a most probable impact parameter bmax from the maximum in the partial integral cross sections, vibration excitation is found to occur at low bmax, while rotational excitation is observed at comparatively higher values. For simultaneous rotational and transitions, bmax decreases with increasing energy transfer.



A deflection angle ©(cl is defined in terms of the impact parameters and the turning point radii for the initial and final channels, and a correlation between this angle and the maxima in the computed angular distributions is found. The transition probabilities for the rotational excitation j = 0 2 with simultaneous vibrational excitation and their physical interpretation are also discussed within the total angular momentum coupling scheme.

Coupled‐channel investigation of rotationally and vibrationally inelastic collisions between He and H2

Comparison of the coupled states, infinite order sudden, and exponential born methods for ArCsF collisions

Collision dynamics of three interacting atoms: foundation of the spectator-stripping model

Rotational excitation of Na2 by the He impact on a model potential energy surface

The atomic exchange reaction A + BC → AB + C is investigated quantum mechanically employing a coupled differential equations approach. The relative motion in reactant and product channels is described in the common coordinate R 3 (the AC nuclear separation) and is developed in three-dimensional space. The total wave functions of the system are expressed as a superposition of valence bond electronic states of the initial (A, BC) and final (AB, C) configurations, with the coefficients describing the relative and internal (vibrational, rotational) nuclear motions. Choosing convenient trial functions with the appropriate boundary conditions and using the Kohn variational principle, a set of differential (rather than the usual integro-differential) equations is obtained for the relative motion wave functions in R 3. The potential matrix elements turn out to be dynamical in that they depend on the initial k 1 and final k 2 wave vectors. Two-state coupled channel calculations of the differential and integral cro...

Paul McGuire

Papers

Coupled‐channel investigation of rotationally and vibrationally inelastic collisions between He and H2

Comparison of the coupled states, infinite order sudden, and exponential born methods for ArCsF collisions

Collision dynamics of three interacting atoms: foundation of the spectator-stripping model

Rotational excitation of Na2 by the He impact on a model potential energy surface

Dynamical coupling in the differential equations approach to atom-diatom exchange reactions