We have analyzed experimental data from a number of exothermic processes in which molecules in well-defined initial states are deactivated by inelastic, dissociative, or reactive collisions. Further, we analyze deactivation processes that do not occur in molecules despite their containing high levels of excitation. Significant common elements are found among these forms of deactivation. The initial step consists of transition to a product state involving minimum rotation state change (Delta j) consistent with energy conservation. Frequently, this process is near-energy-resonant. More critically, it may frequently require substantial angular momentum (AM) change. Analysis of experimental data indicates that constraints act upon on the formation of products in processes that involve release of excess energy. These constraints are associated with the magnitude of AM that must be generated for the initial transition to occur and this AM "load" increases with the amount of energy to be released. In general, the probability of generating rotational AM falls rapidly as Delta j increases, and this effectively limits the size of energy gap that may be bridged by a given reactant pair and at some point the constraint is sufficient to constitute a barrier that prevents the process from taking place. The choice of reactant species strongly affects the probability of each process that increases (i) when molecules efficiently interconvert momentum and (ii) when many product states are available in the critical near-resonant region. These factors increase the proportion of initial trajectories that possess the energy and momentum necessary to open a "product" channel. Evidence is presented showing that AM load-reduction strategies lead to marked enhancement of rates of collision-induced processes, suggesting that reduction of constraints in the exit channels from the transition state may constitute a previously unrecognized form of catalysis.

Vibrational relaxation of the 6(1) level of S(1)((1)B(2u)) benzene is analyzed using the angular momentum model of inelastic processes. Momentum-(rotational) angular momentum diagrams illustrate energetic and angular momentum constraints on the disposal of released energy and the effect of collision partner on resultant benzene rotational excitation. A kinematic "equivalent rotor" model is introduced that allows quantitative prediction of rotational distributions from inelastic collisions in polyatomic molecules. The method was tested by predicting K-state distributions in glyoxal-Ne as well as J-state distributions in rotationally inelastic acetylene-He collisions before being used to predict J and K distributions from vibrational relaxation of 6(1) benzene by H(2), D(2), and CH(4). Diagrammatic methods and calculations illustrate changes resulting from simultaneous collision partner excitation, a particularly effective mechanism in p-H(2) where some 70% of the available 6(1)-->0(0) energy may be disposed into 0-->2 rotation. These results support the explanation for branching ratios in 6(1)-->0(0) relaxation given by Waclawik and Lawrance and the absence of this pathway for monatomic partners. Collision-induced vibrational relaxation in molecules represents competition between the magnitude of the energy gap of a potential transition and the ability of the colliding species to generate the angular momentum (rotational and orbital) needed for the transition to proceed. Transition probability falls rapidly as DeltaJ increases and for a given molecule-collision partner pair will provide a limit to the gap that may be bridged. Energy constraints increase as collision partner mass increases, an effect that is amplified when J(i)>0. Large energy gaps are most effectively bridged using light collision partners. For efficient vibrational relaxation in polyatomics an additional requirement is that the molecular motion of the mode must be capable of generating molecular rotation on contact with the collision partner in order to meet the angular momentum requirements. We postulate that this may account for some of the striking propensities that characterize polyatomic energy transfer.

We describe a rapid, accurate method for calculating rovibrational distributions in diatomic products from elementary chemical reactions. The basis of the model is momentum interconversion at a critical configuration defined in terms of molecular dimensions of the species involved. This approach shares common elements with recent models of inelastic processes and the kinematic reactive model of Elsum and Gordon. We point out that these and related approaches represent a development of Newtonian mechanics equivalent to that followed in the conventional formulation of classical mechanics, but one in which motive force for change at the molecular level is attributed to dp/dt rather than to dV/dq. This leads to a particularly transparent form of mechanics that uses only familiar data such as bond length, mass, spectroscopic constants, and velocity, yet may be applied to the highly resolved single collision experiments of molecular reaction dynamics. We describe key aspects of the computational method, e.g., the definition of the critical configuration, the disposal of reaction enthalpy, the manner of assigning product vibrational states, and the way in which conservation of energy is ensured. Examples are chosen to illustrate the range of reactions to which the method may be applied. Each would represent a challenge to conventional theory. We show that velocity-angular momentum diagrams may be used to interpret data and to give physical insight into the origins of observed rotational distributions. Good agreement is obtained between experimental and calculated (v,j) distributions for a wide range of elementary reactions suggesting that our model, despite its simplicity, captures the principal physics of chemical change at the molecular level

Steady-state fluorescence depolarisation was used to study the hydrodynamics of ethylene glycol flow inside a quartz slit nozzle for 24 mm ( Re ~200) and outside as a free thin jet, for 14 mm. The polarisation profiles (over 1000 points) allowed direct evaluation of the velocity gradient within the flowing liquid from this molecular-level probe. Inside the nozzle two lateral boundary layers were observed. The velocity profile was flattened, which was attributed to strong chemical interactions with the walls of the cell. Within the jet, four polarisation profile maxima were observed for the first time, corresponding to two internal converging streams.

We describe a rapid, accurate technique for computing state-to-state cross-sections in collision-induced vibration–rotation transfer (VRT) using only physical data, i.e. spectroscopic constants, bond length, mass and velocity distribution. The probability of linear-to-angular momentum (AM) conversion is calculated for a set of trajectories, each of which is subjected to energy conservation boundary conditions. No mechanism is specified for inducing vibrational state change. In the model, this constitutes a velocity or momentum barrier that must be overcome before rotational AM may be generated in the new vibrational state. The method is subjected to stringent testing by calculating state-to-state VRT probabilities for diatomics in highly excited vibrational, rotational and electronic states. Comparison is made to experimental data and to results from quantum mechanical and from quasi-classical trajectory calculations. There is quantitative agreement with data from all three sources, indicating that despite its simplicity the essential physics of collisions involving highly excited species is captured in the model. We develop further the concept of the molecular efficiency factor as an indicative parameter in collision dynamics, and derive an expression for ji > 0 and for VRT.

We exploit the accuracy and computational speed of the angular momentum model of inelastic transfer to follow changes in quantum state populations as a gas ensemble evolves from an initial state of dis-equilibrium. Results on two prototype systems in specific initial states are presented and the manner by which these approach equilibrium is discussed. There are wide differences in the rates at which different internal modes equilibrate and although Boltzmann-type distributions are found within a mode, individual modes may not be in equilibrium with one another. These findings have relevance, e.g., to upper atmosphere modeling where the rapid establishment of local thermodynamic equilibrium is often assumed.

We describe an “internal collision” model of vibrational predissociation (vpd) in triatomic van der Waals (vdW) molecules based on the angular momentum (AM) model of collision-induced vibration–rotation transfer. The probability of vpd is related to the probability of disposing the vibrational energy into rotational and orbital AM. In T-shaped species, two internal collision configurations are likely to dominate namely, the turning points of excursions by the weakly bound species relative to the diatomic. These two geometries result in a bimodal distribution of final rotational states. Velocity-AM diagrams demonstrate why halogen and hydride vdW molecules have very different properties and illustrate the physics of quantitative calculations that reproduce experimental distributions in a wide range of vdW molecules. We introduce an analogy between a metastable dissociative state and the optical resonator and define a quality factor (Qjl) that relates vpd lifetime to stored energy and to ease of generating rotational and orbital AM by dissociation. Data on vdW molecules of OH are analyzed using the Qjl concept and the accelerated dissociation on forming the vdW complex with an efficient energy acceptor is likened to the formation of a particularly low-Q molecular resonator.

We present a quantitative version of the velocity–angular momentum plots of Besley et al. that we have used extensively to represent the key processes at work in collisional transfer mechanisms. Rotational state distributions are obtained by incorporating probability distributions of the relevant variables, and the Monte Carlo (MC) trajectory technique is used to sample these distributions. The method is illustrated with the case of weakly quasi-resonant vibration rotation transfer in A(1Σu+)Li2+Ne collisions. The results show excellent agreement with published experimental data, indicating the apparent dominance of the factors governing angular momentum (AM) conversion in shaping rovibrational distributions.

Guided by experimental findings, we develop a nuclear dynamical theory of molecular collisions that accounts quantitatively for product distributions in a wide range of inelastic and reactive processes. Two simple equations are sufficient for this purpose. The first represents the principal mechanism by which linear momentum of relative motion is converted to angular momentum via a torque arm of molecular dimension. The second is a statement of energy conservation and this (together with the requirement that products be formed in well-defined quantum states) constitutes the boundary condition within which the mechanism must operate. Boundary conditions vary widely with system and with process and give great variety to the final rotational state distributions. Both equations may be represented in velocity–angular momentum diagrams from which the origins of the characteristic features of many processes, particularly their product rotational state distributions, may be identified. Quantitative calculations reproduce experimental data over a wide range of inelastic and reactive collisions and for molecules in low-lying or highly excited states. Input data in the calculations consists of little more than atomic mass, bond length and velocity distributions (and reaction enthalpy for reactive processes). Collisional behaviour in this model is characteristic of an individual molecule and we outline the beginnings of a classification scheme that categorises molecules as good (efficient) or bad (inefficient) in terms of their ability to convert linear-to-angular momentum within the constraints appropriate to system and process. Molecules such as the hydrides of heavier elements fall into a category we term ‘eccentric’ as a result of unusual (but predictable) collisional properties.

We present a kinematic hard ellipsoid model of rotational transfer in diatom–diatom collisions. The model extends the principles of the angular momentum (AM) model of rotational transfer (RT) developed for atom–diatom collisions and the hard ellipsoid model of the repulsive potential. Monte Carlo trajectory calculations are performed on the Na2+H2 system which show excellent agreement with published experimental data, using only atomic masses and bond lengths as the input data.

The disposition of the rovibrational levels in a diatomic molecule has a major influence on the outcome of inelastic collisions involving that molecule. In the case of the hydrides of moderately heavy elements, unusual collisional properties are anticipated in view of conflict between the demands of momentum and energy in these species. This arises because hydride rotational and vibrational quanta are generally large yet the species may be quite heavy and thus carry substantial momentum. This leads to competition between the momentum based mechanism for elastic transfer and constraints which result from energy conservation. We illustrate these principles in investigating rotational, vibration-rotation, and quasiresonant vibration-rotation transfer, as well as vibrational predissociation of OH-containing van der Waals molecules. Collisional transfer is (almost) invariably constrained by energy conservation in this species and the impact of this on the linear-to-angular momentum mechanism is strongly evident in the collisional behavior of the OH molecule. Molecular collision partners may accept vibrational energy from OH without generating angular momentum, resulting in more efficient deactivation of vibrationally excited OH. Recent observation of emission from very high N levels of (X)(2)Pi OH in the nightglow appears to represent only the second recorded example of quasiresonant vibration-rotation transfer.

We analyze rotational distributions from collision-induced atom–diatom electronic energy transfer (EET) experiments in terms of the capacity of the diatomic to dispose of the angular momentum (AM) generated in state-to-state change. Two pairs of systems are chosen as representative of processes broadly categorized as “efficient” or “inefficient” in this regard, namely, Na2–Na, Li2–Li in the former category and N2+–He, CN–Ar in the latter. Note that EET involving electron spin change is not considered here. Using velocity-AM diagrams and quantitative calculations we show the factors that govern the probability of state-to-state transfer in EET are the same as those controlling the outcome of rotational and rovibrational transfer within an electronic state. This suggests that requirements of orbital and rotational AM are of critical importance in providing pathways that allow EET to proceed.

Rotational distributions vary widely among the different collisional interactions that initiate chemical and physical change, processes that are often regarded as differing in kind. Here the commonality of mechanism among a variety of collision-induced processes is emphasized. This mechanism is the conversion of linear-to-angular momentum at the hard wall of the intermolecular potential, its operation is constrained by (i) the existence of quantized molecular eigenstates and (ii) boundary conditions set by energy conservation. The wide variation of these boundary conditions under differing kinematic circumstances gives rise to the wide variety of rotational distributions that is observed experimentally. Three cases of vibrotation transfer (VRT), namely Li-2-Ne, NO-NO, and HF-H are considered in detail. It is shown that the natural distribution in VRT is best described as "frustrated exponential-like", only recognized as such by observing the development of rotational distribution shape as the vibrational momentum ''gap" steadily increases, as in the cases considered. The low Deltaj region of the distribution becomes severely truncated as this gap increases, giving distribution shapes which are superficially Boltzmann in appearance. The analysis here indicates that derivation of rotational "temperatures" based on this apparent similarity is likely to give misleading results. Velocity-angular momentum diagrams are used to give physical insight into the operation of the mechanism, the effect of energy boundary conditions and to predict rotational distribution shapes and peak values. The analysis also suggests that in determining vibrational transfer cross section, inaccurate results will generally result unless initial rotational state j(i) similar or equal to 0 and the whole manifold of rotational states in nu (f) is summed.

The collisional behavior of (X)6Li2 molecules in very high rotational levels of v=0 is considered. Highly efficient vibration–rotation transfer is predicted in these “super rotors” particularly when the conditions for quasiresonant transfer are fulfilled. This requires simultaneous near-resonance in energy and in angular momentum. Values of Δj for which quasiresonant vibration–rotation transfer (QRT) occurs become smaller as initial rotor state increases and transfer is likely to become particularly fast for Δj=2, predicted to occur when ji=130. This behavior is contrasted with the inefficiency of pure rotational transfer within the v=0 level for fast-rotating molecules. QRT will take place for quite cold collisions and thus will provide competition for the spinning-up process used to create the super rotors.

An unanswered question in collision-induced rotational transfer (RT) centers on the similarities that characterize the distributions of Delta j states despite very large differences in mass and chemical composition of collision partners (Clegg, S. M.; Burrill, A. B.; Parmenter, C. S. J. Phys. Chem. A 1998, 102, 8447). We show these observations to be consistent with a kinematic model whose mechanism is the conversion of linear momentum of relative motion into rotational angular momentum (AM) via a torque arm (b(n)) of molecular dimension. The mechanism operates strictly within boundary conditions set by energy conservation and, in certain kinematic circumstances, the range of b(n) values that may be accessed is constrained. These constraints are particularly marked when initial rotor state, j(i) much greater than 0 and when reduced mass (mu) is large. The occurrence of constraints is clearly seen in velocity-AM plots and the reduction of b(n) that results is readily quantified. Insights obtained from velocity-AM plots for j(i) > 0 and large mu are confirmed through multi hard ellipsoid Monte Carlo calculations. The analysis presented here indicates that the energy corrected form of the IOS scaling relation does not adequately represent the RT mechanism for j(i) not equal 0 and introduces poorly defined parameters that appear unnecessary for a full description.

Li2 , HF, and H2and other light diatomics at high vibration-rotational excitation exhibit an unusual form of vibration-rotation transfer generally associated with near energy resonance. This quasi-resonant transfer (QRT) gives rise to narrow rotational distributions. Near resonance in angular momentum is also a necessary requirement for the occurrence of QRT. However, the underlying physical processes differ little from those governing the more common forms of collisional transfer which, along with QRT, can be rationalized via the mechanism of linear to angular momentum interconversion within boundary conditions set by energy conservation. Velocity-jplots illustrate that these boundary conditions moderate the mechanism in a unique fashion in the case of QRT since they are sharply defined around a limited set of jvalues. The occurrence of QRT will be widespread in the high lying states of light diatomic molecules, the hydrides for example, and may readily be identified using plots of the energy and angular momentum conservation relations. Energy conservation forces a reduction in the maximum available torque arm in the angular momentum mechanism for all but a narrow range of jtransitions. This analysis of the primary physical mechanism is confirmed via multiellipsoid Monte Carlo calculations for Li2and for H2 . In HF-Ar we show that QRT is a much more likely process than pure rotational transfer giving rise to collisional pumping which will be enhanced in a multicollision environment.

We explore the application of a simple model of collisional processes, developed initially for inelastic collisions, to the analysis of product rovibrational states in elementary chemical reactions. The model depicts collisional transfer as a process of momentum exchange (predominantly linear-to-angular momentum) and is modified to take account of change in center-of-mass and enthalpy change that accompany reaction. The kinematics of center-of-mass shift derived by Elsum and Gordon [J. Chem. Phys. 76, 3009 (1982)] lead to two limiting cases based on the parameter β. The kinematic extremes alternatively may be specified in terms of the molecular torque arm about which interconversion of linear and angular momentum is effected. This torque arm length approximates to the product bond length when β≃0 and the reactant bond length when β≃90°. Our approach shares elements in common with the classical kinematic model of Elsum and Gordon but is somewhat simpler and more transparent. The method is shown to give accurate peak values of v, j states of the products of a wide range of elementary reactions for which experimental data is available. Monte Carlo trajectory calculations based on the physical principles described here give excellent fits to experimental v, j distributions in F+I2→IF+I, H+D2→HD+D, and Cl+H2→HCl+H using input data consisting of atomic radii, atomic masses, velocities, and reaction enthalpies.

A kinematic interpretation for quasiresonant vibration–rotation collisional transfer (QRT) is outlined based on the angular momentum (AM) theory. QRT provides a particularly stringent test since as rotational AM increases, energy decreases (or vice versa). We demonstrate using velocity-AM plots for (A) 1∑u Li2–Ne that although experimentally spectacular, in kinematic terms it constitutes only a slightly unusual energetic constraint to the linear-to-angular momentum conversion.

We construct a path integral based approximation to rotationally inelastic collisions from which differential scattering cross sections are obtained for a number of atom–diatom systems. These are found to be in good agreement with IOS calculations on the same systems. In this approximation, the classical and near-classical paths that control scattering from a quantized system are deduced and this process reveals the origins of interference effects seen in theoretical calculations and some experimental measurements of angular distributions. This formulation provides physical insight into the important trajectories in systems where one or more degrees of freedom are quantized and could be regarded as an extension of classical S matrix theory, which for simple systems do not require root finding methods.