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This study of near-resonant, vibration-vibration (V-V) gas-phase energy transfer in diatomic molecules uses the theoretical/computational method, of Marsh & McCaffery (Marsh & McCaffery 2002 J. Chem. Phys.117, 503 (doi:10.1063/1.1489998)) The method uses the angular momentum (AM) theoretical formalism to compute quantum-state populations within the component molecules of large, non-equilibrium, gas mixtures as the component species proceed to equilibration. Computed quantum-state populations are displayed in a number of formats that reveal the detailed mechanism of the near-resonant V-V process. Further, the evolution of quantum-state populations, for each species present, may be followed as the number of collision cycles increases, displaying the kinetics of evolution for each quantum state of the ensemble's molecules. These features are illustrated for ensembles containing vibrationally excited N2 in H2, O2 and N2 initially in their ground states.This article is part of the theme issue 'Modern theoretical chemistry'.
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We report separate experimental and theoretical studies of the equilibration of highly excited LiH (v = 10; J = 2) in H2 at 680 K. Experiments that follow the time evolution of state-to-state population transfer in multi-collision conditions with µs resolution were carried out by Shen and co-workers at Xinjiang University and East China Institute of Science and Technology. At the same time, theoretical computations on the relaxation of this gas mixture were undertaken by McCaffery and co-workers at Sussex University. Rapid, near-resonant, vibration-vibration energy exchange is a marked feature of the initial relaxation process. However, at later stages of ensemble evolution, slower vibration-rotation transfer forms the dominant relaxation mechanism. The physics of the decay process are complex and, as demonstrated experimentally here, a single exponential expression is unlikely to capture the form of this decay with any accuracy. When these separate studies were complete, the evolution of modal temperatures from the Sussex calculations was compared with experimental measurements of these same quantities from Shanghai and Urumqi. The two sets of data were marked by their near identity, within experimental and computational error, representing an experimental validation of the theoretical/computational model developed by the Sussex group and a significant experimental advancement by the group of Shen et al.
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Until very recently, the computational model of state-to-state energy transfer in large gas mixtures, introduced by the author and co-workers, has had little experimental data with which to assess the accuracy of its predictions. In a novel experiment, Alghazi et al. [Chem. Phys. 448, 76 (2015)] followed the equilibration of highly vibrationally excited CsH(D) in baths of H2(D2) with simultaneous time- and quantum state-resolution. Modal temperatures of vibration, rotation, and translation for CsH(D) were obtained and presented as a function of pump-probe delay time. Here the data from this study are used as a test of the accuracy of the computational method, and in addition, the consequent changes in bath gas modal temperatures, not obtainable in the experiment, are predicted. Despite large discrepancies between initial CsH(D) vibrational states in the experiment and those available using the computational model, the quality of agreement is sufficient to conclude that the model's predictions constitute at least a very good representation of the overall equilibration that, for some measurements, is very accurate.
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Little is known of the mechanism by which H and H2, the principal constituents of the post-re-combination early Universe, cooled sufficiently to permit cluster formation, nucleosynthesis, and, eventually, the formation of structured objects. Radiative decay primarily cools the internal modes of H2, as Δj = - 2 jumps accompany quadrupolar emission. This, however, would be a self-limiting mechanism. In this work, a translational energy cooling mechanism based on collision-induced, translation-to-internal mode conversion, is extended, following an earlier study [A. J. McCaffery and R. J. Marsh, J. Chem. Phys. 139, 234310 (2013)] of ensembles comprising H2 in a H atom bath gas. Here, the possible influence of minor species, such as HD, on this cooling mechanism is investigated. Results suggest that the influence of HD is small but not insignificant. Conversion is very rapid and an overall translation-to-internal energy conversion efficiency of some 5% could be expected. This finding may be of use in the further development of models of this complex phase of early Universe evolution. An unexpected finding in this study was that H2 + HD ensembles are capable of very rapid translation-to-internal conversion with efficiencies of >40% and relaxation rates that appear to be relatively slow. This may have potential as an energy storage mechanism.
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A recent computational study of translation-to-internal energy transfer to H2 (v = 0,j = 0), hereinafter denoted H2 (0;0), in a bath of H atoms [A. J. McCaffery and R. J. Marsh, J. Chem. Phys. 139, 234310 (2013)] revealed an unexpected energy partitioning in which the H2 vibrational temperature greatly exceeds that of rotation. This occurs despite rotation and vibration distributions being close to Boltzmann from early in ensemble evolution. In this work, the study is extended to include H2 (0;0), O2 (0;0), and HF (0;0) in a wide range of atomic bath gases comprising some 22 ensembles in all. Translation-to-internal energy conversion in the systems studied was found to be relatively inefficient, falling approximately with (âµ')(-1) as bath gas mass increases, where µ' is the reduced mass of the diatomic-bath gas pair. In all 22 systems studied, T(v) exceeds T(r)--by a factor > 4 for some pairs. Analysis of the constraints that influence (0;0) â (1;j) excitation for each diatomic-atom pair in momentum-angular momentum space demonstrates that a vibrational preference results from energy constraints that limit permitted collision trajectories to those of low effective impact parameter, i.e., to those that are axial or near axial on impact with the Newton surface. This implies that a steric constraint is an inherent feature of vibration-rotation excitation and arises because momentum and energy barriers must be overcome before rotational states may be populated in the higher vibrational level.
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We use our recently developed computational model of energy flow in gas ensembles to study translation-to-internal energy conversion in an ensemble consisting of H2(0; 0) in a bath of H atoms. This mixture is found in plasmas of industrial importance and also in interstellar clouds. The storage of energy of relative motion as rovibrational energy of H2 represents a potential mechanism for cooling translation. This may have relevance in astrophysical contexts such as the post-recombination epoch of the early universe when hydrogenic species dominated and cooling was a precondition for the formation of structured objects. We find that conversion of translational motion to H2 vibration and rotation is fast and, in our closed system, is complete within around 100 cycles of ensemble collisions. Large amounts of energy become stored as H2 vibration and a tentative mechanism for this unequal energy distribution is suggested. The "structured dis-equilibrium" we observe is found to persist through many collision cycles. In contrast to the rapidity of excitation, the relaxation of H2(6; 10) in H is very slow and not complete after 10(5) collision cycles. The quasi-equilibrium modal temperatures of translation, rotation, and vibration are found to scale linearly with collision energy but at different rates. This may be useful in estimating the partitioning of energy within a given H + H2 ensemble.
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We present a quantum state-resolved computational investigation of the equilibration of rovibrationally excited OH, present as the minor component in an air-like mixture of N(2) and O(2), over the temperature range 100-1200 K. Generic features of the equilibration that are present over the entire range are identified, and the increase in speed of the principal energy exchange mechanism as the temperature increases is quantified. The data demonstrate that partitioning of excess energy and angular momentum among the modes of the three different molecules is independent of the magnitude of excess energy and of its form. The rotational temperature of OH is found to vary widely over the equilibration process, varying with number of collision cycles and with initial temperature. However, at equilibration, the rotational temperature of OH is invariably the lowest of all modes of all three species present in the ensemble. This suggests that rotational temperatures of OH obtained from rotational state populations are unlikely to provide a reliable guide to other modal temperatures in ensembles of the kind we consider.
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State-to-state, collision-induced, energy transfer is followed to equilibrium through sequences of collision cycles in gas ensembles containing vibrationally excited oxygen molecules (v = 8 and 1) in several different atomic and molecular bath gases. Quantum state distributions for each of the constituent species are available at each stage of the ensemble's evolution and enable the dominant energy exchange mechanisms to be identified. Equilibration is generally a complex process that evolves through several phases of inter- and intra-molecular events, each with their characteristic response rate to collisions. The results suggest that single quantum state population loss rate constants, however precisely determined, may miss key features of the overall equilibration process.
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Oxigênio/química , Teoria Quântica , VibraçãoRESUMO
A wide-ranging computational study of equilibration in binary mixtures of diatomic gases reveals the existence of competition between the constituent species for the orbital angular momentum and energy available on collision with the bath gas. The ensembles consist of a bath gas AB(v;j), and a highly excited minor component CD(v';j'), present in the ratio AB:CD = 10:1. Each ensemble contains 8000 molecules. Rotational temperatures (T(r)) are found to differ widely at equilibration with T(r)(AB)/T(r)(CD) varying from 2.74 to 0.92, indicating unequal partitioning of rotational energy and angular momentum between the two species. Unusually, low values of T(r) are found generally to be associated with diatomics of low reduced mass. To test effects of the equi-partition theorem on low T(r) we undertook calculations on HF(6;4) in N(2)(0;10) over the range 100-2000 K. No significant change in T(r)(N2)/T(r)(HF) was found. Two potential sources of rotational inequality are examined in detail. The first is possible asymmetry of -Δj and +Δj probabilities for molecules in mid- to high j states resulting from the quadratic dependence of rotational energy on j. The second is the efficiency of conversion of orbital angular momentum, generated on collision with bath gas molecules, into molecular rotation. Comparison of these two possible effects with computed T(r)(AB)/T(r)(CD) shows the efficiency factor to be an excellent predictor of partitioning between the two species. Our finding that T(r) values for molecules such as HF and OH are considerably lower than other modal temperatures suggests that the determination of gas ensemble temperatures from Boltzmann fits to rotational distributions of diatomics of low reduced mass may require a degree of caution.
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In this work, a computational model of state-to-state energy flow in gas ensembles is used to investigate collisional relaxation of excited OH, present as a minor species in various bath gases. Rovibrational quantum state populations are computed for each component species in ensembles consisting of 8000 molecules undergoing cycles of binary collisions. Results are presented as quantum state populations and as (approximate) modal temperatures for each species after each collision cycle. Equilibration of OH is slow with Ar as the partner but much faster when N(2) and/or O(2) forms the bath gas. This accelerated thermalization is shown to be the result of near-resonant vibration-vibration transfer, with vibrational de-excitation in OH matched in energy by excitation in bath molecules. Successive near-resonant events result in an energy cascade. Such processes are highly dependent on molecule pair and on initial OH vibrational state. OH rotational temperatures initially increase, but at equilibration, they are lower than those of other modes. Possible reasons for this observation in molecules such as OH are suggested. There are indications of an order of precedent in the equilibration process, with vibrations taking priority over rotations, and potential explanations for this phenomenon are discussed.
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Radical Hidroxila/química , Nitrogênio/química , Oxigênio/química , Gases/química , Teoria Quântica , VibraçãoRESUMO
A computational model is used to quantify the evolution of quantum state populations as highly vibrationally excited (14)N(2) ((14)N(2)∗) equilibrates in various bath gases. Multicollision energy disposal follows general principles established in related single collision processes. Thus when state-to-state routes permit, maximum amounts of energy are deposited into partner species by direct vibration-to-vibration (V-V) exchange. When these pathways are absent, e.g., when Ar is the bath species, relaxation is very slow and multistaged. Conversely, in a bath of v = 0 (14)N(2) molecules, 16 vibrational quanta (Δv = ± 8) are resonantly exchanged from (v;j) = (8;10) with vibrational equilibration so rapid that rotation and translation still lag far behind after 1000 collisions. Near-resonant V-V exchange dominates the initial phase when (15)N(2) forms the bath gas and although some rotational warming occurs, vibrational modes remain decoupled from, and significantly hotter than, the low heat capacity modes. These forms of behavior seem likely to characterize excited and bath species that have closely similar vibration and rotation constants. More generic in nature is (14)N(2) in O(2) or in a mixture that closely resembles air. Here, asymmetric V-V exchange is a dominant early feature in ensemble evolution but energy differences in the key vibration and rotation quanta lead to V-V energy defects that are compensated for by the low energy modes. This results in much more rapid ensemble equilibration, generally within 400-500 collisions, when O(2) is present even as a minor constituent. Our results are in good general agreement with those obtained from experimental studies of N(2) plasmas both in terms of modal temperatures and initial (first collision cycle) cross-sections.
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HX rotational state distributions following vibrational predissociation (VP) of C(2)H(2)-HX (X = Cl, F, O) dimers are predicted by expressing the predissociation process as the joint probability of rovibrational excitation in the fragments following "internal collision" in the vibrationally excited dimer. Calculations of these joint probabilities for the T-shaped dimers of acetylene with HCl, DCl, HF, and OH using the angular momentum (AM) method reproduce experimental distributions with reasonable accuracy. In dimers of this complex, many different pathways for the disposal of initial energy and momentum exist in principle. The use of simple physical arguments based on (a) the direction of initial impulse upon excitation and (b) restricted relative geometries due to limited amplitude of relative motion of the dimer components allows the number of effective dissociation pathways to be much reduced. For these, the probability of rotational and rovibrational transfer into the fragments is calculated, a process that generally involves summing over a number of C(2)H(2) rovibrational states for each value of j(HX). In calculating relative rotational populations in the fragments, it was found essential to first calculate the threshold value of available energy for that transition and the threshold value of b(n), the effective impact parameter. Without these modifications, channels of lowest j(HX) and/or j(C(2)H(2)) dominate, which generally is not found experimentally. The need for these modifications is attributed to energy conservation in the dissociation and the limited range of relative orientations that the dimer pair can explore. The AM method is able to predict the very different fragment rotational excitations in this series of dimers fairly well using only readily available data. In addition, a number of new insights into the physical principles that control the dissociation of molecule-molecule dimers have emerged and are discussed. The results suggest that each fragment quantum state pair results from a very specific relative geometry of dissociation and that the balance between vibrational and rotational excitations is determined by the requirement to restrict the angular momentum "load" in the predissociation.
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The method of Marsh and McCaffery [J. Chem. Phys. 117, 503 (2002)] is used to quantify how rovibrational populations and mode temperatures change as an ensemble of CO molecules, initially excited to (v;j)=(8;12), evolves to thermal equilibrium in a bath gas. The bath gases considered are Ar, N(2), O(2), and CO all at 300 K with the diatomics in their (0;8) rovibrational states. Ensembles generally contain 1000 molecules, 10% of which are excited CO (CO( *)) molecules. State (v;j) populations and mode temperatures of CO* and bath molecules are calculated for successive collisions to 1000 or more. We find that relaxation to local thermodynamic equilibrium occurs in distinct phases that vary widely in rate of cooling. There is especially fast vibration-vibration (VV) exchange in CO*-CO mixtures that is largely decoupled from rotation and translation. Several aspects of ensemble behavior may be rationalized using concepts established in quantum state resolved single collision studies. We demonstrate the existence of a simultaneous energy quasiresonant, angular momentum conserving, low Deltaj VV process that can cause either ultrafast relaxation or up pumping of the kind seen in a number of experiments.
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Reactions for which the reactant (r)-to-product (p) mass ratio (mu(r)/mu(p)) is high, the well-known H + LH --> HH + L processes, convert most of available energy to product rotation, while that disposed as recoil is often regarded as negligible. In angular momentum (AM) terms, however, this recoil orbital AM (l(p)) is shown to be a critical component of the overall AM balance. For products of light mu(p), the maximum value of l(p) is energy limited and as a result the formation of products in low rotational (j(p)) states is severely restricted. Here energy constraints on recoil orbital AM and the consequent restrictions on j(p)-state populations are quantified using novel diagrammatic methods that illustrate how constraints on l(p) determine the j(p) states that are allowed or forbidden by the need to conserve energy and AM for each state-to-state transition. The method accurately predicts j(BaI)j (v=0,1,2) peaks from crossed-beam Ba + HI experiments, providing a quantitative and physically transparent rationale for the observed BaI rotational distributions. Extension to a wider range of reactions having mu(r)mu(p)>1 shows that at least some j(p) are formally forbidden for each given reactant relative velocity or, more accurately, l(r). The fraction of inaccessible product states for a given initial velocity rises rapidly with mu(r)/mu(p) (>96% in Ba + HI). The method is also used to demonstrate that recoil orbital AM will be strongly aligned parallel to product rotational AM for high mu(r)/mu(p), although this correlation is generally lost in the low j(p) region as the parallel vector requirement is relaxed.
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Pair correlated fragment rovibrational distributions are presented following vibrational predissociation of the C2H2-DCl van der Waals dimer initiated by excitation of the asymmetric (asym) C-H stretch. The only observed fragmentation pathways are DCl (v= 0; j= 6-9)+ C2H2(nu2= 1; j= 1-5). These and previously reported data on the related C2H2-HCl species are analysed using the angular momentum (AM) method. Calculations accurately reproduce fragment rovibrational distributions following dissociation of the C2H2-HCl dimer initiated either by excitation of the asym C-H stretch or via the HCl stretch, and those from C2H2-DCl initiated via asym C-H stretch excitation. The calculations demonstrate that the dimer is bent at the moment of dissociation. Several geometries are found that lead to H-bond breakage via a clearly identified set of fragment quantum states. The results suggest a hierarchy in the disposal of excess energy and angular momentum between fragment vibration, rotation and recoil. Deposition of the largest portion of energy into a C2H2 vibrational state sets an upper limit on HCl rotation, which then determines the energy and AM remaining for C2H2 rotation and fragment recoil. Acceptor C2H2 vibrational modes follow a previously noted propensity, implying that the dissociating impulse must be able to induce appropriate nuclear motions both in the acceptor vibration and in rotation of the C2H2 fragment.
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Acetileno/química , Deutério/química , Ácido Clorídrico/química , Modelos Químicos , Teoria Quântica , Dimerização , Ligação de Hidrogênio , VibraçãoRESUMO
The state-to-state vibrational predissociation (VP) dynamics of the hydrogen-bonded ammonia-acetylene dimer were studied following excitation in the asymmetric CH stretch. Velocity map imaging (VMI) and resonance-enhanced multiphoton ionization (REMPI) were used to determine pair-correlated product energy distributions. Following vibrational excitation of the asymmetric CH stretch fundamental, ammonia fragments were detected by 2 + 1 REMPI via the B1E'' <-- X1A1' and C'1A1' <-- X1A1' transitions. The fragments' center-of-mass (c.m.) translational energy distributions were determined from images of selected rotational levels of ammonia with one or two quanta in the symmetric bend (nu2 umbrella mode) and were converted to rotational-state distributions of the acetylene co-fragment. The latter is always generated with one or two quanta of bending excitation. All the distributions could be fit well when using a dimer dissociation energy of D0 = 900 +/- 10 cm(-1). Only channels with maximum translational energy <150 cm(-1) are observed. The rotational excitation in the ammonia fragments is modest and can be fit by temperatures of 150 +/- 50 and 50 +/- 20 K for 1nu2 and 2nu2, respectively. The rotational distributions in the acetylene co-fragment pair-correlated with specific rovibrational states of ammonia appear statistical as well. The vibrational-state distributions, however, show distinct state specificity among channels with low translational energy release. The predominant channel is NH3(1nu2) + C2H2(2nu4 or 1nu4 + 1nu5), where nu4 and nu5 are the trans- and cis-bend vibrations of acetylene, respectively. A second observed channel, with much lower population, is NH3(2nu2) + C2H2(1nu4). No products are generated in which the ammonia is in the vibrational ground state or the asymmetric bend (1nu4) state, nor is acetylene ever generated in the ground vibrational state or with CC stretch excitation. The angular momentum (AM) model of McCaffery and Marsh is used to estimate impact parameters in the internal collisions that give rise to the observed rotational distributions. These calculations show that dissociation takes place from bent geometries, which can also explain the propensity to excite fragment bending levels. The low recoil velocities associated with the observed channels facilitate energy exchange in the exit channel, which results in statistical-like fragment rotational distributions.
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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.
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The translational energy release distribution for dissociation of benzene-Ar has been measured and, in combination with the 6(1)(0) rotational contour of the benzene product observed in emission, used to determine the rotational J,K distribution of 0(0) benzene products formed during dissociation from 6(1). Significant angular momentum is transferred to benzene on dissociation. The 0(0) rotational distribution peaks at J=31 and is skewed to low K:Javerage=27, (K)average=10.3. The average angle between the total angular momentum vector and the unique rotational axis is determined to be 68 degrees. This indicates that benzene is formed tumbling about in-plane axes rather than in a frisbeelike motion, consistent with Ar "pushing off" benzene from an off-center position above or below the plane. The J distribution is very well reproduced by angular momentum model calculations based on an equivalent rotor approach [A. J. McCaffery, M. A. Osborne, R. J. Marsh, W. D. Lawrance, and E. R. Waclawik, J. Chem. Phys. 121, 1694 (2004)], indicating that angular momentum constraints control the partitioning of energy between translation and rotation. Calculations for p-difluorobenzene-Ar suggest that the equivalent rotor model can provide a reasonable prediction of both J and K distributions in prolate (or near prolate) tops when dissociation leads to excitation about the unique, in-plane axis. Calculations for s-tetrazine-Ar require a small maximum impact parameter to reproduce the comparatively low J values seen for the s-tetrazine product. The three sets of calculations show that the maximum impact parameter is not necessarily equal to the bond length of the equivalent rotor and must be treated as a variable parameter. The success of the equivalent rotor calculations argues that angular momentum constraints control the partitioning between rotation and translation of the products.
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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.