Kjell Rynefors

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. I. Basic considerations and calculational procedure

Abstract A simulation method is described for the comparison of a molecular decomposition theory, based on the fundamental RRKM theory, with crossed molecular beam experiments. In the present formulation, the method is applied to the case with long-lived collision complexes surrounded by a centrifugal barrier. The procedure uses Monte Carlo techniques to simulate the formation and decomposition of the complexes, thus effectively solving the high-dimensional integrals resulting but seldom solved in the analytical treatments. Several computational problems, like singularities in the c.m. angular distributions, have been circumvented in this procedure. Angular momentum conservation, the simultaneous interaction of several decomposition channels and strict flux conservation are included in the procedure. Dynamical features can be introduced, as will be shown in forthcoming papers.

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. II. Application to angular distributions and absolute cross sections for the system K + RbCl

Abstract The Monte Carlo simulation algorithm, which we have developed recently, is now applied to one of the well studied alkali—alkali halide systems. The calculations show, that quite good agreement between experiment and theory is found with semiclassical energy distributions and ordinary RRKM theory. This applies also to the branching ratio, which is now found to be around 0.67 instead of the previously reported theoretical value of 1.0–1.3. The good agreement here is due to the exact treatment of angular momentum conservation, the correct evaluation including all initial distributions and the elimination of previous inaccuracies, like the SWHT formulas. By inclusion of three nonstatistical effects, based on trajectory calculations and dynamical arguments, excellent agreement between theory and the absolute experiments is found. One conclusion is, that the usual large orbital angular momentum approximation is not good even in this case with large cross sections.

Monte Carlo simulation of O(1D)+H2 and O(1D)+HCl ― rotational excitation of product OH radicals

Abstract Experimental studies with molecular beam and LIF techniques have independently shown that the reaction O( 1 D) + H 2 → OH + H passes through a long-lived complex and gives products with small translational and large rotational excitation. We have previously published a statistical algorithm, based on ordinary RRKM theory with angular momentum restrictions included, which was designed to simulate molecular beam experiments. It has now been modified and applied to simulate the experimental rotational OH distributions from O( 1 D)+H 2 , measured by Luntz et al. The present study also includes simulation of similar results by Luntz for O( 1 D) + HCI → OH + Cl. The purely statistical algorithm successfully simulates the apparently non-statistical experimental rotational distributions. For these reactions the total angular momentum conservation. which is applied at the transition state, proves to be decisive for the product energy distributions.

Monte carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. IV. Product OH angular and velocity distributions from O(1D)+H2

Abstract Statistical simulations of RRKM unimolecular decomposition have been applied to the results from crossed molecular beam experiments by Buss et al. for the system O( 1 D) + H 2 → OH + H. Good agreement was found with the laboratory angular distributions. Inverted rotational product distributions were found from the purely statistical calculations. These results agree with LIF experiments on this system. It is concluded that the correct inclusion of angular momentum conservation gives this feature. It is also shown, under these conditions, that the “freezing” point (uncoupling region) for the rotational degrees of freedom is located far outside the centrifugal barrier in the exit channel for this system.

Realistic translational energy distributions for decomposition of RRKM complexes with a centrifugal barrier

Abstract The RRKM unimolecular decomposition theory and its application to long-lived collision complexes with centrifugal barriers have been studied. A comparison with a Monte Carlo simulation method has shown that the previously used formulas for the translational energy distribution from decomposition of such complexes are not consistent with flux conservation requirements, i.e., each complex formed does not have unit probability of decomposing. Correct expressions for both one- and two-channel decomposition have been developed, and comparisons have been made with existing experimental data. Unfortunately, most data have been fitted to the earlier expressions using arbitrary assumptions or incorrect procedures, which makes comparisons difficult without complete recalculations. However, it is for example demonstrated that the peak of the correct distribution does not shift strongly with the number of oscillators used in the RRKM theory, and that it is always at higher energy than the previously used distribution. This means, that the interpretation of experiments in terms of a low number of “effective” oscillators probably is invalid. Some inconsistencies in previous work are also pointed out.

Efficient microcanonical sampling for triatomic molecular systems: Exact distributions verified

Statistical distributions of several quantities, such as linear and angular momenta, for a triatomic molecular system similar to an excited H2O molecule were obtained with an efficient microcanonical sampling method, previously described by Severin et al. The distributions were recorded as a function of the total angular momentum. Using this sampling procedure to obtain initial values for classical trajectory calculations and comparing with the trajectory quantities after variable times in the range 0.7 fs to 0.2 ps, it was verified that the sampling method gives exact distributions. This may open a way of reducing computer time in future trajectory calculations of unimolecular reactions, particularly important at low total energies. We also illustrate the breakdown of equipartition of energy between the various degrees of freedom in highly excited complexes. In some cases equipartition is not even valid for potential energy surfaces built solely from harmonic terms.

A new approach to angular momentum constraints in bimolecular reactions

Abstract The well-known analysis of angular momentum constraints for diatomic systems in terms of a bond potential containing a J-dependent centrifugal part is here extended to larger systems. The new procedure is based on the identification of the minimal kinetic energy associated with a given spatial configuration and J value. Alternatively, for a given total energy E and spatial configuration the maximum J value can be identified. Constant Jmax curves have been obtained by a Monte Carlo sampling scheme for a model of the KNaCl system at several different total internal energies. Particular attention is given to the estimation of J-dependent reaction thresholds.

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. V. product ox angular and energy distributions from O(3P)+X2 (X = Br, I)

Abstract Statistical simulation was applied to the unimolecular decomposition of the collision complexes formed in the crossed beam experiments on O( 3 P) + Br 2 by Fernie et al. and O( 3 P) + I 2 by Durkin et al. The simulation procedure used the fundamentals of RRKM theory and included exact angular momentum conservation. The impact parameter distributions were varied to obtain the best fits. Good agreement with experimental laboratory angular distributions measured with O atoms seeded in both He and Ne was found for impact parameter distributions which were peaked at quite small values, in most cases between 2 and 3 A. Product OX molecules were found to be rotationally excited and inverted with a mean rotational energy close to twice the value expected without angular momentum restrictions. The differences found between the calculated and the experimental angular distributions do not support any assumptions about osculating or short-lived complexes. The normal exoergicity Δ D 0 of 27 kJ/mol for the O + I 2 reaction agrees well with the experiments by Dunkin et al.

Absolute complex formation cross sections for alkali—alkali halide collisions: a Monte Carlo trajectory study

Abstract A classical Monte Carlo trajectory study has been performed, where the potential energy function used is an ideal dipole potential with its center displaced from the center of mass. The potential shape depends on two parameters. For one choice of parameters, the theoretical Roach and Child surface is well approximated at large and intermediate distances. Several other choices of parameter values have also been used. Complex formation cross sections and angular distributions at the centrifugal barrier have been determined, and a comparison with the theoretical quantities for a spherically symmetric potential is made. The previously proposed mechanisms, assumed to explain the experimentally found low values of σ c and the quantity of Γ, have not been found to be significant. A dynamical picture is used to interpret the present results. It also provides an interpretation of the previous experimental results. In this picture rotational energy transfer at the barrier is of great importance.

Total angular momentum conservation in statistical unimolecular theory should be represented in energy space

Abstract A representation of total angular momentum conservation in energy space is described. Several advantages of such a representation are discussed, primarily in connection with statistical unimolecular theory, experimental branching ratios and product energy distributions. Specific examples are given for the systems K + CsF and O + I2.