Double step-ladder model of activation in the processes of high-temperature dissociation of polyatomic molecules

A unified mechanism of the interaction of vibrational relaxation and dissociation of polyatomic molecules working in a wide temperature range (from 2000 to 10000 K) is proposed, which is described by a double step-ladder model. Relaxation due to collisions with the transfer of small and large portions of energy is taken into account. The transfer efficiency of the portions of thermal energy in the high-temperature decomposition upon the collisions of CO₂ molecules with atomic and molecular partners is determined. The reaction rate constant of high-temperature dissociation of carbon dioxide is calculated. The data presented in the article suggest a new method for elucidating the mechanism of energy exchange in the absence of vibrational and translational equilibrium and at ultrahigh temperatures when the dissociation takes place during the time of several collisions.     

Application of the Monte Carlo Method to Modeling Kinetic Processes of Polyatomic Molecules and Clusters: II. Kinetics of Unimolecular Reactions of Polyatomic Molecules

The method for statistical modeling of the kinetics of unimolecular decomposition of polyatomic molecules based on the construction of nonequilibrium functions of the distribution over the energies of the vibrational excitation of molecules is developed. The rate constants for the two-channel decomposition of a model molecule depending on temperature and pressure are reported. The relaxation characteristics for the dissociation of the model molecule are determined.     

Initial state selection and intramolecular vibrational relaxation in reacting polyatomic molecules. Isopropylcyclobutane precursor

The study of intramolecular vibrational energy transfer in polyatomic molecules excited to the level of chemical reaction is here extended to hydrocarbon species. By insertion of ¹CH₂ into the CH bonds of isopropylcyclobutane a closely related series of chemically activated alkyl cyclobutanes are produced at levels of excitation above 100 kcal mole^?1. The cyclobutane ring decomposes into olefin fragments. The methylene insertion takes place at CH sites on the molecule which are either on the ring or on the side chain. This corresponds to injection of excited molecules into various regions of their energy-coordinate hyperspace which are more or less adjacent to, or remote from the critical hyperplane corresponding to decomposition. A study of the pressure dependence of the relative rates and amounts of decomposition of the several differentially excited cyclobutanes follows theoretical expectations with regard to occurrence of non-randomized decomposition from some of the molecules prior to complete relaxation. Molecules which have been activated on the side chain exhibit only ordinary randomized decomposition. Analysis of the data on a simple model leads to gross rates of intramolecular relaxation, λ = 2.2 × 10¹²s^?1 and λ = 3.5 × 10¹²s^?1, for species excited at different sites on the ring. These rates are several times larger than those previously reported for fluorocyclopropanes.     

Application of the Monte Carlo method to modeling of kinetic processes with the participation of polyatomic molecules and clusters: 1. Kinetics of energy transfer during collisions of polyatomic molecules

The Monte Carlo method was used to model the collisional energy transfer for polyatomic molecules within the framework of the statistical theory of reactions. A model describing energy transfer through the formation of a statistical collisional complex was suggested. It was assumed that the total energy of the complex was randomized in the course of collisions and statistically distributed among the internal and translational degrees of freedom. The method was verified by comparing the equilibrium distribution functions for the vibrational, rotational, and total energies of the molecule. The mean energy portion and the root-mean-square energy portion transferred per collision, as functions of the total molecular energy, were determined. The relaxation parameters of the population distribution over energy after a sharp increase in the bath-gas temperature were calculated.     

A multi-dimensional microcanonical Monte Carlo study of S0 → T1 intersystem crossing of isocyanic acid

A general formula for the multi-dimensional Monte Carlo microcanonical nonadiabatic rate constant expressed in configuration space is applied to calculate the rate of intersystem crossing (ISC) between the ground (S₀) and first excited triplet (T₁) states for isocyanic acid. One-, two- and three-dimensional potential energy surfaces are constructed by coupled-cluster single-double CCSD calculations, which are used for Monte Carlo sampling. The calculated S₀→T₁ ISC rate is in good agreement with experimental findings, which gives us a reason to believe that the multi-dimensional Monte Carlo microcanonical nonadiabatic rate theory is a very effective method for calculating nonadiabatic transition rate of a polyatomic molecule.     

Vibrational-translational/rotational and vibrational-vibrational processes in methane/inert-gas mixtures: Optoacoustic phase measurements

We consider the model with kinetic excitation into the quasicontinuum (KEQ) for resonant polyatomic molecules which absorb laser radiation and are surrounded by buffer molecules. KEQ takes place when the resonant molecules in the lower part of the energy spectrum interact weakly with the laser radiation, but the molecules in the quasicontinuum are rapidly excited to still higher energy and dissociate. Under these conditions the collisions of the resonant and buffer molecules lead to excitation of resonant molecules into the quasicontinuum because the population of the quasicontinuum is much less than its thermodynamical equilibrium value. It is found, that the smaller the V-T relaxation time τ_VT, the larger the rate of KEQ and the dissociation rate (if only τ_VT is not too small). Thus, if we change the experimental conditions and decrease τ_VT (for instance, by passing from the heavy buffer gas Xe to the light buffer gas He), for some resonant molecules we may observe that the probability of dissociation increases.     

Diffusion of vibrationally excited molecules

A treatment is presented for the effect of intermolecular vibrational energy transfer on the diffusion coefficient of vibrationally excited molecules. An analytic treatment based on random walk statistics and a Monte Carlo type calculation have been performed. Both methods yield very similar results which correlate well with existing experimental studies. A hard sphere collision model is treated extensively with comparisons made to other internmolecular potentials. The results support the involvement of long range energy transfer in V → V interactions. The effect of temeprature on the diffusion coefficient of vibrationally excited molecules is calculated, with applications to the CO^*₂CO₂ system.     

Estimation of equilibrium structure and anharmonicity by use of changes in the rz structure by isotopic substitution and vibrational excitation: I. General formulation and application to OCl2

A general formulation is presented on the differences in the average (r_z) structure caused by isotopic substitution and vibrational excitation; the differences in the average structure for both bonded and nonbonded atomic pairs are represented as linear combinations of quadratic average values of the Cartesian displacement coordinates. This method is applicable to a joint analysis of spectroscopic and electron diffraction data so that the equilibrium geometrical parameters and effective anharmonic constants for polyatomic molecules can be estimated even when only a limited number of rotational constants for isotopic species and vibrationally excited states are available. Its application to OCl₂ molecule as an example is discussed.     

Order parameters and molecular shapes of phosphonic acid dialkyl esters in a uniaxial hydrophobic environment. A theoretical study

The conformational behaviour of phosphonic acid dialkyl ester (PAE) molecules in a uniaxial hydrophobic environment was studied using the Monte Carlo method with the well-known Metropolis algorithm. The influence of the surrounding molecules on ordering processes of the intrinsic PAE molecules was taken into account by a molecular field. The intramolecular energy was calculated using 6–12 atom-atom and torsion potential functions. Conformations were analysed using torsion angle distributions, segment and bond order parameters. The order parameters of the C-H bonds are compared with experimental results of²H NMR. Further a general method of determining the effective shape of a molecule is presented. The shape is defined by probability distribution for finding atomic coordinates within volume elements during a Monte Carlo run. Thus the asymmetry of a molecule can be visualized. PAE molecules studied show a positive asymmetry in all cases.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Monte Carlo computation of ground‐state energy derivatives

Monte Carlo is a simple technique, which uses random numbers to compute ground‐state energies of small molecules (and quantum systems in general). The results always have a small statistical error, which poses a major obstacle when estimating properties defined as ground‐state‐energy derivatives (such as the molecule's geometry, its vibrational frequencies, polarizabilities, etc.). In this article, we present and demonstrate an approach that makes an accurate Monte–Carlo estimation of such derivatives possible. This is achieved by realizing that the simulation constitutes an autocorrelated stochastic process, whose proper analysis then enables us to estimate various energy derivatives as a combination of total correlation between readily computable quantities. The resulting procedure is a natural extension of the usual Monte Carlo algorithm for computing the ground‐state energy, with relatively small computational overhead. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Vibrational relaxation induced population inversions in laser pumped polyatomic molecules

Conditions for population inversion in laser pumped polyatomic molecules are described. For systems which exhibit metastable vibrational population distributions [slow vibration—translation/rotation (V—T/R) relaxation], large, long lived inversions are possible even when the vibrational modes are strongly coupled by rapid collisional vibration—vibration (V—V) energy transfer. Overtone states of a hot mode are found to invert with respect to fundamental levels of a cold mode even at V—V steady state. Inversion persists for a V—T/R relaxation time. A gain of 4 m^?1 for the 2v₃ → v₂ transition in CH₃F (λ ≈ 15.9 μ) was found assuming a spontaneous emission lifetime of 10 s for this transition. General equations are derived which can be used to determine the magnitude of population inversion in any laser pumped, vibrationally metastable, polyatomic molecule. A discussion of factors controlling the population maxima of different vibrational states in optically pumped, V—V equilibrated metastable polyatomics is also given.     

Non radiative transition probabilities in the statistical limit

In this paper we derive a general computational scheme for the calculation of the non radiative decay probability of a polyatomic molecule in the statistical limit. Within the framework of the Harmonic Approximation the relaxation rate of any polyatomic molecule can be expressed in terms of an infinite sum where each term consists of a medium distribution function and an intramolecular term. In the statistical limit the medium induced vibrational relaxation widths do not affect the non radiative decay characteristics. Numerical calculations are reported for the T ₁S ₀ intersystem crossing in the benzene molecule.     

Quantum-mechanical and statistical mechanical studies of the torsional barrier of H2O2 in aqueous solution

Monte Carlo simulations were carried out on clusters consisting of one hydrogen peroxide molecule and n water molecules, n being 100 and 250. Quantum-chemical potentials were used for the interactions between the species. The torsional angle was allowed to change in the simulation and its equilibrium value was found to change from ～115° in the dilute vapor phase to ～80° in the aqueous surrounding. At the same time the cis barrier became smaller than the trans barrier, as opposed to in the isolated molecule. A continuum model using the reaction field technique was investigated parallel with the simulations; with a reasonable size of the spherical cavity, containing the H₂O₂ molecule, it was found possible to qualitatively reproduce the Monte Carlo results.     

Semiclassical calculation of rate costants for energy transfer between the asymmetric stretch mode of CO2 and N2

By using a semiclassical method for energy transfer in polyatomic molecules we have calculated 21 rate constants for vibration-vibration transitions between the asymmetric stretch mode of CO₂ and the vibrational mode of N₂ in the temperature range 50–700 K.     

The mechanism of activation and nonequilibrium distribution functions in unimolecular reactions

Nonequilibrium distribution functions for polyatomic molecules undergoing unimolecular reaction are considered. Two limiting cases of activation by collision are investigated: the mechanism of strong impacts, in which each collision with an activated molecule may be regarded as bringing about deactivation; and the diffusion mechanism in which the transition between states is described by the Fokker-Planck equation. An accurate solution of the diffusion equation for the thermal decomposition of a nonlinear triatomic molecule makes it possible to elucidate the kinetics of various reactions in relation to the activation mechansim.     

The Effect of Vibrational Excitation of Molecules on Plasmachemical Reactions Involving Methane and Nitrogen

An experimental study of plasmachemical reaction involving CH₄ and N₂ molecules in rf discharge was studied in order to know the effect of vibrational excitation of N₂ molecules. When the relative nitrogen concentration was greater than 0.8, the main product of CH₄ decomposition was HCN, and the rate of methane decomposition at this condition was faster than that one in pure methane. These results could be confirmed through the mass spectroscopic method. The reason for these results is the vibrational energy of N₂ excited by rf discharge. The chain reaction mechanisms of producing HCN by vibrational excitation of N₂ were examined closely through numerical simulation. The rate-controlling step was the dissociation reaction of excited nitrogen molecule to the atomic nitrogen, so the process of HCN synthesis was limited by the value of reaction constant, k^N.     

Theoretical investigation of unimolecular decomposition channels of furan4

Density functional theory and high-level ab initio calculations were carried out to investigate three unimolecular decomposition channels of furan. All equilibrium and transition state structures along the proposed decomposition channels are fully optimized by B3LYP/6-31G** and characterized at the same level of theory by vibrational and intrinsic reaction coordinate analyses. Relative energies of the optimized structures were evaluated at theoretical levels up to QCISD(T)/6-311++G**. The theoretical results suggest that the unimolecular decomposition channel of isoxazole, proposed in an experimental study and implied to be the main decomposition channel of furan, is responsible only for the formation of HC(TRIPLE BOND)CH and H₂O(DOUBLE BOND)C(DOUBLE BOND)O, minor products of furan thermal decomposition. A new decomposition mechanism, proposed in the present study, is shown to be more likely responsible for the formation of CH₃C(TRIPLE BOND)CH and CO, major products of furan thermal decomposition. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 240–249, 1998     

Incubation in cyclohexene decomposition at high temperatures

A detailed master equation simulation has been carried out for the thermal unimolecular decomposition of C₆H₁₀ in a shock tube. At the highest temperatures studied experimentally [J. H. Kiefer and J. N. Shah, J. Phys. Chem., 91, 3024 (1987)], the average thermal vibrational energy is greater than the reaction threshold and therefore 〈ΔE〉 (up and down steps) is positive for molecules at that energy, rather than negative; the converse is true at lower temperatures. The calculated incubation time, in which the decomposition rate constant rises to 1/e of its steady state value, is found to be only weakly dependent on temperature (at constant pressure) between 1500 K and 2000 K and to depend almost exclusively on 〈ΔE〉_d (down steps, only), and not on collision probability model. Simulations of the experimental data show the magnitude of 〈ΔE〉_d depends weakly on assumed collision probability model, but is nearly independent of temperature. The second moment 〈ΔE〉^½ is found to be independent of both temperature and transition probability model. The experimental data are not very sensitive to the possible energy-dependence of 〈ΔE〉_d for a wide range of assumptions. It is concluded that the observed experimental “delay times” probably can be identified with the incubation time; further experiments are desirable to test this possibility and obtain more direct measures of the incubation time.