Relationship between Mode Specific and Thermal Unimolecular Rate Constants for HOCl → OH + Cl Dissociation

Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Unimolecular Rate Constants versus Energy and Pressure as a Convolution of Unimolecular Lifetime and Collisional Deactivation Probabilities. Analyses of Intrinsic Non-RRKM Dynamics

Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, k_uni(ω, E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N( t)/ N(0), in the expression for k_uni(ω, E). Previous work using this approach is reviewed. In the work presented here, the biexponential f₁ exp(- k₁ t) + f₂ exp(- k₂ t) is used to represent N( t)/ N(0), where f₁ k₁ + f₂ k₂ equals the RRKM rate constant k( E) and f₁ + f₂ = 1. With these two constraints, there are two adjustable parameters in the biexponential N( t)/ N(0) to represent intrinsic non-RRKM dynamics. The rate constant k₁ is larger than k( E) and k₂ is smaller. This biexponential gives k_uni(ω, E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f₁ is made smaller and k₁ made larger. Of considerable interest is the finding that, if the collision frequency ω for the RRKM plot of k_uni(ω, E) versus ω is multiplied by an energy transfer efficiency factor β_c, the RRKM k_uni(ω, E) versus ω plot may be scaled to match those for the intrinsic non-RRKM, biexponential N( t)/ N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.

Unimolecular Reaction of Methyl Isocyanide to Acetonitrile: A High-Level Theoretical Study

A combination of high-level coupled-cluster calculations and two-dimensional master equation approaches based on semiclassical transition state theory is used to reinvestigate the classic prototype unimolecular isomerization of methyl isocyanide (CH₃NC) to acetonitrile (CH₃CN). The activation energy, reaction enthalpy, and fundamental vibrational frequencies calculated from first-principles agree well with experimental results. In addition, the calculated thermal rate constants adequately reproduce those of experiment over a large range of temperature and pressure in the falloff region, where experimental results are available, and are generally consistent with statistical chemical kinetics theory (such as Rice-Ramsperger-Kassel-Marcus (RRKM) and transition state theory (TST)).

Accurate and highly efficient calculation of the highly excited pure OH stretching resonances of O(1D)HCl, using a combination of methods

Accurate calculation of the energies and widths of the resonances of HOCl--an important intermediate in the O(1D)HCl reactive system--poses a challenging benchmark for computational methods. The need for very large direct product basis sets, combined with an extremely high density of states, results in difficult convergence for iterative methods. A recent calculation of the highly excited OH stretch mode resonances using the filter diagonalization method, for example, required 462,000 basis functions, and 180,000 iterations. In contrast, using a combination of new methods, we are able to compute the same resonance states to higher accuracy with a basis less than half the size, using only a few hundred iterations-although the CPU cost per iteration is substantially greater. Similar performance enhancements are observed for calculations of the high-lying bound states, as reported in a previous paper [J. Theo. Comput. Chem. 2, 583 (2003)].