The RRKM theory of unimolecular reaction rates is a statistical mechanical theory based on an assumption of microcanonical equilibrium in the reactant phase space. The energy transfer in reactant medium collisions was originally described by a canonical strong collision assumption, i.e., an assumption of full thermal equilibration in each collision. In our work we first introduce a microcanonical strong collision assumption which gives the RRKM theory a consistent form. We then introduce parametrizations of the degree of weakness (nonergodicity) of the collisions. A concept of collision efficiency is defined. The weakness of the collision is expressed in terms of reduced subsets of active reactant and medium degrees of freedom. The corresponding partially ergodic collision theory (PECT) yields physical functional forms of the collisional energy transfer kernel P(E,E). In order to resolve the energy and temperature dependence and the dependence on interaction strength a multiple encounter theory is introduced (PEMET). Initially each encounter may be described by a semiempirical PECT model. Eventually the encounters may be resolved by quantum dynamical calculations of the semiclassical or CAQE (classical approach quantum encounter) type. Simple statistical collision models only distinguish between hits and misses . In reality the energy transfer efficiency exhibits characteristic fall off with increasing impact parameter b. This b-dependence can be explicitly accounted for in the master equation for the reaction rate coefficient.
Earlier work on the activation-deactivation mechanism of gas phase unimolecular reactions is extended to the study of the detailed energy transfer mechanism in collisions of water molecules. Molecular dynamics simulations of binary collisions between a reactant water molecule at high internal energy with medium molecules at various selected initial temperatures are compared with results from approximate statistical theory. Energy transfer is related to i. interaction strength, ii. hard atom–atom encounters, iii. multiple minima in the center of mass separation, iv. collision lifetime and v. anharmonicity of the intramolecular potential function. The observed trends are interpreted within the framework of the partially ergodic multiple encounter theory PEMET. of collisional energy transfer. By comparison with typical stable molecule collisions the water–water collisions are more efficient as a reflection of the strong hydrogen bonding interactions. A good agreement between PEMET and molecular dynamics simulations over a wide range of interaction strengths and initial reactant energies is shown, indicating the possibility of a priori use of the PEMET model.
A study of the sensitivity of energy transfer efficiency in molecular collisions is reported with special focus on the hardness of repulsion in atomÈatom contact. An improved pair potential is proposed with independent parameters for atomic size, attraction and hardness determined speciÐcally for a chosen atom pair by supermolecular quantum chemistry or equivalent experimental interaction data. Colinear and full 3D collisions of atomÈdiatomic molecule collisions are simulated using classical or quantum (in the colinear case) mechanics to illustrate : (i) remarkable agreement between classical and quantum dynamics for VÈT energy transfer ; (ii) greater sensitivity to hardness than to attraction and (iii) suitability of MP2 energies in symmetry constrained axial directions as a data set for the determination of pair-potential parameters.
The detailed mechanisms of ro-vibrational energy transfer in collisions between CF3I and argon or propane are investigated. Molecular dynamics simulations of collisions between a reactant CF3I molecule at energies from 50 to 200 kJrmol with medium argon or propane at selected initial temperatures are interpreted in terms of ergodic collision limits. The intramolecular potential used for CF3I is a Morse-stretchrharmonic-bend type function with parameters fitted to equilibrium structure, normal mode frequencies and dissociation energies. Simple generic Buckingham type pair-potentials are used for intermolecular atom–atom interactions. Energy transfer is related to i. geometry of collision, ii. impact parameter, iii. number of atom–atom encounters, iv. average dynamical hardness of interaction at atom–atom collisions, v. number of minima in the center of mass separation and vi. lifetime of the collisional complex. The energy transfer in our molecular dynamics calculations is compared with experimental results for the same colliders. The observed trends are interpreted in terms of detailed collisional mechanisms. Our results highlight the importance of rotational excitation and the repulsive part of the intermolecular potential.
We have investigated and compared four different theoretical and empirical procedures for the generation of simple but reliable pairwise atomÈatom potentials to be used as components in the construction of intermolecular potentials. A method is proposed wherein the parameters of a modified Buckingham potential with atomic monopoles (mBq potential) is obtained by Ðtting to MP2 energies for interacting molecules confined to approach in selected symmetry directions. The results for 31 atomic pairs are compared with earlier results obtained by electron gas density functional theory, best available quantum chemical calculation or spectroscopic Ðt. The evidence is that the mBq potentials can be of signiÐcant practical value in a wide range of applications.