Long-range transition state theory

Abstract

The implementation of variational transition state theory (VTST) for long-range asymptotic potential forms is considered, with particular emphasis on the energy and total angular momentum resolved (microJ-VTST) implementation. A long-range transition state approximation yields a remarkably simple and universal description of the kinetics of reactions governed by long-range interactions. The resulting (microJ-VTST) implementation is shown to yield capture-rate coefficients that compare favorably with those from trajectory simulations (deviating by less than 10%) for a wide variety of neutral and ionic long-range potential forms. Simple analytic results are derived for many of these cases. A brief comparison with a variety of low-temperature experimental studies illustrates the power of this approach as an analysis tool. The present VTST approach allows for a simple analysis of the applicability conditions for some related theoretical approaches. It also provides an estimate of the temperature or energy at which the "long-range transition state" moves to such short separations that short-range effects, such as chemical bonding, steric repulsion, and electronic state selectivity, must be considered.

A Two Transition State Model for Radical−Molecule Reactions: Applications to Isomeric Branching in the OH−Isoprene Reaction

“…Dipole moments of 1.68 and 1.69 D were evaluated with the uB3LYP/cc-pVQZ and uMP2/cc-pVQZ methods, respectively. These compare favorably with the experimental OH dipole moment of 1.66 D. 85 The same calculations yielded largest principle quadrupole moments 74 for C 2 H 4 of 6.39 and 6.62 D Å, respectively; again agreeing well with the experimental value of 6.48 D Å. 86 The asymmetry in the quadrupole is very small, with the quadrupole moments for the other two axes being nearly identical.…”

“…The temperature dependence of these components are illustrated in Figure 9. The long-range transition state theory of ref 74, predicts a temperature-independent capture rate of 3.6 × 10 -10 cm 3 molecule -1 s -1 for the present reaction. In contrast, the present negative saddle point energy corresponds to an inner transition state rate coefficient that is about 1 × 10 -11 cm 3 molecule -1 s -1 near room temperature and then rapidly rises to infinity as the temperature decreases toward zero.…”

“…A recently described classical variational transition state theory treatment of the kinetics on long-range potentials is employed here. 74 For the addition of OH to C 2 H 4 , the dipole-quadrupole interaction provides the longest-ranged interaction. For that case, the capture rate on the long-range potential is predicted to be 74 where d is the dipole moment of OH, Q is the largest principal quadrupole moment of C 2 H 4 , µ is the reduced mass for the C 2 H 4 , OH collision, and C ) 4.49 when all quantities are expressed in atomic units.…”

“…74 For the addition of OH to C 2 H 4 , the dipole-quadrupole interaction provides the longest-ranged interaction. For that case, the capture rate on the long-range potential is predicted to be 74 where d is the dipole moment of OH, Q is the largest principal quadrupole moment of C 2 H 4 , µ is the reduced mass for the C 2 H 4 , OH collision, and C ) 4.49 when all quantities are expressed in atomic units. This expression yields a temperature independent rate coefficient of 3.6 × 10 -10 cm 3 molecule -1 s -1 .…”

“…Thus, we implement a particularly simple, yet classically accurate, version of variational transition state theory appropriate in the limit of large transition state separations. 74 The inner transition state is in the neighborhood of the saddle point on the potential energy surface. This saddle point arises as the chemical bond between the carbon and oxygen atoms begins to form, while the CC π bond begins to break.…”