Oscillating reactivity of collinear symmetric heavy+light–heavy atom reactions

Abstract

A quasiclassical trajectory study of the heavy-light-heavy ClHCl and IHI reactions: Do threedimensional partial cross sections oscillate as a function of energy? J. Chem. Phys. 86, 5534 (1987); 10.1063/1.452525Collinear quantum mechanical treatment of the heavy−light−heavy mass combination: Cl+HBr→HCl+BrThe oscillatory reaction probability (as a function of energy) of collinear heavy + light-heavy systems (e.g., I + HI~IH + I) that has been seen in earlier quantum mechanical reactive scattering calculations is shown to be described quantitatively by a semiclassical WKB model. Because these reactions are highly vibrationally adiabatic they reduce to a two-state symmetric resonance system (analogous to symmetric charge transfer, e.g., H+ + H~H + H+) that involves only the phase shifts of the one-<limensional g (symmetric) and u (antisymmetric) combinations of the two states. Comparisons of the semiclassical and quantum mechanical reaction probabilities over a wide range of energy for the cases I + Mul~IMu + I and I + HI-.IH + I show almost perfect agreement. The vibrationally adiabatic symmetric exchange problem is also solved classically (analytically) and is seen to have an interesting relation to the quantum/semiclassical result. The classical reaction probability is also an oscillatory function of energy, although the structure of the oscillations is different from the quantum/semiclassical ones ("saw-tooth" rather than sinusoidal) and the phase of the classical oscillations is only approximately the same as that of the quantum/semiclassical case. (In the high energy limit, the phase of the oscillations increases roughly as the square root of collision energy.) Thus, though the classical (light atom hopping between two heavy atoms) and quantum mechanical (resonance interference of g and u collision channels) interpretations of the oscillatory reactivity seem at first to be quite different, they are seen in fact to be essentially the same.The vibrational adlabaticity renders the collinear re-3850

Exact quantum and vibrationally adiabatic quantum, semiclassical and quasiclassical study of the collinear reactions Cl + MuCl, Cl + HCl, Cl + DCl

“…Qualitative arguments exploiting these properties of Delves' coordinates have been given by Babamov and Marcus [67,68]. There have also been a number of quantitative investigations of the validity of the VA approximation for heavy-light-heavy atom reactions [27,33,34,40,41,[68][69][70][71][72][73][74][75]. These calculations have shown that vibrational adiabaticity is a better approximation as the ratio mL/m H decreases.…”

“…Then the v~v reaction probability is given in the VA approximation by [41,68] The phase shift difference increases monotonically with E, which from equation (17) gives rise to an oscillating semiclassical reaction probability Pv._~VASC(E). Figure 8 shows that the semiclassical P0~0vAsc(E) and full quantum Polo(E) are in good agreement.…”

“…These features are studied in more detail in § 4 with the help of a vibrationally adiabatic (VA) model which includes the diagonal corrections to the VA potential. The oscillations are analysed using VA semiclassical and quasiclassical techniques [41] and the positions of the narrow resonances are investigated by VA quantum single channel calculations. Our conclusions are in § 5.…”

Stereomutation dynamics in hydrogen peroxide

“…Particularly after the discovery [7][8][9] and theoretical description [10][11][12][13] of isotope selective coherent infrared multiphoton excitation and laser chemistry of polyatomic molecules and subsequently also the advent of ''Femtosecond Chemistry'' [14,15] there has been much interest in what has been called in a variety of contexts either ''mode selective chemistry'' [16,17] or reaction control [18][19][20][21] including chiral molecules [22,23]. This question has been addressed from a variety of points of view, and Jö rn Manz and his group have been early players in the field, including both bimolecular and unimolecular reactions [24][25][26]. Mode selective chemistry has been discussed for some very simple systems such as O 3 [27] and H 2 O isotopomers as well as other examples [28][29][30][31][32][33].…”

First-principles simulations of transition state spectra of the I + HI and I + DI reactions and vibrational bonding in IMuI

“…HL + H 0 , which involve the transfer of a light atom L from one heavy atom H 0 to a second heavy atom H were extensively studied in the 1980s from the theoretical side [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Due to the large differences in the masses of the light and heavy atoms, the reaction systems have very different time scales between symmetric (H À H 0 stretch) and anti-symmetric (light atom motion corresponding to the reaction coordinate motion) vibrational motions at the transition-state.…”