Transition probabilities found for M + CH₄ reactions (M = zinc, copper)

Abstract

Transition probabilities between the lowest energy levels of M ϩ CH 4 (M ϭ Zn, Cu) reactions were obtained through nonadiabatic crossings using a modification of the Landau-Zener (L-Z) theory. Hartree Fock self consistent field (HF-SCF) ab initio calculations were utilized to obtain the reaction pathways by means of the PSHF program, while pseudopotentials for representing the core-core and corevalence interaction were applied. The correlation energy is taken into account by means of multireference variational and perturbative configuration interaction calculations to second order using CIPSI code. The variational space generated in iterative manner includes more than 250 determinants, while the perturbative space is about 3 ϫ 10 7 configurations. The perturbative contribution is about 40% of the total correlation energy recovered. The time dependent L-Z theory was developed through the reaction coordinate r (distance). An extension of the latter theory to the reaction coordinate (angle) was used in this case. Then, the nonadiabatic crossings depend on both the angular velocity and the moment of inertia, among other things. The transition probability of the system HMCH 3 (M ϭ Zn, Cu) leading from one energy level to another is calculated through an avoided crossing. This method has been previously tested on gallium-methane and gallium-silane reactions for which the theoretical probability transitions between potential energy surfaces of gallium-methane reactions agree with experimental quenching branching fractions with great accuracy.

Transition probabilities for the Au (S2, D2, and P2) with SiH4 reaction

“…We have reported transition probabilities leading toward the product formation of the Au-SiH 4 reactions via an extended version [40][41][42]47,48 of the Landau-Zener 9,10 theory of nonadiabatic transitions at the avoided crossings. Ab initio HF-SCF and MCSCF followed by extensive MR-CI calculations were accomplished to study the Au ͑ 2 S, 2 D, and 2 P͒ ground and excited states plus SiH 4 reactions giving quite good results.…”

Potential Energy Surfaces for Reactions of X Metal Atoms (X = Cu, Zn, Cd, Ga, Al, Au, or Hg) with YH4 Molecules (Y = C, Si, or Ge) and Transition Probabilities at Avoided Crossings in Some Cases

“…We have presented here an overview of this line of research although we evidently must accept that the list of metals studied to date is far from exhaustive. This notwithstanding, we provide here enough examples of the mechanism first advanced in our explanation of the Lash Miller Lab experiments of the activation of methane by copper [60,82]. In short we have advanced a daring hypothesis avoided crossings and transition probabilities for curves of the same symmetry play a systematic and clear-cut role in the activation of methane, silane, and germane.…”

“…P = 0.19 of continuing by the same 2 1 A state. When following via X 1 A (see Figure 7), at the minimum of this state, the product formation can be obtained [82]. Finally, acquiring the formation of the HZnCH 3 intermediate with a calculated energy of ∼25 kcal mol −1 that passes through the avoided crossing of 2 1 A and X 1 A sates, with the subsequent formation of HZn + CH 3 and ZnCH 3 + H final products, b From [10].…”

“…the states 2 D and 2 S (see Table 1 and Figure 3). Transition probability (TP) values at four avoided crossings [82] are obtained when copper is photoexcited to this second excited state Cu ( 2 P: 3d 10 4p 1 ), given that this copper atom is inserted in the methane molecule. It is also noteworthy [60] that the ground state is initially repulsive, but due to the avoided crossings, it became attractive after surmounting a rather high barrier.…”

“…Luna-García et al [11,12,81] found the interaction potential curves of the mercury-Germane, cadmium-Germane, copper-silane, and copper-germane in the three lowest states of each metal; he improved a computational methodology to get the products of the breaking of the intermediate. Pacheco-Sánchez et al [13,14,40] achieved the calculation of gallium-methane and gallium-silane interactions as much in the ground state as in the two lowest excited states of gallium; he extended Landau-Zener theory [82][83][84][85] to use the angle instead of the distance as reaction parameter in transition probability calculations at avoided crossings. Transition probability theory is described here when the reaction parameter is distance or angle.…”