Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case

Abstract

This work suggests a connection between Landau-Zener transition probabilities between two crossing potentials in the classically accessible WKB regime and Landau-Lifshitz transition probabilities in the classically inaccessible WKB regime. It is based on the uniform Airy (UAi) approximation which represents a generalization of quantum transition probabilities for linear crossing potentials with constant coupling. The performance of the UAi approximation is tested by comparison with distorted-wave probabilities for an exponential potential model and illustrated for potentials that determine the intersection of twoab initiovibronic potential surfaces of the NO-Ar system.

Electronically nonadiabatic mechanism of the vibrational relaxation of NO in Ar: Rate coefficients from ab initio potentials and asymptotic coupling

“…This extension became possible because an appropriate electronic potential surface for the NO-Ar system and an asymptotic method for the estimate of the exchange interaction in nonadiabatic coupling are available. Non-adiabatic transition probability in the uniform Airy approximation 21 shows pronounced quantum effects for overbarrier (interference) and underbarrier (tunneling) regimes across the energy range which is essential for the calculation of thermally averaged rate coefficients at several thousand K and below. This approach well reproduces experimental rate coefficients under shock wave conditions at about T = 1500 K. Rather unexpectedly, a quite similar result is obtained within the surfacehopping approximation, which ignores the quantum effects.…”

“…Recent calculations of the adiabatic electronic PESs for the NO-Ar system [14][15][16] now permit to determine the crossing energy and thus open the possibility for a determination of the rate coefficients. Our recent work 17,18 was aimed at the estimation of tunneling corrections to high-temperature rate coefficients, the latter being identified with experimental values at 1500 K. 19,20 In the present work, a) Email: jtroe@mpibpc.mpg.de we calculate the rate coefficients in the uniform Airy (UAi) approximation, 21 generalizing the original Landau result 13 for collision energies close to and below the crossing energy of the potentials. Accordingly, the plan of this article is as follows.…”

“…17 and 18, these two quantum effects are represented by a correction factor in the rate coefficient. Here, the latter is calculated in the uniform Airy (UAi) approximation 21 that permits one to represent LZ k 1,0 (T ) = LZ k UAi 1,0 (T ) as 17,18 LZ k UAi 1,0 (T ) = C UAi 1,0 (A) × LZ k SH 1,0 (T ), (5.1) where A denotes the Arrhenius ratio A = E a /k B T and C UAi 1,0 (T ) is defined as…”

Reaction of the N Atom with Electronically Excited O2 Revisited: A Theoretical Study

“…A more accurate approximation for P sh can be obtained within the so-called weak coupling (WC) approach , applicable for IC points with not very strong SOC (or, equivalently, with a large difference in gradient on the two diabatic surfaces). Following this, the surface-hopping probability for a single crossing , can be stated as follows Here, Ai­( x ) is the Airy function of the first kind. It should be highlighted that eq , as opposed to the simple Landau–Zener approximation provided by eq , allows for the contribution of tunneling effect, which is vital for energies below the crossing point (i.e., when E tr ≤ E IC ).…”

“…118,126−130 A more accurate approximation for P sh can be obtained within the so-called weak coupling (WC) approach 125,131 applicable for IC points with not very strong SOC (or, equivalently, with a large difference in gradient on the two diabatic surfaces). Following this, the surface-hopping probability for a single crossing 130,132 can be stated as follows…”