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 two ab initio vibronic potential surfaces of the NO-Ar system.
Acknowledgement
We are grateful to I. Litvin for technical help.
References
1. L. D. Landau, Phys. Z. Sowjet. 1 (1932) 88.Search in Google Scholar
2. C. Zener, Proc. R. Soc. Lond. A 137 (1932) 696.10.1098/rspa.1932.0165Search in Google Scholar
3. E. C. G. Stueckelberg, Helv. Phys. Acta 5 (1932) 369.Search in Google Scholar
4. L. D. Landau, E. M. Lifshitz, Quantum Mechanics, Pergamon Press, Oxford (1977).Search in Google Scholar
5. L. D. Landau, Phys. Z. Sowjet. 2 (1932) 46.Search in Google Scholar
6. E. E. Nikitin, S. Y. Umanskii, Theory of Slow Atomic Collisions, Springer-Verlag, Berlin-Heidelberg (1984).10.1007/978-3-642-82045-8Search in Google Scholar
7. M. S. Child, Semiclassical Mechanics with Molecular Applications, Clarendon Press, Oxford (1991).10.1093/oso/9780198556541.001.0001Search in Google Scholar
8. H. Nakamura, Nonadiabatic Transitions: Concepts, Basic Theories and Applications, World Scientific, Singapore (2012).10.1142/8009Search in Google Scholar
9. M. S. Child, Molecular Collision Theory, Academic Press, London-New York (1974), Sect. 8.5.Search in Google Scholar
10. E. I. Dashevskaya, E. E. Nikitin, J. Troe, Phys. Chem. Chem. Phys. 17 (2015) 151.10.1039/C4CP04107KSearch in Google Scholar PubMed
11. E. I. Dashevskaya, I. Litvin, E. E. Nikitin, J. Troe, J. Chem. Phys. 142 (2015) 164310.10.1063/1.4919126Search in Google Scholar PubMed
12. A. O. Lykhin, D. S. Kaliakin, G. E. dePolo, A. A. Kuzubov, S. A. Varganov, Int. J. Quantum Chem. 116 (2016) 750.10.1002/qua.25124Search in Google Scholar
13. A. W. Jasper, B. K. Kendrick, C. A. Mead, D. G. Truhlar, in: X. Yang, K. Liu (Eds.), Modern Trends in Chemical Reaction Dynamics: Experiment and Theory (Part I), World Scientific, Singapore (2004), P. 329.10.1142/9789812565426_0008Search in Google Scholar
14. M. V. Berry, P. R. Soc. Lond. A 422 (1989) 7.10.1098/rspa.1989.0018Search in Google Scholar
15. S. F. C. O’Rourke, B. S. Nesbitt, D. S. F. Crothers, Adv. Chem. Phys. 103 (1998) 217.Search in Google Scholar
16. E. S. Medvedev, V. I. Osherov, Radiationless Transitions in Polyatomic Molecules, Springer Verlag, Berlin Heidelberg (1995), Sect. 5.7.10.1007/978-3-642-85109-4Search in Google Scholar
17. F. H. Mies, Chem. Phys. 40 (1964) 523.10.1063/1.1725148Search in Google Scholar
18. F. W. Olver, Asymptotics and Special Functions, N.Y. Academic Press, New York (1974).Search in Google Scholar
19. S. Y. Umanskii, Khim. Fiz. (Russ) 4 (1985) 435.Search in Google Scholar
©2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case
- Microwave Accelerated Green Synthesis of Gold Nanoparticles Using Gum Arabic and their Physico-Chemical Properties Assessments
- Electrochemical Sensor for the Determination of Paracetamol at Carbamazepine Film Coated Carbon Paste Electrode
- Green Synthesis of CoFe2O4 and Investigation of its Catalytic Efficiency for Degradation of Dyes in Aqueous Medium
- A Rational Study of the Origin and Generality of Anti-Enthalpy–Entropy Compensation (AEEC) Phenomenon
- Molecular Interactions Investigation of L-Histidine in Water and in Aqueous Citric Acid at Different Temperatures Using Volumetric and Acoustic Methods
- Effect of Acid on Surface Hydroxyl Groups on Kaolinite and Montmorillonite
- In situ Synthesis of Reduced Graphene Oxide Supported CoMo Nanoparticles as Efficient Catalysts for Hydrogen Generation from NH3BH3
Articles in the same Issue
- Frontmatter
- Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case
- Microwave Accelerated Green Synthesis of Gold Nanoparticles Using Gum Arabic and their Physico-Chemical Properties Assessments
- Electrochemical Sensor for the Determination of Paracetamol at Carbamazepine Film Coated Carbon Paste Electrode
- Green Synthesis of CoFe2O4 and Investigation of its Catalytic Efficiency for Degradation of Dyes in Aqueous Medium
- A Rational Study of the Origin and Generality of Anti-Enthalpy–Entropy Compensation (AEEC) Phenomenon
- Molecular Interactions Investigation of L-Histidine in Water and in Aqueous Citric Acid at Different Temperatures Using Volumetric and Acoustic Methods
- Effect of Acid on Surface Hydroxyl Groups on Kaolinite and Montmorillonite
- In situ Synthesis of Reduced Graphene Oxide Supported CoMo Nanoparticles as Efficient Catalysts for Hydrogen Generation from NH3BH3