The hyperbolic matrix method for wave packet treatment of atomic and molecular dynamics
DOI:
https://doi.org/10.33910/2687-153X-2024-5-1-21-29Keywords:
wave packet, atomic and molecular collisions, non-adiabatic transitions, nuclear dynamics, matrix exponentialAbstract
The hyperbolic matrix method for the treatment of atomic and molecular nuclear dynamics is derived by means of the wave packet technique within the Born–Oppenheimer approach formalism. This method allows one to calculate the evolution of a wave packet by means of the product of usual matrices instead of the time propagation of matrix exponentials. We provide a detailed description of this method, considering Tully’s model as an example. We also show good agreement with the Landau–Zener model application.
References
Akpinar, S., Surucu, S. (2011) Time dependent wave packet study of the H-+ H2 nonreactive scattering. Journal of Quantum Information Science, 1 (2), 96–103. https://doi.org/10.4236/jqis.2011.12013 (In English)
Al-Mohy, A. H., Higham, N. J. (2010) A new scaling and squaring algorithm for the matrix exponential. SIAM Journal on Matrix Analysis and Applications, 31 (3), 970–989. https://doi.org/10.1137/09074721X (In English)
Al-Mohy, A. H., Higham, N. J. (2011) Computing the action of the matrix exponential, with an application to exponential integrators. SIAM Journal on Scientific Computing, 33 (2), 488–511. https://doi.org/10.1137/100788860 (In English)
Balakrishnan, N., Kalyanaraman, C., Sathyamurthy, N. (1997) Time-dependent quantum mechanical approach to reactive scattering and related processes. Physics Reports, 280 (2), 79–144. https://doi.org/10.1016/S0370-1573(96)00025-7 (In English)
Mao, Y., Buren, B., Yang, Z. , Chen, M. (2022) Time-dependent wave packet dynamics study of the resonances in the H + LiH+ (v = 0, j = 0) → Li+ + H2 reaction at low collision energies. Physical Chemistry Chemical Physics, 24 (25), 15532–15539. https://doi.org/10.1039/D1CP05601H (In English)
Neuhauser, D., Baer, M., Judson, R. S., Kouri, D. J. (1991) The application of time-dependent wavepacket methods to reactive scattering. Computer Physics Communications, 63 (1–3), 460–481. https://doi.org/10.1016/0010-4655(91)90270-U (In English)
Tully, J. C. (1990) Molecular dynamics with electronic transitions. The Journal of Chemical Physics, 93 (2), 1061–1071. https://doi.org/10.1063/1.459170 (In English)
Vaeck, N., Desouter-Lecomte, M., Lievin, J. (1998) Non-adiabatic wave packet dynamics for charge exchange processes: Application to C4+ + H. Journal of Physics B: Atomic, Molecular and Optical Physics, 32 (2), 409–428. https://doi.org/10.1088/0953-4075/32/2/021 (In English)
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Copyright (c) 2024 Maxim Yu. Yakovlev, Andrey K. Belyaev
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