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Quantum propagation using Hagedorn wave packets: generalised scheme.

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Title: Quantum propagation using Hagedorn wave packets: generalised scheme.
Authors: Issa, Rabiou1 (AUTHOR), Afansounoudji, Kokou Mawulonmi Robert1 (AUTHOR), Sodoga, Komi1 (AUTHOR), Lauvergnat, David2 (AUTHOR) david.lauvergnat@universite-paris-saclay.fr
Source: Molecular Physics. Mar2026, Vol. 124 Issue 6, p1-20. 20p.
Subjects: Basis sets (Quantum mechanics), Wave packets, Gaussian quadrature formulas, Photoisomerization, Theory of wave motion, Born-Oppenheimer approximation, Vibrational spectra
Abstract: In this study, we present a novel wave packet propagation method that generalises the Hagedorn approach by introducing alternative primitive basis sets that are better suited to describe various physical processes. We can mix time-dependent (Hagedorn) and time-independent basis sets, such as Fourier series, particle-in-a-box, and harmonic oscillator basis sets. Furthermore, our implementation can handle models with several electronic states, enabling the study of non-adiabatic processes. Instead of the time-dependent variational principle, our propagation scheme uses a three-step procedure (standard propagation, time-dependent parameter evaluation, and projection). This procedure relies on multidimensional integrations performed numerically with Gaussian quadrature, allowing us to avoid constraints on the form of the Hamiltonian operator. We have implemented this numerical algorithm in Fortran code, and validated it by comparing it with standard propagation schemes on harmonic and anharmonic 2D-models. Finally, we have applied our method to compute the vibrational spectrum of the 6D-modified Hénon-Heiles model and we show that our scheme reproduces well the results obtained with the standard approach. As a perspective, we show that with our generalised Hagedorn wave packet method, we are able to study the non-adiabatic dynamics of the cis-trans retinal photoisomerization with a reduced 2D-model. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:In this study, we present a novel wave packet propagation method that generalises the Hagedorn approach by introducing alternative primitive basis sets that are better suited to describe various physical processes. We can mix time-dependent (Hagedorn) and time-independent basis sets, such as Fourier series, particle-in-a-box, and harmonic oscillator basis sets. Furthermore, our implementation can handle models with several electronic states, enabling the study of non-adiabatic processes. Instead of the time-dependent variational principle, our propagation scheme uses a three-step procedure (standard propagation, time-dependent parameter evaluation, and projection). This procedure relies on multidimensional integrations performed numerically with Gaussian quadrature, allowing us to avoid constraints on the form of the Hamiltonian operator. We have implemented this numerical algorithm in Fortran code, and validated it by comparing it with standard propagation schemes on harmonic and anharmonic 2D-models. Finally, we have applied our method to compute the vibrational spectrum of the 6D-modified Hénon-Heiles model and we show that our scheme reproduces well the results obtained with the standard approach. As a perspective, we show that with our generalised Hagedorn wave packet method, we are able to study the non-adiabatic dynamics of the cis-trans retinal photoisomerization with a reduced 2D-model. [ABSTRACT FROM AUTHOR]
ISSN:00268976
DOI:10.1080/00268976.2025.2554271