Quantum propagation using Hagedorn wave packets: generalised scheme.
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| Title: | Quantum propagation using Hagedorn wave packets: generalised scheme. |
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| 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] |
| Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192657065 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quantum propagation using Hagedorn wave packets: generalised scheme. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Issa%2C+Rabiou%22">Issa, Rabiou</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Afansounoudji%2C+Kokou+Mawulonmi+Robert%22">Afansounoudji, Kokou Mawulonmi Robert</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sodoga%2C+Komi%22">Sodoga, Komi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lauvergnat%2C+David%22">Lauvergnat, David</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> david.lauvergnat@universite-paris-saclay.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Molecular+Physics%22">Molecular Physics</searchLink>. Mar2026, Vol. 124 Issue 6, p1-20. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Basis+sets+%28Quantum+mechanics%29%22">Basis sets (Quantum mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Wave+packets%22">Wave packets</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+quadrature+formulas%22">Gaussian quadrature formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Photoisomerization%22">Photoisomerization</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22Born-Oppenheimer+approximation%22">Born-Oppenheimer approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Vibrational+spectra%22">Vibrational spectra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Molecular Physics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00268976.2025.2554271 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 1 Subjects: – SubjectFull: Basis sets (Quantum mechanics) Type: general – SubjectFull: Wave packets Type: general – SubjectFull: Gaussian quadrature formulas Type: general – SubjectFull: Photoisomerization Type: general – SubjectFull: Theory of wave motion Type: general – SubjectFull: Born-Oppenheimer approximation Type: general – SubjectFull: Vibrational spectra Type: general Titles: – TitleFull: Quantum propagation using Hagedorn wave packets: generalised scheme. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Issa, Rabiou – PersonEntity: Name: NameFull: Afansounoudji, Kokou Mawulonmi Robert – PersonEntity: Name: NameFull: Sodoga, Komi – PersonEntity: Name: NameFull: Lauvergnat, David IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00268976 Numbering: – Type: volume Value: 124 – Type: issue Value: 6 Titles: – TitleFull: Molecular Physics Type: main |
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