Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra
The motions of nuclei in a molecule can be mathematically described by using normal modes of vibration, which form a complete orthonormal basis. Each normal mode describes oscillatory motion at a frequency determined by the momentum of the nuclei. Near equilibrium, it is common to apply the quantum...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/2/4/39 |
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| author | Paul C. Arpin Mihail Popa Daniel B. Turner |
| author_facet | Paul C. Arpin Mihail Popa Daniel B. Turner |
| author_sort | Paul C. Arpin |
| collection | DOAJ |
| description | The motions of nuclei in a molecule can be mathematically described by using normal modes of vibration, which form a complete orthonormal basis. Each normal mode describes oscillatory motion at a frequency determined by the momentum of the nuclei. Near equilibrium, it is common to apply the quantum harmonic-oscillator model, whose eigenfunctions intimately involve combinatorics. Each electronic state has distinct force constants; therefore, each normal-mode basis is distinct. Duschinsky proposed a linearized approximation to the transformation between the normal-mode bases of two electronic states using a rotation matrix. The rotation angles are typically obtained by using quantum-chemical computations or via gas-phase spectroscopy measurements. Quantifying the rotation angles in the condensed phase remains a challenge. Here, we apply a two-dimensional harmonic model that includes a Duschinsky rotation to condensed-phase femtosecond coherence spectra (FCS), which are created in transient–absorption spectroscopy measurements through impulsive excitation of coherent vibrational wavepackets. Using the 2D model, we simulate spectra to identify the signatures of Duschinsky rotation. The results suggest that peak multiplicities and asymmetries may be used to quantify the rotation angle, which is a key advance in condensed-phase molecular spectroscopy. |
| first_indexed | 2024-03-09T17:22:50Z |
| format | Article |
| id | doaj.art-335ee3e6928042028bc9f92a56d87c0b |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-09T17:22:50Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-335ee3e6928042028bc9f92a56d87c0b2023-11-24T12:59:21ZengMDPI AGAppliedMath2673-99092022-12-012467568610.3390/appliedmath2040039Signatures of Duschinsky Rotation in Femtosecond Coherence SpectraPaul C. Arpin0Mihail Popa1Daniel B. Turner2Department of Physics, California State University Chico, Chico, CA 95929, USADepartment of Physics, California State University Chico, Chico, CA 95929, USAMicron School for Materials Science and Engineering, Boise State University, Boise, ID 83725, USAThe motions of nuclei in a molecule can be mathematically described by using normal modes of vibration, which form a complete orthonormal basis. Each normal mode describes oscillatory motion at a frequency determined by the momentum of the nuclei. Near equilibrium, it is common to apply the quantum harmonic-oscillator model, whose eigenfunctions intimately involve combinatorics. Each electronic state has distinct force constants; therefore, each normal-mode basis is distinct. Duschinsky proposed a linearized approximation to the transformation between the normal-mode bases of two electronic states using a rotation matrix. The rotation angles are typically obtained by using quantum-chemical computations or via gas-phase spectroscopy measurements. Quantifying the rotation angles in the condensed phase remains a challenge. Here, we apply a two-dimensional harmonic model that includes a Duschinsky rotation to condensed-phase femtosecond coherence spectra (FCS), which are created in transient–absorption spectroscopy measurements through impulsive excitation of coherent vibrational wavepackets. Using the 2D model, we simulate spectra to identify the signatures of Duschinsky rotation. The results suggest that peak multiplicities and asymmetries may be used to quantify the rotation angle, which is a key advance in condensed-phase molecular spectroscopy.https://www.mdpi.com/2673-9909/2/4/39combinatoricsharmonic oscillatorvibronic couplingDuschinsky mixingfemtosecond spectroscopy |
| spellingShingle | Paul C. Arpin Mihail Popa Daniel B. Turner Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra AppliedMath combinatorics harmonic oscillator vibronic coupling Duschinsky mixing femtosecond spectroscopy |
| title | Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra |
| title_full | Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra |
| title_fullStr | Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra |
| title_full_unstemmed | Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra |
| title_short | Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra |
| title_sort | signatures of duschinsky rotation in femtosecond coherence spectra |
| topic | combinatorics harmonic oscillator vibronic coupling Duschinsky mixing femtosecond spectroscopy |
| url | https://www.mdpi.com/2673-9909/2/4/39 |
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