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First-principles modelling of infrared and Rama...

First-principles modelling of infrared and Raman spectra

Presented at the 7th UK Materials Chemistry Consortium (MCC) Conference on 8th July 2025.

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Jonathan Skelton

July 08, 2025
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  1. J. M. Skelton, C. Umeh and A. R. Pallipurath University

    of Manchester and University of Leeds ([email protected]) First-principles modelling of infrared and Raman spectra
  2. Phonopy-Spectroscopy Dr J. M. Skelton MCC Conference, 8th July 2025

    | Slide 2 o Motivation: Add capability to simulate infrared and Raman spectra to the Phono(3)py code: Phonopy-Spectroscopy o Features: • (Complex) IR dielectric function 𝜀(𝜔) → (complex) refractive index & 𝑛 𝜔 = 𝑛(𝜔) + 𝑖𝑘(𝜔) → reflectivity 𝑅(𝜔), absorption 𝛼(𝜔), loss function 𝐿(𝜔) • Ionic and static dielectric constants 𝜺!"#!$ /𝜺% + POP frequency 𝜔&" • Raman polarizability tensors 𝜶'( , activities 𝐼'( and differential cross sections ⁄ 𝑑𝜎'( 𝑑Ω, with a partial description of resonance effects • Include calculated phonon linewidths from e.g. Phono3py • Simulate measurements on single crystals and powders, or powders with preferred orientation, for arbitrary instrument geometries • Python API designed for easy interoperability with other codes and for implementing more advanced experiments (e.g. Jupyter notebooks)
  3. Simulating IR spectra Mode effective charges 𝒁'( : 𝑍'( )

    = 𝜕𝑃) 𝜕𝑄'( = ; *,, 𝑍* ∗,),𝑋 '(,* , Dipole oscillator strengths 𝑺'( : 𝑆'( ), = 𝑍'( ) 𝑍'( , Infrared dielectric function 𝜺 𝜔 : 𝜀), 𝜔 = 𝜀. ), + 1 𝑉 ; ( 𝑆'( ), 𝜔'( / − (𝜔 + 𝑖𝛾'( )/ Scalar 𝑆'( and 𝜀 𝜔 for single-crystal measurements: 𝑆'( = D 𝒆0 F 𝑹𝑺'( 𝑹1 F D 𝒆2 𝜀 𝜔 = 𝜀. + 1 𝑉 ; ( 𝑆'( 𝜔'( / − (𝜔 + 𝑖𝛾'( )/ Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 5
  4. IR dielectric function Dr J. M. Skelton MCC Conference, 8th

    July 2024 | Slide 6 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
  5. IR activity and symmetry Dr J. M. Skelton MCC Conference,

    8th July 2024 | Slide 7 Irrep ! 𝒗 / cm-1 𝜸 / cm-1 𝑺 / 𝒆𝟐 amu-1 𝑺𝒙𝒙 𝑺𝒚𝒚 𝑺𝒛𝒛 B1u 97.1 0.8 0.17 - - 176.3 6.62 1.76 - - 225.17 3.19 0.22 - - B2u 142.22 22.24 - 2.93 - B3u 64.39 0.6 - - 7.79 × 10-3 175.57 7.35 - - 2.62 214.61 1.31 - - 0.14
  6. Simulating IR spectra Infrared dielectric function for single-crystal measurements: 𝜀

    𝜔 = 𝜀. + 1 𝑉 ; ( 𝑆'( 𝜔'( / − (𝜔 + 𝑖𝛾'( )/ Complex refractive index: & 𝑛 𝜔 = 𝜀 𝜔 = 𝑛(𝜔) + 𝑖𝑘 𝜔 Reflectivity (normal incidence): 𝑅 𝜔 = & 𝑛 𝜔 − 1 & 𝑛 𝜔 + 1 / Absorption coefficient: 𝛼 𝜔 = 2𝜔 𝑐 𝑘 𝜔 Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 8
  7. IR reflectance/absorption Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 9 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
  8. Simulating Raman spectra Dr J. M. Skelton MCC Conference, 8th

    July 2024 | Slide 10 Raman polarizability tensors: 𝜶'( (𝐸) = 1 𝑉 𝜕𝜺(𝐸) 𝜕𝑄'( ≈ 1 𝑉 ∆𝜺(𝐸) ∆𝑄'( Raman intensities: 𝐼'( = D 𝒆0 F 𝑹𝜶'( 𝑹1 F D 𝒆2 / Differential cross sections (Stokes scattering): 𝑑𝜎'( % 𝑑Ω = 𝜎'( % 3 = ℎ 4𝜋𝑐4 𝜔2 − 𝜔'( 4 𝜔'( 𝑛'( + 1 𝐼'( Phonon occupation number: 𝑛'( 𝑇 = 1 exp ⁄ −ℏ𝜔 𝑘5 𝑇 − 1 Raman spectrum: 𝑑𝜎(𝜔) 𝑑Ω = ; ( 𝜎'( % 3 𝜋 ⁄ 𝛾'( 2 𝜔 − 𝜔'( / + ⁄ 𝛾'( 2 /
  9. Resonance effects Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 11 Lasers with photon energy 𝐸 > 𝐸6 can couple to electronic states → resonance effects Common to use the far-from-resonance approximation (FFR): 𝜺 𝐸 = 𝜺 𝐸 = 0 ≡ 𝜺. Unlikely to be reasonable for SnS/SnSe because direct 𝐸6 ≈ 1 eV (1240 nm) is lower than all common laser wavelengths Can partially capture resonance effects by using 𝜺 𝐸 - but need accurate model for dielectric function TD-DFT with dielectric-dependent hybrid functional in principle makes it possible to calculate 𝜺 𝐸 similar accuracy to “gold standard” 𝐺𝑊 + BSE
  10. Dielectric function Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 12 Nguyen et al., Sci. Rep. 10, 18396 (2020)
  11. Raman spectra Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 13 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
  12. Raman spectra Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 14 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
  13. Raman spectra Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 15 Irrep ! 𝒗 / cm-1 𝜸 / cm-1 𝑰 / Å4 amu-1 𝒄 𝒃𝒃 * 𝒄 𝒄 𝒂𝒂 * 𝒄 𝒄 𝒂𝒃 * 𝒄 𝒂 𝒃𝒄 ! 𝒂 Ag 34.66 1.33 1.04 1.54 - - 67.98 1.52 5.36 5.21 - - 131.44 4.52 75.12 23.78 - - 153.58 1.37 45.62 4.55 - - B1g 54.45 0.78 - - - 0.38 137 1.66 - - - 6.44 B2g 65.19 1.22 - - - - 68.8 0.7 - - - - 146.71 1.82 - - - - 180.73 8.42 - - - - B3g 37.14 0.51 - - 0.13 - 111.99 5.99 - - 40.07 -
  14. Energy-dependent ⁄ 𝒅𝝈 𝒅𝛀 Dr J. M. Skelton MCC Conference,

    8th July 2024 | Slide 16 𝑐 𝑎𝑎 ̅ 𝑐: Ag 𝑏 𝑎𝑐 % 𝑏 : B2g
  15. Simulation workflow Dr J. M. Skelton MCC Conference, 8th July

    2024 | Slide 17 Python API mostly complete and available on develop branch of Phonopy-Spectroscopy GitHub repo: https://github.com/skelton- group/Phonopy-Spectroscopy Will shortly add minimal working examples for reproducing SnS/SnSe calculations using a Jupyter notebook Front-end CLI for setting up calculations and post processing in progress
  16. Acknowledgements Dr J. M. Skelton MCC Conference, 5th July 2024

    | Slide 18 Implementation (inc. maths + sanity checks): o Jonathan Skelton (UoM) o Anuradha Pallipurath (UoL) o Chidimma Umeh (UoM) Initial testing (i.e. bug squashing): o Joseph Flitcroft (UoM) o Guanping Li (UoM) o David Collins (UoL) … plus other collaborators too numerous to mention