First-principles modelling of infrared and Raman spectra

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

Transcript

1. J. M. Skelton, C. Umeh and A. R. Pallipurath University of Manchester and University of Leeds (jonathan.skelton@manchester.ac.uk) 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 𝜺ionic /𝜺S + POP frequency 𝜔po • Raman polarizability tensors 𝜶Γ𝑗 , activities 𝐼Γ𝑗 and differential cross sections Τ 𝑑𝜎Γ𝑗 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. Test system: Pnma SnS/SnSe Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 3
4. Single-crystal simulations Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 4
5. Simulating IR spectra Mode effective charges 𝒁Γ𝑗 : 𝑍Γ𝑗 𝛼 = 𝜕𝑃𝛼 𝜕𝑄Γ𝑗 = ෍ 𝑘,𝛽 𝑍 𝑘 ∗,𝛼𝛽𝑋 Γ𝑗,𝑘 𝛽 Dipole oscillator strengths 𝑺Γ𝑗 : 𝑆 Γ𝑗 𝛼𝛽 = 𝑍Γ𝑗 𝛼 𝑍 Γ𝑗 𝛽 Infrared dielectric function 𝜺 𝜔 : 𝜀𝛼𝛽 𝜔 = 𝜀∞ 𝛼𝛽 + 1 𝑉 ෍ 𝑗 𝑆 Γ𝑗 𝛼𝛽 𝜔Γ𝑗 2 − (𝜔 + 𝑖𝛾Γ𝑗 )2 Scalar 𝑆Γ𝑗 and 𝜀 𝜔 for single-crystal measurements: 𝑆Γ𝑗 = ො 𝒆𝑠 ∙ 𝑹𝑺Γ𝑗 𝑹𝑇 ∙ ො 𝒆𝑖 𝜀 𝜔 = 𝜀∞ + 1 𝑉 ෍ 𝑗 𝑆Γ𝑗 𝜔Γ𝑗 2 − (𝜔 + 𝑖𝛾Γ𝑗 )2 Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 5
6. IR dielectric function Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 6 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
7. IR activity and symmetry Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 7 Irrep ഥ 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
8. Simulating IR spectra Infrared dielectric function for single-crystal measurements: 𝜀 𝜔 = 𝜀∞ + 1 𝑉 ෍ 𝑗 𝑆Γ𝑗 𝜔Γ𝑗 2 − (𝜔 + 𝑖𝛾Γ𝑗 )2 Complex refractive index: ෤ 𝑛 𝜔 = 𝜀 𝜔 = 𝑛(𝜔) + 𝑖𝑘 𝜔 Reflectivity (normal incidence): 𝑅 𝜔 = ෤ 𝑛 𝜔 − 1 ෤ 𝑛 𝜔 + 1 2 Absorption coefficient: 𝛼 𝜔 = 2𝜔 𝑐 𝑘 𝜔 Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 8
9. IR reflectance/absorption Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 9 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
10. Simulating Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 10 Raman polarizability tensors: 𝜶Γ𝑗 (𝐸) = 1 𝑉 𝜕𝜺(𝐸) 𝜕𝑄Γ𝑗 ≈ 1 𝑉 ∆𝜺(𝐸) ∆𝑄Γ𝑗 Raman intensities: 𝐼Γ𝑗 = ො 𝒆𝑠 ∙ 𝑹𝜶Γ𝑗 𝑹𝑇 ∙ ො 𝒆𝑖 2 Differential cross sections (Stokes scattering): 𝑑𝜎Γ𝑗 S 𝑑Ω = 𝜎Γ𝑗 S ′ = ℎ 4𝜋𝑐4 𝜔𝑖 − 𝜔Γ𝑗 4 𝜔Γ𝑗 𝑛Γ𝑗 + 1 𝐼Γ𝑗 Phonon occupation number: 𝑛Γ𝑗 𝑇 = 1 exp Τ −ℏ𝜔 𝑘B 𝑇 − 1 Raman spectrum: 𝑑𝜎(𝜔) 𝑑Ω = ෍ 𝑗 𝜎Γ𝑗 S ′ 𝜋 Τ 𝛾Γ𝑗 2 𝜔 − 𝜔Γ𝑗 2 + Τ 𝛾Γ𝑗 2 2
11. Resonance effects Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 11 Lasers with photon energy 𝐸 > 𝐸g 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 𝐸g ≈ 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
12. Dielectric function Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 12 Nguyen et al., Sci. Rep. 10, 18396 (2020)
13. Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 13 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
14. Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 14 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
15. Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 15 Irrep ഥ 𝒗 / cm-1 𝜸 / cm-1 𝑰 / Å4 amu-1 𝒄 𝒃𝒃 ത 𝒄 𝒄 𝒂𝒂 ത 𝒄 𝒄 𝒂𝒃 ത 𝒄 𝒂 𝒃𝒄 ഥ 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 -
16. Energy-dependent Τ 𝒅𝝈 𝒅𝛀 Dr J. M. Skelton MCC Conference, 8th July 2025 | Slide 16 𝑐 𝑎𝑎 ҧ 𝑐: Ag 𝑏 𝑎𝑐 ത 𝑏 : B2g
17. Simulation workflow Dr J. M. Skelton MCC Conference, 8th July 2025 | 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
18. Acknowledgements Dr J. M. Skelton MCC Conference, 5th July 2025 | 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
19. These slides are available on Speaker Deck: https://bit.ly/3TXeQJ0