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 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. Test system: Pnma SnS/SnSe Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 3
4. Single-crystal simulations Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 4
5. 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
6. IR dielectric function Dr J. M. Skelton MCC Conference, 8th July 2024 | 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 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
8. 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
9. IR reflectance/absorption Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 9 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
10. 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 /
11. 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
12. Dielectric function Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 12 Nguyen et al., Sci. Rep. 10, 18396 (2020)
13. Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 13 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
14. Raman spectra Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 14 Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977)
15. 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 -
16. Energy-dependent ⁄ 𝒅𝝈 𝒅𝛀 Dr J. M. Skelton MCC Conference, 8th July 2024 | Slide 16 𝑐 𝑎𝑎 ̅ 𝑐: Ag 𝑏 𝑎𝑐 % 𝑏 : B2g
17. 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
18. 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
19. These slides are available on Speaker Deck: https://bit.ly/3TXeQJ0