First-principles modelling of infrared and Raman spectra

Presented at the Materials Chemistry Consortium & Faraday Institution Energy Applications and Batteries 2026 workshop on 4th March 2026.

Transcript

1. J. M. Skelton, C. Umeh, A. R. Pallipurath, L. Kiltinavicius and J. M. Flitcroft 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/Faraday Workshop, 4th March 2026 | Slide 2 o Motivation: Add capability to simulate infrared and Raman spectra to the Phono(3)py code: Phonopy-Spectroscopy o Design goals: • Flexible - capable of modelling routine and advanced experiments • General - easy to interface to other codes and/or implement new experiments • Efficient - extensive use of NumPy/SciPy, Numba used for “slow” processes o Features • Raman spectrum simulations for arbitrary instrument geometry and partial capture of resonance effects • Complex IR dielectric function 𝜀(𝜔) and simulations of optical spectra - can be easily repurposed for UV/vis measurements • Python API designed for easy interoperability and for implementing more advanced simulations (e.g. from Jupyter notebooks) • Additional analysis tools via API (e.g. for characterising phonon modes)
3. Simulating Raman spectra Dr J. M. Skelton Raman polarizability tensors: 𝜶!" (𝐸) = 1 𝑉 𝜕𝜺(𝐸) 𝜕𝑄!" ≈ 1 𝑉 ∆𝜺(𝐸) ∆𝑄!" Raman intensities: 𝐼!" = 0 𝒆# $ 2 𝑹𝜶!" 𝑹% 2 0 𝒆& ' Differential cross sections (Stokes scattering): 𝑑𝜎!" ( 𝑑Ω = 𝜎!" ( ) = ℎ 4𝜋𝑐* 𝜔& − 𝜔!" * 𝜔!" 𝑛!" + 1 𝐼!" Phonon occupation number: 𝑛!" 𝑇 = 1 exp ⁄ −ℏ𝜔!" 𝑘+ 𝑇 − 1 Raman spectrum: 𝑑𝜎(𝜔) 𝑑Ω = E " 𝜎!" ( ) 𝜋 ⁄ 𝛾!" 2 𝜔 − 𝜔!" ' + ⁄ 𝛾!" 2 ' Can partially account for resonance effects with suitable 𝜺(𝐸) Can handle complex 0 𝒆& /0 𝒆, (circularly-polarised light) Power/temperature modulation crucial for matching experiment Can include calculated linewidths (e.g. Phono3py) MCC/Faraday Workshop, 4th March 2026 | Slide 3
4. Simulating Raman spectra Dr J. M. Skelton For powders, average the 𝐼!" over Euler angles: 𝐼!" = H - '. H - . H - '. 1 8𝜋' 0 𝒆, 2 𝑹(𝜙, 𝜃, 𝜓) 2 𝜶!" 2 𝑹(𝜙, 𝜃, 𝜓)% 2 0 𝒆& ' sin 𝜃 d𝜓 d𝜃 d𝜙 • Analytical formula for ”standard” measurement geometries and numerical integration for non-standard geometries Include preferred orientation with an orientation-distribution function 𝑤: 𝐼!" = H - '. H - . H - '. 𝑤 𝜙, 𝜃, 𝜓 𝐼!" 𝜙, 𝜃, 𝜓 sin 𝜃 d𝜓 d𝜃 d𝜙 • Currently implemented the March-Dollase distribution function for a single preferred orientation MCC/Faraday Workshop, 4th March 2026 | Slide 4
5. Raman: SnSe Dr J. M. Skelton Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977) MCC/Faraday Workshop, 4th March 2026 | Slide 5
6. Raman: Zirconolite Dr J. M. Skelton ̅ 𝑣 / cm-1 Irrep 𝛾 / cm-1 ⁄ 𝑑𝜎 𝑑𝛺 / 10-14 Å2 sr-1 93.5 Ag 2.16 1.15 111 Bg 2.20 3.55 118 Bg 2.11 2.70 119 Ag 3.34 3.43 125 Ag 1.44 11.3 ⋯ ⋯ ⋯ ⋯ 780 Ag 23.6 16.1 800 Bg 26.5 0.23 800 Ag 26.3 1.69 807 Bg 23.2 1.13 830 Bg 23.6 0.78 MCC/Faraday Workshop, 4th March 2026 | Slide 6
7. Raman: Paracetamol Dr J. M. Skelton Collins et al., CrystEngComm 28 (4), 836 (2026)
8. Simulating IR spectra Mode effective charges 𝒁!" : 𝑍!" 0 = 𝜕𝑃0 𝜕𝑄!" = E 1,3 𝑍1 ∗,03𝑋 !",1 3 Dipole oscillator strengths 𝑺!" : 𝑆 !" 03 = 𝑍!" 0 𝑍 !" 3 Infrared dielectric function 𝜺 𝜔 : 𝜀03 𝜔 = 𝜀5 03 + 1 𝑉 E " 𝑹𝑆 !" 03𝑹% 𝜔!" ' − (𝜔 + 𝑖𝛾!" )' Dr J. M. Skelton Can include calculated linewidths (e.g. Phono3py) MCC/Faraday Workshop, 4th March 2026 | Slide 8
9. Measurement geometry Dr J. M. Skelton o Raman: • No restrictions on experimental geometry o Infrared: • Implementation tightly couped to geometry • Currently assume collinear geometry, but plans to support “off-axis” reflectivity measurements including ATR soon MCC/Faraday Workshop, 4th March 2026 | Slide 9
10. Simulating optical spectra Complex refractive index: [ 𝑛" 𝜔 = 𝜀" 𝜔 = 𝑛" (𝜔) + 𝑖𝑘" 𝜔 Reflectivity at normal incidence: 𝑅" 𝜔 = [ 𝑛" 𝜔 − 1 [ 𝑛" 𝜔 + 1 ' Absorption coefficient: 𝛼" 𝜔 = 2𝜔 𝑐 𝑘" 𝜔 Optical conductivity: 𝜎" 𝜔 = −𝑖𝜔𝜀- 𝜀" 𝜔 − 1 Energy loss function: 𝐿" 𝜔 = Im − 1 𝜀" 𝜔 Dr J. M. Skelton Dielectric function Optical eigenmodes Diagonalise MCC/Faraday Workshop, 4th March 2026 | Slide 10
11. Simulating optical spectra Intrinsic transmission: 𝑇" 678 𝜔 = exp −𝛼 𝜔 ×𝑑 Normal transmission: 𝑇" 79:; 𝜔 = 1 − 𝑅(𝜔) ' exp −𝛼 𝜔 ×𝑑 Incoherent transmission: 𝑇" 67<9= 𝜔 = 1 − 𝑅(𝜔) ' exp −𝛼 𝜔 ×𝑑 1 − 𝑅'(𝜔) exp −2𝛼 𝜔 ×𝑑 Absorption: 𝐴" = − ln 𝑇" Dr J. M. Skelton Dielectric function Optical eigenmodes Diagonalise MCC/Faraday Workshop, 4th March 2026 | Slide 11
12. Simulating optical spectra Power coupling for incident polarisation 0 𝒆& : 𝑐" 𝜔 = Λ(𝜔) >? 0 𝒆& ' Mode-average properties: 𝑃 𝜔 = E " 𝑐" 𝜔 𝑃 " 𝜔 Mode-average absorbance: 𝐴 𝜔 = − ln 𝑇 𝜔 Also possible using OEs as a basis: • Jones/Airy-Jones method for polarised measurements • Berreman 4×4 method for ATR (non- collinear geometry) • Transfer-matrix method for thin-film stacks Dr J. M. Skelton Dielectric function Optical eigenmodes Optical spectrum Diagonalise Combine MCC/Faraday Workshop, 4th March 2026 | Slide 12
13. Simulating optical spectra Effective-medium approximation (1): 𝜀@AA 𝜔 = 1 3 Tr 𝜺 𝜔 Effective-medium approximation (2): 𝜀@AA 𝜔 = 1 3 E " 𝜀" 𝜔 Single-crystal (collinear geometry): 𝜺 𝜔 = 𝜀BB 𝜔 𝜀BC 𝜔 𝜀BD 𝜔 𝜀CB 𝜔 𝜀CC 𝜔 𝜀CD 𝜔 𝜀DB 𝜔 𝜀CD 𝜔 𝜀DD 𝜔 N. B. Could ”intercept” either EMA method and average with the 𝜀/𝜀(𝜔) of a pelleting medium - Maxwell-Garnett model Dr J. M. Skelton Dielectric function Optical eigenmodes Optical spectrum Diagonalise Combine EELS MCC/Faraday Workshop, 4th March 2026 | Slide 13
14. IR: Zirconolite Dr J. M. Skelton MCC/Faraday Workshop, 4th March 2026 | Slide 14
15. IR: Zirconolite Dr J. M. Skelton MCC/Faraday Workshop, 4th March 2026 | Slide 15
16. IR: Zirconolite Dr J. M. Skelton MCC/Faraday Workshop, 4th March 2026 | Slide 16 𝑡 = 1 µm
17. IR: SnS Dr J. M. Skelton Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977) MCC/Faraday Workshop, 4th March 2026 | Slide 17
18. IR: SnS Dr J. M. Skelton Chandrasekhar et al., Phys. Rev. B 15 (4), 2177 (1977) MCC/Faraday Workshop, 4th March 2026 | Slide 18
19. Summary o Comprehensive simulations of Raman and IR spectra: • Raman: single crystals and powders, partial inclusion of resonance effects • IR: IR dielectric function and optical spectra • Both show generally good agreement with experiments o There’s more: • IR calculator can also calculate 𝜀6976< /𝜀E8F86< and 𝜔G9 • Analysis tools including for visualisation, classification and band unfolding o Current status: • All functionality shown today is available via the API from the develop branch of the GitHub: https://github.com/skelton-group/Phonopy-Spectroscopy/tree/develop • Plans to implement: (1) improved handling of LO/TO splitting; (2) Maxwell-Garnett model for IR measurements on pellets; (3) fully-polarised single-crystal IR measurements; and (4) ATR/off-axis IR reflectivity • Plans to have a simple CLI for common simulations - in progress and should be available soon (target: next MCC conference) Dr J. M. Skelton MCC/Faraday Workshop, 4th March 2026 | Slide 19
20. Acknowledgements Dr J. M. Skelton Implementation (inc. maths + sanity checks): o Jonathan Skelton (UoM) o Anuradha Pallipurath (UoL) o Chidimma Umeh (UoM) Beta testing (i.e. bug squashing): o Joseph Flitcroft (UoM) o Guanping Li (UoM) o David Collins (UoL) … plus other collaborators too numerous to mention MCC/Faraday Workshop, 4th March 2026 | Slide 20
21. These slides are available on Speaker Deck: https://bit.ly/4758372