What goes in?
Experimental spectroscopic data collected along a controlled perturbation — here, FTIR spectra recorded as pressure increases.
Advanced spectroscopic analysis · reproducible scientific workflow
From spectra to energy-resolved adsorption insight
A series of in situ FTIR spectra recorded at increasing pressure contains more than a growing band. 2D-IRIS inversion resolves that series along a model-defined adsorption-affinity coordinate. Illustrated here with the Ba-GIS data set.
Experimental FTIR spectra → 2D-IRIS inversion → Regularisation & validation → Energy-resolved distribution → Scientific interpretation
What does DataChem do?
Apply and validate the 2D-IRIS inversion methodology, with every setting and check recorded.
What comes out?
An energy-resolved representation that reveals information difficult to extract from the spectra alone.
The scientific question
Inspecting spectra one by one shows how a band grows with pressure, but overlapping contributions that respond differently to pressure remain entangled. Adsorption environments with distinct affinities can share the same spectral region.
2D-IRIS asks a more specific question: which combination of contributions, each following a Langmuir-type response with its own apparent affinity, reproduces the whole experimental series at every wavenumber? The answer is a distribution over wavenumber and a reduced adsorption free energy, ΔadsG°/RT.
The input
A pressure-resolved series of in situ FTIR spectra of adsorbed CO₂, taken from the collaborative Ba-GIS research data.
- Spectral series
- 24 difference spectra (each spectrum minus the activated sample at p = 0), 2400–2250 cm⁻¹, 78 spectral points.
- Experimental variable
- Equilibrium CO₂ pressure from 0 to 77 torr at 25 °C, one pressure per spectrum.
- Preprocessing
- None beyond the exported difference spectra: no baseline correction, smoothing or normalisation was added for the inversion.
- Traceability
- Source file identified by SHA-256; the export was checked against the raw spectrometer files (same preprocessing up to a constant intensity scale).
The analysis
DataChem applies the 2D-IRIS inversion to this series: a physical model of how each contribution responds to pressure, fitted under a regularisation constraint that keeps the result numerically stable. Every choice below is recorded and checked, not left as a hidden default.
Technical details & validation
- Kernel
- Langmuir response θ(p, q) = p·e−q / (1 + p·e−q) with q = ΔadsG°/RT on a grid of 100 values between 1 and 10; pressure in torr, so q is relative to a 1 torr reference state.
- Inversion
- Non-negative distribution f(ν, q) such that the kernel reproduces the measured series: minimise ‖K f − x‖² + λ fᵀSf with f ≥ 0, where S is the second-derivative operator along q (SpectroChemPy 2D-IRIS formulation).
- Regularisation
- 45 values of λ from 10⁻¹⁰ to 10¹. The selected λ is the corner of the log-log L-curve (closest point to the normalised origin between data fidelity and smoothness). Result: λ = 5.6 × 10⁻³.
- Solver & numerical controls
- Exact active-set quadratic-programming solver (quadprog), cross-checked with an independent non-negative least-squares solver and with SpectroChemPy’s own IRIS implementation (agreement better than 10⁻⁹). With the default iterative solver, the L-curve of this data set was neither monotonic nor repeatable, so the regularisation parameter could not be selected reliably; the exact solver removes that ambiguity without changing the model. Monotonic L-curve; identical results on a repeated run; sensitivity checked one decade below and above the selected λ.
How do we validate the inversion?
Two checks accompany the result: is the regularisation strength well chosen, and does the model actually reproduce the measured spectra?
The reconstruction explains most of the series (99.2 % of the variance), but the residuals stay structured near the band maximum: the model does not reproduce every detail of the measured spectra. This is expected from a single Langmuir kernel under a smoothness constraint, and it is part of judging the inversion critically — a high explained-variance figure is a useful check, not proof that the model is a physically perfect description of the system.
The result
The energy-resolved representation of the Ba-GIS series, at the regularisation validated above.
The interpretation
What the representation adds compared with reading the spectra directly.
The distribution separates contributions by how they respond to pressure, not only by where they absorb. Regions of the map at high ΔadsG°/RT gather signal whose intensity keeps growing almost linearly over the measured pressure range; regions at low ΔadsG°/RT gather signal that saturates early. In the Ba-GIS series this contrast is visible within a single spectral band: the centre near 2350 cm⁻¹ behaves differently from the flanks near 2364 and 2339 cm⁻¹.
This is complementary to the MCR-ALS resolution of the same series: MCR-ALS separates spectral shapes, 2D-IRIS resolves the pressure dependence along an explicit model coordinate. Both remain descriptions of the data, and their agreement or disagreement is itself informative.
The Ba-GIS case study places this result alongside PCA, MCR-ALS and independent equilibrium measurements: see the study →
Assumptions & limits
An inversion is only as meaningful as its assumptions. They are stated explicitly.
- Langmuir kernel. Each contribution is assumed to follow an independent Langmuir response; lateral interactions, multilayer behaviour or kinetic limitations are not described.
- Independent environments. Contributions are treated as additive and independent, which is an assumption, not an observation.
- Regularisation. The width and separation of features depend on λ. The selected value is documented, and the sensitivity one decade below and above is kept as a control.
- Spectral window. Results depend on the 2400–2250 cm⁻¹ window and on the reference spectrum subtracted from the series.
- Relative coordinate. ΔadsG°/RT is model-dependent and relative to a 1 torr reference state; it is not an absolute adsorption energy.
- No chemical assignment. The map does not identify species or adsorption sites. Signal that grows almost linearly with pressure, at weak apparent affinity, can also include contributions that are not surface-bound; assignment requires independent evidence.
- No site counting. The number of lobes is not a number of sites. Weak features below the lowest contour level, such as the minor band near 2283 cm⁻¹, are not displayed.
A reproducible workflow, adaptable to your data
2D-IRIS is a scientific analysis methodology implemented by DataChem through a documented Python workflow, not a stand-alone software product.
What is recorded
Source file hashes, software versions, spectral window, pressures, kernel, energy grid, λ grid, selected λ and its selection rule, residuals, reconstruction and the full distribution as CSV.
What you receive
The distribution and L-curve as numerical tables, publication-quality figures, and a written interpretation that states what the result supports and what it does not.
Where it adapts
DataChem can adapt this type of workflow to experimental spectroscopic datasets when the perturbation variable and the physical model are appropriate — for example other spectroscopies (Raman, NIR) or other variables such as dose, time or temperature.
Method reference: Study of the diffusion properties of zeolite mixtures by combined gravimetric analysis, IR spectroscopy and inversion methods (IRIS), PCCP, 2023.
Collaborative research: Ba-exchanged gismondine for CO₂ direct air capture (DAC), J. Mater. Chem. A, 2026. Data analysis: Abdelhafid Ait Blal. These figures do not represent a DataChem client assignment.