Clarification of the scaling-factor role of the first singular vector in singular value decomposition analysis of Fourier-transform infrared spectra: detection of solid-state intermolecular interactions in indomethacin-cimetidine mixtures via the λ2/λ1 ratio.

PURPOSE: Singular value decomposition (SVD) of spectroscopic datasets generates multiple components whose physical roles are frequently left uninterpreted. The present study establishes that, in non-centered Fourier-transform infrared (FTIR) spectral matrices dominated by positive intensity contributions, the first singular vector component (λ1) functions empirically as a global intensity-scaling axis, and that the ratio λ2/λ1 provides a scale-independent index of qualitative spectral change arising from solid-state intermolecular interactions.

METHODS

Transmission FTIR spectra of KBr tablets containing indomethacin (INM), cimetidine (CIM), and their mixtures were collected across the full molar composition range at ambient temperature and after pre-heating at 333-453 K. Non-centered SVD was applied to baseline-corrected differential spectra, and λ2/λ1 was monitored as the primary analytical index. Benzamide-aspirin (BAM-ASP) binary mixtures, chemically unrelated to INM and CIM, were analyzed in parallel as a non-interacting reference system to establish the generality of the interpretive principle.

RESULTS

In BAM-ASP mixtures, λ2/λ1 varied linearly with molar composition, confirming the scaling-factor role of λ1 in the absence of intermolecular interaction. In INM-CIM mixtures at ambient temperature, λ2/λ1 showed pronounced nonlinearity at CIM-predominant compositions, indicating composition-dependent solid-state interactions already present at room temperature. Thermal SVD analysis of pre-heated equimolar INM-CIM mixtures yielded an inflection temperature of Tp = 395 K, consistent with the DSC eutectic point (384.5 K). The second basis function ψ2 identified bathochromic shifts at 2171 cm-1 (CIM C≡N), 1685 cm-1 (INM carboxyl C=O), and 1586 cm-1 (INM amide C=O), implicating these moieties in the solid-state interaction.

CONCLUSIONS

Cross-system validation across a non-interacting pair (BAM-ASP) and a co-amorphous-forming pair (INM-CIM) demonstrates that the partitioning of spectral information between λ1 (intensity scaling) and λ2/λ1 (qualitative compositional and interaction information) is an intrinsic property of non-centered SVD applied to positive-dominant spectral matrices. This framework provides a rigorous and broadly applicable basis for detecting and characterizing solid-state intermolecular interactions in pharmaceutical binary systems by FTIR spectroscopy.