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.