H126 - Composition (Table A)

Cosine similarity measures the angle between two VUV absorption spectra (125-240 nm, 646 channels). A value of 1.0 indicates identical spectral shape. This metric is effective for distinguishing between structurally different compound classes (e.g., aromatics vs. paraffins) but can be insensitive to subtle differences within a homologous series.

Bell method (Bell et al., 2022) goes beyond simple overlay comparison. It fits the measured spectrum against the reference, then analyzes the residuals using 6 diagnostic statistics: mean residual (systematic bias), sigma ratio (noise structure in active vs. inactive spectral regions), skewness, kurtosis, QQ-plot R² (residual normality), and maximum consecutive same-sign run (systematic drift). Each statistic is compared against Monte Carlo bounds from 10,000 simulated noise-only residuals. A score of 6/6 means all residual statistics are consistent with pure noise, meaning the reference spectrum fully explains the measured signal.

Limitation: n-Alkane specificity. VUV absorption in the 125-240 nm range is dominated by sigma-to-sigma* transitions. For n-alkanes, these transitions are very similar across different chain lengths because the chromophore is the C-C and C-H sigma bonding framework, which is structurally repetitive. n-Octane, n-nonane, and n-decane have nearly identical VUV spectra, differing primarily in overall absorption intensity rather than spectral shape. Cosine similarity between adjacent n-alkanes frequently exceeds 0.95. Reliably distinguishing one n-alkane from another by VUV spectrum alone is extremely difficult. The carbon number assignment for n-alkanes relies primarily on the GCxGC retention time (APR template), not spectral matching.

Branched and cyclic compounds exhibit greater spectral diversity because ring strain, branching position, and conformational differences meaningfully shift sigma-to-sigma* absorption features. Aromatics are the most spectroscopically distinct due to their strong pi-to-pi* transitions, which produce characteristic features in the 160-240 nm region that are highly sensitive to ring substitution patterns.

Interpretation: High cosine (>0.9) with high Bell score (5-6/6) = confident identification. High cosine but low Bell = spectral shape is similar but residual structure reveals systematic mismatch (possible co-elution, wrong isomer, or baseline artifact). Low cosine (<0.7) with any Bell score = reference library likely does not contain this specific compound.

Reference: Bell, D.C., Boehm, R.C., Feldhausen, J., Heyne, J.S. (2022). A Data Set Comparison Method Using Noise Statistics Applied to VUV Spectrum Match Determinations. Analytical Chemistry, 94(43), 14861-14868. doi:10.1021/acs.analchem.2c01931