 2D IR diagonal-peak overlap

2D IR diagonal-peak overlap is the contribution of extended diagonal spectral features to regions where an off-diagonal signal might be assigned in two-dimensional infrared spectroscopy. A nonzero value at an off-diagonal coordinate is not sufficient evidence for a separate 2D IR cross peak.

Peak orientation matters as well as width. An original positive-envelope model for a diagonal feature centered at $(c,c)$ isHere $\rho$ specifies 2D IR line-shape correlation. It is a shape parameter in this illustrative model, not automatically a measured population correlation. Let $S=G_a+G_b$ for two diagonal features, with $\Delta =b-a$. At the off-diagonal coordinate $(a,b)$,For original values $a=1600$, $b=1650$ and $\sigma =20$, all in $\mathrm{c}{\mathrm{m}}^{-1}$, the off-diagonal amplitude is approximately 0.0879 at $\rho =0$, but only 0.000340 at $\rho =0.8$. Both models have the same individual marginal width. An overlap estimate based only on that width can therefore miss a substantial shape dependence.

The toy envelope is positive. Actual coherent spectra can contain signed features, so fitting and subtraction must respect the measured response and phase convention. The primary phase-controlled peptide experiment used phase and amplitude information to interpret mode-coupling cross peaks.^[ref]

Useful tests vary the fit region, include plausible neighboring features and compare the proposed cross signal across 2D IR waiting times and other controlled conditions. A residual can indicate a missing feature, an unsuitable diagonal line shape or an unmodeled background. Its persistence alone does not uniquely select one molecular explanation.