= 2D IR cross peak
{c}
A <2D IR cross peak> is an off-diagonal spectral feature correlating excitation and detection frequencies that differ in a <two-dimensional infrared spectroscopy> experiment. Its location is a relation between frequency coordinates, not a second physical location in the sample. Such features can reveal interactions between vibrations, but their interpretation depends on the measured response and timing.
For a concrete primary example, phase-controlled peptide spectra showed cross peaks interpreted as coupling between amide-I modes. The experiment measured the phase as well as amplitude of <vibrational photon echoes>, supplying information beyond an unsigned intensity map.<Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes by M. C. Asplund and others>[Abstract, amide-I coupling and phase-sensitive cross peaks.]{ref}
An original positive-envelope model illustrates <2D IR diagonal-peak overlap>. Let $g(x)=e^{-x^2/(2\sigma^2)}$ and put two purely diagonal features at frequencies $a$ and $b$:
$$
S(x,y)=g(x-a)g(y-a)+g(x-b)g(y-b).
$$
At the off-diagonal coordinate $(a,b)$, this model gives
$$
S(a,b)=2e^{-(b-a)^2/(2\sigma^2)}.
$$
For $a=1600$, $b=1650$ and $\sigma=20$, all in $\mathrm{cm^{-1}}$, the value is approximately0.0879. The diagonal value $S(a,a)$ is approximately1.0019. Thus a nonzero off-diagonal pixel about8.8% of the diagonal height can arise solely from broad diagonal tails, with no separate cross feature in the stipulated model.
A real response can have positive and negative components, so this envelope is not a universal line-shape formula. It demonstrates why a peak assignment needs a fitted background/overlap model and appropriate spectral resolution, rather than the observation of any off-diagonal intensity.
Changing <2D IR waiting time>, polarization or sample conditions can test proposed mechanisms. Growth or decay of a <2D IR cross peak> alone does not uniquely establish chemical conversion: coupling, relaxation and changes in response factors can contribute. Interpret the feature jointly with the rest of the spectrum and the experimental pulse sequence.
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