= 2D IR waiting time
{c}
The <2D IR waiting time> is the controlled interval between excitation-related coherence evolution and later detection-related evolution in a <two-dimensional infrared spectroscopy> pulse sequence. It is often denoted $T$ or $t_2$. Varying it asks how the sample's response changes between preparation and observation; it is distinct from the delays transformed into the two frequency coordinates.
A primary phase-controlled peptide experiment measured vibrational echo phase and amplitude as multiple pulse delays varied, providing a physical implementation of this multidelay spectroscopy.<Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes by M. C. Asplund and others>[Abstract, multiple pulse delays and phase-sensitive detection.]{ref} The exact meaning of a fitted waiting-time change depends on which response pathways the experiment selects.
An original illustrative model separates population loss from growth of a transferred component. Let total observable excited-state population decay as $P(T)=e^{-T/T_1}$ and let a transferred fraction grow as $q(T)=1-e^{-kT}$. Stipulate matched response factors and signals
$$
I_{\rm cross}(T)=P(T)q(T),\qquad
I_{\rm diag}(T)=P(T)[1-q(T)].
$$
With $k=0.5\,\mathrm{ps^{-1}}$ and $T_1=2\,\mathrm{ps}$, the cross signal is approximately0.233 at $T=2\,\mathrm{ps}$ but0.117 at $T=4\,\mathrm{ps}$. Meanwhile the transferred fraction increases from0.632 to0.865. A decreasing raw <2D IR cross peak> need not imply a decreasing transferred fraction.
Under these particular assumptions, <2D IR population normalization> gives $I_{\rm cross}/(I_{\rm cross}+I_{\rm diag})=q$. The raw cross signal reaches its maximum at
$$
T_{\max}=\frac{\ln(1+kT_1)}k,
$$
which is approximately1.39ps here. This is an explicitly stipulated kinetic example, not a universal normalization rule or an inference of exchange from one peak.
At very short intervals, pulse overlap and coherent effects can matter; at long intervals, <vibrational relaxation> can leave little signal. Report pulse timing, normalization and the response model when assigning a waiting-time dependence to molecular dynamics.
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