Multidimensional Spectroscopy Reveals Hidden Information
Motivation
Multidimensional spectroscopy enables direct measurement of dynamical processes in molecules. A single 2D spectrum tells a much richer story than the corresponding linear one, and the ways in which the 2D spectra change reveal chemical information about reactions, relaxation and interactions with the surroundings.
The lineshape tilt towards the frequency diagonal indicates there is inhomogeneous broadening and some frequency memory at early delay time (200 fs). By 10 ps, solvation dynamics has washed away that frequency memory, leading to a symmetrical lineshape. These are general features in 2D spectroscopy.
Pulse Sequence
Although the formal underlying theory is rather complicated, the essential information provided by multidimensional spectroscopy is simple. We break the measurement into two periods—an excitation and a detection—with a waiting time period in between. The amplitude of the signal is plotted in a 2D contour map which basically tells us the amount of signal at a particular detection frequency, given excitation at a particular frequency.
Dynamics: Spectral Diffusion
Most spectral bands in condensed phases are broadened more than they are in the gas phase. Much of this broadening is due to slightly different microscopic environments that cause frequency variations. We call this effect "inhomogeneous broadening" and whereas it is an inconvenience in 1D spectra, it can actually be quite useful in 2D spectroscopy. Since we can correlate excitation and detection frequencies, at early times, before the excited molecules have any chance to move, their excited and detected frequencies will be inhomogeneously distributed, but they will also be correlated. This correlation leads to tilted line shapes like the one above on the left. Because the molecules constantly undergo random fluctuations, as we increase the waiting time between excitation and detection, the initial frequency correlation will be lost. Eventually there will be no correlation, and the molecules will have lost any memory of their initial frequencies. The time scale for this "spectral diffusion" through frequency space is a key observable quantity in 2D spectroscopy.
For example, notice the first spectrum on the page, it is slightly elongated along the frequency diagonal for a short waiting time of 0.2 ps. At later waiting times, 10 ps in the case of the spectrum on the right, the correlation is gone. This spectrum is typical for a 2D-IR experiment, though it happens to belong to a metal carbonyl complex Mn2(CO)10 in methanol solution. We use the time scale for the frequency memory loss to probe a wide range of dynamical environments ranging from protein hydration to photocatalysis.
Structure and Assignment: Cross Peaks
Similar to 2D NMR, in 2D optical spectroscopy, coupled transitions are typically connected by cross peaks in the 2D spectrum. Since cross peaks can only come from transitions on the same type of molecule, it is possible to assign spectra containing mixtures of species, effectively performing an ultrafast separation. If the species interconvert on a fast (<10-20 ps) time scale, it can be possible to monitor the equilibrium chemical exchange using 2D-IR spectroscopy.
In the case above, we are showing a spectrum for an unusual metal carbonyl complex, Co2(CO)8, which exists as three structural isomers at room temperature. All three have distinct infrared spectra, but since cross peaks can only arise from individual isomers, we can easily assign the congested 1D spectrum using the cross peaks to identify which transtions belonging to a given isomer.
It turns out that these isomers also interconvert on a ~10 ps time scale, and we were able to track this process using 2D-IR chemical exchange spectroscopy, including a detailed investigation of the temperature and solvent viscosity dependence of the interconversion kinetics.