# Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Two-dimensional infrared spectroscopy

Pulse Sequence used to obtain a two-dimensional Fourier transform infrared spectrum. The time period ${\displaystyle \tau _{1}}$ is usually referred to as the coherence time and the second time period ${\displaystyle \tau _{2}}$ is known as the waiting time. The excitation frequency is obtained by Fourier transforming along the ${\displaystyle \tau _{1}}$ axis.

Two-dimensional infrared spectroscopy (2DIR) is a nonlinear infrared spectroscopy technique that has the ability to correlate vibrational modes in condensed-phase systems. This technique provides information beyond linear infrared spectra, by spreading the vibrational information along multiple axes, yielding a frequency correlation spectrum.[1][2] A frequency correlation spectrum can offer structural information such as vibrational mode coupling, anharmonicities, along with chemical dynamics such as energy transfer rates and molecular dynamics with femtosecond time resolution. 2DIR experiments have only become possible with the development of ultrafast lasers and the ability to generate femtosecond infrared pulses.

## Systems studied

Among the many systems studied with infrared spectroscopy are water, metal carbonyls, short polypeptides, proteins, and DNA oligomers.[3][4]

## Experimental Approaches

There are two main approaches to two-dimensional spectroscopy, the Fourier-transform method, in which the data is collected in the time-domain and then Fourier-transformed to obtain a frequency-frequency 2D correlation spectrum, and the frequency domain approach in which all the data is collected directly in the frequency domain.

### Time domain

The time-domain approach consists of applying two pump pulses. The first pulse creates a coherence between the vibrational modes of the molecule and the second pulse creates a population, effectively storing information in the molecules. After a determined waiting time, ranging from a zero to a few hundred picoseconds, an interaction with a third pulse again creates a coherence, which, due to an oscillating dipole, radiates an infrared signal. The radiated signal is heterodyned with a reference pulse in order to retrieve frequency and phase information; the signal is usually collected in the frequency domain using a spectrometer yielding detection frequency ${\displaystyle \omega _{3}}$. A two-dimensional Fourier-transform along ${\displaystyle \omega _{1}}$ then yields a (${\displaystyle \omega _{1}}$, ${\displaystyle \omega _{3}}$) correlation spectrum.

### Frequency domain

Similarly, in the frequency-domain approach, a narrowband pump pulse is applied and, after a certain waiting time, then a broadband pulse probes the system. A 2DIR correlation spectrum is obtained by plotting the probe frequency spectrum at each pump frequency.

## Spectral Interpretation

File:Schematic of typical two-dimensional infrared spectrum.jpg
Schematic picture of a 2DIR spectrum. The blue peaks on the diagonal corresponds to bleaching of the ground state. The red peaks corresponds to absorption of the excited states. The smaller cross peaks arise due to coupling between the two states. The linear absorption spectrum is indicated above the 2DIR spectrum. The two peaks here reveal no information on coupling between the two states.

After the waiting time in the experiment it is possible to reach doubly excited states. This results in the appearance of an overtone peak. The anharmonicity of a vibration can be read from the spectra as the distance between the diagonal peak and the overtone peak. One obvious advantage of 2DIR spectra over normal linear absorption spectra is that they reveal the coupling between different states. This for example allows for the determination of the angle between the involved transition dipoles.

The true power of 2DIR spectroscopy is that it allows following dynamical processes as chemical exchange, vibrational population transfer, and molecular reorientation on the sub-picosecond time scale. It has successfully been used to study hydrogen bond forming and breaking and to determine the transition state geometry of a structural rearrangement in an iron carbonyl compound.

## References

1. P. Hamm, M. H. Lim, R. M. Hochstrasser (1998). "Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared spectroscopy". J. Phys. Chem. B 102: 6123. doi:10.1021/jp9813286.
2. Zanni, M.; Hochstrasser, RM (2001). "Two-dimensional infrared spectroscopy: a promising new method for the time resolution of structures". Current Opinion in Structural Biology 11 (5): 516. doi:10.1016/S0959-440X(00)00243-8. PMID 11785750
3. S. Mukamel (2000). "Multidimensional Fentosecond Correlation Spectroscopies of Electronic and Vibrational Excitations". Annual Review of Physics and Chemistry 51: 691. doi:10.1146/annurev.physchem.51.1.691. PMID 11031297.
4. M. H. Cho (2008). "Coherent Two-Dimensional Optical Spectroscopy". Chemical Reviews 108 (4): 1331–1418. doi:10.1021/cr078377b. PMID 18363410.