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[[Image:2dir pulse sequence newversion.png|thumb|300px|right|Pulse sequence used to obtain a two-dimensional [[Fourier transform]] infrared spectrum. The time period <math>\tau_1</math> is usually referred to as the coherence time and the second time period <math>\tau_2</math> is known as the waiting time. The excitation frequency is obtained by Fourier transforming along the <math>\tau_1</math> 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.<ref>{{cite journal | author = P. Hamm, M. H. Lim, R. M. Hochstrasser | title = Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared spectroscopy
| journal =  J. Phys. Chem. B | volume = 102 | pages = 6123 | year = 1998 | doi = 10.1021/jp9813286 | issue = 31}}</ref><ref name=Zanni2001>{{Cite journal | last = Zanni | first =  M. | year = 2001 | title = Two-dimensional infrared spectroscopy: a promising new method for the time resolution of structures | journal = Current Opinion in Structural Biology | volume = 11 | pages = 516–22 | doi = 10.1016/S0959-440X(00)00243-8 | pmid = 11785750 | last2 = Hochstrasser | first2 = RM | issue = 5 | postscript = <!--None-->}}</ref> A frequency correlation spectrum can offer structural information such as vibrational mode coupling, [[anharmonicity|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 laser]]s and the ability to generate femtosecond infrared pulses.

==Systems studied==
Among the many systems studied with infrared spectroscopy are [[water]], [[metal carbonyl]]s, short [[polypeptide]]s, [[protein]]s, and [[DNA]] oligomers.<ref>{{cite journal | author = S. Mukamel | title = Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations | journal = Annual Review of Physics and Chemistry | volume =51 | pages = 691–729 | year = 2000 | doi = 10.1146/annurev.physchem.51.1.691 | pmid = 11031297 }}</ref><ref>{{cite journal | author = M. H. Cho  | title = Coherent Two-Dimensional Optical Spectroscopy  | journal = Chemical Reviews | volume =108 | pages = 1331–1418 | year = 2008 | doi = 10.1021/cr078377b | pmid = 18363410 | issue = 4 }}</ref>

==Experimental approaches==
There are two main approaches to two-dimensional spectroscopy, the [[Fourier transform|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 (physics)|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 [[picosecond]]s, an interaction with a third pulse again creates a coherence, which, due to an oscillating dipole, radiates an [[infrared]] signal. The radiated signal is [[heterodyne]]d with a reference pulse in order to retrieve [[frequency]] and [[phase (waves)|phase]] information; the signal is usually collected in the frequency domain using a [[spectrometer]] yielding detection frequency <math>\omega_3</math>. A two-dimensional Fourier-transform along <math>\omega_1</math> then yields a (<math>\omega_1</math>, <math>\omega_3</math>) correlation spectrum. In all these measurements phase stability among the pulses has to be preserved. Recently, pulse shaping approaches were developed to simplify overcoming this challenge.<ref>{{cite web|title=Mid IR pulse shaper|url=http://zanni.chem.wisc.edu/research/mid-ir-pulse-shaping}}</ref><ref>{{cite web|title=Two Quantum 2D FT Spectroscopy|url=http://www.sciencemag.org/content/324/5931/1169.short}}</ref>

===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==
[[Image:Schematic of typical two-dimensional infrared spectrum.jpg|thumb|300px|right|Schematic of a 2D IR spectrum. The blue circles on the diagonal correspond to bleaching of the ground state. The red circles correspond to absorption of the excited states. The smaller off-diagonal circles to coupling between the two states. The linear absorption spectrum is indicated above the 2D IR 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 state]]s. 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 such as chemical exchange, vibrational population transfer, and molecular reorientation on the sub-picosecond time scale. It has for example been used successfully to study [[hydrogen bond]] forming and breaking  and to determine the [[transition state]] geometry of a structural rearrangement in an iron carbonyl compound.<ref>{{Cite journal | last1 = Cahoon | first1 = J. F. | last2 = Sawyer | first2 = K. R. | last3 = Schlegl | first3 = J. P. | last4 = Harris | first4 = C. B. | title = Determining transition-state geometries in liquids using 2D-IR | journal = Science | volume = 319 | pages = 1820–3 | year = 2008 | doi = 10.1126/science.1154041 | pmid = 18369145 | issue = 5871 }}</ref> Spectral interpretation can be successfully assisted with developed theoretical methods.<ref>{{Cite journal | last1 = Liang | first1 = C. | last2 = Jansen | first2 = T. L. C.  | title = An efficient N3-scaling propagation scheme for simulating two-dimensional infrared and visible spectra | journal = Journal of Chemical Theory and Computation | volume = 8 | pages = 1706–1713 | year = 2012 | doi = 10.1021/ct300045c | issue = 5 }}</ref>

Currently two freely available packages exists for modelling 2D IR spectra. These are the [http://mukamel.ps.uci.edu/software.html SPECTRON] developed by the Mukamel group (University of California, Irvine) and the [http://fwn-nb4-7-208.chem.rug.nl/~lacour/programs.html NISE] program developed by the Jansen group (University of Groningen).

==Solvent effect==
The consideration of the solvent effect has been shown to be crucial <ref>{{Cite journal | last1 = DeChamp | first1 = M. F. | last2 = DeFlores | first2 = L. | last3 = McCraken | first3 = J. M. | last4 = Tokmakoff | first4 = A. | last5 = Kwac | first5 = K. | last6 = Cho | first6 = M.H. |title = Amide I vibrational dynamics of N-methylacetamide in polar solvents: The role of electrostatic interactions | journal = The Journal of Physical Chemistry B | volume = 109 | pages = 11016–26 | year = 2005 | doi = 10.1021/jp050257p | pmid = 16852342 | issue = 21 }}</ref><ref>{{Cite journal | last1 = Lee | first1 = Chewook | last2 = Cho | first2 = Minhaeng | title = Vibrational dynamics of DNA: IV. Vibrational spectroscopic characteristics of A-, B-, and Z-form DNA's  | journal = J. Chem. Phys. | volume = 126 | pages =  145102 | year = 2007 | doi = 10.1063/1.2715602 | pmid = 17444751 | issue = 14 }}</ref> in order to effectively describe the vibrational coupling in solution, since the solvent modify both vibrational frequencies, transition probabilities <ref>{{Cite journal | last1 = Schmidt | first1 = J. R. | last2 = Corcelli | first2 = S. A. | last3 = Skinner | first3 = J. L. | title = Pronounced non-condon effects in the ultrafast infrared spectroscopy of water  | journal = J. Chem. Phys. | volume = 123 | pages =  044513 | year = 2005 | doi = 10.1063/1.1961472 | pmid = 16095375 | issue = 4 }}</ref> and couplings.<ref>{{Cite journal | last1 = Gorbunov | first1 = R. D. | last2 = Kosov | first2 = D. S. | last3 = Stock | first3 = G. | title = Ab initio-based exciton model of amide I vibrations in peptides: Definition, conformational dependence, and transferability  | journal = J. Chem. Phys. | volume = 122 | pages =  224904 | year = 2005 | doi = 10.1063/1.1898215 | pmid = 15974713 | issue = 22 }}</ref><ref>{{Cite journal | last1 = Biancardi | first1 = A. | last2 = Cammi | first2 = R. | last3 = Mennucci | first3 = B. | last4 = Tomasi | first4 = J. | title = Modelling vibrational coupling in DNA oligomers: a computational strategy combining QM and continuum solvation models  | journal = Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta)  | volume = 131 | pages = 1157 | year = 2011 | doi = 10.1007/s00214-012-1157-3  | issue = 3 | last5 = Tomasi | first5 = Jacopo}}</ref> Computer simulations can reveal the spectral signatures arising from solvent degrees of freedom and their change upon water reorganization.<ref>{{Cite journal |pmid=23102165 |year=2012 |last1=Baron |first1=Riccardo |title=Water structure, dynamics, and spectral signatures: changes upon model cavity-ligand recognition |volume=116 |issue=46 |pages=13774–80 |journal=Journal of Physical Chemistry B |doi=10.1021/jp309373q |last2=Setny |first2=Piotr |last3=Paesani |first3=Francesco}}</ref>

== See also ==
*[[Two-dimensional correlation analysis]]

==References==
{{Reflist}}

[[Category:Infrared spectroscopy]]