Heterodyned 3D IR spectroscopy

Breaking Barriers in Ultrafast Spectroscopy and Imaging Using 100 kHz Amplified Yb-Laser Systems

ConspectusUltrafast spectroscopy and imaging have become tools utilized by a broad range of scientists involved in materials, energy, biological, and chemical sciences. Commercialization of ultrafast spectrometers including transient absorption spectrometers, vibrational sum frequency generation spectrometers, and even multidimensional spectrometers have put these advanced spectroscopy measurements into the hands of practitioners originally outside the field of ultrafast spectroscopy. There is now a technology shift occurring in ultrafast spectroscopy, made possible by new Yb-based lasers, that is opening exciting new experiments in the chemical and physical sciences. Amplified Yb-based lasers are not only more compact and efficient than their predecessors but also, most importantly, operate at many times the repetition rate with improved noise characteristics in comparison to the previous generation of Ti:sapphire amplifier technologies. Taken together, these attributes are enabling new experiments, generating improvements to long-standing techniques, and affording the transformation of spectroscopies to microscopies. This Account aims to show that the shift to 100 kHz lasers is a transformative step in nonlinear spectroscopy and imaging, much like the dramatic expansion that occurred with the commercialization of Ti:sapphire laser systems in the 1990s. The impact of this technology will be felt across a great swath of scientific communities. We first describe the technology landscape of amplified Yb-based laser systems used in conjunction with 100 kHz spectrometers operating with shot-to-shot pulse shaping and detection. We also identify the range of different parametric conversion and supercontinuum techniques which now provide a path to making pulses of light optimal for ultrafast spectroscopy. Second, we describe specific instances from our laboratories of how the amplified Yb-based light sources and spectrometers are transformative. For multiple probe time-resolved infrared and transient 2D IR spectroscopy, the gain in temporal span and signal-to-noise enables dynamical spectroscopy measurements from femtoseconds to seconds. These gains widen the applicability of time-resolved infrared techniques across a range of topics in photochemistry, photocatalysis, and photobiology as well as lower the technical barriers to implementation in a laboratory. For 2D visible spectroscopy and microscopy with white light, as well as 2D IR imaging, the high repetition rates of these new Yb-based light sources allow one to spatially map 2D spectra while maintaining high signal-to-noise in the data. To illustrate the gains, we provide examples of imaging applications in the study of photovoltaic materials and spectroelectrochemistry.

Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics

Physical properties are commonly represented by tensors, such as optical susceptibilities. The conventional approach of deriving non-vanishing tensor elements of symmetric systems relies on the intuitive consideration of positive/negative sign flipping after symmetry operations, which could be tedious and prone to miscalculation. Here, we present a matrix-based approach that gives a physical picture centered on Neumann's principle. The principle states that symmetries in geometric systems are adopted by their physical properties. We mathematically apply the principle to the tensor expressions and show a procedure with clear physical intuition to derive non-vanishing tensor elements based on eigensystems. The validity of the approach is demonstrated by examples of commonly known second and third-order nonlinear susceptibilities of chiral/achiral surfaces, together with complicated scenarios involving symmetries such as D6 and Oh symmetries. We then further applied this method to higher-rank tensors that are useful for 2D and high-order spectroscopy. We also extended our approach to derive nonlinear tensor elements with magnetization, which is critical for measuring spin polarization on surfaces for quantum information technologies. A Mathematica code based on this generalized approach is included that can be applied to any symmetry and higher order nonlinear processes.

Phase stable, shot-to-shot measurement of third- and fifth-order two-quantum correlation spectra using a pulse shaper in the pump-probe geometry

We demonstrate the first phase stable measurement of a third-order 2Q spectrum using a pulse shaper in the pump-probe geometry. This measurement was achieved by permuting the time-ordering of the pump pulses, thus rearranging the signal pathways that are emitted in the probe direction. The third-order 2Q spectrum is self-heterodyned by the probe pulse. Using this method, one can interconvert between a 1Q experiment and a 2Q experiment by simply reprogramming a pulse shaper or delay stage. We also measure a fifth-order absorptive 2Q spectrum in the pump-probe geometry, which contains similar information as a third-order experiment but does not suffer from dispersive line shapes. To do so, we introduce methods to minimize saturation-induced artifacts of the pulse shaper, improving fifth-order signals. These techniques add new capabilities for 2D spectrometers that use pulse shapers in the pump-probe beam geometry.

Rapid multiple-quantum three-dimensional fluorescence spectroscopy disentangles quantum pathways

Coherent two-dimensional spectroscopy is a powerful tool for probing ultrafast quantum dynamics in complex systems. Several variants offer different types of information but typically require distinct beam geometries. Here we introduce population-based three-dimensional (3D) electronic spectroscopy and demonstrate the extraction of all fourth- and multiple sixth-order nonlinear signal contributions by employing 125-fold (1⨯5⨯5⨯5) phase cycling of a four-pulse sequence. Utilizing fluorescence detection and shot-to-shot pulse shaping in single-beam geometry, we obtain various 3D spectra of the dianion of TIPS-tetraazapentacene, a fluorophore with limited stability at ambient conditions. From this, we recover previously unknown characteristics of its electronic two-photon state. Rephasing and nonrephasing sixth-order contributions are measured without additional phasing that hampered previous attempts using noncollinear geometries. We systematically resolve all nonlinear signals from the same dataset that can be acquired in 8 min. The approach is generalizable to other incoherent observables such as external photoelectrons, photocurrents, or photoions.

From phage display to structure: an interplay of enthalpy and entropy in the binding of the LDHSLHS polypeptide to silica

Polypeptide based biosilica composites show promise as next generation multi-functional nano-platforms for diagnostics and bio-catalytic applications. Following the identification of a strong silica binder (LDHSLHS) by phage display, we conduct structural analysis of the polypeptide at the interface with amorphous silica nanoparticles in an aqueous environment. Our approach relies on modelling infrared and Raman spectral responses using predictions of molecular dynamics simulations and quantum studies of the normal modes for several potential structures. By simultaneously fitting both infrared and Raman responses in the amide spectral region, we show that the main structural conformer has a beta-like central region and helix-twisted terminals. Classical simulations, as conducted previously (Chem. Mater., 2014, 26, 5725), predict that the association of the main structure with the interface is stimulated by electrostatic interactions though surface binding also requires spatially distributed sodium ions to compensate for negatively charged acidic silanol groups. Accordingly, diffusion of sodium ions would contribute to a stochastic character of the peptide association with the surface. Consistent with the described dynamics at the interface, the results obtained from isothermal titration calorimetry (ITC) confirm a significant enhancement of polypeptide binding to silica at higher concentrations of Na+. The results of this study suggest that the tertiary structure of a phage capsid protein plays a significant role in regulating the conformation of peptide LDHSLHS, increasing its binding to silica during the phage display process. The results presented here support design-led engineering of polypeptide-silica nanocomposites for bio-technological applications.

Ultrafast structural molecular dynamics investigated with 2D infrared spectroscopy methods

Ultrafast, multi-dimensional infrared (IR) spectroscopy has been advanced in recent years to a versatile analytical tool with a broad range of applications to elucidate molecular structure on ultrafast timescales, and it can be used for samples in a many different environments. Following a short and general introduction on the benefits of 2D IR spectroscopy, the first part of this chapter contains a brief discussion on basic descriptions and conceptual considerations of 2D IR spectroscopy. Outstanding classical applications of 2D IR are used afterwards to highlight the strengths and basic applicability of the method. This includes the identification of vibrational coupling in molecules, characterization of spectral diffusion dynamics, chemical exchange of chemical bond formation and breaking, as well as dynamics of intra- and intermolecular energy transfer for molecules in bulk solution and thin films. In the second part, several important, recently developed variants and new applications of 2D IR spectroscopy are introduced. These methods focus on (i) applications to molecules under two- and three-dimensional confinement, (ii) the combination of 2D IR with electrochemistry, (iii) ultrafast 2D IR in conjunction with diffraction-limited microscopy, (iv) several variants of non-equilibrium 2D IR spectroscopy such as transient 2D IR and 3D IR, and (v) extensions of the pump and probe spectral regions for multi-dimensional vibrational spectroscopy towards mixed vibrational-electronic spectroscopies. In light of these examples, the important open scientific and conceptual questions with regard to intra- and intermolecular dynamics are highlighted. Such questions can be tackled with the existing arsenal of experimental variants of 2D IR spectroscopy to promote the understanding of fundamentally new aspects in chemistry, biology and materials science. The final part of the chapter introduces several concepts of currently performed technical developments, which aim at exploiting 2D IR spectroscopy as an analytical tool. Such developments embrace the combination of 2D IR spectroscopy and plasmonic spectroscopy for ultrasensitive analytics, merging 2D IR spectroscopy with ultra-high-resolution microscopy (nanoscopy), future variants of transient 2D IR methods, or 2D IR in conjunction with microfluidics. It is expected that these techniques will allow for groundbreaking research in many new areas of natural sciences.

Advances in multi-dimensional coherent spectroscopy of semiconductor nanostructures

Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.

An Introduction to Coherent Multidimensional Spectroscopy

Coherent multidimensional spectroscopy is a field that has drawn much attention as an optical analogue to multidimensional nuclear magnetic resonance imaging. Coherent multidimensional spectroscopic techniques produce spectra that show the magnitude of an optical signal as a function of two or more pulsed laser frequencies. Spectra can be collected in either the frequency or the time domain. In addition to improving resolution and overcoming spectral congestion, coherent multidimensional spectroscopy provides the ability to investigate and conduct studies based upon the relationship between different peaks. The purpose of this paper is to provide a general introduction to the area of coherent multidimensional spectroscopy, to provide a brief overview of current experimental approaches, and to discuss some emerging developments in this relatively young field.

2D IR spectroscopy at 100 kHz utilizing a Mid-IR OPCPA laser source

We present a 100 kHz 2D IR spectrometer. The system utilizes a ytterbium all normal dispersion fiber oscillator as a common source for the pump and seed beams of a MgO:PPLN OPCPA. The 1030 nm OPCPA pump is generated by amplification of the oscillator in cryocooled Yb:YAG amplifiers, while the 1.68 μm seed is generated in a OPO pumped by the oscillator. The OPCPA outputs are used in a ZGP DFG stage to generate 4.65 μm pulses. A mid-IR pulse shaper delivers pulse pairs to a 2D IR spectrometer allowing for data collection at 100 kHz.

Multidimensional Electronic Spectroscopy of Photochemical Reactions

Coherent multidimensional electronic spectroscopy can be employed to unravel various channels in molecular chemical reactions. This approach is thus not limited to analysis of energy transfer or charge transfer (i.e. processes from photophysics), but can also be employed in situations where the investigated system undergoes permanent structural changes (i.e. in photochemistry). Photochemical model reactions are discussed by using the example of merocyanine/spiropyran-based molecular switches, which show a rich variety of reaction channels, in particular ring opening and ring closing, cis-trans isomerization, coherent vibrational wave-packet motion, radical ion formation, and population relaxation. Using pump-probe, pump-repump-probe, coherent two-dimensional and three-dimensional, triggered-exchange 2D, and quantum-control spectroscopy, we gain intuitive pictures on which product emerges from which reactant and which reactive molecular modes are associated.

Direct observation of multistep energy transfer in LHCII with fifth-order 3D electronic spectroscopy

During photosynthesis, sunlight is efficiently captured by light-harvesting complexes, and the excitation energy is then funneled towards the reaction centre. These photosynthetic excitation energy transfer (EET) pathways are complex and proceed in a multistep fashion. Ultrafast two-dimensional electronic spectroscopy (2DES) is an important tool to study EET processes in photosynthetic complexes. However, the multistep EET processes can only be indirectly inferred by correlating different cross peaks from a series of 2DES spectra. Here we directly observe multistep EET processes in LHCII using ultrafast fifth-order three-dimensional electronic spectroscopy (3DES). We measure cross peaks in 3DES spectra of LHCII that directly indicate energy transfer from excitons in the chlorophyll b (Chl b) manifold to the low-energy level chlorophyll a (Chl a) via mid-level Chl a energy states. This new spectroscopic technique allows scientists to move a step towards mapping the complete complex EET processes in photosynthetic systems.

Photosynthesis is a complex process, involving the transfer of sunlight driven excitation energy to a reaction centre. Here, the authors directly observe the multistep excitation energy transitions in a light-harvesting complex using ultrafast fifth-order three-dimensional electronic spectroscopy.

High resolution coherent three dimensional spectroscopy of NO2

Expansion from coherent 2D spectroscopy to coherent 3D spectroscopy can provide significant advantages when studying molecules that have heavily perturbed energy levels. This paper illustrates such advantages by demonstrating how high resolution coherent 3D (HRC3D) spectroscopy can be used to study a portion of the visible spectrum of nitrogen dioxide. High resolution coherent 2D spectra usually contain rotational and vibrational patterns that are easy to analyze, but severe congestion and complexity preclude its effective use for many parts of the NO2 spectrum. HRC3D spectroscopy appears to be much more effective; multidimensional rotational and vibrational patterns produced by this new technique are easy to identify even in the presence of strong perturbations. A method for assigning peaks, which is based upon analyzing the resulting multidimensional patterns, has been developed. The higher level of multidimensionality is useful for reducing uncertainty in peak assignments, improving spectral resolution, providing simultaneous information on multiple levels and states, and predicting, verifying, and categorizing peaks.

Optical three dimensional coherent spectroscopy

Optical multdimensional coherent spectroscopy has recently been the subject of significant activity. While two-dimensional spectroscopy is most common, it is possible to extend the method into three dimensions. This perspective reviews the different approaches to three-dimensional spectroscopy and the systems that have been studied with it. The advantages of adding an additional dimension are discussed and compared to the resulting experimental challenges.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Rotational and vibrational pattern interpretation for high-resolution coherent 3D spectroscopy

High-resolution coherent multidimensional spectroscopy provides an alternative to conventional methods for generating rotationally resolved electronic spectra of gas phase molecules. In addition to revealing information such as the relationships among peaks, it can provide clearly recognizable patterns for spectra that otherwise appear patternless due to rotational congestion. Despite this improvement, high-resolution coherent 2D spectroscopy can still exhibit congestion problems; expansion to the second dimension is often not sufficient to prevent overlapping of peaks from different patterns. A new 3D version of the technique that provides improved resolution and selectivity to help address cases with severe congestion was recently demonstrated. The experimental design and interpretation of data for the 3D technique are significantly more complicated than that for the 2D version. The purpose of this paper is to provide important information needed to plan, run, and interpret results from high-resolution coherent 3D spectroscopy experiments.

Testing for memory-free spectroscopic coordinates by 3D IR exchange spectroscopy

Using 3D infrared (IR) exchange spectroscopy, the ultrafast hydrogen-bond forming and breaking (i.e., complexation) kinetics of phenol to benzene in a benzene/CCl4 mixture is investigated. By introducing a third time point at which the hydrogen-bonding state of phenol is measured (in comparison with 2D IR exchange spectroscopy), the spectroscopic method can serve as a critical test of whether the spectroscopic coordinate used to observe the exchange process is a memory-free, or Markovian, coordinate. For the system under investigation, the 3D IR results suggest that this is not the case. This conclusion is reconfirmed by accompanying molecular dynamics simulations, which furthermore reveal that the non-Markovian kinetics is caused by the heterogeneous structure of the mixed solvent.

Multidimensional spectroscopy of photoreactivity

Coherent multidimensional electronic spectroscopy is commonly used to investigate photophysical phenomena such as light harvesting in photosynthesis in which the system returns back to its ground state after energy transfer. By contrast, we introduce multidimensional spectroscopy to study ultrafast photochemical processes in which the investigated molecule changes permanently. Exemplarily, the emergence in 2D and 3D spectra of a cross-peak between reactant and product reveals the cis-trans photoisomerization of merocyanine isomers. These compounds have applications in organic photovoltaics and optical data storage. Cross-peak oscillations originate from a vibrational wave packet in the electronically excited state of the photoproduct. This concept isolates the isomerization dynamics along different vibrational coordinates assigned by quantum-chemical calculations, and is applicable to determine chemical dynamics in complex photoreactive networks.

Fully absorptive 3D IR spectroscopy using a dual mid-infrared pulse shaper

This paper presents the implementation of 3D IR spectroscopy by adding a second pump beam to a two-beam 2D IR spectrometer. An independent mid-IR pulse shaper is used for each pump beam, which can be programmed to collect its corresponding dimension in either the frequency or time-domains. Due to the phase matching geometry employed here, absorptive 3D IR spectra are automatically obtained, since all four of the rephasing and non-rephasing signals necessary to generate absorptive spectra are collected simultaneously. Phase cycling is used to isolate the fifth-order from the third-order signals. The method is demonstrated on tungsten hexacarbonyl (W(CO)6) and dicarbonylacetylacetonato rhodium (I), for which the eigenstates are extracted up to the third excited state. Pulse shaping affords a high degree of control over 3D IR experiments by making possible mixed time- and frequency-domain experiments, fast data acquisition and straightforward implementation.

High-resolution coherent three-dimensional spectroscopy of Br2

In the past, high-resolution spectroscopy has been limited to small, simple molecules that yield relatively uncongested spectra. Larger and more complex molecules have a higher density of peaks and are susceptible to complications (e.g., effects from conical intersections) that can obscure the patterns needed to resolve and assign peaks. Recently, high-resolution coherent two-dimensional (2D) spectroscopy has been used to resolve and sort peaks into easily identifiable patterns for molecules where pattern-recognition has been difficult. For very highly congested spectra, however, the ability to resolve peaks using coherent 2D spectroscopy is limited by the bandwidth of instrumentation. In this article, we introduce and investigate high-resolution coherent three-dimensional spectroscopy (HRC3D) as a method for dealing with heavily congested systems. The resulting patterns are unlike those in high-resolution coherent 2D spectra. Analysis of HRC3D spectra could provide a means for exploring the spectroscopy of large and complex molecules that have previously been considered too difficult to study.

Fifth-order three-dimensional electronic spectroscopy using a pump-probe configuration

We present the theoretical details and experimental demonstration of fifth-order three-dimensional (3D) electronic spectroscopy using a pump-probe beam geometry. This is achieved using a pulse shaper and appropriate phase cycling schemes. We show how 8-step and 27-step phase cycling schemes can measure purely absorptive 3D spectra as well as 3D spectra for the individual fifth-order processes that contribute to the purely absorptive spectrum. 3D spectra as a function of two separate controllable waiting time periods can be obtained. The peak shapes and positions of the peaks in the experimental measurement correspond well to theory.

Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy

Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system’s nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system’s Hamiltonian.

Knowledge of the Hamiltonian of a quantum system is essential for predicting and controlling its behaviour. Li et al. use optical three-dimensional Fourier-transform spectroscopy to separate and study each pathway, gaining quantitative insight into the quantum pathways of an atomic vapour Hamiltonian.

Purely absorptive fifth-order three-dimensional electronic spectroscopy

We demonstrate a method to measure a purely absorptive fifth-order three-dimensional (3D) electronic spectrum based on a pulse-shaper assisted pump-probe beam geometry setup. The 3D spectra are measured as a function of two independently controlled population times. With phase-cycling and data processing, purely absorptive 3D spectra of chlorophyll a are obtained.

Correlated High-Frequency Molecular Motions in Neat Liquid Probed with Ultrafast Overtone Two-Dimensional Infrared Spectroscopy

In this work, an overtone two-dimensional infrared (2D IR) method is shown to allow correlated molecular motions at the frequencies of overtone transitions to be studied. Waiting-time-dependent overtone 2D IR results of the C-O stretching in neat liquid methanol reveal that the autocorrelation of the v = 0 → 2 transition and the cross correlation of the v = 0 → 2/v = 2 → 4 transitions differ considerably (relaxation time being 700 fs and 2 ps, respectively), suggesting different spectral diffusion dynamics. Quantum-chemical computations in combination with ab initio molecular dynamics simulations show that the overtone transition frequency of the C-O stretching mode in liquid methanol is of more structural sensitivity than the fundamental frequency. This work demonstrates a new 2D IR approach to examining the structural sensitivities of the anharmonic potential parameters of higher vibrational states, which can be used to gain new insight into the ultrafast structural dynamics particularly for neat liquids.

Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy

We extend traditional two-dimensional (2D) electronic spectroscopy into a third Fourier dimension without the use of additional optical interactions. By acquiring a set of 2D spectra evenly spaced in waiting time and dividing the area of the spectra into voxels, we can eliminate population dynamics from the data and transform the waiting time dimension into frequency space. The resultant 3D spectrum resolves quantum beating signals arising from excitonic coherences along the waiting frequency dimension, thereby yielding up to 2n-fold redundancy in the set of frequencies necessary to construct a complete set of n excitonic transition energies. Using this technique, we have obtained, to our knowledge, the first fully experimental set of electronic eigenstates for the Fenna-Matthews-Olson (FMO) antenna complex, which can be used to improve theoretical simulations of energy transfer within this protein. Whereas the strong diagonal peaks in the 2D rephasing spectrum of the FMO complex obscure all but one of the crosspeaks at 77 K, extending into the third dimension resolves 19 individual peaks. Analysis of the independently collected nonrephasing data provides the same information, thereby verifying the calculated excitonic transition energies. These results enable one to calculate the Hamiltonian of the FMO complex in the site basis by fitting to the experimental linear absorption spectrum.

Local-mode approach to modeling multidimensional infrared spectra of metal carbonyls

We present a general approach for modeling multidimensional infrared spectra based on a combination of phenomenological fitting and ab initio electronic structure calculations. The vibrational Hamiltonian is written in terms of bilinearly coupled Morse oscillators that represent local carbonyl stretches. This should be contrasted with the previous approach, where the anharmonic Hamiltonian was given in terms of normal-mode coordinates ( Baiz et al. J. Phys. Chem. A 2009 , 113 , 9617 ). The bilinearly coupled Morse oscillator Hamiltonian is parametrized such that the frequencies and couplings are consistent with experiment, and the anharmonicities are computed by density functional theory. The advantages of the local-mode versus normal-mode approaches are discussed, as well as the ability of different density functionals to provide accurate estimates of the model parameters. The applicability and usefulness of the new approach are demonstrated in the context of the recently measured multidimensional infrared spectra of dimanganese decacarbonyl. The shifts in local site frequencies, couplings, and anharmonicities due to hydrogen bonding to the individual carbonyls are explored. It is found that, even though the effect of hydrogen bonding is nonlocal, it is additive.

Optical N-wave-mixing spectroscopy with strong and temporally well-separated pulses: the doorway-window representation

We have extended the doorway-window representation of optical pump-probe spectroscopy with weak pulses toward N-wave-mixing spectroscopy with temporally well-separated pulses of arbitrary strength. The expressions for the signals in the strong-pulse doorway-window representation are derived in the framework of the nonperturbative theory of N-wave-mixing spectroscopy. The strong-pulse doorway-window representation is complementary to the equation-of-motion phase-matching approach. The latter fully accounts for pulse-overlap effects in signals induced by weak pulses but is computationally more expensive. The performance of the doorway-window approximation for temporally well-separated strong pulses is illustrated for an electronic two-level system with an underdamped Condon-active vibrational mode.

Three-dimensional electronic spectroscopy of excitons in GaAs quantum wells

We demonstrate three-dimensional (3D) electronic Fourier transform spectroscopy of GaAs quantum wells using four fully phase-coherent, noncollinear optical fields. Since the full complex signal field is measured as a function of all three time intervals, nearly every peak in the resulting 3D spectral solid arises from a distinguishable sequence of transitions represented by a single Feynman pathway. We use the 3D spectral peaks to separate two pathways involving weakly bound mixed biexcitons generated in different time orders. In the process, we reveal a peak that was previously obscured by a correlated but unbound exciton pair coherence. We also demonstrate a calibration procedure for the carrier frequency which yields biexciton binding energy values with high accuracy.

Mode selectivity with polarization shaping in the mid-IR

We report that polarization-shaped mid-infrared (IR) pulses can be used to enhance the vibrational population of one mode over another in a coupled molecular system. A genetic algorithm and a new mid-IR polarization shaper were used to alter the relative vibrational excitation of the two carbonyl stretching modes in Mn(CO)(5)Br. One mode could be selectively enhanced over the other by 2-3 times. Control over the polarization leads to better optimization than phase-only control. Several possible mechanisms that indicate how polarization shaping leads to selective vibrational excitation are discussed using a formalism that separates polarization shaping effects on the signal strength from amplitude or phase shaping. The techniques introduced herein will have broad applications in quantum gating schemes, controlling ground state chemistry and enhancing the sensitivity of multidimensional IR and visible spectroscopies.

Femtosecond spectroscopy from the perspective of a global multidimensional response function

At the microscopic level, multidimensional response functions, such as the nonlinear optical susceptibility or the time-ordered response function, are commonly used tools in nonlinear optical spectroscopy for determining the nonlinear polarization resulting from an arbitrary excitation. In this Account, we point out that the approach successfully developed for the nonlinear polarization can also be used in the case of a directly observable macroscopic quantity. This observable can be, for example, the electric field radiated in a nonlinear mixing experiment, the rate of fluorescence resulting from one- or two-photon absorption, or the rate of a photochemical reaction. For each of these physical processes, perturbation theory can be used to expand the measured quantity in a power series of the exciting field, and an appropriate global response function can be introduced for each order of perturbation. At order n, the multidimensional response function will depend on n variables (either time or frequency) and have the same general properties as the nonlinear susceptibility resulting, for example, from time invariance or causality. The global response function is introduced in this Account in close analogy with the nonlinear susceptibility or the time-ordered microscopic response. We discuss various applications of the global response function formalism. For example, it can be shown that in the weak field limit, a stationary signal induced in a time-invariant system is independent of the spectral phase of the exciting field. Although this result had been demonstrated previously, the global response function enables its derivation in a more general way because no specific microscopic model is needed. Multidimensional spectroscopy is obviously ideally suited to measure the global multidimensional response function. It is shown that the second (or third)-order response can be exactly measured with 2D (or 3D) spectroscopy by taking into account the exact shape of the exciting pulses. In the case of a 2D measurement of the third-order response, a particular projection of the complete 3D response function is actually measured. This projection can be related to a mixed time and frequency representation of the response function when the pulses are assumed to be infinitely short. We thus show that the global response function is a useful tool for deriving general results and that it should help in designing future experimental schemes for femtosecond spectroscopy.

Efficient calculation of time- and frequency-resolved four-wave-mixing signals

"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.

What can we learn from three-dimensional infrared spectroscopy?

The low-frequency part of the vibrational spectrum of a liquid is dominated by intermolecular degrees of freedom. Hence, it reports on the motion of solvent molecules with respect to each other rather than on the intramolecular details of individual molecules. In hydrogen-bonded liquids, in particular water, a detailed understanding of the low-frequency spectrum is enormously complicated because of the complex hydrogen-bond network, which constantly rearranges on an ultrafast femtosecond to picosecond time scale. Many of the peculiar properties of water have their origin in these processes. Conventional far-infrared (far-IR) or Raman spectroscopy, as well as two-dimensional IR (2D-IR) spectroscopy, are all linear with respect to the intermolecular (solvent) degrees of freedom. These spectroscopies tell us much about the density of states in the low-frequency range but little about the dynamics of the hydrogen-bond making and breaking. In this Account, we propose three-dimensional IR (3D-IR) spectroscopy as a novel tool that is nonlinear with respect to these low-frequency degrees of freedom; hence, it may provide much more detailed insights into intermolecular dynamics. The first experimental realizations of 3D-IR spectroscopy have been demonstrated in the literature; the information it affords is similar to that of 2D-Raman spectroscopy. Three-dimensional IR spectroscopy will, for the first time, reveal whether the low-frequency part of the vibrational spectrum of liquids has to be considered mostly homogeneously or inhomogeneously broadened. Alternately, we may find that either of these classifications is completely wrong because the normal mode picture fails when thermal energy is of the same order of magnitude as the ruggedness of the intramolecular potential energy surface. We briefly introduce the theoretical background of 3D-IR spectroscopy and discuss two of its most promising applications: (a) the more thorough characterization of non-Gaussian stochastic processes such as the hydrogen-bond dynamics of water and (b) non-Markovian ultrafast exchange processes. In the ultrafast regime, many of the otherwise valid simplifying assumptions of nonequilibrium statistical mechanics (for example, linear response and Markovian dynamics) are likely to fail; 3D-IR spectroscopy will allow us for the first time to experimentally explore their range of validity.

Purely absorptive three-dimensional infrared spectroscopy

We demonstrate a method to collect purely absorptive three-dimensional (3D) fifth-order vibrational spectra on the model system CO(2) in H(2)O. The six beam interferometer is described, as well as a method to experimentally determine the phase of the 3D spectrum. The measured spectra agree very well with simulations of the data based on the cumulant expansion. There are five peaks corresponding to different paths up and down the vibrational ladder. The positions, signs, and amplitudes of the peaks agree with theoretical predictions, and the intensities of the peaks scale linearly with concentration. Based on the concentration dependence and agreement between the simulations and measurements, we conclude that cascaded lower order signals contribute negligibly to the observed signal.

How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping

We have recently developed a new and simple way of collecting 2D infrared and visible spectra that utilizes a pulse shaper and a partly collinear beam geometry. 2D IR and Vis spectroscopies are powerful tools for studying molecular structures and their dynamics. They can be used to correlate vibrational or electronic eigenstates, measure energy transfer rates, and quantify the dynamics of lineshapes, for instance, all with femtosecond time-resolution. As a result, they are finding use in systems that exhibit fast dynamics, such as sub-millisecond chemical and biological dynamics, and in hard-to-study environments, such as in membranes. While powerful, these techniques have been difficult to implement because they require a series of femtosecond pulses to be spatially and temporally overlapped with precise time-resolution and interferometric phase stability. However, many of the difficulties associated with implementing 2D spectroscopies are eliminated by using a pulse shaper and a simple beam geometry, which substantially lowers the technical barriers required for researchers to enter this exciting field while simultaneously providing many new capabilities. The aim of this paper is to provide an overview of the methods for collecting 2D spectra so that an outsider considering using 2D spectroscopy in their own research can judge which approach would be most suitable for their research aims. This paper focuses primarily on 2D IR spectroscopy, but also includes our recent work on adapting this technology to collecting 2D Vis spectra. We review work that has already been published as well as cover several topics that we have not reported previously, including phase cycling methods to remove background signals, eliminate unwanted scatter, and shift data collection into the rotating frame.