Correlation Effects in the Two-Dimensional Vibrational Spectroscopy of Coupled Vibrations

Elucidating phonon dephasing mechanisms in layered perovskites with coherent Raman spectroscopies

Organic-inorganic hybrid perovskite quantum wells exhibit electronic structures with properties intermediate between those of inorganic semiconductors and molecular crystals. In these systems, periodic layers of organic spacer molecules occupy the interstitial spaces between perovskite sheets, thereby confining electronic excitations to two dimensions. Here, we investigate spectroscopic line broadening mechanisms for phonons coupled to excitons in lead-iodide layered perovskites with phenyl ethyl ammonium (PEA) and azobenzene ethyl ammonium (AzoEA) spacer cations. Using a modified Elliot line shape analysis for the absorbance and photoluminescence spectra, polaron binding energies of 11.2 and 17.5 meV are calculated for (PEA)2PbI4 and (AzoEA)2PbI4, respectively. To determine whether the polaron stabilization processes influence the dephasing mechanisms of coupled phonons, five-pulse coherent Raman spectroscopies are applied to the two systems under electronically resonant conditions. The prominence of inhomogeneous line broadening mechanisms detected in (AzoEA)2PbI4 suggests that thermal fluctuations involving the deformable organic phase broaden the distributions of phonon frequencies within the quantum wells. In addition, our data indicate that polaron stabilization primarily involves photoinduced reorganization of the organic phases for both systems, whereas the impulsively excited phonons represent less than 10% of the total polaron binding energy. The signal generation mechanisms associated with our fifth-order coherent Raman experiments are explored with a perturbative model in which cumulant expansions are used to account for time-coincident vibrational dephasing and polaron stabilization processes.

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

Ultrafast Two-Dimensional Infrared Spectroscopy of a Quasifree Rotor: J Scrambling and Perfectly Anticorrelated Cross Peaks

Ultrafast two-dimensional infrared (2DIR) spectra of the N_{2}O ν_{3} mode in moderately dense SF_{6} gas exhibit complex line shapes with diagonal and antidiagonal features in contrast to condensed phase vibrational 2DIR spectroscopy. Observed spectra for this quasifree rotor system are well captured by a model that includes all 36 possible rovibrational pathways and treats P (ΔJ=-1) and R (ΔJ=+1) branch resonances as distinct Kubo line shape features. Transition frequency correlation decay is due to J scrambling within one to two gas collisions at each density. Studies of supercritical solvation and relaxation at high pressure and temperature are enabled by this methodology.

Hydrophobic Collapse in N-Methylacetamide-Water Mixtures

Aqueous N-methylacetamide solutions were investigated by polarization-resolved pump-probe and 2D infrared spectroscopy (2D IR), using the amide I mode as a reporter. The 2D IR results are compared with molecular dynamics simulations and spectral calculations to gain insight into the molecular structures in the mixture. N-Methylacetamide and water molecules tend to form clusters with "frozen" amide I dynamics. This is driven by a hydrophobic collapse as the methyl groups of the N-methylacetamide molecules cluster in the presence of water. Since the studied system can be considered as a simplified model for the backbone of proteins, the present study forms a convenient basis for understanding the structural and vibrational dynamics in proteins. It is particularly interesting to find out that a hydrophobic collapse as the one driving protein folding is observed in such a simple system.

Dynamics in the isotropic phase of nematogens using 2D IR vibrational echo measurements on natural-abundance 13CN and extended lifetime probes

The long time scale orientational relaxation of nematogens in the isotropic phase is associated with the randomization of pseudonematic domains, which have a correlation length that grows as the isotropic-to-nematic phase transition temperature is approached from above. Here we begin to address the fast dynamics of the nematogen molecules within the domains using two-dimensional infrared (2D IR) vibrational echo experiments. The problems of performing ultrafast IR experiments in pure liquids are discussed, and solutions are presented. In addition, the issue of short vibrational lifetimes, which limit the ability of 2D IR experiments to examine dynamics over a wide range of times, is addressed. The experiments were performed on the nematogen 4-cyano-4'-pentylbiphenyl (5CB), with the CN stretch initially used as the vibrational probe. Although the CN stretch has a small transition dipole, because the sample is a pure liquid it is necessary to use an exceedingly thin sample to perform the experiments. The small sample volume leads to massive heating effects that distort the results. In addition, the high concentration in the pure liquid can result in vibrational excitation transfer that interferes with the measurements of structural dynamics, and the CN vibrational lifetime is very short (3.6 ps). These problems were overcome by performing the experiments on the natural-abundance (13)CN stretch (5(13)CB), which greatly reduced the absorbance, eliminating the heating problems; also, this stretch has a longer lifetime (7.9 ps). Experiments were also performed on benzonitrile, which showed that the heating problems associated with pure liquids are not unique to 5CB. Again, the problems were eliminated by conducting measurements on the (13)CN stretch, which has an even longer lifetime (20.2 ps) compared with the (12)CN stretch (5.6 ps). Finally, to extend the range of the dynamical measurements, 4-pentyl-4'-thiocyanobiphenyl (5SCB) was synthesized and studied as a dilute solute in 5CB. The CN stretch of 5SCB has a vibrational lifetime of 103 ps, which permits dynamical measurements to 200 ps, revealing the full range of fast structural dynamics in the isotropic phase of 5CB. It is shown that the 5SCB probe reports essentially the same dynamics as 5(13)CB on the short time scale that is observable with the 5(13)CB vibrational probe.

Anharmonic vibrational modes of nucleic acid bases revealed by 2D IR spectroscopy

Polarization-dependent two-dimensional infrared (2D IR) spectra of the purine and pyrimadine base vibrations of five nucleotide monophosphates (NMPs) were acquired in D(2)O at neutral pH in the frequency range 1500-1700 cm(-1). The distinctive cross-peaks between the ring deformations and carbonyl stretches of NMPs indicate that these vibrational modes are highly coupled, in contrast with the traditional peak assignment, which is based on a simple local mode picture such as C═O, C═N, and C═C double bond stretches. A model of multiple anharmonically coupled oscillators was employed to characterize the transition energies, vibrational anharmonicities and couplings, and transition dipole strengths and orientations. No simple or intuitive structural correlations are found to readily assign the spectral features, except in the case of guanine and cytosine, which contain a single local CO stretching mode. To help interpret the nature of these vibrational modes, we performed density functional theory (DFT) calculations and found that multiple ring vibrations are coupled and delocalized over the purine and pyrimidine rings. Generally, there is close correspondence between the experimental and computational results, provided that the DFT calculations include explicit waters solvating hydrogen-bonding sites. These results provide direct experimental evidence of the delocalized nature of the nucleotide base vibrations via a nonperturbative fashion and will serve as building blocks for constructing a structure-based model of DNA and RNA vibrational spectroscopy.

Molecular theory and simulation of coherence transfer in metal carbonyls and its signature on multidimensional infrared spectra

We present a general and comprehensive theoretical and computational framework for modeling ultrafast multidimensional infrared spectra of a vibrational excitonic system in liquid solution. Within this framework, we describe the dynamics of the system in terms of a quantum master equation that can account for population relaxation, dephasing, coherence-to-coherence transfer, and coherence-to-population transfer. A unique feature of our approach is that, in principle, it does not rely on any adjustable fitting parameters. More specifically, the anharmonic vibrational Hamiltonian is derived from ab initio electronic structure theory, and the system-bath coupling is expressed explicitly in terms of liquid degrees of freedom whose dynamics can be obtained via molecular dynamics simulations. The applicability of the new approach is demonstrated by employing it to model the recently observed signatures of coherence transfer in the two-dimensional spectra of dimanganese decacarbonyl in liquid cyclohexane. The results agree well with experiment and shed new light on the nature of the molecular interactions and dynamics underlying the spectra and the interplay between dark and bright states, their level of degeneracy, and the nature of their interactions with the solvent.

Transient vibrational echo versus transient absorption spectroscopy: a direct experimental and theoretical comparison

Transient dispersed vibrational echo (DVE) spectroscopy is a practical alternative to transient-absorption spectroscopy because it affords increased sensitivity as well as greater signal-to-noise ratio without the need to detect a reference spectrum. However, as a third-order nonlinear probe, the extraction of kinetic information from transient-DVE is somewhat cumbersome compared to transient absorption. This article provides a direct experimental and theoretical comparison between transient-absorption and transient-DVE measurements and presents a framework for analyzing kinetic measurements while exploring the implications of making some simplifying assumptions in the data analysis. The equations for computing the signal-to-noise ratios under different experimental conditions are derived and used in the analysis of the experimental data. The results, obtained under the same experimental conditions, show that for a relatively strong terminal carbonyl stretching mode, signal-to-noise ratios in transient-DVE spectroscopy are approximately 2.5 times greater than transient absorption. The experimental results along with the theoretical models indicate that transient-DVE could become an attractive alternative to transient-absorption spectroscopy for measuring the kinetics of light-induced processes.

Two-dimensional infrared spectroscopy of metal carbonyls

Metal carbonyl complexes offer both rich chemistry and complex vibrational spectroscopy due to strong coupling among the carbonyl stretches. Using two-dimensional infrared (2DIR) spectroscopy, it is possible to resolve the underlying transitions between vibrational energy levels, determine the orientations and relative magnitude of the corresponding transition dipole moments, measure the coupling between modes due to the anharmonicity of the potential, and probe energy redistribution among the modes as well as energy relaxation to other degrees of freedom. Measurements on metal carbonyl complexes have played, and continue to play, a crucial role in facilitating the development of 2DIR spectroscopy. These compounds have provided powerful demonstrations of the unique ability of 2DIR spectroscopy to resolve vibrational structure and dynamics in multimode systems. In addition, invaluable new information has been obtained on metal-to-ligand charge transfer processes, solvent-solute interactions and fluxionality. Since transition metal complexes play important roles in catalysis and as dye sensitizers for semiconductor nanoparticle photocatalysis, detailed probes of equilibrium and phototriggered dynamics should aid our understanding of these key catalytic systems. The richness and level of detail provided by the 2DIR spectra of metal carbonyl complexes turn them into extremely useful model systems for testing the accuracy of ab initio quantum chemical calculations. Accurate modeling of the 2DIR spectra of solvated metal carbonyl complexes requires the development of new theoretical and computational tools beyond those employed in the standard analysis of one-dimensional IR spectra, and represents an ongoing challenge to currently available computational methodologies. These challenges are further compounded by the increasing interest in triggered 2DIR experiments that involve nonequilibrium vibrational dynamics on multiple electronic potential surfaces. In this Account, we review the various metal carbonyl complexes studied via 2DIR spectroscopy and outline the theoretical approaches used in order to model the spectra. The capabilities of 2DIR spectroscopy and its interplay with modern ab initio calculations are demonstrated in the context of the metal carbonyl complex Mn(2)(CO)(10) recently studied in our lab. Continued progress in experimental implementation and theoretical analysis will enable transient 2D spectroscopy to provide structurally sensitive details of complex, highly interacting nonequilibrium processes that are central to diverse chemical transformations.

Probing dynamics of complex molecular systems with ultrafast 2D IR vibrational echo spectroscopy

Ultrafast 2D IR vibrational echo spectroscopy is described and a number of experimental examples are given. Details of the experimental method including the pulse sequence, heterodyne detection, and determination of the absorptive component of the 2D spectrum are outlined. As an initial example, the 2D spectrum of the stretching mode of CO bound to the protein myoglobin (MbCO) is presented. The time dependence of the 2D spectrum of MbCO, which is caused by protein structural evolution, is presented and its relationship to the frequency-frequency correlation function is described and used to make protein structural assignments based on comparisons to molecular dynamics simulations. The 2D vibrational echo experiments on the protein horseradish peroxidase are presented. The time dependence of the 2D spectra of the enzyme in the free form and with a substrate bound at the active site are compared and used to examine the influence of substrate binding on the protein's structural dynamics. The application of 2D vibrational echo spectroscopy to the study of chemical exchange under thermal equilibrium conditions is described. 2D vibrational echo chemical exchange spectroscopy is applied to the study of formation and dissociation of organic solute-solvent complexes and to the isomerization around a carbon-carbon single bond of an ethane derivative.

Multidimensional infrared spectroscopy of the N-H bond motions in formamide

The heterodyned two-dimensional (2D) IR spectra and equilibrium dynamics of the N-H stretching motion of DCONHD in deuterated formamide, DCOND(2), were studied with 80 fs pulses at 3 microm. The time evolution of the heterodyned 2D IR spectra, pump-probe spectra, and photon echo peak shift demonstrate that interstate dynamics is occurring by relaxation of the original N-H excitation. The N-H vibrational frequency correlation function can be expressed as a sum of three exponentials with correlation times 0.24 ps, 0.8 ps, and 11 ps. The intermediate component is attributed to motions of the N-Hcdots, three dots, centeredO unit involving only slight angular variations of the N-H bond. The slow component is attributed to the structure breaking and making. The anisotropy decay confirmed that the significant angular N-H bond motion occurs on the 11 ps time scale. The fast component, which is the least well determined, might correspond to the modulation of the H-bond distance without angular motion. The correlation coefficient between the pumped and relaxed state distributions was +0.51, implying that the excited state phase memory is only slightly diminished by the relaxation of the N-H excitation. The relaxed modes are concluded to be local to the driven N-H mode.

Spectral signatures of heterogeneous protein ensembles revealed by MD Simulations of 2DIR spectra

A model for the calculation of amide I FTIR and 2DIR spectra taking into account fluctuations in hydrogen bonding and structure from molecular dynamics (MD) simulations is tested on three systems. It is found that although the homogeneous lineshape approximation yields satisfactory FTIR spectra, 2DIR spectra are sensitive to the inhomogeneity naturally present in any solvated protein and the common approximations of a static structure and averaged-effect solvent are invalid. By building on the local amide Hamiltonian and incorporating site energy variation with electrostatic-based models and disorder from MD trajectories, good agreement is obtained between calculated and measured 2DIR spectra. The largest contribution to the observed inhomogeneity is found to be the fluctuating site energies, which in turn are most sensitive to the water solvent. With the ability to accurately predict 2DIR spectra from atomistic simulations, new opportunities to test force fields and mechanistic predictions from MD are revealed.

Ultrafast Two-Dimensional Infrared Vibrational Echo Chemical Exchange Experiments and Theory

Ultrafast two-dimensional (2D) infrared vibrational echo experiments and theory are used to examine chemical exchange between solute-solvent complexes and the free solute for the solute phenol and three solvent complex partners, p-xylene, benzene, and bromobenzene, in mixed solvents of the partner and CCl4. The experiments measure the time evolution of the 2D spectra of the hydroxyl (OD) stretching mode of the phenol. The time-dependent 2D spectra are analyzed using time-dependent diagrammatic perturbation theory with a model that includes the chemical exchange (formation and dissociation of the complexes), spectral diffusion of both the complex and the free phenol, orientational relaxation of the complexes and free phenol, and the vibrational lifetimes. The detailed calculations are able to reproduce the experimental results and demonstrate that a method employed previously that used a kinetic model for the volumes of the peaks is adequate to extract the exchange kinetics. The current analysis also yields the spectral diffusion (time evolution of the dynamic line widths) and shows that the spectral diffusion is significantly different for phenol complexes and free phenol.

A time correlation function theory of two-dimensional infrared spectroscopy with applications to liquid water

A theory describing the third-order response function R((3))(t(1),t(2),t(3)), which is associated with two-dimensional infrared (2DIR) spectroscopy, has been developed. R((3)) can be written as sums and differences of four distinct quantum mechanical dipole (multi)time correlation functions (TCF's), each with the same classical limit; the combination of TCF's has a leading contribution of order variant Planck's over 2pi (3) and thus there is no obvious classical limit that can be written in terms of a TCF. In order to calculate the response function in a form amenable to classical mechanical simulation techniques, it is rewritten approximately in terms of a single classical TCF, B(R)(t(1),t(2),t(3))=micro(j)(t(2)+t(1))micro(i)(t(3)+t(2)+t(1))micro(k)(t(1))micro(l)(0), where the subscripts denote the Cartesian dipole directions. The response function is then given, in the frequency domain, as the Fourier transform of a classical TCF multiplied by frequency factors. This classical expression can then further be quantum corrected to approximate the true response function, although for low frequency spectroscopy no correction is needed. In the classical limit, R((3)) becomes the sum of multidimensional time derivatives of B(R)(t(1),t(2),t(3)). To construct the theory, the response function's four TCF's are rewritten in terms of a single TCF: first, two TCF's are eliminated from R((3)) using frequency domain detailed balance relationships, and next, two more are removed by relating the remaining TCF's to each other within a harmonic oscillator approximation; the theory invokes a harmonic approximation only in relating the TCF's and applications of theory involve fully anharmonic, atomistically detailed molecular dynamics (MD). Writing the response function as a single TCF thus yields a form amenable to calculation using classical MD methods along with a suitable spectroscopic model. To demonstrate the theory, the response function is obtained for liquid water with emphasis on the OH stretching portion of the spectrum. This approach to evaluating R((3)) can easily be applied to chemically interesting systems currently being explored experimentally by 2DIR and to help understand the information content of the emerging multidimensional spectroscopy.

Signatures of β-sheet secondary structures in linear and two-dimensional infrared spectroscopy

Using idealized models for parallel and antiparallel beta sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition-dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel beta sheets and between beta hairpins and extended beta sheets.

Vibrational coherence transfer characterized with Fourier-transform 2D IR spectroscopy

Two-dimensional infrared (2D IR) spectroscopy of the symmetric and asymmetric C[Triple Bond]O stretching vibrations of Rh(CO)(2)acac in hexane has been used to investigate vibrational coherence transfer, dephasing, and population relaxation in a multilevel vibrational system. The transfer of coherence between close-lying vibrational frequencies results in extra relaxation-induced peaks in the 2D IR spectrum, whose amplitude depends on the coherence transfer rate. Coherence transfer arises from the mutual interaction of the bright CO stretches with dark states, which in this case reflects the mutual d-pi(*) back bonding of the Rh center to both the terminal carbonyls and the acetylacenonate ligand. For 2D IR relaxation experiments with variable waiting times, coherent dynamics lead to the modulation of peak amplitudes, while incoherent population relaxation and exchange results in the growth of the relaxation-induced peaks. We have modeled the data by propagating the density matrix with the Redfield equation, incorporating all vibrational relaxation processes during all three experimental time periods and including excitation reorientation effects arising from relaxation. Coherence and population transfer time scales from the symmetric to the asymmetric stretch were found to be 350 fs and 3 ps, respectively. We also discuss a diagrammatic approach to incorporating all vibrational relaxation processes into the nonlinear response function, and show how coherence transfer influences the analysis of structural variables from 2D IR spectroscopy.

Correlated vibrational dynamics revealed by two-dimensional infrared spectroscopy

Two-dimensional infrared (2D IR) spectroscopy has been used to monitor the solvent-induced correlated fluctuations in the transition energies of two coupled vibrations. The elongation of diagonal and cross peaks in a 2D IR correlation spectrum reflects the degree of inhomogeneity in the individual transition energies and the correlation between them. Changes in the 2D line shapes as a function of a variable waiting period have been successfully reproduced by a correlated spectral diffusion model.