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.

The accuracy and robustness of several approximate methods for computing linear and nonlinear optical spectra are considered. The analysis is performed in the context of a benchmark model that consists of a two-state chromophore with shifted harmonic potential surfaces that differ in frequency. The exact one- and two-dimensional spectra for this system are calculated and compared to spectra calculated via the following approximate methods: (1) The semiclassical forward-backward initial-value representation (FB-IVR) method; (2) the linearized semiclassical (LSC) method; (3) the standard second-order cumulant approximation which is based on the ground-state equilibrium frequency-frequency correlation function (2OC); (4) an alternative second-order cumulant approximation which is able to account for nonequilibrium dynamics on the excited-state potential surface (2OCa). All four approximate methods can be shown to reproduce the exact results when the frequencies of the ground and excited harmonic surfaces are identical. However, allowing for the ground and excited surfaces to differ in frequency leads to a more meaningful benchmark model for which none of the four approximate methods is exact. We present a comparison of one- and two-dimensional spectra calculated via the above-mentioned approximate methods to the corresponding exact spectra, as a function of the following parameters: (1) The ratio of excited state to ground-state frequencies; (2) Temperature; (3) The horizontal displacement of the excited-state potential relative to the ground-state potential; (4) The waiting time between the coherence periods in the case of two-dimensional spectra. The FB-IVR method is found to predict spectra which are practically indistinguishable from the exact ones over a wide region of parameter space. The LSC method is found to predict spectra which are in good agreement with the exact ones over the same region of parameter space. The 2OC and 2OCa are found to be highly inaccurate unless the frequencies of the ground and excited states are very similar. These observations give credence to the use of the LSC method for modeling spectra in complex systems, where exact or even FB-IVR-based calculations are prohibitively expensive.

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.

We present a first-principles study of the 2D carbonyl stretch infrared spectra of dimanganese decacarbonyl, Mn2(CO)10, and its photoproducts, Mn2(CO)9 and Mn(CO)5. The corresponding multidimensional anharmonic potential energy surfaces are computed via density functional theory up to fourth-order in the normal mode coordinates. The anharmonic shifts are computed using vibrational perturbation theory and benchmarked against results obtained by diagonalizing the vibrational Hamiltonian in the case of Mn(CO)5. The importance of accounting for couplings between the photoactive and photoinactive CO stretches as well as for contributions that arise from fourth-order force constants is demonstrated. The 2D spectra are compared with experiment in the case of Mn2(CO)10.The reasonable agreement between theory and experiment suggests that an approach combining density functional theory with vibrational perturbation theory can provide a useful route for computing 2D infrared spectra, particularly in cases where direct diagonalization of the vibrational Hamiltonian is not feasible.