Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

Transient absorption (TA) and photoluminescence excitation (PLE) anisotropy measurements were used to investigate the polarization of band-edge and above-band-edge excitonic states in ensembles of CdSe nanocrystals with aspect ratios of 1:1, 3:1, and 10:1, dispersed in hexanes. The 1:1 nanocrystals (quantum dots) are isotropic absorbers and emitters. The 10:1 nanorods have a nonzero but featureless anisotropy spectrum above the band edge due to heterogeneity in the crystal structure and, therefore, electronic structure within single nanorods. The nanocrystals with an aspect ratio of 3:1, which are largely single crystals, have PLE and TA anisotropy spectra with features that correspond to those in the absorption spectrum. Direct measurement of the TA anisotropy spectrum of the nanorods and comparison with the PLE anisotropy spectrum reveal that the band-edge absorptive and emissive transitions contain both linear (z) and planar (xy) character. The degree of planar character at the band-edge states, modulated by classical local field effects arising from the dielectric contrast between the nanorod and the solvent, limits the degree of photoselection at this wavelength. The variation in the magnitude of the xy projection of the absorptive transitions within states above the band edge is responsible for the wavelength dependence of the absorption and emission anisotropies.

Coherent multidimensional spectroscopy (CMDS) is now the optical analogue of nuclear magnetic resonance (NMR). Just as NMR heteronuclear multiple-quantum coherence (HMQC) methods rely on multiple quantum coherences, achieving widespread application requires that CMDS also excites multiple quantum coherences over a wide range of quantum state energies. This Account focuses on frequency-domain CMDS because these methods tune the excitation frequencies to resonance with the desired quantum states and can form multiple quantum coherences between states with very different energies. CMDS methods use multiple excitation pulses to excite multiple quantum states within their dephasing time, so their quantum mechanical phase is maintained. Coherences formed from pairs of the excited states emit coherent beams of light. The temporal ordering of the excitation pulses defines a sequence of coherences that can result in zero, single, double, or higher order coherences as required for multiple quantum coherence CMDS. Defining the temporal ordering and the excitation frequencies and spectrally resolving the output frequency also defines a particular temporal pathway for the coherences, just as an NMR pulse sequence defines an NMR method. Two dimensional contour plots through this multidimensional parameter space allow visualization of the state energies and dynamics. This Account uses nickel and rhodium chelates as models for understanding mixed frequency-/time-domain CMDS. Mixed frequency-/time-domain methods use excitation pulse widths that are comparable to the dephasing times, so multidimensional spectra are obtained by scanning the excitation frequencies, while the coherence and population dynamics are obtained by scanning the time delays. Changing the time delays changes the peaks in the 2D excitation spectra depending upon whether the pulse sequence excites zero, single, or double quantum coherences. In addition, peaks split as a result of the frequency-domain manifestation of quantum beating. Similarly, changing the excitation and monochromator frequencies changes the dependence on the excitation delay times depending upon whether the frequencies match the resonances involved in the different time-ordered pathways. Contour plots that change a time delay and frequency visualize the temporal changes of specific spectral features. Frequency-domain methods are resonant with specific states, so the sequence of coherences and populations is defined. Coherence transfer, however, can cause output beams at unexpected frequencies. Coherence transfer occurs when the thermal bath induces a coherence between two states (a and g) to evolve to a new coherence (b and g). Since the two coherences have different frequencies and since there are different time orderings for the occurrence of coherence transfer, the delay time dependence develops modulations that depend on the coherences' frequency difference. Higher order coherences can also be generated by raising the excitation intensities. New features appear in the 2D spectra and dynam...

Coherent multidimensional spectroscopy (CMDS) has greatly expanded the capabilities of molecular spectroscopy, and it promises to be equally important for materials chemistry. CMDS includes both time domain and multiply resonant frequency domain approaches. Although time domain CMDS has dominated applications, new work shows that multiply resonant CMDS has attractive features for fully coherent spectroscopy of the quantum states that are important for materials spectroscopy. Rather than resolving the temporal oscillations of each coherence, multiply resonant CMDS is an older method that measures the resonance enhancements for different excitation frequencies. It does not require the long-term phase coherence that restricts the coherent pathways and quantum states accessible by time domain methods. This Perspective reviews the multiply resonant CMDS vibrational methods and shows how they can be adapted to the diverse electronic and vibrational states of materials chemistry.