Mixed Frequency-/Time-Domain Coherent Multidimensional Spectroscopy: Research Tool or Potential Analytical Method?

Abstract

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...

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“…8(a). Two-dimensional spectra are usually, but not always [152][153][154][155][156][157], plotted as a function of frequency for the first and third time-delay variables. For the G II11αi expres- This term is independent of time-delay variable τ , meaning its amplitude will not oscillate coherently nor will it decay with the excitedstate lifetime.…”

“…8(a). Two-dimensional spectra are usually, but not always [152][153][154][155][156][157], plotted as a function of frequency for the first and third time-delay variables. For the G II11αi expres- 4) 2D ES spectrum.…”

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