Fully and Partially Coherent Pathways in Multiply Enhanced Odd-Order Wave-Mixing Spectroscopy

Abstract

Nuclear magnetic resonance spectroscopy relies on using multiple excitation pulses to create multiple quantum coherences that provide great specificity for chemical measurements. Coherent multidimensional spectroscopy (CMDS) is the optical analogue of NMR. Current CMDS methods use three excitation pulses and phase matching to create zero, single, and double quantum coherences. In order to create higher order multiple quantum coherences, the number of interactions must be increased by raising the excitation intensities high enough to create Rabi frequencies that are comparable to the dephasing rates of vibrational coherences. The higher Rabi frequencies create multiple, odd-order coherence pathways. The coherence pathways that involve intermediate populations are partially coherent and are sensitive to population relaxation effects. Pathways that are fully coherent involve only coherences and measure the direct coupling between excited quantum states. The fully coherent pathways are related to the multiple quantum coherences created in multiple pulse NMR methods such as heteronuclear multiple quantum coherence (HMQC) spectroscopy with the important difference that HMQC NMR methods have a defined number of interactions and avoid dynamic Stark effects whereas the multiply enhanced odd-order wave-mixing pathways do not. The difference arises because CMDS methods use phase matching to define the interactions and at high intensities, multiple pathways obey the same phase matching conditions. The multiple pathways correspond to the pathways created by dynamic Stark effects. This paper uses rhodium dicarbonyl chelate (RDC) as a model to demonstrate the characteristics of multiply enhanced odd-order wave-mixing (MEOW) methods. Dynamic Stark effects excite vibrational ladders on the symmetric and asymmetric CO stretch modes and create a series of multiple quantum coherences and populations using partially and fully coherent pathways. Vibrational quantum states up to v = 6 are excited. A series of spectra provides different two-dimensional cross sections through the multidimensional parameter space involving two excitation frequencies, the frequency of the output coherence, and the excitation pulse time delays. The spectra allow the identification of 18 different overtone and combination band states. Comparison with a local mode model with two anharmonic Morse oscillators with interbond coupling shows excellent agreement.