Four-dimensional coherent electronic Raman spectroscopy.

The correlations between different quantum-mechanical degrees of freedom of molecular species dictate their chemical and physical properties. Generally, these correlations are reflected in the optical response of the system but in low-order or low-dimensionality measurement the signals are highly averaged. Here, we describe a novel four-dimensional coherent spectroscopic method that directly correlates within and between the manifold of electronic and vibrational states. The optical response theory is developed in terms of both resonant and non-resonant field-matter interactions. Using resonance to select coherences on specific electronic states creates opportunities to directly distinguish coherent dynamics on the ground and electronically excited potentials. Critically, this method is free from lower-order signals that have plagued other electronically non-resonant vibrational spectroscopies. The theory presented here compliments recent work on the experimental demonstration of the 4D spectroscopic method described. We highlight specific means by which non-trivial effects such as anharmonicity (diagonal and off-diagonal), mode-specific vibronic coupling, and curvature of the excited states manifest in different projections of the 4D spectrum.