The theory of electronic structure of many-electron systems, such as molecules, is extraordinarily complicated. A consideration of how electron density is distributed on average in the average field of the other electrons in the system, that is, mean field theory, is very instructive. However, quantitatively describing chemical bonds, reactions, and spectroscopy requires consideration of the way that electrons avoid each other while moving; this is called electron correlation (or in physics, the many-body problem for fermions). Although great progress has been made in theory, there is a need for incisive experimental tests for large molecular systems in the condensed phase. In this Account, we report a two-dimensional (2D) optical coherent spectroscopy that correlates the double-excited electronic states to constituent single-excited states. The technique, termed 2D double-quantum coherence spectroscopy (2D-DQCS), uses multiple, time-ordered ultrashort coherent optical pulses to create double- and single-quantum coherences over time intervals between the pulses. The resulting 2D electronic spectrum is a map of the energy correlation between the first excited state and two-photon allowed double-quantum states. The underlying principle of the experiment is that when the energy of the double-quantum state, viewed in simple models as a double HOMO-to-LUMO (highest occupied to lowest unoccupied molecular orbital) excitation, equals twice that of a single excitation, then no signal is radiated. However, electron-electron interactions, a combination of exchange interactions and electron correlation, in real systems generates a signal that reveals precisely how the energy of the double-quantum resonance differs from twice the single-quantum resonance. The energy shift measured in this experiment reveals how the second excitation is perturbed by both the presence of the first excitation and the way that the other electrons in the system have responded to the presence of that first excitation. We compare a series of organic dye molecules and find that the energy offset for adding a second electronic excitation to the system relative to the first excitation is on the order of tens of millielectronvolts; it also depends quite sensitively on molecular geometry. These results demonstrate the effectiveness of 2D-DQCS for elucidating quantitative information about electron-electron interactions, many-electron wave functions, and electron correlation in electronic excited states and excitons. Our work helps illuminate the implications of electron correlation on chemical systems. In a broad sense, we are trying to help address the fundamental question "How do we go beyond the orbital representation of electrons in the chemical sciences?"
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