Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.

The air-water interface is perhaps the most common liquid interface. It covers more than 70 per cent of the Earth's surface and strongly affects atmospheric, aerosol and environmental chemistry. The air-water interface has also attracted much interest as a model system that allows rigorous tests of theory, with one fundamental question being just how thin it is. Theoretical studies have suggested a surprisingly short 'healing length' of about 3 ångströms (1 Å = 0.1 nm), with the bulk-phase properties of water recovered within the top few monolayers. However, direct experimental evidence has been elusive owing to the difficulty of depth-profiling the liquid surface on the ångström scale. Most physical, chemical and biological properties of water, such as viscosity, solvation, wetting and the hydrophobic effect, are determined by its hydrogen-bond network. This can be probed by observing the lineshape of the OH-stretch mode, the frequency shift of which is related to the hydrogen-bond strength. Here we report a combined experimental and theoretical study of the air-water interface using surface-selective heterodyne-detected vibrational sum frequency spectroscopy to focus on the 'free OD' transition found only in the topmost water layer. By using deuterated water and isotopic dilution to reveal the vibrational coupling mechanism, we find that the free OD stretch is affected only by intramolecular coupling to the stretching of the other OD group on the same molecule. The other OD stretch frequency indicates the strength of one of the first hydrogen bonds encountered at the surface; this is the donor hydrogen bond of the water molecule straddling the interface, which we find to be only slightly weaker than bulk-phase water hydrogen bonds. We infer from this observation a remarkably fast onset of bulk-phase behaviour on crossing from the air into the water phase.