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The fundamental ideas for a nonlocal density functional theory—capable of reliably capturing van der Waals interactions—were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical nonlocal exchange–correlation functional called vdW–DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW–DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance, and the successor vdW–DF2 also updated one internal parameter. Bringing together different insights from almost 2 decades of development and testing, we present the next-generation nonlocal correlation functional called vdW–DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW–DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW–DF framework that can be constrained through empirical input, making our functional semiempirical. For two different parameterizations, we benchmark vdW–DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW–DF framework, the flexibility in functional design offered by vdW–DF3, as well as possible future directions for nonlocal van der Waals density functional theory.

We have developed a high sensitivity time-resolved two-photon scanning microscope. At an excitation wavelength of 960 nm, a spatial point spread function of 0.3 µm (FWHM) radially and 0.9 µm (FWHM) axially is measured for an 1.25 N.A. objective. The light source is a mode-locked titanium-sapphire laser. The time resolution is 400 ps with common chromophores used in microscopy. Time resolution is obtained using the frequency-domain heterodyning technique in which the laser is synchronized at a very high cross-correlation frequency to the rest of the electronics. We demonstrate spatial and time resolution using well-characterized fluorescent microspheres. We show two applications of two-photon time-resolved fluorescence microscopy: time-resolved imaging of multiple dye labeled cells and quantitative cellular calcium concentration using a lifetime indicator.