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Description

Density functional theory (DFT) is a method for solving the electronic structure problem defined by the Schrödinger equation of interacting electrons [1]. It has become an extremely widespread technique in the physical, biological, and materials sciences and it contributes significantly to the world’s overall computational expenses [2, 3, 4].  Its most used implementation relies on the solution of the Kohn-Sham (KS) equations [5]. While DFT is in principle exact, the exchange-correlation (XC) energy must be approximated. High-quality approximations determine the ability of DFT for providing useful predictions of physical phenomena.

As key topic in our workshop, we will address recent progress on XC approximations for ground-state DFT [6, 7, 8] and time-dependent DFT [9, 10, 11]. This includes recent meta-generalized-gradient approximations (meta-GGAs) [12, 13, 14], hybrid [15, 16, 17, 18], local hybrid [19], and range-separated hybrid functionals [20, 21, 22], as well as methods for non-collinear magnetism [23, 24] and dispersion interactions [25, 26, 27].

One of the leading methods for constructing XC approximations relies on known constraints on the unknown exact XC functional [28], which will be another central topic of our workshop. These include the adiabatic connection [29], self-interaction freedom [30], piecewise linearity [31], discontinuities [32, 33, 34], delocalization error [35, 36], ensembles [37, 38, 39, 40, 41, 42], asymptotic behavior [43], integer preference [44], zero-force theorem, memory effects [45]. 

Furthermore, we will cover recent developments for XC approximations beyond the density and its gradients such as the conditional probability densities [46, 47], orbital densities [48], pair densities, and other quantities.

Applying DFT to systems of ever-increasing size is limited by the formally cubic scaling of the KS equations. Circumventing this computational bottleneck is an active area of research and is tackled by orbital-free DFT  [49], linear-scaling algorithms [50], and stochastic methods [51].

Finally, formal developments in DFT are also driven by related methods such as many-body perturbation theory [52], wavefunction theory, and embedding methods [53, 54, 55].

Additionally, our workshop will cover two rapidly emerging topics: Employing machine learning for improving and accelerating DFT calculations are active lines of research [56, 57, 58]. 

Likewise, utilizing DFT in the warm-dense-matter (WDM) regime [59, 60, 61] is an emerging field enabling novel applications in the astrophysical domain (planetary cores, brown dwarfs, white dwarfs, and neutron star atmospheres) and supporting progress towards inertial confinement fusion. However, the unique temperature-pressure phase space of WDM poses significant challenges for first principles methods [62, 63, 64, 65, 66, 67, 68, 69], which will be addressed in our workshop.