In the last 50 years, density functional theory (DFT) has been the working horse of materials simulation.1 DFT success comes from its relatively low computational cost compared to other electronic structure approaches and an often acceptable accuracy. The reliability of DFT has increased over time, thanks to a continuous effort to improve the exchange–correlation (XC) functional approximations. In the last 15 years, DFT also showed a huge improvement in the description of van der Waals dispersion interactions,2,3 which has been for long time an issue due to its non-local nature. A good level of reproducibility of DFT results across different software implementations was recently shown.4 Generally, DFT applications to materials science employ the generalized gradient approximations (GGA) functionals, and the vast majority of studies focus on zero Kelvin total energies. This approach has been useful and has considerably deepened understanding of solids and surfaces; it has, e.g., been the cornerstone of what may become the computational materials discovery revolution. However, for many materials and physical phenomena, this approach is inadequate because the electronic structure is not correctly described by the DFT functionals5–9 used and/or thermal and quantum effects are important.
This special topic will look at work that goes beyond standard DFT total energies with better quality electronic structure methods (higher rung XC functionals, quantum chemistry methods, many body methods, stochastic methods, etc.) and appropriate treatment of thermal and quantum effects. Papers in this special topic demonstrate interest in improving the accuracy, precision, and efficiency of modern electronic structure theories for a wide range of applications. The employed methods include DFT, quantum Monte Carlo (QMC), Green’s function based approaches, and quantum chemical wavefunction based theories.
A large number of articles included in this special topic aim at benchmarking the accuracy of widely used methods for different properties of molecules, solids, and surfaces. QMC methods are employed to study adsorption energies of single atoms on graphite and graphene.10,11 The obtained benchmark results can be employed to improve the accuracy of computationally more efficient approaches. Reference 12 employs QMC to determine Hubbard repulsion parameters for DFT+U calculations in zigzag graphene nanoribbons. Quantum chemical methods on the level of coupled-cluster theory are employed to compute benchmark results in Ref. 13 to investigate the accuracy of a variety of van der Waals-inclusive density functional theory models for intra- and intermolecular interactions of organic molecules. Reference 14 employs a similar range of density functionals for the study of adsorption energies in diamine-functionalized metal–organic frame-works. As demonstrated in Ref. 15, QMC can also be used to compute accurate structural, magnetic, and phonon properties of monolayer CrI3. For the study of CH4 adsorption on the Pt(111) surface, Ref. 16 employs the random-phase approximation to benchmark density functional theory using the Perdew–Burke–Ernzerhof functional augmented with the many-body dispersion scheme of Tkatchenko. In addition to benchmarking approximations to the electronic correlation energy, it is equally important to describe vibrational entropy effects of real materials at the same level of accuracy. Reference 17 reports a density-functional benchmark of harmonic vibrational free-energy corrections for molecular crystal polymorphism.
Recently, the scope of quantum chemical methods, such as coupled cluster theory or even full configuration interaction quantum Monte Carlo methods, has been significantly expanded by employing embedding approaches. This is also illustrated by a number of applications in the present special topic. Reference 18 presents a general embedded cluster protocol for accurate modeling of oxygen vacancies in metal-oxides. For the study of the dissociation of a fluorine atom from a fluorographane surface, Ref. 19 employs an embedded fragment approach. The authors of Ref. 20 use periodic and embedded fragment models to explore hydrogen diffusion on a α-Al2O3(0001). Furthermore, in-RPA-embedding is employed in Ref. 21 to study water adsorption on a monolayer of graphitic carbon nitride.
It should be noted that the need for accurate benchmark results is not limited to ground state properties of materials. As described in Ref. 22, quasi particle energies of solvated benzene radical anion also require a sophisticated treatment that goes beyond DFT approaches.
Many systems are too large to be studied by highly accurate but computationally expensive many-electron theories. In these cases, tailored DFT-based approaches are still often feasible and achieve a good level of accuracy, provided suitable parametrizations can be found. The efficiency of DFT-based studies even allows for performing high-throughput calculations. Such an approach is employed in Ref. 23 to explore cesium–tellurium phase space, employing meta-generalized gradient approximation to the density functional. An identical density functional was employed in Ref. 24 to revisit the link between magnetic properties and chemisorption at the graphene nanoribbon zigzag edge. The importance of van der Waals corrections in the employed meta-generalized gradient density functional for certain applications is again illustrated in Ref. 25 for the example oxygen adsorption on Ag(111). For the study of metal–organic frameworks containing more than 2500 atoms in the unit cell, Ref. 26 employs tailored hybrid functionals in a small basis in combination with semi-classical corrections to account for dispersive interactions and the basis set superposition error.
In addition to the applications referred to above, this special topic includes articles that focus on methodological developments of accurate electronic structure theories and their implementations. Reference 27 describes a regularized second-order correlation method for extended systems that can also be applied to metals. Reference 28 explains an algorithm for massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functional calculations. The precision of Gaussian-orbital-based periodic calculations on the level of DFT is investigated in Ref. 29. Reference 30 investigates the efficiency of the force calculation algorithm on different levels of Monte Carlo theories using the so-called space-warp coordinate transformation. The calculation of forces, gradients, and stress tensors is also investigated on the level of DFT double hybrid functionals in Ref. 31, including an application to water.
The papers in this special topic, thus, demonstrate interest (and successes) in improving the accuracy, precision, and efficiency of modern electronic structure theories for a wide range of applications. They also lay the foundation for achieving similar improvements on the calculation of thermal and nuclear quantum effects, which will surely be the subject of many successful studies in the years to come.