GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

High-Throughput Search for Triplet Point Defects with Narrow Emission Lines in 2D Materials.

We employ a first-principles computational workflow to screen for optically accessible, high-spin point defects in wide band gap, two-dimensional (2D) crystals. Starting from an initial set of 5388 point defects, comprising both native and extrinsic, single and double defects in ten previously synthesized 2D host materials, we identify 596 defects with a triplet ground state. For these defects, we calculate the defect formation energy, hyperfine (HF) coupling, and zero-field splitting (ZFS) tensors. For 39 triplet transitions exhibiting particularly low Huang-Rhys factors, we calculate the full photoluminescence (PL) spectrum. Our approach reveals many spin defects with narrow PL line shapes and emission frequencies covering a broad spectral range. Most of the defects are hosted in hexagonal BN (hBN), which we ascribe to its high stiffness, but some are also found in MgI2, MoS2, MgBr2 and CaI2. As specific examples, we propose the defects vSMoS0 and NiSMoS0 in MoS2 as interesting candidates with potential applications to magnetic field sensors and quantum information technology.

Efficient first principles simulation of electron scattering factors for transmission electron microscopy.

Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These typically use the independent atom approximation that neglects bonding effects, which may, however, be measurable and of physical interest. Since all electrons and the nuclear cores contribute to the scattering potential, simulations that go beyond this approximation have relied on computationally highly demanding all-electron calculations. Here, we describe a new method to generate ab initio electrostatic potentials when describing the core electrons by projector functions. Combined with an interface to quantitative image simulations, this implementation enables an easy and fast means to model electron scattering. We compare simulated transmission electron microscopy images and diffraction patterns to experimental data, showing an accuracy equivalent to earlier all-electron calculations at a much lower computational cost.

Interfacing CRYSTAL/AMBER to Optimize QM/MM Lennard⁻Jones Parameters for Water and to Study Solvation of TiO2 Nanoparticles.

Metal oxide nanoparticles (NPs) are regarded as good candidates for many technological applications, where their functional environment is often an aqueous solution. The correct description of metal oxide electronic structure is still a challenge for local and semilocal density functionals, whereas hybrid functional methods provide an improved description, and local atomic function-based codes such as CRYSTAL17 outperform plane wave codes when it comes to hybrid functional calculations. However, the computational cost of hybrids are still prohibitive for systems of real sizes, in a real environment. Therefore, we here present and critically assess the accuracy of our electrostatic embedding quantum mechanical/molecular mechanical (QM/MM) coupling between CRYSTAL17 and AMBER16, and demonstrate some of its capabilities via the case study of TiO2 NPs in water. First, we produced new Lennard⁻Jones (LJ) parameters that improve the accuracy of water⁻water interactions in the B3LYP/TIP3P coupling. We found that optimizing LJ parameters based on water tri- to deca-mer clusters provides a less overstructured QM/MM liquid water description than when fitting LJ parameters only based on the water dimer. Then, we applied our QM/MM coupling methodology to describe the interaction of a 1 nm wide multilayer of water surrounding a spherical TiO2 nanoparticle (NP). Optimizing the QM/MM water⁻water parameters was found to have little to no effect on the local NP properties, which provide insights into the range of influence that can be attributed to the LJ term in the QM/MM coupling. The effect of adding additional water in an MM fashion on the geometry optimized nanoparticle structure is small, but more evident effects are seen in its electronic properties. We also show that there is good transferability of existing QM/MM LJ parameters for organic molecules⁻water interactions to our QM/MM implementation, even though these parameters were obtained with a different QM code and QM/MM implementation, but with the same functional.

Ab initio van der waals interactions in simulations of water alter structure from mainly tetrahedral to high-density-like.

The structure of liquid water at ambient conditions is studied in ab initio molecular dynamics simulations in the NVE ensemble using van der Waals (vdW) density-functional theory, i.e., using the new exchange-correlation functionals optPBE-vdW and vdW-DF2, where the latter has softer nonlocal correlation terms. Inclusion of the more isotropic vdW interactions counteracts highly directional hydrogen bonds, which are enhanced by standard functionals. This brings about a softening of the microscopic structure of water, as seen from the broadening of angular distribution functions and, in particular, from the much lower and broader first peak in the oxygen-oxygen pair-correlation function (PCF) and loss of structure in the outer hydration shells. Inclusion of vdW interactions is shown to shift the balance of resulting structures from open tetrahedral to more close-packed. The resulting O-O PCF shows some resemblance with experiment for high-density water (Soper, A. K. and Ricci, M. A. Phys. Rev. Lett. 2000, 84, 2881), but not directly with experiment for ambient water. Considering the accuracy of the new functionals for interaction energies, we investigate whether the simulation protocol could cause the deviation. An O-O PCF consisting of a linear combination of 70% from vdW-DF2 and 30% from low-density liquid water, as extrapolated from experiments, reproduces near-quantitatively the experimental O-O PCF for ambient water. This suggests the possibility that the new functionals may be reliable and that instead larger-scale simulations in the NPT ensemble, where the density is allowed to fluctuate in accordance with proposals for supercooled water, could resolve the apparent discrepancy with the measured PCF.

Time-dependent density-functional theory in the projector augmented-wave method.

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.