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.

The atomic simulation environment-a Python library for working with atoms.

The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

Reproducibility in density functional theory calculations of solids.

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Interaction energies in non-covalently bound intermolecular complexes derived using the subsystem formulation of density functional theory.

Interaction energies for a representative sample of 39 intermolecular complexes are calculated using two computational approaches based on the subsystem formulation of density functional theory introduced by Cortona (Phys. Rev. B 44:8454, 1991), adopted for studies of intermolecular complexes (Wesolowski and Weber in Chem. Phys. Lett. 248:71, 1996). The energy components (exchange-correlation and non-additive kinetic) expressed as explicit density functionals are approximated by means of gradient-free- (local density approximation) of gradient-dependent- (generalized gradient approximation) approximations. The sample of the considered intermolecular complexes was used previously by Zhao and Truhlar to compare the interaction energies derived using various methods based on the Kohn-Sham equations with high-level quantum chemistry results considered as the reference. It stretches from rare gas dimers up to strong hydrogen bonds. Our results indicate that the subsystem-based methods provide an interesting alternative to that based on the Kohn-Sham equations. Local density approximation, which is the simplest approximation for the relevant density functionals and which does not rely on any empirical data, leads to a computational approach comparing favorably with more than twenty methods based on the Kohn-Sham equations including the ones, which use extensively empirical parameterizations. For various types of non-bonding interactions, the strengths and weaknesses of gradient-free and gradient-dependent approximations to exchange-correlation and non-additive kinetic energy density functionals are discussed in detail.

Equilibrium Geometries of Noncovalently Bound Intermolecular Complexes Derived from Subsystem Formulation of Density Functional Theory.

The subsystem formulation of density functional theory is used to obtain equilibrium geometries and interaction energies for a representative set of noncovalently bound intermolecular complexes. The results are compared with literature benchmark data. The range of applicability of two considered approximations to the exchange-correlation- and nonadditive kinetic energy components of the total energy is determined. Local density approximation, which does not involve any empirical parameters, leads to excellent intermolecular equilibrium distances for hydrogen-bonded complexes (maximal error 0.13 Å for NH3-NH3). It is a method of choice for a wide class of weak intermolecular complexes including also dipole-bound and the ones formed by rare gas atoms or saturated hydrocarbons. The range of applicability of the chosen generalized gradient approximation, which was shown in our previous works to lead to good interaction energies in such complexes, where π-electrons are involved in the interaction, remains limited to this group because it improves neither binding energies nor equilibrium geometries in the wide class of complexes for which local density approximation is adequate. An efficient energy minimization procedure, in which optimization of the geometry and the electron density of each subsystem is made simultaneously, is proposed and tested.

On the electron leak problem in orbital-free embedding calculations.

Computer simulation methods using orbital level of description only for a selected part of the larger systems are prone to the artificial charge leak to the parts which are described without orbitals. The absence of orbitals in one of the subsystems makes it impossible to impose explicitly the orthogonality condition. Using the subsystem formulation of density functional theory, it is shown that the absence of explicit condition of orthogonality between orbitals belonging to different subsystems, does not cause any breakdown of this type of description for the chosen intermolecular complexes (F(-)H(2)O and Li(+)H(2)O), for which a significant charge-leak problem could be a priori expected.

Water trapped in dibenzo-18-crown-6: theoretical and spectroscopic (IR, Raman) studies.

Experimental (IR and Raman) and theoretical (Kohn-Sham calculations) methods are used in a combined analysis aimed at refining the available structural data concerning the molecular guests in channels formed by stacked dibenzo-18-crown-6 (DB18C6) crown ether. The calculations are performed for a simplified model comprising isolated DB18C6 unit and its complexes with either H2O or H3O+ guests, which are the simplest model ingredients of a one-dimensional diluted acid chain, to get structural and energetic data concerning the formation of the complex and to assign the characteristic spectroscopic bands. The oxygen centers in the previously reported crystallographic structure are assigned to either H2O or protonated species.

Mechanism of nitrate reduction by Desulfovibrio desulfuricans nitrate reductase--a theoretical investigation.

The oxidative half-reaction of oxygen atom transfer from nitrate to an Mo(IV) complex has been investigated at various levels of theory. Two models have been used to simulate the enzyme active site. In the second, more advanced model, additional amino acid residues capable of significantly affecting the catalytic efficiency of the enzyme were included. B3LYP/6-31+G*, ONIOM, and orbital-free embedding approaches have been used to construct the potential energy profile and to qualitatively compare the results of a QM/MM study with those obtained by a full quantum mechanical strategy. The study has confirmed the utility of the orbital-free embedding method in the description of enzymatic processes.

Nonlinearity of the Bifunctional of the Nonadditive Kinetic Energy: Numerical Consequences in Orbital-Free Embedding Calculations.

The bifunctional of the nonadditive kinetic energy in the reference system of noninteracting electrons ([Formula: see text] [ρA, ρB] = Ts[ρA + ρB] - Ts[ρA] - Ts[ρB]) is the key quantity in orbital-free embedding calculations because they hinge on approximations to[Formula: see text] [ρA,ρB]. Since[Formula: see text] [ρA,ρB] is not linear in ρA, the associated potential (functional derivative)[Formula: see text] [ρ,ρB]/δρ|ρ=ρA(r⃗) changes if ρA varies. In this work, for two approximations to[Formula: see text] [ρA,ρB], which are nonlinear in ρA (gradient-free and gradient-dependent), their linearized versions are constructed, and the resulting changes (linearization errors) in various properties of embedded systems (orbital energies, dipole moments, interaction energies, and electron densities) are analyzed. The considered model embedded systems represent typical nonbonding interactions: van der Waals contacts, hydrogen bonds, complexes involving charged species, and intermolecular complexes of the charge-transfer character. For van der Waals and hydrogen bonded complexes, the linearization of[Formula: see text] [ρA,ρB] affects negligibly the calculated properties. Even for complexes, for which large complexation induced changes of the electron density can be expected, such as the water molecule in the field of a cation, the linearization errors are about 2 orders of magnitude smaller than the interaction induced shifts of the corresponding properties. Linearization of[Formula: see text] [ρA,ρB] is shown to be inadequate for the complexes of a strong charge-transfer character. Compared to gradient-free approximation to[Formula: see text] [ρA,ρB], introduction of gradients increases the linearization error.