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.

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials.

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H2O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

Polarizable Force Field for Acetonitrile Based on the Single-Center Multipole Expansion.

A polarizable potential function describing the interaction between acetonitrile molecules is introduced. The molecules are described as rigid and linear, with three mass sites corresponding to the CH3 group (methyl, Me), the central carbon atom (C), and the nitrogen atom (N). The electrostatic interaction is represented using a single-center multipole expansion as has been done previously for H2O [Wikfeldt et al., Phys. Chem. Chem. Phys. 15, 16542 (2013)], by including multipole moments from dipole up to and including hexadecapole, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model is free of point charges. The non-electrostatic part is described in a pair-wise fashion by a Born-Mayer repulsion and damped dispersion attraction. The potential function is parameterized to fit the interaction energy of small (CH3CN)n, n = 2-6, clusters calculated using the PBE0 hybrid functional with an additional atomic many-body dispersion contribution. The parameterized potential function is found to compare well with results of the electronic structure calculations of dissociation curves for different dimer orientations and cohesive properties (the equilibrium volume, cohesive energy, and the bulk modulus) of the α-phase of acetonitrile crystal. The average value of the molecular dipole moment obtained in the α-phase is 5.53 D, corresponding to ca. 40% increase as compared to the dipole moment of an isolated acetonitrile molecule, 3.92 D. The calculated densities of solid and liquid acetonitrile turn out to be 8-10% higher than experimental values. This appears to be caused by an overestimate of the atomic many-body dispersion interaction in the density functional calculations used as input in the parametrization of the potential function.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion.

A potential function is presented for describing a system of flexible H2O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H2O)n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Elastic Collision Based Dynamic Partitioning Scheme for Hybrid Simulations.

In hybrid simulations, such as the QM/MM approach, the system is partitioned into regions that are treated at different levels of theory. The key question then becomes how to evaluate the interactions between particles on opposite sides of the boundary. One approach is to place the boundary in such a way that particles near the boundary on both sides are of the same type, thus simplifying the evaluation of the interactions. If mobile particles are present, such as solvent molecules, and particles are allowed to cross the boundary, the conservation of energy and atomic forces is problematic unless the computational effort is increased significantly. By preventing particles from crossing the boundary but allowing the boundary to be flexible, an accurate estimate of average thermodynamic properties is obtained in principle as illustrated by the flexible inner region ensemble separator (FIRES) method [C. Rowley and B. Roux, J. Chem. Theory Comput. 2012, 8, 3526]. In FIRES, a harmonic restraint is applied to particles near the boundary. Therefore, it can occur that particle cross the boundary to some extent resulting in anomalies in the particle density. Here, a constraint approach is presented where particles instantaneously scatter from the boundary. This scattering-adapted FIRES (SAFIRES) implementation makes use of a variable-time-step propagation algorithm where the time step is scaled automatically to identify the moment a collision should occur. If the length of the time step is kept constant, this propagator reduces to a regular Langevin dynamics algorithm, and to the velocity Verlet algorithm for conservative dynamics if the friction coefficient is set to zero. Correct average ensemble statistics are obtained as demonstrated in simulations where, for testing purposes, the particles in the two regions are treated at the same level of theory, namely, a homogeneous Lennard-Jones (LJ) liquid and liquid water based on the TIP4P potential function. In order to illustrate this approach in solid-liquid interface simulations, a LJ liquid in contact with the surface of a crystal is also simulated. The simulations using SAFIRES are shown to reproduce the unconstrained reference simulations without significant deviations in the particle density and the dynamics are shown to conserve energy when coupling to the heat bath is turned off.

Polarizable Embedding with a Transferable H2O Potential Function II: Application to (H2O)n Clusters and Liquid Water.

The incorporation of polarization in multiscale quantum-mechanics/molecular-mechanics (QM/MM) simulations is important for a variety of applications, for example, charge-transfer reactions. A recently developed formalism based on a density functional theory description of the QM region and a potential energy function for H2O molecules that includes quadrupole as well as dipole polarizability of the MM region is used to simulate liquid water and water clusters. Analysis of the energy, atomic forces, MM polarization, and structure is presented. A quantitative assessment of the QM/MM-MM/MM interaction energy differences of all possible QM/MM configurations of (H2O)n clusters shows that the interquartile range of the distributions of the QM/MM binding energies is never more than 20 meV/molecule higher or lower than the binding energies produced with either of the single-model results. Comparing these interaction energy differences with the QM/MM induction differences show that they are not systematically caused by the induced MM moments of our polarizable embedding scheme. Optimized hexamer geometries as well as the liquid water structure are shown to be improved in comparison with results obtained using point-charge based embedding models neglecting polarization.

Polarizable Embedding with a Transferable H2O Potential Function I: Formulation and Tests on Dimer.

The incorporation of mutual polarization in multiscale simulations where different regions of the system are treated at different level of theory is important in studies of, for example, electronic excitations and charge transfer processes. We present here an energy functional for describing a quantum mechanics/molecular mechanics (QM/MM) scheme that includes reciprocal polarization between the two subsystems. The inclusion of polarization alleviates shortcomings inherent in electrostatic embedding QM/MM models based on point-charge force fields. A density functional theory (DFT) description of the QM subsystem is coupled to a single center multipole expansion (SCME) description of H2O molecules in the MM subsystem that includes anisotropic dipole and quadrupole polarizability as well as static multipoles up to and including the hexadecapole. The energy functional and the coupling scheme is general and can be extended to arbitrary order in terms of both the static and induced moments. Tests of the energy surface for the H2O dimer show that the QM/MM results lie in between the pure DFT and pure SCME values. The consistency of the many-body contributions to the energy and analytical forces is demonstrated for an H2O pentamer.

Folding of the cocaine aptamer studied by EPR and fluorescence spectroscopies using the bifunctional spectroscopic probe Ç.

The cocaine aptamer is a DNA molecule that binds cocaine at the junction of three helices. The bifunctional spectroscopic probe Ç was incorporated independently into three different positions of the aptamer and changes in structure and dynamics upon addition of the cocaine ligand were studied. Nucleoside Ç contains a rigid nitroxide spin label and can be studied directly by electron paramagnetic resonance (EPR) spectroscopy and fluorescence spectroscopy after reduction of the nitroxide to yield the fluoroside Ç(f). Both the EPR and the fluorescence data for aptamer 2 indicate that helix III is formed before cocaine binding. Upon addition of cocaine, increased fluorescence of a fully base-paired Ç(f), placed at the three-way junction in helix III, was observed and is consistent with a helical tilt from a coaxial stack of helices II and III. EPR and fluorescence data clearly show that helix I is formed upon addition of cocaine, concomitant with the formation of the Y-shaped three-way helical junction. The EPR data indicate that nucleotides in helix I are more mobile than nucleotides in regular duplex regions and may reflect increased dynamics due to the short length of helix I.