Local Fitting of the Kohn–Sham Density in a Gaussian and Plane Waves Scheme for Large-Scale Density Functional Theory Simulations

A local resolution-of-the-identity (LRI) approach is introduced in combination with the Gaussian and plane waves (GPW) scheme to enable large-scale Kohn–Sham density functional theory calculations. In GPW, the computational bottleneck is typically the description of the total charge density on real-space grids. Introducing the LRI approximation, the linear scaling of the GPW approach with respect to system size is retained, while the prefactor for the grid operations is reduced. The density fitting is an <i>O</i>(<i>N</i>) scaling process implemented by approximating the atomic pair densities by an expansion in one-center fit functions. The computational cost for the grid-based operations becomes negligible in LRIGPW. The self-consistent field iteration is up to 30 times faster for periodic systems dependent on the symmetry of the simulation cell and on the density of grid points. However, due to the overhead introduced by the local density fitting, single point calculations and complete molecular dynamics steps, including the calculation of the forces, are effectively accelerated by up to a factor of ∼10. The accuracy of LRIGPW is assessed for different systems and properties, showing that total energies, reaction energies, intramolecular and intermolecular structure parameters are well reproduced. LRIGPW yields also high quality results for extended condensed phase systems such as liquid water, ice XV, and molecular crystals

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

A novel algorithm, based on a hybrid Gaussian and plane waves (GPW) approach, is developed for the canonical second-order Møller–Plesset perturbation energy (MP2) of finite and extended systems. The key aspect of the method is that the electron repulsion integrals (<i>ia</i>|<i>λσ</i>) are computed by direct integration between the products of Gaussian basis functions <i>λσ</i> and the electrostatic potential arising from a given occupied-virtual pair density <i>ia</i>. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. In particular, for condensed phase systems, this scheme is highly efficient. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed within minutes, while systems up to 1000 atoms and 10 000 basis functions remain feasible. Solid LiH has been employed as a benchmark to study basis set and system size convergence. Lattice constants and cohesive energies of various molecular crystals have been studied with MP2 and double-hybrid functionals

<i>GW</i> in the Gaussian and Plane Waves Scheme with Application to Linear Acenes

We present an implementation of <i>G</i>₀<i>W</i>₀ and eigenvalue-self-consistent <i>GW</i> (ev<i>GW</i>) in the Gaussian and plane waves scheme for molecules. We calculate the correlation self-energy for imaginary frequencies employing the resolution of the identity. The correlation self-energy for real frequencies is then evaluated by analytic continuation. This technique allows an efficient parallel implementation and application to systems with several hundreds of atoms. Various benchmark calculations are presented. In particular, the convergence with respect to the most important numerical parameters is assessed for the benzene molecule. Comparisons with respect to other <i>G</i>₀<i>W</i>₀ implementations are reported for a set of molecules, while the performance of the method has been measured for water clusters containing up to 480 atoms in a cc-TZVP basis. Additionally, <i>G</i>₀<i>W</i>₀ has been applied for studying the influence of the ligands on the gap of small CdSe nanoparticles. ev<i>GW</i> has been employed to calculate the HOMO–LUMO gaps of linear acenes, linear chains formed of connected benzene rings. Distinct differences between the closed and the open-shell (broken-symmetry) ev<i>GW</i> HOMO–LUMO gaps for long acenes are found. In future experiments, a comparison of measured HOMO–LUMO gaps and our calculated ev<i>GW</i> values may be helpful to determine the electronic ground state of long acenes

Efficient Linear-Scaling Density Functional Theory for Molecular Systems

Despite recent progress in linear scaling (LS) density function theory (DFT), the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate nonself-consistent approach. We demonstrate that, even for challenging condensed-phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those previously treated

Thermal Effects on CH₃NH₃PbI₃ Perovskite from <i>Ab Initio</i> Molecular Dynamics Simulations

We present a molecular dynamics simulation study of CH₃NH₃PbI₃ based on forces calculated from density functional theory. The simulations were performed on model systems having 8 and 27 unit cells, and for a total simulation time of 40 ps in each case. Analysis of the finite size effects, in particular the mobility of the organic component, suggests that the smaller system is over-correlated through the long-range electrostatic interaction. In the larger system, this finite size artifact is relaxed, producing a more reliable description of the anisotropic rotational behavior of the methylammonium molecules. The thermal effects on the optical properties of the system were also analyzed. The HOMO–LUMO energy gap fluctuates around its central value with a standard deviation of approximately 0.1 eV. The projected density of states consistently place the Fermi level on the p orbitals of the I atoms and the lowest virtual state on the p orbitals of the Pb atoms throughout the whole simulation trajectory

Local Disorder in Lithium Imide from Density Functional Simulation and NMR Spectroscopy

Born–Oppenheimer molecular dynamics simulations in combination with calculations of ¹H, ⁷Li, and ¹⁵N NMR chemical shifts are used to characterize lithium imide structures at different temperatures. Indications of the onset of local disorder in the lithium sublattice, leading eventually to superionicity, are recognized already at low temperature (100 K). Between 100 and 400 K, a new structure could be stabilized, which presents features that are intermediate between the previously reported <i>Fm</i>3<i>m̅</i> and the <i>Fd</i>3<i>m̅</i> structures. The disorder in the Li positions is associated with the reorientation of the NH bonds, which preferentially point toward Li-vacant sites. Clear signatures of such structural rearrangements are visible in the simulated NMR spectra, where smoother profiles are associated with a reduced amount of Li interstitials and a higher occupation probability of the antifluorite sites

Computational Investigation and Design of Cobalt Aqua Complexes for Homogeneous Water Oxidation

We study the water oxidation mechanism of the cobalt aqua complex [Co­(H₂O)₆]²⁺ in a photocatalytic setup by means of density functional theory. Assuming a water-nucleophilic-attack or radical coupling mechanism, we investigate how the oxidation state and spin configuration change during the catalytic cycle. In addition, different ligand environments are employed by substituting a water ligand with a halide, pyridine, or derivative thereof. This allows exploration of the effect of such ligands on the frontier orbitals and the thermodynamics of the water oxidation process. Moreover, the thermodynamically most promising water oxidation catalyst can be identified by comparing the computed free energy profiles to the one of an “ideal catalyst”. Examination of such simple (hypothetical) water oxidation catalysts provides a basis for the derivation of design guidelines, which are highly sought for the development of efficient homogeneous water oxidation catalysts

Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

MP2 provides a good description of hydrogen bonding in water clusters and includes long-range dispersion interactions without the need to introduce empirical elements in the description of the interatomic potential. To assess its performance for bulk liquid water under ambient conditions, an isobaric–isothermal (<i>NpT</i>) Monte Carlo simulation at the second-order Møller–Plesset perturbation theory level (MP2) has been performed. The obtained value of the water density is excellent (1.02 g/mL), and the calculated radial distribution functions are in fair agreement with experimental data. The MP2 results are compared to a few density functional approximations, including semilocal functionals, hybrid functionals, and functionals including empirical dispersion corrections. These results demonstrate the feasibility of directly sampling the potential energy surface of condensed-phase systems using correlated wave function theory, and their quality paves the way for further applications

Coverage Effect of the CO₂ Adsorption Mechanisms on CeO₂(111) by First Principles Analysis

The adsorption of carbon dioxide on CeO₂(111) has been studied using density functional theory. At low coverage (1/9 monolayer), CO₂ is found to preferably adsorb in a monodentate configuration forming a carbonate species with a surface O atom. In this configuration, the CO₂ molecule is bent with an O–C–O angle of 129° and a remarkable elongation (to 1.27 Å) of the C–O bond length compared to the gas phase molecule, indicating a high degree of CO₂ activation. A similar activation is observed when the CO₂ molecule adsorbs as bidentate carbonate; however, this configuration is less stable. Linear configurations are found to adsorb very weakly at low coverage by physisorption. Increasing the coverage leads to a decrease of the stability of mono- and bidentate configurations which can be attributed to repulsive interactions between adjacent adsorbates and the limited capacity of the CeO₂(111) surface to donate electrons to the adsorbates. In contrast, the binding energy of linearly adsorbed CO₂ is shown to be coverage independent. At coverages >1/4 monolayer, we have also addressed the stability of mixed configurations where monodentate, bidentate, and linear species are present simultaneously on the surface. The most stable configurations are found when 1/3 monolayer CO₂ is bound as monodentate species, and additional molecules are physisorbed forming partial layers of linear species. Analysis of the projected density of states has shown that the orbitals of linear species in the first partial layer lie at lower energies than the ones of the second partial layer suggesting stabilization of the former through interactions with preadsorbed monodentate species. These findings provide fundamental insight into the CO₂ adsorption mechanism on CeO₂ and potentially assist the design of new Ce-based materials for CO₂ catalysis