Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions

Unraveling the Hydration Shell Structure and Dynamics of Group 10 Aqua Ions

We present ab initio simulations based on subsystem DFT of group 10 aqua ions accurately compared against experimental data on hydration structure. Our simulations provide insights into the molecular structures and dynamics of hydration shells, offering recalibrated interpretations of experimental results. We observe a soft, but distinct second hydration shell in Palladium (Pd) due to a balance between thermal fluctuations, metal-water interactions, and hydrogen bonding. Nickel (Ni) and platinum (Pt) exhibit more rigid hydration shells. Notably, our simulations align with experimental findings for Pd, showing axial hydration marked by a broad peak at about 3 Å in the Pd-O radial distribution function, revising the previously sharp "mesoshell" prediction. We introduce the "hydrogen bond dome" concept to describe a resilient network of hydrogen-bonded water molecules around the metal, which plays a critical role in the axial hydration dynamics.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

A variational formulation of the Harris functional as a correction to approximate Kohn-Sham density functional theory

Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn-Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.

Pushing the limits: Efficient wavefunction methods for excited states in complex systems using frozen-density embedding

Frozen density embedding (FDE) is an embedding method for complex environments that is simple for users to set up. It reduces the computation time by dividing the total system into small subsystems and approximating the interaction by a functional of their densities. Its combination with wavefunction methods is, however, limited to small- or medium-sized molecules because of the steep scaling in computation time of these methods. To mitigate this limitation, we present a combination of the FDE approach with pair natural orbitals (PNOs) in the TURBOMOLE software package. It combines the uncoupled FDE (FDEu) approach for excitation energy calculations with efficient implementations of second-order correlation methods in the ricc2 and pnoccsd programs. The performance of this combination is tested for tetraazaperopyrene (TAPP) molecular crystals. It is shown that the PNO truncation error on environment-induced shifts is significantly smaller than the shifts themselves and, thus, that the local approximations of PNO-based wavefunction methods can without the loss of relevant digits be combined with the FDE method. Computational wall times are presented for two TAPP systems. The scaling of the wall times is compared to conventional supermolecular calculations and demonstrates large computational savings for the combination of FDE- and PNO-based methods. Additionally, the behavior of excitation energies with the system size is investigated. It is found that the excitation energies converge quickly with the size of the embedding environment for the TAPPs investigated in the current study.

Adaptive Subsystem Density Functional Theory

Subsystem density functional theory (DFT) is emerging as a powerful electronic structure method for large-scale simulations of molecular condensed phases and interfaces. Key to its computational efficiency is the use of approximate nonadditive noninteracting kinetic energy functionals. Unfortunately, currently available nonadditive functionals lead to inaccurate results when the subsystems interact strongly such as when they engage in chemical reactions. This work disrupts the status quo by devising a workflow that extends subsystem DFT's applicability also to strongly interacting subsystems. This is achieved by implementing a fully automated adaptive definition of subsystems which is realized during geometry optimizations or ab initio molecular dynamics simulations. The new method prescribes subsystem merging and splitting events redistributing the resources (both for work and data) in an efficient way making use of modern parallelization strategies and object-oriented programming. We showcase the method with examples probing from moderate-to-strong inter-subsystem interactions, opening the door to using subsystem DFT for modeling chemical reactions in molecular condensed phases with a black box computational tool.

Density Embedding Method for Nanoscale Molecule-Metal Interfaces

In this work, we extend the applicability of standard Kohn-Sham DFT (KS-DFT) to model realistically sized molecule-metal interfaces where the metal slabs venture into the tens of nanometers in size. Employing state-of-the-art noninteracting kinetic energy functionals, we describe metallic subsystems with orbital-free DFT and combine their electronic structure with molecular subsystems computed at the KS-DFT level resulting in a multiscale subsystem DFT method. The method reproduces within a few millielectronvolts the binding energy difference of water and carbon dioxide molecules adsorbed on the top and hollow sites of an Al(111) surface compared to KS-DFT of the combined supersystem. It is also robust for Born-Oppenheimer molecular dynamics simulations. Very large system sizes are approached with standard computing resources thanks to a parallelization scheme that avoids accumulation of memory at the gather-scatter stage. The results as presented are encouraging and open the door to ab initio simulations of realistically sized, mesoscopic molecule-metal interfaces.

Orbital-Free Methods for Plasmonics: Linear Response

Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.

Role of Dielectric Screening in Calculating Excited States of Solvated Azobenzene: A Benchmark Study Comparing Quantum Embedding and Polarizable Continuum Model for Representing the Solvent

The low energy excited states of the conformational isomers of solvated azobenzene are calculated with several DFT methods accounting for the solute-solvent interaction implicitly with the polarizable continuum model or explicitly with subsystem DFT. For the latter, embedding potentials are calculated for 21 sampled snapshots of the solvent molecules. First, we find that accounting for the solvent implicitly or explicitly has little effect on the predicted cis-trans S₁ excitation energy gap. Second, we find that azobenzene's S₁ cis and trans energies are accurate as long as a screened range-separated hybrid exchange-correlation functional is employed. Finally, we also tested a simplified workflow whereby a single, averaged, embedding potential is used. Unfortunately, we find larger deviations against the experiment for the simplified workflow. This highlights a basic flaw in the approach, where the time scale of solvent averaging is much longer than that of the solute's electronic polarization.

Revisiting the trapping of noble gases (He-Kr) by the triatomic H3+ and Li3+ species: a density functional reactivity theory study

Small atomic clusters with exotic stability, bonding, aromaticity, and reactivity properties can be made use of for various purposes. In this work, we revisit the trapping of noble gas atoms (He-Kr) by the triatomic H₃⁺ and Li₃⁺ species by using some analytical tools from density functional theory, conceptual density functional theory, and the information-theoretic approach. Our results showcase that though similar in geometry, H₃⁺ and Li₃⁺ exhibit markedly different behavior in bonding, aromaticity, and reactivity properties after the addition of noble gas atoms. Moreover, the exchange-correlation interaction and steric effect are key energy components in stabilizing the clusters. This study also finds that the origin of the molecular stability of these species is due to the spatial delocalization of the electron density distribution. Our work provides an additional arsenal towards a better understanding of small atomic clusters capturing noble gases.

Nonlocal pseudopotential energy density functional for orbital-free density functional theory

Orbital-free density functional theory (OF-DFT) is an electronic structure method with a low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations. It is generally considered that OF-DFT strictly requires the use of local pseudopotentials, rather than orbital-dependent nonlocal pseudopotentials, for the calculation of electron-ion interaction energies, as no orbitals are available. This is unfortunate situation since the nonlocal pseudopotentials are known to give much better transferability and calculation accuracy than local ones. We report here the development of a theoretical scheme that allows the direct use of nonlocal pseudopotentials in OF-DFT. In this scheme, a nonlocal pseudopotential energy density functional is derived by the projection of nonlocal pseudopotential onto the non-interacting density matrix (instead of "orbitals") that can be approximated explicitly as a functional of electron density. Our development defies the belief that nonlocal pseudopotentials are not applicable to OF-DFT, leading to the creation for an alternate theoretical framework of OF-DFT that works superior to the traditional approach.

Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

Employing Pseudopotentials to Tackle Excited-State Electron Spill-Out in Frozen Density Embedding Calculations

In frozen density embedding (FDE), the properties of a target molecule are computed in the presence of an effective embedding potential, which accounts for the attractive and repulsive contributions of the environment. The formally exact embedding potential, however, is in practice calculated using explicit kinetic-energy functionals for which the resulting potentials are in many cases not repulsive enough to account fully for Pauli repulsion by the electrons of the environment and to compensate thereby the strong electron-nuclear attraction. For the excited states on the target molecule, this leads to charge spill-out when diffuse basis functions are included, which allow that valence electrons are excited to those regions of the environment where the strong nuclear attraction is not sufficiently compensated by repulsive contributions. To reduce this insufficiency, we propose in the present work the inclusion of atomic all-electron pseudopotentials for all environment atoms on top of the conventional embedding potential. In the current work, the pseudopotentials are applied for computing vertical excitation energies of local excited states in complex systems employing the second-order algebraic diagrammatic construction (ADC(2)) scheme. The proposed approach leads to significantly reduced charge spill-out and an improved agreement of FDE and supermolecular calculations in the frozen solvent approximation. In particular, when diffuse functions are employed, the mean absolute deviation (MAD) is reduced from 0.27 to 0.05 eV for the investigated cases.

Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn-Sham Accuracy

Simulations based on electronic structure theory naturally include polarization and have no transferability problems. In particular, Kohn-Sham density functional theory (KS-DFT) has become the method of reference for ab initio molecular dynamics simulations of condensed matter systems. However, the high computational cost often poses strict limits on the affordable system size as well as on the extension of sampling (number of configurations). In this work, we propose an improvement to the subsystem density functional theory approach, known as the Kim-Gordon (KG) scheme, thus enabling the sampling of configurations for condensed molecular systems keeping the KS-DFT level accuracy at a fraction of computer time. Our scheme compensates the known KG shortcomings of the electronic kinetic energy term by adding a simple correction and can match KS-DFT accuracy in energies and forces. The computationally cheap correction is determined by means of a machine learning procedure. The proposed KG scheme is applied within a linear scaling self-consistent field formalism and is assessed by a series of molecular dynamics simulations of liquid water under different conditions. Although system-dependent, the correction is transferable between system sizes and temperatures.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.

Local Temperature as a Chemical Reactivity Descriptor

Using the electron density and its associated quantities in a molecular system to quantify chemical reactivity in density functional theory is of considerable recent interest. Local temperature based on the kinetic energy density is an intrinsic property of a molecular system, which can be employed for this purpose. In this work, we explore such a possibility. To this end, we examine the local behavior of local temperature with a few choices of the kinetic energy density, apply it to determine regioselectivity of nucleophilic and electrophilic compounds, and then investigate its performance in appreciating reactions along the intrinsic reaction pathway for exothermic, endothermic, and thermoneutral transformations. Our results confirm that local temperature can be used as an effective descriptor of molecular reactivity.

Benchmark of the Extension of Frozen-Density Embedding Theory to Nonvariational Correlated Methods: The Embedded-MP2 Case

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput. 2020, 16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys. 2019, 150, 121101]. Local density approximation is used for E_xcT^nad[ρ_A,ρ_B] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for E_xcT^nad[ρ_A,ρ_B] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for E_xcT^nad[ρ_A,ρ_B] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

GGA-Level Subsystem DFT Achieves Sub-kcal/mol Accuracy Intermolecular Interactions by Mimicking Nonlocal Functionals

The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of low-density/high reduced density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals, retaining the computational complexity of typical semilocal functionals. Crucially, this functional depends on the inter-subsystem density overlap. The new functional reproduces Kohn-Sham DFT and benchmark CCSD(T) interaction energies of weakly interacting dimers in the S22-5 and S66 test sets with a mean absolute deviation well below 1 kcal/mol.

Analysis of the kinetic energy functional in the generalized gradient approximation

A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

Role of hemibonding in the structure and ultraviolet spectroscopy of the aqueous hydroxyl radical

The presence of a two-center, three-electron hemibond in the solvation structure of the aqueous hydroxl radical has long been debated, as its appearance can be sensitive to self-interaction error in density functional theory.

Ab Initio Structure and Dynamics of CO2 at Supercritical Conditions

Green technologies rely on green solvents and fluids. Among them, supercritical CO₂ already finds many important applications. The molecular-level understanding of the dynamics and structure of this supercritical fluid is a prerequisite for rational design of future green technologies. Unfortunately, the commonly employed Kohn-Sham density functional theory (DFT) is too computationally demanding to produce meaningfully converged dynamics within a reasonable time and with a reasonable computational effort. Thanks to subsystem DFT, we analyze finite-size effects by considering simulation cells of varying sizes (up to 256 independent molecules in the cell) and finite-time effects by running 100 ps trajectories. We find that the simulations are in reasonable and semiquantitative agreement with the available neutron diffraction experiments and that, as opposed to the gas phase, the CO₂ molecules in the fluid are bent with an average OCO angle of 175.8°. Our simulations also confirm that the dimer T-shape is the most prevalent configuration. Our results further strengthen the experiment-simulation agreement for this fluid when comparing radial distribution functions and diffusion coefficient, confirming subsystem DFT as a viable tool for modeling structure and dynamics of condensed-phase systems.

The Role of the Reduced Laplacian Renormalization in the Kinetic Energy Functional Development

The Laplacian of the electronic density diverges at the nuclear cusp, which complicates the development of Laplacian-level meta-GGA (LLMGGA) kinetic energy functionals for all-electron calculations. Here, we investigate some Laplacian renormalization methods, which avoid this divergence. We developed two different LLMGGA functionals, which improve the kinetic energy or the kinetic potential. We test these KE functionals in the context of Frozen-Density-Embedding (FDE), for a large palette of non-covalently interacting molecular systems. These functionals improve over the present state-of-the-art LLMGGA functionals for the FDE calculations.

Using Pauli energy to appraise the quality of approximate semilocal non-interacting kinetic energy density functionals

It is well-known that the kinetic energy density (KED) functional is the most difficult to approximate in density functional theory (DFT), yet to take full advantage of DFT with its density-based descriptive capability of molecular properties, an accurate account of KED is a must. To have a better idea of how an approximate KED formula behaves and where we should focus in the future development of better approximate KEDs, in this work we propose to employ the Pauli energy to assess their quality. We tested the performance of a total of 22 approximate semilocal noninteracting KED functionals from the literature for 18 neutral atoms and 20 small molecules. We found that generalized gradient approximation formulas of the KED functional can often reasonably accurately predict the total kinetic energy value for atoms and molecules but failed miserably to forecast the integrated values for Pauli energy related properties. The reason behind this is that presently available approximate KED functionals are unable to accurately account for the kinetic energy distribution in the medium range away from nuclei, where the Pauli energy plays a crucial role. Our results strongly suggest that the key information missing in approximate KED functionals comes from the medium regions, not nuclear cusps nor asymptotic areas, and the Pauli energy is a reliable measure of the quality of approximate KED functionals. Future efforts in developing better KED approximations should be invested in the regions of molecules where chemical bonds are formed in order to accurately account for the Pauli energy.

Semilocal Pauli-Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids

Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of nonlocal functionals, possibly employing system-dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that, instead, properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian level of theory, can indeed achieve similar accuracy as nonlocal functionals and can be accurate for both metals and semiconductors, without the need for system-dependent parameters.

Non-additive non-interacting kinetic energy of rare gas dimers

Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

Exploiting the locality of periodic subsystem density-functional theory: efficient sampling of the Brillouin zone

In order to approximately satisfy the Bloch theorem, simulations of complex materials involving periodic systems are made n(k) times more complex by the need to sample the first Brillouin zone at n(k) points. By combining ideas from Kohn-Sham density-functional theory (DFT) and orbital-free DFT, for which no sampling is needed due to the absence of waves, subsystem DFT offers an interesting middle ground capable of sizable theoretical speedups against Kohn-Sham DFT. By splitting the supersystem into interacting subsystems, and mapping their quantum problem onto separate auxiliary Kohn-Sham systems, subsystem DFT allows an optimal topical sampling of the Brillouin zone. We elucidate this concept with two proof of principle simulations: a water bilayer on Pt[1 1 1]; and a complex system relevant to catalysis-a thiophene molecule physisorbed on a molybdenum sulfide monolayer deposited on top of an α-alumina support. For the latter system, a speedup of 300% is achieved against the subsystem DTF reference by using an optimized Brillouin zone sampling (600% against KS-DFT).

Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model (SC-HDM), where both the ground state and the excited state properties of an inhomogeneous electron gas can be determined. With this method we are able to explain the size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The results we obtain are in good agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio methods.

Frozen density embedding with non-integer subsystems' particle numbers

We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the relation between the non-integer particle-number partition scheme and the resulting embedding errors. Finally, we provide a discussion of the implications of the present theory for the derivative discontinuity issue and the calculation of chemical reactivity descriptors.

A periodic charge-dipole electrostatic model. II. A kinetic-exchange-correlation correction

We extend the periodic charge-dipole electrostatic model, see I. V. Bodrenko, M. Sierka, E. Fabiano, and F. Della Sala, J. Chem. Phys. 137, 134702 (2012), to include a kinetic-exchange-correlation (KXC) correction. The KXC correction is approximated by means of an extended-Hückel-type formula, it is exact in the infinite jellium model and it is also computationally efficient as it requires only the computation of overlap integrals. Tests on the linear response of silver slabs to an external electrostatic perturbation show that the KXC correction yields a very accurate description of induced dipole and of the whole induced charge density profile. We also show that the KXC parameters are quite transferable and related to the atomic polarizability.