Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas.

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.

Orbital-free methods for plasmonics: Linear response.

Plasmonic systems, such as metal nanoparticles, are widely used in different areas of application, 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, nonlocal 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 then be 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 and without system-tuned parameters. The accuracy of these methods depends only on the accuracy of the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will also be indicated.

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.

Minimal auxiliary basis set for time-dependent density functional theory and comparison with tight-binding approximations: Application to silver nanoparticles.

The modeling of optical spectra of plasmonic nanoparticles via first-principles approaches is computationally expensive; thus, methods with high accuracy/computational cost ratio are required. Here, we show that the Time-Dependent Density Functional Theory (TDDFT) approach can be strongly simplified if only one s-type function per atom is employed in the auxiliary basis set, with a properly optimized exponent. This approach (named TDDFT-as, for auxiliary s-type) predicts excitation energies for silver nanoparticles with different sizes and shapes with an average error of only 12 meV compared to reference TDDFT calculations. The TDDFT-as approach resembles tight-binding approximation schemes for the linear-response treatment, but for the atomic transition charges, which are here computed exactly (i.e., without approximation from population analysis). We found that the exact computation of the atomic transition charges strongly improves the absorption spectra in a wide energy range.

Nanowire-Intensified Metal-Enhanced Fluorescence in Hybrid Polymer-Plasmonic Electrospun Filaments.

Hybrid polymer-plasmonic nanostructures might combine high enhancement of localized fields from metal nanoparticles with light confinement and long-range transport in subwavelength dielectric structures. Here, the complex behavior of fluorophores coupling to Au nanoparticles within polymer nanowires, which features localized metal-enhanced fluorescence (MEF) with unique characteristics compared to conventional structures, is reported. The intensification effect when the particle is placed in the organic filaments is remarkably higher with respect to thin films of comparable thickness, thus highlighting a specific, nanowire-related enhancement of MEF effects. A dependence on the confinement volume in the dielectric nanowire is also indicated, with MEF significantly increasing upon reduction of the wire diameter. These findings are rationalized by finite element simulations, predicting a position-dependent enhancement of the quantum yield of fluorophores embedded in the fibers. Calculation of the ensemble-averaged fluorescence enhancement unveils the possibility of strongly enhancing the overall emission intensity for structures with size twice the diameter of the embedded metal particles. These new, hybrid fluorescent systems with localized enhanced emission, and the general nanowire-enhanced MEF effects associated to them, are highly relevant for developing nanoscale light-emitting devices with high efficiency and intercoupled through nanofiber networks, highly sensitive optical sensors, and novel laser architectures.

Assessment of interaction-strength interpolation formulas for gold and silver clusters.

The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different interpolation formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.

Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals.

The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method.

Accurate Kohn-Sham ionization potentials from scaled-opposite-spin second-order optimized effective potential methods.

One important property of Kohn-Sham (KS) density functional theory is the exact equality of the energy of the highest occupied KS orbital (HOMO) with the negative ionization potential of the system. This exact feature is out of reach for standard density-dependent semilocal functionals. Conversely, accurate results can be obtained using orbital-dependent functionals in the optimized effective potential (OEP) approach. In this article, we investigate the performance, in this context, of some advanced OEP methods, with special emphasis on the recently proposed scaled-opposite-spin OEP functional. Moreover, we analyze the impact of the so-called HOMO condition on the final quality of the HOMO energy. Results are compared to reference data obtained at the CCSD(T) level of theory. © 2016 Wiley Periodicals, Inc.

Hartree potential dependent exchange functional.

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

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.

Orbital-dependent second-order scaled-opposite-spin correlation functionals in the optimized effective potential method.

The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn-Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite-spin OEP functional [I. Grabowski, E. Fabiano, and F. Della Sala, Phys. Rev. B 87, 075103 (2013)] which is the most advantageous from a computational point of view. We find that for high accuracy, a careful, system dependent, selection of the scaling coefficient is required. We analyse several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort.

A simple non-empirical procedure for spin-component-scaled MP2 methods applied to the calculation of the dissociation energy curve of noncovalently-interacting systems.

We present a simple and non-empirical method to determine optimal scaling coefficients, within the (spin-component)-scaled MP2 approach, for calculating intermolecular potential energies of noncovalently-interacting systems. The method is based on an observed proportionality between (spin-component) MP2 and CCSD(T) energies for a wide range of intermolecular distances and allows us to compute with high accuracy a large portion of the dissociation curve at the cost of a single CCSD(T) calculation. The accuracy of the present procedure is assessed for a series of noncovalently-interacting test systems: the obtained results reproduce CCSD(T) quality in all cases and definitely outperform conventional MP2, CCSD and SCS-MP2 results. The difficult case of the beryllium dimer is also considered.

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules.

We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.

Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost.

Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Nonuniform scaling applied to surface energies of transition metals.

We construct a generalized gradient approximation of the exchange-correlation energy that satisfies the nonuniform scaling in one dimension and is accurate in the whole quasi-two-dimensional (Q2D) regime. Using spatial and energetic analyses of metal (111) surfaces, we show that the Q2D behavior is important at the surface of most transition metals, and that the here proposed Q2D-generalized gradient approximation functional predicts for these metals accurate surface energies as well as bulk properties.

Spin-dependent gradient correction for more accurate atomization energies of molecules.

We discuss, simplify, and improve the spin-dependent correction of Constantin et al. [Phys. Rev. B 84, 233103 (2011)] for atomization energies, and develop a density parameter of the form v ∝ |∇n|/n(10/9), found from the statistical ensemble of one-electron densities. The here constructed exchange-correlation generalized gradient approximations (GGAs), named zvPBEsol and zvPBEint, show a broad applicability, and a good accuracy for many applications, because these corrected functionals significantly improve the atomization and binding energies of molecular systems, without worsening the behavior of the original functionals (PBEsol and PBEint) for other properties. This spin-dependent correction is also applied to meta-GGA dynamical correlation functionals combined with exact-exchange; in this case a significant (about 30%) improvement in atomization energies of small molecules is found.