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.

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.

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.

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.

Self-Consistent Implementation of Kohn-Sham Adiabatic Connection Models with Improved Treatment of the Strong-Interaction Limit.

Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange-correlation functionals. If the exact weak-interaction expansion from the second-order perturbation theory is included, a self-consistent implementation of these functionals is challenging and still absent in the literature. In this work, we fill this gap by presenting a fully self-consistent-field (SCF) implementation of some popular ACM functionals. While using second-order perturbation theory at weak interactions, we have also introduced new generalized gradient approximations (GGAs), beyond the usual point-charge-plus-continuum model, for the first two leading terms at strong interactions, which are crucial to ensure robustness and reliability. We then assess the SCF-ACM functionals for molecular systems and for prototypical strong-correlation problems. We find that they perform well for both the total energy and the electronic density and that the impact of SCF orbitals is directly connected to the accuracy of the ACM functional form. For the H2 dissociation, the SCF-ACM functionals yield significant improvements with respect to standard functionals also thanks to the use of the new GGAs for the strong-coupling functionals.

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.

Noncovalent Interactions from Models for the Møller-Plesset Adiabatic Connection.

Given the omnipresence of noncovalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with nondegenerate ground states, have the same cost as double hybrids, and require no dispersion corrections to capture NCIs accurately. These interpolations greatly reduce large MP2 errors for typical π-stacking complexes (e.g., benzene-pyridine dimers) and for the L7 data set. They are also competitive with state-of-the-art dispersion enhanced functionals and can even significantly outperform them for a variety of data sets, such as CT7 and L7.

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.

Performance of Semilocal Kinetic Energy Functionals for Orbital-Free Density Functional Theory.

We assess several generalized gradient approximations (GGAs) and Laplacian-level meta-GGAs (LL-MGGA) kinetic energy (KE) functionals for orbital-free density functional theory calculations of bulk metals and semiconductors, considering equilibrium distances, bulk moduli, total and kinetic energies, and the electron densities. We also considered the effects of the pseudopotentials, the vacancy formation energies, and the bond lengths of molecular dimers. We found that LL-MGGA KE functionals are distinctively superior to GGA functionals, showing the importance of the Laplacian of the density in the functional construction. We extended the recently developed Pauli-Gaussian second-order and Laplacian (PGSL) functional ( J. Phys. Chem. Lett. 2018 , 9 , 4385 , DOI: 10.1021/acs.jpclett.8b01926 ) including high-order corrections, achieving higher transferability and accuracy than conventional nonlocal functionals based on the Lindhard response function.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation.

We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials have also been investigated and discussed.

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.

Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection.

Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.

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.

Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients.

Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.

Electrostatic Mechanophores in Tuneable Light-Emitting Piezopolymer Nanowires.

Electromechanical coupling through piezoelectric polymer chains allows the emission of organic molecules in active nanowires to be tuned. This effect is evidenced by highly bendable arrays of counter-ion dye-doped nanowires made of a poly(vinylidenefluoride) copolymer. A reversible redshift of the dye emission is found upon the application of dynamic stress during highly accurate bending experiments. By density functional theory calculations it is found that these photophysical properties are associated with mechanical stresses applied to electrostatically interacting molecular systems, namely to counterion-mediated states that involve light-emitting molecules as well as charged regions of piezoelectric polymer chains. These systems are an electrostatic class of supramolecular functional stress-sensitive units, which might impart new functionalities in hybrid molecular nanosystems and anisotropic nanostructures for sensing devices and soft robotics.