Comparison of the performance of exact-exchange-based density functional methods

Cross-over from pyrene to acene optical and electronic properties: a theoretical investigation of a series of pyrene derivatives fused with N-, S, and O-containing heterocycles

Pyrene and acene derivatives are an important source of materials for optoelectronic device applications both as emitters and organic semiconductors. The mobility of major charge carriers is correlated with the coupling constants of the respective major charge carrier as well as the relaxation energies. Herein, we have applied range-separated density functionals for the estimation of said values. A series of five alkylated derivatives of pyrene laterally extended by heteroaromatic or phenyl groups were explored and contrasted to nascent pyrene, alkylated pyrene and tetracene. The ground state geometries along with absorption properties and relaxation energies are presented as well as a discussion of the suitability of the material toward hole and electron transport materials.

Tuning the degree of CO2 activation by carbon doping Cun- (n = 3-10) clusters: an IR spectroscopic study

Copper clusters on carbide surfaces have shown a high catalytic activity towards methanol formation. To understand the interaction between CO₂ and the catalytically active sites during this process and the role that carbon atoms could play in this, they are modeled by copper clusters, with carbon atoms incorporated. The formed clusters Cu_nC_m^- (n = 3-10, m = 1-2) are reacted with CO₂ and investigated by IR multiple-photon dissociation (IR-MPD) spectroscopy to probe the degree of CO₂ activation. IR spectra for the reaction products [Cu_nC·CO₂]^-, (n = 6-10), and [Cu_nC₂·CO₂]^-, (n = 3-8) are compared to reference spectra recorded for products formed when reacting the same cluster sizes with CO, and with density functional theory (DFT) calculated spectra. The results reveal a size- and carbon load-dependent activation and dissociation of CO₂. The complexes [Cu_nC·CO₂]^- with n = 6 and 10 show predominantly molecular activation of CO₂, while those with n = 7-9 show only dissociative adsorption. The addition of the second carbon to the cluster leads to the exclusive molecular activation of the CO₂ on all measured cluster sizes, except for Cu₅C₂^- where CO₂ dissociates. Combining these findings with DFT calculations leads us to speculate that at lower carbon-to-metal ratios (CMRs), the C can act as an oxygen anchor facilitating the OCO bond rupture, whereas at higher CMRs the carbon atoms increasingly attract negative charge, reducing the Cu cluster's ability to donate electron density to CO₂, and consequently its ability to activate CO₂.

Benchmarking Density Functionals, Basis Sets, and Solvent Models in Predicting Thermodynamic Hydricities of Organic Hydrides

Many renewable energy technologies, such as hydrogen gas synthesis and carbon dioxide reduction, rely on chemical reactions involving hydride anions (H^-). When selecting molecules to be used in such applications, an important quantity to consider is the thermodynamic hydricity, which is the free energy required for a species to donate a hydride anion. Theoretical calculations of thermodynamic hydricity depend on several parameters, mainly the density functional, basis set, and solvent model. In order to assess the effects of the above three parameters, we carry out hydricity calculations with different combinations of density functionals, basis sets, and solvent models for a set of organic molecules with known experimental hydricity values. The data are analyzed by comparing the R² and root-mean-squared error (RMSE) of linear fits with a fixed slope of 1 and using the Akaike Information Criterion to determine statistical significance of the RMSE rank ordering. Based on these results, we quantified the accuracy of theoretical predictions of hydricity and found that the best compromise between accuracy and computational cost was obtained by using the B3LYP-D3 density functional for the geometry optimization and free-energy corrections, either ωB97X-D3 or M06-2X-D3 for single-point energy corrections, combined with a basis set no larger than def-TZVP and the C-PCM ISWIG solvation model. At this level of theory, the RMSEs of hydricity calculations for organic molecules in acetonitrile and dimethyl sulfoxide were found to be <4 and <10 kcal/mol, respectively, for an experimental data set with a dynamic range of 20-150 kcal/mol.

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

IR spectroscopic characterization of the co-adsorption of CO2 and H2 onto cationic Cun+ clusters

To understand elementary reaction steps in the hydrogenation of CO2 over copper-based catalysts, we experimentally study the adsorption of CO2 and H2 onto cationic Cun+ clusters. For this, we react Cun+ clusters formed by laser ablation with a mixture of H2 and CO2 in a flow tube-type reaction channel and characterize the products formed by IR multiple-photon dissociation spectroscopy employing the IR free-electron laser FELICE. We analyze the spectra by comparing them to literature spectra of Cun+ clusters reacted with H2 and with new spectra of Cun+ clusters reacted with CO2. The latter indicate that CO2 is physisorbed in an end-on configuration when reacted with the clusters alone. Although the spectra for the co-adsorption products evidence H2 dissociation, no signs for CO2 activation or reduction are observed. This lack of reactivity for CO2 is rationalized by density functional theory calculations, which indicate that CO2 dissociation is hindered by a large reaction barrier. CO2 reduction to formate should energetically be possible, but the lack of formate observation is attributed to kinetic hindering.

Screening of transition metal doped copper clusters for CO2 activation

Activation of CO₂ is the first step towards its reduction to more useful chemicals. Here we systematically investigate the CO₂ activation mechanism on Cu₃X (X is a first-row transition metal atom) using density functional theory computations. The CO₂ adsorption energies and the activation mechanisms depend strongly on the selected dopant. The dopant electronegativity, the HOMO-LUMO gap and the overlap of the frontier molecular orbitals control the CO₂ dissociation efficiency. Our calculations reveal that early transition metal-doped (Sc, Ti, V) clusters exhibit a high CO₂ adsorption energy, a low activation barrier for its dissociation, and a facile regeneration of the clusters. Thus, early transition metal-doped copper clusters, particularly Cu₃Sc, may be efficient catalysts for the carbon capture and utilization process.

General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study

We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Correcting the Charge Delocalization Error of Density Functional Theory

The charge delocalization error, besides nondynamic correlation, has been a major challenge to density functional theory. Contemporary functionals undershoot the dissociation of symmetric charged dimers A₂⁺, a simple but stringent test, predict a spurious barrier, and improperly delocalize charges for charged molecular clusters. We extend a functional designed for nondynamic correlation to treat the charge delocalization error by modifying the nondynamic correlation for parallel spins. The modified functional eliminates those problems and reduces the multielectron self-interaction error. Furthermore, its results are the closest to those of CCSD(T) in the whole range of the dissociation compared with contemporary functionals. It correctly localizes the net positive charge in (CH₄)_n⁺ clusters and predicts a nearly constant ionization potential as a result. Testing of the SIE4x4 set shows that the new functional outperforms a wide variety of functionals assessed for this set in the literature. Overall, we show the feasibility of treating charge delocalization together with nondynamic correlation.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Non-covalent Interactions and Charge Transfer between Propene and Neutral Yttrium-Doped and Pure Gold Clusters

The dopant and size-dependent propene adsorption on neutral gold (Aun ) and yttrium-doped gold (Aun-1 Y) clusters in the n=5-15 size range are investigated, combining mass spectrometry and gas phase reactions in a low-pressure collision cell and density functional theory calculations. The adsorption energies, extracted from the experimental data using an RRKM analysis, show a similar size dependence as the quantum chemical results and are in the range of ≈0.6-1.2 eV. Yttrium doping significantly alters the propene adsorption energies for n=5, 12 and 13. Chemical bonding and energy decomposition analysis showed that there is no covalent bond between the cluster and propene, and that charge transfer and other non-covalent interactions are dominant. The natural charges, Wiberg bond indices, and the importance of charge transfer all support an electron donation/back-donation mechanism for the adsorption. Yttrium plays a significant role not only in the propene binding energy, but also in the chemical bonding in the cluster-propene adduct. Propene preferentially binds to yttrium in small clusters (n<10), and to a gold atom at larger sizes. Besides charge transfer, relaxation also plays an important role, illustrating the non-local effect of the yttrium dopant. It is shown that the frontier molecular orbitals of the clusters determine the chemical bonding, in line with the molecular-like electronic structure of metal clusters.

Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error

Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.

Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations

The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC–DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.

Phenol-Induced O-O Bond Cleavage in a Low-Spin Heme-Peroxo-Copper Complex: Implications for O2 Reduction in Heme-Copper Oxidases

This study evaluates the reaction of a biomimetic heme-peroxo-copper complex, {[(DCHIm)(F8)FeIII]-(O22-)-[CuII(AN)]}+ (1), with a phenolic substrate, involving a net H-atom abstraction to cleave the bridging peroxo O-O bond that produces FeIV═O, CuII-OH, and phenoxyl radical moieties, analogous to the chemistry carried out in heme-copper oxidases (HCOs). A 3D potential energy surface generated for this reaction reveals two possible reaction pathways: one involves nearly complete proton transfer (PT) from the phenol to the peroxo ligand before the barrier; the other involves O-O homolysis, where the phenol remains H-bonding to the peroxo OCu in the transition state (TS) and transfers the H+ after the barrier. In both mechanisms, electron transfer (ET) from phenol occurs after the PT (and after the barrier); therefore, only the interaction with the H+ is involved in lowering the O-O cleavage barrier. The relative barriers depend on covalency (which governs ET from Fe), and therefore vary with DFT functional. However, as these mechanisms differ by the amount of PT at the TS, kinetic isotope experiments were conducted to determine which mechanism is active. It is found that the phenolic proton exhibits a secondary kinetic isotope effect, consistent with the calculations for the H-bonded O-O homolysis mechanism. The consequences of these findings are discussed in relation to O-O cleavage in HCOs, supporting a model in which a peroxo intermediate serves as the active H+ acceptor, and both the H+ and e- required for O-O cleavage derive from the cross-linked Tyr residue present at the active site.

Ground-State Charge Transfer: Lithium-Benzene and the Role of Hartree-Fock Exchange

Most approximations to the exchange-correlation functional of Kohn-Sham density functional theory lead to delocalization errors that undermine the description of charge-transfer phenomena. We explore how various approximate functionals and charge-distribution schemes describe ground-state atomic-charge distributions in the lithium-benzene complex, a model system of relevance to carbon-based supercapacitors. To understand the trends, we compare Hartree-Fock (HF) and correlated post-HF calculations, confirming that the HOMO-LUMO gap is narrower in semilocal functionals but widened by hybrid functionals with large fractions of HF exchange. For semilocal functionals, natural bond orbital (NBO) and Mulliken schemes yield opposite pictures of how charge transfer occurs. In PBE, for example, when lithium and benzene are <1.5 Å apart, NBO yields a positive charge on the lithium atom, but the Mulliken scheme yields a negative charge. Furthermore, the partial charges in conjugated materials depend on the interplay between the charge-distribution scheme employed and the underlying exchange-correlation functional, being critically sensitive to the admixture of HF exchange. We analyze and explain why this happens, discuss implications, and conclude that hybrid functionals with an admixture of about one-fourth of HF exchange are particularly useful in describing charge transfer in the lithium-benzene model.

Perspective: Fifty years of density-functional theory in chemical physics

Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

Density functional theory for field emission from carbon nano-structures

Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on density functional theory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission.