New generalized gradient approximation functionals

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Uncovering Factors Controlling Reactivity of Metal-TEMPO Reaction Systems in the Solid State and Solution

Nitroxides find application in various areas of chemistry, and a more in-depth understanding of factors controlling their reactivity with metal complexes is warranted to promote further developments. Here, we report on the effect of the metal centre Lewis acidity on both the distribution of the O- and N-centered spin density in 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) and turning TEMPO from the O- to N-radical mode scavenger in metal-TEMPO systems. We use Et(Cl)Zn/TEMPO model reaction system with tuneable reactivity in the solid state and solution. Among various products, a unique Lewis acid-base adduct of Cl2Zn with the N-ethylated TEMPO was isolated and structurally characterised, and the so-called solid-state 'slow chemistry' reaction led to a higher yield of the N-alkylated product. The revealed structure-activity/selectivity correlations are exceptional yet are entirely rationalised by the mechanistic underpinning supported by theoretical calculations of studied model systems. This work lays a foundation and mechanistic blueprint for future metal/nitroxide systems exploration.

Molecular Hydrogen Acts as a Hydrogen Bond Proton Acceptor: From Protonated Betaine Tagging to the Weakest Hydrogen Bond

In an attempt to gain further insights into the intermolecular interactions implied by Rizzo's group's cautionary tale related to molecular tagging in infrared multiple photon dissociation (IRMPD) spectroscopy with molecular messengers [Masson, A. . J. Chem. Phys. 2015, 143, 104313], in the present study, we provide an in-depth analysis of the noncovalent interaction between the molecular hydrogen and protonated betaine molecule in the gas phase. We aim to shed some new light on the fundamental issues concerning the wide diapason of hydrogen-bonding-type intermolecular interactions, with a wide variety of proton acceptors. We demonstrate that in the course of tagging the protonated betaine with molecular hydrogen from the OH group side, it is the σ bond of molecular hydrogen that plays the role of hydrogen-bonding proton acceptor. The tagging thus induces a small yet significant red shift of the protonated betaine O-H stretching mode. We investigate the performance of a wide range of density functional theory (DFT) functionals for the calculation of anharmonic vibrational frequency shifts of the studied system, which are essential for the correct interpretation of the experimental IRMPD data. For an accurate prediction of the OH stretching frequency shifts, specifically designed functionals such as Handy's group HCTH/407 should be applied. The empirical dispersion correction enhances the systematic overestimation of the anharmonic frequency shift, characteristic of the most widely used DFT functionals. Combining the full-wave function approach with the charge field perturbation and natural bond orbital (NBO) deletion analyses, we demonstrate that the frequency shift in the OH-tagged structure is governed by the σHH → σ*OH intermolecular charge transfer. This interaction stabilizes the OH-tagged dimer as well, in contrast to the dipole-quadrupole electrostatic interaction energy term. Topological analysis of the electron density reveals the presence of an intermolecular bond critical point with a positive value of the density Laplacian very close to the lower limit for hydrogen bonds. NCI analyses demonstrate that the OH···H2 interaction is weaker than the intramolecular CH···O one within the protonated betaine molecule, with the through of reduced density gradient appearing at less negative sign(λ2)·ρ values. Analyzing the O-H stretching vibrational potential with the second-generation absolutely localized molecular orbitals energy decomposition analysis (ALMO-EDA 2) revealed that in the case of betaineH(+) tagged from the OH group side, the permanent electrostatics (ΔEelec), polarization (ΔEpol), and charge-transfer (ΔEct) contributions to the total intermolecular interaction energy contribute favorably to the weak hydrogen bond formation and to the red shift of the fundamental O-H stretching frequency, the ΔEct contribution being the most significant in the last context. The Pauli repulsion term, on the other hand, favors an O-H stretching frequency blue shift as a consequence of the vibrational confinement effects.

Comparative assessment of structure-property relationships of new Cu(II) complex in selected density functionals

In order to evaluate the structure-property relationships of Cu(II) complex by using DFT methods, the structure of the newly synthesized Cu(II) complex, [Cu(6-Brpic)2(bpy)], was investigated by XRD, FTIR, UV-Vis, and fluorescence spectroscopic methods. In addition, Hirshfeld surface and NBO analyses were fulfilled to identify possible interactions in the intermolecular and coordination environment. The five different DFT methods (HCTH, M06L, TPSSTPSS, B3LYP, and CAM-B3LYP levels), having four different functionalities (the GGA, meta-GGA, hybrid-GGA, and range-separated hybrid), were carried out so as to investigate the structure-property relationship, considering the geometric parameters (bond lengths and angles), vibrational frequencies, electronic absorption wavelengths, electronic transitions, and linear and nonlinear optical parameters. The R2 for structural and vibrational parameters, as well as MPD%, MAD, an optimal scaling factor (λ) and overall root mean square (RMS) deviation, were considered only at vibration frequencies. While it was determined that M06-L and TPSSTPSS levels gave the best results for the bond lengths and angles of the Cu(II) complex, the best results for vibrational frequencies were obtained in the HCTH method along with these methods. In NLO parameters, the static and dynamic first-order hyperpolarizability (<β(0;0,0)> and β(-ω;ω,0)/<β(-2ω;ω,ω)>) values, the largest values were obtained in the HCTH method (38.817 × 10-30 and 437.86 × 10-30/201.55 × 10-30 esu), whereas the smallest values were found to be in the CAM-B3LYP/TPSSTPSS levels (6.118 × 10-30 esu, 8.270 × 10-30/11.730 × 10-30 esu). By regarding the static γ (<γ(0;0,0,0)>) and dynamic (<γ(-ω;ω,0,0)> parameters, the largest values were calculated in the M06L (232.101 × 10-36) and HCTH (1711.52 × 10-36) methods and the smallest values were obtained in the CAM-B3LYP (43.281 × 10-36 and 60.844 × 10-36) method. In fact, it is obviously seen that the β and γ values obtained by the aforementioned DFT levels are many times higher than that of the standard molecule of urea. These results indicate that the Cu(II) complex may be used as a potential NLO material to evolve optoelectronic devices.

Unveiling the impact of exchange-correlation functionals on the description of key electronic properties of non-fullerene acceptors in organic photovoltaics

Non-fullerene electron acceptors have emerged as promising alternatives to traditional electron-acceptors in the active layers of organic photovoltaics. This is due to their tunable energy levels, optical response in the visible light spectrum, high electron mobility, and photochemical stability. In this study, the electronic properties of two representative non-fullerene acceptors, ITIC and Y5, have been calculated within the framework of density functional theory using a range of hybrid and non-hybrid density functionals. Screened range-separated hybrid (SRSH) approaches were also tested. The results are analyzed in light of the previously reported experimental outcomes. Specifically, we have calculated the oxidation and reduction potentials, fundamental and optical gaps, the highest occupied molecular orbital and lowest unoccupied molecular orbital energies, and exciton binding energies. Additionally, we have investigated the effects of the medium dielectric constant on these properties employing a universal implicit solvent model. It was found that hybrid functionals generally perform poorly in predicting oxidation potentials, while non-hybrid functionals tend to overestimate reduction potentials. The inclusion of a large Hartree-Fock contribution to the global or long range was identified as the source of inaccuracy for many hybrid functionals in predicting both redox potentials and the fundamental and optical gaps. Corroborating with the available literature, ∼50% of all tested functionals predicted very small exciton binding energies, within the range of ±0.1 eV, that become even smaller by increasing the dielectric constant of the material. Finally, the OHSE2PBE and tHCTHhyb functionals and the optimal tuning SRSH approach emerged as the best-performing methods, with good accuracy in the description of the electronic properties of interest.

DFT approach towards accurate prediction of 1H/13C NMR chemical shifts for dipterocarpol oxime

A computational NMR approach for accurate predicting the 1H/13C chemical shifts of triterpenoid oximes featuring the screening of 144 DFT methods was demonstrated. Efficiently synthesized dipterocarpol oxime was employed as a model compound. The six highest accurate methods from the screening generated root-mean-square-error (RMSE) values in the range of 0.84 ppm (0.55%) to 1.14 ppm (0.75%) for calculated 13C shifts. For 1H results, simple, economical 6-31G basis set unexpectedly outperformed other more expensive basic sets; and the couple of it with selected functionals provided high accuracy shifts (0.0617 ppm (1.49%) ≤ RMSE ≤ 0.0870 ppm (2.04%)). These computational results strongly supported the proton and carbon assignments of the oxime including the difficult ones of diastereotopic methyl groups, the methyl groups attached to an internal olefin, and diastereotopic α-protons.

Reproducibility of density functional approximations: How new functionals should be reported

Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations are published every year. To become available in program packages, the novel density functional approximations (DFAs) need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al., SoftwareX 7, 1 (2018)], a constant problem in this task is verification due to the lack of reliable reference data. As we discuss in this work, this lack has led to several non-equivalent implementations of functionals such as Becke-Perdew 1986, Perdew-Wang 1991, Perdew-Burke-Ernzerhof, and Becke's three-parameter hybrid functional with Lee-Yang-Parr correlation across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs. DFAs must be verifiable in order to prevent the reappearance of the above-mentioned errors and incompatibilities. A common framework for verification and testing is, therefore, needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters-especially the quadrature grid-need to be converged to guarantee a ≲0.1 μEh precision in the total energy, which is nowadays routinely achievable in fully numerical calculations. Moreover, as such sub-μEh level agreement can only be achieved when fully equivalent implementations of the DFA are used, the source code of the reference implementation should also be made available in any publication describing a new DFA.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

DELTA50: A Highly Accurate Database of Experimental 1H and 13C NMR Chemical Shifts Applied to DFT Benchmarking

Density functional theory (DFT) benchmark studies of ¹H and ¹³C NMR chemical shifts often yield differing conclusions, likely due to non-optimal test molecules and non-standardized data acquisition. To address this issue, we carefully selected and measured ¹H and ¹³C NMR chemical shifts for 50 structurally diverse small organic molecules containing atoms from only the first two rows of the periodic table. Our NMR dataset, DELTA50, was used to calculate linear scaling factors and to evaluate the accuracy of 73 density functionals, 40 basis sets, 3 solvent models, and 3 gauge-referencing schemes. The best performing DFT methodologies for ¹H and ¹³C NMR chemical shift predictions were WP04/6-311++G(2d,p) and ωB97X-D/def2-SVP, respectively, when combined with the polarizable continuum solvent model (PCM) and gauge-independent atomic orbital (GIAO) method. Geometries should be optimized at the B3LYP-D3/6-311G(d,p) level including the PCM solvent model for the best accuracy. Predictions of 20 organic compounds and natural products from a separate probe set had root-mean-square deviations (RMSD) of 0.07 to 0.19 for ¹H and 0.5 to 2.9 for ¹³C. Maximum deviations were less than 0.5 and 6.5 ppm for ¹H and ¹³C, respectively.

Structural and Dynamic Properties of Solvated Hydroxide and Hydronium Ions in Water from Ab Initio Modeling

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water has been a challenging task from ab initio molecular dynamics (AIMD). The difficulty mainly comes from a lack of accurate and efficient exchange-correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly-constrained and appropriately normed (SCAN) meta-GGA functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange-correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice in describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. Our AIMD simulations indicate hydroxide diffuses slower than hydronium in water, which is consistent with the experiments.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Benchmarking of Density Functionals for the Description of Optical Properties of Newly Synthesized π-Conjugated TADF Blue Emitters

Computational modeling of the optical characteristics of organic molecules with potential for thermally activated delayed fluorescence (TADF) may assist markedly the development of more efficient emitting materials for organic light-emitting diodes. Recent theoretical studies in this area employ mostly methods from density functional theory (DFT). In order to obtain accurate predictions within this approach, the choice of a proper functional is crucial. In the current study, we focus on testing the performance of a set of DFT functionals for estimation of the excitation and emission energy and the excited singlet-triplet energy gap of three newly synthesized compounds with capacity for TADF. The emitters are designed specifically to enable charge transfer by π-electron conjugation, at the same time possessing high-energy excited triplet states. The functionals chosen for testing are from various groups ranging from gradient-corrected through global hybrids to range-separated ones. The results show that the monitored optical properties are especially sensitive to how the long-range part of the exchange energy is treated within the functional. The accurate functional should also be able to provide well balanced distribution of the π-electrons among the molecular fragments. Global hybrids with moderate (less than 0.4) share of exact exchange (B3LYP, PBE0) and the meta-GGA HSE06 are outlined as the best performing methods for the systems under study. They can predict all important optical parameters correctly, both qualitatively and quantitatively.

An inexpensive density functional theory-based protocol to predict accurate 19 F-NMR chemical shifts

Thanks to its advantages, ¹⁹ F-NMR is an increasingly popular technique for the structural characterization of F-containing molecules, among which polymers, materials, fluorophores, pharmaceuticals, and so forth. However, the computational calculation of the ¹⁹ F-NMR chemical shifts, both for prediction and interpretation of experimental spectra, remains a challenge. In this work a density functional theory (DFT) based protocol for the calculation of the chemical shifts is established within the framework of the gauge-independent atomic orbital method, upon verifying the performance of Hartree-Fock and 60 DFT functionals coupled with seven different basis sets. The benchmark is conducted using two sets of molecules, namely one used for testing methods and another used for probing; the former set consists of 134 molecules, the latter 50, yet both of them with F in different chemical environments. Following Bally-Rablen-Tantillo strategy, the scaling parameters and other statistical quantities were computed for each method upon least squares linear regression between experimental and computed chemical shifts. The designed computational workflow is computationally inexpensive and represents a significant improvement with respect to the current state of the art.

Effectiveness of Oxygen-Saturated Seawater Injections and Air Sparging Technologies in Remediation of Coastal Marine Sediments from Sludge

The occurrence of hypoxic muddy sediments on shallow beaches and other sheltered areas is a well-known environmental problem, which negatively affects coastal areas, tourism potential, the public use of beaches and sediment biodiversity. The usual solution is limited to dredging and removal of sludge to a landfill site. In this study, a laboratory-scale experiment was performed to determine the effectiveness of two technologies: a modification of air sparging and a new approach based on injecting oxygen-saturated seawater in hypoxic muddy sediments (oxygen-saturated seawater injections method), for remediating sludge in coastal sediments, minimizing environmental impact respect to dredging. Our results showed that both technologies significantly increased dissolved oxygen content in pore water, facilitating the oxidation of more than 90% of the organic matter, and other reduced inorganic compounds such as sulphide, with the consequent increase in sulphate concentration from 0.3 to 3.0 g·L^-1. Moreover, a rise of redox potential from - 258 mV to above 200 mV, and a dramatic drop in chemical oxygen demand were also indicators that oxic conditions had been restored. After 65 days, soft, black, muddy and hypoxic sediment with high organic matter content and a characteristic foul odour was transformed into well-oxygenated sediment, which had a low organic matter content and had lost its initial shiny black colour and odour. The main difference between both technologies was the depth influenced by sediment remediation; oxygen-saturated seawater injections affected deeper areas than clean pressurized air injections.

The best density functional theory functional for the prediction of 1 H and 13 C chemical shifts of protonated alkylpyrroles

The prediction of ¹³ C chemical shifts can be challenging with density functional theory (DFT). In this study 39 different functionals and three different basis sets were tested on three neutral alkylpyrroles and their corresponding protonated species. The calculated shielding constants were compared to experimental data and results from previous calculations at the MP2. We find that the meta-hybrid functional TPSSh with either the Pople style basis set 6-311++G(2d,p) or the polarization consistent basis set pcSseg-1 gives the best results for the ¹³ C chemical shifts, whereas for the ¹ H chemical shifts it is the TPSSh functional with either the 6-311++G(2d,p) or pcSseg-2 basis set. Including an explicit solvent molecule hydrogen bonded to NH in the alkylpyrroles improves the results slightly for the ¹³ C chemical shifts. On the other hand, for ¹ H chemical shifts the opposite is true. Compared to calculations at the MP2 level none of the DFT functionals can compete with MP2 for the ¹³ C chemical shifts but for the ¹ H chemical shifts the investigated DFT functionals are shown to give better agreement with experiment than MP2 calculations.

Do Secondary Electrostatic Interactions Influence Multiple Dihydrogen Bonds? AA-DD Array on an Amine-Borane Aza-Coronand: Theoretical Studies and Synthesis

Hydrogen bond plays a key role in a wide range of inorganic, organic, as well as biological systems. The understanding on how the chemical environment can affect this kind of interaction is crucial to predict its binding strength and consequently the robustness and the dynamic properties of many supramolecular systems. In this paper a new donor-acceptor complex was synthesized and characterized by SCXRD, showing for the first time in an organic system an AA-DD pattern of a particular hydrogen interaction, called dihydrogen bond. Over 250 functionals were computationally evaluated to select the best method to reproduce the binding interaction geometry of this new pattern. Moreover, a new vector force model was used to split the contribution of primary and secondary electrostatic interactions (SEIs), in order to evaluate how the latter one can modify the binding strength of this unusual hydrogen-hydrogen interaction.

Accurate Prediction of Mössbauer Hyperfine Parameters in Bis-Axially Coordinated Iron(II) Phthalocyanines Using Density Functional Theory Calculations: A Story of a Single Orbital Revealed by Natural Bond Orbital Analysis

Density Functional Theory (DFT) calculations coupled with several exchange-correlation functionals were used for the prediction of Mössbauer hyperfine parameters of 36 bis-axially coordinated iron(II) phthalocyanine complexes with the general formulas PcFeL₂, PcFeL'L″, and [PcFeX₂]^2-, including four new compounds. Both gas-phase and PCM calculations using BPW91 and MN12L exchange-correlation functionals were found to accurately predict both Mössbauer quadrupole splittings and the correct trends in experimentally observed isomer shifts. In comparison, hybrid exchange-correlation functionals underestimated quadrupole splittings, while still accurately predicted isomer shifts. Out of ∼40 exchange-correlation functionals tested, only MN12L was found to correctly reproduce quadrupole splitting trends in the PcFeL₂ complexes coordinated with phosphorus-donor axial ligands (i.e., P(OnBu)₃ ≈ P(OEt)₃ < PMe₃ < P[(CH₂O)₂CH₂]-p-C₆H₄NO₂ < PEt₃ ≈ PnBu₃). Natural Bond Orbital (NBO) analysis was successfully used to explain the general trends in the observed quadrupole splitting for all compounds of interest. In particular, the general trends in the quadrupole splitting correlate well with the axial ligand dependent, NBO-predicted population of the 3d_z2 orbital of the Fe ion and are reflective of the hypothesis proposed by Ohya and co-workers ( Inorg. Chem., 1984, 23, 1303) on the adaptability of the phthalocyanine's π-system toward Fe-L_ax interactions. The first X-ray crystal structure of a PcFeL₂ complex with axial phosphine ligands is also reported.

The Devil's Triangle of Kohn-Sham density functional theory and excited states

Exchange-correlation (XC) functionals from Density Functional Theory (DFT) developed under the rigorous arguments of Correlated Orbital Theory (COT) address the Devil's Triangle of prominent errors in Kohn-Sham (KS) DFT. At the foundation of this triangle lie the incorrect one-particle spectrum, the lack of integer discontinuity, and the self-interaction error. At the top level, these failures manifest themselves in incorrect charge transfer and Rydberg excitation energies, along with poor activation barriers. Accordingly, the Quantum Theory Project (QTP) XC functionals have been created to address several of the long-term issues encountered in KS theory and its Time Dependent DFT (TDDFT) variant for electronic excitations. Recognizing that COT starts with a correct one-particle spectrum, a condition imposed on the QTP functionals by means of minimum parameterization, the question that arises is how does this affect the electronically excited states? Among up to 28 XC functionals considered, the QTP family provides one of the smallest mean absolute deviations for charge-transfer excitations while also showing excellent results for Rydberg states. However, there is some room for improvement in the case of excitation energies to valence states, which are systematically underestimated by all functionals investigated. An alternative path for better treatment of excitation energies, mainly for valence states, is offered by using orbital energies from QTP functionals, especially by CAM-QTP-02 and LC-QTP. In this case, the deviations from the reference data can be reduced approximately by half.

Meta-Local Density Functionals: A New Rung on Jacob's Ladder

The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density n_σ, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a geometric average n_σ^avg(r) = n_σ^1-x(r)ñ_σ^x(r) of the local spin density n_σ(r) and the spin density ñ_σ(r) of a HEG that has the local kinetic energy density τ_σ(r) of the inhomogeneous system. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG and which form a new rung of Jacob's ladder of density functionals [ AIP Conf. Proc. 2001, 577, 1]. The first functional of this ladder, the local τ approximation (LTA) of Ernzerhof and Scuseria [ J. Chem. Phys. 1999, 111, 911] that corresponds to x = 1 is unfortunately not stable enough to be used in self-consistent field calculations because it leads to divergent potentials, as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of x not only leads to numerical stability of the resulting functional but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional (x = 1/4) of Eich and Hellgren [ J. Chem. Phys. 2014, 141, 224107]. We choose x = 0.50, as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice x = 0.50 also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.

Using electronegativity and hardness to test density functionals

Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy-density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV-0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most "universal" among the tested functionals. B98 and B97-1 are accurate for very diverse metal-ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E²/∂N², via χ and η, is probably a first simple probe of universality.

Frontiers in molecular simulation of solvated ions, molecules and interfaces

This themed collection is a collection of articles on frontiers in molecular simulation of solvated ions, molecules and interfaces.

Structure, Properties, and Reactivity of Porphyrins on Surfaces and Nanostructures with Periodic DFT Calculations

Porphyrins are fascinating molecules with applications spanning various scientific fields. In this review we present the use of periodic density functional theory (PDFT) calculations to study the structure, electronic properties, and reactivity of porphyrins on ordered two dimensional surfaces and in the formation of nanostructures. The focus of the review is to describe the application of PDFT calculations for bridging the gaps in experimental studies on porphyrin nanostructures and self-assembly on 2D surfaces. A survey of different DFT functionals used to study the porphyrin-based system as well as their advantages and disadvantages in studying these systems is presented.

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.

Large-Scale Benchmark of Exchange-Correlation Functionals for the Determination of Electronic Band Gaps of Solids

We compile a large data set designed for the efficient benchmarking of exchange–correlation functionals for the calculation of electronic band gaps. The data set comprises information on the experimental structure and band gap of 472 nonmagnetic materials and includes a diverse group of covalent-, ionic-, and van der Waals-bonded solids. We used it to benchmark 12 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. We included both general purpose functionals, like the Perdew–Burke–Ernzerhof approximation, and functionals specifically crafted for the determination of band gaps. The comparison of experimental and theoretical band gaps shows that the modified Becke–Johnson is at the moment the best available density functional, closely followed by the Heyd–Scuseria–Ernzerhof screened hybrid from 2006 and the high-local-exchange generalized-gradient approximation.

The multiple dissociation constants of glutathione disulfide: interpreting experimental pH-titration curves with ab initio MD simulations

The hexapeptide glutathione disulfide (GSSG) has six ionizable groups with six associated dissociation constants. The experimentally measured pH-titration curve, however, does not exhibit the six corresponding equivalence points and bears little resemblance to standard textbook examples of acid-base pH-titration curves. The curve highlights the difficulties in determining multiple pKa values of polyprotic acids - typically proteins and peptides - from experiment. The six pKa values of GSSG can, however, be estimated using Car-Parrinello molecular dynamics (CPMD) simulations in conjunction with metadynamics sampling of the underlying free energy landscape of the dissociation reactions. Ab initio MD simulations were performed on a GSSG molecule solvated by 200 water molecules. Using the estimated pKa values the theoretical titration curve was calculated and found to be in good agreement with experiment. The results clearly highlight how dissociation constants estimated from ab initio MD simulations can facilitate the interpretation of the pH-titration curves of complex chemical and biological systems.

Evaluating Density Functionals by Examining Molecular Structures, Chemical Bonding, and Relative Energies of Mononuclear Ru-Cl-H-PR3 Isomers

In order to define a robust level of theory using density functionals for investigating the reactivity of ruthenium complexes, we used benchmark wave function theory, with saturated basis sets to validate generalized gradient approximation (GGA), meta-GGA, and hyper-GGA functionals in the presence and absence of empirical dispersion and range-separated corrections. We first selected potentially suitable functionals that gave accurate predictions of the relative energetics of coordination isomers. These functionals were further evaluated for the chemical accuracy of their predicted geometric and electronic structures. For the latter, both the ionic and covalent interactions were considered. The reference level of theory for comparison was coupled-cluster perturbation theory using full treatment of singles and doubles (CCSD) with a saturated triple-ζ quality basis set (TZVP) and corresponding small-core, effective core potentials for ruthenium. Several population analysis methods were evaluated to predict the ionic interactions. We found that the atomic charges obtained from fitting the electrostatic potential provided the most reasonable estimates for the ruthenium complexes. The covalent interactions were quantified by considering the atomic compositions of Ru 4d _{x²- y²}- and 4d _z²-based frontier unoccupied orbitals. Comparison of more than two dozen functionals with reference data from high-level wave function calculations revealed trends that allowed for the formulation of an optimal hybrid density functional: PBE exchange and correlation functionals with 50% HF exchange component. This level of theory was found to reproduce the experimental structure of Ru^(II) complexes. These complexes were used to investigate chemical speciation in a simplified model for an ionic liquid environment.

Statistically representative databases for density functional theory via data science

Cluster analysis applied to quantum chemistry: a new broad database of chemical properties with a reasonable computational cost.

Finding the best density functional approximation to describe interaction energies and structures of ionic liquids in molecular dynamics studies

Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.

What Happens Without Nickel? Cyclization Reactions of Ethylene with Ethanedithial and Related Molecules

We present a computational study of the mechanism of the formation of 6-member heterocycles through the binding of ethylene to oxaldehyde, ethanedithial, and 2-thioxoacetaldehyde. This process is related to the olefin separation technology by metal dithiolenes and dioxolenes, being the formation of those heterocycles the main decomposition route. We also present a benchmark of 26 density functionals (spanning hybrid, double-hybrid, range-separated, semilocal, and local functionals) related to CCSD(T)/CBS reference values. Both the cyclization reaction and the isomerization of the cyclic product are included in the benchmark. The best functional among those tested for these reactions is ωB97XD, and the effect of the basis set is also investigated for it. © 2017 Wiley Periodicals, Inc.

Density Functional Theory for Microwave Spectroscopy of Noncovalent Complexes: A Benchmark Study

In this work, we compare the results obtained with 89 computational methods for predicting noncovalent bond lengths in weakly bound complexes. Evaluations for the performance in noncovalent interaction energies and covalent bond lengths obtained from five other data sets are included. The overall best performing density functional is the ωB97M-V method, achieving balanced results across all three categories. For noncovalent geometries, the best methods include B97M-V, B3LYP-D3(BJ) and DSD-PBEPBE-D3(BJ). The effects of systematic improvement of the density functional approximation and of dispersion corrections are also discussed.

The cationic dye basic orange 21 (BO21) as a potential fluorescent sensor

The cationic dye BO21's unique fluorescence properties in aqueous glycerol solution – a potential sensor for white blood cells and heparin.

Ground-State Gas-Phase Structures of Inorganic Molecules Predicted by Density Functional Theory Methods

We tested a battery of density functional theory (DFT) methods ranging from generalized gradient approximation (GGA) via meta-GGA to hybrid meta-GGA schemes as well as Møller-Plesset perturbation theory of the second order and a single and double excitation coupled-cluster (CCSD) theory for their ability to reproduce accurate gas-phase structures of di- and triatomic molecules derived from microwave spectroscopy. We obtained the most accurate molecular structures using the hybrid and hybrid meta-GGA approximations with B3PW91, APF, TPSSh, mPW1PW91, PBE0, mPW1PBE, B972, and B98 functionals, resulting in lowest errors. We recommend using these methods to predict accurate three-dimensional structures of inorganic molecules when intramolecular dispersion interactions play an insignificant role. The structures that the CCSD method predicts are of similar quality although at considerably larger computational cost. The structures that GGA and meta-GGA schemes predict are less accurate with the largest absolute errors detected with BLYP and M11-L, suggesting that these methods should not be used if accurate three-dimensional molecular structures are required. Because of numerical problems related to the integration of the exchange-correlation part of the functional and large scattering of errors, most of the Minnesota models tested, particularly MN12-L, M11, M06-L, SOGGA11, and VSXC, are also not recommended for geometry optimization. When maintaining a low computational budget is essential, the nonseparable gradient functional N12 might work within an acceptable range of error. As expected, the DFT-D3 dispersion correction had a negligible effect on the internuclear distances when combined with the functionals tested on nonweakly bonded di- and triatomic inorganic molecules. By contrast, the dispersion correction for the APF-D functional has been found to shorten the bonds significantly, up to 0.064 Å (AgI), in Ag halides, BaO, BaS, BaF, BaCl, Cu halides, and Li and Na halides and hydrides. These results do not agree well with very accurate structures derived from microwave spectroscopy; we therefore believe that the dispersion correction in the APF-D method should be reconsidered. Finally, we found that inaccurate structures can easily lead to errors of few kcal/mol in single-point energies.

Evaluation of the Factors Impacting the Accuracy of 13C NMR Chemical Shift Predictions using Density Functional Theory-The Advantage of Long-Range Corrected Functionals

The various factors influencing the accuracy of ¹³C NMR calculations using density functional theory (DFT), including the basis set, exchange-correlation (XC) functional, and isotropic shielding calculation method, are evaluated. A wide selection of XC functionals (over 70) were considered, and it was found that long-range corrected functionals offer a significant improvement over the other classes of functionals. Based on a thorough study, it is recommended that for calculating NMR chemical shifts (δ) one should use the CSGT method, the COSMO solvation model, and the LC-TPSSTPSS exchange-correlation functional in conjunction with the cc-pVTZ basis set. A selection of problems in natural product identification are considered in light of the newly recommended level of theory.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.