Improving Quantum Chemical Solvation Models by Dynamic Radii Adjustment for Continuum Solvation (DRACO).

We present the Dynamic Radii Adjustment for COntinuum solvation (DRACO) approach, which employs precomputed atomic partial charges and coordination numbers of the solute atoms to improve the solute cavity. As such, DRACO is compatible with major solvation models, improving their performance significantly and robustly at virtually no extra cost, especially for charged solutes. Combined with the purely electrostatic CPCM and COSMO models, DRACO reduces the mean absolute deviation (MAD) of the solvation free energy by up to 4.5 kcal mol-1 (67%) for a large data set of polar and ionic solutes. Even in combination with the highly empirical universal solvation model (SMD), DRACO substantially reduces the MAD for charged solutes by up to 1.5 kcal mol-1 (39%), while neutral solutes are slightly improved (0.2 kcal mol-1 or 16%). We present an interface of DRACO with two computationally efficient atomic charge models that enables fully automated, out-of-the-box calculations with the widely used program packages Orca and TurboMole.

Do Optimally Tuned Range-Separated Hybrid Functionals Require a Reparametrization of the Dispersion Correction? It Depends.

For ground- and excited-state studies of large molecules, it is the state of the art to combine (time-dependent) DFT with dispersion-corrected range-separated hybrid functionals (RSHs), which ensures an asymptotically correct description of exchange effects and London dispersion. Specifically for studying excited states, it is common practice to tune the range-separation parameter ω (optimal tuning), which can further improve the accuracy. However, since optimal tuning essentially changes the functional, it is unclear if and how much the parameters used for the dispersion correction depend on the chosen ω value. To answer this question, we explore this interdependency by refitting the DFT-D4 dispersion model for six established RSHs over a wide range of ω values (0.05-0.45 a0-1) using a set of noncovalently bound molecular complexes. The results reveal some surprising differences among the investigated functionals: While PBE-based RSHs and ωB97M-D4 generally exhibit a weak interdependency and robust performance over a wide range of ω values, B88-based RSHs, specifically LC-BLYP, are strongly affected. For these, even a minor reduction of ω from the default value manifests in strong systematic overbinding and poor performance in the typical range of optimally tuned ω values. Finally, we discuss strategies to mitigate these issues and reflect the results in the context of the employed D4 parameter optimization algorithm and fit set, outlining strategies for future improvements.

Either Accurate Singlet-Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters.

The energy gap between the lowest singlet and triplet excited states (ΔEST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm-Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,1 exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔEST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency.

Charge-Transfer Transitions Govern the Reactivity and Photophysics of Vicinally Diphosphanyl-Substituted Diborapentacenes.

2,3-Difluoro-5,14-dihydro-5,14-diborapentacene (DBP) was endowed with two vicinal Ph2 P groups by an SN Ar reaction at both CF sites using Ph2 PSiMe3 . Computations reveal the ambipolar product P to undergo P-to-B charge transfer under ambient light irradiation. Consequently, P is prone to photooxidation by air, yielding the Ph2 P(O) species PO. With S8 or [Me3 O][BF4 ], P furnishes the Ph2 P(S) or Ph2 P(Me)+ derivatives PS or [PMe][BF4 ]2 . Along the series P, PO, PS, and [PMe][BF4 ]2 , the redox potentials shift anodically from E1/2 =-1.89 V to -1.02 V (CH2 Cl2 ). Thus, derivatization of the Ph2 P group allows late-stage modulation of the LUMO-energy level of the DBP. Derivatization also influences the emission properties of the compounds, as PO shows green (521 nm) and [PMe][BF4 ]2 red (622 nm) fluorescence in C6 H6 , while P and PS are dark. With CuBr and AgBr, P forms dimeric [M(µ-Br)]2 complexes [PCu]2 and [PAg]2 , which show pronounced metal-to-ligand charge transfer (MLCT), making P a promising ligand for photocatalysts.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry.

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

From the gas phase to the solid state: The chemical bonding in the superheavy element flerovium.

As early as 1975, Pitzer suggested that copernicium, flerovium, and oganesson are volatile substances behaving like noble gas because of their closed-shell configurations and accompanying relativistic effects. It is, however, precarious to predict the chemical bonding and physical behavior of a solid by knowledge of its atomic or molecular properties only. Copernicium and oganesson have been analyzed very recently by our group. Both are predicted to be semiconductors and volatile substances with rather low melting and boiling points, which may justify a comparison with the noble gas elements. Here, we study closed-shell flerovium in detail to predict its solid-state properties, including the melting point, by decomposing the total energy into many-body forces derived from relativistic coupled-cluster theory and from density functional theory. The convergence of such a decomposition for flerovium is critically analyzed, and the problem of using density functional theory is highlighted. We predict that flerovium in many ways does not behave like a typical noble gas element despite its closed-shell 7p1/2 2 configuration and resulting weak interactions. Unlike the case of noble gases, the many-body expansion in terms of the interaction energy does not converge smoothly. This makes the accurate prediction of phase transitions very difficult. Nevertheless, a first prediction by Monte Carlo simulation estimates the melting point at 284 ± 50 K. Furthermore, calculations for the electronic bandgap suggests that flerovium is a semiconductor similar to copernicium.

Exploring Structure-Property Relations of B,S-Doped Polycyclic Aromatic Hydrocarbons through the Trinity of Synthesis, Spectroscopy, and Theory.

Polycyclic aromatic hydrocarbons (PAHs) are prominent lead structures for organic optoelectronic materials. This work describes the synthesis of three B,S-doped PAHs with heptacene-type scaffolds via nucleophilic aromatic substitution reactions between fluorinated arylborane precursors and 1,2-(Me3SiS)2C6H4/1,8-diazabicyclo[5.4.0]undec-7-ene (72-92% yield). All compounds contain tricoordinate B atoms at their 7,16-positions, kinetically protected by mesityl (Mes) substituents. PAHs 1/2 feature two/four S atoms at their 5,18-/5,9,14,18-positions; PAH 3 is a 6,8,15,17-tetrafluoro derivative of 2. For comparison, we also prepared the skewed naphtho[2,3-c]pentaphene-type isomer 4. The simultaneous presence of electron-accepting B atoms and electron-donating S atoms results in a redox-ambiphilic behavior; the radical cations [1•]+ and [2•]+ were characterized by electron paramagnetic resonance spectroscopy. Several low-lying charge-transfer states exist, some of which (especially S-to-B and Mes-to-B transitions) compete on the excited-state potential-energy surface. Consistent with the calculated state characters and oscillator strengths, this competition results in a spread of fluorescence quantum yields (2-27%). The optoelectronic properties of 1 change drastically upon addition of Ag+ ions: while the color of 1 in CH2Cl2 changes bathochromically from yellow to red (λmax from 463 to 486 nm; -0.13 eV), the emission band shifts hypsochromically from 606 to 545 nm (+0.23 eV), and the fluorescence quantum yield increases from 12 to 43%. According to titration experiments, higher order adducts [Agn1m]n+ are formed. As a suitable system for modeling Ag+ complexation, our calculations predict a dimer structure (n = m = 2) with Ag2S4 core, approximately linear S-Ag-S fragments, and Ag-Ag interaction. The computed optoelectronic properties of [Ag212]2+ agree well with the experimentally observed ones.

It's Complicated: On Relativistic Effects and Periodic Trends in the Melting and Boiling Points of the Group 11 Coinage Metals.

While the color of metallic gold is a prominent and well-investigated example for the impact of relativistic effects, much less is known regarding the influence on its melting and boiling point (MP/BP). To remedy this situation, this work takes on the challenging task of exploring the phase transitions of the Group 11 coinage metals Cu, Ag, and Au through nonrelativistic (NR) and scalar/spin-orbit relativistic (SR/SOR) Gibbs energy calculations with λ-scaled density-functional theory (λDFT). At the SOR level, the calculations provide BPs in excellent agreement with experimental values (1%), while MPs exhibit more significant deviations (2-10%). Comparing SOR calculations to those conducted in the NR limit reveals some remarkably large and, at the same time, some surprisingly small relativistic shifts. Most notably, the BP of Au increases by about 800 K due to relativity, which is in line with the strong relativistic increase of the cohesive energy, whereas the MP of Au is very similar at the SOR and NR levels, defying the typically robust correlation between MP and cohesive energy. Eventually, an inspection of thermodynamic quantities traces the trend-breaking behavior of Au back to phase-specific effects in liquid Au, which render NR Au more similar to SOR Ag, in line with a half-a-century-old hypothesis of Pyykkö.

PCM-ROKS for the Description of Charge-Transfer States in Solution: Singlet-Triplet Gaps with Chemical Accuracy from Open-Shell Kohn-Sham Reaction-Field Calculations.

The adiabatic energy gap between the lowest singlet and triplet excited states ΔEST is a central property of thermally activated delayed fluorescence (TADF) emitters. Since these states are dominated by a charge-transfer character, causing strong orbital-relaxation and environmental effects, an accurate prediction of ΔEST is very challenging, even with modern quantum-chemical excited-state methods. Addressing this major challenge, we present an approach that combines spin-unrestricted (UKS) and restricted open-shell Kohn-Sham (ROKS) self-consistent field calculations with a polarizable-continuum model and range-separated hybrid functionals. Tests on a new representative benchmark set of 27 TADF emitters with accurately known ΔEST values termed STGABS27 reveal a robust and unprecedented performance with a mean absolute deviation of only 0.025 eV (∼0.5 kcal/mol) and few deviations greater than 0.05 eV (∼1 kcal/mol), even in electronically challenging cases. Requiring only two geometry optimizations per molecule at the ROKS/UKS level in a compact double-ζ basis, the approach is computationally efficient and can routinely be applied to molecules with more than 100 atoms.

Comment on "The Nature of Chalcogen-Bonding-Type Tellurium-Nitrogen Interactions": Fixing the Description of Finite-Temperature Effects Restores the Agreement Between Experiment and Theory.

Mitzel and co-workers recently presented an intriguing molecule displaying a tellurium-nitrogen interaction. Structural data obtained in the solid and in gas phase indicated a large increase of the Te-N equilibrium distance re from 2.64 to 2.92 Å, respectively. Although some DFT calculations appear to support the large re in gas phase, we argue that the lions share of the increase is due to an incomplete description of finite-temperature effects in the back-corrected experimental data. This hypothesis is based on high-level coupled-cluster (CC) and periodic DFT calculations, which consistently point towards a much smaller re in the isolated molecule. Further support comes through MD simulations with a tuned GFN2-xTB Hamiltonian: Calibrated against a CC reference, these show a six-times larger influence of temperature than with the originally used GFN1-xTB. Taking this into account, the back-corrected re in gas phase becomes 2.67±0.08 Å, in good agreement with high-level CC theory and most DFT methods.

Exclusively Relativistic: Periodic Trends in the Melting and Boiling Points of Group†12.

First-principles simulations can advance our understanding of phase transitions but are often too costly for the heavier elements, which require a relativistic treatment. Addressing this challenge, we recently composed an indirect approach: A precise incremental calculation of absolute Gibbs energies for the solid and liquid with a relativistic Hamiltonian that enables an accurate determination of melting and boiling points (MPs and BPs). Here, we apply this approach to the Group 12 elements Zn, Cd, Hg, and Cn, whose MPs and BPs we calculate with a mean absolute deviation of only 5 % and 1 %, respectively, while we confirm the previously predicted liquid aggregate state of Cn. At a non-relativistic level of theory, we obtain surprisingly similar MPs and BPs of 650±30 K and 1250±20 K, suggesting that periodic trends in this group are exclusively relativistic in nature. Ultimately, we discuss these results and their implication for Groups 11 and 14.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method.

The recently proposed r2SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r2SCAN-3c. To this end, the unaltered r2SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r2SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r2SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

Accurate elemental boiling points from first principles.

The normal boiling point (NBP) is a fundamental property of liquids and marks the intersection of the Gibbs energies of the liquid and the gas-phase at ambient pressure. This work provides the first comprehensive demonstration of the calculation of boiling points of atomic liquids through first-principles molecular-dynamics simulations. To this end, thermodynamic integration (TDI) and perturbation theory (TPT) are combined with a density-functional theory (DFT) Hamiltonian, which provides absolute Gibbs energies, internal energies, and entropies of atomic liquids with an accuracy of a few meV/atom. Linear extrapolation to the intersection with the Gibbs energy of a non-interacting gas-phase eventually pins-down the NBPs. While these direct results can already be quite accurate, they are susceptible to a systematic over or underbinding of the employed density functional. It is shown how this dependency can be strongly reduced and the robustness of the method increased through a simple linear correction termed λ-scaling. Eventually, by carefully tuning of the technical parameters of the approach, the walltime per element is reduced from weeks to about a day (10-20k core-hours), enabling extensive testing for B, Al, Na, K, Ca, Sr, Ba, Mn, Cu, Xe, and Hg. This comprehensive benchmark demonstrates the excellent performance and robustness of the approach with a mean absolute deviation (MAD) of less than 2% from experimental NBPs and very similar accuracy for liquid entropies (MAD 2.3 J (mol K)-1, 2% relative). In some cases, the uncertainties in the predictions are several times smaller than the variation between literature values, allowing us to clear out long-standing ambiguities in the NBPs of B and Ba.

Oganesson: A Noble Gas Element That Is Neither Noble Nor a Gas.

Oganesson (Og) is the last entry into the Periodic Table completing the seventh period of elements and group 18 of the noble gases. Only five atoms of Og have been successfully produced in nuclear collision experiments, with an estimate half-life for 294 118 Og of 0. 69 + 0 . 64 - 0 . 22  ms.[1] With such a short lifetime, chemical and physical properties inevitably have to come from accurate relativistic quantum theory. Here, we employ two complementary computational approaches, namely parallel tempering Monte-Carlo (PTMC) simulations and first-principles thermodynamic integration (TI), both calibrated against a highly accurate coupled-cluster reference to pin-down the melting and boiling points of this super-heavy element. In excellent agreement, these approaches show Og to be a solid at ambient conditions with a melting point of ≈325 K. In contrast, calculations in the nonrelativistic limit reveal a melting point for Og of 220 K, suggesting a gaseous state as expected for a typical noble gas element. Accordingly, relativistic effects shift the solid-to-liquid phase transition by about 100 K.

Extension and evaluation of the D4 London-dispersion model for periodic systems.

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredients are additional reference polarizabilities for highly-coordinated group 1-5 elements derived from pseudo-periodic electrostatically-embedded cluster calculations. To illustrate the performance of the updated method, several test cases are considered, for which we compare D4 to its predecessor D3(BJ), as well as to a comprehensive set of other dispersion-corrected methods. The largest improvements are observed for solid-state polarizabilities of 16 inorganic salts, where the D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides values in good agreement with experimental and/or high-level references. These results suggest the application of the proposed D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.

Copernicium: A Relativistic Noble Liquid.

The chemical nature and aggregate state of superheavy copernicium (Cn) have been subject of speculation for many years. While strong relativistic effects render Cn chemically inert, which led Pitzer to suggest a noble-gas-like behavior in 1975, Eichler and co-workers in 2008 reported substantial interactions with a gold surface in atom-at-a-time experiments, suggesting a metallic character and a solid aggregate state. Herein, we explore the physicochemical properties of Cn by means of first-principles free-energy calculations, which confirm Pitzer's original hypothesis: With predicted melting and boiling points of 283±11 K and 340±10 K, Cn is indeed a volatile liquid and exhibits a density very similar to that of mercury. However, in stark contrast to mercury and the lighter Group 12 metals, we find bulk Cn to be bound by dispersion and to exhibit a large band gap of 6.4 eV, which is consistent with a noble-gas-like character. This non-group-conforming behavior is eventually traced back to strong scalar-relativistic effects, and in the non-relativistic limit, Cn appears as a common Group 12 metal.

Oganesson Is a Semiconductor: On the Relativistic Band-Gap Narrowing in the Heaviest Noble-Gas Solids.

Oganesson (Og) is the most recent addition to Group 18. Investigations of its atomic electronic structure have unraveled a tremendous impact of relativistic effects, raising the question whether the heaviest noble gas lives up to its position in the periodic table. To address the issue, we explore the electronic structure of bulk Og by means of relativistic Kohn-Sham density functional theory and many-body perturbation theory in the form of the GW method. Calculating the band structure of the noble-gas solids from Ne to Og, we demonstrate excellent agreement for the band gaps of the experimentally known solids from Ne to Xe and provide values of 7.1 eV and 1.5 eV for the unknown solids of Rn and Og. While this is in line with periodic trends for Rn, the band gap of Og completely breaks with these trends. The surprisingly small band gap of Og moreover means that, in stark contrast to all other noble-gas solids, the solid form of Og is a semiconductor.

Exploring the chemical nature of super-heavy main-group elements by means of efficient plane-wave density-functional theory.

The design, implementation, and evaluation of a computationally efficient approach for exploring the chemical nature and bulk properties of the super-heavy main-group elements (SHEs) Cn-Og with nuclear charges of Z = 112-118 is described. The approach combines plane-wave density-functional theory (DFT) based on a newly devised set of projector-augmented wave potentials (PAWs) with the D3 dispersion correction, whose parameter-space is extended for this purpose. Regarding both, the fitting of the PAWs as well as the calculation of the D3 parameters, it is shown that the peculiar electronic structure of the SHEs with strong relativistic effects makes it necessary to adapt the well established computational protocols. Eventually, the methodology is tested employing various common functionals (PW91, PBE, PBE-D3, PBE0-D3, PBEsol and SCAN) by comparison to experimental and high-level results for the bulk of Cn and Og, as well as by calculating adsorption energies of Cn-Og on a gold surface and comparing these to the lighter congeners Hg-Rn as well as experimentally derived data. These tests establish that our approach provides a consistent and accurate description of the reactivity of the SHEs and is largely in excellent agreement with experimental and high-level references, and moreover underline the great relevance of dispersion interactions, as well the game-changing impact of spin-orbit coupling on SHE reactivity. Ultimately, the conducted calculations provide novel insights into the chemical behavior and nature of the SHEs, showcase the breakdown of periodic trends in the seventh period, and allow us to revisit and confirm an empirical relation between adsorption on gold and the cohesive energy.

Solid Oganesson via a Many-Body Interaction Expansion Based on Relativistic Coupled-Cluster Theory and from Plane-Wave Relativistic Density Functional Theory.

Many-body potentials up to fourth order are constructed using nonrelativistic, scalar-relativistic, and relativistic coupled-cluster theory to accurately describe the interaction between superheavy oganesson atoms. The obtained distance-dependent energy values were fitted to extended two-body Lennard-Jones and three-body Axilrod-Teller-Muto potentials, with the fourth-order term treated through a classical long-range Drude dipole interaction model. From these interaction potentials, spectroscopic constants for the oganesson dimer and solid-state properties were obtained. Furthermore, these high-level results are compared to scalar-relativistic and two-component plane-wave DFT calculations based on a tailor-made projector augmented wave pseudopotential (PAW-PP) and newly derived parameters for Grimme's dispersion correction. It is shown that the functionals PBE-D3(BJ), PBEsol, and in particular SCAN provide excellent agreement with the many-body reference for solid oganesson. Finally, the results for oganesson are compared and related to the lighter rare gas elements, and periodic trends are discussed.