Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets.

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

Reaction-Free Energies for Complexation of Carbohydrates by Tweezer Diboronic Acids.

The accurate calculation of reaction-free energies (ΔrG°) for diboronic acids and carbohydrates is challenging due to reactant flexibility and strong solute-solvent interactions. In this study, these challenges are addressed with a semiautomatic workflow based on quantum chemistry methods to calculate conformational free energies, generate microsolvated solute structural ensembles, and compute ΔrG°. Workflow parameters were optimized for accuracy and precision while controlling computational costs. We assessed the accuracy by studying three reactions of diboronic acids with glucose and galactose, finding that the conformational entropy contributes significantly (by 3-5 kcal/mol at room temperature). Explicit solvent molecules improve the computed ΔrG° accuracy by about 4 kcal/mol compared to experimental data, though using 13 or more water molecules reduced precision and increased computational overhead. After fine-tuning, the workflow demonstrated remarkable accuracy, with an absolute error of about 2 kcal/mol compared to experimental ΔrG° and an average interquartile range of 2.4 kcal/mol. These results highlight the workflow's potential for designing and screening tweezer-like ligands with tailored selectivity for various carbohydrates.

Extension of the D3 and D4 London dispersion corrections to the full actinides series.

Efficient dispersion corrections are an indispensable component of modern density functional theory, semi-empirical quantum mechanical, and even force field methods. In this work, we extend the well established D3 and D4 London dispersion corrections to the full actinides series, francium, and radium. To keep consistency with the existing versions, the original parameterization strategy of the D4 model was only slightly modified. This includes improved reference Hirshfeld atomic partial charges at the ωB97M-V/ma-def-TZVP level to fit the required electronegativity equilibration charge (EEQ) model. In this context, we developed a new actinide data set called AcQM, which covers the most common molecular actinide compound space. Furthermore, the efficient calculation of dynamic polarizabilities that are needed to construct CAB6 dispersion coefficients was implemented into the ORCA program package. The extended models are assessed for the computation of dissociation curves of actinide atoms and ions, geometry optimizations of crystal structure cutouts, gas-phase structures of small uranium compounds, and an example extracted from a small actinide complex protein assembly. We found that the novel parameterizations perform on par with the computationally more demanding density-dependent VV10 dispersion correction. With the presented extension, the excellent cost-accuracy ratio of the D3 and D4 models can now be utilized in various fields of computational actinide chemistry and, e.g., in efficient composite DFT methods such as r2SCAN-3c. They are implemented in our freely available standalone codes (dftd4, s-dftd3) and the D4 version will be also available in the upcoming ORCA 6.0 program package.

Molecular folding governs switchable singlet oxygen photoproduction in porphyrin-decorated bistable rotaxanes.

Rotaxanes are mechanically interlocked molecules where a ring (macrocycle) is threaded onto a linear molecule (thread). The position of the macrocycle on different stations on the thread can be controlled in response to external stimuli, making rotaxanes applicable as molecular switches. Here we show that bistable rotaxanes based on the combination of a Zn(II) tetraphenylporphyrin photosensitizer, attached to the macrocycle, and a black-hole-quencher, attached to the thread, are capable of singlet oxygen production which can be switched on/off by the addition of base/acid. However, we found that only a sufficiently long linker between both stations on the thread enabled switchability, and that the direction of switching was inversed with regard to the original design. This unexpected behavior was attributed to intramolecular folding of the rotaxanes, as indicated by extensive theoretical calculations. This evidences the importance to take into account the conformational flexibility of large molecular structures when designing functional switchable systems.

dxtb-An efficient and fully differentiable framework for extended tight-binding.

Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.

Structure and intermolecular interactions in ionic liquid 1-ethyl-3-methylimidazolium bromide and its aqueous solutions investigated by vibrational spectroscopy and quantum chemical computations.

The recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions (S. A. Katsyuba, S. Spicher, T. P. Gerasimova, S. Grimme, J. Phys. Chem. B 2020, 124, 6664) is applied to ionic liquid (IL) 1-ethyl-3-methylimidazolium bromide (EmimBr), its C2-deuterated analog [Emim-d]Br and its aqueous solutions. It is shown that the solvation strongly modifies frequencies and IR intensities of the CH/CD stretching vibrations (νCH/νCD) of the imidazolium ring. The main vibrational spectroscopic features of the neat IL are reproduced by the simulations for a cluster (EmimBr)9, in which all three imidazolium CH moieties of the solvated cation form short contacts with three Br- anions, and another two Br- anions are located on top and bottom of imidazolium ring. Cluster models of aqueous solutions reproduce the experimental vibrational frequencies of actual solutions, provided that the Br- anion of solvated contact ion pair (CIP) is situated on top of imidazolium ring, and CH/CD moieties of the latter participate in short contacts with surrounding water molecules. Both structural and spectroscopic analysis allow to interpret the short contacts CH/CD⋯Br- and CH/CD⋯OH2 as hydrogen bonds of approximately equal strength. Enthalpies of bonding of these liquid-state H-bonds, estimated with the use of empirical correlations, amount to ca. 1.4 kcal⋅mol-1, while the analogous estimates obtained for the gas-phase charged species [Emim]2Br+ increase to 5.6 kcal⋅mol-1. It is shown that formation of solvent-shared ion pair (SIP) in aqueous solution, where the counterions of IL are separated by two water molecules H-bonded to a Br- anion, produces frequency shifts ΔνCH/CD, strongly different from the case of CIP formation. This difference can be used for IR/Raman spectroscopic differentiation of the type of solvated ion pairs of EmimBr or other related ILs.

Size-Increased All-Phenylene Molecular Spoked Wheels - A Combined Theoretical and Experimental Approach.

A lateral expansion of molecular spoked wheels (MSWs) based on an all-phenylene backbone is described. The MSWs contain a central hub, six spokes and a rim that is formed by a sixfold Yamamoto coupling of the respective non-cyclized dodecabromo precursor yielding MSWs with up to 30 phenylene rings in the perimeter. Attempts to prepare compounds of such size without flexible side groups at the spokes were unsuccessful, most probably due to an aggregation and accompanying oligomerization of the precursors during the cyclization. To overcome these problems, fluorene units are inserted into the spokes. These contain additional alkyl chains and lead to a curvature of the wheels. Quantum chemical calculations on the mechanism of the Yamamoto coupling leads to geometry and strain-related criteria for the successful rim closure to the respective MSW. Subsequently, MSWs are prepared with four and even six phenylene units at each edge of the hexagonal wheels. The resulting MSWs are characterized by spectroscopic methods, and additionally some of them are visualized via scanning tunneling microscopy (STM).

ΔDFT Predicts Inverted Singlet-Triplet Gaps with Chemical Accuracy at a Fraction of the Cost of Wave Function-Based Approaches.

Efficient OLEDs need to quickly convert singlet and triplet excitons into photons. Molecules with an inverted singlet-triplet energy gap (INVEST) are promising candidates for this task. However, typical INVEST molecules have drawbacks like too low oscillator strengths and excitation energies. High-throughput screening could identify suitable INVEST molecules, but existing methods are problematic: The workhorse method TD-DFT cannot reproduce gap inversion, while wave function-based methods are too slow. This study proposes a state-specific method based on unrestricted Kohn-Sham DFT with common hybrid functionals. Tuned on the new INVEST15 benchmark set, this method achieves an error of less than 1 kcal/mol, which is traced back to error cancellation between spin contamination and dynamic correlation. Applied to the larger and structurally diverse NAH159 set in a black-box fashion, the method maintains a small error (1.2 kcal/mol) and accurately predicts gap signs in 83% of cases, confirming its robustness and suitability for screening workflows.

Pushing the Limits of Organometallic Redox Chemistry with an Isolable Mn(-I) Dianion.

We report an incredibly reducing and redox-active Mn-I dianion, [Mn(CO)3(Ph2B(tBuNHC)2)]2- (NHC = N-heterocyclic carbene), furnished via 2e- reduction of the parent 16e- MnI complex with Na0 or K0. Cyclic voltammograms show a Mn0/-I redox couple at -3.13 V vs Fc+/0 in tetrahydrofuran (THF), -3.06 V in 1,2-dimethoxyethane, and -2.85 V in acetonitrile. The diamagnetic Mn-I dianion is stable in solution and solid-state at room temperature, tolerating a wide range of countercations ([M(2.2.2)crypt]+, [M(18-crown-6)]+, [nBu4N]+; M = Na, K). Countercation identity does not significantly alter 13C NMR spectral signatures with [nBu4N]+ and Na+, suggesting minimal ion pairing in solution. IR spectroscopy reveals a significant decrease in CO stretching frequencies from MnI to Mn-I (ca. 240 cm-1), consistent with a drastic increase in electron density at Mn. State-of-the-art DFT calculations are in excellent agreement with the observed IR spectral data. Moreover, the Mn-I dianion behaves as a chemical reductant, smoothly releasing 1e- or 2e- to regenerate the oxidized Mn0 or MnI species in solution. The reducing potential of [Mn(CO)3(Ph2B(tBuNHC)2)]2- surpasses the naphthalenide anion in THF (-3.09 V) and represents one of the strongest isolable chemical redox agents.

Benchmarking Charge-Transfer Excited States in TADF Emitters: ΔDFT Outperforms TD-DFT for Emission Energies.

Charge-transfer (CT) excited states are crucial to organic light-emitting diodes (OLEDs), particularly to those based on thermally activated delayed fluorescence (TADF). However, accurately modeling CT states remains challenging, even with modern implementations of (time-dependent) density functional theory [(TD-)DFT], especially in a dielectric environment. To identify shortcomings and improve the methodology, we previously established the STGABS27 benchmark set with highly accurate experimental references for the adiabatic energy gap between the lowest singlet and triplet excited states (ΔEST). Here, we diversify this set to the STGABS27-EMS benchmark by including experimental emission energies (Eem) and use this new set to (re)-evaluate various DFT-based approaches. Surprisingly, these tests demonstrate that a state-specific (un)restricted open-shell Kohn-Sham (U/ROKS) DFT coupled with a polarizable continuum model for perturbative state-specific nonequilibrium solvation (ptSS-PCM) provides exceptional accuracy for predicting Eem over a wide range of density functionals. In contrast, the main workhorse of the field, Tamm-Dancoff-approximated TD-DFT (TDA-DFT) paired with the same ptSS-PCM, is distinctly less accurate and strongly functional-dependent. More importantly, while TDA-DFT requires the choice of two very different density functionals for good performance on either ΔEST or Eem, the time-independent U/ROKS/PCM approaches deliver excellent accuracy for both quantities with a wide variety of functionals.

Fluorination/Dearomatization of C6F5 Groups: An FLP Route to an Electrophilic Borane and Non-Coordinating Anions.

B(C6F5)3 and the corresponding anion [B(C6F5)4]- are ubiquitous in main group and transition metal chemistry. Known derivatives are generally limited to the incorporation of electron donating substituents. Herein we describe electrophilic fluorination and dearomatization of such species using XeF2 in the presence of BF3 or Lewis acidic cations. In this fashion the anions [HB(C6F5)3]-, [B(C6F5)4]- and [(C6F5)3BC≡NB(C6F5)3]-, are converted to [FB(C6F7)3]-, [B(C6F7)4]-, and [(C6F7)3BC≡NB(C6F7)3]-, respectively. Similarly, the borane adducts (L)B(C6F7)3 (L=MeCN, OPEt3) are produced. These rare examples of electrophilic attack of electron deficient rings proceed as [XeF][BF4] acts as a frustrated Lewis pair effecting fluorination and dearomatization of C6F5 rings.

Mechanism of Alkaline Earth Metal Amide Catalyzed Hydrogenation of Challenging Alkenes and Arenes.

Recently, bulky alkaline earth (Ae=Mg, Ca, Sr, Ba) metal amide complexes AeN"2 (N"=N[Si(iPr)3]2) are shown to be active for catalyzing the hydrogenation of unactivated alkenes and arenes, presumably via the monomer N"AeH as catalyst. In sharp contrast, our extensive DFT calculations disclose that the double Ae-H-Ae bridged dimer (N"AeH)2 is kinetically more favorable in catalytic hydrogenation with H2, although rate-limited by the initial hydrogenolysis of AeN"2 to form the monomer N"AeH.

The eXact integral simplified time-dependent density functional theory (XsTD-DFT).

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

Stereoconvergent Approach to the Enantioselective Construction of α-Quaternary Alcohols by Radical Epoxide Allylation.

We describe a highly stereoconvergent radical epoxide allylation towards diastereomerically and enantiomerically enriched α-quaternary alcohols in two steps from olefins. Our approach combines the stereospecifity and enantioselectivity of the Shi epoxidation with the unprecedented Ti(III)-promoted intramolecular radical group transfer allylation of epoxides. A directional isomerization step via configurationally labile radical intermediates enables the selective preparation of all-carbon quaternary stereocenters in a unique fashion.

Structural flexibility of favipiravir and its structural analogues in solutions: experimental and computational insight.

Combined UV-vis and quantum chemical studies of the structural flexibility and tautomerism of 6-R-3-hydroxy-2-pyrazine carboxamides in solutions revealed that their keto-enol transformations are accompanied by the deprotonation of enol tautomers and the formation of the corresponding anionic species. Both the solvent and the 6-R substituent strongly influence the relative abundance of the above forms in solutions. Anions are not formed in 1,2-dichloroethane (DCE), but the probability of deprotonation in neutral water and N,N-dimethylformamide (DMF) increases in the order R = H < F < NO2. Only enol tautomers of all solutes are found in DCE. DMF stabilizes keto forms only moderately and assists much strongly in the deprotonation of all three compounds. Water tends to stabilize both keto tautomers and deprotonated anions: the keto form dominates in the case of R = H (antiviral drug T-1105), the anions are found exclusively for R = NO2, and the aqueous solution of another antiviral drug, favipiravir (R = F), contains both the keto tautomer and the anionic form. The results of quantum chemical free energy calculations are in agreement with the experimental observations.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations.

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

CREST-A program for the exploration of low-energy molecular chemical space.

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Benchmark Study on the Calculation of 207Pb NMR Chemical Shifts.

A benchmark set for the computation of 207Pb nuclear magnetic resonance (NMR) chemical shifts is presented. The PbS50 set includes conformer ensembles of 50 lead-containing molecular compounds and their experimentally measured 207Pb NMR chemical shifts. Various bonding motifs at the Pb center with up to seven bonding partners are included. Six different solvents were used in the measurements. The respective shifts lie in the range between +10745 and -5030 ppm. Several calculation settings are assessed by evaluating computed 207Pb NMR shifts for the use with different density functional approximations (DFAs), relativistic approaches, treatment of the conformational space, and levels for geometry optimization. Relativistic effects were included explicitly with the zeroth order regular approximation (ZORA), for which only the spin-orbit variant was able to yield reliable results. In total, seven GGAs and three hybrid DFAs were tested. Hybrid DFAs significantly outperform GGAs. The most accurate DFAs are mPW1PW with a mean absolute deviation (MAD) of 429 ppm and PBE0 with an MAD of 446 ppm. Conformational influences are small as most compounds are rigid, but more flexible structures still benefit from Boltzmann averaging. Including explicit relativistic treatments such as SO-ZORA in the geometry optimization does not show any significant improvement over the use of effective core potentials (ECPs).

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.