We present q-vSZPs, a polarized, environment-adaptive minimal Gaussian basis set parameterized for elements Z = 1-86 (excluding lanthanides) and designed for efficient mean-field quantum-mechanical calculations on large molecular systems. Building on the previously introduced q-vSZP basis set, the number of primitive functions is substantially reduced while retaining the key feature of charge- and coordination-number-dependent contraction coefficients, which enable environment-dependent "breathing" of the atomic orbitals. The effective atomic charges required for the basis set setup are obtained from the bond-capacity electronegativity equilibration model (EEQBC), which accurately reproduces density functional theory (DFT)-level Hirshfeld charges at negligible computational cost. Comprehensive benchmarking on the GMTKN55 database demonstrates that q-vSZPs incurs only a moderate loss in accuracy relative to q-vSZP (WTMAD-2 increase of 2.9 kcal⋅mol-1), while substantially outperforming conventional non-adaptive minimal basis sets (MBs). For non-covalent interactions, the performance even surpasses that of the double-ζ def2-SVP basis set, owing to a substantially lower basis set superposition error as a consequence of the molecular optimization strategy. A non-adaptive variant using averaged charges and coordination numbers (qavg-vSZPs) is additionally provided as a drop-in minimal basis for any quantum-chemical program. For a representative 4108-atom system, q-vSZPs achieves a twofold reduction in both SCF wall time and memory consumption for DFT calculations relative to q-vSZP, placing it in the efficiency range of other MBs. The utility of q-vSZPs is further demonstrated through a mixed-basis application for the computation of the Raman spectrum of adenine in water.

Non-local exchange (NLX) is a key ingredient for accurate density functional calculations, but its effective strength is often hard to quantify beyond simple global hybrids. To this end, we introduce a molecular probe based on the isomerization of hexaethynylbenzene to carbo-benzene, a reaction with exceptional sensitivity to exchange effects. Using the isomerization energy, we define a simple relative measure, 𝑡 X , that gauges the effective NLX of a method on a scale ranging from 0 for the local density approximation to 100 for Hartree-Fock. Across a broad set of density functional approximations, 𝑡 X closely tracks the formal Hartree-Fock exchange content of global hybrids, while revealing that most common GGAs, meta-GGAs, and global hybrids still provide too little effective exchange. Several range-separated hybrid, double hybrid, and some local hybrid functionals perform much better and closely approach the near-basis-set-limit coupled-cluster reference value of 𝑡 X = 60. The 𝑡 X values of various semiempirical quantum mechanical and machine-learned interatomic potential methods indicate that they empirically account for NLX effects to a varying degree. Thus, the proposed reaction serves as a compact thermochemical benchmark for assessing and developing methods that aim to reliably describe non-local exchange.

We introduce the total atomization energy periodic table compass (TAE-PTComp), a collection of 67 atomization energy data sets, each specifically designed to probe various chemical environments of a characteristic element of the periodic table. In total, this set comprises 2,097 carefully curated closed-shell, single-reference molecules containing up to 50 atoms, with an average of 31 structures per element-specific subset. The chemical space covered ranges from conventional covalent and coordination compounds to noncovalently bound clusters, extracted fragments of periodic crystalline structures, and artificial "mindless" molecules. Additionally, we include a balanced amount of charged species with charges of ±1. For each molecule, as well as its constituent atoms (and ions), we provide high-level coupled cluster reference energies. We therefore envision this benchmark as a resource for parameter fitting, validation, and testing of approximate density functional theory methods, semi-empirical models, and machine-learning interatomic potentials. An initial assessment of TAE-PTComp for a representative set of density functional approximations, together with the semi-empirical g-xTB method and the machine-learned Universal Model for Atoms (UMA), shows that this benchmark can efficiently differentiate between broadly robust methods, such as the range-separated hybrid ωB97M-V, and approaches that exhibit localized, element-specific failures, such as the hybrid M06-2X functional.

We present g-xTB, a next-generation semi-empirical electronic structure method derived from tight-binding (TB) approximations to Kohn–Sham density functional theory (KS-DFT). Designed to bridge the gap between semi-empirical quantum mechanical (SQM) approaches and DFT in terms of accuracy, robustness, and general applicability, g-xTB targets the performance of the ωB97M-V range-separated hybrid density functional with large basis sets while maintaining TB speed. Key innovations include an atom-in-molecule adaptive atomic orbital basis, a refined Hamiltonian incorporating range-separated approximate Fock exchange, up to fourth-order charge-fluctuation terms with a novel first-order electronic contribution, and atomic correction potentials (ACPs), as well as a charge-dependent semi-classical repulsion function. Parameterized on extended and extremely diverse molecular training sets – including “mindless molecules” – g-xTB achieves excellent accuracy across a broad chemical space, including the actinide elements. Benchmarking against around 32k relative energies across thermochemistry, conformational energetics, non-covalent interactions, and reaction barriers shows that g-xTB consistently outperforms GFN2-xTB, often reducing mean absolute errors by half. Notably, it achieves a WTMAD-2 of 9.3 kcal mol−1 on the full GMTKN55 benchmark, comparable to low-cost DFT methods. It also shows substantial improvements for transition-metal complexes, relative spin state energies, and orbital energy gaps – areas where many SQM and even DFT methods often struggle. In summary, g-xTB offers DFT-like accuracy with minimal computational overhead compared to its predecessor, GFN2-xTB, making it a robust, minimally empirical, transferable, and efficient alternative to machine learning interatomic potentials for a wide range of molecular simulations. It is proposed as a general replacement for the GFNn-xTB family and, in many practical cases, a viable substitute for low- and mid-level DFT methods.

The Acceleration Consortium and Merck KGaA hosted a 2-day virtual hackathon on March 27- 28, 2024, bringing together scientists to explore, collaborate, and innovate in the field of Bayesian optimization for the physical sciences. Participants were encouraged to select or develop Bayesian optimization algorithms, apply them to benchmarking tasks, design new benchmarks, create instructional tutorials, and describe real-world applications. With over 100 participants across 69 academic, industry, and government organizations located in 59 cities, 19 countries, and 4 continents, this was a global event. The outputs from this event, including developed algorithms, benchmarks, and tutorials, will serve as valuable resources for the research community, in addition to the new skills learned and connections formed. Released projects and general information are available at https://ac-bo-hackathon.github.io/ and other locations linked from individual project pages. This event demonstrates the potential of community-driven research efforts to accelerate advances in Bayesian optimization in chemistry and materials science.

The accurate and efficient assignment of atomic partial charges is crucial for many applications in theoretical and computational chemistry, including polarizable force fields, dispersion corrections, and charge-dependent basis sets. Classical charge models struggle to distinguish between neutral and zwitterionic fragments because, unlike quantum mechanical methods, there are no discrete electronic states. This limitation can lead to either reduced or additional artificial charge transfer (CT) at different interfragment distances. To address this issue, we propose a new version of a bond capacity electronegativity equilibration (EEQBC) model, which limits artificial CT between distant fragments in the simple EEQ framework. EEQBC offers excellent agreement with DFT-based reference charges for elements up to lawrencium (Z = 103) with mean absolute errors as low as 0.02 and 0.07 e- for random PubChem molecules and "mindless" molecules (MLMs), respectively. Thanks to its computational efficiency for both atomic charges and their analytical nuclear gradients, EEQBC is highly suitable as an initial charge guess for next-generation tight-binding methods. For seamless accessibility, EEQBC is implemented in the upcoming 0.5.0 release of the freely available multicharge program at github.com/grimme-lab/multicharge.

Effective single-particle theories, such as Hartree-Fock, density functional theory, and tight-binding, are limited by the computational cost of the self-consistent field (SCF) procedure, which typically scales cubically with the system size. This makes large-scale applications impractical without specialized algorithms and hardware. Here, we present the submatrix and graphical processing unit (GPU)-accelerated software implementation of the PTB tight-binding potential, realized in the open-source ptb codebase [M. Mueller, A. Katbashev, and S. Ehlert (2025). "grimme-lab/ptb: v3.8.1," Zenodo. https://zenodo.org/records/17015872]. We first benchmark a traditional diagonalization-based SCF solver against density-matrix-based purification approaches, systematically varying both system size and computer hardware. Our findings show that the usage of GPUs permits shifting the boundaries to much larger systems than previously thought feasible, achieving an overall 10-15-fold performance speedup. Second, we introduce the implementation of a decomposition-type submatrix method, specifically designed for efficient operation on mid- to large-sized systems, to address the computational overhead associated with full-system diagonalization. We demonstrate that, from a certain dimension (≈104 basis functions) on, our submatrix method reduces the overall computational cost while maintaining acceptable numerical accuracy. Our study demonstrates the significance of the interplay between modern hardware, algorithmic considerations, and novel tight-binding methods, paving the way for further development in this direction.

We introduce MindlessGen, a Python-based generator for creating chemically diverse, "mindless" molecules through random atomic placement and subsequent geometry optimization. Using this framework, we constructed the MB2061 benchmark set, containing 2061 molecules with high-level PNO-LCCSD(T)-F12 reference data for H2-promoted decomposition reactions. This set provides a challenging benchmark for testing, validating, and training density functional approximations (DFAs), semiempirical methods, force fields, and machine learning potentials using molecular structures beyond conventional chemical space. For DFAs, we initially hypothesized that highly parametrized functionals might perform poorly on this set. However, no consistent relationship between the fitting strategy and accuracy was observed. A clear Jacob's ladder trend emerges, with ωB97X-2 achieving the lowest mean absolute error (MAE) of 8.4 kcal·mol-1 and r2SCAN-3c offering a robust cost-efficient alternative (19.6 kcal·mol-1). Furthermore, we discuss the performance of selected semiempirical methods and contemporary machine-learning interatomic potentials.

The Charge Extended Hückel (CEH) model, initially introduced for adaptive atomic orbital (AO) basis set construction (J. Chem. Phys. 159, 164108 (2023)), has been significantly revised to enhance accuracy and robustness, particularly in challenging electronic situations. This revision includes an extension towards f-elements, covering actinoids with their f-electrons in the valence space. We present a novel non-iterative approximation for the electrostatic contribution to the effective Fock matrix, which substantially improves performance in polar or charged systems. Additionally, the training dataset for elements Z = 1-103 has been expanded to encompass even more chemically diverse reference molecules as well as dipole moments and shell populations in addition to atomic charges. It includes a greater variety of "mindless" molecules (MLMs) as well as more complex electronic structures through open-shell and highly charged species. The revised method achieves mean absolute errors for atomic charges q of approximately 0.02 e- for randomly selected (mostly organic) molecules and 0.09 e- for MLMs, outperforming both classical charge models and established tight-binding methods. Furthermore, the revised CEH model has been validated through density functional theory calculations with the updated adaptive q-vSZP AO basis set on common thermochemical databases. Consistent with the extension of the CEH model, q-vSZP has also been variationally optimized and tested for elements Z = 58-71 and 87-103. The original versions of both CEH and q-vSZP are now considered deprecated.

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.

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations; (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix; (c) new P-dependent terms emulating non-local exchange are included; and (d) only element-specific empirical parameters (about 50 per element) need to be determined. The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3-4 orders of magnitude. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn-Sham potential. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods.

An environmentally responsible synthesis of tezacaftor, a drug approved in 2018 currently in use for treatment of cystic fibrosis, is described utilizing chemistry in water enabled by the nonionic surfactant TPGS-750-M.

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

The P-stereogenic bis(phosphanes) 7 and 9, featuring pairs of P(Mes)-ethynyl or vinyl substituents at the dimethyl xanthene backbone show rather low barriers of stereochemical inversion at phosphorus. π-Conjugative effects are probably causing these low inversion barriers. Compound 7 reacted with B(C6 F5 )3 to form the nine-membered heterocyclic product 10, featuring a [P]-C≡C-B(C6 F5 )3 substituent. Compound 7 was converted to the bis[P(Mes)vinyl] xanthene derivative 9, which gave the zwitterionic P(H)(Mes)-CH=CH-B(C6 F5 )3 containing product 16 upon treatment with B(C6 F5 )3 . Thermally induced epimerization barriers at phosphorus of ca. 20 to 27 kcal mol-1 were calculated by DFT for the alkenyl- and alkynyl-P derived systems 6 to 9, 15 and 16 and experimentally determined for the examples 7 and 16.

Attachment of a pair of P-stereogenic mesityl(alkynyl)phosphanyl groups at the 4- and 5-positions of a 9,9-dimethylxanthene framework gave mixtures of the respective rac- and meso-bisphosphanyl diastereoisomers. They slowly epimerized in a thermally induced reaction with Gibbs activation barriers of about 25 kcal mol(-1) at room temperature (measured and DFT calculated). The reaction of the meso-mesityl(tert-butylethynyl)phosphanyl derivative with two molar equivalents of Piers ' borane [HB(C6F5)(2)] led to the formation of the alkylidene-bridged geminal bisphosphane/borane-frustrated Lewis pair system. The compound was obtained enriched (>85 %) in the rac diastereoisomer. With a variety of bifunctional donor substrates, the rac-bis-P/B FLP formed macrocyclic compounds. They were all formally derived from meso-configurated diastereoisomers of the bisphosphanylxanthene backbone.