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.

Dispersion Energy-Stabilized Boron and Phosphorus Lewis Pairs.

An isostructural series of boron/phosphorus Lewis pairs was systematically investigated. The association constants of the Lewis pairs were determined at variable temperatures, enabling the extraction of thermodynamic parameters. The stabilization of the Lewis adduct increased with increasing size of the dispersion energy donor groups, although the donor and acceptor properties of the Lewis pairs remained largely unchanged. This data was utilized to challenge state-of-the-art quantum chemical methods, which finally led to an enhanced workflow for the determination of thermochemical properties of weakly bound Lewis pairs within an accuracy of 0.6 to 1.0 kcal mol-1 for computed association free energies.

The Role of Packing, Dispersion, Electrostatics, and Solvation in High-Affinity Complexes of Cucurbit[n]urils with Uncharged Polar Guests.

The rationalization of non-covalent binding trends is both of fundamental interest and provides new design concepts for biomimetic molecular systems. Cucurbit[n]urils (CBn) are known for a long time as the strongest synthetic binders for a wide range of (bio)organic compounds in water. However, their host-guest binding mechanism remains ambiguous despite their symmetric and simple macrocyclic structure and the wealth of literature reports. We herein report experimental thermodynamic binding parameters (ΔG, ΔH, TΔS) for CB7 and CB8 with a set of hydroxylated adamantanes, di-, and triamantanes as uncharged, rigid, and spherical/ellipsoidal guests. Binding geometries and binding energy decomposition were obtained from high-level theory computations. This study reveals that neither London dispersion interactions, nor electronic energies or entropic factors are decisive, selectivity-controlling factors for CBn complexes. In contrast, peculiar host-related solvation effects were identified as the major factor for rationalizing the unique behavior and record-affinity characteristics of cucurbit[n]urils.

Automated Molecular Cluster Growing for Explicit Solvation by Efficient Force Field and Tight Binding Methods.

An automated and broadly applicable workflow for the description of solvation effects in an explicit manner is introduced. This method, termed quantum cluster growth (QCG), is based on the semiempirical GFN2-xTB/GFN-FF methods, enabling efficient geometry optimizations and MD simulations. Fast structure generation is provided using the intermolecular force field xTB-IFF. Additionally, the approach uses an efficient implicit solvation model for the electrostatic embedding of the growing clusters. The novel QCG procedure presents a robust cluster generation tool for subsequent application of higher-level (e.g., DFT) methods to study solvation effects on molecular geometries explicitly or to average spectroscopic properties over cluster ensembles. Furthermore, the computation of the solvation free energy with a supermolecular approach can be carried out with QCG. The underlying growing process is physically motivated by computing the leading-order solute-solvent interactions first and can account for conformational and chemical changes due to solvation for low-energy barrier processes. The conformational space is explored with the NCI-MTD algorithm as implemented in the CREST program, using a combination of metadynamics and MD simulations. QCG with GFN2-xTB yields realistic solution geometries and reasonable solvation free energies for various systems without introducing many empirical parameters. Computed IR spectra of some solutes with QCG show a better match to the experimental data compared to well-established implicit solvation models.

Computer-aided simulation of infrared spectra of ethanol conformations in gas, liquid and in CCl4 solution.

The recently developed efficient protocol combining implicit and explicit, accurate quantum-mechanical modeling of the condensed state (Katsyuba et al., J. Chem. Phys. 155, 024507 [2021]) is used to describe the IR spectra of liquid ethanol and its solutions in CCl4 . The relative abundance of the anti and gauche conformers of ethanol is shown to increase from ~40:60 in the gas phase to ~55:45 in the liquid phase. In spite of a moderate impact of media effects on the conformational composition of the liquid, the solvent strongly influences vibrational frequencies, IR intensities, and normal modes of each conformer, producing qualitatively different spectra compared to the gas phase and CCl4 solution. Further, these solvent effects affecting IR frequencies and intensities depend not only on the conformation of the solvated molecule but also on the solvating species. Nevertheless, vibrational frequencies of anti and gauche conformers of liquid ethanol and its several isotopomers practically coincide with each other. Convenient liquid-state conformational markers in the fingerprint region of IR spectra are revealed for the hydroxyl-deuterated species: CH3 CH2 OD, CH3 CHDOD, CH3 CD2 OD, and CD3 CD2 OD.

Quickstart guide to model structures and interactions of artificial molecular muscles with efficient computational methods.

Artificial molecular muscles (AMMs) represent an important group of molecular machines. Their theoretical treatment is challenging due to size, element composition, and complex interaction motifs. Moreover, experimentally determined structures often only yield insights into the covalent connectivity of atoms rather than their 3D structure. Accordingly, a reproducible computational modeling of such structures is complicated. In this work we present a standardized, mostly quantum chemical protocol on how to obtain reliable structures from scratch and to compute contraction free energies ΔGc for daisy-chain rotaxane AMMs efficiently. In this protocol, the recently developed force-field (GFN-FF) and extended tight-binding methods (GFNn-xTB) are employed. For comparison, dispersion-corrected density functional theory (DFT-D) based reference ΔGc were computed. In one case for which data are available, excellent agreement between theoretical and experimental ΔGc values within 1-2 kcal mol-1 is obtained.

Nanoscale π-conjugated ladders.

It is challenging to increase the rigidity of a macromolecule while maintaining solubility. Established strategies rely on templating by dendrons, or by encapsulation in macrocycles, and exploit supramolecular arrangements with limited robustness. Covalently bonded structures have entailed intramolecular coupling of units to resemble the structure of an alternating tread ladder with rungs composed of a covalent bond. We introduce a versatile concept of rigidification in which two rigid-rod polymer chains are repeatedly covalently associated along their contour by stiff molecular connectors. This approach yields almost perfect ladder structures with two well-defined π-conjugated rails and discretely spaced nanoscale rungs, easily visualized by scanning tunnelling microscopy. The enhancement of molecular rigidity is confirmed by the fluorescence depolarization dynamics and complemented by molecular-dynamics simulations. The covalent templating of the rods leads to self-rigidification that gives rise to intramolecular electronic coupling, enhancing excitonic coherence. The molecules are characterized by unprecedented excitonic mobility, giving rise to excitonic interactions on length scales exceeding 100 nm. Such interactions lead to deterministic single-photon emission from these giant rigid macromolecules, with potential implications for energy conversion in optoelectronic devices.

Supramolecular Nanopatterns of Molecular Spoked Wheels with Orthogonal Pillars: The Observation of a Fullerene Haze.

Molecular spoked wheels with intraannular functionalizable pillars are synthesized in a modular approach. The functionalities at their ends are variable, and a propargyl alcohol, a [6,6]-phenyl-C61-butyrate, and a perylene monoimide are investigated. All compounds form two-dimensional crystals on highly oriented pyrolytic graphite at the solid-liquid interface. As determined by submolecularly resolved scanning tunneling microscopy, the pillars adopt equilibrium distances of 6.0 nm. The fullerene has a residual mobility, limited by the length of the flexible connector unit. The experimental results are supported and rationalized by molecular dynamics simulations. These also show that, in contrast, the more rigidly attached perylene monoimide units remain oriented along the surface normal and maintain a smallest distance of 2 nm above the graphite substrate. The robust packing concept also holds for cocrystals with molecular hexagons that expand the pillar-pillar distances by 15 % and block unspecific intercalation.

Revisiting conformations of methyl lactate in water and methanol.

The recently developed efficient protocols to implicit [Grimme et al., J. Phys. Chem. A 125, 4039-4054 (2021)] and explicit quantum mechanical modeling of non-rigid molecules in solution [Katsyuba et al., J. Phys. Chem. B 124, 6664-6670 (2020)] are applied to methyl lactate (ML). Building upon this work, a new combination scheme is proposed to incorporate solvation effects for the computation of infrared (IR) absorption spectra. Herein, Boltzmann populations calculated for implicitly solvated single conformers are used to weight the IR spectra of explicitly solvated clusters with a size of typically ten solvent molecules, i.e., accounting for the first solvation shell. It is found that in water and methanol, the most abundant conformers of ML are structurally modified relative to the gas phase, where the major form is ML1, in which the syn conformation of the -OH moiety is stabilized by a OH⋯O=C intramolecular hydrogen bond (HB). In solution, this syn conformation transforms to the gauche form because the intramolecular HB is disrupted by explicit water molecules that form intermolecular HBs with the hydroxyl and carbonyl groups. Similar changes induced by the gas-solution transition are observed for the minor conformers, ML2 and/or ML3, characterized by OH⋯OCH3 intramolecular HB in the gas phase. The relative abundance of ML1 is shown to decrease from ∼96% in gas to ∼51% in water and ∼92% in methanol. The solvent strongly influences frequencies, IR intensities, and normal modes, resulting in qualitatively different spectra compared to the gas phase. Some liquid-state conformational markers in the fingerprint region of IR spectra are revealed.

Robust and Efficient Implicit Solvation Model for Fast Semiempirical Methods.

We present a robust and efficient method to implicitly account for solvation effects in modern semiempirical quantum mechanics and force fields. A computationally efficient yet accurate solvation model based on the analytical linearized Poisson-Boltzmann (ALPB) model is parameterized for the extended tight binding (xTB) and density functional tight binding (DFTB) methods as well as for the recently proposed GFN-FF general force field. The proposed methods perform well over a broad range of systems and applications, from conformational energies over transition-metal complexes to large supramolecular association reactions of charged species. For hydration free energies of small molecules, GFN1-xTB(ALPB) is reaching the accuracy of sophisticated explicitly solvated approaches, with a mean absolute deviation of only 1.4 kcal/mol compared to the experiment. Logarithmic octanol-water partition coefficients (log Kow) are computed with a mean absolute deviation of about 0.65 using GFN2-xTB(ALPB) compared to experimental values indicating a consistent description of differential solvent effects. Overall, more than twenty solvents for each of the six semiempirical methods are parameterized and tested. They are readily available in the xtb and dftb+ programs for diverse computational applications.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions.

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

Efficient Quantum Chemical Calculation of Structure Ensembles and Free Energies for Nonrigid Molecules.

The application of quantum chemical, automatic multilevel modeling workflows for the determination of thermodynamic (e.g., conformation equilibria, partition coefficients, pKa values) and spectroscopic properties of relatively large, nonrigid molecules in solution is described. Key points are the computation of rather complete structure (conformer) ensembles with extremely fast but still reasonable GFN2-xTB or GFN-FF semiempirical methods in the CREST searching approach and subsequent refinement at a recently developed, accurate r2SCAN-3c DFT composite level. Solvation effects are included in all steps by accurate continuum solvation models (ALPB, (D)COSMO-RS). Consistent inclusion of thermostatistical contributions in the framework of the modified rigid-rotor-harmonic-oscillator approximation (mRRHO) based on xTB/FF computed PES is also recommended.

Single-Point Hessian Calculations for Improved Vibrational Frequencies and Rigid-Rotor-Harmonic-Oscillator Thermodynamics.

The calculation of harmonic vibrational frequencies (HVF) to interpret infrared (IR) spectra and to convert molecular energies to free energies is one of the essential steps in computational chemistry. A prerequisite for accurate thermostatistics so far was to optimize the molecular input structures in order to avoid imaginary frequencies, which inevitably leads to changes in the geometry if different theoretical levels are applied for geometry optimization and frequency calculations. In this work, we propose a new method termed single-point Hessian (SPH) for the computation of HVF and thermodynamic contributions to the free energy within the modified rigid-rotor-harmonic-oscillator approximation for general nonequilibrium molecular geometries. The key ingredient is the application of a biasing potential given as Gaussian functions expressed with the root-mean-square-deviation (RMSD) in Cartesian space in order to retain the initial geometry. The theory derived herein is generally applicable to quantum mechanical (QM), semiempirical QM, and force-field (FF) methods. Besides a detailed description of the underlying theory including the important back-correction of the biased HVF, the SPH approach is tested for reaction paths, molecular dynamics snapshots of crambin, and supramolecular association free energies in comparison to high-level density functional theory (DFT) values. Furthermore, the effect on IR spectra is investigated for organic dimers and transition-metal complexes revealing improved spectra at low theoretical levels. On average, DFT reference free energies are better reproduced by the newly developed SPH scheme than by conventional calculations on freely optimized geometries or without any relaxation.

Ox-SLIM: Synthesis of and Site-Specific Labelling with a Highly Hydrophilic Trityl Spin Label.

The combination of pulsed dipolar electron paramagnetic resonance spectroscopy (PDS) with site-directed spin labelling is a powerful tool in structural biology. Rational design of trityl-based spin labels has enabled studying biomolecular structures at room temperature and within cells. However, most current trityl spin labels suffer either from aggregation with proteins due to their hydrophobicity, or from bioconjugation groups not suitable for in-cell measurements. Therefore, we introduce here the highly hydrophilic trityl spin label Ox-SLIM. Engineered as a short-linked maleimide, it combines the most recent developments in one single molecule, as it does not aggregate with proteins, exhibits high resistance under in-cell conditions, provides a short linker, and allows for selective and efficient spin labelling via cysteines. Beyond establishing synthetic access to Ox-SLIM, its suitability as a spin label is illustrated and ultimately, highly sensitive PDS measurements are presented down to protein concentrations as low as 45 nm resolving interspin distances of up to 5.5 nm.

Modeling of spin-spin distance distributions for nitroxide labeled biomacromolecules.

Electron Paramagnetic Resonance (EPR) spectroscopy is a powerful method for unraveling structures and dynamics of biomolecules. Out of the EPR tool box, Pulsed Electron-Electron Double Resonance spectroscopy (PELDOR or DEER) enables one to resolve such structures by providing distances between spin centers on the nanometer scale. Most commonly, both spin centers are spin labels or one is a spin label and the other is a paramagnetic metal ion, cluster, amino acid or cofactor radical. Often, the translation of the measured distances into structures is complicated by the long and flexible linker connecting the spin center of the spin label with the biomolecule. Nowadays, this challenge is overcome by computational methods but the currently available approaches have a rather large mean error of roughly 2-3 Å. Here, the new GFN-FF general force-field is combined with the fully automated Conformer Rotamer Ensemble Search Tool (CREST) [P. Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles of the R1 side chain (methanthiosulfonate spin label (MTSL) covalently bound to a cysteine) in several cysteine mutants of azurin and T4 lysozyme. In order to determine the Cu2+-R1 and R1-R1 distance distributions, GFN-FF based MD simulations were carried out starting from the most probable R1 conformers found by CREST. The deviation between theory and experiment in mean inter-spin distances was 0.98 Å on average for the mutants of azurin (1.84 Å for T4 lysozyme) and the right modality was obtained. The error of the most probable distances for each mode was only 0.76 Å in the case of azurin. This CREST/MD procedure does thus enable precise distance-to-structure translations and provides a means to disentangle label from protein conformers.

Efficient Computation of Free Energy Contributions for Association Reactions of Large Molecules.

Modern density functional theory (DFT) methods are capable of providing accurate association energies for supramolecular systems and even protein-ligand complexes. However, the calculation of the essential harmonic vibrational frequencies needed to obtain free energies is often too computationally demanding. In this work, the corresponding thermostatistical contributions are computed in the well-established (modified) rigid-rotor-harmonic-oscillator approximation with structures and frequencies taken from low-cost quantum chemical methods, namely, GFN2-xTB and PM6-D3H4. Additionally, a recently developed new general force field (GFN-FF) is tested for this purpose. DFT reference values for 59 complexes composed of three standard noncovalent and supramolecular benchmark sets (S22, L7, and S30L) are used in the evaluation. Overall, the accuracy of the low-cost methods is remarkable with typical deviations of only 0.5-2 kcal mol-1 (5-10%) from the DFT reference values. In particular, the performance of the GFN-FF is promising considering the acceleration of 5 and 2-3 orders of magnitude compared to DFT and GFN2-xTB, respectively. This opens new perspectives for computing thermodynamic properties of, e.g., biomacromolecules as shown, for example, for the binding of retinol and rivaroxaban in protein complexes consisting of ≤4700 atoms.

Fast and Accurate Quantum Chemical Modeling of Infrared Spectra of Condensed-Phase Systems.

An efficient approach for an accurate quantum mechanical (QM) modeling of infrared (IR) spectra of condensed-phase systems is described. An ensemble of energetically low-lying cluster structures of a solute molecule surrounded by an explicit shell of solvent molecules is efficiently generated at the semiempirical tight-binding QM level and then reoptimized at the density functional theory level of theory. The IR spectrum of the solvated molecule is obtained as a thermodynamic average of harmonically computed QM spectra for all significantly populated cluster structures. The accuracy of such simulations in comparison to experimental data for some organic compounds and their solutions is shown to be the same or even better than the corresponding QM computations of the gas-phase IR spectrum for the isolated molecule.

Robust Atomistic Modeling of Materials, Organometallic, and Biochemical Systems.

Modern chemistry seems to be unlimited in molecular size and elemental composition. Metal-organic frameworks or biological macromolecules involve complex architectures and a large variety of elements. Yet, a general and broadly applicable theoretical method to describe the structures and interactions of molecules beyond the 1000-atom size regime semi-quantitatively is not self-evident. For this purpose, a generic force field named GFN-FF is presented, which is completely newly developed to enable fast structure optimizations and molecular-dynamics simulations for basically any chemical structure consisting of elements up to radon. The freely available computer program requires only starting coordinates and elemental composition as input from which, fully automatically, all potential-energy terms are constructed. GFN-FF outperforms other force fields in terms of generality and accuracy, approaching the performance of much more elaborate quantum-mechanical methods in many cases.

Pulsed EPR Dipolar Spectroscopy on Spin Pairs with one Highly Anisotropic Spin Center: The Low-Spin FeIII Case.

Pulsed electron paramagnetic resonance (EPR) dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling constants and thus the distance between electron spin centers. Up to now, PDS measurements have been mostly applied to spin centers whose g-anisotropies are moderate and therefore have a negligible effect on the dipolar coupling constants. In contrast, spin centers with large g-anisotropy yield dipolar coupling constants that depend on the g-values. In this case, the usual methods of extracting distances from the raw PDS data cannot be applied. Here, the effect of the g-anisotropy on PDS data is studied in detail on the example of the low-spin Fe3+ ion. First, this effect is described theoretically, using the work of Bedilo and Maryasov (Appl. Magn. Reson. 2006, 30, 683-702) as a basis. Then, two known Fe3+ /nitroxide compounds and one new Fe3+ /trityl compound were synthesized and PDS measurements were carried out on them using a method called relaxation induced dipolar modulation enhancement (RIDME). Based on the theoretical results, a RIDME data analysis procedure was developed, which facilitated the extraction of the inter-spin distance and the orientation of the inter-spin vector relative to the Fe3+ g-tensor frame from the RIDME data. The accuracy of the determined distances and orientations was confirmed by comparison with MD simulations. This method can thus be applied to the highly relevant class of metalloproteins with, for example, low-spin Fe3+ ions.

Pulsed EPR Dipolar Spectroscopy under the Breakdown of the High-Field Approximation: The High-Spin Iron(III) Case.

Pulsed EPR dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling and thus the distance between electron-spin centers. To date, PDS measurements to metal centers were limited to ions that adhere to the high-field approximation. Here, the PDS methodology is extended to cases where the high-field approximation breaks down on the example of the high-spin Fe3+ /nitroxide spin-pair. First, the theory developed by Maryasov et al. (Appl. Magn. Reson. 2006, 30, 683-702) was adapted to derive equations for the dipolar coupling constant, which revealed that the dipolar spectrum does not only depend on the length and orientation of the interspin distance vector with respect to the applied magnetic field but also on its orientation to the effective g-tensor of the Fe3+ ion. Then, it is shown on a model system and a heme protein that a PDS method called relaxation-induced dipolar modulation enhancement (RIDME) is well-suited to measuring such spectra and that the experimentally obtained dipolar spectra are in full agreement with the derived equations. Finally, a RIDME data analysis procedure was developed, which facilitates the determination of distance and angular distributions from the RIDME data. Thus, this study enables the application of PDS to for example, the highly relevant class of high-spin Fe3+ heme proteins.