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.

Multilevel Framework for Analysis of Protein Folding Involving Disulfide Bond Formation.

In this study, a three-layered multicenter ONIOM approach is implemented to characterize the naive folding pathway of bovine pancreatic trypsin inhibitor (BPTI). Each layer represents a distinct level of theory, where the initial layer, encompassing the entire protein, is modeled by a general all-atom force-field GFN-FF. An intermediate electronic structure layer consisting of three multicenter fragments is introduced with the state-of-the-art semiempirical tight-binding method GFN2-xTB. Higher accuracy, specifically addressing the breaking and formation of the three disulfide bonds, is achieved at the innermost layer using the composite DFT method r2SCAN-3c. Our analysis sheds light on the structural stability of BPTI, particularly the significance of interlinking disulfide bonds. The accuracy and efficiency of the multicenter QM/SQM/MM approach are benchmarked using the oxidative formation of cystine. For the folding pathway of BPTI, relative stabilities are investigated through the calculation of free energy contributions for selected intermediates, focusing on the impact of the disulfide bond. Our results highlight the intricate trade-off between accuracy and computational cost, demonstrating that the multicenter ONIOM approach provides a well-balanced and comprehensive solution to describe electronic structure effects in biomolecular systems. We conclude that multiscale energy landscape exploration provides a robust methodology for the study of intriguing biological targets.

Exploring energy landscapes for solid-state systems with variable cells at the extended tight-binding level.

The design of novel materials requires a theoretical understanding of dynamical processes in the solid state, including polymorphic transitions and associated pathways. The organization of the potential energy landscape plays a crucial role in such processes, which may involve changes in the periodic boundaries. This study reports the implementation of a general framework for periodic condensed matter systems in our energy landscape analysis software, allowing for variation in both the unit cell and atomic positions. This implementation provides access to basin-hopping global optimization, the doubly nudged elastic band procedure for identifying transition state candidates, the missing connection approach for multi-step pathways, and general tools for the construction and analysis of kinetic transition networks. The computational efficacy of the procedures is explored using the state-of-the-art semiempirical method GFN1-xTB for the first time in this solid-state context. We investigate the effectiveness of this level of theory by characterizing the potential energy and enthalpy landscapes of several systems, including silicon, CdSe, ZnS, and NaCl, and discuss further technical challenges, such as translational permutation of the cell. Despite the expected limitations of the semiempirical method, we find that the resulting energy landscapes provide useful insight into solid-state simulations, which will facilitate detailed analysis of processes such as defect and ion migration, including refinement at higher levels of theory.

Finding Excited-State Minimum Energy Crossing Points on a Budget: Non-Self-Consistent Tight-Binding Methods.

The automated exploration and identification of minimum energy conical intersections (MECIs) is a valuable computational strategy for the study of photochemical processes. Due to the immense computational effort involved in calculating non-adiabatic derivative coupling vectors, simplifications have been introduced focusing instead on minimum energy crossing points (MECPs), where promising attempts were made with semiempirical quantum mechanical methods. A simplified treatment for describing crossing points between almost arbitrary diabatic states based on a non-self-consistent extended tight-binding method, GFN0-xTB, is presented. Involving only a single diagonalization of the Hamiltonian, the method can provide energies and gradients for multiple electronic states, which can be used in a derivative coupling-vector-free scheme to calculate MECPs. By comparison with high-lying MECIs of benchmark systems, it is demonstrated that the identified geometries are good starting points for further MECI refinement with ab initio methods.

Multifaceted View on the Mechanism of a Photochemical Deracemization Reaction.

Upon irradiation in the presence of a chiral benzophenone catalyst (5 mol %), a racemic mixture of a given chiral imidazolidine-2,4-dione (hydantoin) can be converted almost quantitatively into the same compound with high enantiomeric excess (80-99% ee). The mechanism of this photochemical deracemization reaction was elucidated by a suite of mechanistic experiments. It was corroborated by nuclear magnetic resonance titration that the catalyst binds the two enantiomers by two-point hydrogen bonding. In one of the diastereomeric complexes, the hydrogen atom at the stereogenic carbon atom is ideally positioned for hydrogen atom transfer (HAT) to the photoexcited benzophenone. Detection of the protonated ketyl radical by transient absorption revealed hydrogen abstraction to occur from only one but not from the other hydantoin enantiomer. Quantum chemical calculations allowed us to visualize the HAT within this complex and, more importantly, showed that the back HAT does not occur to the carbon atom of the hydantoin radical but to its oxygen atom. The achiral enol formed in this process could be directly monitored by its characteristic transient absorption signal at λ ≅ 330 nm. Subsequent tautomerization leads to both hydantoin enantiomers, but only one of them returns to the catalytic cycle, thus leading to an enrichment of the other enantiomer. The data are fully consistent with deuterium labeling experiments and deliver a detailed picture of a synthetically useful photochemical deracemization reaction.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods.

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S0/T1 minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S0/S1ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

Towards understanding solvation effects on the conformational entropy of non-rigid molecules.

The absolute molecular entropy is a fundamental quantity for the accurate description of thermodynamic properties. For non-rigid molecules, a substantial part of the entropy can be attributed to a conformational contribution. Systems and properties where this is relevant, e.g., protein-ligand binding affinities or pKa values refer usually to the liquid phase. In this work, the influence of solvation on the conformational entropy is investigated. A recently introduced state-of-the-art and automated computational protocol for the computation of conformational entropies [Pracht et al., Chem. Sci., 2021, 12, 6551-6568.] is applied in combination with fast and accurate semiempirical quantum-chemical methods and implicit solvation models for a set of 25 commercially available drug molecules and five transition metal compounds. Computed gas-phase conformational entropies are compared with values obtained in implicit n-hexane and water. It is found that implicit solvation can have a substantial effect of several cal mol-1 K-1 on the entropy as a result of large conformational changes in the different phases. We conclude that for flexible molecules chemical accuracy for free energies in solution can only be achieved if solvation effects on the conformational ensemble are considered.

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.

High-Throughput Non-targeted Chemical Structure Identification Using Gas-Phase Infrared Spectra.

The high-throughput identification of unknown metabolites in biological samples remains challenging. Most current non-targeted metabolomics studies rely on mass spectrometry, followed by computational methods that rank thousands of candidate structures based on how closely their predicted mass spectra match the experimental mass spectrum of an unknown. We reasoned that the infrared (IR) spectra could be used in an analogous manner and could add orthologous structure discrimination; however, this has never been evaluated on large data sets. Here, we present results of a high-throughput computational method for predicting IR spectra of candidate compounds obtained from the PubChem database. Predicted spectra were ranked based on their similarity to gas-phase experimental IR spectra of test compounds obtained from the NIST. Our computational workflow (IRdentify) consists of a fast semiempirical quantum mechanical method for initial IR spectra prediction, ranking, and triaging, followed by a final IR spectra prediction and ranking using density functional theory. This approach resulted in the correct identification of 47% of 258 test compounds. On average, there were 2152 candidate structures evaluated for each test compound, giving a total of approximately 555,200 candidate structures evaluated. We discuss several variables that influenced the identification accuracy and then demonstrate the potential application of this approach in three areas: (1) combining IR and mass spectra rankings into a single composite rank score, (2) identifying the precursor and fragment ions using cryogenic ion vibrational spectroscopy, and (3) the incorporation of a trimethylsilyl derivatization step to extend the method compatibility to less-volatile compounds. Overall, our results suggest that matching computational with experimental IR spectra is a potentially powerful orthogonal option for adding significant high-throughput chemical structure discrimination when used with other non-targeted chemical structure identification methods.

Efficient Quantum-Chemical Calculations of Acid Dissociation Constants from Free-Energy Relationships.

The calculation of acid dissociation constants (pKa) is an important task in computational chemistry and chemoinformatics. Theoretically and with minimal empiricism, this is possible from computed acid dissociation free energies via so-called linear free-energy relationships. In this study some modifications are introduced to the latter, providing a straightforward, broadly applicable protocol with an adjustable degree of sophistication for quantum chemistry-based calculations of pKa in water. It targets a wide pKa range (∼70 units) and medium-sized, flexible molecules. Herein, a focus is set on the recently published r2SCAN-3c and related efficient composite density functionals and the semiempirical GFN2-xTB method, including a newly introduced energy correction for heterolytic dissociation, both in combination with implicit solvation models. The performance is evaluated in comparison with experimental data, showing mean errors often smaller than a targeted 1 pKa unit accuracy. Larger deviations are observed only upon inclusion of challenging highly negative (<-5) or positive (>15) pKa values. Among all those tested, it is found that B97-3c is the best performing functional, although rather independently of the density functional theory (DFT) method used; low root-mean-square errors of 0.8-1.0 pKa units for typical drugs are obtained. For optimal performance, it is recommended to employ DFT functional specific free-energy relationship parameters. Additionally, a significant conformational dependence of the pKa values is revealed and quantified for some nonrigid drug molecules.

Calculation of absolute molecular entropies and heat capacities made simple.

We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs-Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol-1 K-1 (about <1-2%) for the total gas phase molecular entropy of medium-sized molecules. Even for the hardship case of extremely flexible linear alkanes (C14H30-C16H34), errors are only about 3 cal mol-1 K-1. Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.

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.

Theoretical study on conformational energies of transition metal complexes.

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

Comprehensive Assessment of GFN Tight-Binding and Composite Density Functional Theory Methods for Calculating Gas-Phase Infrared Spectra.

Vibrational spectroscopy is a valuable and widely used analytical tool for the characterization of chemical substances. We investigate the performance of semiempirical quantum mechanical GFN tight-binding and force-field methods for the calculation of gas-phase infrared spectra in comparison to experiment and low-cost (B3LYP-3c) density functional theory. A data set of 7247 experimental references was used to evaluate method performance based on automatic spectra comparison. Various quantitative spectral similarity measures were employed for the comparison between theory and experiment and for determining empirical scaling factors. It is shown that the scaling of atomic masses provides an accurate yet simple alternative to standard global frequency scaling in density functional theory (DFT) and semiempirical calculations. Furthermore, the method performance for 58 exemplary transition metal complexes was investigated. The efficient DFT composite method B3LYP-3c, that was introduced in the course of this work, was found to be excellently suited for general IR spectra calculations. The GFN1- and GFN2-xTB tight-binding methods clearly outperformed the PMx competitors. Conformational changes were investigated for a subset of the data and are found to have a mediocre strong influence on the simulated spectra suggesting that the corresponding elaborate sampling steps may be neglected in automated compound identification workflows.

Automated exploration of the low-energy chemical space with fast quantum chemical methods.

We propose and discuss an efficient scheme for the in silico sampling for parts of the molecular chemical space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodynamic ensembles at a quantum chemical level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated minimum energy structures normally form the basis of further, mostly DFT computational work, such as the calculation of spectra or macroscopic properties. By using basic quantum chemical methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chemical methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized molecules) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chemistry and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.

High accuracy quantum-chemistry-based calculation and blind prediction of macroscopic pKa values in the context of the SAMPL6 challenge.

Recent advances in the development of low-cost quantum chemical methods have made the prediction of conformational preferences and physicochemical properties of medium-sized drug-like molecules routinely feasible, with significant potential to advance drug discovery. In the context of the SAMPL6 challenge, macroscopic pKa values were blindly predicted for a set of 24 of such molecules. In this paper we present two similar quantum chemical based approaches based on the high accuracy calculation of standard reaction free energies and the subsequent determination of those pKa values via a linear free energy relationship. Both approaches use extensive conformational sampling and apply hybrid and double-hybrid density functional theory with continuum solvation to calculate free energies. The blindly calculated macroscopic pKa values were in excellent agreement with the experiment.

Automated and efficient quantum chemical determination and energetic ranking of molecular protonation sites.

We present an automated quantum chemical protocol for the determination of preferred protonation sites in organic and organometallic molecules containing up to a few hundred atoms. It is based on the Foster-Boys orbital localization method, whereby we automatically identify lone pairs and π orbitals as possible protonation sites. The method becomes efficient in conjunction with the robust and fast GFN-xTB semiempirical method proposed recently (Grimme et al., J. Chem. Theory Comput. 2017, 13, 1989). The protonated isomers that are found within a few seconds to minutes of computational wall-time on a standard desktop computer are then energetically refined using density functional theory (DFT), where we use a high-level double-hybrid reference method to benchmark GFN-xTB and low-cost DFT approaches. The proposed DFT/GFN-xTB/LMO composite protocol is generally applicable to almost arbitrary molecules including transition metal complexes. Importantly it is found that even in electronically complicated cases, the GFN-xTB optimized protomer structures are reasonable and can safely be used in single-point DFT calculations. Corrections from energy to free energy mostly have a small effect on computed protomer populations. The resulting protomer equilibrium is valuable, for example, in the context of electrospray ionization mass spectrometry where it may help identify the ionized species and assist the interpretation of the experiment. © 2017 Wiley Periodicals, Inc.

Fully Automated Quantum-Chemistry-Based Computation of Spin-Spin-Coupled Nuclear Magnetic Resonance Spectra.

We present a composite procedure for the quantum-chemical computation of spin-spin-coupled 1 H NMR spectra for general, flexible molecules in solution that is based on four main steps, namely conformer/rotamer ensemble (CRE) generation by the fast tight-binding method GFN-xTB and a newly developed search algorithm, computation of the relative free energies and NMR parameters, and solving the spin Hamiltonian. In this way the NMR-specific nuclear permutation problem is solved, and the correct spin symmetries are obtained. Energies, shielding constants, and spin-spin couplings are computed at state-of-the-art DFT levels with continuum solvation. A few (in)organic and transition-metal complexes are presented, and very good, unprecedented agreement between the theoretical and experimental spectra was achieved. The approach is routinely applicable to systems with up to 100-150 atoms and may open new avenues for the detailed (conformational) structure elucidation of, for example, natural products or drug molecules.