Understanding Conformational Entropy in Small Molecules

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

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.

SQM2.20: Semiempirical quantum-mechanical scoring function yields DFT-quality protein-ligand binding affinity predictions in minutes

Accurate estimation of protein-ligand binding affinity is the cornerstone of computer-aided drug design. We present a universal physics-based scoring function, named SQM2.20, addressing key terms of binding free energy using semiempirical quantum-mechanical computational methods. SQM2.20 incorporates the latest methodological advances while remaining computationally efficient even for systems with thousands of atoms. To validate it rigorously, we have compiled and made available the PL-REX benchmark dataset consisting of high-resolution crystal structures and reliable experimental affinities for ten diverse protein targets. Comparative assessments demonstrate that SQM2.20 outperforms other scoring methods and reaches a level of accuracy similar to much more expensive DFT calculations. In the PL-REX dataset, it achieves excellent correlation with experimental data (average R2 = 0.69) and exhibits consistent performance across all targets. In contrast to DFT, SQM2.20 provides affinity predictions in minutes, making it suitable for practical applications in hit identification or lead optimization.

Microsecond Timescale Conformational Dynamics of a Small-Molecule Ligand within the Active Site of a Protein

The possible internal dynamics of non-isotope-labeled small-molecule ligands inside a target protein is inherently difficult to capture. Whereas high crystallographic temperature factors can denote either static disorder or motion, even moieties with very low B-factors can be subject to vivid motion between symmetry-related sites. Here we report the experimental identification of internal μs timescale dynamics of a high-affinity, natural-abundance ligand tightly bound to the enzyme human carbonic anhydrase II (hCAII) even within a crystalline lattice. The rotamer jumps of the ligand's benzene group manifest themselves both, in solution and fast magic-angle spinning solid-state NMR 1 H R1ρ relaxation dispersion, for which we obtain further mechanistic insights from molecular-dynamics (MD) simulations. The experimental confirmation of rotameric jumps in bound ligands within proteins in solution or the crystalline state may improve understanding of host-guest interactions in biology and supra-molecular chemistry and may facilitate medicinal chemistry for future drug campaigns.

Systematic Comparison of Experimental Crystallographic Geometries and Gas-Phase Computed Conformers for Torsion Preferences

We performed exhaustive torsion sampling on more than 3 million compounds using the GFN2-xTB method and performed a comparison of experimental crystallographic and gas-phase conformers. Many conformer sampling methods derive torsional angle distributions from experimental crystallographic data, limiting the torsion preferences to molecules that must be stable, synthetically accessible, and able to be crystallized. In this work, we evaluate the differences in torsional preferences of experimental crystallographic geometries and gas-phase computed conformers from a broad selection of compounds to determine whether torsional angle distributions obtained from semiempirical methods are suitable priors for conformer sampling. We find that differences in torsion preferences can be mostly attributed to a lack of available experimental crystallographic data with small deviations derived from gas-phase geometry differences. GFN2 demonstrates the ability to provide accurate and reliable torsional preferences that can provide a basis for new methods free from the limitations of experimental data collection. We provide Gaussian-based fits and sampling distributions suitable for torsion sampling and propose an alternative to the widely used "experimental torsion and knowledge distance geometry" (ETKDG) method using quantum torsion-derived distance geometry (QTDG) methods.

The Relationship Between Molecular Symmetry and Physicochemical Properties Involving Boiling and Melting of Organic Compounds

OBJECTIVE AND METHODS

The reliable estimation of phase transition physicochemical properties such as boiling and melting points can be valuable when designing compounds with desired physicochemical properties. This study explores the role of external rotational symmetry in determining boiling and melting points of select organic compounds. Using experimental data from the literature, the entropies of boiling and fusion were obtained for 541 compounds. The statistical significance of external rotational symmetry number on entropies of phase change was determined by using multiple linear regression. In addition, a series of aliphatic hydrocarbons, polysubstituted benzenes, and di-substituted napthalenes are used as examples to demonstrate the role of external symmetry on transition temperature.

RESULTS

The results reveal that symmetry is not well correlated with boiling point but is statistically significant in melting point.

CONCLUSION

The lack of correlation between the boiling point and the symmetry number reflects the fact that molecules have a high degree of rotational freedom in both the liquid and the vapor. On the other hand, the strong relationship between symmetry and melting point reflects the fact that molecules are rotationally restricted in the crystal but not in the liquid. Since the symmetry number is equal to the number of ways that the molecule can be properly oriented for incorporation into the crystal lattice, it is a significant determinant of the melting point.

Pressure-freezing of dodecane: exploring the crystal structures, formation kinetics and phase diagrams for colossal barocaloric effects in n-alkanes

Barocaloric (BC) materials provide cheaper and more energy efficient alternatives to traditional refrigerants. Some liquid alkanes were recently shown to exhibit a colossal BC effect, matching the entropy changes in commercial vapour-liquid refrigerants. Dodecane was predicted to have the largest entropy change among the studied alkanes. Using synchrotron powder and single-crystal X-ray diffraction, Raman spectroscopy, and lattice energy calculations, we investigated the BC effects of n-dodecane at high pressures and room temperature. Remarkably, a colossal entropy change |ΔS| of 778 J kg-1 K-1 at 0.15(3) GPa and 295 K was observed. Spectroscopic studies revealed that this entropy change correlates closely with the conformational transition from mixed gauche to all-trans forms during pressure-induced crystallization. Additionally, the usage of a diamond anvil cell allowed the determination of the crystal structures of in situ crystallized n-un- and dodecane, as well as evaluation of the pressure-dependent crystal growth kinetics. Furthermore, our research suggests that the entropy change (per kilogram) upon compression should be similar for all n-alkanes within the range of 9-18 carbon atoms in the molecule, based on their lattice energies. Even-numbered alkanes are predicted to exhibit superior BC properties compared to their odd-numbered counterparts due to the more symmetric crystal structures and lower propensity to form plastic phases with lower transition entropy.

Hydrogen-Atom Tunneling in a Homochiral Environment

The role-exchanging concerted torsional motion of two hydrogen atoms in the homochiral dimer of trans-1,2-cyclohexanediol was characterized through a combination of broadband rotational spectroscopy and theoretical modeling. The results reveal that the concerted tunneling motion of the hydrogen atoms leads to the inversion of the sign of the dipole moment components along the a and b principal axes, due to the interchange motion that cooperatively breaks and reforms one intermolecular hydrogen bond. This motion is also coupled with two acceptor switching motions. The energy difference between the two ground vibrational states arising from this tunneling motion was determined to be 29.003(2) MHz. The corresponding wavefunctions suggest that the two hydrogen atoms are evenly delocalized on two equivalent potential wells, which differs from the heterochiral case where the hydrogen atoms are confined in separate wells, as the permutation-inversion symmetry breaks down. This intriguing contrast in hydrogen-atom behavior between homochiral and heterochiral environments could further illuminate our understanding of the role of chirality in intermolecular interactions and dynamics.

Insights into structure-property relationships in ionic liquids using cyclic perfluoroalkylsulfonylimides

Room temperature ionic liquids of cyclic sulfonimide anions ncPFSI (ring size: n = 4-6) with the cations [EMIm]⁺ (1-ethyl-3-methylimidazolium), [BMIm]⁺ (1-butyl-3-methylimidazolium) and [BMPL]⁺ (BMPL = 1-butyl-1-methylpyrrolidinium) have been synthesized. Their solid-state structures have been elucidated by single-crystal X-ray diffraction and their physicochemical properties (thermal behaviour and stability, dynamic viscosity and specific conductivity) have been assessed. In addition, the ion diffusion was studied by pulsed field gradient stimulated echo (PFGSTE) NMR spectroscopy. The decisive influence of the ring size of the cyclic sulfonimide anions on the physicochemical properties of the ILs has been revealed. All ILs show different properties compared to those of the non-cyclic TFSI anion. While these differences are especially distinct for ILs with the very rigid 6cPFSI anion, the 5-membered ring anion 5cPFSI was found to result in ILs with relatively similar properties. The difference between the properties of the TFSI anion and the cyclic sulfonimide anions has been rationalized by the rigidity (conformational lock) of the cyclic sulfonimide anions. The comparison of selected IL properties was augmented by MD simulations. These highlight the importance of π⁺-π⁺ interactions between pairs of [EMIm]⁺ cations in the liquid phase. The π⁺-π⁺ interactions are evident for the solid state from the molecular structures of the [EMIm]⁺-ILs with the three cyclic imide anions determined by single-crystal X-ray diffraction.

Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

A high quality, industrial data set for binding affinity prediction: performance comparison in different early drug discovery scenarios

We release a new, high quality data set of 1162 PDE10A inhibitors with experimentally determined binding affinities together with 77 PDE10A X-ray co-crystal structures from a Roche legacy project. This data set is used to compare the performance of different 2D- and 3D-machine learning (ML) as well as empirical scoring functions for predicting binding affinities with high throughput. We simulate use cases that are relevant in the lead optimization phase of early drug discovery. ML methods perform well at interpolation, but poorly in extrapolation scenarios-which are most relevant to a real-world application. Moreover, we find that investing into the docking workflow for binding pose generation using multi-template docking is rewarded with an improved scoring performance. A combination of 2D-ML and 3D scoring using a modified piecewise linear potential shows best overall performance, combining information on the protein environment with learning from existing SAR data.

Exploring Glycan Binding Specificity of Odorranalectin by Alanine Scanning Library

Fluorescently labelled alanine scan analogues of odorranalectin (OL), a cyclic peptide that exhibits lectin like properties, were screened for binding BSA-conjugated monosaccharides using an enzyme-linked lectin assay (ELLA). Results revealed that Lys⁵, Phe⁷, Tyr⁹, Gly¹², Leu¹⁴, and Thr¹⁷ were crucial for binding BSA-L-fucose, BSA-D-galactose and BSA-N-acetyl-D-galactosamine. Notably, Ala substitution of Ser³, Pro⁴, and Val¹³ resulted in higher binding affinities compared to the native OL. The obtained data also indicated that Arg⁸ plays an important role in differentiation of binding for BSA-L-fucose/D-galactose from BSA-N-acetyl-D-galactosamine. The thermodynamics of binding of the selected alanine analogues was evaluated by isothermal titration calorimetry. Low to moderate binding affinities were determined for the tetravalent MUC1 glycopeptide and asialofetuin, respectively, and high for the fucose rich polysaccharide, fucoidan. The thermodynamic profile of interactions with asialofetuin exhibits shift to an entropy-driven mechanism compared to the fucoidan, which displayed an enthalpyentropy compensation, typically associated with the carbohydratelectin recognition process.

Machine learning to accelerate screening for Marcus reorganization energies

Understanding and predicting the charge transport properties of π-conjugated materials is an important challenge for designing new organic electronic devices, such as solar cells, plastic transistors, light-emitting devices, and chemical sensors. A key component of the hopping mechanism of charge transfer in these materials is the Marcus reorganization energy which serves as an activation barrier to hole or electron transfer. While modern density functional methods have proven to accurately predict trends in intramolecular reorganization energy, such calculations are computationally expensive. In this work, we outline active machine learning methods to predict computed intramolecular reorganization energies of a wide range of polythiophenes and their use toward screening new compounds with low internal reorganization energies. Our models have an overall root mean square error (RMSE) of ±0.113 eV, but a much smaller RMSE of only ±0.036 eV on the new screening set. Since the larger error derives from high-reorganization energy compounds, the new method is highly effective to screen for compounds with potentially efficient charge transport parameters.

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.

Understanding Ring Puckering in Small Molecules and Cyclic Peptides

The geometry of a molecule plays a significant role in determining its physical and chemical properties. Despite its importance, there are relatively few studies on ring puckering and conformations, often focused on small cycloalkanes, 5- and 6-membered carbohydrate rings, and specific macrocycle families. We lack a general understanding of the puckering preferences of medium-sized rings and macrocycles. To address this, we provide an extensive conformational analysis of a diverse set of rings. We used Cremer-Pople puckering coordinates to study the trends of the ring conformation across a set of 140 000 diverse small molecules, including small rings, macrocycles, and cyclic peptides. By standardizing using key atoms, we show that the ring conformations can be classified into relatively few conformational clusters, based on their canonical forms. The number of such canonical clusters increases slowly with ring size. Ring puckering motions, especially pseudo-rotations, are generally restricted and differ between clusters. More importantly, we propose models to map puckering preferences to torsion space, which allows us to understand the inter-related changes in torsion angles during pseudo-rotation and other puckering motions. Beyond ring puckers, our models also explain the change in substituent orientation upon puckering. We also present a novel knowledge-based sampling method using the puckering preferences and coupled substituent motion to generate ring conformations efficiently. In summary, this work provides an improved understanding of general ring puckering preferences, which will in turn accelerate the identification of low-energy ring conformations for applications from polymeric materials to drug binding.