Systematic and Automated Development of Quantum Mechanically Derived Force Fields: The Challenging Case of Halogenated Hydrocarbons

Influence of the Lennard-Jones Combination Rules on the Simulated Properties of Organic Liquids at Optimal Force-Field Parametrization

We recently introduced the CombiFF scheme [Oliveira et al., J. Chem. Theory Comput. 2020, 16, 7525], an approach for the automated refinement of force-field parameters against experimental condensed-phase data for large compound families. Using this scheme, once the time-consuming task of target-data selection and curation has been performed, the force-field optimization itself is both straightforward and fast. As a result, CombiFF provides an ideal framework for evaluating the influence of functional-form decisions on the accuracy of a force field at an optimal level of parametrization. We already used this approach to assess the effect of using an all-atom representation compared to united-atom representations in the force field [Oliveira et al., J. Chem. Theory Comput. 2022, 18, 6757]. Here, CombiFF is applied to assess the effect of three Lennard-Jones combination rules, geometric-mean (GM), Lorentz-Berthelot (LB), or Waldman-Hagler (WH), on the simulated properties of organic liquids. The comparison is performed in terms of the experimental liquid density ρ_liq, vaporization enthalpy ΔH_vap, surface-tension coefficient γ, static relative dielectric permittivity ϵ, and self-diffusion coefficient D. The calibrations of the three force-field variants are carried out independently against 2044 experimental values for ρ_liq, and ΔH_vap concerning 1516 compounds. The resulting root-mean-square deviations from experiment are 30.0, 26.9, and 36.7 kg m^-3 for ρ_liq and 2.8, 2.8, and 2.9 kJ mol^-1 for ΔH_vap, when applying the GM, LB, and WH combination rules, respectively. In terms of these (and the other) properties, the three combination rules perform comparatively well, with the GM and LB results being more similar to each other and slightly more accurate compared to experiment. In contrast, the use of distinct combination rules for the parameter calibration and property calculation leads to much larger errors.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation

The reliability of molecular dynamics (MD) simulations in predicting macroscopic properties of complex fluids and soft materials, such as liquid crystals, colloidal suspensions, or polymers, relies on the accuracy of the adopted force field (FF). We present an automated protocol to derive specific and accurate FFs, fully based on ab initio quantum mechanical (QM) data. The integration of the Joyce and Picky procedures, recently proposed by our group to provide an accurate description of simple liquids, is here extended to larger molecules, capable of exhibiting more complex fluid phases. While the standard Joyce protocol is employed to parameterize the intramolecular FF term, a new automated procedure is here proposed to handle the computational cost of the QM calculations required for the parameterization of the intermolecular FF term. The latter is thus obtained by integrating the old Picky procedure with a fragmentation reconstruction method (FRM) that allows for a reliable, yet computationally feasible sampling of the intermolecular energy surface at the QM level. The whole FF parameterization protocol is tested on a benchmark liquid crystal, and the performances of the resulting quantum mechanically derived (QMD) FF were compared with those delivered by a general-purpose, transferable one, and by the third, "hybrid" FF, where only the bonded terms were refined against QM data. Lengthy atomistic MD simulations are carried out with each FF on extended 5CB systems in both isotropic and nematic phases, eventually validating the proposed protocol by comparing the resulting macroscopic properties with other computational models and with experiments. The QMD-FF yields the best performances, reproducing both phases in the correct range of temperatures and well describing their structure, dynamics, and thermodynamic properties, thus providing a clear protocol that may be explored to predict such properties on other complex fluids or soft materials.

New insights into chloromethyl-oxirane and chloromethyl-thiirane in liquid and solid phase from low-temperature infrared spectroscopy and ab initio modeling

A detailed study of the conformational landscape of chloromethyl-oxirane and chloromethyl-thiirane is here reported. The equilibrium of the three different conformers of the two molecules was assessed, using a joint approach of experimental and theoretical methods. High quality infrared spectroscopy measurements of the liquid and of the crystalline phases were interpreted with the aid of ab initio Molecular Dynamics (AIMD) simulations, anharmonic frequencies and free energy calculations, obtaining a very good reproduction of the experimental data. The modulation of the conformational equilibrium upon the addition of polar and non-polar solvents was computationally evaluated and results found a confirmation in experimental measures.

On the faithfulness of molecular mechanics representations of proteins towards quantum-mechanical energy surfaces

Force fields based on molecular mechanics (MM) are the main computational tool to study the relationship between protein structure and function at the molecular level. To validate the quality of such force fields, high-level quantum-mechanical (QM) data are employed to test their capability to reproduce the features of all major conformational substates of a series of blocked amino acids. The phase-space overlap between MM and QM is quantified in terms of the average structural reorganization energies over all energy minima. Here, the structural reorganization energy is the MM potential-energy difference between the structure of the respective QM energy minimum and the structure of the closest MM energy minimum. Thus, it serves as a measure for the relative probability of visiting the QM minimum during an MM simulation. We evaluate variants of the AMBER, CHARMM, GROMOS and OPLS biomolecular force fields. In addition, the two blocked amino acids alanine and serine are used to demonstrate the dependence of the measured agreement on the QM method, the phase, and the conformational preferences. Blocked serine serves as an example to discuss possible improvements of the force fields, such as including polarization with Drude particles, or using tailored force fields. The results show that none of the evaluated force fields satisfactorily reproduces all energy minima. By decomposing the average structural reorganization energies in terms of individual energy terms, we can further assess the individual weaknesses of the parametrization strategies of each force field. The dominant problem for most force fields appears to be the van der Waals parameters, followed to a lesser degree by dihedral and bonded terms. Our results show that performing a simple QM energy optimization from an MM-optimized structure can be a first test of the validity of a force field for a particular target molecule.

Automated parameterization of quantum-mechanically derived force-fields including explicit sigma holes: A pathway to energetic and structural features of halogen bonds in gas and condensed phase

In classical molecular dynamics, general purpose atomistic force-fields (FFs) often deliver inaccurate results when dealing with halogen bonds (XBs), notwithstanding their crucial role in many fields of science, ranging from material design to drug development. Given the large dimensions of the systems of interest, it would be therefore desirable to increase the FF accuracy maintaining the simplicity of the standard Lennard-Jones (LJ) plus point charge description to avoid an excessive computational cost. A simple yet effective strategy consists in introducing a number of virtual sites able to mimic the so-called "explicit σ-hole." In this work, we present an automated FF parameterization strategy based on a global optimization of both LJ and charge parameters with respect to accurate quantum mechanical data, purposely computed for the system under investigation. As a test case, we report on two homologue series, characterized either by weak or strong XBs, namely, the di-halogenated methanes and the mono-, di-, and tri-substituted acetonitriles, taking into consideration Cl, Br, and I substituents. The resulting quantum mechanically derived FFs are validated for each compound in the gas and in the condensed phase by comparing them to general purpose and specific FFs without virtual sites and to highly accurate reference quantum mechanical data. The results strongly support the adoption of the specific FFs with virtual sites, which overcome the other investigated models in representing both gas phase energetics and the structural patterns of the liquid phase structure related to the presence of XBs.

Modelling flexible protein–ligand binding in p38α MAP kinase using the QUBE force field

The accuracy of quantum mechanical bespoke (QUBE) force fields for protein–ligand binding free energy calculations are benchmarked against experiment.

Coupled hydroxyl and ether functionalisation in EAN derivatives: the effect of hydrogen bond donor/acceptor groups on the structural heterogeneity studied with X-ray diffractions and fixed charge/polarizable simulations

We present a study by energy-dispersive X-ray diffraction of liquid 2-(2-hydroxyethoxy)ethan-1-ammonium nitrate, NH₃CH₂CH₂(OCH₂CH₂OH)⁺NO₃^- (22HHEAN). This ionic liquid is derived from the parent ethylammonium nitrate (EAN) with an ether link in the chain and a hydroxyl group in the terminal position. The absence of peaks at low-q values in the experimental diffraction curve indicates that the added polar groups and the high conformational isomerism of the cations alter strongly the nanosegregation of the parent EAN liquid. Aggregation between ionic species may involve hydrogen bonding between cations and anions and a variety of intermolecular hydrogen bonds between cations. Diffraction patterns are compared with the results of molecular dynamics simulations with two different force fields: the fixed point charge force field (GAFF) with different charge scaling protocols and the polarizable AMOEBA force field. Most point charge models lead to the appearance of a quite evident low q-peak which decreases gradually, when the percentage and type of the scaling (uniform vs. non-uniform) are increased. In the polarisable model and in the model where only anion charges are scaled to 20%, instead, the pre-peak is absent in agreement with our experiments.

Halogen bonding in halocarbon-protein complexes and computational tools for rational drug design

Introduction: Halogens have a prominent role in drug design. Often used as a mean to improve ADME properties, they are also becoming a tool in protein-ligand recognition given their ability to form a non-covalent interaction, termed halogen bond, where halogens act as electrophilic species interacting with electron-rich partners. Rational drug design of halogen-bonding lead molecules requires an accurate description of halocarbon-protein complexes by computational tools though not all methods are able to tackle this non-covalent interaction. Areas covered: The authors present a review of computational methodologies that can be used to properly describe halogen bonds in the context of protein-ligand complexes, providing also insights on how these methods can be used in the context of computer-aided drug design. Expert opinion: Although in the last few years many computational tools, ranging from fast screening methods to the more expensive QM calculations, have been developed to tackle the halogen bonding phenomenon, they are not yet standard in the literature. This will eventually change as official software distributions are including support for halogen bonding in their methods. Tackling desolvation of halogenated species seems to be a good strategy to improve the accuracy of computational methods, that will be more commonly used prior to laboratory work in the future.

Development and Validation of Quantum Mechanically Derived Force-Fields: Thermodynamic, Structural, and Vibrational Properties of Aromatic Heterocycles

A selection of several aromatic molecules, representative of the important class of heterocyclic compounds, has been considered for testing and validating an automated Force Field (FF) parametrization protocol, based only on Quantum Mechanical data. The parametrization is carried out separately for the intra- and intermolecular contributions, employing respectively the Joyce and Picky software packages, previously implemented and refined in our research group. The whole approach is here automated and integrated with a computationally effective yet accurate method, devised very recently ( J. Chem.

THEORY

Comput., 2018, 14, 543-556) to evaluate a large number of dimer interaction energies. The resulting quantum mechanically derived FFs are then used in extensive molecular dynamics simulations, in order to evaluate a number of thermodynamic, structural, and dynamic properties of the heterocycle's gas and liquid phases. The comparison with the available experimental data is good and furnishes a validation of the presented approach, which can be confidently exploited for the design of novel and more complex materials.

Structure and dynamics of propylammonium nitrate-acetonitrile mixtures: An intricate multi-scale system probed with experimental and theoretical techniques

In this article, we report the study of structural and dynamical properties for a series of acetonitrile/propylammonium nitrate mixtures as a function of their composition. These systems display an unusual increase in intensity in their X-ray diffraction patterns in the low-q regime, and their ¹H-NMR diffusion-ordered NMR spectroscopy (DOSY) spectra display unusual diffusivities. However, the magnitude of both phenomena for mixtures of propylammonium nitrate is smaller than those observed for ethylammonium nitrate mixtures with the same cosolvent, suggesting that the cation alkyl tail plays an important role in these observations. The experimental X-ray scattering data are compared with the results of molecular dynamics simulations, including both ab initio studies used to interpret short-range interactions and classical simulations to describe longer range interactions. The higher level calculations highlight the presence of a strong hydrogen bond network within the ionic liquid, only slightly perturbed even at high acetonitrile concentration. These strong interactions lead to the symmetry breaking of the NO₃^- vibrations, with a splitting of about 88 cm^-1 in the ν₃ antisymmetric stretch. The classical force field simulations use a greater number of ion pairs, but are not capable of fully describing the longest range interactions, although they do successfully account for the observed concentration trend, and the analysis of the models confirms the nano-inhomogeneity of these kinds of samples.

Validating an optimized GAFF force field for liquid crystals: TNI predictions for bent-core mesogens and the first atomistic predictions of a dark conglomerate phase

Atomistic simulations of bent core mesogens provide excellent T_NI predictions and show the formation of a dark conglomerate phase.

Bio ionic liquids and water mixtures: a structural study

In this study we have explored, by means of ab initio molecular dynamics, a subset of three different water/cho⁺–phe⁻ mixtures.