Conformational Analysis of 1,3-Difluorinated Alkanes.

Fluorine substitution can have a profound impact on molecular conformation. Here, we present a detailed conformational analysis of how the 1,3-difluoropropylene motif (-CHF-CH2-CHF-) determines the conformational profiles of 1,3-difluoropropane, anti- and syn-2,4-difluoropentane, and anti- and syn-3,5-difluoroheptane. It is shown that the 1,3-difluoropropylene motif strongly influences alkane chain conformation, with a significant dependence on the polarity of the medium. The conformational effect of 1,3-fluorination is magnified upon chain extension, which contrasts with vicinal difluorination. Experimental evidence was obtained from NMR analysis, where polynomial complexity scaling simulation algorithms were necessary to enable J-coupling extraction from the strong second-order spectra, particularly for the large 16-spin systems of the difluorinated heptanes. These results improve our understanding of the conformational control toolkit for aliphatic chains, yield simple rules for conformation population analysis, and demonstrate quantum mechanical time-domain NMR simulations for liquid state systems with large numbers of strongly coupled spins.

Does a Machine-Learned Potential Perform Better Than an Optimally Tuned Traditional Force Field? A Case Study on Fluorohydrins.

We present a comparative study that evaluates the performance of a machine learning potential (ANI-2x), a conventional force field (GAFF), and an optimally tuned GAFF-like force field in the modeling of a set of 10 γ-fluorohydrins that exhibit a complex interplay between intra- and intermolecular interactions in determining conformer stability. To benchmark the performance of each molecular model, we evaluated their energetic, geometric, and sampling accuracies relative to quantum-mechanical data. This benchmark involved conformational analysis both in the gas phase and chloroform solution. We also assessed the performance of the aforementioned molecular models in estimating nuclear spin-spin coupling constants by comparing their predictions to experimental data available in chloroform. The results and discussion presented in this study demonstrate that ANI-2x tends to predict stronger-than-expected hydrogen bonding and overstabilize global minima and shows problems related to inadequate description of dispersion interactions. Furthermore, while ANI-2x is a viable model for modeling in the gas phase, conventional force fields still play an important role, especially for condensed-phase simulations. Overall, this study highlights the strengths and weaknesses of each model, providing guidelines for the use and future development of force fields and machine learning potentials.

Using molecular dynamics to simulate realistic structures of nitrocellulose of different nitration levels.

Nitrocellulose is a reactive derivative of cellulose, one of the most commonly occurring natural materials. Nitration of cellulose decreases the stability of the structure, meaning less is understood about its structure and reactions. Although cellulose is often found in fully crystalline forms, nitrocellulose is more commonly paracrystalline, or amorphous. We present a protocol based on molecular dynamics simulations for creating realistic structures of nitrocellulose, particularly focusing on the crystallinity of the systems being created. We will also provide a detailed analysis of the geometric and dynamical parameters used to quantify the degree of crystallinity for the structures created here, with nitration levels varying from 0-14.14 wt% nitrogen content. Paracrystalline cellulose was not created using the protocol designed here, although it was found that the more nitrated a nitrocellulose system, the more the structure tends to paracrystallinity. This is due to a decrease in the number of hydrogen bonds present, and an increase in the size of the functional groups pushing the chains apart and weakening the interactions between the chains of the structure. The structures created are representative of realistic systems, which in the future will be able to be used to build further understanding of long-term storage of nitrocellulose.

Energy decomposition analysis method for metallic systems.

In this work, we present the first extension of an energy decomposition analysis (EDA) method to metallic systems. We extend the theory of our Hybrid Absolutely Localized Molecular Orbitals (HALMO) EDA to take into account that molecular orbitals in metallic systems are partially occupied, which is done by weighted orthogonalization (WO) of the molecular orbitals using their associated fractional occupancies as weights in the construction of the projection operators. These operators are needed for the self-consistent field for molecular interaction (SCF MI) computation of the polarization-energy contribution to the interaction. The method gives more weight to orbitals that have higher occupancies and treats each fragment as metallic. The resulting HALMO EDA for metallic systems naturally reduces to the insulator version and produces the same results when applied to an insulating system. We present the theory and implementation of our new approach, and we demonstrate it with sample calculations of relevance to industrial materials. This work provides a new EDA paradigm and tool for the study and analysis of interactions in metallic systems within large-scale DFT calculations.

BRD4: quantum mechanical protein-ligand binding free energies using the full-protein DFT-based QM-PBSA method.

Fully quantum mechanical approaches to calculating protein-ligand free energies of binding have the potential to reduce empiricism and explicitly account for all physical interactions responsible for protein-ligand binding. In this study, we show a realistic test of the linear-scaling DFT-based QM-PBSA method to estimate quantum mechanical protein-ligand binding free energies for a set of ligands binding to the pharmaceutical drug-target bromodomain containing protein 4 (BRD4). We show that quantum mechanical QM-PBSA is a significant improvement over traditional MM-PBSA in terms of accuracy against experiment and ligand rank ordering and that the quantum and classical binding energies are converged to a similar degree. We test the interaction entropy and normal mode entropy correction terms to QM- and MM-PBSA.

ParaMol: A Package for Automatic Parameterization of Molecular Mechanics Force Fields.

The ensemble of structures generated by molecular mechanics (MM) simulations is determined by the functional form of the force field employed and its parameterization. For a given functional form, the quality of the parameterization is crucial and will determine how accurately we can compute observable properties from simulations. While accurate force field parameterizations are available for biomolecules, such as proteins or DNA, the parameterization of new molecules, such as drug candidates, is particularly challenging as these may involve functional groups and interactions for which accurate parameters may not be available. Here, in an effort to address this problem, we present ParaMol, a Python package that has a special focus on the parameterization of bonded and nonbonded terms of druglike molecules by fitting to ab initio data. We demonstrate the software by deriving bonded terms' parameters of three widely known drug molecules, viz. aspirin, caffeine, and a norfloxacin analogue, for which we show that, within the constraints of the functional form, the methodologies implemented in ParaMol are able to derive near-ideal parameters. Additionally, we illustrate the best practices to follow when employing specific parameterization routes. We also determine the sensitivity of different fitting data sets, such as relaxed dihedral scans and configurational ensembles, to the parameterization procedure, and discuss the features of the various weighting methods available to weight configurations. Owing to ParaMol's capabilities, we propose that this software can be introduced as a routine step in the protocol normally employed to parameterize druglike molecules for MM simulations.

Analysis of DNA interactions and GC content with energy decomposition in large-scale quantum mechanical calculations.

GC content is a contributing factor to the stability of nucleic acids due to hydrogen bonding. More hydrogen bonding generally results in greater stability. Empirical evidence, however, has suggested that the GC content of a nucleic acid is a poor predictor of its stability, implying that there are sequence-dependent interactions besides what its GC content indicates. To examine how much such sequence-dependent interactions affect the interaction energies of double-stranded DNA (dsDNA) molecules, dsDNA molecules of different sequences are generated and examined in silico for variabilities in the interaction energies within each group of dsDNA molecules of the same GC content. Since the amount of hydrogen bonding depends on the GC content, holding the GC content fixed when examining the differences in interaction energies allows sequence-dependent interactions to be isolated. The nature of sequence-dependent interactions is then dissected using energy decomposition analysis (EDA). By using EDA, the components of the interactions that depend on the neighboring base pairs help explain some of the variability in the interaction energies of the dsDNA molecules despite having the same GC content. This work provides a new paradigm and tool for the study and analysis of the distributions of interaction components in dsDNA with the same GC content using EDA within large-scale quantum chemistry calculations.

Protein-ligand free energies of binding from full-protein DFT calculations: convergence and choice of exchange-correlation functional.

The accurate prediction of protein-ligand binding free energies with tractable computational methods has the potential to revolutionize drug discovery. Modeling the protein-ligand interaction at a quantum mechanical level, instead of relying on empirical classical-mechanics methods, is an important step toward this goal. In this study, we explore the QM-PBSA method to calculate the free energies of binding of seven ligands to the T4-lysozyme L99A/M102Q mutant using linear-scaling density functional theory on the whole protein-ligand complex. By leveraging modern high-performance computing we perform over 2900 full-protein (2600 atoms) DFT calculations providing new insights into the convergence, precision and reproducibility of the QM-PBSA method. We find that even at moderate sampling over 50 snapshots, the convergence of QM-PBSA is similar to traditional MM-PBSA and that the DFT-based energy evaluations are very reproducible. We show that in the QM-PBSA framework, the physically-motivated GGA exchange-correlation functional PBE outperforms the more modern, dispersion-including non-local and meta-GGA-nonlocal functionals VV10 and B97M-rV. Different empirical dispersion corrections perform similarly well but the three-body dispersion term, as included in Grimme's D3 dispersion, is significant and improves results slightly. Inclusion of an entropy correction term sampled over less than 25 snapshots is detrimental while an entropy correction sampled over the same 50 or 100 snapshots as the enthalpies improves the accuracy of the QM-PBSA method. As full-protein DFT calculations can now be performed on modest computational resources our study demonstrates that they can be a useful addition to the toolbox of free energy calculations.

Massively parallel linear-scaling Hartree-Fock exchange and hybrid exchange-correlation functionals with plane wave basis set accuracy.

We extend our linear-scaling approach for the calculation of Hartree-Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree-Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results.

Electrochemistry from first-principles in the grand canonical ensemble.

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson-Boltzmann equation (P-BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P-BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages.

The Role of Electrostatics in Enzymes: Do Biomolecular Force Fields Reflect Protein Electric Fields?

Preorganization of large, directionally oriented, electric fields inside protein active sites has been proposed as a crucial contributor to catalytic mechanism in many enzymes, and it may be efficiently investigated at the atomistic level with molecular dynamics simulations. Here, we evaluate the ability of the AMOEBA polarizable force field, as well as the additive Amber ff14SB and Charmm C36m models, to describe the electric fields present inside the active site of the peptidyl-prolyl isomerase cyclophilin A. We compare the molecular mechanical electric fields to those calculated with a fully first-principles quantum mechanical (QM) representation of the protein, solvent, and ions, and find that AMOEBA consistently shows far greater correlation with the QM electric fields than either of the additive force fields tested. Catalytically relevant fields calculated with AMOEBA were typically smaller than those observed with additive potentials, but were generally consistent with an electrostatically driven mechanism for catalysis. Our results highlight the accuracy and the potential advantages of using polarizable force fields in systems where accurate electrostatics may be crucial for providing mechanistic insights.

Strain effects in core-shell PtCo nanoparticles: a comparison of experimental observations and computational modelling.

Strain in Pt nanoalloys induced by the secondary metal has long been suggested as a major contributor to the modification of catalytic properties. Here, we investigate strain in PtCo nanoparticles using a combination of computational modelling and microscopy experiments. We have used a combination of molecular dynamics (MD) and large-scale density functional theory (DFT) for our models, alongside experimental work using annular dark field scanning transmission electron microscopy (ADF-STEM). We have performed extensive validation of the interatomic potential against DFT using a Pt568Co18 nanoparticle. Modelling gives access to 3 dimensional structures that can be compared to the 2D ADF-STEM images, which we use to build an understanding of nanoparticle structure and composition. Strain has been measured for PtCo and pure Pt nanoparticles, with MD annealed models compared to ADF-STEM images. Our analysis was performed on a layer by layer basis, where distinct trends between the Pt and PtCo alloy nanoparticles are observed. To our knowledge, we show for the first time a way in which detailed atomistic simulations can be used to augment and help interpret the results of ADF-STEM strain mapping experiments, which will enhance their use in characterisation towards the development of improved catalysts.

Electronic structure calculations in electrolyte solutions: Methods for neutralization of extended charged interfaces.

Density functional theory (DFT) is often used for simulating extended materials such as infinite crystals or surfaces, under periodic boundary conditions (PBCs). In such calculations, when the simulation cell has non-zero charge, electrical neutrality has to be imposed, and this is often done via a uniform background charge of opposite sign ("jellium"). This artificial neutralization does not occur in reality, where a different mechanism is followed as in the example of a charged electrode in electrolyte solution, where the surrounding electrolyte screens the local charge at the interface. The neutralizing effect of the surrounding electrolyte can be incorporated within a hybrid quantum-continuum model based on a modified Poisson-Boltzmann equation, where the concentrations of electrolyte ions are modified to achieve electroneutrality. Among the infinite possible ways of modifying the electrolyte charge, we propose here a physically optimal solution, which minimizes the deviation of concentrations of electrolyte ions from those in open boundary conditions (OBCs). This principle of correspondence of PBCs with OBCs leads to the correct concentration profiles of electrolyte ions, and electroneutrality within the simulation cell and in the bulk electrolyte is maintained simultaneously, as observed in experiments. This approach, which we call the Neutralization by Electrolyte Concentration Shift (NECS), is implemented in our electrolyte model in the Order-N Electronic Total Energy Package (ONETEP) linear-scaling DFT code, which makes use of a bespoke highly parallel Poisson-Boltzmann solver, DL_MG. We further propose another neutralization scheme ("accessible jellium"), which is a simplification of NECS. We demonstrate and compare the different neutralization schemes on several examples.

The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

CD1b-restricted GEM T cell responses are modulated by Mycobacterium tuberculosis mycolic acid meromycolate chains.

Tuberculosis (TB), caused by Mycobacterium tuberculosis, remains a major human pandemic. Germline-encoded mycolyl lipid-reactive (GEM) T cells are donor-unrestricted and recognize CD1b-presented mycobacterial mycolates. However, the molecular requirements governing mycolate antigenicity for the GEM T cell receptor (TCR) remain poorly understood. Here, we demonstrate CD1b expression in TB granulomas and reveal a central role for meromycolate chains in influencing GEM-TCR activity. Meromycolate fine structure influences T cell responses in TB-exposed individuals, and meromycolate alterations modulate functional responses by GEM-TCRs. Computational simulations suggest that meromycolate chain dynamics regulate mycolate head group movement, thereby modulating GEM-TCR activity. Our findings have significant implications for the design of future vaccines that target GEM T cells.

Mechanism of Os-Catalyzed Oxidative Cyclization of 1,5-Dienes.

The oxidative cyclization of 1,5-dienes by metal-oxo species is a powerful method for stereocontrolled synthesis of tetrahydrofuran diols (THF-diols), structural motifs present in many bioactive natural products. Oxidative cyclization of (2E,6E)-octa-2,6-diene catalyzed by OsO4/NMO has been studied using density functional theory (DFT) calculations (M06-2X/aug-cc-pVDZ/Hay-Wadt VDZ (n+1) ECP), highlighting the remarkable effect of acid on the fate of the first intermediate, an Os(VI) dioxoglycolate. A strong acid promotes cyclization of the Os(VI) dioxoglycolate, or its NMO complex, through protonation of an oxo ligand to give more electrophilic species. By contrast, in the absence of acid, reoxidation may occur to afford the Os(VIII) trioxoglycolate, which is shown to favor conventional "second cycle" dihydroxylation reactivity rather than cyclization. The results of the calculations are consistent with experimental results for reactions of OsO4/NMO with 1,5-dienes with acid (oxidative cyclization) and without acid (second cycle osmylation/dihydroxylation). Detailed evaluation of potential catalytic cycles supports oxidation of the cyclized Os(IV) THF-diolate intermediate to the corresponding Os(VI) species followed by slow hydrolysis and, finally, regeneration of OsO4.

Modification of O and CO binding on Pt nanoparticles due to electronic and structural effects of titania supports.

Metal oxide supports often play an active part in heterogeneous catalysis by moderating both the structure and the electronic properties of the metallic catalyst particle. In order to provide some fundamental understanding on these effects, we present here a density functional theory (DFT) investigation of the binding of O and CO on Pt nanoparticles supported on titania (anatase) surfaces. These systems are complex, and in order to develop realistic models, here, we needed to perform DFT calculations with up to ∼1000 atoms. By performing full geometry relaxations at each stage, we avoid any effects of "frozen geometry" approximations. In terms of the interaction of the Pt nanoparticles with the support, we find that the surface deformation of the anatase support contributes greatly to the adsorption of each nanoparticle, especially for the anatase (001) facet. We attempt to separate geometric and electronic effects and find a larger contribution to ligand binding energy arising from the former. Overall, we show an average weakening (compared to the isolated nanoparticle) of ∼0.1 eV across atop, bridge and hollow binding sites on supported Pt55 for O and CO, and a preservation of site preference. Stronger effects are seen for O on Pt13, which is heavily deformed by anatase supports. In order to rationalize our results and examine methods for faster characterization of metal catalysts, we make use of electronic descriptors, including the d-band center and an electronic density based descriptor. We expect that the approach followed in this study could be applied to study other supported metal catalysts.

Mutually polarizable QM/MM model with in situ optimized localized basis functions.

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K+, and Cl-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

Cholesteryl esters stabilize human CD1c conformations for recognition by self-reactive T cells.

Cluster of differentiation 1c (CD1c)-dependent self-reactive T cells are abundant in human blood, but self-antigens presented by CD1c to the T-cell receptors of these cells are poorly understood. Here we present a crystal structure of CD1c determined at 2.4 Å revealing an extended ligand binding potential of the antigen groove and a substantially different conformation compared with known CD1c structures. Computational simulations exploring different occupancy states of the groove reenacted these different CD1c conformations and suggested cholesteryl esters (CE) and acylated steryl glycosides (ASG) as new ligand classes for CD1c. Confirming this, we show that binding of CE and ASG to CD1c enables the binding of human CD1c self-reactive T-cell receptors. Hence, human CD1c adopts different conformations dependent on ligand occupancy of its groove, with CE and ASG stabilizing CD1c conformations that provide a footprint for binding of CD1c self-reactive T-cell receptors.

Electronic annealing Fermi operator expansion for DFT calculations on metallic systems.

Density Functional Theory (DFT) calculations with computational effort which increases linearly with the number of atoms (linear-scaling DFT) have been successfully developed for insulators, taking advantage of the exponential decay of the one-particle density matrix. For metallic systems, the density matrix is also expected to decay exponentially at finite electronic temperature and linear-scaling DFT methods should be possible by taking advantage of this decay. Here we present a method for DFT calculations at finite electronic temperature for metallic systems which is effectively linear-scaling (O(N)). Our method generates the elements of the one-particle density matrix and also finds the required chemical potential and electronic entropy using polynomial expansions. A fixed expansion length is always employed to generate the density matrix, without any loss in accuracy by the application of a high electronic temperature followed by successive steps of temperature reduction until the desired (low) temperature density matrix is obtained. We have implemented this method in the ONETEP linear-scaling (for insulators) DFT code which employs local orbitals that are optimised in situ. By making use of the sparse matrix machinery of ONETEP, our method exploits the sparsity of Hamiltonian and density matrices to perform calculations on metallic systems with computational cost that increases asymptotically linearly with the number of atoms. We demonstrate the linear-scaling computational cost of our method with calculation times on palladium nanoparticles with up to ∼13 000 atoms.