Enhancing LC×LC separations through multi-task Bayesian optimization

Method development in comprehensive two-dimensional liquid chromatography (LC×LC) is a challenging process. The interdependencies between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, make trial-and-error method development time-consuming and highly dependent on user experience. Retention modeling and Bayesian optimization (BO) have been proposed as solutions to mitigate these issues. However, both approaches have their strengths and weaknesses. On the one hand, retention modeling, which approximates true retention behavior, depends on effective peak tracking and accurate retention time and width predictions, which are increasingly challenging for complex samples and advanced gradient assemblies. On the other hand, Bayesian optimization may require many experiments when dealing with many adjustable parameters, as in LC×LC. Therefore, in this work, we investigate the use of multi-task Bayesian optimization (MTBO), a method that can combine information from both retention modeling and experimental measurements. The algorithm was first tested and compared with BO using a synthetic retention modeling test case, where it was shown that MTBO finds better optima with fewer method-development iterations than conventional BO. Next, the algorithm was tested on the optimization of a method for a pesticide sample and we found that the algorithm was able to improve upon the initial scanning experiments. Multi-task Bayesian optimization is a promising technique in situations where modeling retention is challenging, and the high number of adjustable parameters and/or limited optimization budget makes traditional Bayesian optimization impractical.

Redox Properties of Flavin in BLUF and LOV Photoreceptor Proteins from Hybrid QM/MM Molecular Dynamics Simulation

Flavins play an important role in many oxidation and reduction processes in biological systems. For example, flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN) are common cofactors found in enzymatic proteins that use the special redox properties of these flavin molecules for their catalytic or photoactive functions. The redox potential of the flavin is strongly affected by its (protein) environment; however, the underlying molecular interactions of this effect are still unknown. Using hybrid quantum mechanics/molecular mechanics (QM/MM) simulation techniques, we have studied the redox properties of flavin in the gas phase, aqueous solution, and two different protein environments, in particular, a BLUF and a LOV photoreceptor domain. By mapping the changes in electrostatic potential and solvent structure, we gain insight into how specific polarization of the flavin by its environment tunes the reduction potential. We find also that accurate calculation of the reduction potentials of these systems by using the hybrid QM/MM approach is hampered by a too limited sampling of the counterion configurations and by artifacts at the QM/MM boundary. We make suggestions for how these issues can be overcome.

Predicting RP-LC retention indices of structurally unknown chemicals from mass spectrometry data

Non-target analysis combined with liquid chromatography high resolution mass spectrometry is considered one of the most comprehensive strategies for the detection and identification of known and unknown chemicals in complex samples. However, many compounds remain unidentified due to data complexity and limited number structures in chemical databases. In this work, we have developed and validated a novel machine learning algorithm to predict the retention index (r[Formula: see text]) values for structurally (un)known chemicals based on their measured fragmentation pattern. The developed model, for the first time, enabled the predication of r[Formula: see text] values without the need for the exact structure of the chemicals, with an [Formula: see text] of 0.91 and 0.77 and root mean squared error (RMSE) of 47 and 67 r[Formula: see text] units for the NORMAN ([Formula: see text]) and amide ([Formula: see text]) test sets, respectively. This fragment based model showed comparable accuracy in r[Formula: see text] prediction compared to conventional descriptor-based models that rely on known chemical structure, which obtained an [Formula: see text] of 0.85 with an RMSE of 67.

Closed-loop automatic gradient design for liquid chromatography using Bayesian optimization

Contemporary complex samples require sophisticated methods for full analysis. This work describes the development of a Bayesian optimization algorithm for automated and unsupervised development of gradient programs. The algorithm was tailored to LC using a Gaussian process model with a novel covariance kernel. To facilitate unsupervised learning, the algorithm was designed to interface directly with the chromatographic system. Single-objective and multi-objective Bayesian optimization strategies were investigated for the separation of two complex (n>18, and n>80) dye mixtures. Both approaches found satisfactory optima in under 35 measurements. The multi-objective strategy was found to be powerful and flexible in terms of exploring the Pareto front. The performance difference between the single-objective and multi-objective strategy was further investigated using a retention modeling example. One additional advantage of the multi-objective approach was that it allows for a trade-off to be made between multiple objectives without prior knowledge. In general, the Bayesian optimization strategy was found to be particularly suitable, but not limited to, cases where retention modelling is not possible, although its scalability might be limited in terms of the number of parameters that can be simultaneously optimized.

Fast Proton Transport in FeFe Hydrogenase via a Flexible Channel and a Proton Hole Mechanism

Di-iron hydrogenases are a class of enzymes that are capable of reducing protons to form molecular hydrogen with high efficiency. In addition to the catalytic site, these enzymes have evolved dedicated pathways to transport protons and electrons to the reaction center. Here, we present a detailed study of the most likely proton transfer pathway in such an enzyme using QM/MM molecular dynamics simulations. The protons are transported through a channel lined out from the protein exterior to the di-iron active site, by a series of hydrogen-bonded, weakly acidic or basic, amino acids and two incorporated water molecules. The channel shows remarkable flexibility, which is an essential feature to quickly reset the hydrogen-bond direction in the channel after each proton passing. Proton transport takes place via a “hole” mechanism, rather than an excess proton mechanism, the free energy landscape of which is remarkably flat, with a highest transition state barrier of only 5 kcal/mol. These results confirm our previous assumptions that proton transport is not rate limiting in the H₂ formation activity and that cysteine C299 may be considered protonated at physiological pH conditions. Detailed understanding of this proton transport may aid in the ongoing attempts to design artificial biomimetic hydrogenases for hydrogen fuel production.

Linear Scaling Relationships to Predict pKa's and Reduction Potentials for Bioinspired Hydrogenase Catalysis

Biomimetic catalysts inspired by the active site of the [FeFe] hydrogenase enzyme can convert protons into molecular hydrogen. Minimizing the overpotential of the electrocatalytic process remains a major challenge for practical application of the catalyst. The catalytic cycle of the hydrogen production follows an ECEC mechanism (E represents an electron transfer step, and C refers to a chemical step), in which the electron and proton transfer steps can be either sequential or coupled (PCET). In this study, we have calculated the pKa's and the reduction potentials for a series of commonly used ligands (80 different complexes) using density functional theory. We establish that the required acid strength for protonation at the Fe-Fe site correlates with the standard reduction potential of the di-iron complexes with a linear energy relationship. These linear relationships allow for fast screening of ligands and tuning of the properties of the catalyst. Our study also suggests that bridgehead ligand properties, such as bulkiness and aromaticity, can be exploited to alter or even break the linear scaling relationships.

Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks

With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson-Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.

Frontiers in Multiscale Modeling of Photoreceptor Proteins

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

Strong Reduction of the Chain Rigidity of Hyaluronan by Selective Binding of Ca2+ Ions

The biological functions of natural polyelectrolytes are strongly influenced by the presence of ions, which bind to the polymer chains and thereby modify their properties. Although the biological impact of such modifications is well recognized, a detailed molecular picture of the binding process and of the mechanisms that drive the subsequent structural changes in the polymer is lacking. Here, we study the molecular mechanism of the condensation of calcium, a divalent cation, on hyaluronan, a ubiquitous polymer in human tissues. By combining two-dimensional infrared spectroscopy experiments with molecular dynamics simulations, we find that calcium specifically binds to hyaluronan at millimolar concentrations. Because of its large size and charge, the calcium cation can bind simultaneously to the negatively charged carboxylate group and the amide group of adjacent saccharide units. Molecular dynamics simulations and single-chain force spectroscopy measurements provide evidence that the binding of the calcium ions weakens the intramolecular hydrogen-bond network of hyaluronan, increasing the flexibility of the polymer chain. We also observe that the binding of calcium to hyaluronan saturates at a maximum binding fraction of ∼10–15 mol %. This saturation indicates that the binding of Ca²⁺ strongly reduces the probability of subsequent binding of Ca²⁺ at neighboring binding sites, possibly as a result of enhanced conformational fluctuations and/or electrostatic repulsion effects. Our findings provide a detailed molecular picture of ion condensation and reveal the severe effect of a few, selective and localized electrostatic interactions on the rigidity of a polyelectrolyte chain.

Optimizing the Energetics of FLP-Type H2 Activation by Modulating the Electronic and Structural Properties of the Lewis Acids: A DFT Study

The great potential of frustrated Lewis pairs (FLPs) as metal-free catalysts for activation of molecular hydrogen has attracted increasing interest as an alternative to transition-metal catalysts. However, the complexity of FLP systems, involving the simultaneous interaction of three molecules, impedes a detailed understanding of the activation mechanism and the individual roles of the Lewis acid (LA) and Lewis base (LB). In the present work, using density functional theory (DFT) calculations, we examine the reactivity of 75 FLPs for the H₂ splitting reaction, including a series of experimentally investigated LAs combined with conventional phosphine-based (tBu₃P) and oxygen-based (i.e., ethereal solvent) Lewis bases. We find that the catalytic activity of the FLP is the result of a delicate balance of the LA and LB strengths and their bulkiness. The H₂ splitting reaction can be changed from endergonic to exergonic by tuning the electrophilicity of the LA. Also, a more nucleophilic LB results in a more stable ion pair product and a lower barrier for the hydrogen splitting. The bulkiness of the LB leads to an early transition state to reduce steric hindrance and lower the barrier height. The bulkiness of the fragments determines the cavity size in the FLP complex, and a large cavity allows for a larger charge separation in the ion pair configuration. A shorter proton-hydride distance in this product complex correlates with a stronger attraction between the fragments, which forms more reactive ion pairs and facilitates the proton and hydride donations in the subsequent hydrogenation process. These insights may help with rationalizing the experimentally observed reactivities of FLPs and with designing better FLP systems for hydrogenation catalysis and hydrogen storage.

Peptide Side-COOH Groups Have Two Distinct Conformations under Biorelevant Conditions

The carboxyl (COOH) side chain groups of amino acids, such as aspartic acid, play an important role in biochemical processes, including enzymatic proton transport. In many theoretical studies, it was found that the (bio)chemical reactivity of the carboxyl group strongly depends on the conformation of this group. Interestingly, up to now there has been no experimental investigation of the geometry and the stability of different COOH conformers under biorelevant conditions. Here, we investigate the conformational isomerism of the side chain COOH group of N-acetyl aspartic acid amide using polarization-resolved two-dimensional infrared spectroscopy. We find that the carboxyl group shows two distinct near-planar conformers (syn and anti) when dissolved in water at room temperature. Both conformers are significantly populated in aqueous solution (75 ± 10% and 25 ± 10% for syn and anti, respectively). Molecular dynamics simulations show that the anti conformer interacts more strongly with water molecules than the syn conformer, explaining why this conformer is significantly present in aqueous solution.

Unraveling the mechanism of biomimetic hydrogen fuel production – a first principles molecular dynamics study

The Fe₂(bdt)(CO)₆ [bdt = benzenedithiolato] complex, a synthetic mimic of the [FeFe] hydrogenase enzyme can electrochemically convert protons into molecular hydrogen. The free energy landscape reveals a different mechanism for the biomimetic cycle.

A DFT study of structure and electrochemical properties of diiron-hydrogenase models with benzenedithiolato and benzenediselenato ligands

The chalcogen atom substitution in the Fe₂(bdt)(CO)₆ complex results in higher and lower proton affinities of iron and chalcogen atoms, respectively.

Hydration interactions beyond the first solvation shell in aqueous phenolate solution

We investigate the orientational dynamics of water molecules solvating phenolate ions using ultrafast vibrational spectroscopy and density functional theory-based molecular dynamics simulations.

Accurate calculation of zero point energy from molecular dynamics simulations of liquids and their mixtures

The two-phase thermodynamic (2PT) method is used to compute the zero point energy (ZPE) of several liquids and their mixtures. The 2PT method uses the density of states (DoS), which is computed from the velocity autocorrelation (VAC) function obtained from a short classical molecular dynamics trajectory. By partitioning the VAC and the DoS of a fluid into solid and gaslike components, quantum mechanical corrections to thermodynamical properties can be computed. The ZPE is obtained by combining the partition function of the quantum harmonic oscillator with the vibrational part of the solidlike DoS. The resulting ZPE is found to be in excellent agreement with both experimental and ab initio results. Solvent effects such as hydrogen bonding and polarization can be included by the utilization of ab initio density functional theory based molecular dynamics simulations. It is found that these effects significantly influence the DoS of water molecules. The obtained results demonstrate that the 2PT model is a powerful method for efficient ZPE calculations, in particular, to account for solvent effects and polarization.

Microscopic Picture of the Solvent Reorganization During Electron Transfer to Flavin in Water

The redox potential of molecular species is largely modulated by its molecular environment so that a change of the environment will lead to a different redox potential. However, a detailed molecular picture of reorganization of the environment upon reduction is still unclear. To unravel the details of the solvent reorganization during electron transfer, we have performed density functional theory-based molecular dynamics (DFT-MD) and hybrid quantum mechanics/molecular mechanics (QM/MM) simulations of the reduction of lumiflavin. Previously, we have calculated the reduction free energy curves of the redox half reactions of lumiflavin in water as a function of the instantaneous gap energy (ΔE) ( J. Chem. Theory Comput. 2013 , 9 , 3889 - 3899 ). In this work, we focus on finding the changes in the solvent environment that correlate with this ΔE reaction coordinate. Comparing the QM/MM simulations, in which the solvent is modeled with an empirical force field, with the (full) DFT-MD simulations, we find that the response through electronic polarization plays a significant role in the latter case. Also a small charge transfer between flavin and solvent is observed in the full DFT treatment. As a result, we find only in the case of the QM/MM model a strong correlation between ΔE and the (pairwise computed) electrostatic potential (ESP) at the flavin due to the solvent. By analyzing the contribution of the ESP at the flavin per solvent molecule, we cannot only distinguish between the different modes of hydration by solvent molecules that coordinate at the hydrophilic and hydrophobic sides of the flavin molecule but also quantify their contribution to the reorganization free energy by measuring the ESP fluctuations per solvent molecule.

On the origin of the extremely different solubilities of polyethers in water

The solubilities of polyethers are surprisingly counter-intuitive. The best-known example is the difference between polyethylene glycol ([-CH₂-CH₂-O-]_n) which is infinitely soluble, and polyoxymethylene ([-CH₂-O-]_n) which is completely insoluble in water, exactly the opposite of what one expects from the C/O ratios of these molecules. Similar anomalies exist for oligomeric and cyclic polyethers. To solve this apparent mystery, we use femtosecond vibrational and GHz dielectric spectroscopy with complementary ab initio calculations and molecular dynamics simulations. We find that the dynamics of water molecules solvating polyethers is fundamentally different depending on their C/O composition. The ab initio calculations and simulations show that this is not because of steric effects (as is commonly believed), but because the partial charge on the O atoms depends on the number of C atoms by which they are separated. Our results thus show that inductive effects can have a major impact on aqueous solubilities.

Mechanisms behind the enhancement of thermal properties of graphene nanofluids

While the dispersion of nanomaterials is known to be effective in enhancing the thermal conductivity and specific heat capacity of fluids, the mechanisms behind this enhancement remain to be elucidated. Herein, we report on highly stable, surfactant-free graphene nanofluids, based on N,N-dimethylacetamide (DMAc) and N,N-dimethylformamide (DMF), with enhanced thermal properties. An increase of up to 48% in thermal conductivity and 18% in specific heat capacity was measured. The blue shift of several Raman bands with increasing graphene concentration in DMF indicates that there is a modification in the vibrational energy of the bonds associated with these modes, affecting all the molecules in the liquid. This result indicates that graphene has the ability to affect solvent molecules at long-range, in terms of vibrational energy. Density functional theory and molecular dynamics simulations were used to gather data on the interaction between graphene and solvent, and to investigate a possible order induced by graphene on the solvent. The simulations showed a parallel orientation of DMF towards graphene, favoring π-π stacking. Furthermore, a local order of DMF molecules around graphene was observed suggesting that both this special kind of interaction and the induced local order may contribute to the enhancement of the fluid's thermal properties.

Impact of the Ligand Flexibility and Solvent on the O-O Bond Formation Step in a Highly Active Ruthenium Water Oxidation Catalyst

By advanced molecular dynamics simulations, we show that for a highly active ruthenium-based water oxidation catalyst the dangling carboxylate group of the catalyst plays an important role in the crucial O-O bond formation step. The interplay of the flexible group and solvent molecules facilitates two possible pathways: a direct pathway with a single solvent water molecule or a mediated pathway involving two solvent water molecules, which have similar activation barriers. Our results provide an example for which a realistic molecular dynamics approach, incorporating an explicit description of the solvent, is required to reveal the full complexity of an important catalytic reaction in aqueous solvent.

Highly Selective Oxidation of Ethyl Lactate to Ethyl Pyruvate Catalyzed by Mesoporous Vanadia-Titania

The direct oxidative dehydrogenation of lactates with molecular oxygen is a “greener” alternative for producing pyruvates. Here we report a one-pot synthesis of mesoporous vanadia–titania (VTN), acting as highly efficient and recyclable catalysts for the conversion of ethyl lactate to ethyl pyruvate. These VTN materials feature high surface areas, large pore volumes, and high densities of isolated vanadium species, which can expose the active sites and facilitate the mass transport. In comparison to homogeneous vanadium complexes and VO_x/TiO₂ prepared by impregnation, the meso-VTN catalysts showed superior activity, selectivity, and stability in the aerobic oxidation of ethyl lactate to ethyl pyruvate. We also studied the effect of various vanadium precursors, which revealed that the vanadium-induced phase transition of meso-VTN from anatase to rutile depends strongly on the vanadium precursor. NH₄VO₃ was found to be the optimal vanadium precursor, forming more monomeric vanadium species. V⁴⁺ as the major valence state was incorporated into the lattice of the NH₄VO₃-derived VTN material, yielding more V⁴⁺–O–Ti bonds in the anatase-dominant structure. In situ DRIFT spectroscopy and density functional theory calculations show that V⁴⁺–O–Ti bonds are responsible for the dissociation of ethyl lactate over VTN catalysts and for further activation of the deprotonation of β-hydrogen. Molecular oxygen can replenish the surface oxygen to regenerate the V⁴⁺–O–Ti bonds.

Acidity Constant (pKa ) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods

pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK_a). Obtaining molecular control over the factors that influence the pK_a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK_a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.

Reactive trajectories of the Ru2+/3+ self-exchange reaction and the connection to Marcus' theory

Outer sphere electron transfer between two ions in aqueous solution is a rare event on the time scale of first principles molecular dynamics simulations. We have used transition path sampling to generate an ensemble of reactive trajectories of the self-exchange reaction between a pair of Ru²⁺ and Ru³⁺ ions in water. To distinguish between the reactant and product states, we use as an order parameter the position of the maximally localised Wannier center associated with the transferring electron. This allows us to align the trajectories with respect to the moment of barrier crossing and compute statistical averages over the path ensemble. We compare our order parameter with two typical reaction coordinates used in applications of Marcus theory of electron transfer: the vertical gap energy and the solvent electrostatic potential at the ions.

Do solid-to-solid polymorphic transitions in DL-norleucine proceed through nucleation?

DL-Norleucine is a molecular crystal exhibiting two enantiotropic phase transitions. The high temperature α ↔ γ transition has been shown to proceed through nucleation and growth [Mnyukh et al., J. Phys. Chem. Solids, 1975, 36, 127]. We focus on the low temperature β ↔ α transition in a combined computational and experimental study. The temperature dependence of the structural and energetic properties of both polymorphic forms is nearly identical. Molecular dynamics simulations and nudged elastic band calculations of the transition process itself, suggest that the transition is governed by cooperative movements of bilayers over relatively large energy barriers.

Understanding DABCO Nanorotor Dynamics in Isostructural Metal-Organic Frameworks

Flexible framework dynamics present in the subset of metal-organic frameworks known as soft porous crystals give rise to interesting structural properties that are unique to this class of materials. In this work, we use experiments and molecular simulation to understand the highly dynamic nanorotor behavior of the 1,4-diazabicyclo[2.2.2]octane (DABCO) ligand in the pillared Zn-DMOF and Zn-DMOF-TM (TM = tetramethyl) structures. While DABCO is known to be displaced in the presence of water in the parent Zn-DMOF structure, the Zn-DMOF-TM variation is highly stable even after adsorbing significant amounts of water vapor. The dynamics of DABCO in the presence of water guest molecules is therefore also explored in the Zn-DMOF-TM structure via in situ NMR and IR experiments. This analysis shows that the rotational motion of the DABCO linkers is dependent on water content, but not a likely source of water instability because the dynamics are fast and largely unaffected by the presence of methyl functional groups.

On the slowdown mechanism of water dynamics around small amphiphiles

Partitioning the water molecules depending on their location with respect to the solute makes it possible to probe the cause of the orientational slowdown in aqueous tetramethylurea.

Local orientational order in liquids revealed by resonant vibrational energy transfer

We demonstrate that local orientational ordering in a liquid can be observed in the decay of the vibrational anisotropy caused by resonant transfer of vibrational excitations between its constituent molecules. We show that the functional form of this decay is determined by the (distribution of) angles between the vibrating bonds of the molecules between which energy transfer occurs, and that the initial drop in the decay reflects the average angle between nearest neighbors. We use this effect to observe the difference in local orientational ordering in the two hydrogen-bonded liquids ethanol and N-methylacetamide.

Acidity constants of lumiflavin from first principles molecular dynamics simulations

DFT-based molecular dynamics simulations predict the acidity of lumiflavin in different redox states.

Path finding on high-dimensional free energy landscapes

We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the cost with the number of collective variables. Controlling the sampling of the orthogonal modes recovers the average path and the minimum free energy path as the limiting cases. The method is applied to resolve the path and the free energy of a conformational transition in alanine dipeptide.

Quantitative Assessment of Force Fields on Both Low-Energy Conformational Basins and Transition-State Regions of the (ϕ-ψ) Space

The free energy surfaces (FESs) of alanine dipeptide are studied to illustrate a new strategy to assess the performance of classical molecular mechanics force field on the full range of the (ϕ-ψ) conformational space. The FES is obtained from metadynamics simulations with five commonly used force fields and from ab initio density functional theory calculations in both gas phase and aqueous solution. The FESs obtained at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d,p) level of theory are validated by comparison with previously reported MP2 and LMP2 results as well as with experimentally obtained probability distribution between the C5-β (or β-PPII) and αR states. A quantitative assessment is made for each force field in three conformational basins, LeRI (C5-β-C7eq), LeRII (β2-αR), and LeRIII(αL-C7ax-αD) as well as three transition-state regions linking the above conformational basins. The performance of each force field is evaluated in terms of the average free energy of each region in comparison with that of the ab initio results. We quantify how well a force field FES matches the ab initio FES through the calculation of the standard deviation of a free energy difference map between the two FESs. The results indicate that the performance varies largely from region to region or from force field to force field. Although not one force field is able to outperform all others in all conformational areas, the OPLSAA/L force field gives the best performance overall, followed by OPLSAA and AMBER03. For the three top performers, the average free energies differ from the corresponding ab initio values from within the error range (<0.4 kcal/mol) to ∼1.5 kcal/mol for the low-energy regions and up to ∼2.0 kcal/mol for the transition-state regions. The strategy presented and the results obtained here should be useful for improving the parametrization of force fields targeting both accuracy in the energies of conformers and the transition-state barriers.

Adaptive multiscale molecular dynamics of macromolecular fluids

Until now, adaptive atomistic-coarse-grain (A/CG) molecular dynamics simulations have had very limited applicability because the on-the-fly CG → A transformation is problematic for all but those molecules whose CG representation consists of a single particle. Here, we solve this problem by combining a transitional healing region with a rotational dynamics of rigid atomistic fragments in the CG region. Error control is obtained by analysis of the A ↔ CG energy flow. We illustrate the method with adaptive multiscale simulations of liquid hexane and of a dilute polymer solution in a theta solvent.