Condensed Phase Simulations Research Articles

Convergence of Computed Aqueous Absorption Spectra with Explicit Quantum Mechanical Solvent.

For reliable condensed phase simulations, an accurate model that includes both short- and long-range interactions is required. Short- and long-range interactions can be particularly strong in aqueous solution, where hydrogen-bonding may play a large role at short range and polarization may play a large role at long range. Although short-range solute-solvent interactions such as charge transfer, hydrogen bonding, and solute-solvent polarization can be taken into account with a quantum mechanical (QM) treatment of the solvent, it is unclear how much QM solvent is necessary to accurately model interactions with different solutes. In this work, we investigate the effect of explicit QM solvent on absorption spectra computed for a series of solutes with decreasing polarity. By adjusting the boundary between QM and classical molecular mechanical solvent to include up to 400 QM water molecules, convergence of the calculated absorption spectra with respect to the size of the QM region is achieved. We find that the rate of convergence does not correlate with solute polarity when excitation energies are calculated using time-dependent density functional theory with a range-separated hybrid functional, but it does correlate with solute polarity when using configuration interaction singles. We also find that larger basis sets converge the computed spectrum with fewer QM solvent molecules. To optimize the computational cost with respect to convergence, we test a mixed basis set with more basis functions for atoms of the chromophore and the solvent molecules that are nearest to it and fewer basis functions for the atoms of the remaining solvent molecules in the QM region. Our results show that using a mixed basis set is a potentially effective way to significantly lower the computational cost while reproducing the results computed with larger basis sets.

1.14*CM1A-LBCC: Localized Bond-Charge Corrected CM1A Charges for Condensed-Phase Simulations.

The quality of the 1.14*CM1A and 1.20*CM5 charge models was evaluated for calculations of free energies of hydration. For a set of 426 neutral molecules, 1.14*CM1A and 1.20*CM5 yield MADs of 1.26 and 1.21 kcal/mol, respectively. The 1.14*CM1A charges, which can be readily obtained for large systems, exhibit large deviations only for a subset of functional groups. The results for these cases were systematically improved using localized bond-charge corrections (LBCC) by which offsetting adjustments are made to the partial charges for atoms in specified bond types. Only 19 LBCCs were needed to yield 1.14*CM1A-LBCC charges that reduce the errors for the 426 ΔGhyd values to only 0.61 kcal/mol. The modified charge method was also tested in computation of heats of vaporization and densities for pure organic liquids, yielding average errors of 1.40 kcal/mol and 0.024 g/cm3, similar to those for 1.14*CM1A.

Equivalence of M- and P-Summation in Calculations of Ionic Solvation Free Energies.

Condensed-phase simulations commonly use periodic boundary conditions (PBCs) to represent the thermodynamic limit. For the vapor to liquid transfer of an ion, the gas/liquid boundary and its associated potential change are then missing. Furthermore, the electric potential and field at a given point are given by conditionally convergent infinite series, for which different summation schemes give different results. Nevertheless, standard simulation protocols can be used to compute experimental quantities unambiguously. In particular, using an auxiliary test particle and a multistep solvation path, we show that particle-based, Ewald, and common molecule-based summation schemes for the potential and field are all essentially equivalent. However, all methods require prior knowledge of the gas/liquid boundary potential to compute ionic solvation free energies using PBC protocols for both force-field and quantum-mechanical models.

Polarizable Multipole-Based Force Field for Aromatic Molecules and Nucleobases.

Aromatic molecules with π electrons are commonly involved in chemical and biological recognitions. For example, nucleobases play central roles in DNA/RNA structure and their interactions with proteins. The delocalization of the π electrons is responsible for the high polarizability of aromatic molecules. In this work, the AMOEBA force field has been developed and applied to 5 regular nucleobases and 12 aromatic molecules. The permanent electrostatic energy is expressed as atomic multipole interactions between atom pairs, and many-body polarization is accounted for by mutually induced atomic dipoles. We have systematically investigated aromatic ring stacking and aromatic-water interactions for nucleobases and aromatic molecules, as well as base–base hydrogen-bonding pair interactions, all at various distances and orientations. van der Waals parameters were determined by comparison to the quantum mechanical interaction energy of these dimers and fine-tuned using condensed phase simulation. By comparing to quantum mechanical calculations, we show that the resulting classical potential is able to accurately describe molecular polarizability, molecular vibrational frequency, and dimer interaction energy of these aromatic systems. Condensed phase properties, including hydration free energy, liquid density, and heat of vaporization, are also in good overall agreement with experimental values. The structures of benzene liquid phase and benzene-water solution were also investigated by simulation and compared with experimental and PDB structure derived statistical results.

Correction to A Toolkit to Fit Nonbonded Parameters from and for Condensed Phase Simulations.

Correction to A Toolkit to Fit Nonbonded Parameters from and for Condensed Phase Simulations.

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

A robust and automated protocol for the derivation of sound force field parameters, suitable for condensed-phase classical simulations, is here tested and validated on several halogenated hydrocarbons, a class of compounds for which standard force fields have often been reported to deliver rather inaccurate performances. The major strength of the proposed protocol is that all of the parameters are derived only from first principles because all of the information required is retrieved from quantum mechanical data, purposely computed for the investigated molecule. This a priori parametrization is carried out separately for the intra- and intermolecular contributions to the force fields, respectively exploiting the Joyce and Picky programs, previously developed in our group. To avoid high computational costs, all quantum mechanical calculations were performed exploiting the density functional theory. Because the choice of the functional is known to be crucial for the description of the intermolecular interactions, a specific procedure is proposed, which allows for a reliable benchmark of different functionals against higher-level data. The intramolecular and intermolecular contribution are eventually joined together, and the resulting quantum mechanically derived force field is thereafter employed in lengthy molecular dynamics simulations to compute several thermodynamic properties that characterize the resulting bulk phase. The accuracy of the proposed parametrization protocol is finally validated by comparing the computed macroscopic observables with the available experimental counterparts. It is found that, on average, the proposed approach is capable of yielding a consistent description of the investigated set, often outperforming the literature standard force fields, or at least delivering results of similar accuracy.

Real space electrostatics for multipoles. III. Dielectric properties.

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids.

Advanced Potential Energy Surfaces for Molecular Simulation.

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

A Toolkit to Fit Nonbonded Parameters from and for Condensed Phase Simulations.

The quality of atomistic simulations depends decisively on the accuracy of the underlying energy function (force field). Of particular importance for condensed-phase properties are nonbonded interactions, including the electrostatic and Lennard-Jones terms. Permanent atomic multipoles (MTPs) are an extension to common point-charge (PC) representations in atomistic simulations. MTPs are commonly determined from and fitted to an ab initio Electrostatic Potential (ESP), and Lennard-Jones (LJ) parameters are obtained from comparison of experimental and computed observables using molecular dynamics (MD) simulations. For this a set of thermodynamic observables such as density, heat of vaporization, and hydration free energy is chosen, to which the parametrization is fitted. The current work introduces a comprehensive computing environment (Fitting Wizard (FW)) for optimizing nonbonded interactions for atomistic force fields of different qualities. The FW supports fitting of standard PC-based force fields and more physically motivated multipolar (MTP) force fields. A broader study including 20 molecules ranging from N-methyl-acetamide and benzene to halogenated benzenes, phenols, anilines, and pyridines yields a root mean squared deviation for hydration free energies of 0.36 kcal/mol over a range of 8 kcal/mol. It is furthermore shown that PC-based force fields are not necessarily inferior compared to MTP parametrizations depending on the molecule considered.

Convergence of the Many-Body Expansion for Energy and Forces for Classical Polarizable Models in the Condensed Phase.

We analyze convergence of energies and forces for the AMOEBA classical polarizable model when evaluated as a many-body expansion (MBE) against the corresponding N-body parent potential in the context of a condensed-phase water simulation. This is in contrast to most MBE formulations based on quantum mechanics, which focus only on convergence of energies for gas-phase clusters. Using a single water molecule as a definition of a body, we find that truncation of the MBE at third order, 3-AMOEBA, captures direct polarization exactly and yields apparent good convergence of the mutual polarization energy. However, it renders large errors in the magnitude of polarization forces and requires at least fourth-order terms in the MBE to converge toward the parent potential gradient values. We can improve the convergence of polarization forces for 3-AMOEBA by embedding the polarization response of dimers and trimers within a complete representation of the fixed electrostatics of the entire system. We show that the electrostatic embedding formalism helps identify the specific configurations involving linear hydrogen-bonding arrangements that are poorly convergent at the 3-body level. By extending the definition of a body to be a large water cluster, we can reduce errors in forces to yield an approximate polarization model that is up to 10 times faster than the parent potential. The 3-AMOEBA model offers new ways to investigate how the properties of bulk water depend on the degree of connectivity in the liquid.

Impact of Quadrupolar Electrostatics on Atoms Adjacent to the Sigma-Hole in Condensed-Phase Simulations.

Halogenation is one of the cases for which advanced molecular simulation methods are mandatory for quantitative and predictive studies. The present work provides a systematic investigation of the importance of higher-order multipoles on specific sites of halobenzenes, other than the halogen, for static and dynamic properties in condensed-phase simulations. For that purpose, solute-solvent interactions using point charge (PC), multipole (MTP), and hybrid point charge/multipole (HYB) electrostatic models are analyzed in regions of halogen bonding and extended to regions of π orbitals of phenyl carbons. Using molecular dynamics simulations and quantum chemical methods, it is found that the sigma-hole does not only affect the halogen and the carbon bound to it but its effect extends to the carbons adjacent to the CX bond. This effect increases with the magnitude of the positive potential of the sigma-hole. With the MTP and HYB3 models, all hydration free energies of the PhX compounds are reproduced within 0.1 kcal/mol. Analysis of pair distribution functions and hydration free energies of halogenated benzenes provides a microscopic explanation why "point charge"-based representations with off-site charges fail in reproducing thermodynamic properties of the sigma-hole. Application of the hybrid models to study protein-ligand binding demonstrates both their accuracy and computational efficiency.

Drude Polarizable Force Field for Modeling Divalent Cations in Biological Systems

Accurate potential energy functions are crucial for in-depth investigations of biological systems through molecular dynamics simulations. Classical additive force fields with fixed point charges has been proven to be insufficient for describing phenomenon such as ion binding to macromolecules. It is thus important to incorporate polarization effects in modeling of biological systems. In our previous work, we have developed a protocol for developing models of monovalent ions along with Ca2+, by bridging the gap between experimental measurements of bulk-phase properties and quantum mechanics (QM) calculation of gas phase clusters. With a focus on divalent cations and their interactions with amino acids, we have advanced the methodology of parametrization by utilizing a large number of configurations of model compound clusters from relevant condensed phase simulations. Cations currently being studied include (Fe2+), barium (Ba2+), zinc (Zn2+), and magnesium (Mg2+). Based on the classical Drude oscillator model, we have developed a Fe2+ model in fully solvated aqueous solution and in the protein environment. Despite challenges of describing accurately transitional metals through computational approaches, the developed model exhibits robust performance in predicting a wide range of properties that are critical to understanding the structure and function of cations in biological systems. These range from sophisticated coordination geometries to energetics such as water interaction energies and free energies of cation binding in liquids. The developed parameters will be enable discoveries in the area of metalloproteins and other relevant systems.

Time-Domain Simulations of Transient Species in Experimentally Relevant Environments.

Simulating the spectroscopic properties of short-lived thermal and photochemical reaction intermediates and products is a challenging task, as these species often feature atypical molecular and electronic structures. The complex environments in which such species typically reside in practice add further complexity to the problem. Herein, we tackle this problem in silico using ab initio molecular dynamics (AIMD) simulations, employing iso-CHBr3, namely H(Br)C-Br-Br, as a prototypical system. This species was chosen because it features both a nonconventional C-Br-Br bonding pattern, as well as a strong dependence of its spectral features on the local environment in which it resides, as illustrated in recent experimental reports. We simulate the UV-vis and IR spectra of iso-CHBr3 in the gas phase, as well as in a Ne cluster (64 atoms) and in a methylcyclohexane cage (14 solvent molecules) representative of the previously characterized matrix isolated and solvated iso-CHBr3 species. We exclusively perform fully quantum mechanical static and dynamic simulations. By comparing our condensed phase simulations to their experimental analogues, we stress the importance of (i) conformational sampling, even at cryogenic temperatures, and (ii) using a fully quantum mechanical description of both solute and bath to properly account for the experimental observables.

Charge-dependent many-body exchange and dispersion interactions in combined QM/MM simulations.

Accurate modeling of the molecular environment is critical in condensed phase simulations of chemical reactions. Conventional quantum mechanical/molecular mechanical (QM/MM) simulations traditionally model non-electrostatic non-bonded interactions through an empirical Lennard-Jones (LJ) potential which, in violation of intuitive chemical principles, is bereft of any explicit coupling to an atom's local electronic structure. This oversight results in a model whereby short-ranged exchange-repulsion and long-ranged dispersion interactions are invariant to changes in the local atomic charge, leading to accuracy limitations for chemical reactions where significant atomic charge transfer can occur along the reaction coordinate. The present work presents a variational, charge-dependent exchange-repulsion and dispersion model, referred to as the charge-dependent exchange and dispersion (QXD) model, for hybrid QM/MM simulations. Analytic expressions for the energy and gradients are provided, as well as a description of the integration of the model into existing QM/MM frameworks, allowing QXD to replace traditional LJ interactions in simulations of reactive condensed phase systems. After initial validation against QM data, the method is demonstrated by capturing the solvation free energies of a series of small, chlorine-containing compounds that have varying charge on the chlorine atom. The model is further tested on the SN2 attack of a chloride anion on methylchloride. Results suggest that the QXD model, unlike the traditional LJ model, is able to simultaneously obtain accurate solvation free energies for a range of compounds while at the same time closely reproducing the experimental reaction free energy barrier. The QXD interaction model allows explicit coupling of atomic charge with many-body exchange and dispersion interactions that are related to atomic size and provides a more accurate and robust representation of non-electrostatic non-bonded QM/MM interactions.

Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations.

The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r(-1) term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.

Evaluation of CM5 Charges for Nonaqueous Condensed-Phase Modeling.

Partial atomic charges for neutral molecules from quantum mechanical calculations are typically scaled for use in molecular modeling of liquid-phase systems. Optimal scale factors of 1.14 for CM1A and 1.27 for CM5 charges were previously determined for minimizing errors in free energies of hydration. The adequacy of the 1.14*CM1A and 1.27*CM5 models are evaluated here in pure liquid simulations in combination with the OPLS-AA force field. For 22 organic liquids, the 1.14*CM1A and 1.27*CM5 models yield mean unsigned errors (MUEs) of ca. 1.40 kcal/mol for heats of vaporization. Not surprisingly, this reflects overpolarization with the scale factors derived for aqueous media. Prediction of pure liquid properties using CM5 charges is optimized using a scale factor of 1.14, which reduces the MUE for heats of vaporization to 0.89 kcal/mol. However, due to the impracticality of using different scale factors in different explicit-solvent condensed-phase simulations, a universal scale factor of 1.20 emerged for CM5 charges. This provides a balance between errors in computed pure liquid properties and free energies of hydration. Computation of free energies of hydration by the GB/SA method further found that 1.20 is equally suited for use in explicit or implicit treatments of aqueous solvation. With 1.20*CM5 charges, a variety of condensed-phase simulations can be pursued while maintaining average errors of 1.0 kcal/mol in key thermodynamic properties.

Multipolar Ewald methods, 1: theory, accuracy, and performance.

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Theoretical Approaches for Understanding the Interplay Between Stress and Chemical Reactivity.

The use of mechanical stresses to induce chemical reactions has attracted significant interest in recent years. Computational modeling can play a significant role in developing a comprehensive understanding of the interplay between stresses and chemical reactivity. In this review, we discuss techniques for simulating chemical reactions occurring under mechanochemical conditions. The methods described are broadly divided into techniques that are appropriate for studying molecular mechanochemistry and those suited to modeling bulk mechanochemistry. In both cases, several different approaches are described and compared. Methods for examining molecular mechanochemistry are based on exploring the force-modified potential energy surface on which a molecule subjected to an external force moves. Meanwhile, it is suggested that condensed phase simulation methods typically used to study tribochemical reactions, i.e., those occurring in sliding contacts, can be adapted to study bulk mechanochemistry.

Cooperative Helix Formation in the (AAQAA)3 Peptide Obtained with the Drude Polarizable Force Field

Molecular simulations can provide atomic-level details of protein folding. However, their accuracy is limited by approximations made in the underlying empirical force fields. Recently we presented a force field for peptides and proteins that includes explicit treatment of electronic polarization based on the classical Drude oscillator model.[1] The Drude force field was found to maintain protein native structures during microsecond molecular dynamics simulations of multiple folded proteins, and leads to significant variability of backbone and side chain dipole moments as a function of environment.[2] Here we report replica exchange simulations of the helix-forming (AAQAA)3 peptide and the β-sheet-forming GB1 hairpin using this fully polarizable model. Polarizable simulations of (AAQAA)3 reveal the presence of folding cooperativity consistent with experimental observations. The cooperativity is significantly larger than that modeled by currently available non-polarizable force fields and is shown to be directly associated with enhanced dipole moments of the peptide backbone upon helix formation.[3] The GB1 hairpin is found to be less stable with the Drude force field compared to the experimental observation. Results from these extensive condensed phase simulations of peptide folding will be utilized, together with QM calculations of model alanine polypeptide systems, to further refine the backbone parameters in the Drude protein force field. In summary, our results demonstrate that the inclusion of explicit electronic polarizability leads to a fundamentally improved model of the physical forces dictating the structure and dynamics of polypeptides. [1] P. Lopes, J. Huang, J. Shim, Y. Luo, H. Li, B. Roux, and A.D. MacKerell, J. Chem. Theo. Comput., 2013, 9, 5430. [2] J. Huang, P. Lopes, B. Roux, and A.D. MacKerell, J. Phys. Chem. Lett., 2014, 5, 3144. [3] J. Huang and A.D. MacKerell, Biophys. J., 2014, 107, 991.

Ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins.

We present the ff14ipq force field, implementing the previously published IPolQ charge set for simulations of complete proteins. Minor modifications to the charge derivation scheme and van der Waals interactions between polar atoms are introduced. Torsion parameters are developed through a generational learning approach, based on gas-phase MP2/cc-pVTZ single-point energies computed of structures optimized by the force field itself rather than the quantum benchmark. In this manner, we sacrifice information about the true quantum minima in order to ensure that the force field maintains optimal agreement with the MP2/cc-pVTZ benchmark for the ensembles it will actually produce in simulations. A means of making the gas-phase torsion parameters compatible with solution-phase IPolQ charges is presented. The ff14ipq model is an alternative to ff99SB and other Amber force fields for protein simulations in programs that accommodate pair-specific Lennard–Jones combining rules. The force field gives strong performance on α-helical and β-sheet oligopeptides as well as globular proteins over microsecond time scale simulations, although it has not yet been tested in conjunction with lipid and nucleic acid models. We show how our choices in parameter development influence the resulting force field and how other choices that may have appeared reasonable would actually have led to poorer results. The tools we developed may also aid in the development of future fixed-charge and even polarizable biomolecular force fields.