Atomistic Simulation Study of Cu0.327Ni0.673 Alloys: from Solid Solution to Phase Segregation

We present a combined Monte‐Carlo/molecular dynamics study of a Cu_0.327Ni_0.673 alloy system. On the basis of nearest‐neighbor coordination number analyses atomic clustering and phase segregation is explored. Along this line, free energy profiles are calculated and separated into entropic and energetic contributions. The competition of both terms was found in accordance to the experimental phase diagrams (phase separation of the solid solution below about 600 Kelvin). Two independent simulation runs were performed. At 1000 Kelvin the observed configurations correspond to solid solutions exhibiting a weak tendency to cluster atoms of identical species. At room temperature the energetic favoring of atomic separation is clearly dominant and leads to the formation of Ni‐rich and Cu‐rich domains. The latter are separated by interfacial regions whose width ranges from 0.5 to 1 nanometers.     

Calculation of absolute binding free energies for charged ligands and effects of long-range electrostatic interactions

A recently proposed molecular dynamics method for estimating binding free energies is applied to the complexation of two charged benzamidine inhibitors with trypsin. The difficulties with calculations of absolute binding energies for charged molecules, associated with long-range electrostatic contributions, are discussed and it is shown how to deal with these effectively. In particular, energetic effects caused by the trunction of dipole-dipole interactions in the medium surrounding the charged ligand are examined and found to be significant. Calculations of the absolute binding energy for benzamidine using the free energy perturbation approach are also reported. These simulations illustrate the typical problems associated with annihilation transformations of molecules bound inside proteins. © 1996 by John Wiley & Sons, Inc.     

Constructing a multidimensional free energy surface like a spider weaving a web

Complete free energy surface in the collective variable space provides important information of the reaction mechanisms of the molecules. But, sufficient sampling in the collective variable space is not easy. The space expands quickly with the number of the collective variables. To solve the problem, many methods utilize artificial biasing potentials to flatten out the original free energy surface of the molecule in the simulation. Their performances are sensitive to the definitions of the biasing potentials. Fast‐growing biasing potential accelerates the sampling speed but decreases the accuracy of the free energy result. Slow‐growing biasing potential gives an optimized result but needs more simulation time. In this article, we propose an alternative method. It adds the biasing potential to a representative point of the molecule in the collective variable space to improve the conformational sampling. And the free energy surface is calculated from the free energy gradient in the constrained simulation, not given by the negative of the biasing potential as previous methods. So the presented method does not require the biasing potential to remove all the barriers and basins on the free energy surface exactly. Practical applications show that the method in this work is able to produce the accurate free energy surfaces for different molecules in a short time period. The free energy errors are small in the cases of various biasing potentials. © 2017 Wiley Periodicals, Inc.     

Application of the frozen atom approximation to the GB/SA continuum model for solvation free energy

The generalized Born/surface area (GB/SA) continuum model for solvation free energy is a fast and accurate alternative to using discrete water molecules in molecular simulations of solvated systems. However, computational studies of large solvated molecular systems such as enzyme-ligand complexes can still be computationally expensive even with continuum solvation methods simply because of the large number of atoms in the solute molecules. Because in such systems often only a relatively small portion of the system such as the ligand binding site is under study, it becomes less attractive to calculate energies and derivatives for all atoms in the system. To curtail computation while still maintaining high energetic accuracy, atoms distant from the site of interest are often frozen; that is, their coordinates are made invariant. Such frozen atoms do not require energetic and derivative updates during the course of a simulation. Herein we describe methodology and results for applying the frozen atom approach to both the generalized Born (GB) and the solvent accessible surface area (SASA) parts of the GB/SA continuum model for solvation free energy. For strictly pairwise energetic terms, such as the Coulombic and van-der-Waals energies, contributions from pairs of frozen atoms can be ignored. This leaves energetic differences unaffected for conformations that vary only in the positions of nonfrozen atoms. Due to the nonlocal nature of the GB analytical form, however, excluding such pairs from a GB calculation leads to unacceptable inaccuracies. To apply a frozen-atom scheme to GB calculations, a buffer region within the frozen-atom zone is generated based on a user-definable cutoff distance from the nonfrozen atoms. Certain pairwise interactions between frozen atoms in the buffer region are retained in the GB computation. This allows high accuracy in conformational GB comparisons to be maintained while achieving significant savings in computational time compared to the full (nonfrozen) calculation. A similar approach for using a buffer region of frozen atoms is taken for the SASA calculation. The SASA calculation is local in nature, and thus exact SASA energies are maintained. With a buffer region of 8 A for the frozen-atom cases, excellent agreement in differences in energies for three different conformations of cytochrome P450 with a bound camphor ligand are obtained with respect to the nonfrozen cases. For various minimization protocols, simulations run 2 to 10.5 times faster and memory usage is reduced by a factor of 1.5 to 5. Application of the frozen atom method for GB/SA calculations thus can render computationally tractable biologically and medically important simulations such as those used to study ligand-receptor binding conformations and energies in a solvated environment.     

Kinetics of phase transitions in two dimensional Ising models studied with the string method

The kinetics of phase transitions in the two dimensional Ising model under different conditions is studied using the string method. The key idea is to work in collective variables, consisting of block of spins, which allow for a continuous approximation of the collective variable state-space. The string method computes the minimum free energy path (MFEP) in this collective variable space, which is shown to explain the mechanism of the phase transformation (in particular, an approximation of its committor function, its free energy and its transition state). In this paper the theoretical background of the technique as well as its computational aspects are discussed in details. The string method is then used to analyze phase transition in the Ising model with imposed boundary conditions and in a periodic system under an external field of increasing magnitude. In each case, the mechanism of the phase transformation is elucidated.     

Mesoscale model parameters from molecular cluster calculations

We present an efficient, systematic, and universal method to estimate the interaction parameters used in mesoscale simulation methods such as dissipative particle dynamics and self-consistent field methods from molecular cluster calculations. The method is based on a generalized Flory-Huggins model in which molecules, or fragments thereof, are in contact with their van der Waals surface. We sample the density of states of molecular clusters in the space spanned by the coarse-grained degrees of freedom. From here, we calculate the sum over states and free energy of the cluster at a temperature of interest by histogram reweighting. The method allows to calculate the energy and entropy contributions to the cluster free energy explicitly. For two components, we then obtain the excess free energy of mixing and the Flory-Huggins chi-parameter, and their energetic and entropic contributions. We present two applications of the method: a simple liquid mixture of hexane and nitrobenzene, and a series of polymer blends. In the case of hexane/nitrobenzene, we compare to alternative simulation methods; here we find that the energy of mixing alone is too high to explain the critical point. By including the excess entropy of mixing, however, the predicted phase behavior is in reasonable agreement with experiment. The tendency of calculations based on average energy alone to overestimate the chi-parameter is also apparent in the polymer blend calculations.     

Improved convergence in dual-topology free energy calculations through use of harmonic restraints

When calculating free energy differences between two molecular systems by means of molecular dynamics simulation, accessory potential functions can help eliminate uninteresting configurational entropy contributions, improve convergence, and facilitate reversibility. In this work, we demonstrate that the use of a harmonic potential function to restrain key portions of a molecular system in a free energy perturbation dual-topology molecular dynamics approach dramatically improves convergence and precision of the calculation. Limitations of this technique are illustrated, and its use in conjunction with a fixed bond-length constraint is developed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1278–1283, 1998     

Efficient and precise solvation free energies via alchemical adiabatic molecular dynamics

A new molecular dynamics method for calculating free energies associated with transformations of the thermodynamic state or chemical composition of a system (also known as alchemical transformations) is presented. The new method extends the adiabatic dynamics approach recently introduced by Rosso et al. [J. Chem. Phys. 116, 4389 (2002)] and is based on the use of an additional degree of freedom, lambda, that is used as a switching parameter between the potential energy functions that characterize the two states. In the new method, the coupling parameter lambda is introduced as a fictitious dynamical variable in the Hamiltonian, and a system of switching functions is employed that leads to a barrier in the lambda free energy profile between the relevant thermodynamic end points. The presence of such a barrier, therefore, enhances sampling in the end point (lambda = 0 and lambda = 1) regions which are most important for computing relevant free energy differences. In order to ensure efficient barrier crossing, a high temperature T(lambda) is assigned to lambda and a fictitious mass m(lambda) is introduced as a means of creating an adiabatic separation between lambda and the rest of the system. Under these conditions, it is shown that the lambda free energy profile can be directly computed from the adiabatic probability distribution function of lambda without any postprocessing or unbiasing of the output data. The new method is illustrated on two model problems and in the calculation of the solvation free energy of amino acid side-chain analogs in TIP3P water. Comparisons to previous work using thermodynamic integration and free energy perturbation show that the new lambda adiabatic free energy dynamics method results in very precise free energy calculations using significantly shorter trajectories.     

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this “Multi-Map” variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich–Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.     

Validation of improved simple method for prediction of activation energy of the thermal decomposition of energetic compounds

This study presents a new simple model for predicting activation energy of the thermolysis of various classes of energetic compounds. The new model can help to elucidate the cause of thermal stability and, therefore, shelf life of some energetic compounds. The methodology assumes that activation energy of an energetic compound with general formula C _a H _b N _c O _d can be expressed as a function of optimized elemental composition as well as the contribution of specific molecular structural parameters. The new correlation has the root mean square and the average deviations of 9.8 and 7.4 kJ mol^?1, respectively, for 86 energetic compounds with different molecular structures. The proposed new method is also tested for 20 energetic compounds, which have complex molecular structures, e.g. 4,10-dinitro-2,6,8,12-tetraoxa-4,10-diazaisowurtzitane, 2,4,6-tris(2,4,6-Trinitrophenyl)-1,3,5-triazine and 1-(2,4,6-Trinitrophenyl)-5,7-dinitrobenzotriazole.     

Selectivity of neutral/weakly basic P1 group inhibitors of thrombin and trypsin by a molecular dynamics study

Molecular dynamics (MD) simulations followed by molecular mechanics generalized Born surface area (MM-GBSA) analyses have been carried out to study the selectivity of two neutral and weakly basic P1 group inhibitors (177 and CDA) to thrombin and trypsin. Detailed binding free energies between these inhibitors and individual protein residues are calculated by using a per-residue basis decomposition method. The analysis of the detailed interaction energies provides insight on the protein-inhibitor-binding mechanism and helps to elucidate the basis for achieving selectivity through interpretation of the structural and energetic results from the simulations. The study shows that the dominant factor of selectivity for both inhibitors is van der Waals energy, which suggests better shape complementarity and packing with thrombin. Nonpolar solvation free energy and total entropy contribution are also in favor of selectivity, but the contributions are much smaller. Binding mode and structural analysis show that 177 binds to thrombin and trypsin in a similar binding mode. In contrast, the CDA binds to thrombin and trypsin in very different modes.     

Toward accurate solvation dynamics of lanthanides and actinides in water using polarizable force fields: from gas-phase energetics to hydration free energies

In this contribution, we focused on the use of polarizable force fields to model the structural, energetic, and thermodynamical properties of lanthanides and actinides in water. In a first part, we chose the particular case of the Th(IV) cation to demonstrate the capabilities of the AMOEBA polarizable force field to reproduce both reference ab initio gas-phase energetics and experimental data including coordination numbers and radial distribution functions. Using such model, we predicted the first polarizable force field estimate of Th(IV) solvation free energy, which accounts for −1,638 kcal/mol. In addition, we proposed in a second part of this work a full extension of the SIBFA (Sum of Interaction Between Fragments Ab initio computed) polarizable potential to lanthanides (La(III) and Lu(III)) and to actinides (Th(IV)) in water. We demonstrate its capabilities to reproduce all ab initio contributions as extracted from energy decomposition analysis computations, including many-body charge transfer and discussed its applicability to extended molecular dynamics and its parametrization on high-level post-Hartree–Fock data.     

Topology of energy hypersurfaces

Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.     

An exact stoichiometric representation of the resonance energy

The energetic measure of aromaticity usually referred to as resonance energy (RE) is shown to possess a remarkable stoichiometric interpretation. Namely, the RE may be uniquely partitioned into a linear sum of contributions associated with group additivity (GA) response reactions (RERs). This new result is a powerful tool for critical analyses of various energetic approaches to RE. In particular, the single reaction scheme approach that is routinely used to evaluate RE is shown to be a particular case of the general GA method.     

A novel method for risk assessment of electrostatic sensitivity of nitroaromatics through their activation energies of thermal decomposition

This study presents a novel relationship between electric spark sensitivity of nitroaromatic energetic compounds and their activation energies of thermal decomposition. The new correlation can help to elucidate the mechanism of initiation of energetic materials by electric spark. It can be used to predict the magnitude of electric spark sensitivity of new nitroaromatics, which is difficult to measure. The methodology assumes that electric spark sensitivity of a nitroaromatic energetic compound with general formula C_aH_bN_cO_d can be expressed as a function of its activation energy of thermal decomposition as well as optimized elemental composition and the contribution of specific molecular structural parameters. The new correlation has the root mean square and the average deviations of 1.43 and 1.17 J, respectively, for 22 nitroaromatic energetic compounds with different molecular structures. The proposed new method is also tested for eight nitroaromatic energetic compounds, which have complex molecular structures, e.g., 1,3,7,9-tetranitrophenoxazine, 2,4,6-tris(2,4,6-trinitrophenyl)-1,3,5-triazine, and 1-(2,4,6-trinitrophenyl)-5,7-dinitrobenzotriazole.     

A link between impact sensitivity of energetic compounds and their activation energies of thermal decomposition

A new relationship is introduced between impact sensitivity of energetic compounds and their activation energies of thermal decomposition. In this relationship, the impact sensitivity of an energetic compound with general formula C_aH_bN_cO_d is a function of its activation energy of thermal decomposition as well as the ratio of \( \left( {\frac{{n_{\text{H}} }}{{n_{\text{O}} }}} \right) \) and the contribution of specific molecular structural parameters. The new correlation can help us to elucidate the mechanism of initiation of energetic materials by impact. It can be used to predict the magnitude of impact sensitivity of new energetic materials. The new correlation has the root mean square and the average deviations of 2.22 and 1.79 J, respectively, for 40 energetic compounds with different molecular structures. The proposed new method is also tested for 11 energetic compounds, which have complex molecular structures, e.g., 4,10-dinitro-2,6,8,12-tetraoxa-4,10-diazaisowurtzitane and 1,3,7,9-tetranitrophenoxazine.     

The free energy of the metastable supersaturated vapor via restricted ensemble simulations

Pressure, excess chemical potential, and excess free energy, with respect to ideal gas data at different densities of the supersaturated Lennard-Jones particle vapor at the reduced temperature 0.7 are obtained by the restricted canonical ensemble Monte Carlo simulation method [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)]. The excess free energy values depend upon the constraints imposed on the system with local minima exhibited for densities below the spinodal density and monotonic variation for densities larger than the spinodal density. The results are compared with a molecular dynamics simulation study [A. Linharton et al., J. Chem. Phys. 122, 144506 (2005)] on the same system. The current study verifies the conclusion drawn by the simulation work that clustering of Lennard-Jones atoms exists even in the vicinity of spinodal. Our method gives an alternative to molecular dynamic simulations for the determination of equilibrium properties of a metastable fluid, especially close to the spinodal, and does not require a very large system to carry out the simulation.