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1.
We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.  相似文献   

2.
We developed a multistep thermodynamic perturbation method to compute the interfacial free energies by nonequilibrium work measurements with cleaving potential procedure. Using this method, we calculated the interfacial free energies of different crystal orientations for the Lennard-Jones system. Our results are in good agreement with the results by thermodynamic integration method. Compared with thermodynamic integration method, the multistep thermodynamic perturbation method is more efficient. For each stage of the cleaving process, only a few thermodynamic perturbation steps are needed, and there is no requirement on the reversibility of the path.  相似文献   

3.
Thermodynamic integration is a widely used method to calculate and analyze the effect of a chemical modification on the free energy of a chemical or biochemical process, for example, the impact of an amino acid substitution on protein association. Numerical fluctuations can introduce large uncertainties, limiting the domain of application of the method. The parametric energy function describing the chemical modification in the thermodynamic integration, the "Alchemical path," determines the amplitudes of the fluctuations. In the present work, I propose a measure of the fluctuations in the thermodynamic integration and an approach to search for a parametric energy path minimizing that measure. The optimal path derived with this approach is very close to the theoretical minimum of the measure, but produces nonergodic sampling. Nevertheless, this path is used to guide the design of a practical and efficient path producing correct sampling. The convergence with this practical path is evaluated on test cases, and compares favorably with that of other methods such as power or polynomial path, soft-core van der Waals, and some other approaches presented in the literature.  相似文献   

4.
The phase diagram of water has been calculated from the TIP4PQ/2005 model, an empirical rigid non-polarisable model. The path integral Monte Carlo technique was used, permitting the incorporation of nuclear quantum effects. The coexistence lines were traced out using the Gibbs-Duhem integration method, once having calculated the free energies of the liquid and solid phases in the quantum limit, which were obtained via thermodynamic integration from the classical value by scaling the mass of the water molecule. The resulting phase diagram is qualitatively correct, being displaced to lower temperatures by 15-20 K. It is found that the influence of nuclear quantum effects is correlated to the tetrahedral order parameter.  相似文献   

5.
The polynomial path is introduced for the calculation of liquid state free energies. The well-characterized SPC, TIP4P, and MCY water models were used to demonstrate its efficiency, as well as its range of applicability in conjunction with Monte Carlo computer simulations using thermodynamic integration based on Gaussian quadratures. The technique employed is compared with the slow-growth method (another variant of thermodynamic integration), the perturbation method, and the use of the grand-canonical ensemble.  相似文献   

6.
Monte Carlo simulations are presented for two models of aluminum: an embedded-atom model and an explicit many-body model. Vapor/liquid coexistence curves are determined using Gibbs ensemble Monte Carlo simulations. The normal boiling points predicted by both models are somewhat higher (by about 10%) than the experimental value. Isothermal constant-stress simulations are used to simulate solid Al from 300 K to the triple point. The solid structures are at least metastable in the face-centered cubic configuration, and the specific heat is determined to be lower than the experimental value. The melting point for the embedded-atom model determined via thermodynamic integration along a pseudo-supercritical path is approximately 20% higher than the experimental value.  相似文献   

7.
The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.  相似文献   

8.
A critical drawback with first-principles thermodynamic calculations is the absence of the vibrational and entropic contributions to the prediction of reaction mechanisms, which could conclusively show that the predicted reaction mechanism might be not the most stable reaction path. This study focused on providing an answer to this problem by examining possible metastable paths for five reactant mixtures whose reaction mechanisms were previously predicted using first-principles thermodynamic calculations. The aim of this study was to find a minimum free energy path among all the possible paths of each reactant mixture. This effort provided the clear conclusion that the original reaction paths predicted from first-principles thermodynamic calculations were the most stable reaction paths at an appropriate H(2) pressure range for all cases. An additional examination associated with density functional theory uncertainty suggests how the ambiguity of reaction mechanisms predicted based on thermodynamic calculations should be understood and dealt with.  相似文献   

9.
The structure and special features of a software for work with a data bank are described. A method for storing thermodynamic information about mineral and gas phases and solution components is suggested. The purpose of the creation of the data bank was the provision with the initial thermodynamic data and programs that minimized the Gibbs energy for the solution of physicochemical simulation problems and the construction of mineral equilibrium diagrams. The possibilities of the software were demonstrated for the example of the construction of mineral equilibrium diagrams for minerals containing rare-earth metals.  相似文献   

10.
The results of a thermodynamic analysis of an elementary process of distillation in which the separation of the components of the solution occurs due to the absence of thermodynamic equilibrium between the phases are summarized and compared with results of studies of a single event of separation of a mixture at the expense of the energy supplied from an external source. A thermodynamic interpretation is proposed for optimum conditions of fine separation of an equimolar binary mixture by single-stage distillation.  相似文献   

11.
The entropy of a system transiently driven out of equilibrium by a time-inhomogeneous stochastic dynamics is first expressed as a transient response function generalizing the nonlinear Kawasaki-Crooks response. This function is then reformulated into three statistical averages defined over ensembles of nonequilibrium trajectories. The first average corresponds to a space-time thermodynamic perturbation relation, while the two following ones correspond to space-time thermodynamic integration relations. Provided that trajectories are initiated starting from a distribution of states that is analytically known, the ensemble averages are computationally amenable to Markov chain Monte Carlo methods. The relevance of importance sampling in path ensembles is confirmed in practice by computing the nonequilibrium entropy of a driven toy system. We finally study a situation where the dynamics produces entropy. In this case, we observe that space-time thermodynamic integration still yields converged estimates, while space-time thermodynamic perturbation turns out to converge very slowly.  相似文献   

12.
We derive expressions for the equilibrium entropy and energy changes in the context of the Jarzynski equality relating nonequilibrium work to equilibrium free energy. The derivation is based on a stochastic path integral technique that reweights paths at different temperatures. Stochastic dynamics generated by either a Langevin equation or a Metropolis Monte Carlo scheme are treated. The approach enables the entropy-energy decomposition from trajectories evolving at a single-temperature and does not require simulations or measurements at two or more temperatures. Both finite difference and analytical formulae are derived. Testing is performed on a prototypical model system and the method is compared with existing thermodynamic integration and thermodynamic perturbation approaches for entropy-energy decomposition. The new formulae are also put in the context of more general, dynamics-independent expressions that derive from either a fluctuation theorem or the Feynman-Kac theorem.  相似文献   

13.
The free-energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum-energy path directly on the free-energy surface at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free-energy gradient for a given RC. These derivatives are then used to find the actual minimum-energy reaction path at finite temperature, in a way similar to the intrinsic reaction path of Fukui on the potential-energy surface. [K. Fukui, J. Phys. Chem. 74, 4161 (1970)]. Once the path is known, one can calculate the free-energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum-free-energy path at 300 K for the addition of CCl2 to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.  相似文献   

14.
Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate.  相似文献   

15.
A new thermodynamic integration approach to conformational free energy simulations is presented. The method is applicable both to one-dimensional cases (reaction coordinates) and multidimensional situations (free energy surfaces). Analysis of the properties of the thermodynamic integration algorithm is used to formulate methods of calculating multidimensional free energy gradients. The method is applied to calculate the free energy profile for rotation around the central C—C bond of n-butane in the gas and liquid phase and to generate maps of the 18-dimensional free energy gradient with respect to all nine ϕ and nine ψ dihedrals of the decaalanine and deca-α-methylalanine peptides in vacuum. For n-butane essentially no change in the gauche–trans equilibrium between the gas and liquid is predicted within the CHARMM explicit hydrogen model, with the thermodynamic integration, thermodynamic perturbation, and direct simulation methods yielding free energy profiles that are identical within errors. For the decapeptides the right-handed helical region of conformational space is investigated. For decaalanine a minimum on the free energy surface is found in the vicinity of (ϕ, ψ) = (-64.5°, -42.5°) in the α-helix region; no minimum exists for 310-helix-type conformers. For deca-α-methylalanine free energy minima corresponding to both the α-helix at ( - 55.5°, - 51.5°) and the 310-helix at ( - 54°, - 29°) are found; the α-helix state is favored by about 4 kcal/mol and the barrier for the concerted 310-helix → α-helix transition is about 3 kcal/mol. The α-methylation also considerably increases the rigidity of the α-helix with respect to deformations. The computational efficiency, ease of generalization to calculations of multidimensional gradients, and analytical capability due to component analysis of free energy differences make the method a novel, powerful tool to improve the basic understanding of conformational equilibria of flexible molecules in condensed phases. A related scheme for energy minimization in the presence of holonomic constraints is also presented, allowing generation of adiabatic energy surfaces in constrained systems. © 1996 by John Wiley & Sons, Inc.  相似文献   

16.
Regarding the surface phase of liquid mixtures as a thermodynamic phase, ideal surface phases are designed so that at fixed bulk‐phase composition, real and ideal surface phases have the same chemical composition and identical limiting slopes for the dependence of surface tension on mole fraction. Standard chemical potentials are introduced for surface phase components, and quasi‐exact expressions are worked out to compute ideal surface tensions and surface‐phase compositions of real liquid mixtures. Guidelines for choosing molecular models to estimate the molar surface area of pure constituents are given. Ideal and excess surface tensions are calculated by using literature data for aqueous ethanol solutions at 298 K. These results show treatment based on Butler’s equations grossly overestimate predicted surface tensions, thus leading to lower ethanol content in the surface phase. These inaccuracies are ascribed to the use of molar surface areas in model equations that are too small.  相似文献   

17.
We describe a method for calculating free energies and chemical potentials for molecular models of gas hydrate systems using Monte Carlo simulations. The method has two components: (i) thermodynamic integration to obtain the water and guest molecule chemical potentials as functions of the hydrate occupancy; (ii) calculation of the free energy of the zero-occupancy hydrate system using thermodynamic integration from an Einstein crystal reference state. The approach is applicable to any classical molecular model of a hydrate. We illustrate the methodology with an application to the structure-I methane hydrate using two molecular models. Results from the method are also used to assess approximations in the van der Waals-Platteeuw theory and some of its extensions. It is shown that the success of the van der Waals-Platteeuw theory is in part due to a cancellation of the error arising from the assumption of a fixed configuration of water molecules in the hydrate framework with that arising from the neglect of methane-methane interactions.  相似文献   

18.
We investigate the system-size dependence of the Helmholtz free energy of crystalline solids from computer simulation. We employ a standard thermodynamic integration technique along a reversible path that links the crystalline solid with a noninteracting Einstein crystal with the same structure. The key contribution to the free energy is computed by using the so-called expanded-ensemble technique and the results are compared with those obtained from conventional integration of the derivative of the free energy along the path using Gaussian-Legendre quadrature. We find that both methods yield fully consistent results. The free energy is found to exhibit a strong dependence with system size, in agreement with the behavior found by Polson et al. [J. Chem. Phys. 112, 5339 (2000)] but at variance with the dependence reported more recently by Chang and Sandler [J. Chem. Phys. 118, 8390 (2003)]. This has been tested for the face-centered cubic (fcc) and hexagonal close-packed phases of a crystal of hard spheres at a density close to the melting point. We also investigate any possible dependence of the free energy of the solid phase with the shape of the simulation box. We find that this contribution may not be as important as previous investigations suggest. The present results seem to indicate that there is a non-negligible contribution to the free energy arising from the orientation of the closed-packed crystal layers with respect to the simulation cell. This contribution is particularly noticeable for small system sizes and is believed to be an effect of the periodic boundary conditions used in the simulations. The results presented here corroborate the stability of the fcc phase of the hard-sphere solid close to melting.  相似文献   

19.
The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient "virial" estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum mechanically and uses an empirical valence bond potential based on a molecular mechanics force field.  相似文献   

20.
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