Equality Of Chemical Potentials Research Articles

Comment on “Classical polarizable force fields parametrized from ab initio calculations” [J. Chem. Phys. 117, 1416 (2002)

Recently [J. Chem. Phys. 117, 1416 (2002)], Tabacchi et al. proposed a treatment, based on the chemical potential equalization, to account for polarization in classical molecular mechanics. In view of a possible generalization of that approach, intended to build a transferable polarizable force field, we discuss several shortcomings that may arise when the Tabacchi’s model is applied to complex molecular systems.

A transferable polarizable electrostatic force field for molecular mechanics based on the chemical potential equalization principle

A polarizable electrostatic potential model for classical molecular mechanics is presented. Based on the chemical potential equalization (CPE) principle, the model is developed starting from the original formulation of Mortier, Ghosh, and Shankar [J. Am. Chem. Soc. 108, 4315 (1986)]. Following York and Yang [J. Chem. Phys. 104, 159 (1996)] we present an SP-basis CPE parametrization to describe realistically any sort of molecular system. By fitting ab initio electronic properties, such as dipole moment, polarizability and global molecular hardness of a restricted set of organic molecules, we derive atomic parameters to be applied to a more vast target set of compounds. We show, indeed, that the atomic CPE parameters calculated for the learning set of molecules give reliable values for several electronic properties of various compounds not included in the learning set. The multipole moments obtained by using the proposed CPE parametrization are compared to the results of a fixed charge parametrization like that used by a popular classical molecular mechanics force field, such as AMBER. We show that the fixed charge parametrization can well reproduce only the multipole moments of the molecular conformation or the isomer used for the fit, while being inaccurate when different molecular conformations or isomers are considered. On the contrary, the CPE model realistically reproduces the charge reorganization due to nuclear structural changes of the molecule, such as isomerization or conformational transition. The CPE model has been also tested on various molecular complexes to investigate the polarization response in the case of realistic molecule–molecule interactions. The main result of the paper is the demonstration that the construction of a general polarizable electrostatic force field for classical molecular mechanics is now a viable way.

Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.

New approach to dense plasma thermodynamics in the superconfiguration approximation

We propose a new approach to the calculation of ion populations in the LTE dense plasmas in the superconfiguration approximation. The screening of plasma ions is obtained using the same free-electron chemical potential for each ion charge. This chemical potential is determined by iteration keeping the total density constant and varying the volume of each ion. In such a way our approach not only gives the charge neutrality of the plasma, but also assures that the free-electron density is equal in the vicinity of each ion. The resulting ion charge distribution is different with respect to the one obtained without imposing the constraint of equal chemical potential. For instance, the effective charge is a little bit higher, which can change the shape of the absorption spectra, especially at higher densities. Examples of absorption spectra of medium-Z plasmas in a temperature and density range close to the present opacity measurements are shown.

Towards a polarizable force field for molecular liquids

Modern time resolved spectroscopic techniques, such as off resonant transient birifrangence, or in the frequency domain, such as Fourier transform infrared, constitute a valuable experimental source of information for the dynamical and structural properties of molecular liquids. Many important spectroscopic physical observables can be in principle straight-forwardly computed using classical molecular dynamics (MD) simulations. However, MD in its standard implementation has important drawbacks which severely limit its use in the study of light scattering phenomena. In particular, the lack of an adequate representation of the molecular electronic response to the external and local field prevents the accurate simulation of spectroscopic properties. The chemical potential equalization (CPE) method can be used to derive a realistic parameterization for describing electronic polarization effects. The CPE approach is a semi-empirical density functional method. The total molecular energy is expanded to the second order in terms of local atomic electron densities, represented by fluctuating point charges. The empirical parameters of the expansion are atomic electronegativity and hardness which can be fitted onto accurate ab initio calculations of the isolated molecule. CPE is parameterized so as to reproduce global ground state properties of the molecule such as polarizability, ionization potential and electronic affinity as well as local properties such as atomic charges and Fukui indices. From a computational standpoint, the CPE method is simple and inexpensive and can be either straightforwardly implemented in a Car-Parrinello fashion, or used as an analytic tool for computing, a posteriori, spectroscopic properties from trajectories generated by conventional MD simulations. Here we present an extension of the CPE method including atomic dipolar charge distributions and apply it to the simple case of the water monomer and dimer. Very encouraging results are found.

Fluctuating Charge Study of Polarization Effects in Chlorinated Organic Liquids

The role of polarization has been systematically studied for the methylchloromethane family ((CH3)4-nCCln) of organic liquids. Special attention has been paid to dynamical properties (translational diffusion and rotational relaxation) for which good agreement with experiment is obtained, although structural and electrostatic effects have been addressed as well. Molecular dynamics simulations have been performed, with and without the inclusion of polarization, over a substantial range of temperatures. Polarizability has been handled with the chemical potential equalization (fluctuating charge) method, with a transferable set of parameters having been developed for the methyl group. As a general rule, the inclusion of polarization does not affect structure and slightly slows down the dynamics at all temperatures. The overall muted influence of polarization contrasts with the substantial induced dipole moments obtained, exceeding what had been found in other organic (albeit hydrogen-bonding) liquids.

Collision-induced absorption in liquid carbon tetrachloride

Molecular dynamics (MD) simulation has been used for the computation of the far infrared absorption coefficient of CCl 4, with an excellent accord with experimental results at all frequencies. Nonadditive polarization interactions have been implemented with the chemical potential equalization method, which requires the gas phase values of the octupole moment and mean polarizability tensor. It is shown that the absorption coefficient constitutes an exacting probe of interaction potentials, strongly favoring a physically reasonable set of atomic charges.

A set of phase-equilibrium equations in covariant form and its use for developing a general method of calculation of two-phase conodes in multicomponent systems

In the last 25–30 years, thermodynamic calculations of phase diagrams for both binary and multicomponent systems received wide application. The computer programs [1–7] developed in various research centers of the world are of wide use. The numerical methods involved in these programs can be divided into two classes. In studies of the first class [2], the Gibbsenergy minimum is sought for a heterogeneous system. In studies of the second class, the set of phase-equilibrium equations (establishing the equality of chemical potentials for the components of various phases) is solved [1, 3–7]. In this case, either the Newton–Raphson iterative method [1] or the Nelder–Mead modified simplex method is used to minimize the objective function representing the sum of residuals of the phaseequilibrium equations [7]. An essential constraint of the former methods is the impossibility of guaranteeing attainment of the global minimum of the Gibbs energy for a heterogeneous system. This means that the calculated phase diagram can be both stable and metastable. An essential disadvantage of the latter methods is the necessity of selecting a successful initial approximation for starting the iterative process, for which there is no assurance that the iterations will converge to the desired solution. Thus, the calculating methods of both the first and second class render it principally impossible to create autonomous computer programs for calculating phase diagrams and thermodynamic properties of multicomponent alloys of systems with three or more components.

A chemical potential equalization model for treating polarization in molecular mechanical force fields

A chemical potential equalization model for treating polarization in molecular mechanical force fields

A chemical potential equalization model for treating polarization in molecular mechanical force fields

Molecular mechanical force fields are widely used in molecular simulation studies due to their simplicity and efficiency. Although accurate enough for many purposes, force fields are approximations and neglect several effects that are important at an atomic level. Probably the most significant of these, that is not taken into account by the majority of force fields, is the ability of the charge distribution of a molecule to polarize in response to changes in its environment. There are several ways of including polarization effects in force fields but, in this paper, we investigate a relatively new approach, called the chemical potential equalization model, which is based upon the principle of electronegativity equalization and which is a generalization of the class of fluctuating charge models. We detail the principles behind the model and of our implementation of it and then present parametrizations of the model for the molecules, methane and water, and the chloride anion. Gas- and solution-phase calculations to test the parametrizations indicate that the model gives results that are in good agreement with experiment and that compare well to those obtained with non-polarizable force fields and other polarizable models.

Charge sensitivities of the externally interacting open reactants

Effective chemical potential, hardness, softness, and Fukui function quantities of the simultaneously open reactants, e.g., adsorbates in catalytic systems, are examined. The derived reduced expressions in terms of the canonical chemical potentials and condensed hardness matrix elements of such molecular subsystems are compared with the corresponding analogs for the case of the closed complementary subsystem. Implications of the catalyst-induced changes in the condensed hardness matrix of the reactive system consisting of a pair of donor/acceptor adsorbates, in the preferred complementary arrangement with the acidic/basic active sites of the surface, respectively, are discussed and interpreted as manifestations of the Le Châtelier–Braun principle. Only in such a complementary arrangement is the in-phase, concerted, mutually enhancing pattern of the polarizational and charge transfer flows of electrons in a catalytic system obtained. The activating influence of the catalyst is identified through its softening, decoupling effect on the adsorbates. The catalyst-induced chemical potential equalization creates electronic instability in the system of adsorbed species, thus increasing their reactivity. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 168–178, 2000

Electrical response in chemical potential equalization schemes

In this paper we compare the polarization response given by two different chemical potential equalization schemes to be applied to molecular dynamics simulations: the standard fluctuating point charge model (FQ) and the atom–atom charge transfer model (AACT). We have tested the transferability of FQ and AACT parameters, fitted to the polarizability of small size alkanes and polyenes, to large size homologues. We show that the FQ scheme is not adequate for the n-alkanes as it strongly overestimates the polarizability tensor components as the number of carbon atoms increases. The FQ approach has been found more predictive for highly conjugated systems like polyenes, although still unsatisfactory. The AACT parameters tuned on ethane are instead perfectly transferable to alkanes of any length and conformation. The AACT scheme satisfactorily reproduces the polarization response also for highly conjugated systems.

Calculation of optical spectra in liquid methanol using molecular dynamics and the chemical potential equalization method

We apply the chemical potential equalization (CPE) method to the calculation of the optical spectra in liquid methanol at 298 K and normal pressure. The configurations of the liquid are obtained by conventional molecular dynamics (MD) using a completely flexible all-atoms model. The infrared and Raman spectra are computed a posteriori using a CPE parametrization of methanol calibrated to reproduce the electronic properties of the isolated molecule evaluated with accurate ab initio calculations. The MD/CPE method reproduces correctly the optical spectra in the region of the intermolecular motions. The spectra are discussed and interpreted on the basis of hydrogen bonding structure and dynamics.

1,3-Dipolar Cycloaddition Reactions: A DFT and HSAB Principle Theoretical Model

The hard and soft acids and bases principle is used together with the condensed fukui function to analyze the regioselectivity and reactivity of two model 1,3-dipolar cycloaddition reactions. Results obtained for benzonitrile oxide with vinyl p-nitrobenzoate or 1-acetyl vinyl p-nitrobenzoate illustrate the value of these concepts to describe their inherent reactivity. The calculations of the interaction energy by density functional theory using a perturbative, orbital independent method suggest the specific direction of the electronic process at each of the reaction sites. The electrophilic nature of the 1,3-dipole and the nucleophilic nature of the two dipolarophiles was determined by this model. The partitioning of the interaction energy in a term resulting from the chemical potential equalization principle at constant external potential and a term resulting from the maximum hardness principle at constant chemical potential show that the former term, arising from the charge-transfer process, contributes...

Complex Multiphase Equilibrium Calculations by Direct Minimization of Gibbs Free Energy by Use of Simulated Annealing

Summary The computational problems in reservoir fluid systems are mainly in the critical region and in liquid-liquid (LL), vapor-liquid-liquid (VLL), and higher-phase equilibria. The conventional methods to perform phase-equilibrium calculations with the equality of chemical potentials cannot guarantee a correct solution. In this study, we propose a simple method to calculate the equilibrium state by direct minimization of the Gibbs free energy of the system at constant temperature and pressure. We use the simulated annealing (SA) algorithm to perform the global minimization. Estimates of key parameters of the SA algorithm are also made for phase-behavior calculations. Several examples, including (1) VL equilibria in the critical region, (2) VLL equilibria for reservoir fluid systems, (3) VLL equilibria for an H2S-containing mixture, and (4) VL-multisolid equilibria for reservoir fluids, show the reliability of the method.

Chemical Potential Equalization Principle: Direct Approach from Density Functional Theory

In the framework of the density functional theory (DFT) we develop an approximation in which the energy of a molecule is expressed as a functional of perturbations of the atomic electron densities. The result depends on atomic densities, atomic chemical potentials, and hardness kernels that can be found from the solutions of the appropriate atomic DFT problem. A generalized formulation of the chemical potential (electronegativity) equalization principle is suggested. We show how the energy functional can be transformed into a function of the net charges on atoms and discuss the relationship between our approach and the earlier introduced chemical potential (electronegativity) equalization schemes. We present examples where by approximating density perturbations with the squares of Slater orbitals, we obtain values for the net charges that are in reasonable agreement with experiment. This approach can be used for predictions of the transferred charges in the molecules of any size, and its accuracy can be continuously improved by the use of more accurate approximations to the density perturbations.

Influence of adsorption on thin film thermodynamics.

The thermodynamics of a system composed of a substrate, a deposit, and an adsorbed layer is considered with a lattice model in the framework of Gibbs ensemble statistics. Expressions for the thermodynamic functions (free energy, chemical potential, etc.) are derived. The thermodynamic condition for equilibrium in such a multicomponent multiphase system (equality of chemical potentials of each component in all phases), combined with the requirement of minimal free energy, leads to a criterion for stability of the two-dimensional (2D) phase of the deposit. It is shown that an adsorbate could invert the relative thermodynamic stability of both possible deposit phases. It is found also that the adsorbate drastically influences the chemical potential of the 2D phase, and on whatever substrate it becomes practically equal to the chemical potential of the bulk phase at high adsorbate coverages. The influence of the foreign substrate on the layerwise separation in the adlayer is discussed, along with some peculiarities that arise, by defining surface and interfacial free energies of the thin films.

A chemical potential equalization method for molecular simulations

A formulation of the chemical potential (electronegativity) equalization principle is presented from the perspective of density-functional theory. The resulting equations provide a linear-response framework for describing the redistribution of electrons upon perturbation by an applied field. The method has two main advantages over existing electronegativity equalization and charge equilibration methods that allow extension to accurate molecular dynamics simulations. Firstly, the expansion of the energy is taken about the molecular ground state instead of the neutral atom ground states; hence, in the absence of an external field, the molecular charge distribution can be represented by static point charges and dipoles obtained from fitting to high-level ab initio calculations without modification. Secondly, in the presence of applied fields or interactions with other molecules, the density response can be modeled accurately using basis functions. Inclusion of basis functions with dipolar or higher order multipolar character allows molecules or chemical groups to have correct local anisotropic polarizabilities. A modified semiempirical form of the hardness matrix has been introduced that can be evaluated efficiently using Gaussians, and requires only one parameter per basis function. Applications at two basis-set levels demonstrate the method can accurately reproduce induced dipole moments and estimated chemical potentials obtained from density-functional calculations for a variety of molecules. Inclusion of basis functions beyond the conventional spherical-atom type is essential in some instances. The present formulation provides the foundation for a promising semi-empirical model for polarization and charge transfer in molecular simulations.

Stoichiometry of III–V compounds

Abstract The effects of stoichiometry on various features of III-V compounds are investigated. Application of the optimum vapour pressure of group V elements is shown to minimize the deviation from stoichiometric composition. The temperature dependence of the optimum vapour pressure is also obtained from both annealing and liquid phase epitaxial growth experiments. Vapour pressure technology is successfully applied to bulk crystal growth. In view of the defect formation mechanism, the role of the stable interstitial As atoms (IAs) in GaAs is emphasized. The mechanism of stoichiometry control is discussed on the basis of the equality of chemical potentials and the change in saturating solubility in the liquidus phase as a function of the vapour pressure.