A chemical potential equalization method for molecular simulations

The strict Wigner-Witmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, μ, as the negative of the ground-state electronegativity, χ(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, μ(op), the relative deviations from CPE fall between -31% ≤ δμ(op) ≤ +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting μ(op) (i) by Mulliken's valence-state electronegativity, χ(M), for atoms and (ii) its new generalization, the valence-pair-affinity, α(VP), for diatomic molecules. Mulliken's χ(M) is equalized into the α(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using μ(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.

The decoupled (normal) representation of the electronegativity (chemical potential) equalization equations, in which the hardness tensor {ηij}={∂μi/∂Nj} becomes diagonal, is examined in the atoms‐in‐a‐molecule (AIM) approximation; μi=∂E/∂Ni is the chemical potential of the i‐th AIM, Ni is its electron population, and E is the system energy. All relevant chemical potential, hardness, softness, and Fukui function quantities corresponding to the normal electron redistribution channels, Qy, are discussed and expressed in terms of the canonical AIM parameters. The normal chemical potentials, μγ=∂E/∂Qγ, provide a natural classification of the normal modes into three groups: (a) acceptor normal modes (μa < 0, positive mode Fukui function, hardness, and softness), (b) donor normal modes (μd > 0, negative mode Fukui function, hardness, and softness), and (c) polarization normal modes (μp=0, zero mode Fukui function, hardness, and softness). The implications of the normal mode analysis for the theory of chemical reactivity are briefly summarized.

In this report, we have attempted to explore whether the hardness equalization principle can be conceived analogous to the well‐established electronegativity equalization principle. We have relied upon the fact that the hardness, like the electronegativity, is a qualitative property, and there is commonality in the basic philosophy of the origin and the operational significance of these two fundamental descriptors—the electronegativity and the hardness of atoms in physics and chemistry. Starting from the empirical radial dependent formula of computing the hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that hardness equalization principle is operative and justifiably valid. For a validity test, we have applied the suggested ansatz to compute the hardness of as many as four sets of compounds with widely divergent physical and chemical nature. As hardness is not an experimentally measurable property, there is no benchmark to perform any validity test of our computed data. We have, therefore, computed the hardness data of these four different sets of the compound invoking the approximate and operational formula of Parr and Pearson, (I − A)/2, to evaluate hardness values and to compute I and A, we have invoked Koopmans' theorem and an ab initio quantum chemical method. We have observed that there is a close correlation between the four sets of hardness data computed through the semi‐empirical ansatz of this work and the quantum mechanical method. Thus, it appears that the ansatz of computing molecular hardness derived on the basis of the hardness equalization principle is efficacious in computing molecular hardness. The detailed comparative study suggests that the paradigm of the hardness equalization principle may be another law of nature like the established electronegativity equalization principle. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The Xα method with a self-consistent parameter α has been used to calculate the electronegativity of several diatomic molecules. The electronegativities have been determined on the principle of electronegativity equalization using the results of atomic calculations.

Surface engineered phosphorene using boron and arsenic doping/Co-doping for Co-optimizing the adsorption stability, transduction, and recovery of CO, NO, and SO gases – A density functional theory perspective

The precision of several methods for computing the chemical potential by molecular simulation is investigated. The study does not apply molecular simulation to the analysis but instead works with models of the simulation process. These models enable the variance of the chemical potential to be computed accurately and very quickly and thereby permits the methods (freeenergy perturbation, expanded ensembles, thermodynamic integration, and histogram-distribution methods) to be optimized and compared over a range of densities. The study focuses exclusively on the hard-sphere model. This model is simple and well characterized; yet it exhibits the essential features that make the chemical potential calculation difficult; arguments are presented to support the broader applicability of the study. The severe asymmetry of particle insertion against particle deletion is highlighted, and it is shown that any staged free-energy perturbation method with a 'deletion' component is highly prone to systematic error. More generally this implies that such methods should always be staged in the direction of decreasing entropy. Other findings show that uniform sampling is not optimal for umbrellasampling and expanded-ensemble applications, although it remains a good rule of thumb for tuning these approaches. Among the techniques we study, optimally staged insertion and the distribution–histogram methods are the most efficient and precise. The latter is effective only when used in an interpolative fashion, and we identify it as the most likely route to further progress in the field.

Objective: It is known that the electronegativities of functional groups can be significantly to used predict the reaction mechanisms and to explain inductive effects of chemical compounds. Method: Bratsch equation is one of the most important equations used to calculate the electronegativities of functional groups. Conclusion: In the present study, some important comments and contributions related to Bratsch's group electronegativity equation are presented. In addition, it is proposed that absolute electronegativity should be considered in comparison of inductive effects of functional groups. Keywords: Bratsch equation, chemical hardness, conceptual density functional theory, electronegativity, group electronegativity, sanderson's electronegativity equalization principle.

On the basis of the principle of electronegativity equalization and density-functional theory, an atom−bond electronegativity equalization method has been developed for the calculation of the charge distribution in large molecules that are connectivity and geometry dependent. The effective electronegativities of an atom and a bond in a molecule are derived and given by equations that contain respective electronegativities, hardness terms, and contributions that come from other atomic and bond charges. The parameters A, B, C, and D are the valence-state electronegativity and the valence-state hardnesses. They are obtained by calibrating through calculations of more than 100 model molecules and are transferable and consistently usable. The atom−bond electronegativity equalization method is tested through calculation of the charge distributions in several large organic molecules. It has been shown that there is a very good agreement between the results obtained by the atom−bond electronegativity equalization method and those obtained by the corresponding ab initio quantum chemical calculations.

In analogy with Sanderson's electronegativity equalization principle, it is possible to postulate a principle of spin potential equalization in the E[N(alpha), N(beta)] representation of the spin polarized density functional theory, where N(alpha) and N(beta) refer to the number of electrons with spins alpha and beta, respectively. The principle provides simple expressions to evaluate the energy changes DeltaE between two interacting molecules, A and B, together with the electron transfer, DeltaN(alpha) and DeltaN(beta). The model is illustrated for a series of addition reactions of electrophilic, nucleophilic, and ambiphilic carbenes to alkenes in their singlet and triplet multiplicities. The results are in a consistent qualitative agreement with the experimental reactivity established for these systems.

Salt solubility is generally determined under isotropic stress conditions. Yet, in the context of salt weathering of porous media, mechanical constraints on the in-pore growth of salt crystals are likely to be orientation-dependent, resulting in an anisotropic stress state on the crystal. In this paper, we determine by molecular simulation the solubility of NaCl in water when the crystal is subjected to anisotropic stress. Such anisotropy causes the chemical potential of the crystal to be orientation-dependent, and proper thermodynamic formulation requires describing the chemical potential as a tensor. The solute and crystal chemical potentials are computed from free energy calculations using Hamiltonian thermodynamic integration, and the usual condition of solubility is reformulated to account for the tensorial nature of the crystal chemical potential. We investigate in detail how the uniaxial compression of the crystal affects its solubility. The molecular simulation results led to revisiting the Correns law under anisotropic stress. Regarding the solute, the non-ideal behavior of the liquid phase is captured using Pitzer's ion interaction approach up to high concentrations of interest for in-pore crystallization and beyond the concentrations addressed in the existing literature. Regarding NaCl crystals, the validity of the generalized Gibbs-Duhem equation for a tensorial chemical potential is carefully verified, and it is found that crystallization progresses almost orthogonally to the crystal surface even under high shear stresses. Comparing uniaxial and isotropic compression highlights the major differences in solubility caused by stress anisotropy, and the revisited Correns law offers an appropriate framework to capture this phenomenon.

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.

Ab initio calculations were carried out to study the geometry, solvation free energy, dipole moment, molecular electrostatic potential (MESP), Mulliken and Natural charge distribution, polarizability, hyperpolarizability, Natural Bond Orbital (NBO) energetic and different molecular properties like global reactivity descriptors (chemical hardness, softness, chemical potential, electronegativity, electrophilicity index) of 2-methylimidazole. B3LYP/6-31G(d,p) level of theory was used to optimize the structure both in the gas phase and in solution. The solvation free energy, dipole moment and molecular properties were calculated by applying the Solvation Model on Density (SMD) in four solvent systems, namely water, dimethylsulfoxide (DMSO), n-octanol and chloroform. The computed bond distances, bond angles and dihedral angles of 2-methylimidazole agreed reasonably well with the experimental data except for C(2)-N(1), C(4)-C(5) and N(1)-H(7) bond lengths and N(1)-C(5)-C(4) bond angle. The solvation free energy, dipole moment, polarizability, first order hyperpolarizability, chemical potential, electronegativity and electrophilicity index of 2-methylimidazole increased on going from non-polar to polar solvents. Chemical hardness also increased with increasing polarity of the solvent and the opposite relation was found in the case of softness. These results provide better understanding of the stability and reactivity of 2-methylimidazole in different solvent systems.

The NpT + test particle method for the calculation of vapour-liquid phase equilibria by molecular simulation is extended to binary mixtures. The independent thermodynamic variables are the temperature T and the liquid concentration x. On the liquid side, one NpT simulation is performed at a prescribed pressure which determines the chemical potentials and their derivatives with respect to the pressure, i.e., the partial molar volumes. On the vapour side, two NpT simulations are performed at two different concentrations and at a prescribed pressure yielding again the chemical potentials and their derivatives with respect to the pressure. Using first-order Taylor expansions for the chemical potentials, the vapour-liquid phase equilibria are obtained. As an example, the vapour-liquid phase equilibria for the mixture argon + methane are predicted at four temperatures and compared with experimental results. For that purpose, an optimized redetermination of the molecular parameters was made using only excess volumes and enthalpies for the unlike interaction.

The paper aims at a comparison of techniques based on the kinetic Monte Carlo (kMC) and the conventional Metropolis Monte Carlo (MC) methods as applied to the hard-sphere (HS) fluid and solid. In the case of the kMC, an alternative representation of the chemical potential is explored [E. A. Ustinov and D. D. Do, J. Colloid Interface Sci. 366, 216 (2012)], which does not require any external procedure like the Widom test particle insertion method. A direct evaluation of the chemical potential of the fluid and solid without thermodynamic integration is achieved by molecular simulation in an elongated box with an external potential imposed on the system in order to reduce the particle density in the vicinity of the box ends. The existence of rarefied zones allows one to determine the chemical potential of the crystalline phase and substantially increases its accuracy for the disordered dense phase in the central zone of the simulation box. This method is applicable to both the Metropolis MC and the kMC, but in the latter case, the chemical potential is determined with higher accuracy at the same conditions and the number of MC steps. Thermodynamic functions of the disordered fluid and crystalline face-centered cubic (FCC) phase for the hard-sphere system have been evaluated with the kinetic MC and the standard MC coupled with the Widom procedure over a wide range of density. The melting transition parameters have been determined by the point of intersection of the pressure-chemical potential curves for the disordered HS fluid and FCC crystal using the Gibbs-Duhem equation as a constraint. A detailed thermodynamic analysis of the hard-sphere fluid has provided a rigorous verification of the approach, which can be extended to more complex systems.

A 6M digital twin for modeling and simulation in subsurface reservoirs