Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory.

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.

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.

The chemical hardness concept and its realization within the conceptual density functional theory is approached with innovative perspectives, such as the electronegativity and hardness equalization of atoms in molecules connected with the softness kernel, in order to examine the structure-reactivity equalization ansatz between the electronic sharing index and the charge transfer either in the additive or geometrical mean picture of bonding. On the other hand, the maximum hardness principle presents a relation with the chemical stability of the hardness concept. In light of the inverse relation between hardness and polarizability, the minimum polarizability principle has been proposed. Additionally, this review includes important applications of the chemical hardness concept to solid-state chemistry. The mentioned applications support the validity of the electronic structure principles regarding chemical hardness and polarizability in solid-state chemistry.

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.

The oxygen-evolving complex (OEC) of Photosystem II catalyzes the water-splitting reaction using solar energy. Thus, understanding the reaction mechanism will inspire the design of biomimetic artificial catalysts that convert solar energy to chemical energy. Conceptual Density Functional Theory (CDFT) focuses on understanding the reactivity of molecules and the atomic contribution to the overall nucleophilicity and electrophilicity of the molecule using quantum descriptors. However, this method has not been applied to the OEC before. Here, we use Fukui functions and the dual descriptor to provide quantitative measures of the nucleophilicity and electrophilicity of oxygens in the OEC for different models in different S states. Our results show that the μ-oxo bridges connected to terminal Mn4 are nucleophilic, and those in the cube formed by Mn1, Mn2, and Mn3 are mostly electrophilic. The dual descriptors of the bridging oxygens in the OEC showed a similar reactivity to that of bridging oxygens in Mn model compounds. However, the terminal water W1, which is bound to Mn4, showed very strong reactivity in some of the S3 models. Thus, our calculations support the model that proposes the formation of the O2 molecule through nucleophilic attack by a terminal water.

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.

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.

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

Effect of capillary term parameters on the thermodynamic modeling of methane hydrate formation in porous media

Reliability vs. Efficiency When Solving Multiphase Equilibrium Problems with Hybrid Optimization Codes

Lithium-Sulfur battery is very attractive due to its high energy density of 2500 Wh/kg or 2800 Wh/L. The low cost of Sulfur ($0.02/g) provides a significant driving force to obtain a commercial Li-S battery. But their practical use is still hindered by several issues including capacity fading, short lifespan, and low efficiency. The dissolution of long-chain lithium polysulfides (Li2Sx, 2 < x < 8) (LiPS) into the electrolyte and the shuttling of polysulfides between cathode and anode have been generally considered responsible for the capacity degradation. A variety of methods have been applied to prevent the dissolution of LiPS, most of which focus on physical trapping by using carbon matrix as barrier materials. However, the effect of barrier materials is kinetics; LiPS physically trapped in carbon host will eventually leach into the electrolyte. Also, the nonpolar carbon matrix will facilitate the detachment of LiPS, which is highly polar, from the cathode, resulting in loss of active materials. Thus thermal sequestering of LiPS via chemical binding and a polar cathode surface is desired. Herein, we report a facile approach towards high-performance sulfur-carbon cathodes by stabilizing LiPS on amine-functionalized cathode. Specifically, Polyethylenimine (PEI) is chosen for the reason that it possesses a large amount of amine groups within a molecular. PEI is attached to the cathode by reacting with hydroxyl functionalized carbon nanotubes (Figure 1). The strong affinity of LiPS to PEI-functionalized CNT is verified by DFT calculation, showing high binding energy of 1.23 eV, while it is 0.34eV between LiPS and graphene and 0.83eV between LiPS and PVDF. The interaction is also confirmed by FTIR, XPS, and other characterization techniques. With the merits of CNT such as good conductivity and robust mechanical properties, the nanocomposite of amine-functionalized CNT and sulfur exhibits stable cycling performance with high capacities (Figure 1). Furthermore, the kinetic study of polysulfides dissolution is carefully carried out. The dissolution constant k is determined by the method described in Figure 2. k is obtained for cathodes with various compositions: (1) Li2S4 without PEI; (2) Li2S4 with PEI; (3) Li2S9 without PEI; (4) Li2S9 with PEI. By comparing dissolution constants in each case, the much stronger affinity of PEI with the LiPS can be observed with smaller k. Also, the higher solubility and dissolution rate are found with increasing chain length of LiPS. The equilibrium concentration (ceq) of LiPS in the electrolyte is found, where LiPS has equal chemical potential in the electrolyte and cathode. This guides us in adding LiPS with concentration of ceqto the electrolyte when designing Li-S batteries. In this case, LiPS will not leach into the electrolyte since there is no driving force in the condition of equilibrium. The battery performance will be presented in the talk. In summary, the new method takes advantage of the numerous amine groups in PEI and the strong affinity with LiPS to realize a high performance Li-S battery. The systematical kinetic study also reveals the working mechanism and paves the way to further rational design of Li-S battery. Figure 1

Study of phase-diagram domains

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects.

We extend the framework of conceptual density functional theory (DFT) to include fourth-order energy derivatives. We present the series of quantum reactivity descriptors at this order for the canonical and the grand canonical ensembles. After introducing a direct computational methodology, we investigate and describe the quartic curvature λ and the third-order Fukui function f(3)(r). These higher-order descriptors capture nonlinear aspects of electronic reactivity that go beyond the conventional concepts of chemical potential, hardness, or Fukui functions. The global descriptor λ, obtained via finite-difference approximations of frontier orbital energies, quantifies the curvature of the chemical hardness and offers insight into the electronic (in)stability of molecular systems under charge perturbations. The local descriptor f(3)(r), derived as the third-order response of the electron density, reveals spatially resolved regions of charge-transfer sensitivity. We apply these descriptors to a series of push-pull organic molecules and open-shell systems, demonstrating their ability to highlight differences in internal charge transfer character and electronic delocalization. The results support the use of fourth-order conceptual DFT tools as chemically meaningful indicators of reactivity beyond the harmonic regime.