About the difference between density functionals defined by energy criterion and density functionals defined by density criterion: Exchange functionals

The difference between density functionals defined by energy criterion and density functionals defined by density criterion is studied for the exchange functional. It is shown that Slater potentials are exact exchange potentials in the sense that they yield the Hartree–Fock electron density if all operators are given by local expressions. © 2016 Wiley Periodicals, Inc.     

密度泛函理论下的电负性均衡及应用

以密度泛函理论为框架,综述电负性和电负性均衡理论的发展及其在探讨各种分子性质时的应用。     

Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C₆H₆ are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.     

Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

An efficient recursive procedure to solve the density profile equation in the classical density functional theory (DFT) using an inverse Broyden method is described. The present iterative procedure is free of calculation of the Jacobian matrix, and its inversion unavoidable for the well-known Newton-Raphson (NR) method and its variants. Numerical calculation indicates that only the approximate solution and iterative matrix of the lower bulk density case are employed as the corresponding initial guesses of the higher bulk density case, the present recursive procedure can converge quickly to the physical solution with an accuracy of epsilon = 10(-14); therefore, the procedure provides an efficient numerical algorithm for the theory in which acquirement of a density profile of high accuracy is a key step. Extensive numerical calculation shows the advantage of the present inverse Broyden method over Broyles' mixing procedure and a modified Powell hybrid algorithm (a variation of the NR method).     

Tracing the Fingerprint of Chemical Bonds within the Electron Densities of Hydrocarbons: A Comparative Analysis of the Optimized and the Promolecule Densities

The equivalence of the molecular graphs emerging from the comparative analysis of the optimized and the promolecule electron densities in two hundred and twenty five unsubstituted hydrocarbons was recently demonstrated [Keyvani et al. Chem. Eur. J. 2016 , 22, 5003]. Thus, the molecular graph of an optimized molecular electron density is not shaped by the formation of the C?H and C?C bonds. In the present study, to trace the fingerprint of the C?H and C?C bonds in the electron densities of the same set of hydrocarbons, the amount of electron density and its Laplacian at the (3, ?1) critical points associated with these bonds are derived from both optimized and promolecule densities, and compared in a newly proposed comparative analysis. The analysis not only conforms to the qualitative picture of the electron density build up between two atoms upon formation of a bond in between, but also quantifies the resulting accumulation of the electron density at the (3, ?1) critical points. The comparative analysis also reveals a unified mode of density accumulation in the case of 2318 studied C?H bonds, but various modes of density accumulation are observed in the case of 1509 studied C?C bonds and they are classified into four groups. The four emerging groups do not always conform to the traditional classification based on the bond orders. Furthermore, four C?C bonds described as exotic bonds in previous studies, for example the inverted C?C bond in 1,1,1‐propellane, are naturally distinguished from the analysis.     

Double-Layer Contribution to the Surface Tension of Halides of Alkali Metals

Effects of interface charging on the surface tension of simple halides of alkali metals are analyzed. The surface tension, computed within the density functional theory in an approximation of the squared density gradient using a parametrized profile and a mean spherical approximation for a local free energy, satisfactorily conforms to experiment.     

Reply to the comment by Vignale et al

In our Reply, we first explain why the proof of Vignale and Rasolt that the basic variables are the density and paramagnetic current density is in error. We then refute the comments by Vignale et al with regard to our work. © 2012 Wiley Periodicals, Inc.     

Kinetic Energy Density of the Two-Electron Hookean Atom in Terms of the Ground-State Electron Density

An explicit expression is derived for the kinetic energy density, including the correlation contribution, in terms of the ground-state electron density for the two-electron Hookean atom. This model atom has the merit that while the electrons are tied to an origin by springs, the Coulomb interaction energy between the two electrons is fully incorporated.     

Comment on “density and physical current density functional theory” by Xiao‐Yin Pan and Viraht Sahni

A recent paper by Xiao‐Yin Pan and Viraht Sahni [Int. J. Quant. Chem. 110, 2833 (2010)] claims that current density functional theory should be based on the physical current density rather than the paramagnetic current density, as in the standard Vignale‐Rasolt formulation. In this comment we show that the claims in the paper by Pan and Sahni are erroneous. © 2012 Wiley Periodicals, Inc.     

Dipole Cauchy moments of the atoms H through Ar

Summary Dipole Cauchy moments of the atoms through Ar are calculated using the hydrodynamic formulation of time-dependent Kohn-Sham theory. The exchange-correlation energy density functional is approximated by the gradient expansion for atoms. Using variational trial functions that contain both linear and nonlinear variational parameters, we are able to reproduce (to three or four significant figures) the static dipole polarizabilities obtained by explicitly solving the relevant differential equations. The resulting dipole Cauchy moments provide a convenient starting point for calculating other properties which result from the linear interaction of atoms with a time varying electric field.     

平行硬壁间荷电硬球流体的密度泛函理论研究

基于经典流体的密度泛函理论并结合改进的基本度量理论, 研究了受限于平行硬壁间的荷电硬球流体的平衡密度分布. 通过对比有、无外电场时分子数密度分布的相应变化情况, 分析了荷电硬球分子间的库仑排斥势能与场致势能间的竞争作用, 研究了电场对于受限荷电硬球流体系统聚集态结构的影响.     

The topology of the Ehrenfest force density revisited. A different perspective based on Slater‐type orbitals

The topology of the Ehrenfest force density was studied with Slater‐type orbitals (STO). At larger distances from the nuclei, STOs generate similar artefacts as noticed before with Gaussian‐type orbitals. The topology of the Ehrenfest force density was found to be mainly homeomorphic with the topology of the electron density. For the first time, reliable integrations of several properties over force density atomic basins were performed successfully. Integration of the electron density of a number of hydrides, fluorides, and chlorides of first row elements over force density basins indicate substantial differences between the partial charges of the atoms as compared with those obtained from electron density basins. Calculations on saturated hydrocarbons confirm that the electronegativity of carbon atoms increases with increasing geometrical strain. Atomic interaction lines are observed to exist in the Ehrenfest force density between the hydrogen atoms of several so‐called “congested” molecules, and also in some inclusion complexes of alkanes with helium. However, interaction lines are lacking in several other controversial cases. © 2015 Wiley Periodicals, Inc.     

Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

The adiabatic‐connection framework has been widely used to explore the properties of the correlation energy in density‐functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two‐particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one‐particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic‐energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density‐functional theory     

用微扰硬球链理论计算超临界CO-2-溶质二元系的密度

溶质在超临界流体中的溶解度与流体的密度密切相关。本文采用微扰硬球链理论对纯CO2及CO2-正戊烷、CO2-正庚烷、CO2-正癸烷体系在不同条件下的密度进行计算,计算值与文献给出的实验值符合很好。     

元素电负性和硬度的密度泛函理论研究

应用密度泛函理论的DFT LDA、DFT LDA/NL和改进的Slater过渡态方法,把元素的电离能和电子亲合能的计算扩展到周期表的103种元素.并用有限差分方法计算了这103种元素的电负性和硬度.计算中考虑了相对论效应.计算结果比以前Robles等用密度泛函理论的XGL和Xα近似的交换相关泛函的计算结果有所改进,更接近实验值.     

纯流体在临界区内外的表面张力研究

An equation of state(EOS)applicable for both the uniform and non-uniform fluids was established by using thedensity-gradient expansion,in which the influence parameter к[p(r),T] was obtained by the use of direct correlationfunction.The density functional theory(DFT)provides a framework under which both the phase equilibria and in-terfacial properties can be investigated within a single set of molecular parameters.The phase equilibria inside thecritical region can be improved by the renormalization group theory(RGT).However,the correction of interracialproperties by DFT and RGT is computationally difficult.In the present work,the density gradient theory(DGT)inwhich к[p(r),T] is treated as a constant is used to combine with the RGT for interfacial properties inside the criticalregion.     

A DFT variational approach to Hooke''s atom based on local-scaling transformations

The local-scaling transformation version of density functional theory, LS-DFT, is employed in order to construct energy functionals for Hooke's atom. The components of the energy are analyzed and the resulting exchange and correlation potentials are compared with the exact ones. In addition, the representation of the exact one-particle density in terms of the various components of the total energy density is discussed.     

Principles Determining the Structure of Transition Metals

For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic electron density. Here, we exploit modern approaches to electron density analysis to first comprehensively describe transition metal electron density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic polyhedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called “octahedral” to “tetrahedral cages” while the face centered cubic structure of the late transition metals is a consequence of anti-bonding interactions that increase octahedral hole kinetic energy.