The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

An approximate expression for the Pauli kinetic energy functional T_p is advanced in terms of the Liu‐Parr expansion [S. Liu, R.G. Parr, Phys. Rev. A 1997 , 55, 1792] which involves a power series of the one‐electron density. We use this explicit functional for T_p to compute the value of the noninteracting kinetic energy functional T_s of 34 atoms, from Li to Kr (and their positive and negative monoions). In particular, we examine the effect that a shell‐by‐shell mean‐square optimization of the expansion coefficients has on the kinetic energy values and explore the effect that the size of the expansion, given by the parameter n, has on the accuracy of the approximation. The results yield a mean absolute percent error for 34 neutral atoms of 0.15, 0.08, 0.04, 0.03, and 0.01 for expansions with n = 3, 4, 5, 6, and 7, respectively (where ). We show that these results, which are the most accurate ones obtained to date for the representation of the noninteracting kinetic energy functional, stem from the imposition of shell‐inducing traits. We also compare these Liu‐Parr functionals with the exact but nonexplicit functional generated in the local‐scaling transformation version of DFT.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

libKEDF: An accelerated library of kinetic energy density functionals

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital‐free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.     

Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

A simple approximation for the Pauli potential yielding self‐consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg–Kohn variational procedure yields self‐consistent electron densities exhibiting proper atomic shell structure. © 2015 Wiley Periodicals, Inc.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Constraint-based analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as $r\to \infty$. This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.     

On the single-electron local kinetic energy

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A solvation‐free‐energy functional: A reference‐modified density functional formulation

The three‐dimensional reference interaction site model (3D‐RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation‐free‐energy (SFE) for large solute molecules in water. To improve the free‐energy density functional for the SFE of solute molecules, we propose a reference‐modified density functional theory (RMDFT) that is a general theoretical approach to construct the free‐energy density functional systematically. In the RMDFT formulation, hard‐sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction‐site‐model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side‐chain analogues as well as for 504 small organic molecules. © 2015 Wiley Periodicals, Inc.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based on the bifunctional formalism that treats the potential and the electron density as two separate variables, and provides access to the Kohn–Sham Pauli kinetic energy for an appropriately chosen Pauli potential. In the present ansatz, the molecular Pauli potential is approximated by the sum of the bare atomic fragment approach, and a so-called deformation potential that takes the interaction between the atoms into account. It is shown that this model can reproduce the bond-length contraction due to multiple bonding within the list of second-row homonuclear dimers. The present model only relies on the electron densities of the participating atoms, which themselves are represented by a simple monopole expansion. Thus, the bond-length contraction can be rationalized without referring to the angular quantum numbers of the participating atoms.     

Quantum‐based models of charge‐dependent potential energy surfaces: Three‐state models

Quantum‐based models of how potential energies depend on charge are developed from a three‐state model, at the level of neglecting state‐to‐state overlap. The energy as a function of charge is defined as proposed previously (Valone and Atlas, J Chem Phys 2004, 120, 7262). With this definition, addition of a third state smooths the derivatives of the energy model with respect to charge at integer values of charge that are in the interior of the allowed charge range. These derivatives are related to the chemical potential. At the dissociation limit, this model converges to established limits. Another dependence is proposed that uses two different charges simultaneously. The concepts are illustrated, with calculations on an OH molecule. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical studies on the formation mechanism and explosive performance of nitro‐substituted 1,3,5‐triazines

To develop new highly energetic materials, we have considered the design of molecules with high nitrogen content. Possible candidates include 1,3,5‐triazine derivatives. In this work, we studied potential synthetic routes for melamine using the MP2/6‐31+G(d,p)//B3LYP/6‐31G(d) level of theory. The mechanisms studied here are stepwise mechanism beginning with the dimerization of cyanamide and one‐step termolecular mechanism. The same type of mechanism is also applied to nitro‐substituted 1,3,5‐triazines. Values for the heat of formation in the solid phase were predicted from density functional theory calculations. Densities were estimated from a regression equation obtained by molecular surface electrostatic potentials. The Cheetah program was used to study the explosive performance of these compounds. In this study, we found that the explosive properties of 2‐amino‐4, 6‐dinitro‐1, 3,5‐triazine (ADNTA), and 2,4,6‐trinitro‐1,3,5‐triazine (TNTA) are similar to those of RDX and HMX, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006