Kinetic energy density in terms of electron density for closed-shell atoms in a bare Coulomb field

A long-term aim in density functional theory is to obtain the kinetic energy density t(r) in terms of the ground-state electron density ρ(r). Here, t(r) is written explicitly in terms of ρ(r) for an arbitrary number 𝒩 of closed shells in a bare Coulomb field. In the limit as 𝒩→∞, closed results for t(r) follow from the earlier analysis of ρ(r) by Heilmann and Lieb. [Phys. Rev. A 52 , 3628 (1995)]. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 281–283, 1998     

The topology of the Coulomb potential density. A comparison with the electron density,the virial energy density,and the Ehrenfest force density

The topology of the Coulomb potential density has been studied within the context of the theory of Atoms in Molecules and has been compared with the topologies of the electron density, the virial energy density and the Ehrenfest force density. The Coulomb potential density is found to be mainly structurally homeomorphic with the electron density. The Coulomb potential density reproduces the non‐nuclear attractor which is observed experimentally in the molecular graph of the electron density of a Mg dimer, thus, for the first time ever providing an alternative and energetic foundation for the existence of this critical point. © 2017 Wiley Periodicals, Inc.     

Structure of the electron momentum density of atomic systems

The present paper addresses the controversial problem on the nonmonotonic behavior of the spherically-averaged momentum density γ(p) observed previously for some ground-state atoms based on the Roothaan-Hartree-Fock (RHF) wave functions of Clementi and Roetti. Highly accurate RHF wave functions of Koga et al. are used to study the existence of extrema in the momentum density γ(p) of all the neutral atoms from hydrogen to xenon. Three groups of atoms are clearly identified according to the nonmonotonicity parameter μ, whose value is either equal to, larger, or smaller than unity. Additionally, it is found that the function p^?α γ(p) is (i) monotonically decreasing from the origin for α ≥ 0.75, (ii) convex for α ≥ 1.35, and (iii) logarithmically convex for α ≥ 3.64 for all the neutral atoms with nuclear charges Z = 1–54. Finally, these monotonicity properties are applied to derive simple yet general inequalities which involve three momentum moments 〈p ^t≥. These inequalities not only generalize similar inequalities reported so far but also allow us to correlate some fundamental atomic quantities, such as the electron-electron repulsion energy and the peak height of Compton profile, in a simple manner.     

Wavelength-decomposition-based embedded cluster density approximation for systems with nonlocal electron correlation

Local correlation methods rely on the assumption that electron correlation is nearsighted. In this work, we develop a method to alleviate this assumption. This new method is demonstrated by calculating the random phase approximation (RPA) correlation energies in several one-dimensional model systems. In this new method, the first step is to approximately decompose the RPA correlation energy to the nearsighted and farsighted components based on the wavelength decomposition of electron correlation developed by Langreth and Perdew. The short-wavelength (SW) component of the RPA correlation energy is then considered to be nearsighted, and the long-wavelength (LW) component of the RPA correlation energy is considered to be farsighted. The SW RPA correlation energy is calculated using a recently developed local correlation method: the embedded cluster density approximation (ECDA). The LW RPA correlation energy is calculated globally based on the system's Kohn-Sham orbitals. This new method is termed λ-ECDA, where λ indicates the wavelength decomposition. The performance of λ-ECDA is examined on a one-dimensional model system: a H₂₄ chain, in which the RPA correlation energy is highly nonlocal. In this model system, a softened Coulomb interaction is used to describe the electron-electron and electron-ion interactions, and slightly stronger nuclear charges (1.2e ) are assigned to the pseudo-H atoms. Bond stretching energies, RPA correlation potentials, and Kohn-Sham eigenvalues predicted by λ-ECDA are in good agreement with the benchmarks when the clusters are made reasonably large. We find that the LW RPA correlation energy is critical for obtaining accurate prediction of the RPA correlation potential, even though the LW RPA correlation energy contributes to only a few percent of the total RPA correlation energy.     

Pointwise bounds for the electron density and estimates of an expectation value for one-electron systems

Pointwise bounds for wavefunctions of a class of Schrödinger operators for one-electron systems are used to obtain pointwise bounds for the electron density, as well as estimates for the expectation value (r^?1).     

Pair density related to one‐electron information for the ground state of spin‐compensated two‐electron systems

The recent study by Joubert on effects of Coulomb repulsions in a many‐electron system has focused attention on an integral identity involving the pair density. This has motivated the derivation presented here of a vectorial differential form related to this integral result. Our differential identity is then illustrated explicitly by using (i) an exact ground‐state wave function for the so‐called Hookean atom having external potential energy (1/2)kr², with k = 1/4, and (ii) Moshinsky's model in which both the interparticle interaction and the external potential are of harmonic type. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Electron density fitting for the Coulomb problem in relativistic density-functional theory

A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2, Au3+, Au4, Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+.     

New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms

Analytical properties of hydrogen-like atomic orbitals (HAO ) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.     

Coulomb explosion upon electron attachment to a four-coordinate monoanionic metal complex

Electron capture to monoanionic metal complexes in high-energy collisions with sodium vapor is shown to occur with the formation of dianions. In this way, we prepared the small dianions Cr(SCN)42-, Fe(CN)42-, Pt(NO2)22-, and Pt(C2O4)22- in the gas phase. The Cr(SCN)42- dianion Coulomb explodes into Cr(SCN)3- and SCN- with a release of kinetic energy (3.2 +/- 0.4 eV) into translational energy of the fragments. The scheme provides a way to study charge dissociation reactions of molecular dianions that are too short-lived to survive extraction from the ion source.     

On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems

It is shown that, for isolated many‐electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg–Kohn theorem is unsatisfactory since the to‐be‐refuted assumption made about the one‐electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more sophisticated means, and it is shown here that the Kato cusp condition actually leads to a satisfactory proof. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

On the calculation of ab initio quantum molecular similarities for large systems: Fitting the electron density

A set of procedures for rapid calculation of quantum molecular similarities from ab initio wave functions is discussed. In all cases a density fitting is carried out to eliminate the need of calculating costly four-centered integrals. It is proved that this methodology can be applied to large systems to reproduce exact quantum molecular similarity measures at an extremely low computational cost. © 1994 by John Wiley & Sons, Inc.     

Analytic inhomogeneous electron liquid and its density for model spin-compensated two-electron atomic ions with Coulomb confinement: an exact nonrelativistic Hamiltonian

In earlier work, Howard and March (HM) proposed an analytic ground-state electron density ρ( r ) starting from the s-wave model of the He atom. Subsequently Ancarani has constructed by numerical methods a variational approach for this s-wave model with a lower energy than the HM result. This clearly means that the HM ρ( r ) is not the ground-state electron density of the He s-wave model. Therefore, we derive here an exact nonrelativistic Hamiltonian, with strong radial correlation plus Coulomb confinement, for which the HM ρ( r ) is indeed the ground-state electron density.     

A computer program for searching the best model for describing different experimental systems

An algorithm for searching the best polynomial analytical function for describing different experimental systems is presented. It is based

1. (1)on the generation of all possible analytical functions of a given order, with a given number of terms and with a given number of independent variables, and

2. (2)on the calculation of the parameters of all selected functions using the linear regression method.

To show the ability of the program two different examples are given:

1. (1) searching the best univariate polynomial model, and

2. (2) modelling of the stability of a two-component mixture as a function of three factors.

Modeling the electron density kernels

Existing approximation to the softness kernel, successfully explored in earlier work, has been extended; the normal Gauss distribution function has been used instead of the Dirac delta. The softness kernel becomes continuous functions in space and may be used to calculate the linear response function of the electron density. Three-dimensional visualization of the softness kernel and the linear response function are presented for a nitrogen atom as a working example. By using a single parameter of the spatial Gauss distribution, the novel softness kernel has been adjusted to be consistent with the standard form of the hardness kernel, representing the leading fraction of the electronic interactions in the system.     

Existence of time-dependent density-functional theory for open electronic systems: time-dependent holographic electron density theorem

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.