Four-dimensional density and energy density functional

The relations based on an external one-electron operator V( r ) are examined from two view-points, i.e., from the Hohenberg–Kohn approach and the four-dimensional density concept introduced by Wilson and Frost, and extensively studied by Parr and Politzer. The object being to obtain, with the help of the Hellmann–Feynman theorem, new formulas for the energy of atoms and molecules, and to discuss the construction of the universal energy density functional on the basis of the four-dimensional density.     

Approximately N-representable density functional density matrices

For the first time, we obtain practical density matrices approximately N-representable by correlated-determinant wave functions, which are functionals of the electron density and entirely defined by information obtainable from the X-ray coherent diffraction experiment. © 1994 John Wiley & Sons, Inc.     

CAS-DFT based on odd-electron density and radical density

We here propose new schemes of complete active space-density functional theory (CAS-DFT). It is based on the idea that the previous odd-electron density and radical density are used to express the spin-polarizability of CAS wavefunctions. We have applied these schemes to optimize geometries and to calculate the singlet–triplet energy gaps of several molecules and compare the results with those by the other methods and experiment. It was found that our schemes based on radical density give excellent results although our schemes drastically reduce the computational cost.     

Nonspherical model density matrices for Rung 3.5 density functionals

"Rung 3.5" exchange-correlation functionals for Kohn-Sham density functional theory depend linearly on the nonlocal one-particle density matrix of the noninteracting Kohn-Sham reference system. Rung 3.5 functionals also require a semilocal model for the one-particle density matrix. This work presents new model density matrices for Rung 3.5 functionals. The resulting functionals give reasonable predictions for total energies, molecular thermochemistry and kinetics, odd-electron bonds, and conjugated polymer bandgaps. Global-hybrid-like combinations of semilocal and Rung 3.5 exchange, and empirical density matrix models, also show promise.     

Current density distribution,limiting current density and saturation current density in an ion-exchange membrane electrodialyzer

The current density distribution in a seawater electrodialyzer is approximated by a quadratic equation. The equation is solved using a three-dimensional simultaneous equation, and the current density distribution and the coefficients expressing the current density distribution are calculated. The method for estimating the limiting current density and the saturation current density of an electrodialyzer is established using the current density distribution coefficients. Electrodialytic conditions (current density, solution velocity and electrolyte concentration in desalting cells, the thickness and flow-pass length of a desalting cell, the standard deviation of the solution velocity ratio in desalting cells and the overall osmotic coefficient of a membrane pair) versus the current density distribution coefficients, limiting current density and saturation current density are obtained. Electrodialytic conditions at which current density reaches the limiting current density or saturation current density are determined.     

Approximate density matrices and wigner distribution functions from density,kinetic energy density,and idempotency constraints

The Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree–Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.     

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.     

Chirality and spin density: Ab initio and density functional approaches

The spin distribution in a stable nitroxide biradical that shows ferromagnetic interactions in the solid phase has been studied at three levels of theory: First, at the UHF level; then, including correlation effects in UMP 2 calculations; and finally, the results are compared with the spin density obtained using the local density functional (LDF ) approximation. It is shown that LDF spin densities are closer to UMP 2 than to UHF predictions; the difference between the UHF and the (UMP 2, LDF ) results points to a redistribution of the spin repartition between N and O due to electronic correlation. For planar conformations of the NO group, there is symmetric distribution (D_2d) of the spin density on the adamantane skeleton. For nonplanar nitroxides, the molecule is chiral (C₂), which results in a breakdown of the spin transmission on part of the adamantane cage. © 1993 John Wiley & Sons, Inc.     

Excitation energies from range-separated time-dependent density and density matrix functional theory

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.     

Density bifunctional theory using the mass density and the charge density

Can all the properties of a system composed of particles with masses, m _i , and charges, q _i , be determined from the charge density and the mass density? Subject to a small statistical caveat, this is true, and offers the prospect of an elegant extension of density-functional theory beyond the Born-Oppenheimer approximation.     

Obtaining the two-body density matrix in the density matrix renormalization group method

We present an approach that allows to produce the two-body density matrix during the density matrix renormalization group (DMRG) run without an additional increase in the current disk and memory requirements. The computational cost of producing the two-body density matrix is proportional to O(M3k2+M2k4). The method is based on the assumption that different elements of the two-body density matrix can be calculated during different steps of a sweep. Hence, it is desirable that the wave function at the convergence does not change during a sweep. We discuss the theoretical structure of the wave function ansatz used in DMRG, concluding that during the one-site DMRG procedure, the energy and the wave function are converging monotonically at every step of the sweep. Thus, the one-site algorithm provides an opportunity to obtain the two-body density matrix free from the N-representability problem. We explain the problem of local minima that may be encountered in the DMRG calculations. We discuss theoretically why and when the one- and two-site DMRG procedures may get stuck in a metastable solution, and we list practical solutions helping the minimization to avoid the local minima.     

Role of electron–electron coalescence density in density functional theory

An expression for the evaluation of electron–electron coalescence density as a functional of the density for any electron system is proposed. The formula, clarifies previously advanced upper bounds for this quantity and provides a method to independently estimate the system‐averaged on‐top exchange–correlation hole. The relationship with the on‐top pair density shows that producing the true electron–electron coalescense should be considered as a leading physical requirement for trial wave functions in any energy minimization scheme. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Air microwave-induced plasma: Relation between ion density and atomic oxygen density

Electron temperature and ion density are measured in an air microwave-induced plasma (2450 MHz) by means of a floating double probe. A 'cinetic scheme for ion formation and decay is set up, and a relationship between atomic oxygen and ion densities is obtained. From this relationship an order-of-magnitude of atomic oxygen concentration in the discharge is derived and compared with results obtained by optical actinometry in another work.     

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.     

About pycnometric density measurements

Pycnometric density is at the moment the closest approximation of true density calculated from the molecular weight and crystalline lattice of the product. It is determined by using helium pycnometers that offer the advantage of being easy-to-use and rapid, especially fully automated apparatus. If the accuracy and the reproducibility of the technique are sufficient to reveal minute variations, this data is of interest for characterisation of crystalline structures (polymorphs, pseudopolymorphs, amorphous state), detection of defects, pores or impurities, and possible changes in crystal density during compaction. The aim of this article is to investigate on the confidence that can be expected when measuring density with an AccuPyc 1330 pycnometer. The experiments carried out on glass beads, quartz and mannitol have shown that operating parameters can affect the accuracy of pycnometric density to the nearest 0.01 g cm(-3). If measurements are performed in optimal conditions, 0.02% accuracy can be obtained, otherwise it can fail to 0.1% or less, depending on the material and the variations in the standard volume.     

NIST transmission density instrument

The Optical Technology Division of NIST has developed a new instrument for measuring ISO standard visual diffuse transmission densities using the diffuse influx mode. This instrument is used to calibrate both X-ray and photographic film step tablet Standard Reference Materials. The design, characterization, and operation of the instrument are detailed. The instrument was fully characterized both to verify compliance with the applicable international standards and to determine the combined uncertainty in transmission density associated with the calibrations. Results from comparisons with other laboratories are also presented.     

Low density solid ozone

We report a very low density ( approximately 0.5 g/cm(3)) structure of solid ozone. It is produced by irradiation of solid oxygen with 100 keV protons at 20 K followed by heating to sublime unconverted oxygen. Upon heating to 47 K the porous ozone compacts to a density of approximately 1.6 g/cm(3) and crystallizes. We use a detailed analysis of the main infrared absorption band of the porous ozone to interpret previous research, where solid oxygen was irradiated by UV light and keV electrons.     

Linear scaling density fitting

Two modifications of the resolution of the identity (RI)/density fitting (DF) approximations are presented. First, we apply linear scaling and J-engine techniques to speed up traditional DF. Second, we develop an algorithm that produces local, accurate fits with effort that scales linearly with system size. The fits produced are continuous, differentiable, well-defined, and do not require preset fitting domains. This metric-independent technique for producing a priori local fits is shown to be accurate and robust even for large systems. Timings are presented for linear scaling RI/DF calculations on large one-, two-, and three-dimensional carbon systems.