Attainable accuracy in the numerical integration of the Thomas—Fermi kinetic-energy functional using a modeled electron density

In the Hohenberg and Kohn formation of the density-functional theory of an electronic system, the basic variable is the electron (number) density. This quantity, however, is not known. For this reason, in an actual calculation, one has to resort to an approximate electron (number) density in order to evaluate the integral occurring in the Hohenberg and Kohn density functional framework. This poses the question: what is the accuracy beyond which one cannot penetrate in the numerical evaluation of the integrals? The present work attempts to provide an answer to this question by considering the Ne atom as an example and using the simplest energy-density functional, namely the Thomas-Fermi functional. In this functional, composed of three terms, there is only one term, the kinetic-energy functional, that has to be evaluated numerically. The evaluation of this integral is done by modeling the electron (number) density of the Ne atom and resorting to Simpson's compound rule. Following this, an error bound for the integral is established. This is the central result of this paper.     

Broadening of the derivative discontinuity in density functional theory

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter Γ/U, where Γ is the level broadening due to contacting and U is a measure of the charging energy. Our analysis suggests that Kondoesque fluctuations have a tendency to increase the DD-broadening in our model by a factor of two.     

Intracule densities in the strong-interaction limit of density functional theory

The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance r(12) (intracule density) when the electron-electron interaction is multiplied by a real parameter lambda varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the lambda --> infinity limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.     

Symbolic algebra in functional derivative potential calculations

This article gives the details of the methodology used in constructing a symbolic algebra program designed for evaluating potentials as the functional derivatives of so-called functional generators in molecular density-functional theory. The derived formulae are used in illustrative examples involving partial functional integration, the comparison of the exchange potential arising from different mathematical representations of the electron density for a given functional generator, and the evaluation and comparison of the potential for different functional generators with a given density. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 300–307, 1998     

Functional derivative of the kinetic energy functional for spherically symmetric systems

Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory.     

Advancing beyond the atom-centered model in additive and nonadditive molecular mechanics

A computational approach to the inclusion of off-center charges in both additive and nonadditive molecular mechanics calculations is presented. The additional sites in the molecular skeleton are placed in the approximate locations of the chemically intuitive electron lone pair, and are treated as formal particles throughout the calculation. The increase in the number of charge sites results in overall improvement in the energy associated with the angular dependence of hydrogen bonds and improved statistical accuracy of the electrostatic potential derived charges. The addition of lone pairs also results in improved accuracy in relative solvation free energy calculation for the pyridine to benzene and methanol to methane mutations. Because the number of atoms that require lone pairs is small, the extra accuracy can be achieved with little computational overhead. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1632–1646, 1997     

Exact exchange-only density functional theory by means of local scaling transformations

The density-constrained variation of the kinetic energy of a non-interacting system carried out within the framework of local-scaling transformations is employed in the present work for the purpose of determining exchange-only Kohri Sham orbitals for the beryllium atom as well as the Kohn-Sham exchange-only correlation potential. The starting basis functions are those of Clementi-Roetti and Raffenetti-types. We have also performed an optimization via a densitydriven method. The resulting exchange-only potentials for the examples studied are almost indistinguishable from the Talman-Shadwick potential for the beryllium atom.     

A systematic formulation of the virial expansion for nonadditive interaction potentials

A new formulation of the virial expansion for a classical gas is derived without the restriction to pairwise-additive interaction potentials. Explicit expressions up to the eighth virial coefficient, suitable for numerical evaluation, are given in the form of integrals over sums of cluster diagrams. Compared with previous approaches, the number of cluster diagrams increases more moderately with increasing order of the virial coefficient. Thus, the new formulation should be particularly useful for the computation of high-order virial coefficients.     

Photophysical and density functional studies of the interaction of a flavone derivative with the halides

The synthesis, photophysical behavior, and anion-sensing ability of a fluorescent molecular system, N-(3-methoxy-4-oxo-2-phenyl-4H-chromen-7-yl)-benzamide (1H), designed and developed with a view to sensing fluoride ions, are reported. NMR and density functional studies on the system have been carried out to determine the nature of the interaction between 1H and X- (X = halogen atom) responsible for fluoride-induced dramatic changes in the absorption and emission properties of 1H. The color change of 1H, which can be observed by the naked eye, is found specific to fluoride ion; it is unaffected by the presence of a large excess of Cl-, Br-, and I-, thus rendering 1H as a selective fluoride ion sensor in micromolar concentration in the visible region. The changes in the fluorescence behavior of 1H, specifically, the formation of an additional long-wavelength emission band in the presence of fluoride ion, allow ratiometric fluorescence signaling of the fluoride ion as well. The results suggest that abstraction of the acidic proton of 1H by the F- leading to the formation of 1- is responsible for the spectral changes that allow signaling of the F-. Density functional calculations of the optimized geometrical parameters and charge densities of the 1H...halide complexes confirm the proton abstraction mechanism of the signaling of F-. Calculations of the transition energies of the 1H, 1-, and 1H...F- (hydrogen-bonded complex) show that only 1- is responsible for the long-wavelength absorption and emission band observed in the presence of F-.     

Temperature and heat capacity of atomic clusters as estimated in terms of kinetic-energy release of atomic evaporation

The temperature and heat capacity of isolated atomic clusters are studied in terms of an ab initio statistical theory of kinetic energy distribution by atomic evaporation. Two definitions of canonical temperature are examined and numerically compared: One is based on the most probable kinetic energy release (KER), whereas the other is determined with use of the entire distribution of the KER. The mutual relationship and their advantages are discussed.     

ATRP of methyl methacrylate initiated with a bifunctional initiator bearing bromomethyl functional groups: Synthesis of the block and graft copolymers

This article reports the synthesis of the block and graft copolymers using peroxygen‐containing poly(methyl methacrylate) (poly‐MMA) as a macroinitiator that was prepared from the atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) in the presence of bis(4,4′‐bromomethyl benzoyl peroxide) (BBP). The effects of reaction temperatures on the ATRP system were studied in detail. Kinetic studies were carried out to investigate controlled ATRP for BBP/CuBr/bpy initiating system with MMA at 40 °C and free radical polymerization of styrene (S) at 80 °C. The plots of ln ([M_o]/[M_t]) versus reaction time are linear, corresponding to first‐order kinetics. Poly‐MMA initiators were used in the bulk polymerization of S to obtain poly (MMA‐b‐S) block copolymers. Poly‐MMA initiators containing undecomposed peroygen groups were used for the graft copolymerization of polybutadiene (PBd) and natural rubber (RSS‐3) to obtain crosslinked poly (MMA‐g‐PBd) and poly(MMA‐g‐RSS‐3) graft copolymers. Swelling ratio values (q_v) of the graft copolymers in CHCl₃ were calculated. The characterizations of the polymers were achieved by Fourier‐transform infrared spectroscopy (FTIR), ¹H‐nuclear magnetic resonance (¹H NMR), gel‐permeation chromatography (GPC), differential scanning calorimetry (DSC), thermogravimetric analysis, scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), and the fractional precipitation (γ) techniques. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1364–1373, 2010     

Direct enantio- and diastereoselective Mannich reactions of malonate and beta-keto esters with N-Boc and N-Cbz aldimines catalysed by a bifunctional cinchonine derivative

A highly enantioselective Mannich reaction between malonate esters and N-Boc and N-Cbz aldimines, catalysed by a bifunctional cinchonine derivative, has been developed; extension of this methodology to encompass the use of 2-substituted-1,3-dicarbonyl nucleophiles allows the formation of adjacent stereocentres, one of which is quaternary, in high relative and absolute stereocontrol.     

Further insights in the ability of classical nonadditive potentials to model actinide ion–water interactions

Pursuing our efforts on the development of accurate classical models to simulate radionuclides in complex environments (Réal et al., J. Phys. Chem. A 2010, 114, 15913; Trumm et al. J. Chem. Phys. 2012, 136, 044509), this article places a large emphasis on the discussion of the influence of models/parameters uncertainties on the computed structural, dynamical, and temporal properties. Two actinide test cases, trivalent curium and tetravalent thorium, have been studied with three different potential energy functions, which allow us to account for the polarization and charge‐transfer effects occurring in hydrated actinide ion systems. The first type of models considers only an additive energy term for modeling ion/water charge‐transfer effects, whereas the other two treat cooperative charge‐transfer interactions with two different analytical expressions. Model parameters are assigned to reproduce high‐level ab initio data concerning only hydrated ion species in gas phase. For the two types of cooperative charge‐transfer models, we define two sets of parameters allowing or not to cancel out possible errors inherent to the force field used to model water/water interactions at the ion vicinity. We define thus five different models to characterize the solvation of each ion. For both ions, our cooperative charge‐transfer models lead to close results in terms of structure in solution: the coordination number is included within 8 and 9, and the mean ion/water oxygen distances are 2.45 and 2.49 Å, respectively, for Th(IV) and Cm(III). © 2012 Wiley Periodicals, Inc.     

Exact theorems concerning noninteracting kinetic energy density functional in D dimensions and their implications for gradient expansions

The focal point of the present work is the single-particle kinetic energy density tensor in D dimensions. This quantity enters both differential and various integral forms of the virial theorems, which are again set up in D dimensions. Major new results lie in (i) demonstrating that, by one-dimensional quadrature, it is possible to construct the Pauli potential directly from the kinetic energy tensor, without the need for functional differentiation and (ii) generating the gradient expansion for the kinetic energy tensor, in D dimensions. © 1995 John Wiley & Sons, Inc.     

Dynamics of photoprocesses in novel bifunctional salicylideneiminospironaphthoxazines

The dynamics of photochemical processes in a number of novel photobifunctional compounds, whose molecules combine a photochromic spironaphthoxazine fragment with the salicylideneimine moiety containing different substituents, was studied by the flash photolysis technique. Three products of photolysis of these compounds were detected, and the effects of the substituents and the solvent nature (toluene and methanol) on their spectral and kinetic characteristics and quantum yields were studied.