Exact and approximate forms of the kinetic energy functional<Emphasis Type="Italic"> T</Emphasis><Subscript>s</Subscript>[ρ] for molecules obtained via local-scaling transformations

By means of a constructive procedure based on local-scaling transformations, we have obtained the following exact form for the noninteractive kinetic energy functional of general molecular systems: where (r) is the local-scaling transformation function, T _W[] is the von Weiszäcker term and ^l _N (r _l ) and ^l _N (r _l ) are the radial and angular enhancement factors, respectively, within an atomic domain _I. The terms ^C _N (r _l ) and ^C _N (r _l ) (where C stands for complement of I) contain all contributions to the radial and angular enhancement factors within _I coming from the tails of functions centered on nuclei outside _I. Also, in the context of an atoms-in-a-molecule approach, we discuss the construction of approximations to the kinetic energy enhancement factors appearing in the previous expression for T _s[]. Acknowledgement.The authors gratefully acknowledge support of this work by FONACIT of Venezuela through Group Project No. G-97000741.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

A finite B-spline basis set for accurate diatomic molecule calculations

A finite basis set particularly adapted for solving the Hartree-Fock equation for diatomic molecules in prolate spheroidal coordinates has been constructed. These basis functions have been devised as products of B-splines times associated Legendre polynomials. Due to the large number of B-splines, the resulting set of eigenfunctions is amply distributed over excited states. This gives the possibility of using these basis sets to calculate sums over excited states, appearing in various orders of perturbation theory. As an illustration, the second-order corrections to the ground-state energy of some atoms and diatomic molecules with closed electron shells have been calculated.     

The Standard Model in strong fields: electroweak radiative corrections for highly charged ions

Electroweak radiative corrections to the matrix element are calculated for highly charged hydrogen like ions. The operator represents the parity nonconserving relativistic effective atomic Hamiltonian at the tree level. The deviation of these calculations from the calculations valid for the neutral atoms demonstrates the effect of the strong field. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Elucidating the role of non-radiative processes in charge transfer of core–shell Si–SiO2 nanoparticles

Crystalline silicon is the most commonly used material in photovoltaics but has limitations due to its high cost and non-tunable band gap. A new approach of using inexpensive, non-toxic materials with layers that have different band gaps which absorb a wide range of the solar spectrum has the potential to dramatically increase the efficiencies and lower the costs. Core–shell Si–SiO₂ nanoparticles are ideally suited for the photovoltaic application and have been synthesised by different groups in an array of sizes allowing for absorption in a wide spectral range. A theoretical investigation of fundamental charge transfer processes in these systems can potentially lead to improved devices. Calculations on a model core–shell interface with the formula Si₂₆₄O₁₆₀ which features a silicon layer sandwiched between two SiO₂ layers were performed using the Vienna ab initio software package. The Perdew–Burke–Ernzerhof functional in the basis of plane waves was used along with pseudopotentials to simulate electronic structure. The nuclear motion was considered using ab initio molecular dynamics. The density of states, absorption spectrum, partial charge densities, and radiative recombination lifetimes have been calculated. This interface shows quantum confinement behaviour similar to a particle in a box. The role of non-radiative recombination was also determined by relaxation dynamics.     

Padé approximation for the polynomial representation of the correlation energy density functional

Polynomials in the one-third power of the density were recently proposed to represent approximately the correlation energy density functional [S. Liu and R.G. Parr, Phys. Rev. A 53 (1996) 2211]. Studied in the present work is a Padé-approximant in that same variable which overcomes weaknesses in the polynomial form. Numerical results for atoms and molecules show that Padé forms fairly reproduce the experimental values, and are comparable in accuracy with other commonly used local functionals for the correlation energy.     

Parity Nonconserving (PNC) Electroweak Radiative Corrections for Highly Charged Ions (HCI)

We derive the electroweak radiative corrections to the basic PNC atomic transition amplitude for highly charged hydrogenlike ions. In the case of highly charged ions (HCI) effects of strong fields are reflected by the momentum transfer q ² involved. It is of the order q ²≈m _e ² inHCI, while q ²≈0 inneutral atoms. This may open the possibility to search for “new physics” beyond the Standard Model and to test the Standard Model in experiments with HCI. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of Exact Analytic Total Energy Functional for Hooke’s Atom to He, Li+ and Be++: An Examination of the Universality of the Energy Functional in DFT

We employ the recently generated energy density functional for Hooke’s atom [Ludeña EV et al (2004) Intern J Quantum Chem 99:297], to which we introduce a simplification for the kinetic energy term, to evaluate the total energy of the helium atom and of the two-electron ions Li⁺ and Be⁺⁺. Using accurate representations for the one-particle densities of these systems we show that the energy density functional for Hooke’s atom leads, in these cases, to energy values that are below the exact ones. We discuss the implication of this finding with respect to the existence of a universal energy functional in DFT.