On the connections between the quantum theory of atoms in molecules (QTAIM) and density functional theory (DFT): a letter from Richard F. W. Bader to Lou Massa

A 31-year-old letter from Professor Richard F. W. Bader to Professor Lou Massa outlining the connections between the quantum theory of atoms in molecules (QTAIM) and density functional theory (DFT) especially with regard to the first Hohenberg-Kohn theorem is brought to light. This connection has not often been the topic of such a focused review by Bader and is presented here for the first time. The scientific importance of this letter is, in the opinion of the presenter, as timely today as it was back then in 1986. In Bader’s own opening words: “... that if I sent you a summary of what I think are the important connections between our work and density functional theory, ...”. He then takes us in a grand tour of the foundations of QTAIM culminating into the antecedents of a paper he later published with Professor Pierre Becker, whereby the Hohenberg-Kohn theorem is shown to operate at the level of an atom-in-a-molecule. Bader closes his letter by suggesting to Massa: “Study these two charge distributions – they are proof of the theorem of Hohenberg and Kohn”. By that Bader meant that when the charge distributions of two atoms or groups are identical within a given precision, then the kinetic and total energy contributions of these atoms to the corresponding molecular quantities are also identical. It is revealing to follow the intellectual threads weaved by Bader which provides us with a glimpse of his thought processes and intuition that guided him to some of his key discoveries. The lucidity, rigor, and clarity characteristic of Bader and the informality of style of a letter makes it of pedagogic and historic interest.

     

Theoretical study of combined radiative conductive and convective heat transfer in semi-transparent porous medium in a spherical enclosure

A new method for the solution of the radiative transfer equation in spherical media based on a modified discrete ordinates method is extended to study radiative, conductive and convective heat transfer in a semi-transparent scattering porous medium. The set of differential equations is solved using the fourth-order Runge-Kutta method. Various results are obtained for the case of combined radiative and conductive heat transfer, as well as for the interaction of those modes with convection. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

The Stationary Oseen Equations in $${\mathbb{R}}^{3}$$ . An Approach in Weighted Sobolev Spaces

In this paper we solve the stationary Oseen equations in . The behavior of the solutions at infinity is described by setting the problem in weighted Sobolev spaces including anisotropic weights. The study is based on a L^p theory for 1 < p < ∞.     

Characterization of a closed-shell fluorine-fluorine bonding interaction in aromatic compounds on the basis of the electron density

A bond path linking two saturated fluorine atoms is found to be ubiquitous in crowded difluorinated aromatic compounds. The bond path is shown to persist for a range of internuclear distances (2.3-2.8 A) and a range of relative orientations of the two C-F internuclear axes. The F. . .F bonding is shown to exhibit all the hallmarks of a closed-shell weak interaction. The presence of such a bond path can impart as much as 14 kcal/mol of local stabilization to the molecule in which it exists, a stabilization that can be offset or even overwhelmed by destabilization of other regions in the molecule. Several other weak closed-shell interactions were also found and characterized including F. . .C, F. . .O, and C. . .C interactions, hydrogen bonding, dihydrogen bonding, and hydrogen-hydrogen bonding. This study represents another example of the usefulness and richness of the bond path concept and of the theory of atoms in molecules in general.     

The scalar Oseen operator − Δ + ∂/2202<Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript> in ℝ<Superscript>2</Superscript>

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L ^p theory.     

An STM study of the localized atomic reaction of 1,2- and 1,4-dibromoxylene with Si(1 1 1)-7 × 7

Thermal reactions of 1,2- and 1,4-dibromoxylene (1,2- and 1,4-diBrXy) with Si(1 1 1)-7 × 7 were investigated by STM at room temperature under UHV conditions. Reaction led to the formation of single adsorbed Br-atoms or pairs of Br-atoms, in a ratio approx. 3:1 for both reagents. Experimental results were interpreted in terms of ‘parent-mediated’ (halogen atom accompanied by organic residue), and ‘daughter-mediated’ (no accompanying organic residue) reaction dynamics. Both mechanisms contributed to the bromination of the silicon surface in comparable amounts. For pairs of bromine atoms the Br–Br separation had a most probable value of 7.6 Å for 1,2-diBrXy, and 11.5 Å for 1,4-diBrXy. This separation was in each case greater than that in the diBrXy parent molecule by a few angstroms. For parent-mediated reaction the dynamics were revealed in detail by the STM images which gave the vectorial location of the halogen-atom products (distance and angle of the daughter atoms) relative to the prior location and alignment of the adsorbed parent molecule. Both reagents, 1,2- and 1,4-diBrXy, were found to be less reactive than the corresponding dibromobenzenes studied earlier in this laboratory [S. Dobrin et al., Surf. Sci. 561 (2004) 11], in both parent- and daughter-mediated modes.