The kinetic energy of molecular charge distributions and molecular stability

Abstract

AbstractsThis paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.Dans cet article on examine la relation entre les caracttristiques topographiques d'une distribution de charge molkculaire et l'tnergie cinttique du systtme. Les contributions d'espace de l'tnergie cinttique ont rapport au Laplacien de la densitt de charge totale et aux gradients des densitts des orbitales naturelles. Une condition ntcessaire pour la stabilitt moltculaire est l'existence d'une courbure ntgative nette pour la distribution de charge moltculaire dans la rtgion internuclkaire. On dkmontre que la densitt de charge accumulke dans la rtgion internucltaire d'une moltcule stable est distribute de telle faqon que l'augmentation correspondante de l'tnergie cinttique soit minimiste. Une comparaison des contributions B 1'Cnergie cinktique des distributions de charge atomiques et moltculaires indique, que dans la formation d'une molkcule stable, la contribution de la densitt de charge molkculaire dans la rtgion liante est diminute par rapport A celle des atomes.In diesem Artikel wird die Beziehung zwischen den topographischen Eigenschaften einer molekularen Ladungsverteilung und der kinetischen Energie des Systems untersucht. Die Raumbeitrage zur kinetischen Energie stehen mit dem Laplace-operator der totalen Ladungsdichte und mit den Gradienten der Dichten der naturlichen Orbitalen in Verbindung. Eine notwendige Bedingung fur molekulare Stabilitat ist die Existenz einer negativen Krummung fur die molekulare Ladungsverteilung in der zwischenmolekularen Region. Es wird gezeigt, dass die in der zwischenmolekularen Region angehauftete Ladungsdichte eines stabilen Molekuls in so einer Weise verteilt ist, dass der begleitende Zuwachs der kinetischen Energie minimisiert sei. Ein Vergleich der Beitrage zur kinetischen Energie der atomaren und molekularen Ladungsverteilungen deutet an, dass in der Bildung eines stabilen Molekiils der Beitrag der molekularen Ladungsdichte in dem Bindungsbereich bezuglich auf den der Atome vermindert ist.

On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

“…This is this region where bond critical points lie and redistribution of valence density due to chemical bonding takes place. In the general case, the kinetic energy density of a quantum system can be correctly expressed in terms of the first-order density matrix p(r, r') in two alternative ways:~ (Bader & Preston, 1969;Tal & Bader, 1978):…”

“…The two forms of the kinetic energy density are related to each other by the expression (Bader & Preston, 1969) …”

“…The consideration of the nonlocality of the kinetic energy density functional of p(r) in the new scheme fundamentally differs from that in the scheme proposed by Tal & Bader (1978). It arises from the fact that, although the bonding density is dominant in the internuclear region between atoms displaying shared interaction, its contribution to the local kinetic energy in this region is not dominant (Bader & Preston, 1969;Schwarz, Valtazanos & Ruedenberg, 1985). Indeed, according to the second expression for gt[p(r, r')] in (1), the contribution to the local kinetic energy density of the highest occupied cr bonding molecular orbital (MO), for which the d~nsity distribution displays a maximum between two nuclei in compounds with a shared interaction, is low in this region.…”

From topology to geometry

“…There are four kinds of critical points in a three-dimensional space: a local minimum, a local maximum, and two kinds of saddle points. These critical points (cps) are denoted by an index that is the number of positive curvatures minus the number of negative curvatures; for example, a minimum cp has positive curvature in the three orthogonal directions; therefore, it is called a (3,3) cp, where the first number is simply the number of dimensions of the space, and the second number is the net number of positive curvatures. A maximum would be denoted by (3, -3), since all three curvatures are negative.…”

“…In my opinion, this lack of success can be attributed to a less than rigorous definition of the metallic bond. However, the topological model of molecular and solid state structure advanced by Bader et al (3)(4)(5)(6)(7)(8) provides a rigorous definition for all classes of chemical bonds, of which the metallic bond is a subset. Believing that such a rigorous description of the metallic bond should provide the starting point for the application of chemical formalism to explain the structure and properties of metallic systems, we have sought a correlation between the topological properties of the charge density of metals and alloys and their respective properties (9-1 4).…”