The theory of molecular structure determined by the gradient vector field of the charge density ρ identifies the set of atomic interactions present in a molecule. The interactions so defined are characterized in terms of the properties of the Laplacian of the charge density ∇2ρ(r). A scalar field is concentrated in those regions of space where its Laplacian is negative and depleted in those where it is positive. An expression derived from the quantum mechanical stress tensor relates the sign of the Laplacian of ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages. By obtaining a map of those regions where ∇2ρ(r)<0, the regions where electronic charge is concentrated, one obtains a map of the regions where the potential energy density makes its dominant contributions to the energy of a system. It is demonstrated that atomic interactions fall into two broad general classes, closed-shell and shared interactions, each characterized by a particular set of mechanical properties. Interactions resulting from the sharing of charge density between atoms, covalent and polar bonds, are caused by a contraction of the charge density towards the line of interaction linking the nuclei. The curvatures of ρ perpendicular to the interaction line are dominant, electronic charge is concentrated in the internuclear region, and ∇2ρ<0. These interactions are characterized by the large negative value of the potential energy in the internuclear region. Interactions between closed-shell atoms as found in noble gas repulsive states, in ionic bonds, in hydrogen bonds, and in Van der Waals molecules are governed by the contraction of the charge density towards each of the interacting nuclei. Thus one finds the parallel curvature of ρ to be dominant in these interactions, electronic charge is depleted in the interatomic surface and ∇2ρ>0. The mechanics are characterized by the relatively large value of the kinetic energy, particularly the component parallel to the interaction line. In the closed-shell interactions, the regions of dominant potential energy contributions are separately localized within the boundaries of each of the interacting atoms or molecules. In the shared interactions, a region of low potential energy is contiguous over the basins of both of the interacting atoms. The problem of further classifying a given interaction as belonging to a bound or unbound state of a system is also considered, first from the electrostatic point of view wherein the regions of charge concentration as determined by the Laplacian of ρ are related to the forces acting on the nuclei. This is followed by and linked to a discussion of the energetics of interactions in terms of the regions of dominant potential and kinetic energy contributions to the virial as again determined by the Laplacian of ρ. The properties of the Laplacian of the electronic charge thus yield a unified view of atomic interactions, one which incorporates the understandings afforded by both the Hellmann–Feynman and virial theorems.

The force acting on a spinning sphere moving in a rarefied gas is calculated. It is found to have three contributions with different directions. The transversal contribution is of opposite direction compared to the so-called Magnus force normally exerted on a sphere by a dense gas. It is given by F=−ατξ23πR3mnω×v, where ατ is the accommodation coefficient of tangential momentum, R is the radius of the sphere, m is the mass of a gas molecule, n is the number density of the surrounding gas, ω is the angular velocity, and v is the velocity of the center of the sphere relative to the gas. The dimensionless factor ξ is close to unity, but depends on ω and κ, the heat conductivity of the body.

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We review the literature on what classical physics has to say about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner's 1933 statement that flux expulsion has no classical explanation.

AbstractsA new derivation of the Born-Oppenheimer separation of electronic and nuclear motion is presented. The arguments used differ from those in earlier works in not being specially designed for molecules. Instead they aim at an intuitive understanding of the qualitative behavior of the low energy bound states of any, real or hypothetical, Coulomb interacting system of particles. The virial theorem is the starting point o f the discussion. After a brief explanation of how it can be used to understand atomic structure it is applied to molecules. It is found that coordinates of collective and individual motion are natural coordinates for the approximate separation, rather than nuclear and electronic. It is also shown that it is the form of the interaction between the particles that is responsible for the separation; the smallness of mel/MN, is irrelevant.On prtsente une nouvelle faGon dobtenir la separation de Born-Oppenheimer des mouvements Blectroniques et nucltaires. Les arguments different de ceux utilisds ordinairement en n'dtant pas construits sptcialement pour les molecules. Par contre leur but est une comprthension intuitive du comportement qualitatif des dtats lits i b a s e tnergie, de n'importe quel systeme de particules, rtel ou hypothttique, avec des interactions coulombiennes. Le thdorkme du viriel forme le point de ddpart de la discussion. Apres une courte explication de son emploi pour comprendre la structure atomique, il est applique au cas moltculaire. I1 s'avkre que les coordonntes des mouvements collectifs et individuels forment des coordonnees naturelles pour la separation plutbt que les coordonntes nucldaires et tlectroniques. I1 est demontrd aussi que c'est la forme de l'interaction entre les particules qui est responsable pour la separation; la grandeur de mel/MN, est sans importance.Eine neue Ableitung der Born-Oppenheimer'schen Trennung von elektronischer und Kernbewegung wird vorgelegt. Die Argumente unterscheiden sich von den ublichen dadurch, dass sie nicht spezeill fur Molekiile konstruiert sind. Im Gegenteil ist die Absicht das qualitative Verhalten der gebundenen Tiefenergiezustande irgendeines reellen oder hypothetischen Teilchensystems mit Coulombwechselwirkungen intuitiv zu verstehen. Der Virialsatz bildet der Ausgangspunkt der Diskussion. Nach einer kurzen Erklarung seiner Anwendung fur das Verstandnis der Atomstruktur, wird er auf Molekule angewandt. Es zeigt sich, dass die Koordinaten der kollektiven und der individuellen Bewegungen, eher als die der Kern-und Elektronenbewegung die natiirlichen Koordiriaten fur die approximative Trennung sind. Es wird auch gezeigt, dass die Form der Wechselwirkung zwischen den Teilchen eher als die Grosse von mel/MN, fur die Trennung verantwortlich sind.