H. A. Jahn

Bio: H. A. Jahn is an academic researcher from Royal Institution. The author has contributed to research in topics: Degenerate energy levels & Wave function. The author has an hindex of 5, co-authored 5 publications receiving 2486 citations. Previous affiliations of H. A. Jahn include Leipzig University.

Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy

Abstract: In a previous paper (Jahn and Teller 1937) the following theorem was established: A configuration of a polyatomic molecule for an electronic state having orbital degeneracy cannot be stable with respect to all displacements of the nuclei unless in the original configuration the nuclei all lie on a straight line. The proof given of this theorem took no account of the electronic spin, and in the present paper the justification of this is investigated. An extension of the theorem to cover additional degeneracy arising from the spin is established, which shows that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons. The additional instability caused by the spin degeneracy alone, however, is shown to be very small and its effect for all practical purposes negligible. The possibility of spin forces stabilizing a non-linear configuration which is unstable owing to orbital degeneracy is also investigated, and it is shown that this is not possible except perhaps for molecules containing heavy atoms for which the spin forces are large. Thus whilst a symmetrical nuclear configuration in a degenerate orbital state might under exceptional circumstances be rendered stable by spin forces, it is not possible for the spin-orbit interaction to cause instability of an orbitally stable state. 1—General theorem for molecules with spin Just as before we must see how the symmetry of the molecular framework determines whether the energy of a degenerate electronic state with spin depends linearly upon nuclear displacements. This is again determined by the existence of non-vanishing perturbation matrix elements which are linear in the nuclear displacements. These matrix elements are integrals involving the electronic wave functions with spin and the nuclear dis­placements, and we deduce as before from their transformation properties whether for a given molecular symmetry they can be different from zero.

A New Coriolis Perturbation in the Methane Spectrum. II. Energy Levels

Abstract: In the first part of this work (Jahn 1938) we found the correct vibrational-rotational wave functions with which to evaluate any tetrahedrally symmetrical perturbation of the rotational levels of a threefold degenerate mode of vibration of the methane molecule. In this second part we use these wave functions to calculate the perturbation due to the Coriolis term which couples the rotational levels of the one quantum threefold degenerate vibration v4 and the rotational levels of the one quantum twofold degenerate vibration v2. This Coriolis term was derived in part I from the general vibrational-rotational Hamiltonian of the molecule. To carry out the perturbation calculation we shall need those combinations of the vibrational-rotational wave functions of v2which transform according to irreducible representations of the tetrahedral group, and these are derived here. We find also general formulae for the matrix elements in question and use these to calculate explicitly the perturbed rotational energy levels of v4 up to the tenth rotational quantum number. The rotational levels of v2 are of course correspondingly perturbed, but the calculation of these is reserved for another publication.

Diffuse Scattering of X-Rays by Crystals. The Faxen-Waller Theory and the Surfaces of Isodiffusion for Cubic Crystals

Abstract: An elementary derivation is given of the Faxen-Waller formula for the diffuse scattering of X-rays by thermally excited lattice vibrations and the shapes of the surfaces of isodiffusion in reciprocal space for cubic crystals investigated. It is shown that for substances with high elastic anisotropy large deviations from spherical character are to be expected for the surfaces of isodiffusion belonging to each of the individual lattice planes and, moreover, marked differences in shape between surfaces belonging to different lattice planes. The theory is illustrated by calculations made for a single crystal of sodium.

Rotation und Schwingung des Methanmoleküls

Abstract: Die Schrodingersche Wellengleichung von Methan wird auf Eulersche Winkel und Normalkoordinaten transformiert. Bekannte Ausdrucke von Casimir und Teller und Tisza fur die Wechselwirkung zwischen Schwingung und Rotation werden dabei streng begrundet und einige neue Glieder entdeckt, die aber nur im Falle von zufalligen Entartungen von Wichtigkeit sein konnen. Eine allgemeine gruppentheoretische Methode, wodurch die Einteilung der Rotationseigenfunktionen in nicht kombinierende Teilsysteme erhalten werden kann, wird angegeben und auf Methan angewandt. Die Resultate von Elert werden so in einfacher und vollstandiger Weise abgeleitet.

Coriolis Perturbations in the Methane Spectrum. IV. Four General Types of Coriolis Perturbation

Abstract: In previous papers (Jahn 1938, Childs and Jahn 1939) a new Coriolis perturbation in the methane spectrum was investigated. This perturbation arose from a coupling of the rotational levels of an infra-red active threefold degenerate vibration with those of an inactive twofold degenerate vibration. In the present paper, which is a continuation of this work, it is our purpose to show that in a regular tetrahedral molecule there are in all four possible distinct types of Coriolis perturbation. Two of these do not produce a splitting of the rotational levels but merely a displacement of the rotational level as a whole, whilst the other two produce a splitting as well as a displacement, one of these latter perturbations being identical with the type of perturbation previously investigated. General formulae are derived for the matrix elements of these new types of perturbation, and in the case of the new perturbation which produces a splitting of the levels, we factorize the perturbation matrices up to the tenth rotational quantum number, using the group-theoretical method previously developed. These results will be useful in elucidating the rotational structure of the overtones and combination tones of methane.

The Li-ion rechargeable battery: a perspective.

Abstract: Each cell of a battery stores electrical energy as chemical energy in two electrodes, a reductant (anode) and an oxidant (cathode), separated by an electrolyte that transfers the ionic component of the chemical reaction inside the cell and forces the electronic component outside the battery. The output on discharge is an external electronic current I at a voltage V for a time Δt. The chemical reaction of a rechargeable battery must be reversible on the application of a charging I and V. Critical parameters of a rechargeable battery are safety, density of energy that can be stored at a specific power input and retrieved at a specific power output, cycle and shelf life, storage efficiency, and cost of fabrication. Conventional ambient-temperature rechargeable batteries have solid electrodes and a liquid electrolyte. The positive electrode (cathode) consists of a host framework into which the mobile (working) cation is inserted reversibly over a finite solid–solution range. The solid–solution range, which is...

Angle-resolved photoemission studies of the cuprate superconductors

Abstract: The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

Orbital Physics in Transition-Metal Oxides

Abstract: An electron in a solid, that is, bound to or nearly localized on the specific atomic site, has three attributes: charge, spin, and orbital. The orbital represents the shape of the electron cloud in solid. In transition-metal oxides with anisotropic-shaped d-orbital electrons, the Coulomb interaction between the electrons (strong electron correlation effect) is of importance for understanding their metal-insulator transitions and properties such as high-temperature superconductivity and colossal magnetoresistance. The orbital degree of freedom occasionally plays an important role in these phenomena, and its correlation and/or order-disorder transition causes a variety of phenomena through strong coupling with charge, spin, and lattice dynamics. An overview is given here on this "orbital physics," which will be a key concept for the science and technology of correlated electrons.