C.Y. Chung

Spherical (S) and tesseral (T) tensor operators (TOs) have been extensively used in, for example, EMR and optical spectroscopy of transition ions. To enable a systematic review of the published tables of the operators and their matrix elements (MEs) we have generated the relevant tables by computer, using Mathematica programs. Our review reveals several misprints/errors in the major sources of TTOs—the conventional Stevens operators (CSOs—components ) and the extended ones (ESOs—all q) for rank k = 2,4, and 6—as well as of some STOs with . The implications of using incorrect operators and/or MEs for the reliability of EMR-related programs and interpretation of experimental data are discussed. Studies of high-spin complexes like Mn12 (S = 10) and Fe19 (S = 33/2) require operator and ME listings up to k = 2S, which are not presently available. Using the algorithms developed recently by Ryabov, the generalized ESOs and their MEs for arbitrary rank k and spin S are generated by computer, using Mathematica. The extended tables enable simulation of the energy levels for arbitrary spin systems and symmetry cases. Tables are provided for the ESOs not available in the literature, with odd k = 3,5, and 7 for completeness; however, for the newly generalized ESOs with the most useful even rank k = 8,10, and 12 only, in view of the large listings sizes. General source codes for the generation of the ESO listings and their ME tables are available from the authors.

The capability of fast charge and fast discharge is highly desirable for the electrode materials used in supercapacitors and lithium ion batteries. In this article, we report a simple strategy to considerably improve the high rate capability of Co3O4 nanowire array electrodes by uniformly loading Ag nanoparticles onto the surfaces of the Co3O4 nanowires via the silver-mirror reaction. The highly electrically conductive silver nanoparticles function as a network for the facile transport of electrons between the current collectors (Ti substrates) and the Co3O4 active materials. High capacity as well as remarkable rate capability has been achieved through this simple approach. Such novel Co3O4-Ag composite nanowire array electrodes have great potential for practical applications in pseudo-type supercapacitors as well as in lithium ion batteries.