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The site-dependent g factor of a single magnetic molecule, with intramolecular resolution, is demonstrated for the first time by low-temperature, high-magnetic-field scanning tunneling microscopy of dehydrogenated Mn-phthalocyanine molecules on Au(111). This is achieved by exploring the magneticfield dependence of the extended Kondo effect at different atomic sites of the molecule. Importantly, an inhomogeneous distribution of the g factor inside a single molecule is revealed. Our results open up a new route to access local spin properties within a single molecule.

The reversible control of a single spin of an atom or a molecule is of great interest in Kondo physics and a potential application in spin based electronics.Here we demonstrate that the Kondo resonance of manganese phthalocyanine molecules on an Au(111) substrate have been reversibly switched off and on via a robust route through attachment and detachment of single hydrogen atom to the magnetic core of the molecule. As further revealed by density functional theory calculations, even though the total number of electrons of the Mn ion remains almost the same in the process, gaining one single hydrogen atom leads to redistribution of charges within 3d orbitals with a reduction of the molecular spin state from S = 3/2 to S = 1 that directly contributes to the Kondo resonance disappearance. This process is reversed by a local voltage pulse or thermal annealing to desorb the hydrogen atom.

Controlling electronic transport through a single-molecule junction is crucial for molecular electronics or spintronics. In magnetic molecular devices, the spin degree-of-freedom can be used to this end since the magnetic properties of the magnetic ion centers fundamentally impact the transport through the molecules. Here we demonstrate that the electron pathway in a single-molecule device can be selected between two molecular orbitals by varying a magnetic field, giving rise to a tunable anisotropic magnetoresistance up to 93%. The unique tunability of the electron pathways is due to the magnetic reorientation of the transition metal center, resulting in a re-hybridization of molecular orbitals. We obtain the tunneling electron pathways by Kondo effect, which manifests either as a peak or a dip line shape. The energy changes of these spin-reorientations are remarkably low and less than one millielectronvolt. The large tunable anisotropic magnetoresistance could be used to control electronic transport in molecular spintronics.

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory (DFT). This has been the main stumbling block for the development of a general-purpose framework on this basis. Here, we show that on the basis of a two-density model, which represents many-electron systems by mass density and spin density components, we can derive the exact form of such a functional. The exact functional is shown to contain previously suggested functionals to some extent, with the notable exception of the Thomas-Fermi kinetic energy functional.

I revisit the reply of Bohr to Einstein. Bohr's assertion that there are no causes in atomic scale systems is, as a closer analysis reveals, not in line with the Copenhagen interpretation since it would contain a statement about reality. What Bohr should have written is that there are no causes in mathematics, which is universally acknowledged. The law of causality requires physical effects to be due to physical causes. For this reason any theoretical model which replaces physical causes by mathematical objects is creationism, that is, it creates physical objects out of mathematical elements. I show that this is the case for most of quantum mechanics., Comment: 8 pages, no in-depth knowledge of mathematics required, sets out the case for a major revision of theoretical physics. This revision expands the case against Bohm and the analysis whether quantum mechanics actually meets Popper's requirement for a scientific theory (it does not, since it is not falsifiable) and corrects a few typos

An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the many-body electronic problem here resembles the Kohn-Sham formulation of standard density functional theory. However, rather than referring electronic properties to a large set of single electron orbitals, the extended electron model uses only mass density and field components, leading to a substantial increase in computational efficiency. To date, the Hohenberg-Kohn theorems have not been proved for a model of this type, nor has a universal energy functional been presented. In this paper, we address these problems and show that the Hohenberg-Kohn theorems do also hold for a density model of this type. We then present a proof-of-concept practical implementation of this method and show that it reproduces the accuracy of more widely used methods on a test-set of small atomic systems, thus paving the way for the development of fast, efficient and accurate codes on this basis., Comment: 6 pages, 4 figure

It has been found that a model of extended electrons is more suited to describe theoretical simulations and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are easily incorporated, magnetic properties, and in particular electron spin properties pose a problem due to their conceived isotropy in the absence of measurement. The spin of an electron reacts with a magnetic field and thus has the properties of a vector. However, electron spin is also isotropic, suggesting that it does not have the properties of a vector. This central conflict in the description of an electron's spin, we believe, is the root of many of the paradoxical properties measured and postulated for quantum spin particles. Exploiting a model in which the electron spin is described consistently in real three-dimensional space - an extended electron model - we demonstrate that spin may be described by a vector and still maintain its isotropy. In this framework, we re-evaluate the Stern-Gerlach experiments, the Einstein-Podolsky-Rosen experiments, and the effect of consecutive measurements and find in all cases a fairly intuitive explanation., Comment: 5 pages, 1 figure

Owing to the renewed interest in dark matter after the upgrade of the large hadron collider and its dedication to dark matter research it is timely to reassess the whole problem. Considering dark matter is one way to reconcile the discrepancy between the velocity of matter in the outer regions of galaxies and the observed galactic mass. So far, no credible candidate for dark matter has been identified. Here, we develop a model accounting for observations by rotations and interactions between rotating objects analogous to magnetic fields and interactions with moving charges. The magnitude of these fields is described by a fundamental constant of the order 10-41kg-1. The same interactions can be observed in the solar system where they lead to small changes in planetary orbits., Comment: 4 pages and 3 figures