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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

A methodology of atomically resolved Land\'{e} g factor mapping of a single molecule is reported. Mn(II)-phthalocyanine (MnPc) molecules on Au(111) surface can be dehydrogenated via atomic manipulation with manifestation of tailored extended Kondo effect, which can allow atomically resolved imaging of the Land\'{e} g factor inside a molecule for the first time. By employing dehydrogenated MnPc molecules with removal of six H atoms (-6H-MnPc) as an example, Land\'{e} g factor of atomic constituents of the molecule can be obtained, therefore offering a unique g factor mapping of single molecule. Our results open up a new avenue to access local spin texture of a single molecule.

A methodology of atomically resolved Land�� g factor mapping of a single molecule is reported. Mn(II)-phthalocyanine (MnPc) molecules on Au(111) surface can be dehydrogenated via atomic manipulation with manifestation of tailored extended Kondo effect, which can allow atomically resolved imaging of the Land�� g factor inside a molecule for the first time. By employing dehydrogenated MnPc molecules with removal of six H atoms (-6H-MnPc) as an example, Land�� g factor of atomic constituents of the molecule can be obtained, therefore offering a unique g factor mapping of single molecule. Our results open up a new avenue to access local spin texture of a single molecule.

So far no mechanism is known, which could connect the two measurements in a Bell-type experiment with a speed beyond the speed of light, commonly considered the ultimate limit of propagation of any field-like interaction. Here, we suggest such a mechanism, based on the phase of a photon field during its propagation. We show that two measurements, corresponding to two independent rotations of the fields, are connected, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense., Comment: Corrected some (very minor) typos. 3 pages, 1 figure

A Reply to the Comment by M. Calatayud et al.

A reply to the Comment by M. Calatayud et al. on "Imaging of the Hydrogen Subsurface Site in Rutile TiO2" (Physical Review Letters, Volume 102, Issue 13). DOI: 10.1103/physrevlett.102.136103.

The atomic-scale contrast in noncontact atomic force microscopy (nc-AFM) images is determined by thegeometry and exact atomic structure of the tip apex. However, the tip state is an experimentally unknown parameter, and the lack of insight into the tip apex often limits the possibilities of extracting precise quantitative and qualitative atomistic information on the surface under inspection. From an interplay between simultaneously recorded nc-AFM and scanning tunneling microscopy (STM) data, and atomistic STM simulations based on multiple scattering theory, we demonstrate how the state of the scanning probe microscopy (SPM) tip in the experiments may be determined. The analysis of a large number of experimental SPM images recorded with different tips reveals that no general correlation exists between the contrast observed in the nc-AFM and the tunneling current (It) images on TiO2(110) surface. The exact state of the SPM tip must, therefore, bedetermined for each specific case, which is normally a very difficult endeavor. However, our analysis of the AFM contrast on TiO2(110) surface allows us to considerably reduce the number of tips to be considered in a full simulation. By carefully evaluating the contrast of a handpicked library of SPM tips, we manage to determine a very accurate model of the SPM tip used in an experiment for the first time. It is envisioned that the approach presented here may eventually be used in future studies to screen for and select a SPM tip with a special functionalization prior to imaging an unknown sample, and in that way facilitate precise modeling and chemical identification of surface species.

The atomic-scale contrast in noncontact atomic force microscopy (nc-AFM) images is determined by the geometry and exact atomic structure of the tip apex. However, the tip state is an experimentally unknown parameter, and the lack of insight into the tip apex often limits the possibilities of extracting precise quantitative and qualitative atomistic information on the surface under inspection. From an interplay between simultaneously recorded nc-AFM and scanning tunneling microscopy (STM) data, and atomistic STM simulations based on multiple scattering theory, we demonstrate how the state of the scanning probe microscopy (SPM) tip in the experiments may be determined. The analysis of a large number of experimental SPM images recorded with different tips reveals that no general correlation exists between the contrast observed in the nc-AFM and the tunneling current (It) images on TiO2(110) surface. The exact state of the SPM tip must, therefore, be determined for each specific case, which is normally a very difficult endeavor. However, our analysis of the AFM contrast on TiO2(110) surface allows us to considerably reduce the number of tips to be considered in a full simulation. By carefully evaluating the contrast of a handpicked library of SPM tips, we manage to determine a very accurate model of the SPM tip used in an experiment for the first time. It is envisioned that the approach presented here may eventually be used in future studies to screen for and select a SPM tip with a special functionalization prior to imaging an unknown sample, and in that way facilitate precise modeling and chemical identification of surface species.

We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and numerical. Conceptually, it allows to formulate a physical principle for the development of quantum mechanical systems: it is the principle of energetic equilibrium, because the energy principle, in this case, applies not only globally, but also on a local level. The method is an order-$N$ method, scaling linearly with the number of atoms. It is used to calculate the electronic groundstate of a metallic surface, where we find good agreement with experimental values., 31 pages and 6 figures. Included an explicit derivation of the many-electron wavefunction from the Green's function of an N-electron system

It has been shown that electron transitions, as measured in a scanning tunnelling microscope (STM), are related to chemical interactions in a tunnelling barrier. Here, we show that the shape and apparent height of subatomic features in an atomic force microscopy (AFM) experiment on Si(111) depend directly on the available electron states of the silicon surface and the silicon AFM tip. Simulations and experiments confirm that forces and currents show similar subatomic variations for tip-sample distances approaching the bulk bonding length., Comment: 5 pages and 4 figures

In this thesis a range of phenomena related to molecular adsorption on silicon surfaces is investigated. The majority of the studies are performed in response to experimental results, where, using newly developed methods within the framework of density functional theory, we aim to elucidate some of the underlying physics as well as test the performance of the chosen methodology. The studies cover a range of subjects such as molecularly mediated pinning of surface geometry, single molecular adsorptions, molecule migration via exited states and finally an analysis of coverage dependent adsorption phenomena, where interactions between molecules are mediated by the surface or enacted via dipole interactions. The main molecules of our simulations were water, ethylene, acetylene, and benzene, as well as halogenated hydrocarbons. We studied processes at two different surfaces, the Si(111)-7 x 7 surface, and the Si(100)-c(4 x 2) surface. Finally we simulated and characterized one type of grain boundary observed experimentally for a set of photovoltaic absorbers (CuInSe_{2}) and kesterite and stannite(Cu_{2}ZnSnSe_{4} or Cu_{2}ZnSnS_{4}) in order to resolve the open question of how these grain boundaries influence efficiencies of the photovoltaic device.

We investigated the adsorption and reactivity of substituted hydrocarbons on Si and Cu surfaces using Grimme’s vdW–corrected DFT, CI–NEB and STM simulations. Halogenated hydrocarbons on surfaces are systems of particular interest. These molecules adsorb and self–assembly at surfaces and many experimental works show that, if one provides energy to the complex, in the form of heat, light, or electrons dropped with an STM tip, they easily react resulting in single, or patterns of, chemisorbed atoms at specific and controllable sites. For instance, 1–chloropentane forms asymmetric (A) and symmetric (S) pairs on Si(001)–2×1. The rate of thermal reaction of A is greater than S in chlorinating room-temperature silicon. The energy threshold for electron–induced reaction is also different. We have used DFT and NEB tools to explain the features of this system and we simulated STM images in agreement with the experiments. On the other hand, diiodobenzenes physisorbed on Cu(110) can act as molecular calipers. We have computationally modelled the adsorption of 1,3-diiodobenzene (m–DIB) on Cu(110) and simulated STM images for the four most stable configurations using the Tersoff–Hamann approach at different bias voltages. We find that all the adsorption orientations have comparable energy and we discuss the relative probabilities of experimental observation as well as the structural details. We have furthermore compared the electronic ground–state reactivity of 1,3– and 1,4–diiodobenzene in order to show that the different symmetry of the initial adsorbed state greatly affects reactivity. Since the studied systems provide a means to surface functionalization via site–specific imprinting of single atoms, we also propose a model for Cu nanoclusters on Cu(110) supported by one or two chemisorbed S (or Cl) atoms.