Once again, also in the specific case of single atoms, there is not an hierarchical relation between physics and chemistry but rather a mutually beneficial relationship in which the strength of chemical theory and approach to matter that constitutes the core of its rich conceptual body complements the modern approach of physics to electrons in molecules and materials focusing on the ways individual particles interact with each other (for example in the presence of a magnetic field which led a team of physicists to lately discover a completely unexpected effect of the magnetic field on electronic properties of ferromagnetic material Fe 3 Sn 2 ). 
A technique compatible with single atoms for measuring the energy distribution in the trap is to reduce the potential depth and to observe whether the atoms are lost. However, if this reduction of the potential is done quickly compared to the atomic oscillation period, the instantaneous kinetic en- ergy determines whether the atom escapes from the lowered potential. Thus, the loss probability depends on the phase of the oscillation at the moment the potential depth is reduced. If, in contrast, the trap depth is reduced slowly compared to the oscillation period, i.e., adiabatically, the trap depth U 1 at which the atom escapes is a function of its total initial energy E 0 only. By changing the potential depth from its
Abstract: Nanoparticles of platinum‐group metals (PGM) on carbon supports are widely used as catalysts for a number of chemical and electrochemical conversions on laboratory and industrial scale. The newly emerging field of single atom catalysis focuses on the ultimate level of metal dispersion, i.e. atomically dispersed metal species anchored on the substrate surface. However, the presence of single atoms in traditional nanoparticle‐based catalysts remains largely overlooked. In this work we use aberration‐corrected scanning transmission electron microscope to investigate four commercially available nanoparticle‐based PGM/C catalysts (PGM = Ru, Rh, Pd, Pt). We show that in addition to nanoparticles, single atoms are also present on the surface of carbon substrates. These observations raise questions about the role that single atoms play in conventional nanoparticle PGM/C catalysts. We critically discuss the observations with regard to the quickly developing field of single atom catalysis.
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Potential differences in the direct and post-synthetic methodologies were also analyzed by varying the initial metal distributions in the simulations, placing the atoms all over the material (Figure 7b,d) or at one surface (Figure 7a,c), respectively. Significant dimerization was observed for Pt in both cases, while Pd mostly remained as single atoms. However, post-synthetic approaches have drawbacks in the isolation of single atoms as the local surface concentration might be very high, promoting aggregation. Direct methodologies are better suited for this purpose, but the entrapment of the metal within the carrier may decrease the atom efficiency, in agreement with the catalytic tests (vide infra). The metal precursor can also be expected to play an important role as the adhesion of the precursor to the surface might be different as we have illustrated by the adsorption of the different precursors to the voids in the C 3 N 4 polymers. Comparison of the
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(2) as the DSF forms from a SF phase, disappearance of the interference peak in the single-particle momen- tum distribution. This is because the long range order for single atoms goes away. To see long range order for dimers, the dimers could be associated to molecules and then released from the lattice to perform a time-of flight measurement of the momentum distribution. In princi- ple, this could be done with Feshbach molecules, at the risk of some collisional loss from colliding molecules dur- ing the measurement process. Another alternative would be to detect the dimer-dimer correlation functions using noise-correlation measurements [73, 74]. We discuss the adiabatic preparation of states in these regimes below.
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Determination of the diffusive behaviour of atoms moving across a surface is of fundamental scientific importance and crucial to a better understanding of many surface-related phenomena such as surface phase formation, Ostwald ripening, epitaxial growth and heterogeneous catalysis [1–5]. For example, the reali- sation that spatially-isolated single atoms [6–9] and nanoclusters  offer the potential for highly efficient and selective catalytic reactions warrants greater understanding of their interaction with industrially-relevant substrates, which are often heterogeneous in nature. To date, experimental and theoretical investigations of sur- face diffusion have tended to focus on model systems such as clean metal surfaces [11,12], while similar studies of catalytically-active systems have been limited. However, the development of detailed models describing the surface diffusion at the atomic scale in these heterogeneous systems is of paramount importance to optimize the stability and reactivity of single-atom catalysts . A system with spatial and energetic heterogeneity is known to result in devi- ations from the classical model of Brownian motion and can lead to a diverse range of behaviours known as anomalous diffusion . To investigate such diffusive behaviour, it is necessary to track single atom motion over extended time periods, and high resolu- tion (scanning) transmission electron microscopy ((S)TEM) can provide the necessary spatial and temporal resolution [15–19]. Previous (S)TEM work has provided some insight into atom diffu- sion, e.g. the anomalous diffusion of Fe atoms along a graphene
dynamics of formation of metal nanocrystals to be observed, all the way from single atoms to molecules, clusters and then nanocrystals. This method has been exempliﬁed by the production of a graphitic matrix doped with sulfur and boron, decorated with ångstro¨m-sized crystals of osmium, opening-up possible new perspectives for the design of nanoscopic highly-dense and pressure-resistant materials. The technology can readily be extended to expand the range of dopants in the supporting graphitic matrix, for example by replacing sulfur with selenium. It is also facile to fabricate a range of homo- and hetero-metal angstrom-size nanocrystals. We have illustrated this for mixed ruthenium–osmium crystals. Other combinations that might be readily accessible include Pd, Rh, Ir and Au, as the synthesis of the precursor carborane complexes of these metals is feasible. There is also wide scope for adapting this polymer-encapsulated metal complex synthetic procedure by variation of the block copolymer. The possibility of creating individual vacancies at desired locations in carbon nanotubes using electron beams has been recently demonstrated 38 , and might also be combined with our procedure to allow the grafting of Os nanocrystals onto speciﬁc hotspots. Our synthetic route, which gives rise to a self- supporting graphitic matrix, also offers attractive possibilities for studying the formation of multi-heteroatom-doped-graphitic sheets and the inﬂuence of dopants and defects without inﬂuence from the underlying support grids (for example, copper), a problem which often complicates the interpretation of metal deposition experiments. A combination of new experiments and computation will be necessary in future work for fully understanding the detailed mechanisms of doping, hopping, cluster rolling and coalescence. Finally, these nanocrystals may contribute to conceptual advances in the design of a new range of nanodevices, for example, for information storage, electronic circuitry, chemosensing and catalysis.
as having no width. This is valid for the pum p as the walls are well sepa rated and an atom will spend most of its time away from the laser beams. In contrast, the lasing cavity has a longitudinal confinement which is small. Typ ically this is of the same scale as the transverse confinement. Because of this we m ust consider the effect of the width of the light beams which form the potential walls. Having two beams with only a couple of microns of darkness betw een them is close to the optical diffraction limit, thus assuming that the re sulting optical potential in this case is a square well is not realistic. In practice such a small cavity will always be close to harmonic. Therefore, we model the longitudinal lasing cavity potential as harmonic. This will lead to an increased chance of spontaneous emission due to the atoms being present in the light field. This problem was discussed in the context of the transversely confining beam s previously. In both cases (longitudinal and transverse confinement) the potential barrier is provided by the dipole force and the dimensions of the cavity are very small so that light will leak into the cavity. The discussion on spontaneous emission in the previous section, however, assumed (as an over estimate) that the atoms were constantly in the presence of the far detuned light field. Thus, the am ount of spontaneous emission from the longitudinal confinement will be at most of similar order to the effect considered there.
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The famous theorem of Savage is based on the richness of the states space, by assuming a continuum nature for this set. In order to fill the gap, this article considers Savage’s theorem with discrete state space. The article points out the importance the existence of pair event in the existence of utility function and the subjective probability. Under the discrete states space, this can be ensured by the intuitive atom swarming condition. Applications for the establishment of an inter-temporal evaluation à la Koopman , , and for the configuration under unlikely atoms of Mackenzie  are provided.
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This research was initially motivated by the need for more accurate semiclassical methods of interpretation and modelling of non-hydrogenic spectra in external fields. It combines two important theories, on one hand quantum defect theory (QDT) (see, for example ) and on the other periodic orbit theory augmented by the inclusion of diffractive orbits [2,3]. Diffractive contributions are derived from the geometric theory of diffraction (GTD) which represents an identifiable subsidiary body of knowledge. Calculation of the density of states of singly excited (Rydberg) atoms in an external magnetic field offers a relevant problem in which these areas of research may be combined. This combination allows the analysis of spectral properties beyond the scope of standard periodic orbit theory.
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Single crystal X-ray diffraction studies were performed using a Bruker SMART APEX diffractometer equipped with a Bruker Kryo-flex cryostream device and Mo-Kα radiation or on a Bruker Duo diffractometer equipped with an Oxford cryostream device using Mo- Kα radiation. Crystals were examined in paratone oil and mounted on a goniometer head using a cryo-loop. Data were typically collected at 173 K and processed using SAINTPLUS with absorption corrections applied using SADABS or TWINABS. Structures were solved by direct methods and refined using full-matrix least squares within SHELXTL. All non-H atoms were refined anisotropically and H atoms added at calculated positions and refined using a riding model. A summary of structural information including unit cell parameters and final residuals are tabulated in the Appendices.
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The hypothesis of the present paper is that all multiple covalent bonds in 2D structural formulas of ions and mo- lecules could be replaced by single covalent-bonds. This modification causes internally a redistribution of charges. The scope of the even-odd rule, described in previous papers for well-known ions and molecules, is therefore expanded to multiple-bonded compounds and offers many advantages. This rule simplifies the drawing of com- pounds in several cases, for instance HN2 and HN3(+) are represented here with only one structure. It preserves the symmetry of large compounds like methylene blue. Compounds like C6H6, classically represented with reso- nance structures, have now a fixed configuration. The distinctive chemical properties of O2 and N2 can be ex- plained by the presence or the absence of local charges. This rule can also be applied to covalent planar solids like graphite. Finally, as the even-odd rule was applied to many known compounds in past and present papers, it confirms the ability of this rule to address covalent-bonded compounds such as molecules, ions or planar crystals.
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The famous theorem of Savage is based on the richness of the states space, by assuming a continuum nature for this set. In order to fill the gap, this article considers Savage’s theorem where the existence of atom sets is possible. The article points out the importance of the existence of pair event (the event which is equivalent to its complement) in the establishment of the mean expected utility behaviour, using an utility function and the subjective probability. Under the discrete states space, this existence can be ensured by the intuitive atom swarming condition. Applications for the establishment of an inter-temporal evaluation à la Koopman , , and for the configuration under unlikely atoms of Mackenzie  are provided.
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exhibited is diffraction [ 43 ] . This effect occurs whenever the atomic wave-packet interacts with anything that shifts its phase or even its amplitude, through absorption. Diffraction can split the atomic wavefunction into a coherent super- position of momentum and/or angular momentum states. To achieve atomic diffraction atoms are normally sent through a light ﬁeld with which they interact for a short time, normally smaller than Γ − 1 which ensures that the probability of a spontaneous photon emission is negligible. In this case, when the detuning is large, the potential which corresponds to the atom-light interaction is real, acts as a pure phase object and the interaction potential operates as a thin diffraction grating. This is known as the Kapitza-Dirac scattering and occurs in the Raman-Nath limit . Some experiments have shown that similar effects may arise when the interaction time is larger than Γ − 1 , but in addition we have far-detuning . Over the years, diffraction of electromagnetic ﬁ elds has played a key role for the generation of electromagnetic waves with a phase topological charge such as the optical LG beams [ 66 ] . But diffraction is a general wave effect and is not limited to light beams. It can also be present in matter waves. The pro- duction of EV is based on the diffraction of electron waves. The EVs are beams of electrons with a quantised angular momentum along the propagation axis [242, 243, 246]. The creation of such beams has been achieved by passing a plane electron wave through spiral phase plates [ 247 ] or holographic masks [ 248 ] .
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From the above studies it can be seen that Multiple linear regression (MLR) coupled with stepwise variable selection led to a statistically significant model with respect to r 2 (coefficient of determination 0.9176) and q 2 (cross- validation, > 0.6673). Three descriptors are included in 2D- QSAR equation generated by using MLR. The developed MLR model reveals that the descriptor Polar Surface Area is PolarSurfaceAreaExcludingPandS: This descriptor signifies total polar surface area excluding phosphorous and sulphur. Second descriptor is PolarSurfaceAreaIncludingPandS: This descriptor signifies total polarsurfaceareaincludingPhosphorousandsulphur are negatively contributes to the biological activity. The next descriptor is T_O_O_5 it shows the count of number of Oxygen atoms (single double or triple bonded) separated from any other Oxygen atom (single double or triple bonded) by 6 bonds in a molecule, is inversely proportional to the activity. The descriptor T_N_N_6: This is the count of number of Nitrogen atoms (single double or triple bonded) separated from any other Nitrogen atom (single double or triple bonded) by 6 bonds in a molecule. It is also negatively contributing in the biological activity .
In the above subsection, the analysis of site preference behavior shows that Si atoms have a pronounced prefer- ence for occupying 96i site. On the one hand, the number of 96i-96i (Fe-Fe) dumbbell pairs reduces and the nega- tive exchange interaction with the increase of Si atom,
atomic charge (q(Ω)) and the isotropic total atomic magnetizability (χ(Ω)) of boron and nitrogen atoms individually for armchair (4,4) SWBNNT without an external electric field, in Fig. 2 and in the presence of 0.0005, 0.0010 and 0.0012 a.u. external electric field are shown in Figs. 3-5 respectively. The linear relationships between isotropic chemical shielding with atomic charge and isotropic total atomic magnetizability in an armchair (4,4) SWBNNT without external electric field (Fig. 2) and in the presence of 0.0005, 0.0010 and 0.0012 a.u. external electric field (Figs. 3-5) are obtained. The obtained linear relationships between isotropic chemical shielding with an atomic charge for boron and nitrogen atoms are inverse each other. As in Figs. 2(a) through 5(a) can be seen, the isotropic chemical shielding in boron atoms directly related to atomic charge, while this relationship is the reverse for nitrogen atoms. This means that with increasing atomic charge to more positive values for boron atoms, chemical shielding is increased, and conversely with decreasing atomic charge to more negative values for nitrogen atoms, chemical shielding is reduced. This result is in contrary to the expectation for the boron atoms and the chemical shielding should be reduced by increasing the amount atomic charges to more positive. Also, the lack of correlation, the discrepancy between the results and/or lack of compliance between chemical shielding and atomic charges has been observed in previous work [8,10].
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Abstract: A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the context of perturbation theory. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number Z.
Sciences Research Council for a Leadership Fellowship award which supported some of this work ( EP / G007837 / 1 ) and SPJ was funded via an EPSRC PhD + fellowship ( EP / J500483 / 1 ) ; MM is grateful for the award of a Marie Curie fellowship funded by the ACRITAS FP7 initial training net- work ( www.acritas.eu ) under the Marie Skodowska-Curie Actions, project reference ACRITAS-317348-Ares ( 2016 ) 909492. MM also thanks John Randall, James Owen and colleagues at Zyvex Labs ( Richardson, Texas ) for hosting a month-long secondment during which he gained valuable insights into automated scanning probe lithography of H:Si ( 100 ) surfaces. A signi ﬁ cant amount of the research was also funded by the the European Commission ’ s FP7 ICTFET programme via the Atomic Scale and Single Molecule Logic gate Technologies ( AtMol ) project, Contract No. 270028. SPJ was funded via a Leverhulme Trust Early Career Fellowship, ECF-2015-005.
Not a single electron of foregoing parts of atoms and ions “falls” on corresponding atomic nucleus but only moves away from it, revolving around the nucleus along flat spiral and continuously emitting a slight light front in the form of a conical surface. The spiral has the interior maximum of turns density. Moving away from the nucleus, each single electron decelerates with its electric field and the speed of single electrons decreases slightly. As a result single electrons move away from electric fields of atomic nuclei with no expenditures of external energy. I have proved, that the electric field strength of an atomic nuclei of atoms of atomic gas of hy- drogen and hydrogen-like ions in form a gas or a vapour for a point of single electron location (accordingly con- dition (1)) is inversely proportional to the distance between the corresponding atomic nucleus and single elec- tron by greater than the power of 3. I have also found relations (47) and (48) for calculation of cyclic frequency of revolution of single electron around an atomic nucleus in maximum of turns density of flat spiral.
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