Nonuniform random geometric graphs with location-dependent radii

We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function n f(center dot), where n is an element of N, and f is a probability density function on R-d. A vertex located at x connects via directed edges to other vertices that are within a cut-off distance r(n)(x). We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node with out-degree zero for sufficiently large n and (ii) the maximum and minimum vertex degrees. We also provide a characterization of the cut-off function for which the number of nodes with out-degree zero converges in distribution to a Poisson random variable. We illustrate this result for a class of densities with compact support that have at most polynomial rates of decay to zero. Finally, we state a sufficient condition for an enhanced version of the above graph to be almost surely connected eventually.

Mechanistic Aspects for the Formation of Copper Dimer Bridged by Phosphonic Acid and Extending Its Dimensionality by Organic and Inorganic Linkers: Synthesis, Structural Characterization, Magnetic Properties, and Theoretical Studies

Six new copper metal complexes with formulas Cu(H2O)(2,2'-bpy) (H2L)](2) center dot H4L center dot 4 H2O (1), {Cu(H2O)(2,2'-bpy)-(H3L)}(2)(H2L)]center dot 2H(2)O (2), Cu(H2O)(1,10-phen)(H2L)](2)center dot 6H(2)O (3), Cu(2,2'-bpy)(H2L)](n)center dot nH(2)O (4), Cu(1,10-phen)(H2L)](n)center dot 3nH(2)O (5), and {Cu(2,2'-bpy)(MoO3)}(2)(L)](n)center dot 2nH(2)O (6) have been synthesized starting from p-xylylenediphosphonic acid (H4L) and 2,2'-bipyridine (2,2'-bpy) or 1,10-phenanthroline (1,10-phen) as secondary linkers and characterized by single crystal X-ray diffraction analysis, IR spectroscopy, and thermogravimetric (TG) analysis. All the complexes were synthesized by hydrothermal methods. A dinuclear motif (Cu-dimer) bridged by phosphonic acid represents a new class of simple building unit (SBU) in the construction of coordination architectures in metal phosphonate chemistry. The initial pH of the reaction mixture induced by the secondary linker plays an important role in the formation of the molecular phosphonates 1, 2, and 3. Temperature dependent hydrothermal synthesis of the compounds 1, 2, and 3 reveals the mechanism of the self assembly of the compounds based on the solubility of the phosphonic acid H4L. Two-dimensional coordination polymers 4, 5, and 6, which are formed by increasing the pH of the reaction mixture, comprise Cu-dimers as nodes, organic (H2L) and inorganic (Mo4O12) ligands as linkers. The void space-areas, created by the (4,4) connected nets in compounds 4 and 5, are occupied by lattice water molecules. Thus compounds 4 and 5 have the potential to accommodate guest species/molecules. Variable temperature magnetic studies of the compounds 3, 4, 5, and 6 reveal the antiferromagnetic interactions between the two Cu(II) ions in the eight membered ring, observed in their crystal structures. A density functional theory (DFT) calculation correlates the conformation of the Cu-dimer ring with the magnitude of the exchange parameter based on the torsion angle of the conformation.

Activation of Lattice Oxygen of TiO2 by Pd2+ Ion: Correlation of Low-Temperature CO and Hydrocarbon Oxidation with Structure of Ti1-xPdxO2-x (x=0.01-0.03)

Lattice oxygen of TiO2 is activated by the substitution of Pd ion in its lattice. Ti1-xPdxO2-x (x = 0.01-0.03) have been synthesized by solution combustion method crystallizing in anatase TiO2 structure. Pd is in +2 oxidation state and Ti is in +4 oxidation state in the catalyst. Pd is more ionic in TiO2 lattice compared to Pd in PdO. Oxygen storage capacity defined by ``amount of oxygen that is used reversibly to oxidize CO'' is as high as 5100 mu mol/g of Ti0.97Pd0.03O1.97. Oxygen is extracted by CO to CO2 in absence of feed oxygen even at room temperature which is more than 20 times compared to pure TiO2. Rate of CO oxidation is 2.75 mu mol g(-1) s(-1) at 60 degrees C over Ti0.97Pd0.03O1.97 and C2H2 gets oxidized to CO2 and H2O at room temperature. Catalyst is not poisoned on long time operation of the reactor. Such high catalytic activity is due to activated lattice oxygen created by the substitution of Pd ion as seen from first-principles density functional theory (DFT) calculations with 96 atom supercells of Ti32O64, Ti31Pd1O63, Ti30Pd2O62, and Ti29Pd3O61. The compounds crystallize in anatase TiO2 structure with Pd2+ ion in nearly square planar geometry and TiO6 octahedra are distorted by the creation of weakly bound oxygens. Structural analysis of Ti31Pd1O63 which is close to 3% Pd ion substituted TiO2 shows that oxygens associated with both Ti and Pd ions in the lattice show bond valence sum of 1.87, a low value characteristic of weak oxygen in the lattice compared to oxygens with valence 2 and above in the same lattice. Exact positions of activated oxygens have been identified in the lattice from DFT calculations.

Intermolecular charge transfer and vibrational analysis of hydrogen bonding in acetazolamide

In the present work the structural and spectral characteristics of acetazolamide have been studied by methods of infrared, Raman spectroscopy and quantum chemistry. Electrostatic potential surface, optimized geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by density functional theory (DFT) employing B3LYP with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. Based on these results, we have discussed the correlation between the vibrational modes and the structure of the dimers of acetazolamide. The calculated vibrational spectra of three dimers of acetazolamide have been compared with observed spectra, and the assignment of observed bands was carried out using potential energy distribution. The observed spectra agree well with the values computed from the OFT. A comparison of observed and calculated vibrational spectra clearly shows the effect of hydrogen bonding. The frequency shifts observed for the different dimers are in accord with the hydrogen bonding in acetazolamide. Natural bond orbital (NBO) analyses reflect the charge transfer interaction in the individual hydrogen bond units and the stability of different dimers of acetazolamide. (C) 2012 Elsevier B.V. All rights reserved.

Effect of chlorine substitution on triplet state structure of thioxanthone: A time-resolved resonance Raman study

Substitution plays an important role in determining the triplet state reactivity. In this paper, we have studied the effect of chlorine substitution on the triplet state structure and the reactivity of thioxanthone (TX). We have employed time-resolved resonance Raman technique to understand the structure of the lowest triplet excited state of 2-chlorothioxanthone (CTX). The experimental findings have been corroborated with the computational results using density functional theory. Akin to the parent compound (TX), coexistence of two lowest triplet states has been observed in case of CTX, which has been substantiated using resonant probe wavelength dependence study. The relative contribution of 3n-pi* to 3 pi-pi* to the equilibrated triplet state has been found to be more for CTX compared to TX suggesting increase in the triplet state reactivity after the substitution. The above observation has been further supported by the flash photolysis experiments. Copyright (C) 2013 John Wiley & Sons, Ltd.

A Bottom-Up Approach toward Fabrication of Ultrathin PbS Sheets

Two-dimensional (2D) sheets are currently in the spotlight of nanotechnology owing to high-performance device fabrication possibilities. Building a free-standing quantum sheet with controlled morphology is challenging when large planar geometry and ultranarrow thickness are simultaneously concerned. Coalescence of nanowires into large single-crystalline sheet is a promising approach leading to large, molecularly thick 2D sheets with controlled planar morphology. Here we report on a bottom-up approach to fabricate high-quality ultrathin 2D single crystalline sheets with well-defined rectangular morphology via collective coalescence of PbS nanowires. The ultrathin sheets are strictly rectangular with 1.8 nm thickness, 200-250 nm width, and 3-20 mu m length. The sheets show high electrical conductivity at room and cryogenic temperatures upon device fabrication. Density functional theory (DFT) calculations reveal that a single row of delocalized orbitals of a nanowire is gradually converted into several parallel conduction channels upon sheet formation, which enable superior in-plane carrier conduction.

Cu-II-azide polynuclear complexes of Cu-4 building clusters with Schiff-base co-ligands: synthesis, structures, magnetic behavior and DFT studies

Three new copper-azido complexes Cu-4(N-3)(8)(L-1)(2)](n) (1), Cu-4(N-3)(6)(L-2)(2)(H2O)(2)] (2), and Cu-4(N-3)(6)(L-3)(2)](n) (3) L-1 is the imine resulting from the condensation of pyridine-2-carboxaldehyde with N-methylethylenediamine, HL2 and HL3 are the condensation products of 2-hydroxy-3-methoxybenzaldehyde with N,N-diethylethylenediamine and N-ethylethylenediamine respectively] have been synthesized by using 0.5 molar equivalents of the Schiff base ligands with Cu(NO3)(2)center dot 3H(2)O and an excess of NaN3. Single crystal X-ray structures show that the basic unit of these complexes contains very similar Cu-4(II) building blocks. While 1 and 3 have overall 1D structures, 2 forms discrete tetranuclear clusters due to blocking of two coordination sites on the tetranuclear cluster by water molecules. Magnetic susceptibility measurements over a wide range of temperatures exhibit the presence of both antiferromagnetic and ferromagnetic exchanges within the tetranuclear unit structures. Density functional theory calculations (using B3LYP functional and two different basis sets) have been performed on the complexes 1-3 to provide a qualitative theoretical interpretation of their overall magnetic behavior.

A computational study of flame dynamics on soot production and transport for an acetylene-air laminar diffusion flame in the field of a convecting line vortex

The present work involves a computational study of soot formation and transport in case of a laminar acetylene diffusion flame perturbed by a convecting line vortex. The topology of the soot contours (as in an earlier experimental work [4]) have been investigated. More soot was produced when vortex was introduced from the air side in comparison to a fuel side vortex. Also the soot topography was more diffused in case of the air side vortex. The computational model was found to be in good agreement with the experimental work [4]. The computational simulation enabled a study of the various parameters affecting soot transport. Temperatures were found to be higher in case of air side vortex as compared to a fuel side vortex. In case of the fuel side vortex, abundance of fuel in the vort ex core resulted in stoichiometrically rich combustion in the vortex core, and more discrete soot topography. Overall soot production too was low. In case of the air side vortex abundance of air in the core resulted in higher temperatures and more soot yield. Statistical techniques like probability density function, correlation coefficient and conditional probability function were introduced to explain the transient dependence of soot yield and transport on various parameters like temperature, a cetylene concentration.

Pressure induced structural phase transformation in TiN: a first-principles study

Titanium nitride (TiN), which is widely used for hard coatings, reportedly undergoes a pressure-induced structural phase transformation, from a NaCl to a CsCl structure, at similar to 7 GPa. In this paper, we use first-principles calculations based on density functional theory with a generalized gradient approximation of the exchange correlation energy to determine the structural stability of this transformation. Our results show that the stress required for this structural transformation is substantially lower (by more than an order of magnitude) when it is deviatoric in nature vis-a-vis that under hydrostatic pressure. Local stability of the structure is assessed with phonon dispersion determined at different pressures, and we find that CsCl structure of TiN is expected to distort after the transformation. From the electronic structure calculations, we estimate the electrical conductivity of TiN in the CsCl structure to be about 5 times of that in NaCl structure, which should be observable experimentally. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4798591]

Spectral-envelope-group-delay models for transients

Transient signals such as plosives in speech or Castanets in audio do not have a specific modulation or periodic structure in time domain. However, in the spectral domain they exhibit a prominent modulation structure, which is a direct consequence of their narrow time localization. Based on this observation, a spectral-domain AM-FM model for transients is proposed. The spectral AM-FM model is built starting from real spectral zero-crossings. The AM and FM correspond to the spectral envelope (SE) and group delay (GD), respectively. Taking into account the modulation structure and spectral continuity, a local polynomial regression technique is proposed to estimate the GD function from the real spectral zeros. The SE is estimated based on the phase function computed from the estimated GD. Since the GD estimation is parametric, the degree of smoothness can be controlled directly. Simulation results based on synthetic transient signals generated using a beta density function are presented to analyze the noise-robustness of the SEGD model. Three specific applications are considered: (1) SEGD based modeling of Castanet sounds; (2) appropriateness of the model for transient compression; and (3) determining glottal closure instants in speech using a short-time SEGD model of the linear prediction residue.

Exploring the color of transition metal ions in irregular coordination geometries: new colored inorganic oxides based on the spiroffite structure, Zn2-xMxTe3O8 (M = Co, Ni, Cu)

We describe the synthesis, crystal structures, and optical absorption spectra of transition metal substituted spiroffite derivatives, Zn2-xMxTe3O8 (M-II = Co, Ni, Cu; 0 < x <= 1.0). The oxides are readily synthesized by solid state reaction of stoichiometric mixtures of the constituent binaries at 620 degrees C. Reitveld refinement of the crystal structures from powder X-ray diffraction (XRD) data shows that the Zn/MO6 octahedra are strongly distorted, as in the parent Zn2Te3O8 structure, consisting of five relatively short Zn/M-II-O bonds (1.898-2.236 angstrom) and one longer Zn/M-II-O bond (2.356-2.519 angstrom). We have interpreted the unique colors and the optical absorption/diffuse reflectance spectra of Zn2-xMxTe3O8 in the visible, in terms of the observed/irregular coordination geometry of the Zn/M-II-O chromophores. We could not however prepare the fully substituted M2Te3O8 (M-II = Co, Ni, Cu) by the direct solid state reaction method. Density Functional Theory (DFT) modeling of the electronic structure of both the parent and the transition metal substituted derivatives provides new insights into the bonding and the role of transition metals toward the origin of color in these materials. We believe that transition metal substituted spiroffites Zn2-xMxTe3O8 reported here suggest new directions for the development of colored inorganic materials/pigments featuring irregular/distorted oxygen coordination polyhedra around transition metal ions.

Li diffusion through doped and defected graphene

We investigate the effect of nitrogen and boron doping on Li diffusion through defected graphene using first principles based density functional theory. While a high energy barrier rules out the possibility of Li-diffusion through the pristine graphene, the barrier reduces with the incorporation of defects. Among the most common defects in pristine graphene, Li diffusion through the divacancy encounters the lowest energy barrier of 1.34 eV. The effect of nitrogen and boron doping on the Li diffusion through doped defected-graphene sheets has been studied. N-doping in graphene with a monovacancy reduces the energy barrier significantly. The barrier reduces with the increasing number of N atoms. On the other hand, for N doped graphene with a divacancy, Li binds in the plane of the sheet, with an enhanced binding energy. The B doping in graphene with a monovacancy leads to the enhancement of the barrier. However, in the case of B-doped graphene with a divacancy, the barrier reduces to 1.54 eV, which could lead to good kinetics. The barriers do not change significantly with B concentration. Therefore, divacancy, B and N doped defected graphene has emerged as a better alternative to pristine graphene as an anode material for Li ion battery.

Fe as Hydrogen/Halogen Bond Acceptor in Square Pyramidal Fe(CO)(5)

Hydrogen bonded complexes formed between the square pyramidal Fe(CO)(5) with HX (X = F, Cl, Br), showing X-H center dot center dot center dot Fe interactions, have been investigated theoretically using density functional theory (DFT) including dispersion correction. Geometry, interaction energy, and large red shift of about 400 cm(-1) in the FIX stretching frequency confirm X-H center dot center dot center dot Fe hydrogen bond formation. In the (CO)(5)Fe center dot center dot center dot HBr complex, following the significant red shift, the HBr stretching mode is coupled with the carbonyl stretching modes. This clearly affects the correlation between frequency shift and binding energy, which is a hallmark of hydrogen bonds. Atoms in Molecule (AIM) theoretical analyses show the presence of a bond critical point between the iron and the hydrogen of FIX and significant mutual penetration. These X-H center dot center dot center dot Fe hydrogen bonds follow most but not all of the eight criteria proposed by Koch and Popelier (J. Phys. Chem. 1995, 99, 9747) based on their investigations on C-H center dot center dot center dot O hydrogen bonds. Natural bond orbital (NBO) analysis indicates charge transfer from the organometallic system to the hydrogen bond donor. However, there is no correlation between the extent of charge transfer and interaction,energy, contrary to what is proposed in the recent IUPAC recommendation (Pure Appl.. Chem. 2011, 83, 1637). The ``hydrogen bond radius'' for iron has been determined to be 1.60 +/- 0.02 angstrom, and not surprisingly it is between the covalent (127 angstrom) and van der Waals (2.0) radii of Fe. DFT and AIM theoretical studies reveal that Fe in square pyramidal Fe(CO)(5) can also form halogen bond with CIF and ClH as ``halogen bond donor''. Both these complexes show mutual penetration as well, though the Fe center dot center dot center dot Cl distance is closer to the sum of van der Waals radii of Fe and Cl in (CO)5Fe center dot center dot center dot ClH, and it is about 1 angstrom less in (CO)(5)Fe center dot center dot center dot ClF.

Proposal for Graphene-Boron Nitride Heterobilayer-Based Tunnel FET

We investigate the gate-controlled direct band-to-band tunneling (BTBT) current in a graphene-boron nitride (G-BN) heterobilayer channel-based tunnel field effect transistor. We first study the imaginary band structure of hexagonal and Bernal-stacked heterobilayers by density functional theory, which is then used to evaluate the gate-controlled current under the Wentzel-Kramers-Brillouin approximation. It is shown that the direct BTBT is probable for a certain interlayer spacing of the G-BN which depends on the stacking orders.

NiS - An unusual self-doped, nearly compensated antiferromagnetic metal

NiS, exhibiting a text-book example of a first-order transition with many unusual properties at low temperatures, has been variously described in terms of conflicting descriptions of its ground state during the past several decades. We calculate these physical properties within first-principle approaches based on the density functional theory and conclusively establish that all experimental data can be understood in terms of a rather unusual ground state of NiS that is best described as a self-doped, nearly compensated, antiferromagnetic metal, resolving the age-old controversy. We trace the origin of this novel ground state to the specific details of the crystal structure, band dispersions and a sizable Coulomb interaction strength that is still sub-critical to drive the system in to an insulating state. We also show how the specific antiferromagnetic structure is a consequence of the less-discussed 90 degrees and less than 90 degrees superexchange interactions built in to such crystal structures.