Search results for "localize"
showing 10 items of 300 documents
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
The interaction of surface plasmon polaritons with a silver film edge.
2001
A prism coupling arrangement is used to excite surface plasmons at the surface of a thin silver film and a photon scanning tunnelling microscope is used to detect the evanescent field above the silver surface. Excitation of the silver/air mode of interest is performed at lambda1 = 632.8 nm using a tightly focused beam, while the control of the tip is effected by exciting a counter-propagating surface plasmon field at a different wavelength, lambda2 = 543.5 nm, using an unfocused beam covering a macroscopic area. Propagation of the red surface plasmon is evidenced by an exponential tail extending away from the launch site, but this feature is abruptly truncated if the surface plasmon encount…
Electronic and vibronic problems of nanosized mixed valence clusters: Advances and challenges
2013
Here we discuss the electronic and vibronic problems of mixed valency (MV) in molecular clusters which are of current interest in areas as diverse as solid-state chemistry, biochemistry, and molecular magnetism. Modern research in these areas is focused on the nanosized clusters at the border between classical and quantum scales and for this reason they are particularly difficult to study. First, we describe a general approach to the evaluation of the energy pattern of MV systems containing arbitrary number of localized spins and itinerant electrons with due account for the double exchange and other relevant interactions, like interelectronic Coulomb repulsion in instantly localized configu…
Crystal structures of 2,2′-bipyridin-1-ium 1,1,3,3-tetracyano-2-ethoxyprop-2-en-1-ide and bis(2,2′-bipyridin-1-ium) 1,1,3,3-tetracyano-2-(dicyanometh…
2015
In each of the title compounds, the anion shows evidence of extensive electronic delocalization. A combination of N—H⋯N and X—H⋯N hydrogen bonds links the ions in (I) into a ribbon of alternating centrosymmetric (18) and (26) rings, and those in (II) into simple (7) chains of alternating cations and anion with further cations pendent from the chain.
An ab initio study of the unimolecular decomposition mechanism of formamidine. 4-31G Characterization of potential energy hypersurface
1991
Ab initio MO calculations have been carried out for the unimolecular decomposition of formamidine. The Hartree–Fock method in LCAO approximation with the 4-31G basis set was used. The 4-31G potential hypersurface has been further studied. The stationary points (R, TS, and P) were localized. A reaction analysis by correlation of bond-order indices and localized molecular orbitals demonstrated that the decomposition is an asynchronous process. The TS can be described as four-membered ring.
Rational Design of Single-Ion Magnets and Spin Qubits Based on Mononuclear Lanthanoid Complexes
2012
Here we develop a general approach to calculating the energy spectrum and the wave functions of the low-lying magnetic levels of a lanthanoid ion submitted to the crystal field created by the surrounding ligands. This model allows us to propose general criteria for the rational design of new mononuclear lanthanoid complexes behaving as single-molecule magnets (SMMs) or acting as robust spin qubits. Three typical environments exhibited by these metal complexes are considered, namely, (a) square antiprism, (b) triangular dodecahedron, and (c) trigonal prism. The developed model is used to explain the properties of some representative examples showing these geometries. Key questions in this ar…
Spin Density Distribution in Transition Metal Complexes: Some Thoughts and Hints
1998
Abstract The spin density distribution in transition metal complexes is discussed in qualitative terms, taking into account the coexistence of spin delocalization and spin polarization mechanisms, with the help of numerical results for several complexes obtained from density functional calculations. The covalent character of the metal-ligand bonds as well as the σ- or π-characteristics of the partially filled d orbitals must be taken into account to qualitatively predict the sign of the spin density at a particular atom within a ligand. The same patterns can be applied to binuclear complexes and can be helpful in determining the ferro- or antiferromagnetic character of the exchange coupling…
Variations on Weyl's theorem
2006
AbstractIn this note we study the property (w), a variant of Weyl's theorem introduced by Rakočević, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).
Analysis of Localized Surface Plasmon Resonances in Spherical Jellium Clusters and Their Assemblies
2017
Due to multiple possible applications of physico-chemical properties of plasmonic metal nanoparticles and particle systems, there is high interest to understand the mechanisms that underlie the birth of localized surface plasmon resonance (LSPR). Here we studied the birth of the LSPR in spherical jellium clusters with the density of sodium and with 8, 20, 34, 40, 58, 92, 138, and 186 electrons, by using the linear response time-dependent density functional theory (lr-TDDFT). The coupling of the individual plasmon resonances in dimer, trimer, tetramer, and hexamer cluster assemblies consisting of the 8-electron cluster was also studied. The Kohn-Sham electron-hole transitions contributing to…