Related papers: The Madelung Problem of Finite Crystals
In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract…
A new method of computing the Madelung constants for hypercubic crystal structures in any dimension $n\geq 2$ is given. It is shown for $n\geq 3$ that the Madelung constant may be obtained in a simple, efficient and unambiguous way as the…
We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles: i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite and…
A direct summation method for the Madelung constant calculation is presented where a crystal lattice is constructed from linear arrays of charges or axial multipoles. An array is designed to have vanishing low order electric moments such…
A general formula is obtained from which the madelung type constant: $$ C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}] $$ extensively used in the finite-size scaling theory is computed…
We present an analytic ansatz to find the effective electrostatic potential and Coulomb correlations in multicenter problems, specifically homogeneous and doped clusters of metal atoms. The approach is based on a quasi-classical…
Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals.…
A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D.…
An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in…
Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…
Macromolecules, when immersed in a polar solvent like water, become charged by a fixed surface charge density which is compensated by ``counter-ions'' moving out of the surface. Such classical particle systems exhibit poor screening…
We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which…
Coulomb systems in which the particles interact through the $d$-dimensional Coulomb potential but are confined in a flat manifold of dimension $d - 1$ are considered. The Coulomb potential is defined with some boundary condition involving a…
We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are…
We demonstrate light-induced localization of Coulomb-interacting particles in multi-dimensional structures. Subwavelength localization of ions within small multi-dimensional Coulomb crystals by an intracavity optical standing wave field is…
Recent experiments have created supersolids of dipolar quantum droplets. The resulting crystals lack, however, a genuine cohesive energy and are maintained by the presence of an external confinement, bearing a resemblance to the case of ion…
The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional…
An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in…
We consider two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we study the two-component plasma in detail. When the coulombic coupling constant $\Gamma=2$ the model is exactly solvable. We…
A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure…