Some results on a special case of a general continued fraction of Ramanujan

We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\), \(C(q^{2})\), \(C(q^{3})\), \(C(q^{5})\), \(C(q^{7})\), \(C(q^{11})\), \(C(q^{13})\) and \(C(q^{17})\). We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants.     

On dynamic image potential

Self consistent calculations for the dynamic image potential are carried out, taking the finite acceleration of the incoming charge into account. Results indicate that the effect of the inclusion of acceleration is rather small, and the simpler self consistent approach neglecting the acceleration and using a local speed approximation seems to be adequate. Our theoretical framework also provides a mathematical justification of the latter simpler approach which was earlier employed by Ray and Mahan in an ad hoc manner.     

Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8}

Let A? _?(n) denote the number of overpartitions of a non-negative integer n with no part divisible by ?, where ? is a positive integer. In this paper, we prove infinite family of congruences for A? ₅(n) modulo 4, A? ₆(n) modulo 3, and A? ₈(n) modulo 4. In the process, we also prove some other congruences.     

Neutral all metal aromatic half-sandwich complexes between alkaline earth and transition metals: an ab initio exploration

Structural Chemistry - Sandwich complexes find their interests among the chemists after the breakthrough discovery of ferrocene. Since then, a number of sandwich and half-sandwich complexes were...     

Ultra-Weak Metal−Metal Bonding: Is There a Beryllium-Beryllium Triple Bond?

Metal-metal triple bonds featuring s-block element have not been reported until now. Only Be−Be double bonds between have been predicted theoretically based on the intuitive electron donation from four s¹ type electron-donating ligands. Herein, we theoretically predicted a novel species featuring a Be−Be triple bond in the Li₆Be₂ molecule. The molecule was found to be thermodynamically stable. The presence of the triple bond was confirmed by adaptive natural density partitioning (AdNDP), electron localization function (ELF), and atoms in molecules (AIM) analyses. Moreover, the mechanical strength of the Be−Be triple bond was analyzed by using compliance matrix, pointing towards its ultra-weak nature.     

Dynamic response and frequency dependent local field correction for an electron gas system

We present here an approximate scheme to obtain the complex frequency-dependent local field correction,G (q, ω). Using the equation of motion approach we develop here a methodology from which the results obtained by earlier workers, for density-density response function of an electron gas, can be arrived at in a simple systematic manner. We study in detail an approximation made along the similar lines as Singwi and coworkers, which leads to a compact expression for a complex frequency-dependent local field correction. We give results for damping coefficient of long wavelength plasmons which depends on ImG(q, ω). The real and imaginary parts ofG(q, ω) as functions ofω for various values ofq are also calculated. The dynamic structure factorS(q, ω) is evaluated forq=1.6q _F and compared with earlier theoretical and experimental results. An erratum to this article is available at .     

Carbonyl oxide chemistry in water cluster: An extended computational study

An extended computational approach has been utilized to explore the reactions of acids with carbonyl oxide, also known as Criegee intermediate (CI). The reactions were explored inside a water cluster containing 50 water molecules. All possibilities of product formation were considered. Among the considered acids, the rate of 1,4-insertion follows the order HCOO < HCl < HNO₃. The most stable products of the reactions between the considered acids and CI have been identified.     

Dynamic response approach to dynamic image potential

A dielectric response approach to the dynamic image potential of a charged particle approaching a planar metal surface is formulated. A self-consistent scheme for calculating the instantaneous speed of the particle, and its image potential is also derived. It is shown that the scheme does not rely on the actual approximations made while describing the response of the metal with surface. Various approximations are discussed and the corresponding numerical results compared. The effect of self-consistency and inclusion of dispersion in metal is noticeable.