Ligand effects toward the modulation of magnetic anisotropy and design of magnetic systems with desired anisotropy characteristics

Magnetic anisotropy of a set of octahedral Cr(III) complexes is studied theoretically. The magnetic anisotropy is quantified in terms of zero-field splitting (ZFS) parameter D, which appeared sensitive toward ligand substitution. The increased π-donation capacity of the ligand enhances the magnetic anisotropy of the complexes. The axial π-donor ligand of a complex is found to produce an easy-plane type (D > 0) magnetic anisotropy, while the replacement of the axial ligands with π-acceptors entails the inversion of magnetic anisotropy into the easy-axis type (D < 0). This observation enables one to fabricate a single molecule magnet for which easy-axis type magnetic anisotropy is an indispensable criterion. The equatorial ligands are also found to play a role in tuning the magnetic anisotropy. The magnetic anisotropy property is also correlated with the nonlinear optical (NLO) response. The value of the first hyperpolarizability varies proportionately with the magnitude of the ZFS parameter. Finally, it has also been shown that a rational design of simple octahedral complexes with desired anisotropy characteristics is possible through the proper ligand selection.     

Effect of ionic solutes on the hydrogen bond network dynamics of water: power spectral analysis of aqueous NaCl solutions

To understand the modifications of the hydrogen bond network of water by ionic solutes, power spectra as well as static distributions of the potential energies of tagged solvent molecules and solute ions have been computed from molecular dynamics simulations of aqueous NaCl solutions. The key power spectral features of interest are the presence of high-frequency peaks due to localized vibrational modes, the existence of a multiple time scale or 1/falpha frequency regime characteristic of networked liquids, and the frequency of crossover from 1/falpha type behavior to white noise. Hydrophilic solutes, such as the sodium cation and the chloride anion, are shown to mirror the multiple time scale behavior of the hydrogen bond network fluctuations, unlike hydrophobic solutes which display essentially white noise spectra. While the power spectra associated with tagged H2O molecules are not very sensitive to concentration in the intermediate frequency 1/falpha regime, the crossover to white noise is shifted to lower frequencies on going from pure solvent to aqueous alkali halide solutions. This suggests that new and relatively slow time scales enter the picture, possibly associated with processes such as migration of water molecules from the hydration shell to the bulk or conversion of contact ion pairs into solvent-separated ion pairs which translate into variations in equilibrium transport properties of salt solutions with concentration. For anions, cations, and solvent molecules, the trends in the alpha exponents of the multiple time scale region and the self-diffusivities are found to be strongly correlated.     

Retarded boson-fermion interaction in atomic systems

The retarded interaction between an electron and a spin-0 nucleus is derived from electrodynamical perturbation theory. The contribution of retardation at order v(2)c(2) mimics the Breit interaction [Phys. Rev. 34, 553 (1929); 36, 388 (1930); 39, 616 (1932)] with the Dirac matrix alpha(2) being replaced by p(2)m(2)c where p(2) is the linear momentum operator for the nucleus. An effective one-electron retardation operator is obtained in relative coordinates, and this can be used through all orders in perturbation theory without any problem of infinite degeneracy. A few steps of unitary transformation lead to the nonrelativistic limit. The leading terms in retardation corrections to energy are of order (m(e)m(n))alpha(2)Z(4)(alpha(2)m(e)c(2)). The implications for atomic systems are discussed.     

How happy is your web browsing? A model to quantify satisfaction of an Internet user searching for desired information

We feel happy when web browsing operations provide us with necessary information; otherwise, we feel bitter. How to measure this happiness (or bitterness)? How does the profile of happiness grow and decay during the course of web browsing? We propose a probabilistic framework that models the evolution of user satisfaction, on top of his/her continuous frustration at not finding the required information. It is found that the cumulative satisfaction profile of a web-searching individual can be modeled effectively as the sum of a random number of random terms, where each term is a mutually independent random variable, originating from ‘memoryless’ Poisson flow. Evolution of satisfaction over the entire time interval of a user’s browsing was modeled using auto-correlation analysis. A utilitarian marker, a magnitude of greater than unity of which describes happy web-searching operations, and an empirical limit that connects user’s satisfaction with his frustration level—are proposed too. The presence of pertinent information in the very first page of a website and magnitude of the decay parameter of user satisfaction (frustration, irritation etc.) are found to be two key aspects that dominate the web user’s psychology. The proposed model employed different combinations of decay parameter, searching time and number of helpful websites. The obtained results are found to match the results from three real-life case studies.     

Germanium microsphere high-Q resonator

In this Letter, the fabrication and characterization of a microsphere resonator from the semiconductor germanium is demonstrated. Whispering gallery modes are excited in a 46 μm diameter germanium microsphere resonator using evanescent coupling from a tapered silica optical fiber with a waist diameter of 2 μm. Resonances with Q factors as high as 3.8×10(4) at wavelengths near 2 μm are observed. Because of their ultrahigh optical nonlinearities and extremely broad transparency window, germanium microsphere resonators offer the potential for optical processing devices, in particular at long wavelengths, such as around 2 μm.     

Upper Tail Large Deviations of Regular Subgraph Counts in Erdős-Rényi Graphs in the Full Localized Regime

For a -regular connected graph H the problem of determining the upper tail large deviation for the number of copies of H in , an Erdős-Rényi graph on n vertices with edge probability p, has generated significant interest. For and , where is the number of vertices in H, the upper tail large deviation event is believed to occur due to the presence of localized structures. In this regime the large deviation event that the number of copies of H in exceeds its expectation by a constant factor is predicted to hold at a speed , and the rate function is conjectured to be given by the solution of a mean-field variational problem. After a series of developments in recent years, covering progressively broader ranges of p, the upper tail large deviations for cliques of fixed size were proved by Harel, Mousset, and Samotij in the entire localized regime. This paper establishes the conjecture for all connected regular graphs in the whole localized regime. © 2021 Wiley Periodicals LLC.