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Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed.

Shannon entropy (S), Fisher information (I) and a measure equivalent to Fisher-Shannon complexity (C IS ) of a ro-vibrational state of diatomic molecules (O 2 , O + 2 , NO, NO + ) with generalized Kratzer potential is analyzed. Exact analytical expression of I r is derived for the arbitrary state, whereas the same could be done for I p with {n, ℓ, m = 0} state. It is found that shifting from neutral to the cationic system, I r increases while S r decreases, consistent with the interpretation of a localization in the probability distribution. Additionally, this study reveals that C IS increases with the number of nodes in a system.Ever since the early days of quantum mechanics, diatomic molecular potentials have received much attention due to their importance to describe intra-molecular and intermolecular interactions as well as atomic-pair correlations. Over the years, a large number of such potentials have been adopted in a multitude of physical/chemical problems. Since the literature is quite vast, here we mention a few prominent ones, such as generalized Morse, Mie, Kratzer-Fues, pseudoharmonic, non-central, deformed Rosen-Morse, generalized Woods-Saxon, Pöschl-Teller potential etc [1]. They have fundamental relevance and utility in quantum description of natural phenomena, processes and systems, not only in the 3D world, but also in non-relativistic and relativistic D-dimensional physics. This work focuses on generalized Kratzer (Kratzer-type) potential, which is a simple realistic zero-order model for describing the vibration-rotation motion of diatomic molecules. It has importantproperties like (i) correct asymptotic behaviour at r = 0 and r = ∞ (ii) exactly solvable for a given state with an arbitrary angular momentum (iii) allows the system to dissociate, which is forbidden for a harmonic oscillator-based model. The mixed energy spectrum of this potential contains both discrete and continuum parts, corresponding to bound and scattering states respectively. While bound-state wave functions have been widely used in studies related to molecular spectroscopy, latter states are important in the context of the photo-dissociation process, diatomic molecular scattering, radiative recombination in an atom-atom collision [2], etc. Recently its use as a universal potential for diatomic molecules has been reported in two excellent review articles [3,4]. Apart from these, this has also been heavily studied in molecular, chemical and solid-state physics, due to its general feature of true interaction energy as well as interatomic, inter-molecular and dynamical properties [5][6][7].In recent years, there has been a burgeoning activity in studies related to informationtheoretic measures in quantum chemical systems. The delocalizing properties of electronic distribution that characterize the quantum states of these molecular potentials have been analyzed quite extensively by information theoretical tools such as Shannon entropy (S) [8], Fisher information (I) [9], Rényi entropy (R) [10], Tsallis entropy (T ) [11] and Onic...

Several well-known statistical measures similar to LMC and Fisher-Shannon complexity have been computed for confined hydrogen atom in both position (r) and momentum (p) spaces. Further, a more generalized form of these quantities with Rényi entropy (R) is explored here. The role of scaling parameter in the exponential part is also pursued. R is evaluated taking order of entropic moments α, β as ( 2 3 , 3) in r and p spaces. Detailed systematic results of these measures with respect to variation of confinement radius r c is presented for low-lying states such as, 1s-3d, 4f and 5g.For nodal states, such as 2s, 3s and 3p, as r c progresses there appears a maximum followed by a minimum in r space, having certain values of the scaling parameter. However, the corresponding p-space results lack such distinct patterns. This study reveals many other interesting features.Quantum particles experience intense changes in their physical and chemical properties under spatial confinement. Spherically confined quantum systems have been explored extensively [1], with wide-spread applications in quantum dot, quantum wells and quantum wires, etc. Dramatic changes in various observable properties such as energy spectrum, transition frequencies, transition probabilities, polarizability, chemical reactivity, ionization potential etc., were reported to occur under such situations [1,2].Recently there has been a growing interest in using statistical quantities namely, Fisher information (I), Onicescu energy (E), Shannon entropy (S) and Rényi entropy (R) as descriptors of certain chemical, physical properties of a quantum system. Along these lines, complexity, another relevant concept, is directly related to aforementioned measures, representing their combined effect. A universal characterization has not been possible, but can be proposed as an indicator of pattern, structure or correlation associated with the distribution function in a given system. It depends on the scale of observation, and constitutes an important area of research with contemporary interest in disordered systems, spatial patterns, language, multi-electronic systems, molecular or DNA analysis, social science, [3][4][5][6] etc.An atom is a complex system; restricting its motion in an enclosure makes it even more fascinating according to a complex world [7,8]. Complexity, in a system, arises due to breakdown of certain symmetry rules. For finite complexity, the system is either in a state having some less than maximal order or not in equilibrium. Stated differently, it vanishes at two limiting cases, viz., when it is (a) at equilibrium (maximum disorder) or b) completely ordered (maximum distance from equilibrium) [8,9]. It gives a qualitative idea of organization in a system and is considered as a general indicator of structure and correlation. In literature various definitions are available; some of them are Shiner, Davidson, Landsberg (SDL) [10-12], López-Ruiz, Mancini, Calbet (LMC) shape (C LM C ) [13-16], Fisher-Shannon (C IS ) [17, 18], Cramér-Rao [18-20] or Genera...

An atom placed inside a cavity of finite dimension offers many interesting features, and thus has been a topic of great current activity. This work proposes a density functional approach to pursue both ground and excited states of a multi‐electron atom under a spherically impenetrable enclosure. The radial Kohn‐Sham (KS) equation has been solved by invoking a physically motivated work‐function‐based exchange potential, which offers near‐Hartree‐Fock‐quality results. Accurate numerical eigenfunctions and eigenvalues are obtained through a generalized pseudospectral method (GPS) fulfilling the Dirichlet boundary condition. Two correlation functionals, viz., (i) simple, parametrized local Wigner‐type, and (ii) gradient‐ and Laplacian‐dependent non‐local Lee‐Yang‐Parr (LYP) functionals are adopted to analyze the electron correlation effects. Preliminary exploratory results are offered for ground states of He‐isoelectronic series (Z = 2 − 4), as well as Li and Be atom. Several low‐lying singly excited states of He atom are also reported. These are compared with available literature results–which offers excellent agreement. Radial densities as well as expectation values are also provided. The performance of correlation energy functionals are discussed critically. In essence, this presents a simple, accurate scheme for studying atomic systems inside a hard spherical box within the rubric of KS density functional theory.