Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

Alcoba, Diego R.; Torre, Alícia; Laín, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.; Ayers, Paul W.; Raemdonck, Mario Van; Bultinck, Patrick; Neck, Dimitri Van

doi:10.1007/s00214-016-1905-x

Cited by 19 publications

(10 citation statements)

References 49 publications

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“…Former measures extent of concentration of the system wave function in respective space, whereas latter symbolizes expectation values of density. S has its application in illuminating colin conjecture, atomic avoided crossing, orbital free density functional theory [52][53][54][55][56] in many-electron systems, etc. Likewise, E has been widely used to estimate correlation energy and first ionisation potential [40].…”

Section: Introductionmentioning

confidence: 99%

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Mukherjee

Roy

2018

Eur. Phys. J. D

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Rényi entropy (R), Tsallis entropy (T ), Shannon entropy (S), and Onicescu energy (E) are studied in a spherically confined H atom (CHA), in conjugate space, with special emphasis on non-zero l states. This work is a continuation of our recently published work [1]. Representative calculations are done by employing exact analytical wave functions in r space. Accurate p space-wave functions are generated numerically by performing Fourier transform on respective r-space counterparts.Further, these are extended for H-isoelectronic series by applying the scaling relations. R, T are evaluated by choosing the order of entropic moments (α, β) as ( 3 5 , 3) in r and p spaces. Detailed, systematic results of all these measures with respect to variations of confinement radius r c are offered here for arbitrary n, l quantum numbers. For a given n, at small r c , R α r , T α r , S r collapse with rise of l, attain a minimum, then again grow up. Growth in r c shifts the point of inflection towards higher l values. An increase in Z enhances localization of a particular state. Several other new interesting inferences are uncovered. Comparison with literature results (available only for S in 2p, 3d states), offers excellent agreement. Confinement of an atom or molecule inside an impenetrable cavity was first studied in the fourth decade of twentieth century [2]. Progress of research on such quantum systems was reviewed several times [2-5] recording their importance in both fundamental physics and chemistry as well as in various engineering branches. They have relevance in many different physical situations, e.g., atoms under plasma environment, impurities in crystal lattice and semiconductor materials, trapping of atoms/molecules in zeolite cages or inside an endohedral cobweb of fullerenes, quantum wells, quantum wires, quantum dots [6] and so forth. Furthermore, such models were designed to mimic the high pressure environment inside the core of planets. Also, they have contemporary significance in interpreting various astrophysical phenomena [7] and many other interesting areas.Theoretical study of a Hydrogen atom within an infinite spherical cavity was first published in 1937 [8]. Over the years, this simple confined hydrogen atom (CHA) model has served as a precursor to improve our understanding about the consequences of confinement in atomic electronic structure. In last decade, a CHA under the influence of various restricted environment has been extensively followed. Majority of these investigations include trapping of H atom either in a spherical box of penetrable, impenetrable walls or inside a hard box of different geometrical shape and size [5,[9][10][11][12]. In the realm of atomic physics, CHA provides us with many attractive physical and chemical properties. Numerous theoretical methods like perturbation theory, Padé approximation, WKB method, Hypervirial theorem, power-series solution, Lie algebra, Lagrange-mesh method, asymptotic iteration method, generalized pseudo-spectral (GPS) method were invoked for their prop...

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Section: Introductionmentioning

confidence: 99%

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Mukherjee

Roy

2018

Eur. Phys. J. D

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“…Therefore, in this occasion, disequilibrium and information energy have same form. Like the previous measures, it is also utilized in orbital-free DFT [105], testing normality [136], electron correlation [110], Colin conjecture [100,101], configuration interaction [137] etc. By definition, E refers to the 2nd-order entropic moment [127]; for central Neetik Mukherjee and Amlan K. Roy potential it assumes the form (E t is the Onicescu energy product),…”

Section: Onicescu Energy (E)mentioning

confidence: 99%

Information analysis in free and confined harmonic oscillator

Mukherjee¹,

Roy²

2021

Preprint

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In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator (CHO). Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology, etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information (I), Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T ), Onicescu energy (E) and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physico-chemical properties of a system under investigation. Kullback-Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another.The one-dimensional confined harmonic oscillator (1DCHO), defined by v), can be classified into two forms, (a) symmetrically confined harmonic oscillator (SCHO) (when d m = 0), (b) asymmetrically confined harmonic oscillator (ACHO) (corresponding to d m = 0). Further, in latter case, confinement can be accomplished two different ways: (i) by changing the box boundary, keeping box length and d m fixed at zero; (ii) another route is to adjust d m by keeping box length and boundary fixed. SCHO can be treated as an intermediate between a particle-ina-box (PIB) and a 1DQHO. Though the Schrödinger equation for SCHO can be solved exactly, for ACHO it cannot be. We have employed two different methods for the latter, viz., (i) an imaginary time propagation (ITP), leading to minimization of an expectation value (ii) a variation-induced exact diagonalization procedure that utilizes SCHO eigenfunctions as basis. It is found that, at very low x c region, I, S, R, T, E remain invariant with change confinement length, x c . At moderate x c region S x , R x , T x progress and I x , E x decrease with rise in x c . Additionally, special attention has been paid to study relative information in SCHO and ACHO.Analogously, a 3DCHO (radically confined within an impenetrableFree and confined harmonic oscillator • • • spherical well) can act as a bridge between particle in a spherical box (PISB) and isotropic 3DQHO. The time-independent Schrödinger equation for D-dimensional harmonic oscillator in both free and confined condition can be solved exactly, within a Dirichlet boundary condition. Here a detailed exploration of information measures has been carried out in r and p spaces, for a 3DCHO. Some ex...

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“…While rotation of the orbitals can be addressed by orbital optimization or other techniques, most of those strategies only find a local minimum. [22,23,53,95,[113][114][115][116] A sensible permutation of orbitals therefore needs to be selected from the beginning.…”

Section: F Strategies For Assigning Orbitals To Setsmentioning

confidence: 99%

Strategies for extending geminal-based wavefunctions: Open shells and beyond

Johnson

Limacher

Kim

et al. 2017

Computational and Theoretical Chemistry

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We discuss some strategies for extending recent geminal-based methods to open-shells by replacing the geminal-creation operators with more general composite boson creation operators, and even creation operators that mix fermionic and bosonic components. We also discuss the utility of symmetry-breaking and restoration, but using a projective (not a variational) approach. Both strategies-either together or separately-give a pathway for extending geminals-based methods to open shells, while retaining the computational efficiency and conceptual simplicity of existing geminal product wavefunctions.

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Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

Cited by 19 publications

References 49 publications

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Information analysis in free and confined harmonic oscillator

Strategies for extending geminal-based wavefunctions: Open shells and beyond

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