Atomic information entropies beyond the Hartree-Fock limit

Abstract

Atomic information entropies are computed from configuration interaction wavefunctions for members of the lithium isoelectronic series. For each member of the series, a sequence of wavefunctions built from increasingly larger basis sets is generated which satisfies a density convergence criterion, and exhibits a monotonic behaviour with respect to the density generated from the wavefunctions. Studies of the behaviour of the entropies along a sequence for a particular atom includes trends which have been shown to be present at the Hartree-Fock level. Results suggest that the position and momentum entropies are sensitive to small changes in density and thus can be useful indicators of the quality of the density. The sum of the entropies is also shown to be a useful indicator when density differences are larger. The nature of the information entropy-energy relationship is examined.

The confined helium atom: An information–theoretic approach

“…Gadre et al [81] and Hô et al [104] used the Shannon entropy as a measure of the quality of the basis set of a free molecular system. They constructed a wave function as an expansion in a certain basis, observing that increasing the number of basis functions resulted in a better wave function, and that the Shannon entropy increased as the quality of the wave function improved.…”

“…Gadre et al [81] and Hô et al [104] used the Shannon entropy as a measure of the quality of the basis set of a free molecular system.…”

Information and complexity measures in molecular reactivity studies

“…The concepts of uncertainty, randomness, and disorder or delocalization are the basic quantities appearing in various chemical applications. In quantum chemistry, the IT objects were used to optimize and improve the basis set, to measure the amount of correlation included in a wavefunction, [20][21][22][23][24] to measure the similarity, [25][26][27][28] and to perform a very promising IT investigation of the molecular bond [29][30][31][32][33][34] and reaction path. [35][36][37][38] One of the challenges is the recognition of the chemical reactivity by employing IT based measures and statistical complexity.…”

Química de la información: aspectos clásicos y cuánticos de fenómenos moleculares

“…El an alisis te orico-informacional, de la densidad electr onica, en atomos y mol eculas surge del inter es de diversos grupos de investigaci on, a nivel mundial, quienes han sido pioneros en el desarrollo de estos conceptos y herramientas aplicables a las ciencias f sicas [43,44,45,46,47,48,49,50,51,52,53,54,55,56]. Estas contribuciones sacaron provecho de los m etodos y conceptos desarrollados por Fisher [13], Frieden [57], Jaynes [21,22,58] R enyi [59], Shannon [20], Tsallis [60], Stam [61], Komolgorov [62], von Neumann [63] y otros m as; los aplicaron y otros m as los mejoraron con la nalidad de poder estudiar sistemas cu anticos nitos.…”

“…La densidad mono-electr onica, y la densidad por part cula, son de gran utilidad para poder explicar propiedades de sistemas N -fermi onicos. Convenientemente, al ser funciones que describen una distribuci on de probabilidades pueden ser, y han sido, analizadas directamente con las medidas te orico-informacionales [54,55,56,110,111] y de complejidad estad stica [112,113] abordadas en las dos secciones anteriores.…”