Complexity of Dirac–Fock atom increases with atomic number

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

“…The utility of this improved complexity has been verified in many fields [15][16][17] and allows reliable detection of periodic, quasiperiodic, linear stochastic, and chaotic dynamics [22][23][24]. The LMC measure is constructed as the product of two important information-theoretic quantities (see below): the so-called disequilibrium D (also known as self-similarity [25] or information energy [26]), which quantifies the departure of the probability density from uniformity [18,19,23] (equiprobability) and the Shannon entropy S, which is a general measure of randomness/uncertainty of the probability density [3], and quantifies the departure of the probability density from localizability.…”

Statistical measure of complexity and correlated behavior of Fermi systems

“…e S and D [50]. The usefulness of the improved version has been shown in many fields [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]. Moreover, the specific measure is suitably tailored for quantum systems, described by their very nature probabilistically via density distributions in position and momentum spaces, which are necessary for and enable a relatively easy calculation of S and D, entering the formulas C LMC = SD or C = e S D. The motivation of the present work, in the spirit of the above statements, is to extend our previous study of uniform Fermi systems [16], beyond information entropy, in order to include the complexity measure proposed by López-Ruiz et al [22], using probability distributions in momentum space.…”

“…Information-theoretical methods play an important role, not just in the clarification of fundamental concepts of quantum mechanics, but also provide a series of results concerning the information content of systems, the presence of interactions, correlation with experimental measured quantities, extraction of universal relations etc [2,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Additionally, many complexity measures have been proposed as indicators of complex behavior found in different systems scattered in a broad spectrum of fields [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48].…”

Statistical Complexity. Applications in Electronic Systems

“…The use of these statistical magnitudes to study the electronic structure of atoms is another interesting application [43][44][45][46][47][48][49][50]20]. The basic ingredient to calculate these statistical indicators is the electron probability density, ρ(r), that can be obtained from the numerically derived Hartree-Fock atomic wave function in the non-relativistic case [45,46], and from the Dirac-Fock atomic wave function in the relativistic case [47].…”