Finite size scaling for the atomic Shannon-information entropy

The Journal of Chemical Physics
Qicun Shi, Sabre Kais

Abstract

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values...Continue Reading

References

Nov 1, 1985·Physical Review A: General Physics·S R GadreR D Bendale
Jul 23, 2004·The Journal of Chemical Physics·Alejandro FerrónSabre Kais
Jul 23, 2004·The Journal of Chemical Physics·Qicun ShiDudley R Herschbach

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Citations

Oct 19, 2005·The Journal of Chemical Physics·K D Sen
Apr 20, 2005·The Journal of Chemical Physics·Nicolais L GuevaraRodolfo O Esquivel
Aug 13, 2005·The Journal of Chemical Physics·Robin P Sagar, Nicolais L Guevara
Feb 6, 2008·The Journal of Chemical Physics·Alejandro FerrónSabre Kais
Sep 20, 2018·Physical Chemistry Chemical Physics : PCCP·Leonardo A MillánGustavo A Aucar
Nov 28, 2013·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Alexander OdriazolaAri Harju
May 22, 2008·The Journal of Physical Chemistry. a·Winton MoySabre Kais

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