{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T14:46:22Z","timestamp":1787064382799,"version":"build-2736575974"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,25]],"date-time":"2019-12-25T00:00:00Z","timestamp":1577232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11204243"],"award-info":[{"award-number":["11204243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004775","name":"Natural Science Foundation of Gansu Province","doi-asserted-by":"publisher","award":["1506RJYA131"],"award-info":[{"award-number":["1506RJYA131"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Northwest Normal University","award":["NWNU-LKQN-10-7"],"award-info":[{"award-number":["NWNU-LKQN-10-7"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Discrete Shannon entropy was introduced in view of the mathematical properties of multiconfiguration methods and then used to interpret the information in atomic states expressed by the multiconfiguration Dirac\u2013Hartree\u2013Fock wavefunction for Ni-like isoelectronic sequence. Moreover, the relationship between the concepts, including sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction, was clarified by induction on the basis of the present calculation of the energy structure for Ni-like isoelectronic sequence. It was found that there is an interesting connection between the change of Shannon entropies and eigenlevel anticrossings, along with the nuclear charge Z, which is helpful to conveniently locate the position of eigenlevel anticrossings and information exchanging and understand them from the point of view of information, besides the traditional physical concepts. Especially, it is concluded that in a given configuration space eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, which is also a sufficient condition for information exchange.<\/jats:p>","DOI":"10.3390\/e22010033","type":"journal-article","created":{"date-parts":[[2019,12,25]],"date-time":"2019-12-25T11:07:48Z","timestamp":1577272068000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Shannon Entropy in Configuration Space for Ni-Like Isoelectronic Sequence"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7153-0728","authenticated-orcid":false,"given":"Jianjie","family":"Wan","sequence":"first","affiliation":[{"name":"College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Na","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113001","DOI":"10.1103\/PhysRevLett.91.113001","article-title":"Shannon entropy as an indicator of atomic avoided crossings in strong parallel magnetic and electric fields","volume":"91","author":"Dehesa","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1140\/epjd\/e2015-60397-7","article-title":"Shannon entropy as an indicator of atomic avoided crossings for Rydberg potassium atoms interacting with a static electric field","volume":"69","author":"He","year":"2015","journal-title":"Eur. Phys. J. D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1103\/PhysRevA.50.267","article-title":"Structure of compound states in the chaotic spectrum of the Ce atom: Localization properties, matrix elements, and enhancement of weak perturbations","volume":"50","author":"Flambaum","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0370-1573(96)00007-5","article-title":"The nuclear shell model as a testing ground for many-body quantum chaos","volume":"276","author":"Zelevinsky","year":"1996","journal-title":"Phys. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1103\/PhysRevA.22.551","article-title":"Oscillator-strength trends in the presence of level crossings","volume":"22","author":"Fischer","year":"1980","journal-title":"Phys. Rev. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1103\/PhysRevA.50.3065","article-title":"Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom","volume":"50","author":"Dehesa","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"91","DOI":"10.4310\/MAA.1997.v4.n1.a7","article-title":"Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and coulomb potentials","volume":"4","author":"Dehesa","year":"1997","journal-title":"Meth. Appl. Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0377-0427(00)00633-6","article-title":"Quantum information entropies and orthogonal polynomials","volume":"133","author":"Dehesa","year":"2001","journal-title":"J. Comput. Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.cam.2004.09.040","article-title":"Information measures of hydrogenic systems, Laguerre polynomials and spherical harmonics","volume":"179","author":"Dehesa","year":"2005","journal-title":"J. Comput. Appl. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"074110","DOI":"10.1063\/1.2008212","article-title":"Characteristic features of Shannon information entropy of confined atoms","volume":"123","author":"Sen","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/S0009-2614(03)00669-9","article-title":"Diamagnetic informational exchange in hydrogenic avoided crossings","volume":"373","author":"Dehesa","year":"2003","journal-title":"Chem. Phys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"042511","DOI":"10.1103\/PhysRevA.90.042511","article-title":"Relativistic global and local divergences in hydrogenic systems: A study in position and momentum spaces","volume":"90","author":"Angulo","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.cplett.2015.05.029","article-title":"Shannon information entropy in position space for two-electron atomic systems","volume":"633","author":"Lin","year":"2015","journal-title":"Chem. Phys. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"422","DOI":"10.3390\/atoms3030422","article-title":"Quantum entanglement and Shannon information entropy for the doubly excited resonance state in positronium negative ion","volume":"3","author":"Lin","year":"2015","journal-title":"Atoms"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e25375","DOI":"10.1002\/qua.25375","article-title":"Benchmark values of Shannon entropy for spherically confined hydrogen atom","volume":"117","author":"Jiao","year":"2017","journal-title":"Int. J. Quantum Chem."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ou, J.H., and Ho, Y.K. (2017). Shannon information entropy in position space for the ground and singly excited states of helium with finite confinements. Atoms, 5.","DOI":"10.3390\/atoms5020015"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.physa.2017.02.003","article-title":"On the correlation measure of two-electron systems","volume":"474","author":"Saha","year":"2017","journal-title":"Physica A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4742","DOI":"10.1039\/b916509f","article-title":"Shannon entropy as a new measure of aromaticity, Shannon aromaticity","volume":"12","author":"Noorizadeh","year":"2010","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0375-9601(95)00867-5","article-title":"A statistical measure of complexity","volume":"209","author":"Mancini","year":"1995","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"011102","DOI":"10.1103\/PhysRevE.66.011102","article-title":"Features of the extension of a statistical measure of complexity to continuous systems","volume":"66","author":"Garay","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"032502","DOI":"10.1103\/PhysRevA.76.032502","article-title":"Fisher-Shannon analysis of ionization processes and isoelectronic series","volume":"76","author":"Sen","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.physleta.2007.07.077","article-title":"Fisher-Shannon plane and statistical complexity of atoms","volume":"372","author":"Angulo","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5283","DOI":"10.1016\/j.physleta.2008.06.012","article-title":"Statistical complexity and Fisher-Shannon information in the H-atom","volume":"372","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.cplett.2007.07.003","article-title":"Complexity of Dirac-Fock atom increases with atomic number","volume":"444","author":"Borgoo","year":"2007","journal-title":"Chem. Phys. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0010-4655(91)90133-6","article-title":"The MCHF atomic-structure package","volume":"64","author":"Fischer","year":"1991","journal-title":"Comput. Phys. Comm."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Grant, I.P. (2007). Relativistic Quantum Theory of Atoms and Molecules, Springer.","DOI":"10.1007\/978-0-387-35069-1"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"023102","DOI":"10.1088\/0256-307X\/32\/2\/023102","article-title":"Shannon entropy as a measurement of the information in a multiconfiguration Dirac-Fock wavefunction","volume":"32","author":"Wan","year":"2015","journal-title":"Chin. Phys. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"152","DOI":"10.7498\/aps.56.152","article-title":"Theoretical study of forbidden M1, M2, E2 transitions for highly charged Ni-like ions","volume":"56","author":"Wan","year":"2007","journal-title":"Acta. Phys. Sin."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1088\/0031-8949\/43\/2\/006","article-title":"Transition rates and wavelengths in the X-ray spectra of nickel-like ions (Ag XX-Pb LV)","volume":"43","author":"Quinet","year":"1991","journal-title":"Phys. Scr."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"052505","DOI":"10.1103\/PhysRevA.62.052505","article-title":"Relativistic many-body calculations of excitation energies and oscillator strengths in Ni-like ions","volume":"62","author":"Safronova","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1103\/PhysRevA.11.97","article-title":"Comparison of doubly-excited helium energy levels, isoelectronic series, autoionization lifetimes, and group-theoretical configuration-mixing predictions with large-configuration-interaction calculations and experimental spectra","volume":"11","author":"Herrick","year":"1975","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0065-2199(08)60335-8","article-title":"Doubly excited states, including new classification schemes","volume":"22","author":"Lin","year":"1986","journal-title":"Adv. At. Mol. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1016\/j.radphyschem.2006.05.001","article-title":"The search for quantum chaos: From celestial mechanics to the helium atom","volume":"75","author":"Schlachter","year":"2006","journal-title":"Radiat. Phys. Chem."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Blatt, J.M., and Weisskopf, V.F. (1979). Theoretical Nuclear Physics, Springer.","DOI":"10.1007\/978-1-4612-9959-2"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:45:39Z","timestamp":1760190339000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,25]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010033"],"URL":"https:\/\/doi.org\/10.3390\/e22010033","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,25]]}}}