{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:57Z","timestamp":1760243577692,"version":"build-2065373602"},"reference-count":91,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2013,9,26]],"date-time":"2013-09-26T00:00:00Z","timestamp":1380153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An information-theoretical complexity analysis of the SN2 exchange reaction for CH3Cl + F\u2212 is performed in both position and momentum spaces by means of the following composite functionals of the one-particle density: D-L and I-J planes and Fisher-Shannon\u2019s (FS) and L\u00f3pez-Ruiz-Mancini-Calbet (LMC) shape complexities. It was found that all the chemical concepts traditionally assigned to elementary reactions such as the breaking\/forming regions (B-B\/F), the charge transfer\/reorganization and the charge repulsion can be unraveled from the phenomenological analysis performed in this study through aspects of localizability, uniformity and disorder associated with the information-theoretical functionals. In contrast, no energy-based functionals can reveal the above mentioned chemical concepts. In addition, it is found that the TS critical point for this reaction does not show any chemical meaning (other than the barrier height) as compared with the concurrent processes revealed by the information-theoretical analysis. Instead, it is apparent from this study that a maximum delocalized state could be identified in the transition region which is associated to the charge transfer process as a new concurrent phenomenon associated with the charge transfer region (CT) for the ion-complex is identified. Finally it is discussed why most of the chemical features of interest (e.g., CT, B-B\/F) are only revealed when some information-theoretic properties are taken into account, such as localizability, uniformity and disorder.<\/jats:p>","DOI":"10.3390\/e15104084","type":"journal-article","created":{"date-parts":[[2013,9,26]],"date-time":"2013-09-26T12:48:59Z","timestamp":1380199739000},"page":"4084-4104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Concurrent Phenomena at the Reaction Path of the  SN2 Reaction CH3Cl + F\u2212. Information Planes and  Statistical Complexity Analysis"],"prefix":"10.3390","volume":"15","author":[{"given":"Moyocoyani","family":"Molina-Esp\u00edritu","sequence":"first","affiliation":[{"name":"Departamento de Qu\u00edmica, Universidad Aut\u00f3noma Metropolitana-Iztapalapa, M\u00e9xico D.F. 09340, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodolfo","family":"Esquivel","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica, Universidad Aut\u00f3noma Metropolitana-Iztapalapa, M\u00e9xico D.F. 09340, Mexico"},{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, Granada 18071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan","family":"Angulo","sequence":"additional","affiliation":[{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, Granada 18071, Spain"},{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada,  Granada 18071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4397-9426","authenticated-orcid":false,"given":"Jes\u00fas","family":"Dehesa","sequence":"additional","affiliation":[{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, Granada 18071, Spain"},{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada,  Granada 18071, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1139\/v76-234","article-title":"Gas-phase reactions of anions with halogenated methanes at 297 \u00b1 2 K","volume":"54","author":"Tanaka","year":"1976","journal-title":"Can. J. Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3715","DOI":"10.1021\/ja00508a002","article-title":"Gas phase nucleophilic displacement reactions of negative ions with carbonyl compounds","volume":"101","author":"Asubiojo","year":"1979","journal-title":"J. Am. Chem. Soc."},{"key":"ref_3","first-page":"427","article-title":"Structure-reactivity coefficients. Do they measure transition state structure?","volume":"13","author":"Pross","year":"1989","journal-title":"Nouv. J. Chim."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7351","DOI":"10.1021\/ja0004635","article-title":"Experimental and theoretical evaluation of energetics for nucleophilic solvent participation in the solvolysis of tertiary alkyl chlorides on the basis of gas phase bridgehead carbocation stabilities","volume":"122","author":"Takeuchi","year":"2000","journal-title":"J. Am. Chem. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1021\/ja993093x","article-title":"Reactivity and secondary kinetic isotope effects in the SN2 reaction mechanism: Dioxygen radical anion and related nucleophiles","volume":"122","author":"Davico","year":"2000","journal-title":"J. Am. Chem. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1021\/jp993066t","article-title":"Direct ab initio dynamics study on a gas phase microsolvated SN2 Reaction of F-(H2O) with CH3Cl","volume":"104","author":"Tachikawa","year":"2000","journal-title":"J. Phys. Chem. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2925","DOI":"10.1021\/ja9940221","article-title":"Theoretical examination of solvent reorganization and nonequilibrium solvation effects in microhydrated reactions","volume":"122","author":"Okuno","year":"2000","journal-title":"J. Am. Chem. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7724","DOI":"10.1021\/ja984315e","article-title":"Intrinsic barriers in identity SN2 reactions and the periodic table","volume":"121","author":"Hoz","year":"1999","journal-title":"J. Am. Chem. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8783","DOI":"10.1021\/ja000881+","article-title":"Non-statistical effects in the gas phase SN2 reaction","volume":"122","author":"Tonner","year":"2000","journal-title":"J. Am. Chem. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1021\/ja00187a007","article-title":"Transition-state electronic structures in SN2 reactions","volume":"111","author":"Shi","year":"1989","journal-title":"J. Am. Chem. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9160","DOI":"10.1021\/ja00073a035","article-title":"Theoretical investigation on base-induced 1, 2-eliminations in the model system fluoride ion+ fluoroethane. The role of the base as a catalyst","volume":"115","author":"Bickelhaupt","year":"1993","journal-title":"J. Am. Chem. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1021\/ja00112a016","article-title":"Gas-phase identity SN2 reactions of halide anions with methyl halides: a high-level computational study","volume":"117","author":"Glukhovtsev","year":"1995","journal-title":"J. Am. Chem. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6273","DOI":"10.1021\/ja953665n","article-title":"Gas-phase non-identity SN2 reactions of halide anions with methyl halides: A high-level computational study","volume":"118","author":"Glukhovtsev","year":"1996","journal-title":"J. Am. Chem. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1021\/jp0031000","article-title":"Benchmark ab initio energy profiles for the gas-phase SN2 reactions Y-+ CH3X\u2192 CH3Y+ X-(X, Y= F, Cl, Br). Validation of hybrid DFT methods","volume":"105","author":"Parthiban","year":"2001","journal-title":"J. Phys. Chem. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"11327","DOI":"10.1021\/jp012892a","article-title":"Assessment of density functional theory for model SN2 reactions: CH3X+ F-(X= F, Cl, CN, OH, SH, NH2, PH2)","volume":"105","author":"Gonzales","year":"2001","journal-title":"J. Phys. Chem. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1021\/ar030162a","article-title":"A conversation on VB vs MO theory: A never-ending rivalry?","volume":"36","author":"Hoffmann","year":"2003","journal-title":"Acc. Chem. Res."},{"key":"ref_17","unstructured":"Lawley, K.P. (2007). Advances in Chemical Physics: Ab Initio Methods in Quantum Chemistry Part I, Wiley."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1021\/ar00072a001","article-title":"The path of chemical reactions-the IRC approach","volume":"14","author":"Fukui","year":"1981","journal-title":"Accounts Chem. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2657","DOI":"10.1021\/j100238a002","article-title":"Development of transition-state theory","volume":"87","author":"Laidler","year":"1983","journal-title":"J. Phys. Chem."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2664","DOI":"10.1021\/j100238a003","article-title":"Current status of transition-state theory","volume":"87","author":"Truhlar","year":"1983","journal-title":"J. Phys. Chem."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1021\/ja00080a030","article-title":"Is the avoided crossing state a good approximation for the transition state of a chemical reaction? An analysis of Menschutkin and ionic SN2 reactions","volume":"116","author":"Shaik","year":"1994","journal-title":"J. Am. Chem. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1021\/ja01607a027","article-title":"A correlation of reaction rates","volume":"77","author":"Hammond","year":"1955","journal-title":"J. Am. Chem. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1126\/science.117.3039.340","article-title":"Parameters for the description of transition states","volume":"117","author":"Leffler","year":"1953","journal-title":"Science"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1063\/1.1749604","article-title":"The Activated Complex in Chemical Reactions","volume":"3","author":"Eyring","year":"1935","journal-title":"J. Chem. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1039\/tf9383400029","article-title":"The transition state method","volume":"34","author":"Wigner","year":"1938","journal-title":"Trans. Faraday Soc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1126\/science.242.4886.1645","article-title":"Laser femtochemistry","volume":"242","author":"Zewail","year":"1988","journal-title":"Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5660","DOI":"10.1021\/jp001460h","article-title":"Femtochemistry: Atomic-scale dynamics of the chemical bond","volume":"104","author":"Zewail","year":"2000","journal-title":"J. Phys. Chem. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6345","DOI":"10.1063\/1.465873","article-title":"Experimental and theoretical studies of the F + H2 transition state region via photoelectron spectroscopy of FH\u22122","volume":"99","author":"Bradforth","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1021\/ja00004a002","article-title":"Charge development at the transition state: a second-order Moeller-Plesset perturbation study of gas-phase SN2 reactions","volume":"113","author":"Shi","year":"1991","journal-title":"J. Am. Chem. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6788","DOI":"10.1021\/ja00310a007","article-title":"Toward a theory of chemical reactivity based on the charge density","volume":"107","author":"Bader","year":"1985","journal-title":"J. Am. Chem. Soc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/0009-2614(89)85027-4","article-title":"Maximization of entropy during a chemical reaction","volume":"164","author":"Balakrishnan","year":"1989","journal-title":"Chem. Phys. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1021\/jp0028711","article-title":"Toward a density-based representation of reactivity: SN2 reaction","volume":"105","author":"Knoerr","year":"2001","journal-title":"J. Phys. Chem. A"},{"key":"ref_33","unstructured":"Shaik, S.S., Schlegel, H.B., and Wolfe, S. (1992). Theoretical Aspects of Physical Organic Chemistry: The SN2 Mechanism, Wiley."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1063\/1.1384012","article-title":"Electronic energy density in chemical reaction systems","volume":"115","author":"Tachibana","year":"2001","journal-title":"J. Chem. Phys."},{"key":"ref_35","unstructured":"Coulson, C.A. (1961). Valence, Oxford University Press. [2nd ed.]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1007\/s00894-008-0431-8","article-title":"The reaction force and the transition region of a reaction","volume":"15","author":"Murray","year":"2009","journal-title":"J. Mol. Model."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2619","DOI":"10.1080\/00268970701604663","article-title":"A new perspective on chemical and physical processes: The reaction force","volume":"105","author":"Murray","year":"2007","journal-title":"Mol. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s00894-008-0400-2","article-title":"Analysis of diatomic bond dissociation and formation in terms of the reaction force and the position-dependent reaction force constant","volume":"15","author":"Murray","year":"2009","journal-title":"J. Mol. Model."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1021\/jp807754f","article-title":"Theoretical study of the regioselectivity of [2 + 2] photocycloaddition reactions of acrolein with olefins","volume":"113","author":"Jaque","year":"2008","journal-title":"J. Phys. Chem. A"},{"key":"ref_40","first-page":"476","article-title":"Analyzing Kullback\u2013Leibler information profiles: An indication of their chemical relevance","volume":"11","author":"Borgoo","year":"2009","journal-title":"Phys. Chem."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRevA.30.620","article-title":"Information entropy and Thomas-Fermi theory","volume":"30","author":"Gadre","year":"1984","journal-title":"Phys. Rev. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/0009-2614(85)85222-2","article-title":"Analysis of atomic electron momentum densities: Use of information entropies in coordinate and momentum space","volume":"117","author":"Gadre","year":"1985","journal-title":"Chem. Phys. Lett."},{"key":"ref_43","first-page":"970","article-title":"Information entropies in quantum chemistry","volume":"54","author":"Gadre","year":"1985","journal-title":"Curr. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1103\/PhysRevA.32.2602","article-title":"Some novel characteristics of atomic information entropies","volume":"32","author":"Gadre","year":"1985","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1063\/1.445972","article-title":"Maximum\u2010entropy inference and momentum density approach@fa@f","volume":"79","author":"Koga","year":"1983","journal-title":"J. Chem. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"8028","DOI":"10.1073\/pnas.81.24.8028","article-title":"Transcription of ground-state density-functional theory into a local thermodynamics","volume":"81","author":"Ghosh","year":"1984","journal-title":"Proc. Natl. Acad. Sci.USA"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"6485","DOI":"10.1063\/1.463710","article-title":"Tight rigorous bounds to atomic information entropies","volume":"97","author":"Angulo","year":"1992","journal-title":"J. Chem. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/S0375-9601(98)00524-6","article-title":"Universal property of the information entropy in atoms, nuclei and atomic clusters","volume":"246","author":"Massen","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"7391","DOI":"10.1021\/jp004414q","article-title":"Information theory thermodynamics of molecules and their Hirshfeld fragments","volume":"105","author":"Nalewajski","year":"2001","journal-title":"J. Phys. Chem. A"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9401","DOI":"10.1063\/1.1615765","article-title":"Fisher information in density functional theory","volume":"119","author":"Nagy","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"8906","DOI":"10.1063\/1.1697374","article-title":"The Fisher\u2013Shannon information plane, an electron correlation tool","volume":"120","author":"Romera","year":"2004","journal-title":"J. Chem. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.cplett.2004.03.118","article-title":"Order of Coulomb and Fermi pairs: Application in a \u03c0-system","volume":"389","author":"Karafiloglou","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"ref_53","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_54","doi-asserted-by":"crossref","first-page":"3957","DOI":"10.1021\/jp0404596","article-title":"What is an atom in a molecule?","volume":"109","author":"Parr","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1140\/epjd\/e2004-00182-3","article-title":"Characterization of atomic avoided crossings by means of Fisher\u2019s information","volume":"32","author":"Dehesa","year":"2005","journal-title":"Eur. Phys. J. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"084101","DOI":"10.1063\/1.1848092","article-title":"Local correlation measures in atomic systems","volume":"122","author":"Guevara","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.chemphys.2004.08.020","article-title":"Discontinuity of Shannon information entropy for two-electron atoms","volume":"309","author":"Shi","year":"2005","journal-title":"Chem. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"174111","DOI":"10.1063\/1.2121610","article-title":"Information entropy, information distances, and complexity in atoms","volume":"123","author":"Chatzisavvas","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"074117","DOI":"10.1063\/1.2263710","article-title":"Information entropies for eigendensities of homogeneous potentials","volume":"125","author":"Sen","year":"2006","journal-title":"J. Chem. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.cplett.2006.05.013","article-title":"Fisher information in a two-electron entangled artificial atom","volume":"425","author":"Nagy","year":"2006","journal-title":"Chem. Phys. Lett."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s00214-005-0019-7","article-title":"Density bifunctional theory using the mass density and the charge density","volume":"115","author":"Ayers","year":"2006","journal-title":"Theor. Chem. Acc."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2005.12.001","article-title":"Maximum entropy production principle in physics, chemistry and biology","volume":"426","author":"Martyushev","year":"2006","journal-title":"Phys. Rep."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"191107","DOI":"10.1063\/1.2741244","article-title":"On the relationship between densities of Shannon entropy and Fisher information for atoms and molecules","volume":"126","author":"Liu","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1039\/C0CP01046D","article-title":"Information carriers and (reading them through) information theory in quantum chemistry","volume":"13","author":"Geerlings","year":"2011","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"3578","DOI":"10.1002\/qua.24219","article-title":"Concurrent phenomena at the transition region of selected elementary chemical reactions: An information-theoretical complexity analysis","volume":"112","author":"Esquivel","year":"2012","journal-title":"Int. J. Quant. Chem."},{"key":"ref_66","unstructured":"Deloumeaux, P., and Gorzalk, J.D. (2012). Information Theory: New Research, Nova Science Publishers. Chapter 8."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/S0375-9601(97)00855-4","article-title":"Measures of statistical complexity: Why?","volume":"238","author":"Feldman","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_68","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, University of Illinois Press."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.physa.2003.11.005","article-title":"Intensive entropic non-triviality measure","volume":"334","author":"Lamberti","year":"2004","journal-title":"Phys. A"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1016\/S0375-9601(96)00756-6","article-title":"Some features of the L\u00f3pez-Ruiz-Mancini-Calbet (LMC) statistical measure of complexity","volume":"223","author":"Anteneodo","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_71","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_72","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/S0375-9601(03)00491-2","article-title":"Statistical complexity and disequilibrium","volume":"311","author":"Martin","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1002\/qua.560170612","article-title":"How similar is a molecule to another? An electron density measure of similarity between two molecular structures","volume":"17","author":"Leyda","year":"1980","journal-title":"Int. J. Quant. Chem."},{"key":"ref_74","first-page":"841","article-title":"Energie informationnelle","volume":"263","author":"Onicescu","year":"1966","journal-title":"CR Acad. Sci. Paris A"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.physleta.2007.07.077","article-title":"Fisher\u2013Shannon plane and statistical complexity of atoms","volume":"372","author":"Angulo","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_76","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_77","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1021\/j100252a016","article-title":"Molecular electron density distributions in position and momentum space","volume":"89","author":"Rawlings","year":"1985","journal-title":"J. Phys. Chem."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0065-3276(08)60578-X","article-title":"Evaluation of momentum distributions and compton Pro\ufb01les for atomic and molecular systems","volume":"10","author":"Kaijser","year":"1977","journal-title":"Adv. Quantum Chem."},{"key":"ref_79","unstructured":"Kohout, M. (2013). Program Dgrid, version 4.6, Springer."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Emmert-Streib, F., and Dehmer, M. (2009). Algorithmic Probability: Theory and Applications, Information Theory and Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-84816-7"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Arora, S., and Boaz, B. (2009). Computational Complexity: A Modern Approach, Cambridge University Press.","DOI":"10.1017\/CBO9780511804090"},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Sen, K.D. (2010). Monograph Statistical Complexity: Applications in Electronic Structure, Springer.","DOI":"10.1007\/978-90-481-3890-6"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1016\/j.physa.2009.01.037","article-title":"Rigorous properties and uncertainty-like relationships on product-complexity measures: Application to atomic systems","volume":"388","author":"Angulo","year":"2009","journal-title":"Phys. A"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1017\/S0305004100009580","article-title":"Theory of statistical estimation","volume":"22","author":"Fisher","year":"1925","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Frieden, B.R. (2004). Science from Fisher Information: A Unification, Cambridge University Press.","DOI":"10.1017\/CBO9780511616907"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1109\/18.104312","article-title":"Information theoretic inequalities","volume":"37","author":"Dembo","year":"1991","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Politzer, P., and Truhlar, D.G. (1981). Chemical Applications of Atomic and Molecular Electrostatic Potentials: Reactivity, Structure, Scattering, and Energetics of Organic, Inorganic, and Biological Systems, Springer.","DOI":"10.1007\/978-1-4757-9634-6"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1002\/jcc.540110311","article-title":"Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis","volume":"11","author":"Breneman","year":"1990","journal-title":"J. Comput. Chem."},{"key":"ref_89","unstructured":"Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Montgomery, J.A., Vreven, T., Kudin, K.N., and Burant, J.C. (2004). Gaussian 03, Revision D.01, Gaussian, Inc."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/0010-4655(93)90035-B","article-title":"A simple, efficient and more reliable scheme for automatic numerical integration","volume":"77","year":"1993","journal-title":"Comput. Phys. Commun."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"6520","DOI":"10.1063\/1.467061","article-title":"Automatic numerical integration techniques for polyatomic molecules","volume":"100","author":"Becke","year":"1994","journal-title":"J. Chem. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/10\/4084\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:32Z","timestamp":1760219372000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/10\/4084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,26]]},"references-count":91,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2013,10]]}},"alternative-id":["e15104084"],"URL":"https:\/\/doi.org\/10.3390\/e15104084","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2013,9,26]]}}}