{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T03:04:34Z","timestamp":1778295874867,"version":"3.51.4"},"reference-count":97,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T00:00:00Z","timestamp":1756166400000},"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":["22203071"],"award-info":[{"award-number":["22203071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22361051"],"award-info":[{"award-number":["22361051"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"High-Level Talent Special Support Plan","award":["22203071"],"award-info":[{"award-number":["22203071"]}]},{"name":"High-Level Talent Special Support Plan","award":["22361051"],"award-info":[{"award-number":["22361051"]}]},{"name":"China Scholarship Council","award":["22203071"],"award-info":[{"award-number":["22203071"]}]},{"name":"China Scholarship Council","award":["22361051"],"award-info":[{"award-number":["22361051"]}]},{"name":"NSERC","award":["22203071"],"award-info":[{"award-number":["22203071"]}]},{"name":"NSERC","award":["22361051"],"award-info":[{"award-number":["22361051"]}]},{"name":"Canada Research Chairs","award":["22203071"],"award-info":[{"award-number":["22203071"]}]},{"name":"Canada Research Chairs","award":["22361051"],"award-info":[{"award-number":["22361051"]}]},{"name":"Digital Research Alliance of Canada","award":["22203071"],"award-info":[{"award-number":["22203071"]}]},{"name":"Digital Research Alliance of Canada","award":["22361051"],"award-info":[{"award-number":["22361051"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>Employing some simple physics-inspired density-based information-theoretic approach (ITA) quantities to predict the electron correlation energies remains an open challenge. In this work, we expand the scope of the LR(ITA) (LR means linear regression) protocol to more complex systems, including (i) 24 octane isomers; (ii) polymeric structures, polyyne, polyene, all-trans-polymethineimine, and acene; (iii) molecular clusters, such as metallic Ben and Mgn, covalent Sn, hydrogen-bonded protonated water clusters H+(H2O)n, and dispersion-bound carbon dioxide (CO2)n, and benzene (C6H6)n clusters. With LR(ITA), one can simply predict the post-Hartree-Fock (such as MP2 and coupled cluster) electron correlation energies at the cost of Hartree-Fock calculations, even with chemical accuracy. For large molecular clusters, we employ the linear-scaling generalized energy-based fragmentation (GEBF) method to gauge the accuracy of LR(ITA). Employing benzene clusters as an illustration, the LR(ITA) method shows similar accuracy to that of GEBF. Overall, we have verified that ITA quantities can be used to predict the post-Hartree-Fock electron correlation energies of various complex systems.<\/jats:p>","DOI":"10.3390\/molecules30173500","type":"journal-article","created":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T14:18:49Z","timestamp":1756217929000},"page":"3500","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Predicting the Post-Hartree-Fock Electron Correlation Energy of Complex Systems with the Information-Theoretic Approach"],"prefix":"10.3390","volume":"30","author":[{"given":"Ping","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of High Performance Scientific Computation, School of Science, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongxiong","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Basic Medical Sciences, Yunnan University of Chinese Medicine, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linling","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Medicinal Chemistry for Natural Resource, Ministry of Education, Institute of Biomedical Research, School of Chemical Science and Technology, Yunnan University, Kunming 650500, China"},{"name":"Yunnan Key Laboratory of Research Development for Natural Products, School of Pharmacy, Yunnan University, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yilin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingbo","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Medicinal Chemistry for Natural Resource, Ministry of Education, Institute of Biomedical Research, School of Chemical Science and Technology, Yunnan University, Kunming 650500, China"},{"name":"Yunnan Key Laboratory of Research Development for Natural Products, School of Pharmacy, Yunnan University, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2605-3883","authenticated-orcid":false,"given":"Paul W.","family":"Ayers","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9331-0427","authenticated-orcid":false,"given":"Shubin","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Computing Center, University of North Carolina, Chapel Hill, NC 27599, USA"},{"name":"Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0927-4361","authenticated-orcid":false,"given":"Dongbo","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Medicinal Chemistry for Natural Resource, Ministry of Education, Institute of Biomedical Research, School of Chemical Science and Technology, Yunnan University, Kunming 650500, China"},{"name":"Yunnan Key Laboratory of Research Development for Natural Products, School of Pharmacy, Yunnan University, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,26]]},"reference":[{"key":"ref_1","unstructured":"Szabo, A., and Ostlund, N.S. (1996). Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1002\/jcc.20581","article-title":"Electron correlation: The many-body problem at the heart of chemistry","volume":"28","author":"Tew","year":"2007","journal-title":"J. Comput. Chem."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8879","DOI":"10.1073\/pnas.97.16.8879","article-title":"Information theory, atoms in molecules, and molecular similarity","volume":"97","author":"Nalewajski","year":"2000","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1007\/s00214-006-0121-5","article-title":"Information Theory, the Shape Function, and the Hirshfeld Atom","volume":"115","author":"Ayers","year":"2006","journal-title":"Theor. Chem. Acc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Zhao, D., Rong, C., Liu, S., and Ayers, P.W. (2025). Information Theory Meets Quantum Chemistry: A Review and Perspective. Entropy, 27.","DOI":"10.3390\/e27060644"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"244108","DOI":"10.1063\/5.0270709","article-title":"Extending the information-theoretic approach from the (one) electron density to the pair density","volume":"162","author":"Zhao","year":"2025","journal-title":"J. Chem. Phys."},{"key":"ref_7","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_8","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. Camb. Philos. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhao, D., Liu, S., and Chen, D. (2022). A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides. Pharmaceuticals, 15.","DOI":"10.20944\/preprints202207.0080.v1"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhao, D., He, X., Ayers, P.W., and Liu, S. (2023). Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study. Molecules, 28.","DOI":"10.20944\/preprints202302.0116.v1"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1039\/D2CP04690C","article-title":"Efficient and accurate density-based prediction of macromolecular polarizabilities","volume":"25","author":"Zhao","year":"2023","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2655","DOI":"10.1021\/acs.jctc.3c01415","article-title":"Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates","volume":"20","author":"Zhao","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5997","DOI":"10.1021\/acs.jctc.5c00414","article-title":"Multiproperty Deep Learning of the Correlation Energy of Electrons and the Physicochemical Properties of Molecules","volume":"21","author":"Yuan","year":"2025","journal-title":"J. Chem. Theory Comput."},{"key":"ref_14","unstructured":"Zhao, Y., Richer, M., Ayers, P.W., Liu, S., and Zhao, D. (2025). Can the FCI Energies\/Properties be Predicted with HF\/DFT Densities?. J. Chem. Sci., accepted."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.3866\/PKU.WHXB201509183","article-title":"R\u00e9nyi entropy, Tsallis entropy and Onicescu information energy in density functional reactivity theory","volume":"31","author":"Liu","year":"2015","journal-title":"Acta Phys. -Chim. Sin."},{"key":"ref_17","unstructured":"Kullback, S. (1997). Information Theory and Statistics, Dover Publications."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"141103","DOI":"10.1063\/1.5124244","article-title":"Identity for Kullback-Leibler divergence in density functional reactivity theory","volume":"151","author":"Liu","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"19716","DOI":"10.1039\/D1CP02513A","article-title":"Prediction of beryllium clusters (Ben; n = 3\u201325) from first principles","volume":"23","author":"Abyaz","year":"2021","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"26110","DOI":"10.1021\/acs.jpcc.6b08371","article-title":"Thermodynamics of Metal Nanoparticles: Energies and Enthalpies of Formation of Magnesium Clusters and Nanoparticles as Large as 1.3 nm","volume":"120","author":"Duanmu","year":"2016","journal-title":"J. Phys. Chem. C"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5862","DOI":"10.1063\/1.459583","article-title":"Structures and stabilities of sulfur clusters","volume":"93","author":"Raghavachari","year":"1990","journal-title":"J. Chem. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9257","DOI":"10.1063\/1.1568081","article-title":"Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in Sn rings and chains (n = 2 \u2212 18)","volume":"118","author":"Jones","year":"2003","journal-title":"J. Chem. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1021\/acs.jctc.4c01261","article-title":"Accurate Neural Network Fine-Tuning Approach for Transferable Ab Initio Energy Prediction across Varying Molecular and Crystalline Scales","volume":"21","author":"Ng","year":"2025","journal-title":"J. Chem. Theory Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7492","DOI":"10.1021\/jp802872p","article-title":"Geometry Optimization of Carbon Dioxide Clusters (CO2)n for 4 \u2264 n \u2264 40","volume":"112","author":"Takeuchi","year":"2008","journal-title":"J. Phys. Chem. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10172","DOI":"10.1021\/jp305965r","article-title":"Structural Features of Small Benzene Clusters (C6H6)n (n \u2264 30) As Investigated with the All-Atom OPLS Potential","volume":"116","author":"Takeuchi","year":"2012","journal-title":"J. Phys. Chem. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1103\/RevModPhys.23.69","article-title":"New Developments in Molecular Orbital Theory","volume":"23","author":"Roothaan","year":"1951","journal-title":"Rev. Mod. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1103\/PhysRev.46.618","article-title":"Note on an Approximation Treatment for Many-Electron Systems","volume":"46","author":"Plesset","year":"1934","journal-title":"Phys. Rev."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0009-2614(98)00862-8","article-title":"Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations","volume":"294","author":"Weigend","year":"1997","journal-title":"Chem. Phys. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0009-2614(98)00862-8","article-title":"RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency","volume":"294","author":"Weigend","year":"1998","journal-title":"Chem. Phys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0009-2614(89)87372-5","article-title":"The coupled-cluster single and double excitation model for the ground-state correlation energy","volume":"155","author":"Bartlett","year":"1989","journal-title":"Chem. Phys. Lett."},{"key":"ref_31","first-page":"359","article-title":"Coupled-cluster method with singles and doubles for closed-shell systems","volume":"5","author":"Paldus","year":"1971","journal-title":"Int. J. Quantum Chem."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1910","DOI":"10.1063\/1.443164","article-title":"A full coupled-cluster singles and doubles model: The inclusion of disconnected triples","volume":"76","author":"Purvis","year":"1982","journal-title":"J. Chem. Phys."},{"key":"ref_33","unstructured":"Parr, R.G., and Yang, W. (1989). Density Functional Theory of Atoms and Molecules, Oxford University Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"28700","DOI":"10.1039\/D2CP02827A","article-title":"DFT exchange: Sharing perspectives on the workhorse of quantum chemistry and materials science","volume":"24","author":"Teale","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7215","DOI":"10.1021\/ja0427247","article-title":"An Efficient Fragment-Based Approach for Predicting the Ground-State Energies and Structures of Large Molecules","volume":"127","author":"Li","year":"2005","journal-title":"J. Am. Chem. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1021\/jp067721q","article-title":"Generalized Energy-Based Fragmentation Approach for Computing the Ground-State Energies and Properties of Large Molecules","volume":"111","author":"Li","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2712","DOI":"10.1021\/ar500038z","article-title":"Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates","volume":"47","author":"Li","year":"2014","journal-title":"Acc. Chem. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1021\/acs.accounts.0c00580","article-title":"Structures and Spectroscopic Properties of Large Molecules and Condensed-Phase Systems Predicted by Generalized Energy-Based Fragmentation Approach","volume":"54","author":"Li","year":"2021","journal-title":"Acc. Chem. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0009-2614(83)80703-9","article-title":"Localizability of dynamic electron correlation","volume":"100","author":"Pulay","year":"1983","journal-title":"Chem. Phys. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0009-2614(85)85003-X","article-title":"Local configuration interaction: An efficient approach for larger molecules","volume":"113","author":"Pulay","year":"1985","journal-title":"Chem. Phys. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1146\/annurev.pc.44.100193.001241","article-title":"Local Treatment of Electron Correlation","volume":"44","author":"Pulay","year":"1993","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4772","DOI":"10.1021\/acs.jctc.8b00636","article-title":"Transferability in Machine Learning for Electronic Structure via the Molecular Orbital Basis","volume":"14","author":"Welborn","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"131103","DOI":"10.1063\/1.5088393","article-title":"A universal density matrix functional from molecular orbital-based machine learning: Transferability across organic molecules","volume":"150","author":"Cheng","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"6668","DOI":"10.1021\/acs.jctc.9b00884","article-title":"Regression Clustering for Improved Accuracy and Training Costs with Molecular-Orbital-Based Machine Learning","volume":"15","author":"Cheng","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"034103","DOI":"10.1063\/1.2428290","article-title":"Grid-based energy density analysis: Implementation and assessment","volume":"126","author":"Imamura","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"024104","DOI":"10.1063\/1.5100165","article-title":"Machine-learned electron correlation model based on correlation energy density at complete basis set limit","volume":"151","author":"Nudejima","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"5324","DOI":"10.1021\/acs.jpclett.1c00900","article-title":"Fast Estimation of M\u00f8ller\u2013Plesset Correlation Energies Based on Atomic Contributions","volume":"12","author":"Han","year":"2021","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1021\/acs.jctc.0c00898","article-title":"A Machine Learning Approach for MP2 Correlation Energies and Its Application to Organic Compounds","volume":"17","author":"Han","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"5439","DOI":"10.1021\/acs.jctc.3c00518","article-title":"Low-Data Deep Quantum Chemical Learning for Accurate MP2 and Coupled-Cluster Correlations","volume":"19","author":"Ng","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"7453","DOI":"10.1021\/acs.jctc.0c00927","article-title":"Transferable MP2-Based Machine Learning for Accurate Coupled-Cluster Energies","volume":"16","author":"Townsend","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"161725","DOI":"10.1063\/1.4986081","article-title":"Improving the accuracy of M\u00f8ller-Plesset perturbation theory with neural networks","volume":"147","author":"McGibbon","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1103\/RevModPhys.32.296","article-title":"Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another","volume":"32","author":"Boys","year":"1960","journal-title":"Rev. Mod. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1103\/RevModPhys.35.457","article-title":"Localized Atomic and Molecular Orbitals","volume":"35","author":"Edmiston","year":"1963","journal-title":"Rev. Mod. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2863","DOI":"10.1103\/PhysRevLett.69.2863","article-title":"Density matrix formulation for quantum renormalization groups","volume":"69","author":"White","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"10345","DOI":"10.1103\/PhysRevB.48.10345","article-title":"Density-matrix algorithms for quantum renormalization groups","volume":"48","author":"White","year":"1993","journal-title":"Phys. Rev. B"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"034106","DOI":"10.1063\/1.4773581","article-title":"An efficient and near linear scaling pair natural orbital based local coupled cluster method","volume":"138","author":"Riplinger","year":"2013","journal-title":"J. Chem. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1007\/s00894-012-1667-x","article-title":"Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements","volume":"19","author":"Stewart","year":"2013","journal-title":"J. Mol. Model."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Bader, R.F.W. (1990). Atoms in Molecules: A Quantum Theory, Clarendon Press.","DOI":"10.1093\/oso\/9780198551683.001.0001"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2686","DOI":"10.1063\/1.1733573","article-title":"Atomic Screening Constants from SCF Functions","volume":"38","author":"Clementi","year":"1963","journal-title":"J. Chem. Phys."},{"key":"ref_60","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_61","doi-asserted-by":"crossref","first-page":"4626","DOI":"10.1063\/1.442578","article-title":"An information theoretic synthesis and analysis of Compton profiles","volume":"75","author":"Sears","year":"1981","journal-title":"J. Chem. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1002\/ijch.198000018","article-title":"On the Quantum-Mechanical Kinetic Energy as a Measure of the Information in a Distribution","volume":"19","author":"Sears","year":"1980","journal-title":"Isr. J. Chem."},{"key":"ref_63","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_64","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1002\/(SICI)1097-461X(1996)58:4<323::AID-QUA1>3.0.CO;2-#","article-title":"Information entropy as a measure of the quality of an approximate electronic wave function","volume":"58","author":"Nagy","year":"1996","journal-title":"Int. J. Quantum Chem."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1002\/qua.560390607","article-title":"Approximate density matrices and Husimi functions using the maximum entropy formulation with constraints","volume":"39","author":"Morrison","year":"1991","journal-title":"Int. J. Quantum Chem."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"3507","DOI":"10.1103\/PhysRevA.58.3507","article-title":"Amount of information present in the one-particle density matrix and the charge density","volume":"58","author":"Sagar","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"4512","DOI":"10.1103\/PhysRevA.57.4512","article-title":"Calculating the logarithmic mean excitation energy from the Shannon information entropy of the electronic charge density","volume":"57","author":"Weaver","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"5469","DOI":"10.1063\/1.476316","article-title":"Molecular similarity based on information entropies and distances","volume":"108","author":"Smith","year":"1998","journal-title":"J. Chem. Phys."},{"key":"ref_69","first-page":"109","article-title":"An investigation of the dependence of Shannon-information entropies and distance measures on molecular-geometry","volume":"S29","author":"Sagar","year":"1995","journal-title":"Int. J. Quantum Chem."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"5149","DOI":"10.1088\/0953-4075\/27\/21\/009","article-title":"Atomic information entropies beyond the Hartree-Fock limit","volume":"27","author":"Sagar","year":"1994","journal-title":"J. Phys. B At. Mol. Opt. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0009-2614(94)00029-8","article-title":"A numerical study of molecular information entropies","volume":"219","author":"Sagar","year":"1994","journal-title":"Chem. Phys. Lett."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.1016\/j.physleta.2007.10.055","article-title":"Local wave-vector, Shannon and Fisher information","volume":"372","author":"Nagy","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_73","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_74","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1002\/qua.560030308","article-title":"The kinetic energy of molecular charge distributions and molecular stability","volume":"3","author":"Bader","year":"1969","journal-title":"Int. J. Quantum Chem."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/qua.560140813","article-title":"Studies of the energy density functional approach. I. Kinetic energy","volume":"14","author":"Tal","year":"1978","journal-title":"Int. J. Quantum Chem."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1063\/1.437511","article-title":"Local kinetic energy in quantum mechanics","volume":"70","author":"Cohen","year":"1979","journal-title":"J. Chem. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"4277","DOI":"10.1063\/1.447257","article-title":"Representable local kinetic energy","volume":"80","author":"Cohen","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0009-2614(96)00624-0","article-title":"Uniqueness and Asymptotic Behavior of the Local Kinetic Energy","volume":"258","author":"Yang","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1002\/qua.989","article-title":"Local kinetic energy and local temperature in the density-functional theory of electronic structure","volume":"90","author":"Ayers","year":"2002","journal-title":"Int. J. Quantum Chem."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"8884","DOI":"10.1021\/jp1029745","article-title":"How Ambiguous Is the Local Kinetic Energy?","volume":"114","author":"Anderson","year":"2010","journal-title":"J. Phys. Chem. A"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/0009-2614(86)80233-0","article-title":"Exponential approximation for the density matrix and the Wigner distribution","volume":"129","author":"Berkowitz","year":"1986","journal-title":"Chem. Phys. Lett."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1021\/cr990029p","article-title":"Conceptual Density Functional Theory","volume":"103","author":"Geerlings","year":"2003","journal-title":"Chem. Rev."},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Gatti, C., and Macchi, P. (2012). Charge Density and Chemical Reactivity: A Unified View from Conceptual DFT. Modern Charge Density Analysis, Springer.","DOI":"10.1007\/978-90-481-3836-4"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"590","DOI":"10.3866\/PKU.WHXB20090332","article-title":"Conceptual Density Functional Theory and Some Recent Developments","volume":"25","author":"Liu","year":"2009","journal-title":"Acta Phys. -Chim. Sin."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s00214-020-2546-7","article-title":"Conceptual density functional theory: Status, prospects, issues","volume":"139","author":"Geerlings","year":"2020","journal-title":"Theor. Chem. Acc."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF00549096","article-title":"Bonded-atom fragments for describing molecular charge densities","volume":"44","author":"Hirshfeld","year":"1977","journal-title":"Theor. Chim. Acta"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"4219","DOI":"10.1021\/acs.jpca.7b08966","article-title":"Information-Theoretic Ap-proaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes","volume":"122","author":"Ayers","year":"2018","journal-title":"J. Phys. Chem. A"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1063\/1.454033","article-title":"A multicenter numerical integration scheme for polyatomic molecules","volume":"88","author":"Becke","year":"1988","journal-title":"J. Chem. Phys."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"e1461","DOI":"10.1002\/wcms.1461","article-title":"Information-Theoretic approach in density functional theory and its recent applications to chemical problems","volume":"10","author":"Rong","year":"2020","journal-title":"Wiley Interdiscip. Rev. Comput. Mol. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1002\/qua.24831","article-title":"LSQC: Low scaling quantum chemistry program","volume":"115","author":"Li","year":"2015","journal-title":"Int. J. Quantum Chem."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1002\/jcc.22885","article-title":"Multiwfn: A multifunctional wavefunction analyzer","volume":"33","author":"Lu","year":"2012","journal-title":"J. Comput. Chem."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"082503","DOI":"10.1063\/5.0216272","article-title":"A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn","volume":"161","author":"Lu","year":"2024","journal-title":"J. Chem. Phys."},{"key":"ref_93","unstructured":"Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Petersson, G.A., and Nakatsuji, H. (2016). Gaussian 16 Rev. C.01, Gaussian, Inc."},{"key":"ref_94","unstructured":"Zou, J. (2025, May 20). Molecular Orbital Kit (MOKIT). Available online: https:\/\/gitlab.com\/jxzou\/mokit."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"e1606","DOI":"10.1002\/wcms.1606","article-title":"Software update: The ORCA program system\u2014Version 5.0","volume":"12","author":"Neese","year":"2022","journal-title":"Wiley Interdiscip. Rev. Comput. Mol. Sci."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF00526697","article-title":"Orbital-invariant formulation and second-order gradient evaluation in M\u00f8ller\u2013Plesset perturbation theory","volume":"69","author":"Pulay","year":"1986","journal-title":"Theor. Chim. Acta"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0009-2614(92)86093-W","article-title":"A comparison of the efficiency and accuracy of different electron correlation methods for large molecules: Quasi-Newton, MP2, CCSD, and CCSD(T)","volume":"190","author":"Hampel","year":"1992","journal-title":"Chem. Phys. Lett."}],"container-title":["Molecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1420-3049\/30\/17\/3500\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:33:12Z","timestamp":1760034792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1420-3049\/30\/17\/3500"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,26]]},"references-count":97,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["molecules30173500"],"URL":"https:\/\/doi.org\/10.3390\/molecules30173500","relation":{},"ISSN":["1420-3049"],"issn-type":[{"value":"1420-3049","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,26]]}}}