{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T21:44:38Z","timestamp":1768513478353,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T00:00:00Z","timestamp":1573516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>An algorithm for the efficient computation of molecular electrostatic potential is reported. It is based on the partition\/expansion of density into (pseudo) atomic fragments with the method of Deformed Atoms in Molecules, which allows to compute the potential as a sum of atomic contributions. These contributions are expressed as a series of irregular spherical harmonics times effective multipole moments and inverse multipole moments, including short-range terms. The problem is split into two steps. The first one consists of the partition\/expansion of density accompanied by the computation of multipole moments, and its cost depends on the size of the basis set used in the computation of electron density within the Linear Combination of Atomic Orbitals framework. The second one is the actual computation of the electrostatic potential from the quantities calculated in the first step, and its cost depends on the number of computation points. For a precision in the electrostatic potential of six decimal figures, the algorithm leads to a dramatic reduction of the computation time with respect to the calculation from electron density matrix and integrals involving basis set functions.<\/jats:p>","DOI":"10.3390\/computation7040064","type":"journal-article","created":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T09:11:27Z","timestamp":1573636287000},"page":"64","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Efficient Evaluation of Molecular Electrostatic Potential in Large Systems"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9676-7534","authenticated-orcid":false,"given":"Rafael","family":"Lopez","sequence":"first","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica Aplicada, Facultad de Ciencias, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Martinez","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica Aplicada, Facultad de Ciencias, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ignacio","family":"Ema","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica Aplicada, Facultad de Ciencias, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jose Manuel","family":"Garcia de la Vega","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica Aplicada, Facultad de Ciencias, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Ramirez","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica Aplicada, Facultad de Ciencias, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1021\/ja02261a002","article-title":"The atom and the molecule","volume":"38","author":"Lewis","year":"1916","journal-title":"J. Am. Chem. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Politzer, P., and Murray, J.S. (2019). An Overview of Strengths and Directionalities of Noncovalent Interactions: \u03c3-Holes and \u03c0-Holes. Crystals, 9.","DOI":"10.3390\/cryst9030165"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1002\/andp.19273892002","article-title":"Zur Quantentheorie der Molekeln","volume":"389","author":"Born","year":"1927","journal-title":"Ann. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1833","DOI":"10.1063\/1.1740588","article-title":"Electronic Population Analysis on LCAO\u2013MO Molecular Wave Functions","volume":"23","author":"Mulliken","year":"1955","journal-title":"J. Chem. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3341","DOI":"10.1063\/1.1841222","article-title":"Molecular Charge Distributions and Chemical Binding","volume":"46","author":"Bader","year":"1967","journal-title":"J. Chem. Phys."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/3-540-06399-4_6","article-title":"The electrostatic molecular potential as a tool for the interpretation of molecular properties","volume":"Volume 42","author":"Scrocco","year":"1973","journal-title":"New Concepts II"},{"key":"ref_8","first-page":"116","article-title":"Electronic molecular structure, reactivity and intermolecular forces: An heuristic interpretation by means of electrostatic molecular potentials","volume":"11","author":"Scrocco","year":"1978","journal-title":"Advan. Quantum Chem."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3959","DOI":"10.1021\/j100373a017","article-title":"Use of the Electrostatic Potential at the Molecular Surface to Interpret and Predict Nucleophilic Processes","volume":"94","author":"Sjoberg","year":"1990","journal-title":"J. Phys. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5144","DOI":"10.1021\/j100121a049","article-title":"Relationships between Computed Molecular Properties and Solute-Solvent Interactions in Supercritical Solutions","volume":"97","author":"Lane","year":"1993","journal-title":"J. Phys. Chem."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9369","DOI":"10.1021\/j100139a019","article-title":"Relationships of Critical Constants and Boiling Points to Computed Molecular Surface Properties","volume":"97","author":"Murray","year":"1993","journal-title":"J. Phys. Chem."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/qua.1215","article-title":"Computational Characterization of Nucleotide Bases: Molecular Surface Electrostatic Potentials and Local Ionization Energies, and Local Polarization Energies","volume":"83","author":"Murray","year":"2001","journal-title":"Int. J. Quantum Chem."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF02840749","article-title":"Molecular surface electrostatic potentials in the analysis of non-hydrogen-bonding noncovalent interactions","volume":"106","author":"Murray","year":"1994","journal-title":"Proc. Indian Acad. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s00894-006-0130-2","article-title":"Halogen bonding: The \u03c3-hole","volume":"13","author":"Clark","year":"2007","journal-title":"J. Mol. Model."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1063\/1.459703","article-title":"Maximal and minimal characteristics of molecular electrostatic potentials","volume":"93","author":"Pathak","year":"1990","journal-title":"J. Chem. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF02860157","article-title":"Nonexistence of local maxima in nolecular electrostatic potential maps","volume":"102","author":"Gadre","year":"1990","journal-title":"Proc. Ind. Acad. Sci. (Chem. Sci.)"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4384","DOI":"10.1063\/1.460625","article-title":"Shapes and sizes of molecular anions via topographical of electrostatic potential analysis","volume":"94","author":"Gadre","year":"1991","journal-title":"J. Chem. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0009-2614(95)00473-H","article-title":"Basis set dependence of the molecular electrostatic potential topography. A case study of substituted benzenes","volume":"239","author":"Gadre","year":"1995","journal-title":"Chem. Phys. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"174103","DOI":"10.1063\/1.2999558","article-title":"An appraisal of Poincar\u00e9\u2013Hopf relation and application to topography of molecular electrostatic potentials","volume":"129","author":"Roy","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1021\/acs.jctc.6b00073","article-title":"Exploring the Gradient Paths and Zero Flux Surfaces of Molecular Electrostatic Potential","volume":"12","author":"Kumar","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1071\/CH16226","article-title":"Molecular Electrostatic Potential Based Atoms in Molecules: Shielding Effects and Reactivity Patterns","volume":"69","author":"Kumar","year":"2016","journal-title":"Aust. J. Chem."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1472","DOI":"10.1021\/acs.jpca.7b11952","article-title":"Hydrogen-Bonding Acceptor Character of Be3, the Beryllium Three- Membered Ring","volume":"122","author":"Alkorta","year":"2018","journal-title":"J. Phys. Chem."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1886","DOI":"10.1002\/cphc.201800217","article-title":"Complexes of O=C=S with Nitrogen Bases: Chalcogen Bonds, Tetrel Bonds, and Other Secondary Interactions","volume":"19","author":"Alkorta","year":"2018","journal-title":"Chem. Phys. Chem."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.molstruc.2019.05.003","article-title":"Rationalizing the stability and interactions of 2,4-diamino-5-(4-chlorophenyl)-6-ethylpyrimidin-1-ium 2-hydroxy-3, 5-dinitrobenzoate salt","volume":"1193","author":"Tahir","year":"2019","journal-title":"J. Mol. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1080\/22297928.2019.1622448","article-title":"TLC Detection and Theoretical Structure Elucidation of Nitrogen Containing Compounds with Cobalt Thiocyanate","volume":"9","author":"Kote","year":"2019","journal-title":"Anal. Chem. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/jcc.20064","article-title":"Analytical method for the representation of atoms-in-molecules densities","volume":"25","author":"Rico","year":"2004","journal-title":"J. Comput. Chem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1002\/jcc.20061","article-title":"Electrostatic potentials and fields from density expansions of deformed atoms in molecules","volume":"25","author":"Rico","year":"2004","journal-title":"J. Comput. Chem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4213","DOI":"10.1063\/1.478303","article-title":"Analysis of the molecular density","volume":"110","author":"Rico","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_29","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (1980). Table of Integrals, Series and Products, Academic Press. [4th ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1080\/00268978500102891","article-title":"Distributed Multipole Analysis","volume":"56","author":"Stone","year":"1985","journal-title":"Mol. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0953-4075\/22\/1\/004","article-title":"Single-centre expansion of Gaussian basis functions and the angular decomposition of their overlap integrals","volume":"22","author":"Kaufmann","year":"1989","journal-title":"J. Phys. B At. Mol. Opt. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1002\/qua.24356","article-title":"Translation of Real Solid Spherical Harmonics","volume":"113","author":"Rico","year":"2013","journal-title":"Int. J. Quantum Chem."},{"key":"ref_33","unstructured":"Abramowitz, M., and Stegun, I. (1970). Handbook of Mathematical Functions, Dover. [9th printing ed.]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.cpc.2017.01.012","article-title":"Topology of molecular electron density and electrostatic potential with DAMQT","volume":"214","author":"Rico","year":"2017","journal-title":"Comput. Phys. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1063\/1.456153","article-title":"Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen","volume":"90","author":"Dunning","year":"1989","journal-title":"J. Chem. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00894-012-1667-x","article-title":"Optimization of parameters for semiempirical methods VI: More modifications to the NDDO approximations and re-optimization of parameters","volume":"19","author":"Stewart","year":"2013","journal-title":"J. Mol. Model."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/4\/64\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:33:49Z","timestamp":1760189629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/4\/64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,12]]},"references-count":36,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["computation7040064"],"URL":"https:\/\/doi.org\/10.3390\/computation7040064","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,12]]}}}