{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T13:04:04Z","timestamp":1778850244834,"version":"3.51.4"},"reference-count":72,"publisher":"AIP Publishing","issue":"16","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2013,4,28]]},"abstract":"<jats:p>On the basis of the analytical model previously suggested by Dinur, we discuss here a method for the calculation of vibrational charge fluxes in planar molecules, obtained as numerical second derivatives of the molecular dipole moment. This model is consistent with the partitioning of the atomic polar tensors into atomic charge and charge fluxes according to the Equilibrium Charges-Charge Fluxes model and it is directly related to experimentally measurable quantities such as IR intensities. On the basis of density functional theory calculations carried out for several small benchmark molecules, the complete set of charge fluxes is calculated for each molecule and compared with the approximated flux parameters previously derived and reported in the past literature. The degree of localization of charge fluxes is investigated and discussed; in addition, some approximations are analyzed in order to verify the applicability of the method to large and\/or non-planar molecules, aimed at obtaining a description of the electron charge mobility in different molecular environments.<\/jats:p>","DOI":"10.1063\/1.4802009","type":"journal-article","created":{"date-parts":[[2013,4,26]],"date-time":"2013-04-26T13:41:30Z","timestamp":1366983690000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":20,"title":["Charge mobility in molecules: Charge fluxes from second derivatives of the molecular dipole"],"prefix":"10.1063","volume":"138","author":[{"given":"Daria","family":"Galimberti","sequence":"first","affiliation":[{"name":"Politecnico di Milano Dipartimento di Chimica, Materiali e Ingegneria Chimica \u2018Giulio Natta\u2019, , Piazza Leonardo da Vinci 32, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alberto","family":"Milani","sequence":"additional","affiliation":[{"name":"Politecnico di Milano Dipartimento di Chimica, Materiali e Ingegneria Chimica \u2018Giulio Natta\u2019, , Piazza Leonardo da Vinci 32, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chiara","family":"Castiglioni","sequence":"additional","affiliation":[{"name":"Politecnico di Milano Dipartimento di Chimica, Materiali e Ingegneria Chimica \u2018Giulio Natta\u2019, , Piazza Leonardo da Vinci 32, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2013,4,25]]},"reference":[{"key":"2023061914131331400_c1","volume-title":"Computer Simulation of Liquids","year":"1987"},{"key":"2023061914131331400_c2a","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1002\/jcc.10351","volume":"25","year":"2004","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c2b","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/0009-2614(96)00057-7","volume":"250","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c2c","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1002\/jcc.20157","volume":"26","year":"2005","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c2d","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.1021\/ct600295n","volume":"3","year":"2007","journal-title":"J. Chem. Theory Comput."},{"key":"2023061914131331400_c2e","doi-asserted-by":"publisher","first-page":"1198","DOI":"10.1002\/jcc.10067","volume":"23","year":"2002","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c2f","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1002\/(SICI)1096-987X(199803)19:4&lt;377::AID-JCC1&gt;3.0.CO;2-P","volume":"19","year":"1998","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c2g","volume-title":"Recent Developments and Applications of Modern Density Functional Theory","author":"Seminario","year":"1996"},{"key":"2023061914131331400_c3","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1007\/s00214-012-1139-5","volume":"131","year":"2012","journal-title":"Theor. Chem. Acc."},{"key":"2023061914131331400_c4a","volume-title":"Vibrational Intensities of Polyatomic Molecules","year":"1972"},{"key":"2023061914131331400_c4b","first-page":"345","article-title":"Quantitative intensity studies and dipole moment derivatives","volume-title":"Infrared Spectroscopy and Molecular Structure","author":"Davies","year":"1963"},{"key":"2023061914131331400_c4c","volume-title":"Vibrational Intensities in Infrared and Raman Spectroscopy","author":"Zerbi","year":"1982"},{"key":"2023061914131331400_c5a","first-page":"81","volume":"A57","year":"1961","journal-title":"Ann. R. Soc. Espan. Fis. Quim. (Madrid)"},{"key":"2023061914131331400_c5b","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1063\/1.1681972","volume":"61","year":"1974","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c6a","volume-title":"Intensity Theory for Infrared Spectra of Polyatomic Molecules","year":"1964"},{"key":"2023061914131331400_c6b","doi-asserted-by":"publisher","first-page":"3439","DOI":"10.1063\/1.433597","volume":"65","year":"1976","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c6c","first-page":"265","volume":"XLII","year":"1985","journal-title":"Prik. Spectrosck."},{"key":"2023061914131331400_c7a","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1016\/0022-2852(75)90296-9","volume":"57","year":"1975","journal-title":"J. Mol. Spectrosc."},{"key":"2023061914131331400_c7b","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/0022-2852(76)90271-X","volume":"62","year":"1976","journal-title":"J. Mol. Spectrosc."},{"key":"2023061914131331400_c8a","doi-asserted-by":"publisher","first-page":"2521","DOI":"10.1021\/j100563a018","volume":"80","year":"1976","journal-title":"J. Phys. Chem."},{"key":"2023061914131331400_c8b","doi-asserted-by":"publisher","first-page":"4440","DOI":"10.1063\/1.1677887","volume":"56","year":"1972","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c9a","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1016\/0009-2614(87)80654-1","volume":"142","year":"1987","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c9b","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/0022-2860(90)87033-T","volume":"224","year":"1990","journal-title":"J. Mol. Struct."},{"key":"2023061914131331400_c10","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/0009-2614(88)85156-X","volume":"151","year":"1988","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c11","doi-asserted-by":"publisher","first-page":"2680","DOI":"10.1021\/jp045357u","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023061914131331400_c12a","doi-asserted-by":"publisher","first-page":"4839","DOI":"10.1021\/jp060553h","volume":"110","year":"2006","journal-title":"J. Phys. Chem. A"},{"key":"2023061914131331400_c12b","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1021\/jp065422v","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023061914131331400_c12c","doi-asserted-by":"publisher","first-page":"7870","DOI":"10.1021\/jp072763f","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023061914131331400_c13","doi-asserted-by":"publisher","first-page":"8333","DOI":"10.1021\/ja00204a001","volume":"111","year":"1989","journal-title":"J. Am. Chem. Soc."},{"key":"2023061914131331400_c14","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1021\/jp908146d","volume":"114","year":"2010","journal-title":"J. Phys. Chem. A"},{"key":"2023061914131331400_c15","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/j.molstruc.2010.03.031","volume":"976","year":"2010","journal-title":"J. Mol. Struct."},{"key":"2023061914131331400_c16","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.theochem.2010.06.011","volume":"955","year":"2010","journal-title":"J. Mol. Struct.: THEOCHEM"},{"key":"2023061914131331400_c17","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1021\/j150647a053","volume":"88","year":"1984","journal-title":"J. Phys. Chem."},{"key":"2023061914131331400_c18","doi-asserted-by":"crossref","first-page":"2040","DOI":"10.1002\/0470027320","volume-title":"Handbook of Vibrational Spectroscopy","author":"Chalmers","year":"2001"},{"key":"2023061914131331400_c19a","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0166-1280(94)80138-X","volume":"305","year":"1994","journal-title":"J. Mol. Struct.: THEOCHEM"},{"key":"2023061914131331400_c19b","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/0022-2860(89)80058-4","volume":"198","year":"1989","journal-title":"J. Mol. Struct."},{"key":"2023061914131331400_c19c","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/0022-2860(86)80345-3","volume":"141","year":"1986","journal-title":"J. Mol. Struct."},{"key":"2023061914131331400_c19d","doi-asserted-by":"publisher","first-page":"2210","DOI":"10.1021\/j150615a015","volume":"85","year":"1981","journal-title":"J. Phys. Chem."},{"key":"2023061914131331400_c20","doi-asserted-by":"publisher","first-page":"3534","DOI":"10.1063\/1.448932","volume":"82","year":"1985","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c21a","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/0584-8539(85)80118-5","volume":"41","year":"1985","journal-title":"Spectrochim. Acta, Part A"},{"key":"2023061914131331400_c21b","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1016\/0038-1098(85)90421-1","volume":"56","year":"1985","journal-title":"Solid State Commun."},{"key":"2023061914131331400_c22a","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1063\/1.446885","volume":"80","year":"1984","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c22b","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0009-2614(83)80538-7","volume":"99","year":"1983","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c22c","doi-asserted-by":"publisher","first-page":"3916","DOI":"10.1063\/1.447175","volume":"80","year":"1984","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c23a","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1016\/0584-8539(94)00194-G","volume":"51","year":"1995","journal-title":"Spectrochim. Acta, Part A"},{"key":"2023061914131331400_c23b","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.vibspec.2007.09.002","volume":"46","year":"2008","journal-title":"Vib. Spectrosc."},{"key":"2023061914131331400_c23c","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/S0022-2860(00)00932-7","volume":"565\u2013566","year":"2001","journal-title":"J. Mol. Struct."},{"key":"2023061914131331400_c23d","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/j.saa.2005.05.024","volume":"63","year":"2006","journal-title":"Spectrochim. Acta, Part A"},{"key":"2023061914131331400_c24","volume-title":"Vibrational Intensities in Infrared and Raman Spectroscopy","year":"1982"},{"key":"2023061914131331400_c25a","doi-asserted-by":"publisher","first-page":"6201","DOI":"10.1021\/j100169a030","volume":"95","year":"1991","journal-title":"J. Phys. Chem."},{"key":"2023061914131331400_c25b","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/0009-2614(90)87277-X","volume":"166","year":"1990","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c26","doi-asserted-by":"publisher","first-page":"2949","DOI":"10.1063\/1.456965","volume":"91","year":"1989","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c27a","doi-asserted-by":"publisher","first-page":"4626","DOI":"10.1063\/1.464990","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c27b","doi-asserted-by":"publisher","first-page":"2549","DOI":"10.1063\/1.460959","volume":"95","year":"1991","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c27c","doi-asserted-by":"publisher","first-page":"4909","DOI":"10.1063\/1.456587","volume":"90","year":"1989","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c27d","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1063\/1.449434","volume":"83","year":"1985","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c27e","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/0009-2614(84)85001-0","volume":"112","year":"1984","journal-title":"Chem. Phys. Lett."},{"key":"2023061914131331400_c27f","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/0301-0104(85)80131-2","volume":"98","year":"1985","journal-title":"Chem. Phys."},{"key":"2023061914131331400_c27g","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0301-0104(99)00192-5","volume":"246","year":"1999","journal-title":"Chem. Phys."},{"key":"2023061914131331400_c28a","doi-asserted-by":"publisher","first-page":"13403","DOI":"10.1021\/jp106952q","volume":"114","year":"2010","journal-title":"J. Phys. Chem. B"},{"key":"2023061914131331400_c28b","doi-asserted-by":"publisher","first-page":"034504","DOI":"10.1063\/1.3456183","volume":"133","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c28c","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1021\/jz201540r","volume":"3","year":"2012","journal-title":"J. Phys. Chem. Lett."},{"key":"2023061914131331400_c29","volume-title":"Molecular Vibrations","year":"1955"},{"key":"2023061914131331400_c30","doi-asserted-by":"publisher","first-page":"6158","DOI":"10.1063\/1.478522","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023061914131331400_c31","volume-title":"GAUSSIAN 09","year":"2009"},{"key":"2023061914131331400_c32a","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1002\/jcc.540110404","volume":"11","year":"1990","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c32b","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1002\/jcc.540050204","volume":"5","year":"1984","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c33","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1002\/jcc.540080616","volume":"8","year":"1987","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c34","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1002\/jcc.540110311","volume":"11","year":"1990","journal-title":"J. Comput. Chem."},{"key":"2023061914131331400_c35","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF00549096","volume":"44","year":"1977","journal-title":"Theor. Chem. Acc."},{"key":"2023061914131331400_c36","unstructured":"See supplementary material at http:\/\/dx.doi.org\/10.1063\/1.4802009 for table with stretching and bending charge fluxes, tables with the comparison between computed APTs and \u201creconstructed\u201d ones, table with CH stretching principal fluxes on H belonging to many different molecules obtained with different approximations, table with CH stretching fluxes for ethylene, butadiene, and hexatriene."},{"key":"2023061914131331400_c37"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.4802009\/13017936\/164115_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.4802009\/13017936\/164115_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T14:13:23Z","timestamp":1687184003000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/138\/16\/164115\/71461\/Charge-mobility-in-molecules-Charge-fluxes-from"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,25]]},"references-count":72,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2013,4,28]]}},"URL":"https:\/\/doi.org\/10.1063\/1.4802009","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2013,4,28]]},"published":{"date-parts":[[2013,4,25]]},"article-number":"164115"}}