{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T22:35:06Z","timestamp":1781562906530,"version":"3.54.5"},"reference-count":91,"publisher":"AIP Publishing","issue":"17","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,11,7]]},"abstract":"<jats:p>The F\u00f6rster resonance energy transfer theory is generalized for inelastic situations with quantum mechanical modulation of the donor-acceptor coupling. Under the assumption that the modulations are independent of the electronic excitation of the donor and the acceptor, a general rate expression is derived, which involves two dimensional frequency-domain convolution of the donor emission line shape, the acceptor absorption line shape, and the spectral density of the modulation of the donor-acceptor coupling. For two models of modulation, detailed rate expressions are derived. The first model is the fluctuation of the donor-acceptor distance, approximated as a quantum harmonic oscillator coupled to a bath of other quantum harmonic oscillators. The distance fluctuation results in additional terms in the rate, which in the small fluctuation limit depend on the inverse eighth power of the donor-acceptor distance. The second model is the fluctuation of the torsional angle between the two transition dipoles, which is modeled as a quantum harmonic oscillator coupled to a bath of quantum harmonic oscillators and causes sinusoidal modulation of the donor-acceptor coupling. The rate expression has new elastic and inelastic terms, depending sensitively on the value of the minimum energy torsional angle. Experimental implications of the present theory and some of the open theoretical issues are discussed.<\/jats:p>","DOI":"10.1063\/1.2779031","type":"journal-article","created":{"date-parts":[[2007,11,7]],"date-time":"2007-11-07T23:17:55Z","timestamp":1194477475000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":62,"title":["Generalization of the F\u00f6rster resonance energy transfer theory for quantum mechanical modulation of the donor-acceptor coupling"],"prefix":"10.1063","volume":"127","author":[{"given":"Seogjoo","family":"Jang","sequence":"first","affiliation":[{"name":"Queens College of the City University of New York Department of Chemistry and Biochemistry, , 65-30 Kissena Boulevard, Flushing, New York 11367, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2007,11,7]]},"reference":[{"key":"2023080308494083400_c1","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1039\/df9592700007","volume":"27","year":"1953","journal-title":"Discuss. Faraday Soc."},{"key":"2023080308494083400_c2","volume-title":"Modern Quantum Chemistry","author":"Sinanoglu","year":"1965"},{"key":"2023080308494083400_c3","volume-title":"Electronic Excitation Energy Transfer in Condensed Matter","year":"1982"},{"key":"2023080308494083400_c4","volume-title":"Excited States of Biological Molecules","year":"1976"},{"key":"2023080308494083400_c5","volume-title":"Resonance Energy Transfer","author":"Andrews","year":"1999"},{"key":"2023080308494083400_c6","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1146\/annurev.physchem.54.011002.103746","volume":"54","year":"2003","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2023080308494083400_c7","doi-asserted-by":"publisher","first-page":"5595","DOI":"10.1021\/jp010208m","volume":"105","year":"2001","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c8","doi-asserted-by":"publisher","first-page":"4619","DOI":"10.1021\/jp036120l","volume":"108","year":"2004","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c9","doi-asserted-by":"publisher","first-page":"1736","DOI":"10.1021\/ja011038u","volume":"124","year":"2002","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c10","first-page":"4456","volume":"83","year":"1999","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c11","doi-asserted-by":"publisher","first-page":"6264","DOI":"10.1073\/pnas.93.13.6264","volume":"93","year":"1996","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023080308494083400_c12","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1126\/science.1085399","volume":"301","year":"2003","journal-title":"Science"},{"key":"2023080308494083400_c13","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1021\/jp030953u","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023080308494083400_c14","doi-asserted-by":"publisher","first-page":"5752","DOI":"10.1021\/jp037724s","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023080308494083400_c15","doi-asserted-by":"publisher","first-page":"10594","DOI":"10.1021\/jp050792p","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c16","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1021\/jp064603u","volume":"111","year":"2007","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c17","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1126\/science.288.5466.652","volume":"288","year":"2000","journal-title":"Science"},{"key":"2023080308494083400_c18","doi-asserted-by":"publisher","first-page":"11181","DOI":"10.1021\/ja961612f","volume":"118","year":"1996","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c19","doi-asserted-by":"publisher","first-page":"9426","DOI":"10.1021\/jp982729o","volume":"102","year":"1998","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c20","doi-asserted-by":"publisher","first-page":"2605","DOI":"10.1039\/b207905d","volume":"22","year":"2002","journal-title":"Chem. Commun. (Cambridge)"},{"key":"2023080308494083400_c21","doi-asserted-by":"publisher","first-page":"2418","DOI":"10.1021\/ja017442a","volume":"124","year":"2002","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c22","doi-asserted-by":"publisher","first-page":"9668","DOI":"10.1021\/ja030002u","volume":"125","year":"2003","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c23","doi-asserted-by":"publisher","first-page":"12821","DOI":"10.1021\/jp047803j","volume":"108","year":"2004","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c24","doi-asserted-by":"publisher","first-page":"6297","DOI":"10.1073\/pnas.1132025100","volume":"100","year":"2003","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023080308494083400_c25","doi-asserted-by":"publisher","first-page":"17887","DOI":"10.1021\/jp051909c","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c26","doi-asserted-by":"publisher","first-page":"6001","DOI":"10.1021\/jp0557565","volume":"110","year":"2006","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c27","doi-asserted-by":"publisher","first-page":"4436","DOI":"10.1021\/ja017150+","volume":"124","year":"2002","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c28","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1073\/pnas.58.2.719","volume":"58","year":"1967","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023080308494083400_c29","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1073\/pnas.63.1.23","volume":"63","year":"1969","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023080308494083400_c30","doi-asserted-by":"publisher","first-page":"730","DOI":"10.1038\/78948","volume":"7","year":"2000","journal-title":"Nat. Struct. Biol."},{"key":"2023080308494083400_c31","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/S0959-440X(00)00190-1","volume":"11","year":"2001","journal-title":"Curr. Opin. Struct. Biol."},{"key":"2023080308494083400_c32","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/S0958-1669(02)00332-4","volume":"13","year":"2002","journal-title":"Curr. Opin. Biotechnol."},{"key":"2023080308494083400_c33","doi-asserted-by":"publisher","first-page":"L99","DOI":"10.1529\/biophysj.106.096206","volume":"91","year":"2006","journal-title":"Biophys. J."},{"key":"2023080308494083400_c34","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1021\/ar030242e","volume":"37","year":"2004","journal-title":"Acc. Chem. Res."},{"key":"2023080308494083400_c35","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/S0301-0104(01)00538-9","volume":"275","year":"2002","journal-title":"Chem. Phys."},{"key":"2023080308494083400_c36","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1021\/jp983477u","volume":"103","year":"1999","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c37","doi-asserted-by":"publisher","first-page":"1854","DOI":"10.1021\/jp993435l","volume":"104","year":"2000","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c38","doi-asserted-by":"publisher","first-page":"1640","DOI":"10.1021\/JP003571M","volume":"105","year":"2001","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c39","doi-asserted-by":"publisher","first-page":"218301","DOI":"10.1103\/PhysRevLett.92.218301","volume":"92","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c40","doi-asserted-by":"publisher","first-page":"108101","DOI":"10.1103\/PhysRevLett.94.108101","volume":"94","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c41","doi-asserted-by":"publisher","first-page":"2754","DOI":"10.1073\/pnas.0408164102","volume":"102","year":"2005","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023080308494083400_c42","doi-asserted-by":"publisher","first-page":"3115","DOI":"10.1021\/ja043940i","volume":"127","year":"2005","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c43","doi-asserted-by":"publisher","first-page":"5191","DOI":"10.1021\/jp055886d","volume":"110","year":"2006","journal-title":"J. Phys. Chem. A"},{"key":"2023080308494083400_c44","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1021\/ja037088b","volume":"126","year":"2004","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c45","doi-asserted-by":"publisher","first-page":"1242","DOI":"10.1021\/ja045676z","volume":"127","year":"2005","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c46","doi-asserted-by":"publisher","first-page":"24331","DOI":"10.1021\/jp0649706","volume":"110","year":"2006","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c47","doi-asserted-by":"publisher","first-page":"047802","DOI":"10.1103\/PhysRevLett.98.047802","volume":"98","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c48","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1021\/jp0655625","volume":"111","year":"2007","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c49","doi-asserted-by":"publisher","first-page":"11223","DOI":"10.1021\/jp050662g","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c50","doi-asserted-by":"publisher","first-page":"103001","DOI":"10.1103\/PhysRevLett.92.103001","volume":"92","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c51","doi-asserted-by":"publisher","first-page":"8118","DOI":"10.1021\/ja062293n","volume":"128","year":"2006","journal-title":"J. Am. Chem. Soc."},{"key":"2023080308494083400_c52","doi-asserted-by":"publisher","first-page":"22103","DOI":"10.1021\/jp063483n","volume":"110","year":"2006","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c53","doi-asserted-by":"publisher","first-page":"166804","DOI":"10.1103\/PhysRevLett.97.166804","volume":"97","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c54","doi-asserted-by":"publisher","first-page":"1785","DOI":"10.1021\/cr0404343","volume":"106","year":"2006","journal-title":"Chem. Rev. (Washington, D.C.)"},{"key":"2023080308494083400_c55","doi-asserted-by":"publisher","first-page":"9370","DOI":"10.1021\/jp0111968","volume":"105","year":"2001","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c56","doi-asserted-by":"publisher","first-page":"7092","DOI":"10.1021\/jp027746z","volume":"107","year":"2003","journal-title":"J. Phys. Chem. A"},{"key":"2023080308494083400_c57","doi-asserted-by":"publisher","first-page":"8218","DOI":"10.1021\/jp0379998","volume":"108","year":"2004","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c58","doi-asserted-by":"publisher","first-page":"11512","DOI":"10.1021\/jp050611j","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c59","doi-asserted-by":"publisher","first-page":"5058","DOI":"10.1021\/jp027481o","volume":"107","year":"2003","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c60","doi-asserted-by":"publisher","first-page":"11010","DOI":"10.1063\/1.1521156","volume":"117","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c61","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1063\/1.1756577","volume":"121","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c62","doi-asserted-by":"publisher","first-page":"1626","DOI":"10.1021\/jp0478864","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c63","doi-asserted-by":"publisher","first-page":"16340","DOI":"10.1021\/jp052275c","volume":"109","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c64","doi-asserted-by":"publisher","first-page":"4178","DOI":"10.1021\/jp067138+","volume":"111","year":"2007","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c65","doi-asserted-by":"publisher","first-page":"4220","DOI":"10.1021\/jp067657c","volume":"111","year":"2007","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c66","doi-asserted-by":"publisher","first-page":"3821","DOI":"10.1063\/1.474741","volume":"107","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c67","doi-asserted-by":"publisher","first-page":"024501","DOI":"10.1063\/1.1828431","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c68","doi-asserted-by":"publisher","first-page":"5106","DOI":"10.1063\/1.467176","volume":"100","year":"1994","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c69","doi-asserted-by":"publisher","first-page":"2371","DOI":"10.1063\/1.479515","volume":"111","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c70","doi-asserted-by":"publisher","first-page":"064107","DOI":"10.1063\/1.2162887","volume":"124","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c71","doi-asserted-by":"publisher","first-page":"12179","DOI":"10.1063\/1.1626631","volume":"119","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c72","doi-asserted-by":"publisher","first-page":"174104","DOI":"10.1063\/1.1888576","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c73","doi-asserted-by":"publisher","first-page":"3368","DOI":"10.1063\/1.1777575","volume":"121","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c74","doi-asserted-by":"publisher","first-page":"3871","DOI":"10.1063\/1.475790","volume":"108","year":"1998","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c75","doi-asserted-by":"publisher","first-page":"4450","DOI":"10.1063\/1.1394208","volume":"115","year":"2001","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c76","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1063\/1.1423936","volume":"116","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c77","doi-asserted-by":"publisher","first-page":"074107","DOI":"10.1063\/1.2274412","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c78","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1103\/PhysRevB.3.262","volume":"3","year":"1971","journal-title":"Phys. Rev. B"},{"key":"2023080308494083400_c79","doi-asserted-by":"publisher","first-page":"8751","DOI":"10.1103\/PhysRevB.49.8751","volume":"49","year":"1994","journal-title":"Phys. Rev. B"},{"key":"2023080308494083400_c80","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1103\/PhysRevA.57.667","volume":"57","year":"1998","journal-title":"Phys. Rev. A"},{"key":"2023080308494083400_c81","doi-asserted-by":"publisher","first-page":"5075","DOI":"10.1063\/1.458646","volume":"93","year":"1990","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c82","doi-asserted-by":"publisher","first-page":"4118","DOI":"10.1103\/PhysRevLett.82.4118","volume":"82","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c83","doi-asserted-by":"publisher","first-page":"1851","DOI":"10.1103\/PhysRevLett.85.1851","volume":"85","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"2023080308494083400_c84","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1126\/science.290.5492.785","volume":"290","year":"2000","journal-title":"Science"},{"key":"2023080308494083400_c85","doi-asserted-by":"publisher","first-page":"043813","DOI":"10.1103\/PhysRevA.65.043813","volume":"65","year":"2002","journal-title":"Phys. Rev. A"},{"key":"2023080308494083400_c86","doi-asserted-by":"publisher","first-page":"4860","DOI":"10.1063\/1.432142","volume":"64","year":"1976","journal-title":"J. Chem. Phys."},{"key":"2023080308494083400_c87","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S1010-6030(01)00504-4","volume":"142","year":"2001","journal-title":"J. Photochem. Photobiol., A"},{"key":"2023080308494083400_c88","doi-asserted-by":"publisher","first-page":"782","DOI":"10.1038\/nature05678","volume":"446","year":"2007","journal-title":"Nature (London)"},{"key":"2023080308494083400_c89","doi-asserted-by":"publisher","first-page":"11196","DOI":"10.1021\/jp047015u","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023080308494083400_c90","doi-asserted-by":"publisher","first-page":"5289","DOI":"10.1021\/jp013927+","volume":"106","year":"2002","journal-title":"J. Phys. Chem. B"},{"key":"2023080308494083400_c91","volume-title":"Molecular Quantum Electrodynamics: An Introduction to Radiation-Molecule Interactions","year":"1984"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.2779031\/15404519\/174710_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\/1.2779031\/15404519\/174710_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T08:49:56Z","timestamp":1691052596000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/127\/17\/174710\/958725\/Generalization-of-the-Forster-resonance-energy"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,7]]},"references-count":91,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2007,11,7]]}},"URL":"https:\/\/doi.org\/10.1063\/1.2779031","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2007,11,7]]},"published":{"date-parts":[[2007,11,7]]},"article-number":"174710"}}