DOI: 10.1063/1.431152. The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

10.1063/1.431152

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a ’’supermolecule’’ consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of ’’activationless’’ regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.

Bibliography

Ulstrup, J., & Jortner, J. (1975). The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions. The Journal of Chemical Physics, 63(10), 4358â4368.

Authors 2

Jens Ulstrup (first)
Joshua Jortner (additional)

References 39 Referenced 671

10.1063/1.1668703 / J. Chem. Phys. (1968)
10.1063/1.1671552 / J. Chem. Phys. (1969)
{'key': '2024020913390500400_r1b'}
10.1080/00268977000100171 / Mol. Phys. (1970)
10.1016/0009-2614(70)85092-8 / Chem. Phys. Lett. (1970)
10.1063/1.1680979 / J. Chem. Phys. (1974)
10.1063/1.1727525 / J. Chem. Phys. (1966)
10.1021/j100614a017 / J. Phys. Chem. (1974)
{'key': '2024020913390500400_r5', 'first-page': '161', 'volume': '13', 'year': '1955', 'journal-title': 'Prog. Theor. Phys.'} / Prog. Theor. Phys. (1955)
10.1016/0003-4916(59)90002-8 / Ann. Phys. (1959)
{'key': '2024020913390500400_r6', 'first-page': '249', 'volume': '4', 'year': '1966', 'journal-title': 'Adv. Electrochem. Electrochem. Eng.'} / Adv. Electrochem. Electrochem. Eng. (1966)
10.1098/rspa.1952.0139 / Proc. R. Soc. London Ser. A (1952)
{'key': '2024020913390500400_r8'}
10.1063/1.1742723 / J. Chem. Phys. (1956)
{'key': '2024020913390500400_r10'}
{'key': '2024020913390500400_r11'}
{'key': '2024020913390500400_r12', 'first-page': '881', 'volume': '9', 'year': '1973', 'journal-title': 'Elektrokhimiya'} / Elektrokhimiya (1973)
{'key': '2024020913390500400_r13', 'first-page': '612', 'volume': '10', 'year': '1974', 'journal-title': 'Elektrokhimiya'} / Elektrokhimiya (1974)
10.1039/DF9602900021 / Discuss. Faraday Soc. (1960)
10.1002/pssb.2220540111 / Phys. Status Solidi (1972)
10.1002/pssb.2220540206 / Phys. Status Solidi (1972)
{'key': '2024020913390500400_r17', 'first-page': '744', 'volume': '68', 'year': '1972', 'journal-title': 'J. Chem. Soc. Faraday Trans.'} / J. Chem. Soc. Faraday Trans. (1972)
{'key': '2024020913390500400_r18', 'first-page': '34', 'volume': '20', 'year': '1972', 'journal-title': 'J. Res. Inst. Catal. Hokkaido Univ.'} / J. Res. Inst. Catal. Hokkaido Univ. (1972)
10.1002/kin.550060402 / Int. J. Chem. Kinet. (1974)
{'key': '2024020913390500400_r20'}
10.1016/0009-2614(74)80325-8 / Chem. Phys. Lett. (1974)
10.1002/ijch.197000029 / Israel J. Chem. (1970)
{'key': '2024020913390500400_r23'}
{'key': '2024020913390500400_r24'}
10.1016/0013-4686(70)80027-5 / Electrochim. Acta (1970)
10.1021/ja00796a080 / J. Am. Chem. Soc. (1973)
10.1063/1.1672938 / J. Chem. Phys. (1970)
10.1007/BF00527613 / Theor. Chim. Acta (1973)
10.1063/1.1840685 / J. Chem. Phys. (1967)
10.1063/1.1703324 / J. Chem. Phys. (1967)
10.1103/PhysRevB.8.6 / Phys. Rev. B (1973)
10.1088/0370-1298/66/12/310 / Proc. Phys. Soc. London Sect. A (1953)
10.1088/0370-1298/66/12/311 / Proc. Phys. Soc. London Sec. A (1953)
{'key': '2024020913390500400_r34'}

Dates

Type	When
Created	22 years, 5 months ago (Feb. 27, 2003, 3:57 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 9:26 a.m.)
Indexed	2 weeks, 4 days ago (Aug. 7, 2025, 4:46 p.m.)
Issued	49 years, 9 months ago (Nov. 15, 1975)
Published	49 years, 9 months ago (Nov. 15, 1975)
Published Print	49 years, 9 months ago (Nov. 15, 1975)

Funders 0

None

BibTeX

@article{Ulstrup_1975, title={The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions}, volume={63}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.431152}, DOI={10.1063/1.431152}, number={10}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Ulstrup, Jens and Jortner, Joshua}, year={1975}, month=nov, pages={4358–4368} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        7
      ]
    ],
    "date-time": "2025-08-07T20:46:29Z",
    "timestamp": 1754599589387
  },
  "reference-count": 39,
  "publisher": "AIP Publishing",
  "issue": "10",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1975,
        11,
        15
      ]
    ]
  },
  "abstract": "<jats:p>A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a \u2019\u2019supermolecule\u2019\u2019 consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high-frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high-frequency intramolecular modes this provides a rationalization of the experimental observation of \u2019\u2019activationless\u2019\u2019 regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous to the vibrational structure in optical transitions.</jats:p>",
  "DOI": "10.1063/1.431152",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        2,
        27
      ]
    ],
    "date-time": "2003-02-27T20:57:18Z",
    "timestamp": 1046379438000
  },
  "page": "4358-4368",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 671,
  "title": "The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions",
  "prefix": "10.1063",
  "volume": "63",
  "author": [
    {
      "given": "Jens",
      "family": "Ulstrup",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Chemistry Department A, Building 207, The Technical University of Denmark, 2800 Lyngby, Denmark"
        }
      ]
    },
    {
      "given": "Joshua",
      "family": "Jortner",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Chemistry Department IV, H.C. O/rsted Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen O/, Denmark"
        },
        {
          "name": "Department of Chemistry, Tel Aviv University, Tel Aviv, Israel"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020913390500400_r1",
      "doi-asserted-by": "crossref",
      "first-page": "715",
      "DOI": "10.1063/1.1668703",
      "volume": "48",
      "year": "1968",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r1a",
      "doi-asserted-by": "crossref",
      "first-page": "3284",
      "DOI": "10.1063/1.1671552",
      "volume": "50",
      "year": "1969",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r1b"
    },
    {
      "key": "2024020913390500400_r1c",
      "doi-asserted-by": "crossref",
      "first-page": "145",
      "DOI": "10.1080/00268977000100171",
      "volume": "18",
      "year": "1970",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024020913390500400_r1d",
      "doi-asserted-by": "crossref",
      "first-page": "345",
      "DOI": "10.1016/0009-2614(70)85092-8",
      "volume": "6",
      "year": "1970",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020913390500400_r2",
      "doi-asserted-by": "crossref",
      "first-page": "4760",
      "DOI": "10.1063/1.1680979",
      "volume": "60",
      "year": "1974",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r3",
      "doi-asserted-by": "crossref",
      "first-page": "4455",
      "DOI": "10.1063/1.1727525",
      "volume": "45",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r4",
      "doi-asserted-by": "crossref",
      "first-page": "2148",
      "DOI": "10.1021/j100614a017",
      "volume": "78",
      "year": "1974",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2024020913390500400_r5",
      "first-page": "161",
      "volume": "13",
      "year": "1955",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020913390500400_r5a",
      "doi-asserted-by": "crossref",
      "first-page": "325",
      "DOI": "10.1016/0003-4916(59)90002-8",
      "volume": "8",
      "year": "1959",
      "journal-title": "Ann. Phys."
    },
    {
      "key": "2024020913390500400_r6",
      "first-page": "249",
      "volume": "4",
      "year": "1966",
      "journal-title": "Adv. Electrochem. Electrochem. Eng."
    },
    {
      "key": "2024020913390500400_r7",
      "doi-asserted-by": "crossref",
      "first-page": "473",
      "DOI": "10.1098/rspa.1952.0139",
      "volume": "213",
      "year": "1952",
      "journal-title": "Proc. R. Soc. London Ser. A"
    },
    {
      "key": "2024020913390500400_r8"
    },
    {
      "key": "2024020913390500400_r9",
      "doi-asserted-by": "crossref",
      "first-page": "966",
      "DOI": "10.1063/1.1742723",
      "volume": "24",
      "year": "1956",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r10"
    },
    {
      "key": "2024020913390500400_r11"
    },
    {
      "key": "2024020913390500400_r12",
      "first-page": "881",
      "volume": "9",
      "year": "1973",
      "journal-title": "Elektrokhimiya"
    },
    {
      "key": "2024020913390500400_r13",
      "first-page": "612",
      "volume": "10",
      "year": "1974",
      "journal-title": "Elektrokhimiya"
    },
    {
      "key": "2024020913390500400_r14",
      "doi-asserted-by": "crossref",
      "first-page": "21",
      "DOI": "10.1039/DF9602900021",
      "volume": "29",
      "year": "1960",
      "journal-title": "Discuss. Faraday Soc."
    },
    {
      "key": "2024020913390500400_r15",
      "doi-asserted-by": "crossref",
      "first-page": "125",
      "DOI": "10.1002/pssb.2220540111",
      "volume": "54",
      "year": "1972",
      "journal-title": "Phys. Status Solidi"
    },
    {
      "key": "2024020913390500400_r16",
      "doi-asserted-by": "crossref",
      "first-page": "425",
      "DOI": "10.1002/pssb.2220540206",
      "volume": "54",
      "year": "1972",
      "journal-title": "Phys. Status Solidi"
    },
    {
      "key": "2024020913390500400_r17",
      "first-page": "744",
      "volume": "68",
      "year": "1972",
      "journal-title": "J. Chem. Soc. Faraday Trans."
    },
    {
      "key": "2024020913390500400_r18",
      "first-page": "34",
      "volume": "20",
      "year": "1972",
      "journal-title": "J. Res. Inst. Catal. Hokkaido Univ."
    },
    {
      "key": "2024020913390500400_r19",
      "doi-asserted-by": "crossref",
      "first-page": "457",
      "DOI": "10.1002/kin.550060402",
      "volume": "6",
      "year": "1974",
      "journal-title": "Int. J. Chem. Kinet."
    },
    {
      "key": "2024020913390500400_r20"
    },
    {
      "key": "2024020913390500400_r21",
      "doi-asserted-by": "crossref",
      "first-page": "34",
      "DOI": "10.1016/0009-2614(74)80325-8",
      "volume": "25",
      "year": "1974",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020913390500400_r22",
      "doi-asserted-by": "crossref",
      "first-page": "259",
      "DOI": "10.1002/ijch.197000029",
      "volume": "8",
      "year": "1970",
      "journal-title": "Israel J. Chem."
    },
    {
      "key": "2024020913390500400_r23"
    },
    {
      "key": "2024020913390500400_r24"
    },
    {
      "key": "2024020913390500400_r25",
      "doi-asserted-by": "crossref",
      "first-page": "353",
      "DOI": "10.1016/0013-4686(70)80027-5",
      "volume": "15",
      "year": "1970",
      "journal-title": "Electrochim. Acta"
    },
    {
      "key": "2024020913390500400_r26",
      "doi-asserted-by": "crossref",
      "first-page": "5097",
      "DOI": "10.1021/ja00796a080",
      "volume": "95",
      "year": "1973",
      "journal-title": "J. Am. Chem. Soc."
    },
    {
      "key": "2024020913390500400_r27",
      "doi-asserted-by": "crossref",
      "first-page": "6272",
      "DOI": "10.1063/1.1672938",
      "volume": "52",
      "year": "1970",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r28",
      "doi-asserted-by": "crossref",
      "first-page": "217",
      "DOI": "10.1007/BF00527613",
      "volume": "30",
      "year": "1973",
      "journal-title": "Theor. Chim. Acta"
    },
    {
      "key": "2024020913390500400_r29",
      "doi-asserted-by": "crossref",
      "first-page": "440",
      "DOI": "10.1063/1.1840685",
      "volume": "46",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r30",
      "doi-asserted-by": "crossref",
      "first-page": "2411",
      "DOI": "10.1063/1.1703324",
      "volume": "47",
      "year": "1967",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020913390500400_r31",
      "doi-asserted-by": "crossref",
      "first-page": "6",
      "DOI": "10.1103/PhysRevB.8.6",
      "volume": "8",
      "year": "1973",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020913390500400_r32",
      "doi-asserted-by": "crossref",
      "first-page": "1145",
      "DOI": "10.1088/0370-1298/66/12/310",
      "volume": "66",
      "year": "1953",
      "journal-title": "Proc. Phys. Soc. London Sect. A"
    },
    {
      "key": "2024020913390500400_r33",
      "doi-asserted-by": "crossref",
      "first-page": "1153",
      "DOI": "10.1088/0370-1298/66/12/311",
      "volume": "66",
      "year": "1953",
      "journal-title": "Proc. Phys. Soc. London Sec. A"
    },
    {
      "key": "2024020913390500400_r34"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/63/10/4358/18898927/4358_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/63/10/4358/18898927/4358_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T14:26:46Z",
    "timestamp": 1707488806000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/63/10/4358/215978/The-effect-of-intramolecular-quantum-modes-on-free"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1975,
        11,
        15
      ]
    ]
  },
  "references-count": 39,
  "journal-issue": {
    "issue": "10",
    "published-print": {
      "date-parts": [
        [
          1975,
          11,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.431152",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1975,
        11,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1975,
        11,
        15
      ]
    ]
  }
}