DOI: 10.1063/1.1630572. From transition paths to transition states and rate coefficients

From transition paths to transition states and rate coefficients

10.1063/1.1630572

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Transition states are defined as points in configuration space with the highest probability that trajectories passing through them are reactive (i.e., form transition paths between reactants and products). In the high-friction (diffusive) limit of Langevin dynamics, the resulting ensemble of transition states is shown to coincide with the separatrix formed by points of equal commitment (or splitting) probabilities for reaching the product and reactant regions. Transition states according to the new criterion can be identified directly from equilibrium trajectories, or indirectly by calculating probability densities in the equilibrium and transition-path ensembles using umbrella and transition-path sampling, respectively. An algorithm is proposed to calculate rate coefficients from the transition-path and equilibrium ensembles by estimating the frequency of transitions between reactants and products.

Bibliography

Hummer, G. (2004). From transition paths to transition states and rate coefficients. The Journal of Chemical Physics, 120(2), 516â523.

Authors 1

Gerhard Hummer (first)

References 34 Referenced 361

{'key': '2024020706391189900_r1'}
10.1063/1.436049 / J. Chem. Phys. (1978)
10.1021/j100324a007 / J. Chem. Phys. (1988)
10.1002/bbpc.19910950318 / Ber. Bunsenges. Phys. Chem. (1991)
10.1063/1.475393 / J. Chem. Phys. (1998)
{'key': '2024020706391189900_r6', 'first-page': '3706', 'volume': '103', 'year': '1999', 'journal-title': 'J. Phys. Chem. B'} / J. Phys. Chem. B (1999)
10.1073/pnas.100127697 / Proc. Natl. Acad. Sci. U.S.A. (2000)
10.1146/annurev.physchem.53.082301.113146 / Annu. Rev. Phys. Chem. (2002)
{'key': '2024020706391189900_r9', 'first-page': '1', 'volume': '123', 'year': '2002', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (2002)
10.1103/PhysRev.54.554 / Phys. Rev. (1938)
10.1016/S0959-440X(98)80012-2 / Curr. Opin. Struct. Biol. (1998)
10.1063/1.451695 / J. Chem. Phys. (1986)
10.1063/1.475562 / J. Chem. Phys. (1998)
10.1063/1.476378 / J. Chem. Phys. (1998)
10.1016/0378-4371(87)90019-7 / Physica A (1987)
10.1007/BF01009355 / J. Stat. Phys. (1987)
10.1063/1.467002 / J. Chem. Phys. (1994)
10.1103/PhysRev.124.983 / Phys. Rev. (1961)
10.1063/1.1519861 / J. Chem. Phys. (2002)
10.1016/0009-2614(74)80109-0 / Chem. Phys. Lett. (1974)
10.1063/1.1699114 / J. Chem. Phys. (1953)
10.1103/RevModPhys.62.251 / Rev. Mod. Phys. (1990)
10.1063/1.478569 / J. Chem. Phys. (1999)
10.1063/1.480278 / J. Chem. Phys. (1999)
10.1063/1.1562614 / J. Chem. Phys. (2003)
10.1063/1.1529192 / J. Chem. Phys. (2003)
{'key': '2024020706391189900_r27'}
10.1016/S0031-8914(40)90098-2 / Physica (Amsterdam) (1940)
10.1063/1.476800 / J. Chem. Phys. (1998)
{'key': '2024020706391189900_r30'}
10.1063/1.438028 / J. Chem. Phys. (1979)
10.1021/ar50156a002 / Acc. Chem. Res. (1980)
10.1063/1.451844 / J. Chem. Phys. (1986)
{'key': '2024020706391189900_r34'}

Dates

Type	When
Created	21 years, 8 months ago (Dec. 24, 2003, 6 p.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 6:04 a.m.)
Indexed	21 minutes ago (Aug. 27, 2025, 4:33 a.m.)
Issued	21 years, 7 months ago (Jan. 8, 2004)
Published	21 years, 7 months ago (Jan. 8, 2004)
Published Print	21 years, 7 months ago (Jan. 8, 2004)

Funders 0

None

BibTeX

@article{Hummer_2004, title={From transition paths to transition states and rate coefficients}, volume={120}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1630572}, DOI={10.1063/1.1630572}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Hummer, Gerhard}, year={2004}, month=jan, pages={516–523} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        27
      ]
    ],
    "date-time": "2025-08-27T08:33:05Z",
    "timestamp": 1756283585894
  },
  "reference-count": 34,
  "publisher": "AIP Publishing",
  "issue": "2",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2004,
        1,
        8
      ]
    ]
  },
  "abstract": "<jats:p>Transition states are defined as points in configuration space with the highest probability that trajectories passing through them are reactive (i.e., form transition paths between reactants and products). In the high-friction (diffusive) limit of Langevin dynamics, the resulting ensemble of transition states is shown to coincide with the separatrix formed by points of equal commitment (or splitting) probabilities for reaching the product and reactant regions. Transition states according to the new criterion can be identified directly from equilibrium trajectories, or indirectly by calculating probability densities in the equilibrium and transition-path ensembles using umbrella and transition-path sampling, respectively. An algorithm is proposed to calculate rate coefficients from the transition-path and equilibrium ensembles by estimating the frequency of transitions between reactants and products.</jats:p>",
  "DOI": "10.1063/1.1630572",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        12,
        24
      ]
    ],
    "date-time": "2003-12-24T23:00:45Z",
    "timestamp": 1072306845000
  },
  "page": "516-523",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 361,
  "title": "From transition paths to transition states and rate coefficients",
  "prefix": "10.1063",
  "volume": "120",
  "author": [
    {
      "given": "Gerhard",
      "family": "Hummer",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Building 5 Bethesda, Maryland\u200920892-0520"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020706391189900_r1"
    },
    {
      "key": "2024020706391189900_r2",
      "doi-asserted-by": "crossref",
      "first-page": "2959",
      "DOI": "10.1063/1.436049",
      "volume": "68",
      "year": "1978",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r3",
      "doi-asserted-by": "crossref",
      "first-page": "3711",
      "DOI": "10.1021/j100324a007",
      "volume": "92",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r4",
      "doi-asserted-by": "crossref",
      "first-page": "331",
      "DOI": "10.1002/bbpc.19910950318",
      "volume": "95",
      "year": "1991",
      "journal-title": "Ber. Bunsenges. Phys. Chem."
    },
    {
      "key": "2024020706391189900_r5",
      "doi-asserted-by": "crossref",
      "first-page": "334",
      "DOI": "10.1063/1.475393",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r6",
      "first-page": "3706",
      "volume": "103",
      "year": "1999",
      "journal-title": "J. Phys. Chem. B"
    },
    {
      "key": "2024020706391189900_r7",
      "doi-asserted-by": "crossref",
      "first-page": "5877",
      "DOI": "10.1073/pnas.100127697",
      "volume": "97",
      "year": "2000",
      "journal-title": "Proc. Natl. Acad. Sci. U.S.A."
    },
    {
      "key": "2024020706391189900_r8",
      "doi-asserted-by": "crossref",
      "first-page": "291",
      "DOI": "10.1146/annurev.physchem.53.082301.113146",
      "volume": "53",
      "year": "2002",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2024020706391189900_r9",
      "first-page": "1",
      "volume": "123",
      "year": "2002",
      "journal-title": "Adv. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r10",
      "doi-asserted-by": "crossref",
      "first-page": "554",
      "DOI": "10.1103/PhysRev.54.554",
      "volume": "54",
      "year": "1938",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020706391189900_r11",
      "doi-asserted-by": "crossref",
      "first-page": "68",
      "DOI": "10.1016/S0959-440X(98)80012-2",
      "volume": "8",
      "year": "1998",
      "journal-title": "Curr. Opin. Struct. Biol."
    },
    {
      "key": "2024020706391189900_r12",
      "doi-asserted-by": "crossref",
      "first-page": "5045",
      "DOI": "10.1063/1.451695",
      "volume": "85",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r13",
      "doi-asserted-by": "crossref",
      "first-page": "1964",
      "DOI": "10.1063/1.475562",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r14",
      "doi-asserted-by": "crossref",
      "first-page": "9236",
      "DOI": "10.1063/1.476378",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r15",
      "doi-asserted-by": "crossref",
      "first-page": "103",
      "DOI": "10.1016/0378-4371(87)90019-7",
      "volume": "142",
      "year": "1987",
      "journal-title": "Physica A"
    },
    {
      "key": "2024020706391189900_r16",
      "doi-asserted-by": "crossref",
      "first-page": "751",
      "DOI": "10.1007/BF01009355",
      "volume": "49",
      "year": "1987",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2024020706391189900_r17",
      "doi-asserted-by": "crossref",
      "first-page": "334",
      "DOI": "10.1063/1.467002",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r18",
      "doi-asserted-by": "crossref",
      "first-page": "983",
      "DOI": "10.1103/PhysRev.124.983",
      "volume": "124",
      "year": "1961",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020706391189900_r19",
      "doi-asserted-by": "crossref",
      "first-page": "10789",
      "DOI": "10.1063/1.1519861",
      "volume": "117",
      "year": "2002",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r20",
      "doi-asserted-by": "crossref",
      "first-page": "578",
      "DOI": "10.1016/0009-2614(74)80109-0",
      "volume": "28",
      "year": "1974",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2024020706391189900_r21",
      "doi-asserted-by": "crossref",
      "first-page": "1087",
      "DOI": "10.1063/1.1699114",
      "volume": "21",
      "year": "1953",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r22",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1103/RevModPhys.62.251",
      "volume": "62",
      "year": "1990",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024020706391189900_r23",
      "doi-asserted-by": "crossref",
      "first-page": "6617",
      "DOI": "10.1063/1.478569",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r24",
      "doi-asserted-by": "crossref",
      "first-page": "9475",
      "DOI": "10.1063/1.480278",
      "volume": "111",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r25",
      "doi-asserted-by": "crossref",
      "first-page": "7762",
      "DOI": "10.1063/1.1562614",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r26",
      "doi-asserted-by": "crossref",
      "first-page": "1085",
      "DOI": "10.1063/1.1529192",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r27"
    },
    {
      "key": "2024020706391189900_r28",
      "doi-asserted-by": "crossref",
      "first-page": "284",
      "DOI": "10.1016/S0031-8914(40)90098-2",
      "volume": "7",
      "year": "1940",
      "journal-title": "Physica (Amsterdam)"
    },
    {
      "key": "2024020706391189900_r29",
      "doi-asserted-by": "crossref",
      "first-page": "2325",
      "DOI": "10.1063/1.476800",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r30"
    },
    {
      "key": "2024020706391189900_r31",
      "doi-asserted-by": "crossref",
      "first-page": "4056",
      "DOI": "10.1063/1.438028",
      "volume": "70",
      "year": "1979",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r32",
      "doi-asserted-by": "crossref",
      "first-page": "440",
      "DOI": "10.1021/ar50156a002",
      "volume": "13",
      "year": "1980",
      "journal-title": "Acc. Chem. Res."
    },
    {
      "key": "2024020706391189900_r33",
      "doi-asserted-by": "crossref",
      "first-page": "1018",
      "DOI": "10.1063/1.451844",
      "volume": "85",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020706391189900_r34"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/120/2/516/19289109/516_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/120/2/516/19289109/516_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T11:04:32Z",
    "timestamp": 1707303872000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/120/2/516/295224/From-transition-paths-to-transition-states-and"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2004,
        1,
        8
      ]
    ]
  },
  "references-count": 34,
  "journal-issue": {
    "issue": "2",
    "published-print": {
      "date-parts": [
        [
          2004,
          1,
          8
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1630572",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2004,
        1,
        8
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2004,
        1,
        8
      ]
    ]
  }
}