DOI: 10.1063/1.2104507. Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method

Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method

10.1063/1.2104507

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jónnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.

Authors 3

Andreas Heyden (first)
Alexis T. Bell (additional)
Frerich J. Keil (additional)

References 32 Referenced 829

10.1103/PhysRev.76.1169 / Phys. Rev. (1949)
10.1016/0022-3697(57)90059-8 / J. Phys. Chem. Solids (1957)
10.1063/1.442352 / J. Chem. Phys. (1981)
10.1021/j100238a013 / J. Phys. Chem. (1983)
10.1021/j100247a015 / J. Phys. Chem. (1985)
10.1063/1.458435 / J. Chem. Phys. (1990)
10.1063/1.457316 / J. Chem. Phys. (1989)
10.1002/jcc.540070402 / J. Comput. Chem. (1986)
10.1093/comjnl/13.2.185 / Comput. J. (1970)
{'volume-title': 'Nonlinear Programming', 'year': '1970', 'key': '2023072507070945300_c10'} / Nonlinear Programming (1970)
10.1002/jcc.540150102 / J. Comput. Chem. (1994)
10.1063/1.480097 / J. Chem. Phys. (1999)
10.1103/PhysRevE.62.7723 / Phys. Rev. E (2000)
10.1063/1.1323224 / J. Chem. Phys. (2000)
10.1103/PhysRevLett.72.1124 / Phys. Rev. Lett. (1994)
10.1063/1.1691018 / J. Chem. Phys. (2004)
W. Ren, Ph.D. thesis, Department of Mathematics, New York University, 2002.
10.1103/PhysRevB.66.052301 / Phys. Rev. B (2002)
{'volume-title': 'Density Functional Theory of Atoms and Molecules', 'year': '1989', 'key': '2023072507070945300_c19'} / Density Functional Theory of Atoms and Molecules (1989)
10.1021/j100096a001 / J. Phys. Chem. (1994)
10.1063/1.469408 / J. Chem. Phys. (1995)
10.1063/1.467146 / J. Chem. Phys. (1994)
10.1016/0009-2614(89)85118-8 / Chem. Phys. Lett. (1989)
{'volume-title': 'Methods and Techniques in Computational Chemistry: METECC-95', 'year': '1995', 'author': 'Clementi', 'key': '2023072507070945300_c24'} / Methods and Techniques in Computational Chemistry: METECC-95 by Clementi (1995)
10.1002/(SICI)1096-987X(199605)17:7<888::AID-JCC12>3.0.CO;2-7 / J. Comput. Chem. (1996)
10.1063/1.454172 / J. Chem. Phys. (1988)
10.1063/1.465995 / J. Chem. Phys. (1993)
10.1063/1.461606 / J. Chem. Phys. (1991)
10.1063/1.1809574 / J. Chem. Phys. (2004)
{'year': '2003', 'key': '2023072507070945300_c30'} (2003)
{'key': '2023072507070945300_c31', 'first-page': '1857', 'volume': '109', 'year': '2005', 'journal-title': 'J. Phys. Chem. B'} / J. Phys. Chem. B (2005)
{'key': '2023072507070945300_c32', 'first-page': '35', 'volume': '16', 'year': '1969', 'journal-title': 'Rev. Fr. Inform. Rech. Oper.'} / Rev. Fr. Inform. Rech. Oper. (1969)

Dates

Type	When
Created	19 years, 8 months ago (Dec. 8, 2005, 6:03 p.m.)
Deposited	2 years, 1 month ago (July 25, 2023, 3:34 a.m.)
Indexed	53 minutes ago (Aug. 27, 2025, 9:56 p.m.)
Issued	19 years, 8 months ago (Dec. 8, 2005)
Published	19 years, 8 months ago (Dec. 8, 2005)
Published Online	19 years, 8 months ago (Dec. 12, 2005)
Published Print	19 years, 8 months ago (Dec. 8, 2005)

Funders 0

None

BibTeX

@article{Heyden_2005, title={Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method}, volume={123}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2104507}, DOI={10.1063/1.2104507}, number={22}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Heyden, Andreas and Bell, Alexis T. and Keil, Frerich J.}, year={2005}, month=dec }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        28
      ]
    ],
    "date-time": "2025-08-28T01:56:28Z",
    "timestamp": 1756346188471,
    "version": "3.41.2"
  },
  "reference-count": 32,
  "publisher": "AIP Publishing",
  "issue": "22",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2005,
        12,
        8
      ]
    ]
  },
  "abstract": "<jats:p>A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and J\u00f3nnson J. Chem. Phys.\u2008111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.</jats:p>",
  "DOI": "10.1063/1.2104507",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        12,
        8
      ]
    ],
    "date-time": "2005-12-08T23:03:29Z",
    "timestamp": 1134083009000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 829,
  "title": "Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method",
  "prefix": "10.1063",
  "volume": "123",
  "author": [
    {
      "given": "Andreas",
      "family": "Heyden",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Hamburg University of Technology Department of Chemical Engineering, , D-21073 Hamburg, Germany"
        }
      ]
    },
    {
      "given": "Alexis T.",
      "family": "Bell",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "University of California Department of Chemical Engineering, , Berkeley, California 94720-1462"
        }
      ]
    },
    {
      "given": "Frerich J.",
      "family": "Keil",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Hamburg University of Technology Department of Chemical Engineering, , D-21073 Hamburg, Germany"
        }
      ]
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2005,
        12,
        12
      ]
    ]
  },
  "reference": [
    {
      "key": "2023072507070945300_c1",
      "doi-asserted-by": "publisher",
      "first-page": "1169",
      "DOI": "10.1103/PhysRev.76.1169",
      "volume": "76",
      "year": "1949",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2023072507070945300_c2",
      "doi-asserted-by": "publisher",
      "first-page": "121",
      "DOI": "10.1016/0022-3697(57)90059-8",
      "volume": "3",
      "year": "1957",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "2023072507070945300_c3",
      "doi-asserted-by": "publisher",
      "first-page": "2800",
      "DOI": "10.1063/1.442352",
      "volume": "75",
      "year": "1981",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c4",
      "doi-asserted-by": "publisher",
      "first-page": "2745",
      "DOI": "10.1021/j100238a013",
      "volume": "87",
      "year": "1983",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023072507070945300_c5",
      "doi-asserted-by": "publisher",
      "first-page": "52",
      "DOI": "10.1021/j100247a015",
      "volume": "89",
      "year": "1985",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023072507070945300_c6",
      "doi-asserted-by": "publisher",
      "first-page": "340",
      "DOI": "10.1063/1.458435",
      "volume": "92",
      "year": "1990",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c7",
      "doi-asserted-by": "publisher",
      "first-page": "7002",
      "DOI": "10.1063/1.457316",
      "volume": "91",
      "year": "1989",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c8",
      "doi-asserted-by": "publisher",
      "first-page": "385",
      "DOI": "10.1002/jcc.540070402",
      "volume": "7",
      "year": "1986",
      "journal-title": "J. Comput. Chem."
    },
    {
      "key": "2023072507070945300_c9",
      "doi-asserted-by": "crossref",
      "first-page": "185",
      "DOI": "10.1093/comjnl/13.2.185",
      "volume": "13",
      "year": "1970",
      "journal-title": "Comput. J."
    },
    {
      "volume-title": "Nonlinear Programming",
      "year": "1970",
      "key": "2023072507070945300_c10"
    },
    {
      "key": "2023072507070945300_c11",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1002/jcc.540150102",
      "volume": "15",
      "year": "1994",
      "journal-title": "J. Comput. Chem."
    },
    {
      "key": "2023072507070945300_c12",
      "doi-asserted-by": "publisher",
      "first-page": "7010",
      "DOI": "10.1063/1.480097",
      "volume": "111",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c13",
      "doi-asserted-by": "publisher",
      "first-page": "7723",
      "DOI": "10.1103/PhysRevE.62.7723",
      "volume": "62",
      "year": "2000",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2023072507070945300_c14",
      "doi-asserted-by": "publisher",
      "first-page": "9978",
      "DOI": "10.1063/1.1323224",
      "volume": "113",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c15",
      "doi-asserted-by": "publisher",
      "first-page": "1124",
      "DOI": "10.1103/PhysRevLett.72.1124",
      "volume": "72",
      "year": "1994",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023072507070945300_c16",
      "doi-asserted-by": "publisher",
      "first-page": "7877",
      "DOI": "10.1063/1.1691018",
      "volume": "120",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c17",
      "unstructured": "W.\u2008Ren, Ph.D. thesis, Department of Mathematics, New York University, 2002."
    },
    {
      "key": "2023072507070945300_c18",
      "doi-asserted-by": "publisher",
      "first-page": "052301",
      "DOI": "10.1103/PhysRevB.66.052301",
      "volume": "66",
      "year": "2002",
      "journal-title": "Phys. Rev. B"
    },
    {
      "volume-title": "Density Functional Theory of Atoms and Molecules",
      "year": "1989",
      "key": "2023072507070945300_c19"
    },
    {
      "key": "2023072507070945300_c20",
      "doi-asserted-by": "publisher",
      "first-page": "11623",
      "DOI": "10.1021/j100096a001",
      "volume": "98",
      "year": "1994",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023072507070945300_c21",
      "doi-asserted-by": "publisher",
      "first-page": "346",
      "DOI": "10.1063/1.469408",
      "volume": "102",
      "year": "1995",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c22",
      "doi-asserted-by": "publisher",
      "first-page": "5829",
      "DOI": "10.1063/1.467146",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c23",
      "doi-asserted-by": "publisher",
      "first-page": "165",
      "DOI": "10.1016/0009-2614(89)85118-8",
      "volume": "162",
      "year": "1989",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "volume-title": "Methods and Techniques in Computational Chemistry: METECC-95",
      "year": "1995",
      "author": "Clementi",
      "key": "2023072507070945300_c24"
    },
    {
      "key": "2023072507070945300_c25",
      "doi-asserted-by": "publisher",
      "first-page": "888",
      "DOI": "10.1002/(SICI)1096-987X(199605)17:7&lt;888::AID-JCC12&gt;3.0.CO;2-7",
      "volume": "17",
      "year": "1996",
      "journal-title": "J. Comput. Chem."
    },
    {
      "key": "2023072507070945300_c26",
      "doi-asserted-by": "publisher",
      "first-page": "922",
      "DOI": "10.1063/1.454172",
      "volume": "88",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c27",
      "doi-asserted-by": "publisher",
      "first-page": "5269",
      "DOI": "10.1063/1.465995",
      "volume": "99",
      "year": "1993",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c28",
      "doi-asserted-by": "publisher",
      "first-page": "5853",
      "DOI": "10.1063/1.461606",
      "volume": "95",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023072507070945300_c29",
      "doi-asserted-by": "publisher",
      "first-page": "9776",
      "DOI": "10.1063/1.1809574",
      "volume": "121",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
    },
    {
      "year": "2003",
      "key": "2023072507070945300_c30"
    },
    {
      "key": "2023072507070945300_c31",
      "first-page": "1857",
      "volume": "109",
      "year": "2005",
      "journal-title": "J. Phys. Chem. B"
    },
    {
      "key": "2023072507070945300_c32",
      "first-page": "35",
      "volume": "16",
      "year": "1969",
      "journal-title": "Rev. Fr. Inform. Rech. Oper."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2104507/13124124/224101_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2104507/13124124/224101_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        7,
        25
      ]
    ],
    "date-time": "2023-07-25T07:34:38Z",
    "timestamp": 1690270478000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/123/22/224101/776452/Efficient-methods-for-finding-transition-states-in"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2005,
        12,
        8
      ]
    ]
  },
  "references-count": 32,
  "journal-issue": {
    "issue": "22",
    "published-print": {
      "date-parts": [
        [
          2005,
          12,
          8
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.2104507",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2005,
        12,
        8
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2005,
        12,
        8
      ]
    ]
  },
  "article-number": "224101"
}