DOI: 10.1063/1.464349. Gradient extremals and steepest descent lines on potential energy surfaces

Gradient extremals and steepest descent lines on potential energy surfaces

10.1063/1.464349

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Relationships between steepest descent lines and gradient extremals on potential surfaces are elucidated. It is shown that gradient extremals are the curves which connect those points where the steepest descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient extremals which is illustrated on the Müller–Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the steepest-descent-line curvatures and, from them, for the gradient extremal tangents. With the help of these formulas, a new gradient extremal following algorithm is formulated.

Bibliography

Sun, J.-Q., & Ruedenberg, K. (1993). Gradient extremals and steepest descent lines on potential energy surfaces. The Journal of Chemical Physics, 98(12), 9707â9714.

Authors 2

Jun-Qiang Sun (first)
Klaus Ruedenberg (additional)

References 6 Referenced 96

10.1007/BF00527704 / Theor. Chim. Acta (1986)
10.1016/0301-0104(82)85194-X / Chem. Phys. (1982)
{'key': '2024020715320536300_r1b'}
10.1007/BF01113240 / Theor. Chim. Acta (1992)
10.1007/BF00547608 / Theor. Chim. Acta (1979)
{'key': '2024020715320536300_r4', 'volume': '73', 'year': '1988', 'journal-title': 'Theor. Chim. Acta'} / Theor. Chim. Acta (1988)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:22 a.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 4:57 p.m.)
Indexed	1 week, 3 days ago (Aug. 23, 2025, 9:17 p.m.)
Issued	32 years, 2 months ago (June 15, 1993)
Published	32 years, 2 months ago (June 15, 1993)
Published Print	32 years, 2 months ago (June 15, 1993)

Funders 0

None

BibTeX

@article{Sun_1993, title={Gradient extremals and steepest descent lines on potential energy surfaces}, volume={98}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.464349}, DOI={10.1063/1.464349}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Sun, Jun-Qiang and Ruedenberg, Klaus}, year={1993}, month=jun, pages={9707–9714} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        24
      ]
    ],
    "date-time": "2025-08-24T01:17:55Z",
    "timestamp": 1755998275341
  },
  "reference-count": 6,
  "publisher": "AIP Publishing",
  "issue": "12",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1993,
        6,
        15
      ]
    ]
  },
  "abstract": "<jats:p>Relationships between steepest descent lines and gradient extremals on potential surfaces are elucidated. It is shown that gradient extremals are the curves which connect those points where the steepest descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient extremals which is illustrated on the M\u00fcller\u2013Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the steepest-descent-line curvatures and, from them, for the gradient extremal tangents. With the help of these formulas, a new gradient extremal following algorithm is formulated.</jats:p>",
  "DOI": "10.1063/1.464349",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:22:38Z",
    "timestamp": 1027686158000
  },
  "page": "9707-9714",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 96,
  "title": "Gradient extremals and steepest descent lines on potential energy surfaces",
  "prefix": "10.1063",
  "volume": "98",
  "author": [
    {
      "given": "Jun-Qiang",
      "family": "Sun",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Ames Laboratory, USDOE, and Department of Chemistry, Iowa State University, Ames, Iowa 50011"
        }
      ]
    },
    {
      "given": "Klaus",
      "family": "Ruedenberg",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Ames Laboratory, USDOE, and Department of Chemistry, Iowa State University, Ames, Iowa 50011"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020715320536300_r1",
      "doi-asserted-by": "crossref",
      "first-page": "265",
      "DOI": "10.1007/BF00527704",
      "volume": "69",
      "year": "1986",
      "journal-title": "Theor. Chim. Acta"
    },
    {
      "key": "2024020715320536300_r1a",
      "doi-asserted-by": "crossref",
      "first-page": "337",
      "DOI": "10.1016/0301-0104(82)85194-X",
      "volume": "67",
      "year": "1982",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "2024020715320536300_r1b"
    },
    {
      "key": "2024020715320536300_r2",
      "doi-asserted-by": "crossref",
      "first-page": "15",
      "DOI": "10.1007/BF01113240",
      "volume": "83",
      "year": "1992",
      "journal-title": "Theor. Chim. Acta"
    },
    {
      "key": "2024020715320536300_r3",
      "doi-asserted-by": "crossref",
      "first-page": "75",
      "DOI": "10.1007/BF00547608",
      "volume": "53",
      "year": "1979",
      "journal-title": "Theor. Chim. Acta"
    },
    {
      "key": "2024020715320536300_r4",
      "volume": "73",
      "year": "1988",
      "journal-title": "Theor. Chim. Acta"
    }
  ],
  "updated-by": [
    {
      "updated": {
        "date-parts": [
          [
            1994,
            1,
            15
          ]
        ],
        "date-time": "1994-01-15T00:00:00Z",
        "timestamp": 758592000000
      },
      "DOI": "10.1063/1.467291",
      "type": "correction",
      "source": "publisher",
      "label": "Correction"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/98/12/9707/19328499/9707_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/98/12/9707/19328499/9707_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T21:57:08Z",
    "timestamp": 1707343028000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/98/12/9707/461924/Gradient-extremals-and-steepest-descent-lines-on"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1993,
        6,
        15
      ]
    ]
  },
  "references-count": 6,
  "journal-issue": {
    "issue": "12",
    "published-print": {
      "date-parts": [
        [
          1993,
          6,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.464349",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1993,
        6,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1993,
        6,
        15
      ]
    ]
  }
}