DOI: 10.1063/1.1415342. An improved reactive flux method for evaluation of rate constants in dissipative systems

An improved reactive flux method for evaluation of rate constants in dissipative systems

10.1063/1.1415342

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We present an improved method for numerical evaluation of the least nonvanishing eigenvalue in dissipative systems. It is based on a modified version of the reactive flux formula for the rate which eliminates the principal shortcomings of the original formulation. A new fourth-order algorithm is used to efficiently integrate the underlying generalized Langevin equation. The proposed methodology provides accurate eigenvalues with a small computational effort for systems which could not be accurately treated with the standard techniques. Its efficiency is tested for Brownian motion in a symmetric double well subject to an exponential friction kernel. The presented results demonstrate the applicability of the method in all regimes of interest, reaching from underdamped to overdamped Brownian motion.

Bibliography

Drozdov, A. N., & Tucker, S. C. (2001). An improved reactive flux method for evaluation of rate constants in dissipative systems. The Journal of Chemical Physics, 115(21), 9675â9684.

Authors 2

Alexander N. Drozdov (first)
Susan C. Tucker (additional)

References 54 Referenced 12

{'key': '2024021015370047800_r1'}
{'key': '2024021015370047800_r2'}
10.1103/RevModPhys.62.251 / Rev. Mod. Phys. (1990)
10.1016/0370-1573(91)90108-X / Phys. Rep. (1991)
{'key': '2024021015370047800_r2c'}
{'key': '2024021015370047800_r2d'}
10.1016/S0031-8914(40)90098-2 / Physica (Utrecht) (1940)
{'key': '2024021015370047800_r4'}
10.1007/BF01008729 / J. Stat. Phys. (1973)
10.1143/PTP.33.423 / Prog. Theor. Phys. (1965)
10.1143/PTP.34.399 / Prog. Theor. Phys. (1965)
10.1063/1.440485 / J. Chem. Phys. (1980)
10.1063/1.481792 / J. Chem. Phys. (2000)
10.1063/1.436049 / J. Chem. Phys. (1978)
10.1063/1.449172 / J. Chem. Phys. (1985)
10.1063/1.450425 / J. Chem. Phys. (1986)
10.1021/j100324a007 / J. Phys. Chem. (1988)
10.1063/1.458535 / J. Chem. Phys. (1990)
10.1002/bbpc.19910950317 / Ber. Bunsenges. Phys. Chem. (1991)
{'key': '2024021015370047800_r12', 'first-page': '5809', 'volume': '95', 'year': '1991', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1991)
10.1063/1.462893 / J. Chem. Phys. (1992)
10.1063/1.469381 / J. Chem. Phys. (1995)
10.1063/1.478569 / J. Chem. Phys. (1999)
10.1103/PhysRevE.61.2457 / Phys. Rev. E (2000)
{'key': '2024021015370047800_r17'}
10.1080/00268978000101351 / Mol. Phys. (1980)
{'key': '2024021015370047800_r19', 'first-page': '61', 'volume': '53', 'year': '1983', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1983)
10.1063/1.445244 / J. Chem. Phys. (1983)
10.1063/1.449379 / J. Chem. Phys. (1985)
10.1103/PhysRevA.40.3381 / Phys. Rev. A (1989)
{'key': '2024021015370047800_r23', 'first-page': '1304', 'volume': '92', 'year': '1991', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1991)
10.1063/1.461794 / J. Chem. Phys. (1991)
10.1016/0378-4371(93)90604-3 / Physica A (1993)
10.1063/1.474690 / J. Chem. Phys. (1997)
{'key': '2024021015370047800_r26'}
10.1063/1.436694 / J. Chem. Phys. (1978)
10.1103/PhysRevE.55.2496 / Phys. Rev. E (1997)
10.1016/S0375-9601(97)00851-7 / Phys. Lett. A (1998)
10.1063/1.476380 / J. Chem. Phys. (1998)
{'key': '2024021015370047800_r31', 'first-page': '1284', 'volume': '57', 'year': '1998', 'journal-title': 'Phys. Rev. E'} / Phys. Rev. E (1998)
10.1063/1.476721 / J. Chem. Phys. (1998)
10.1016/0896-8446(91)90037-7 / J. Supercrit. Fluids (1991)
10.1021/ie9605802 / Ind. Eng. Chem. Res. (1997)
10.1002/aic.690431107 / AIChE J. (1997)
10.1021/ie9602318 / Ind. Eng. Chem. Res. (1997)
{'key': '2024021015370047800_r33'}
10.1063/1.469826 / J. Chem. Phys. (1995)
10.1063/1.471930 / J. Chem. Phys. (1996)
10.1063/1.472580 / J. Chem. Phys. (1996)
{'key': '2024021015370047800_r35'}
10.1002/j.1538-7305.1944.tb00874.x / Bell Syst. Tech. J. (1944)
{'key': '2024021015370047800_r36a', 'first-page': '46', 'volume': '25', 'year': '1945', 'journal-title': 'Bell Syst. Tech. J.'} / Bell Syst. Tech. J. (1945)
{'key': '2024021015370047800_r37'}
{'key': '2024021015370047800_r37a', 'first-page': '6287', 'volume': '78', 'year': '1982', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1982)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:01 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 11:41 a.m.)
Indexed	1 year, 1 month ago (July 10, 2024, 9:56 a.m.)
Issued	23 years, 8 months ago (Dec. 1, 2001)
Published	23 years, 8 months ago (Dec. 1, 2001)
Published Print	23 years, 8 months ago (Dec. 1, 2001)

Funders 0

None

BibTeX

@article{Drozdov_2001, title={An improved reactive flux method for evaluation of rate constants in dissipative systems}, volume={115}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1415342}, DOI={10.1063/1.1415342}, number={21}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Drozdov, Alexander N. and Tucker, Susan C.}, year={2001}, month=dec, pages={9675–9684} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        7,
        10
      ]
    ],
    "date-time": "2024-07-10T13:56:28Z",
    "timestamp": 1720619788180
  },
  "reference-count": 54,
  "publisher": "AIP Publishing",
  "issue": "21",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2001,
        12,
        1
      ]
    ]
  },
  "abstract": "<jats:p>We present an improved method for numerical evaluation of the least nonvanishing eigenvalue in dissipative systems. It is based on a modified version of the reactive flux formula for the rate which eliminates the principal shortcomings of the original formulation. A new fourth-order algorithm is used to efficiently integrate the underlying generalized Langevin equation. The proposed methodology provides accurate eigenvalues with a small computational effort for systems which could not be accurately treated with the standard techniques. Its efficiency is tested for Brownian motion in a symmetric double well subject to an exponential friction kernel. The presented results demonstrate the applicability of the method in all regimes of interest, reaching from underdamped to overdamped Brownian motion.</jats:p>",
  "DOI": "10.1063/1.1415342",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:01:09Z",
    "timestamp": 1027684869000
  },
  "page": "9675-9684",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 12,
  "title": "An improved reactive flux method for evaluation of rate constants in dissipative systems",
  "prefix": "10.1063",
  "volume": "115",
  "author": [
    {
      "given": "Alexander N.",
      "family": "Drozdov",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Chemistry, University of California, Davis, California\u200995616"
        }
      ]
    },
    {
      "given": "Susan C.",
      "family": "Tucker",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemistry, University of California, Davis, California\u200995616"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021015370047800_r1"
    },
    {
      "key": "2024021015370047800_r2"
    },
    {
      "key": "2024021015370047800_r2a",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1103/RevModPhys.62.251",
      "volume": "62",
      "year": "1990",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024021015370047800_r2b",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1016/0370-1573(91)90108-X",
      "volume": "209",
      "year": "1991",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "2024021015370047800_r2c"
    },
    {
      "key": "2024021015370047800_r2d"
    },
    {
      "key": "2024021015370047800_r3",
      "doi-asserted-by": "crossref",
      "first-page": "284",
      "DOI": "10.1016/S0031-8914(40)90098-2",
      "volume": "7",
      "year": "1940",
      "journal-title": "Physica (Utrecht)"
    },
    {
      "key": "2024021015370047800_r4"
    },
    {
      "key": "2024021015370047800_r4a",
      "doi-asserted-by": "crossref",
      "first-page": "215",
      "DOI": "10.1007/BF01008729",
      "volume": "9",
      "year": "1973",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "2024021015370047800_r5",
      "doi-asserted-by": "crossref",
      "first-page": "423",
      "DOI": "10.1143/PTP.33.423",
      "volume": "33",
      "year": "1965",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024021015370047800_r5a",
      "doi-asserted-by": "crossref",
      "first-page": "399",
      "DOI": "10.1143/PTP.34.399",
      "volume": "34",
      "year": "1965",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024021015370047800_r6",
      "doi-asserted-by": "crossref",
      "first-page": "2715",
      "DOI": "10.1063/1.440485",
      "volume": "73",
      "year": "1980",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r7",
      "doi-asserted-by": "crossref",
      "first-page": "258",
      "DOI": "10.1063/1.481792",
      "volume": "113",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r8",
      "doi-asserted-by": "crossref",
      "first-page": "2959",
      "DOI": "10.1063/1.436049",
      "volume": "68",
      "year": "1978",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r9",
      "doi-asserted-by": "crossref",
      "first-page": "3172",
      "DOI": "10.1063/1.449172",
      "volume": "83",
      "year": "1985",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r9a",
      "doi-asserted-by": "crossref",
      "first-page": "1788",
      "DOI": "10.1063/1.450425",
      "volume": "84",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r9b",
      "doi-asserted-by": "crossref",
      "first-page": "3711",
      "DOI": "10.1021/j100324a007",
      "volume": "92",
      "year": "1988",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2024021015370047800_r10",
      "doi-asserted-by": "crossref",
      "first-page": "5307",
      "DOI": "10.1063/1.458535",
      "volume": "92",
      "year": "1990",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r11",
      "doi-asserted-by": "crossref",
      "first-page": "327",
      "DOI": "10.1002/bbpc.19910950317",
      "volume": "95",
      "year": "1991",
      "journal-title": "Ber. Bunsenges. Phys. Chem."
    },
    {
      "key": "2024021015370047800_r12",
      "first-page": "5809",
      "volume": "95",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r13",
      "doi-asserted-by": "crossref",
      "first-page": "5460",
      "DOI": "10.1063/1.462893",
      "volume": "96",
      "year": "1992",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r14",
      "doi-asserted-by": "crossref",
      "first-page": "104",
      "DOI": "10.1063/1.469381",
      "volume": "102",
      "year": "1995",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r15",
      "doi-asserted-by": "crossref",
      "first-page": "6617",
      "DOI": "10.1063/1.478569",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r16",
      "doi-asserted-by": "crossref",
      "first-page": "2457",
      "DOI": "10.1103/PhysRevE.61.2457",
      "volume": "61",
      "year": "2000",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021015370047800_r17"
    },
    {
      "key": "2024021015370047800_r18",
      "doi-asserted-by": "crossref",
      "first-page": "141",
      "DOI": "10.1080/00268978000101351",
      "volume": "40",
      "year": "1980",
      "journal-title": "Mol. Phys."
    },
    {
      "key": "2024021015370047800_r19",
      "first-page": "61",
      "volume": "53",
      "year": "1983",
      "journal-title": "Adv. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r20",
      "doi-asserted-by": "crossref",
      "first-page": "3256",
      "DOI": "10.1063/1.445244",
      "volume": "78",
      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r21",
      "doi-asserted-by": "crossref",
      "first-page": "1917",
      "DOI": "10.1063/1.449379",
      "volume": "83",
      "year": "1985",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r22",
      "doi-asserted-by": "crossref",
      "first-page": "3381",
      "DOI": "10.1103/PhysRevA.40.3381",
      "volume": "40",
      "year": "1989",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024021015370047800_r23",
      "first-page": "1304",
      "volume": "92",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r24",
      "doi-asserted-by": "crossref",
      "first-page": "4389",
      "DOI": "10.1063/1.461794",
      "volume": "95",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r25",
      "doi-asserted-by": "crossref",
      "first-page": "258",
      "DOI": "10.1016/0378-4371(93)90604-3",
      "volume": "196",
      "year": "1993",
      "journal-title": "Physica A"
    },
    {
      "key": "2024021015370047800_r25a",
      "doi-asserted-by": "crossref",
      "first-page": "3505",
      "DOI": "10.1063/1.474690",
      "volume": "107",
      "year": "1997",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r26"
    },
    {
      "key": "2024021015370047800_r27",
      "doi-asserted-by": "crossref",
      "first-page": "1010",
      "DOI": "10.1063/1.436694",
      "volume": "69",
      "year": "1978",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r28",
      "doi-asserted-by": "crossref",
      "first-page": "2496",
      "DOI": "10.1103/PhysRevE.55.2496",
      "volume": "55",
      "year": "1997",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021015370047800_r29",
      "doi-asserted-by": "crossref",
      "first-page": "119",
      "DOI": "10.1016/S0375-9601(97)00851-7",
      "volume": "237",
      "year": "1998",
      "journal-title": "Phys. Lett. A"
    },
    {
      "key": "2024021015370047800_r30",
      "doi-asserted-by": "crossref",
      "first-page": "9253",
      "DOI": "10.1063/1.476380",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r31",
      "first-page": "1284",
      "volume": "57",
      "year": "1998",
      "journal-title": "Phys. Rev. E"
    },
    {
      "key": "2024021015370047800_r31a",
      "doi-asserted-by": "crossref",
      "first-page": "2080",
      "DOI": "10.1063/1.476721",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r32",
      "doi-asserted-by": "crossref",
      "first-page": "91",
      "DOI": "10.1016/0896-8446(91)90037-7",
      "volume": "4",
      "year": "1991",
      "journal-title": "J. Supercrit. Fluids"
    },
    {
      "key": "2024021015370047800_r32a",
      "doi-asserted-by": "crossref",
      "first-page": "923",
      "DOI": "10.1021/ie9605802",
      "volume": "36",
      "year": "1997",
      "journal-title": "Ind. Eng. Chem. Res."
    },
    {
      "key": "2024021015370047800_r32b",
      "doi-asserted-by": "crossref",
      "first-page": "2944",
      "DOI": "10.1002/aic.690431107",
      "volume": "43",
      "year": "1997",
      "journal-title": "AIChE J."
    },
    {
      "key": "2024021015370047800_r32c",
      "doi-asserted-by": "crossref",
      "first-page": "246",
      "DOI": "10.1021/ie9602318",
      "volume": "36",
      "year": "1997",
      "journal-title": "Ind. Eng. Chem. Res."
    },
    {
      "key": "2024021015370047800_r33"
    },
    {
      "key": "2024021015370047800_r34",
      "doi-asserted-by": "crossref",
      "first-page": "1160",
      "DOI": "10.1063/1.469826",
      "volume": "103",
      "year": "1995",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r34a",
      "doi-asserted-by": "crossref",
      "first-page": "628",
      "DOI": "10.1063/1.471930",
      "volume": "105",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r34b",
      "doi-asserted-by": "crossref",
      "first-page": "7543",
      "DOI": "10.1063/1.472580",
      "volume": "105",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021015370047800_r35"
    },
    {
      "key": "2024021015370047800_r36",
      "doi-asserted-by": "crossref",
      "first-page": "282",
      "DOI": "10.1002/j.1538-7305.1944.tb00874.x",
      "volume": "23",
      "year": "1944",
      "journal-title": "Bell Syst. Tech. J."
    },
    {
      "key": "2024021015370047800_r36a",
      "first-page": "46",
      "volume": "25",
      "year": "1945",
      "journal-title": "Bell Syst. Tech. J."
    },
    {
      "key": "2024021015370047800_r37"
    },
    {
      "key": "2024021015370047800_r37a",
      "first-page": "6287",
      "volume": "78",
      "year": "1982",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/115/21/9675/19011576/9675_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/115/21/9675/19011576/9675_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T16:41:16Z",
    "timestamp": 1707583276000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/115/21/9675/453031/An-improved-reactive-flux-method-for-evaluation-of"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2001,
        12,
        1
      ]
    ]
  },
  "references-count": 54,
  "journal-issue": {
    "issue": "21",
    "published-print": {
      "date-parts": [
        [
          2001,
          12,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1415342",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2001,
        12,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2001,
        12,
        1
      ]
    ]
  }
}