DOI: 10.1063/1.2387950. Using neural networks to represent potential surfaces as sums of products

Using neural networks to represent potential surfaces as sums of products

10.1063/1.2387950

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.

Bibliography

Manzhos, S., & Carrington, T. (2006). Using neural networks to represent potential surfaces as sums of products. The Journal of Chemical Physics, 125(19).

Authors 2

Sergei Manzhos (first)
Tucker Carrington (additional)

References 56 Referenced 165

{'volume-title': 'Photodissociation Dynamics', 'year': '1995', 'key': '2023071503542386100_c1'} / Photodissociation Dynamics (1995)
{'volume-title': 'Dynamics of Molecules and Chemical Reactions', 'year': '1996', 'author': 'Wyatt', 'key': '2023071503542386100_c2'} / Dynamics of Molecules and Chemical Reactions by Wyatt (1996)
10.1063/1.474210 / J. Chem. Phys. (1997)
10.1016/S0009-2614(01)01381-1 / Chem. Phys. Lett. (2002)
10.1063/1.1804174 / J. Chem. Phys. (2004)
10.1063/1.2001654 / J. Chem. Phys. (2005)
10.1063/1.1857472 / J. Chem. Phys. (2005)
10.1063/1.1759627 / J. Chem. Phys. (2004)
10.1063/1.478750 / J. Chem. Phys. (1999)
10.1007/s002140050379 / Theor. Chem. Acc. (1998)
10.1016/S0010-4655(98)00152-0 / Comput. Phys. Commun. (1999)
10.1023/A:1019188517934 / J. Math. Chem. (1999)
10.1021/jp010450t / J. Phys. Chem. A (2001)
10.1063/1.2336223 / J. Chem. Phys. (2006)
10.1063/1.471513 / J. Chem. Phys. (1996)
10.1063/1.476977 / J. Chem. Phys. (1998)
10.1063/1.469292 / J. Chem. Phys. (1995)
{'key': '2023071503542386100_c18', 'first-page': '115', 'volume': '5', 'year': '1986', 'journal-title': 'Comput. Phys. Rep.'} / Comput. Phys. Rep. (1986)
10.1063/1.465576 / J. Chem. Phys. (1993)
10.1016/0167-7977(86)90005-5 / Comput. Phys. Rep. (1986)
10.1146/annurev.physchem.40.1.469 / Annu. Rev. Phys. Chem. (1989)
{'key': '2023071503542386100_c22', 'first-page': '1', 'volume': '9', 'year': '1990', 'journal-title': 'Annu. Rev. Phys. Chem.'} / Annu. Rev. Phys. Chem. (1990)
10.1002/0470845015 / Encyclopedia of Computational Chemistry by Schleyer (1998)
{'key': '2023071503542386100_c24', 'first-page': '263', 'volume': '114', 'year': '2000', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (2000)
10.1021/j100319a003 / J. Phys. Chem. (1988)
10.1002/0470845015 / Encyclopedia of Computational Chemistry by Schleyer (1998)
10.1021/ar00028a007 / Acc. Chem. Res. (1993)
{'volume-title': 'Numerical Recipes in Fortran 77: The Art of Scientific Computing', 'year': '1992', 'key': '2023071503542386100_c28'} / Numerical Recipes in Fortran 77: The Art of Scientific Computing (1992)
10.1063/1.467273 / J. Chem. Phys. (1994)
10.1063/1.463916 / J. Chem. Phys. (1992)
10.1063/1.1407277 / J. Chem. Phys. (2001)
10.1063/1.1348274 / J. Chem. Phys. (2001)
10.1063/1.460317 / J. Chem. Phys. (1991)
10.1063/1.473908 / J. Chem. Phys. (1997)
10.1063/1.463332 / J. Chem. Phys. (1992)
10.1016/S0370-1573(99)00047-2 / Phys. Rep. (2000)
10.1007/BF01449770 / Math. Ann. (1906)
10.1063/1.2192499 / J. Chem. Phys. (2006)
10.1063/1.2171246 / J. Chem. Phys. (2006)
10.1063/1.2085167 / J. Chem. Phys. (2005)
10.1016/j.chemphys.2004.06.006 / Chem. Phys. (2004)
{'volume-title': 'Neural Network Learning: Theoretical Foundations', 'year': '1999', 'key': '2023071503542386100_c42'} / Neural Network Learning: Theoretical Foundations (1999)
10.1146/annurev.physchem.45.1.439 / Annu. Rev. Phys. Chem. (1994)
10.1021/jp055253z / J. Phys. Chem. A (2006)
10.1063/1.2185638 / J. Chem. Phys. (2006)
10.1016/j.cplett.2004.07.076 / Chem. Phys. Lett. (2004)
10.1063/1.477550 / J. Chem. Phys. (1998)
10.1063/1.1850458 / J. Chem. Phys. (2005)
10.1016/0893-6080(89)90003-8 / Neural Networks (1989)
10.1016/S0925-2312(98)00111-8 / Neurocomputing (1999)
{'key': '2023071503542386100_c51', 'first-page': '45', 'volume': '11', 'year': '1998', 'journal-title': 'Appl. Math. Lett.'} / Appl. Math. Lett. (1998)
10.1016/S0893-6080(97)00118-4 / Neural Networks (1998)
10.1109/72.761726 / IEEE Trans. Neural Netw. (1999)
10.1016/S0893-6080(03)00189-8 / Neural Networks (2004)
10.1063/1.479534 / J. Chem. Phys. (1999)
{'year': '2002', 'key': '2023071503542386100_c56'} (2002)

Dates

Type	When
Created	18 years, 9 months ago (Nov. 16, 2006, 6:06 p.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 4:30 a.m.)
Indexed	2 weeks, 3 days ago (Aug. 7, 2025, 4:53 p.m.)
Issued	18 years, 9 months ago (Nov. 16, 2006)
Published	18 years, 9 months ago (Nov. 16, 2006)
Published Online	18 years, 9 months ago (Nov. 16, 2006)
Published Print	18 years, 9 months ago (Nov. 21, 2006)

Funders 0

None

BibTeX

@article{Manzhos_2006, title={Using neural networks to represent potential surfaces as sums of products}, volume={125}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2387950}, DOI={10.1063/1.2387950}, number={19}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Manzhos, Sergei and Carrington, Tucker}, year={2006}, month=nov }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        7
      ]
    ],
    "date-time": "2025-08-07T20:53:38Z",
    "timestamp": 1754600018571,
    "version": "3.41.2"
  },
  "reference-count": 56,
  "publisher": "AIP Publishing",
  "issue": "19",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2006,
        11,
        21
      ]
    ]
  },
  "abstract": "<jats:p>By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.</jats:p>",
  "DOI": "10.1063/1.2387950",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        11,
        16
      ]
    ],
    "date-time": "2006-11-16T23:06:03Z",
    "timestamp": 1163718363000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 165,
  "title": "Using neural networks to represent potential surfaces as sums of products",
  "prefix": "10.1063",
  "volume": "125",
  "author": [
    {
      "given": "Sergei",
      "family": "Manzhos",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Universit\u00e9 de Montr\u00e9al D\u00e9partement de chimie, , Case Postale 6128, succursale Centre-ville, Montr\u00e9al, (Qu\u00e9bec) H3C 3J7, Canada"
        }
      ]
    },
    {
      "suffix": "Jr.",
      "given": "Tucker",
      "family": "Carrington",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Universit\u00e9 de Montr\u00e9al D\u00e9partement de chimie, , Case Postale 6128, succursale Centre-ville, Montr\u00e9al, (Qu\u00e9bec) H3C 3J7, Canada"
        }
      ]
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2006,
        11,
        16
      ]
    ]
  },
  "reference": [
    {
      "volume-title": "Photodissociation Dynamics",
      "year": "1995",
      "key": "2023071503542386100_c1"
    },
    {
      "volume-title": "Dynamics of Molecules and Chemical Reactions",
      "year": "1996",
      "author": "Wyatt",
      "key": "2023071503542386100_c2"
    },
    {
      "key": "2023071503542386100_c3",
      "doi-asserted-by": "publisher",
      "first-page": "10458",
      "DOI": "10.1063/1.474210",
      "volume": "107",
      "year": "1997",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c4",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/S0009-2614(01)01381-1",
      "volume": "352",
      "year": "2002",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2023071503542386100_c5",
      "doi-asserted-by": "publisher",
      "first-page": "9313",
      "DOI": "10.1063/1.1804174",
      "volume": "121",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c6",
      "doi-asserted-by": "publisher",
      "first-page": "064317",
      "DOI": "10.1063/1.2001654",
      "volume": "123",
      "year": "2005",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c7",
      "doi-asserted-by": "publisher",
      "first-page": "061101",
      "DOI": "10.1063/1.1857472",
      "volume": "122",
      "year": "2005",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c8",
      "doi-asserted-by": "publisher",
      "first-page": "2071",
      "DOI": "10.1063/1.1759627",
      "volume": "121",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c9",
      "doi-asserted-by": "publisher",
      "first-page": "8417",
      "DOI": "10.1063/1.478750",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c10",
      "doi-asserted-by": "publisher",
      "first-page": "191",
      "DOI": "10.1007/s002140050379",
      "volume": "100",
      "year": "1998",
      "journal-title": "Theor. Chem. Acc."
    },
    {
      "key": "2023071503542386100_c11",
      "doi-asserted-by": "publisher",
      "first-page": "11",
      "DOI": "10.1016/S0010-4655(98)00152-0",
      "volume": "117",
      "year": "1999",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "2023071503542386100_c12",
      "doi-asserted-by": "publisher",
      "first-page": "197",
      "DOI": "10.1023/A:1019188517934",
      "volume": "25",
      "year": "1999",
      "journal-title": "J. Math. Chem."
    },
    {
      "key": "2023071503542386100_c13",
      "doi-asserted-by": "publisher",
      "first-page": "7765",
      "DOI": "10.1021/jp010450t",
      "volume": "105",
      "year": "2001",
      "journal-title": "J. Phys. Chem. A"
    },
    {
      "key": "2023071503542386100_c14",
      "doi-asserted-by": "publisher",
      "first-page": "084109",
      "DOI": "10.1063/1.2336223",
      "volume": "125",
      "year": "2006",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c15",
      "doi-asserted-by": "publisher",
      "first-page": "7974",
      "DOI": "10.1063/1.471513",
      "volume": "104",
      "year": "1996",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c16",
      "doi-asserted-by": "publisher",
      "first-page": "3772",
      "DOI": "10.1063/1.476977",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c17",
      "doi-asserted-by": "publisher",
      "first-page": "5605",
      "DOI": "10.1063/1.469292",
      "volume": "102",
      "year": "1995",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c18",
      "first-page": "115",
      "volume": "5",
      "year": "1986",
      "journal-title": "Comput. Phys. Rep."
    },
    {
      "key": "2023071503542386100_c19",
      "doi-asserted-by": "publisher",
      "first-page": "8519",
      "DOI": "10.1063/1.465576",
      "volume": "99",
      "year": "1993",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c20",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/0167-7977(86)90005-5",
      "volume": "4",
      "year": "1986",
      "journal-title": "Comput. Phys. Rep."
    },
    {
      "key": "2023071503542386100_c21",
      "doi-asserted-by": "publisher",
      "first-page": "469",
      "DOI": "10.1146/annurev.physchem.40.1.469",
      "volume": "40",
      "year": "1989",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2023071503542386100_c22",
      "first-page": "1",
      "volume": "9",
      "year": "1990",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2023071503542386100_c23",
      "doi-asserted-by": "crossref",
      "DOI": "10.1002/0470845015",
      "volume-title": "Encyclopedia of Computational Chemistry",
      "author": "Schleyer",
      "year": "1998"
    },
    {
      "key": "2023071503542386100_c24",
      "first-page": "263",
      "volume": "114",
      "year": "2000",
      "journal-title": "Adv. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c25",
      "doi-asserted-by": "publisher",
      "first-page": "2087",
      "DOI": "10.1021/j100319a003",
      "volume": "92",
      "year": "1988",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023071503542386100_c26",
      "doi-asserted-by": "crossref",
      "first-page": "2699",
      "DOI": "10.1002/0470845015",
      "volume-title": "Encyclopedia of Computational Chemistry",
      "author": "Schleyer",
      "year": "1998"
    },
    {
      "key": "2023071503542386100_c27",
      "doi-asserted-by": "publisher",
      "first-page": "174",
      "DOI": "10.1021/ar00028a007",
      "volume": "26",
      "year": "1993",
      "journal-title": "Acc. Chem. Res."
    },
    {
      "volume-title": "Numerical Recipes in Fortran 77: The Art of Scientific Computing",
      "year": "1992",
      "key": "2023071503542386100_c28"
    },
    {
      "key": "2023071503542386100_c29",
      "doi-asserted-by": "publisher",
      "first-page": "6175",
      "DOI": "10.1063/1.467273",
      "volume": "100",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c30",
      "doi-asserted-by": "publisher",
      "first-page": "4115",
      "DOI": "10.1063/1.463916",
      "volume": "97",
      "year": "1992",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c31",
      "doi-asserted-by": "publisher",
      "first-page": "9781",
      "DOI": "10.1063/1.1407277",
      "volume": "115",
      "year": "2001",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c32",
      "doi-asserted-by": "publisher",
      "first-page": "4763",
      "DOI": "10.1063/1.1348274",
      "volume": "114",
      "year": "2001",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c33",
      "doi-asserted-by": "publisher",
      "first-page": "6388",
      "DOI": "10.1063/1.460317",
      "volume": "94",
      "year": "1991",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c34",
      "doi-asserted-by": "publisher",
      "first-page": "8527",
      "DOI": "10.1063/1.473908",
      "volume": "106",
      "year": "1997",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c35",
      "doi-asserted-by": "publisher",
      "first-page": "9062",
      "DOI": "10.1063/1.463332",
      "volume": "97",
      "year": "1992",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c36",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/S0370-1573(99)00047-2",
      "volume": "324",
      "year": "2000",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "2023071503542386100_c37",
      "doi-asserted-by": "publisher",
      "first-page": "433",
      "DOI": "10.1007/BF01449770",
      "volume": "63",
      "year": "1906",
      "journal-title": "Math. Ann."
    },
    {
      "key": "2023071503542386100_c38",
      "doi-asserted-by": "publisher",
      "first-page": "194304",
      "DOI": "10.1063/1.2192499",
      "volume": "124",
      "year": "2006",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c39",
      "doi-asserted-by": "publisher",
      "first-page": "074706",
      "DOI": "10.1063/1.2171246",
      "volume": "124",
      "year": "2006",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c40",
      "doi-asserted-by": "publisher",
      "first-page": "174311",
      "DOI": "10.1063/1.2085167",
      "volume": "123",
      "year": "2005",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c41",
      "doi-asserted-by": "publisher",
      "first-page": "3",
      "DOI": "10.1016/j.chemphys.2004.06.006",
      "volume": "304",
      "year": "2004",
      "journal-title": "Chem. Phys."
    },
    {
      "volume-title": "Neural Network Learning: Theoretical Foundations",
      "year": "1999",
      "key": "2023071503542386100_c42"
    },
    {
      "key": "2023071503542386100_c43",
      "doi-asserted-by": "publisher",
      "first-page": "439",
      "DOI": "10.1146/annurev.physchem.45.1.439",
      "volume": "45",
      "year": "1994",
      "journal-title": "Annu. Rev. Phys. Chem."
    },
    {
      "key": "2023071503542386100_c44",
      "doi-asserted-by": "publisher",
      "first-page": "5295",
      "DOI": "10.1021/jp055253z",
      "volume": "110",
      "year": "2006",
      "journal-title": "J. Phys. Chem. A"
    },
    {
      "key": "2023071503542386100_c45",
      "doi-asserted-by": "publisher",
      "first-page": "134306",
      "DOI": "10.1063/1.2185638",
      "volume": "124",
      "year": "2006",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c46",
      "doi-asserted-by": "publisher",
      "first-page": "210",
      "DOI": "10.1016/j.cplett.2004.07.076",
      "volume": "395",
      "year": "2004",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "key": "2023071503542386100_c47",
      "doi-asserted-by": "publisher",
      "first-page": "8801",
      "DOI": "10.1063/1.477550",
      "volume": "109",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c48",
      "doi-asserted-by": "publisher",
      "first-page": "084104",
      "DOI": "10.1063/1.1850458",
      "volume": "122",
      "year": "2005",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071503542386100_c49",
      "doi-asserted-by": "publisher",
      "first-page": "183",
      "DOI": "10.1016/0893-6080(89)90003-8",
      "volume": "2",
      "year": "1989",
      "journal-title": "Neural Networks"
    },
    {
      "key": "2023071503542386100_c50",
      "doi-asserted-by": "publisher",
      "first-page": "81",
      "DOI": "10.1016/S0925-2312(98)00111-8",
      "volume": "25",
      "year": "1999",
      "journal-title": "Neurocomputing"
    },
    {
      "key": "2023071503542386100_c51",
      "first-page": "45",
      "volume": "11",
      "year": "1998",
      "journal-title": "Appl. Math. Lett."
    },
    {
      "key": "2023071503542386100_c52",
      "doi-asserted-by": "publisher",
      "first-page": "259",
      "DOI": "10.1016/S0893-6080(97)00118-4",
      "volume": "11",
      "year": "1998",
      "journal-title": "Neural Networks"
    },
    {
      "key": "2023071503542386100_c53",
      "doi-asserted-by": "publisher",
      "first-page": "672",
      "DOI": "10.1109/72.761726",
      "volume": "10",
      "year": "1999",
      "journal-title": "IEEE Trans. Neural Netw."
    },
    {
      "key": "2023071503542386100_c54",
      "doi-asserted-by": "crossref",
      "first-page": "247",
      "DOI": "10.1016/S0893-6080(03)00189-8",
      "volume": "17",
      "year": "2004",
      "journal-title": "Neural Networks"
    },
    {
      "key": "2023071503542386100_c55",
      "doi-asserted-by": "publisher",
      "first-page": "2565",
      "DOI": "10.1063/1.479534",
      "volume": "111",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "year": "2002",
      "key": "2023071503542386100_c56"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2387950/15389646/194105_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2387950/15389646/194105_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        8
      ]
    ],
    "date-time": "2024-02-08T09:30:11Z",
    "timestamp": 1707384611000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/125/19/194105/566326/Using-neural-networks-to-represent-potential"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2006,
        11,
        16
      ]
    ]
  },
  "references-count": 56,
  "journal-issue": {
    "issue": "19",
    "published-print": {
      "date-parts": [
        [
          2006,
          11,
          21
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.2387950",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2006,
        11,
        21
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2006,
        11,
        16
      ]
    ]
  },
  "article-number": "194105"
}