DOI: 10.1063/1.432526. Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids

Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids

10.1063/1.432526

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A general theoretical framework for introducing many-body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) -particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

Bibliography

Adelman, S. A., & Doll, J. D. (1976). Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids. The Journal of Chemical Physics, 64(6), 2375â2388.

Authors 2

S. A. Adelman (first)
J. D. Doll (additional)

References 54 Referenced 745

10.1063/1.1672253 / J. Chem. Phys. (1969)
10.1063/1.1678670 / J. Chem. Phys. (1972)
10.1063/1.1678671 / J. Chem. Phys. (1972)
10.1063/1.1670205 / J. Chem. Phys. (1968)
{'key': '2024020913544135200_r1d', 'first-page': '2919', 'volume': '48', 'year': '1968', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1968)
10.1016/0039-6028(72)90021-0 / Surf. Sci. (1972)
10.1063/1.1682431 / J. Chem. Phys. (1974)
10.1088/0022-3719/5/24/006 / J. Phys. C (1972)
10.1063/1.1679617 / J. Chem. Phys. (1973)
10.1063/1.1682041 / J. Chem. Phys. (1974)
{'key': '2024020913544135200_r4'}
10.1063/1.1726446 / J. Chem. Phys. (1966)
10.1063/1.1670153 / J. Chem. Phys. (1968)
10.1016/0039-6028(73)90270-7 / Surf. Sci. (1973)
10.1016/0039-6028(74)90334-3 / Surf. Sci. (1974)
10.1063/1.1676222 / J. Chem. Phys. (1971)
10.1063/1.1671848 / J. Chem. Phys. (1969)
10.1063/1.1681723 / J. Chem. Phys. (1974)
10.1063/1.431022 / J. Chem. Phys. (1975)
10.1063/1.431234 / J. Chem. Phys. (1975)
10.1088/0034-4885/29/1/306 / Rep. Prog. Theor. Phys. (1966)
10.1143/PTP.33.423 / Prog. Theor. Phys. (1965)
10.1063/1.1730869 / J. Chem. Phys. (1960)
10.1063/1.1730869 / J. Chem. Phys. (1960)
10.1063/1.1734433 / J. Chem. Phys. (1963)
10.1016/0022-3697(62)90173-7 / J. Phys. Chem. Solids (1962)
10.1016/0001-8686(75)85007-X / Adv. Colloid Interface Sci. (1975)
{'key': '2024020913544135200_r16'}
{'key': '2024020913544135200_r17'}
{'key': '2024020913544135200_r18'}
{'key': '2024020913544135200_r19'}
{'key': '2024020913544135200_r20'}
10.1063/1.1703637 / J. Math. Phys. (1960)
10.1063/1.1703664 / J. Math. Phys. (1960)
10.1063/1.1703723 / J. Math. Phys. (1961)
10.1063/1.1704304 / J. Math. Phys. (1965)
10.1103/PhysRevA.3.2049 / Phys. Rev. A (1971)
10.1143/PTP.49.129 / Prog. Theor. Phys. (1973)
10.1143/PTP.48.1173 / Prog. Theor. Phys. (1972)
10.1080/00268977400102321 / Mol. Phys. (1974)
{'key': '2024020913544135200_r21'}
{'key': '2024020913544135200_r22'}
{'key': '2024020913544135200_r23', 'first-page': '264', 'volume': '20', 'year': '1973', 'journal-title': 'Phys. Rev. Lett.'} / Phys. Rev. Lett. (1973)
10.1063/1.1680961 / J. Chem. Phys. (1974)
10.1103/RevModPhys.15.1 / Rev. Mod. Phys. (1943)
10.1103/RevModPhys.17.323 / Rev. Mod. Phys. (1945)
10.1063/1.431961 / J. Chem. Phys. (1976)
10.1098/rspa.1948.0069 / Proc. R. Soc. London Ser. A (1948)
{'key': '2024020913544135200_r28'}
{'key': '2024020913544135200_r29'}
{'key': '2024020913544135200_r30'}
{'key': '2024020913544135200_r31'}
{'key': '2024020913544135200_r32'}
10.1063/1.430620 / J. Chem. Phys. (1975)

Dates

Type	When
Created	22 years, 5 months ago (Feb. 27, 2003, 5:10 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 9:41 a.m.)
Indexed	4 days, 21 hours ago (Aug. 19, 2025, 6:27 a.m.)
Issued	49 years, 5 months ago (March 15, 1976)
Published	49 years, 5 months ago (March 15, 1976)
Published Print	49 years, 5 months ago (March 15, 1976)

Funders 0

None

BibTeX

@article{Adelman_1976, title={Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids}, volume={64}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.432526}, DOI={10.1063/1.432526}, number={6}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Adelman, S. A. and Doll, J. D.}, year={1976}, month=mar, pages={2375–2388} }

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  "URL": "http://dx.doi.org/10.1063/1.432526",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1976,
        3,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1976,
        3,
        15
      ]
    ]
  }
}