DOI: 10.1063/1.1726605. Dipole Moment Function and Vibration

Dipole Moment Function and Vibration—Rotation Matrix Elements for CO

10.1063/1.1726605

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Electric dipole matrix elements for vibration—rotation transitions in CO have been calculated using a computer program developed by Cooley for the solution of the radial Schrödinger equation. By means of this program four possible cubic dipole moment functions M(r) for CO were obtained from room-temperature measurements of the integrated intensities of the fundamental and first two overtone infrared bands. Relative measurements of rotational line intensities in the overtone bands indicate clearly that the most linear of these four functions is the correct one: M(r)=±0.112+3.11(r−re)−0.15(r−re)2−2.36(r−re)3D. (The internuclear separation r and its equilibrium value, re, are in angstroms.) Using this expression we find in the case of the overtone bands that there is an appreciable deviation of the vibrational matrix elements from the usual binomial expression, and that the matrix elements have a significant rotational dependence.

Bibliography

Young, L. A., & Eachus, W. J. (1966). Dipole Moment Function and VibrationâRotation Matrix Elements for CO. The Journal of Chemical Physics, 44(11), 4195â4206.

Authors 2

Lee A. Young (first)
W. James Eachus (additional)

References 48 Referenced 143

10.1007/BF01948682 / Z. Physik (1952)
10.1063/1.1740094 / J. Chem. Phys. (1954)
10.1063/1.1742069 / J. Chem. Phys. (1955)
10.1086/146014 / Astrophys. J. (1955)
10.1016/0022-2852(58)90088-2 / J. Mol. Spectry. (1958)
10.1016/0022-2852(63)90168-1 / J. Mol. Spectry. (1963)
10.1016/0022-2852(62)90222-9 / J. Mol. Spectry. (1962)
10.1103/PhysRev.35.1347 / Phys. Rev. (1930)
10.1063/1.1725130 / J. Chem. Phys. (1964)
{'key': '2024020900513105600_r10', 'first-page': '363', 'volume': '15', 'year': '1961', 'journal-title': 'Math. Computation'} / Math. Computation (1961)
{'key': '2024020900513105600_r11'}
{'key': '2024020900513105600_r11a'}
10.1063/1.1734545 / J. Chem. Phys. (1963)
10.1063/1.1725846 / J. Chem. Phys. (1964)
10.1016/0022-4073(65)90039-7 / J. Quant. Spectry. Radiative Transfer (1965)
10.1063/1.1725425 / J. Chem. Phys. (1964)
10.1139/p56-092 / Can. J. Phys. (1956)
10.1063/1.1730791 / J. Chem. Phys. (1960)
10.1063/1.1725213 / J. Chem. Phys. (1964)
10.1063/1.1695905 / J. Chem. Phys. (1965)
10.1063/1.1697300 / J. Chem. Phys. (1965)
10.1063/1.1725063 / J. Chem. Phys. (1964)
10.1063/1.1696786 / J. Chem. Phys. (1965)
{'key': '2024020900513105600_r23'}
10.1063/1.1696966 / J. Chem. Phys. (1965)
10.1063/1.1731475 / J. Chem. Phys. (1960)
10.1103/PhysRev.54.726 / Phys. Rev. (1938)
{'key': '2024020900513105600_r27'}
{'key': '2024020900513105600_r28'}
10.1063/1.1748386 / J. Chem. Phys. (1951)
10.1063/1.1700164 / J. Chem. Phys. (1952)
10.1139/p53-050 / Can. J. Phys. (1953)
{'key': '2024020900513105600_r32', 'first-page': '251', 'volume': '239', 'year': '1954', 'journal-title': 'Compt. Rend.'} / Compt. Rend. (1954)
10.1016/0022-4073(61)90023-1 / J. Quant. Spectry. Radiative Transfer (1961)
10.1086/147265 / Astrophys. J. (1962)
10.1016/0022-4073(62)90004-3 / J. Quant. Spectry. Radiative Transfer (1962)
10.1364/AO.1.000587 / Appl. Opt. (1962)
10.1139/p65-051 / Can. J. Phys. (1965)
{'key': '2024020900513105600_r38'}
{'key': '2024020900513105600_r39'}
10.6028/jres.067A.022 / J. Res. Natl. Bur. Std. (1963)
10.1063/1.1744151 / J. Chem. Phys. (1958)
10.1103/PhysRev.109.400 / Phys. Rev. (1958)
10.1063/1.1695707 / J. Chem. Phys. (1965)
{'key': '2024020900513105600_r44'}
{'key': '2024020900513105600_r45'}
{'key': '2024020900513105600_r46'}
{'key': '2024020900513105600_r47'}

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 3:17 a.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 7:51 p.m.)
Indexed	1 week, 2 days ago (Aug. 23, 2025, 9:13 p.m.)
Issued	59 years, 3 months ago (June 1, 1966)
Published	59 years, 3 months ago (June 1, 1966)
Published Print	59 years, 3 months ago (June 1, 1966)

Funders 0

None

BibTeX

@article{Young_1966, title={Dipole Moment Function and Vibration—Rotation Matrix Elements for CO}, volume={44}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1726605}, DOI={10.1063/1.1726605}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Young, Lee A. and Eachus, W. James}, year={1966}, month=jun, pages={4195–4206} }

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