An Effective Hamiltonian to Treat Adiabatic and Nonadiabatic Effects in the Rotational and Vibrational Spectra of Diatomic Molecules

Herman, R. M.; Ogilvie, J. F.

doi:10.1002/9780470141625.ch2

Cited by 29 publications

(9 citation statements)

References 32 publications

(20 reference statements)

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“…The values of Y ij are those given in Table 3. Herman and Ogilvie [30], Uehara and Ogilvie [22], and Uehara [18] published relations between the rotational g factor g J (n), the permanent electric dipole moment M(n), and the nonadiabatic expansion coefficients r i a,b :…”

Section: Discussionmentioning

confidence: 99%

Vibrational–rotational spectra of 13CS and global multi-isotopologue analysis

Uehara

Horiai

Sakamoto

2015

Journal of Molecular Spectroscopy

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a b s t r a c tIn total, 626 vibrational-rotational spectral lines of the Dv = 1 transitions of 13 C 32 S up to band v = 5-4 have been measured with a Fourier-transform spectrometer at resolution 0.010 cm À1 . To calibrate accurately the spectral lines, a separate observation of the vibrational-rotational bands of 12 C 32 S was made with simultaneous recording of the N 2 O spectrum in absorption, to serve as wavenumber standards, with dual sample cells at resolution 0.008 cm À1 . The spectral wavenumbers of 12 C 32 S in turn become calibration standards. All present vibrational-rotational spectra of 13 C 32 S and 12 C 32 S, the reported vibrationalrotational spectra of 12 C 32 S, 12 C 33 S, 12 C 34 S, and 13 C 32 S, and the reported rotational spectra of 12 C 32 S, 12 C 33 S, 12 C 34 S, 12 C 36 S, 13 C 32 S, 13 C 33 S and 13 C 34 S were subjected to a global multi-isotopologue analysis, which reduced them to molecular parameters in a single set. The wavenumbers of 3974 spectral lines, in total, comprising data of seven isotopologues were fitted with 22 isotopically invariant, traditional molecular parameters in a single set. As the normalized standard deviation is 1.38, the obtained fit is satisfactory. To facilitate the calculation of spectral wavenumbers, the values of the Dunham coefficients of 42 Y ij for each of 12 the spectra of the latter five isotopologues are not yet reported, were back-calculated with uncertainties using the evaluated 22 molecular parameters. The physical significance of the conventional treatments of the adiabatic and nonadiabatic corrections for D 01 C and D 01 S is discussed.

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Section: Discussionmentioning

confidence: 99%

Vibrational–rotational spectra of 13CS and global multi-isotopologue analysis

Uehara

Horiai

Sakamoto

2015

Journal of Molecular Spectroscopy

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“…As was shown by Watson [19] and formally presented by Herman and Ogilvie [11], the function b (r) is isotopologue-dependent, and may be written as a sum of contributions from the two atoms A and B which form the molecule, …”

Section: Theorymentioning

confidence: 96%

“…In recent work, however, Rey and Tyuterev [8,9] were testing a new variational method of determining the eigenvalues and eigenfunctions of the Herman-Asgharian (HA) Hamiltonian [10,11] for a diatomic molecule, and they discovered a problem. This Hamiltonian includes terms b (r) and a (r) which take account of non-adiabatic corrections to the radial and angular kinetic energy operators, respectively, as well as the adiabatic correction DV ad (r) to the ''clamped nuclei'' potential energy function function V CN (r):…”

Section: Introductionmentioning

confidence: 99%

Resolution of a convergence problem in direct-potential-fit data analyses: Applications to GaH(X1Σ+) and ArH+(X1Σ+)

Rey

Tyuterev

Coxon

et al. 2006

Journal of Molecular Spectroscopy

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“…Watson [80] showed that it is not possible to separate the adiabatic and nonadiabatic contributions on the basis of line positions alone. However, an alternative formulation of the Hamiltonian by Herman and Ogilvie [173] does allow the contributions to be separated, using constraints from the molecular dipole moment function or rotational g-factor. This approach has not yet been applied to alkali-metal dimers, but Coxon and Hajigeorgiou have shown that, for HCl [10] and CO [16], the empirical true and effective adiabatic corrections have similar values near R e but very different gradients (actually of opposite sign for HCl).…”

Section: Comparison With Empirical Isotope Shiftsmentioning

confidence: 99%

Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics

Lutz

Hutson

2016

Journal of Molecular Spectroscopy

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We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr 2 and Yb 2 diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but field shifts contribute significantly for Rb and Sr and are dominant for Yb. We compare the ab initio mass-shift functions for Li 2 , LiK and LiRb with spectroscopically derived ground-state BOB functions from the literature. We find good agreement in the values of the functions for LiK and LiRb at their equilibrium geometries, but significant disagreement with the shapes of the functions for all 3 systems. The differences may be due to contributions of nonadiabatic terms to the empirical BOB functions. We present a semiclassical model for the effect of BOB corrections on the binding energies of near-threshold states and the positions of zero-energy Feshbach resonances.

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An Effective Hamiltonian to Treat Adiabatic and Nonadiabatic Effects in the Rotational and Vibrational Spectra of Diatomic Molecules

Cited by 29 publications

References 32 publications

Vibrational–rotational spectra of 13CS and global multi-isotopologue analysis

Vibrational–rotational spectra of 13CS and global multi-isotopologue analysis

Resolution of a convergence problem in direct-potential-fit data analyses: Applications to GaH(X1Σ+) and ArH+(X1Σ+)

Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics

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