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

Rey, M.; Tyuterev, Vladimir G.; Coxon, John A.; Roy, Robert J. Le

doi:10.1016/j.jms.2006.05.006

Cited by 9 publications

(11 citation statements)

References 13 publications

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“…The level of correction of a set of eleven Y* ij (0) and the Dunham potential constants up to a 9 are found to be sufficient for the present analysis, i.e., a set of 41 Y ij that connected the fitting parameters with the energy levels is that of Y* ij (0) + Y ij (2) for ij ) 01, 02, 03, 04, 05, 10, 11, 12, 13, 20, and 21 and Y ij (0) for ij ) 06, 07, 08, 09, 010, 011, 14,15,16,17,18,19,22,23,24,25,26,27,30,31,32,33,34,35,40,41,42,43,50, and 51. The spectral uncertainties, δ obs , are those given in each paper.…”

Section: Analysis and Resultsmentioning

confidence: 99%

Analysis of Rotational and Vibrational−Rotational Spectra of HF Based on the Non-Born−Oppenheimer Effective Hamiltonian

2009

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Rotational transitions of HF that are important as a wavenumber standard have been analyzed by simultaneous fitting of the reported rotational and vibrational-rotational transitions plus rotational measurements of the present study with the non-Born-Oppenheimer effective Hamiltonian expressed with the optimal parameters, i.e., the determinable clusters of the expansion coefficients of the correction functions for the breakdown of the Born-Oppenheimer approximation. Since the spectral fit is made with the analytical solution of the Schrödinger equation, one can easily reproduce the fitting procedure. This is the first example of the non-Born-Oppenheimer analysis of a single isotopologue with physically meaningful parameters based on the traditional concept of the molecular constants. Fitting of a data set for HF has generated 15 independent parameter values that include 4 determinable clusters of the expansion coefficients. These 15 parameters are sufficient to generate 41 Yij coefficients and 72 rotational constants, which provide comprehensive sets of molecular constants of HF.

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Section: Analysis and Resultsmentioning

confidence: 99%

Analysis of Rotational and Vibrational−Rotational Spectra of HF Based on the Non-Born−Oppenheimer Effective Hamiltonian

2009

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“…The origin of these discrepancies has been found thanks to a cooperation with LeRoy and Coxon in a series of numerical tests using our computer programs in the same conditions as programs LEVEL and SSPOT that have been employed for obtaining a lot of numerical results in this domain in the literature so far. Such a comparative study 44 has allowed to conclude that these errors were due to the insufficiency of the approximation of the practical eqn (10) in the case of molecules exhibiting relatively strong vibrational non-adiabatic contributions. For the GaH molecule, these b-contributions are much more important compared to molecules discussed in the previous section, for example |b( 69 GaH)/b( 74 Ge 32 S)| B 40.…”

Section: Radial Equation In Case Of Large Vibrational Non-adiabatic C...mentioning

confidence: 99%

“…Alternatively, one can extend the transformed eqn (9) using higher order terms in (23) that decreases the truncation error to B10 À6 cm À1 or better, as is seen in panel B of Table 2. Such an extension of the DPF method 44 with a re-fitting of isotopically invariant BOB parameters does not substantially increase a computational cost and represents conceptually a more satisfactory way of making both methods totally compatible. A least-squares determination of corresponding new parameters for the isotopic species of GaH, ArH 1 not affected by a truncation error is a subject of a separate study.…”

Section: Moleculementioning

confidence: 99%

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Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Rey

Tyuterev

2007

Phys. Chem. Chem. Phys.

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Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.

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“…Watson [8,29] showed, that only two of these corrections can be determined simultaneously. Moreover, due to the mass dependence the contributions by β are expected to be very small [30]. Thus we chose β = 0 in our approach; contributions of it will be absorbed in effective BOC functions V corr (R) and α(R), and the effective Hamiltonian for the radial motion is written as [7,29,30]:…”

Section: Modeling Of the Spectramentioning

confidence: 99%

Improved potentials and Born-Oppenheimer corrections by new measurements of transitions of 129I2 and 127I 129I in the B3 $\Pi_{\rm O^+_u}$ - X1 $\Sigma^+_{\rm g}$ band system

et al. 2008

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Abstract. The light from one single frequency cw laser was employed in a double saturation spectroscopy experiment to record high resolution spectra of 129 I2 and 127 I 129 I together with spectra of 127 I2 which is used as a simultaneous frequency reference. Two separate saturation spectroscopy set ups were used. The frequencies of lines of 129 I2 and 127 I 129 I were determined with respect to lines of 127 I2. More than 380 frequency differences between lines of 127 I2 and of the other isotopomers have been included in the data set. By a direct potential fit a precise description of the potential energy curves of the B and the X state and of effective Born-Oppenheimer correction functions valid for all three isotopomers of I2 are given.PACS. 33.15.Pw Fine and hyperfine structure -33.20.-t Molecular spectra -33.20.Kf Visible spectra

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

Cited by 9 publications

References 13 publications

Analysis of Rotational and Vibrational−Rotational Spectra of HF Based on the Non-Born−Oppenheimer Effective Hamiltonian

Analysis of Rotational and Vibrational−Rotational Spectra of HF Based on the Non-Born−Oppenheimer Effective Hamiltonian

Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Improved potentials and Born-Oppenheimer corrections by new measurements of transitions of 129I2 and 127I 129I in the B3 $\Pi_{\rm O^+_u}$ - X1 $\Sigma^+_{\rm g}$ band system

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