Franck-Condon Factors and R-Centroids for the Band System a1Π-X1Σ+ of the InH Molecule

1993 ◽  
Vol 58 (7) ◽  
pp. 1491-1494 ◽  
Author(s):  
Narayanan Rajamanickam ◽  
Thangamariappan Murali ◽  
Thangasamy Sakthivel ◽  
Manuel Fernandez Gomez ◽  
Juan Jesus Lopez Gonzalez
Keyword(s):  
Numerical Integration ◽  
Transition Probabilities ◽  
Band System ◽  
Vibrational Transition ◽  
Integration Procedure ◽  
Condon Factors ◽  
Franck Condon ◽  
Suitable Potential ◽  
Numerical Integration Procedure

The Franck-Condon factors (vibrational transition probabilities) and r-centroids have been evaluated by a numerical integration procedure for the bands of the a3Π1-X1Σ+ system of the InH molecule using a suitable potential.

scholarly journals Molecular parameters for the gas phase molecules SbO and SbP

2008 ◽  
Vol 73 (1) ◽  
pp. 65-71
Author(s):  
Sri Ramachandran ◽  
V. Raja ◽  
N. Rajamanickam
Keyword(s):  
Numerical Integration ◽  
Gas Phase ◽  
Transition Probabilities ◽  
Vibrational Transition ◽  
Molecular Parameters ◽  
Gas Phase Molecules ◽  
Condon Factors ◽  
Franck Condon ◽  
Suitable Potential ◽  
Numerical Integration Procedure

Franck-Condon factors and r-centroids, which are very closely related to relative vibrational transition probabilities, were evaluated by the numerical integration procedure for the bands of the A2?3/2 - X2?3/2, C2? - X2?3/2 and D2? - X2? systems of the isotopic SbO molecule and for the B1? - X1?+ system of the isotopic SbP molecule, using a suitable potential.

scholarly journals Evaluation of astrophysically useful parameters for strontium monohydride and deuteride

2006 ◽  
pp. 13-16 ◽  
Author(s):  
Sri Ramachandran ◽  
N. Rajamanickam ◽  
S.P. Bagare
Keyword(s):  
Numerical Integration ◽  
Transition Probabilities ◽  
Integration Procedure ◽  
Giant Stars ◽  
Condon Factors ◽  
Astrophysical Molecules ◽  
Franck Condon ◽  
Numerical Integration Procedure

The Franck-Condon factors and r-centroids which are very closely related to transition probabilities, have been evaluated by the more reliable numerical integration procedure for the band systems B2?-X2?, C2?-X2? and F2?-X2? of astrophysical molecules strontium monohydride and strontium deuteride using an adequate potential. The Franck-Condon factors are more intense, particularly for the ?? = 0 bands, for all the systems examined here. Thus the bands of the molecules are expected to be present in sunspot spectra, SC-stars, cool M-giant stars and other prominent astrophysical sources.

Vibrational Transition Probabilities and Dissociation Energy of the PF Molecule

1993 ◽  
Vol 58 (4) ◽  
pp. 748-753 ◽  
Author(s):  
Narayanan Rajamanickam ◽  
Manuel Fernandez Gomez ◽  
Juan Jesus Lopez Gonzalez
Keyword(s):  
Dissociation Energy ◽  
Ground State ◽  
Potential Energy Curve ◽  
Transition Probabilities ◽  
Energy Curve ◽  
Vibrational Transition ◽  
Condon Factors ◽  
Franck Condon ◽  
Suitable Potential ◽  
Electronic Ground

The Franck-Condon factors (vibrational transition probabilities) and r-centroids have been evaluated by a more reliable numerical interogation procedure for the bands of b1Σ+ - X3Σ- system of the PF molecule, using a suitable potential. The dissociation energy, De = 318 kJ mol-1 for the electronic ground state of this molecule has been estimated by fitting the electronegativity function to the experimental potential energy curve.

A theoretical study of the B′2Σ+–X2Σ+ band system in MgH and MgD

1979 ◽  
Vol 57 (8) ◽  
pp. 1178-1184 ◽  
Author(s):  
M. L. Sink ◽  
A. D. Bandrauk
Keyword(s):  
Dipole Moment ◽  
Theoretical Study ◽  
Transition Probabilities ◽  
Band System ◽  
Dipole Moments ◽  
Electronic States ◽  
Oscillator Strengths ◽  
Moment Functions ◽  
Condon Factors ◽  
Franck Condon

Ab initio Cl calculations of the transition moment for the B′2Σ+–X2Σ+ transition in MgH are reported. Theoretical values for the Franck–Condon factors, band strengths, band oscillator strengths, and transition probabilities have been computed for MgH and MgD. An analysis of our results for this system predicts many bands to be observable which have not yet been identified. Dipole moment functions and vibrationally averaged dipole moments are given for the X2Σ+, A2Π, and B′2Σ+ electronic states.

scholarly journals Evaluation of the Effective Temperature of Sunspots Using Molecular Parameters of AlF

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
K. Balachandrakumar ◽  
V. Raja ◽  
B. Karthikeyan ◽  
S. P. Bagare ◽  
N. Rajamanickam
Keyword(s):  
Potential Energy ◽  
Numerical Integration ◽  
Effective Temperature ◽  
Spectroscopic Analysis ◽  
Vibrational Temperature ◽  
Potential Energy Curves ◽  
Physical Conditions ◽  
Franck Condon ◽  
Suitable Potential ◽  
Numerical Integration Procedure

The physical conditions of celestial objects can be analyzed using the spectrum of atoms or molecules present in the object. The present work focuses on the spectroscopic analysis of astrophysically significant molecule AlF. The evaluation of Franck-Condon (FC) factors andr-centroids is done by a numerical integration procedure using the suitable potential energy curves forC1Σ+-A1Σ+,b3Σ+-a3Πr,c3Σ-a3Πr, andf3Π-a3Πrband systems of AlF molecule. The intensity of various bands is discussed with the help of derived FC factors. The band degradation and the nature of potential energy curves are studied usingr-centroid values. The vibrational temperature of sunspot is estimated to be around 1220 ± 130 K which falls in the reported temperature range of cold sunspots.

scholarly journals Franck-Condon factors and r-centroids for the diatomic fluorides of germanium and silicon

2008 ◽  
Vol 73 (5) ◽  
pp. 555-560
Author(s):  
S. Kanagaprabha ◽  
Rajeswara Palanichamy ◽  
V. Sathiyabama
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Close Agreement ◽  
Band System ◽  
Potential Energy Function ◽  
Wave Functions ◽  
Integration Technique ◽  
Condon Factors ◽  
Franck Condon ◽  
Suitable Potential

A suitable potential energy function was found by analysing the potential functions proposed by Morse, Mohammad and Rafi et al. for the A2?+-X2?3/2 and B2?+-X2?3/2 band systems of GeF and the 1?-1? band system of SiF. It was found that the potential proposed by Rafi et al. is in close agreement with the Rydberg-Klein-Rees (R-K-R) potential. Using this potential, the wave functions were evaluated by the Wentzel-Kramer-Brillouin (W-K-B) method. The Franck-Condon factors and r-centroids were computed by a numerical integration technique. The results are compared with available theoretical values. The intensities of the various bands were investigated.

THEORETICAL TRANSITION PROBABILITIES FOR THE $\tilde{A}^{2}A_{1} -\tilde{X}^{2}B_{1}$ SYSTEM OF H2O+ AND D2O+ AND RELATED FRANCK–CONDON FACTORS BASED ON GLOBAL POTENTIAL ENERGY SURFACES

2005 ◽  
Vol 04 (01) ◽  
pp. 225-245 ◽  
Author(s):  
IKUO TOKUE ◽  
KATSUYOSHI YAMASAKI ◽  
SATOSHI MINAMINO ◽  
SHINKOH NANBU
Keyword(s):  
Potential Energy ◽  
Photoelectron Spectroscopy ◽  
Potential Energy Surfaces ◽  
Least Squares Method ◽  
Transition Probabilities ◽  
Three Dimensional ◽  
Equilibrium Geometry ◽  
Condon Factors ◽  
Energy Surfaces ◽  
Franck Condon

To elucidate the ionization dynamics, in particular the vibrational distribution, of H 2 O +(Ã) produced by photoionization and the Penning ionization of H 2 O and D 2 O with He *(2 3S) atoms, Franck–Condon factors (FCFs) were given for the [Formula: see text] ionization, and the transition probabilities were presented for the [Formula: see text] emission. The FCFs were obtained by quantum vibrational calculations using the three-dimensional potential energy surfaces (PESs) of [Formula: see text] and [Formula: see text] electronic states. The global PESs were determined by the multi-reference configuration interaction calculations with the Davidson correction and the interpolant moving least squares method combined with the Shepard interpolation. The obtained FCFs exhibit that the [Formula: see text] state primarily populates the vibrational ground state, as its equilibrium geometry is almost equal to that of [Formula: see text], while the bending mode (ν2) is strongly enhanced for the H 2 O +(Ã) state; the maximums in the population of H 2 O + and D 2 O + are approximately v2 = 11–12 and 15–17, respectively. These results are consistent with the distributions observed by photoelectron spectroscopy. Transition probabilities for the [Formula: see text] system of H 2 O + and D 2 O + show that the bending progressions consist primarily of the [Formula: see text] emission, with combination bands from the (1, v′2 = 4–8, 0) level being next most important.

The use of gas-liquid chromatography to determine activity coefficients and second virial coefficients of mixtures I. Theory and verification of method of data analysis

1966 ◽  
Vol 295 (1442) ◽  
pp. 259-270 ◽  
Keyword(s):  
Numerical Integration ◽  
Retention Volume ◽  
Simple Extension ◽  
Gas Liquid Chromatography ◽  
Local Pressure ◽  
Integration Procedure ◽  
Carrier Gas ◽  
Wide Range ◽  
Analytical Integration ◽  
Numerical Integration Procedure

This paper reformulates the differential equation describing the local elution rate in a g. l. c. column in terms of the local pressure and the carrier gas outlet flow rate. Analytical integration for an ideal carrier gas suggests an accurate method for extrapolating a function of the retention volume linearly to zero pressure, where the intercept V ° N is simply related to the thermodynamic activity coefficient of the solute (1) in the stationary liquid (3) and the gradient β gives B 12 for the mixture solute + carrier gas (2). We argue that a simple extension of the method should apply also, with fair accuracy, to a non-ideal carrier gas. We support this argument with data obtained by a numerical integration procedure which gives retention volume in terms of specified V ° N and B for a range of inlet and outlet pressures. The reliability of the numerical integration procedure is established by comparing results for the ideal gas case with the results of analytical integration. The retention volumes obtained by numerical integration for a non-ideal carrier gas are then treated as ‘experimental’ observations, using in addition to our extrapolation procedure, two previously published procedures. Our procedures are consistently more successful than the others and recover accurately the V ° N originally specified over a wide range of flow conditions, even when the carrier gas shows large deviations from ideality. In the case of β , our method is significantly in error only when the carrier gas deviates largely from ideality in a low pressure column with large pressure drop. A simple refinement of our method is satisfactory for even this case.

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