Franck-condon factors and ladder operators. I. harmonic oscillator

2009 ◽  
Vol 24 (S17) ◽  
pp. 393-400 ◽  
Author(s):  
A. Palma ◽  
J. Morales
Keyword(s):  
Harmonic Oscillator ◽  
Ladder Operators ◽  
Condon Factors ◽  
Franck Condon

Properties of the Quantum Double Oscillator

1975 ◽  
Vol 30 (12) ◽  
pp. 1730-1741 ◽  
Author(s):  
Jürgen Brickmann
Keyword(s):  
Harmonic Oscillator ◽  
Large Class ◽  
Electronic Transitions ◽  
Matrix Elements ◽  
Quantum Double ◽  
The Matrix ◽  
Analytic Expressions ◽  
Condon Factors ◽  
Finite Sums ◽  
Franck Condon

Abstract A formalism is presented to obtain approximate analytic expressions for the eigenstates and eigenvalues of a quantum double oscillator (QDO). The matrix elements of a large class of operators with respect to states of different double oscillators result as finite sums of explicit functions of the respective parameters. Matrix elements between states of a harmonic oscillator and a double oscillator are also determined. The analytic expressions were used to calculate Franck-Condon factors for electronic transitions including double oscillator anharmonicities.

Identification of the photoelectron spectra of HFCS via computing Franck–Condon factors

2021 ◽  
pp. 113393
Author(s):  
Jia-Lin Chang ◽  
Wen-Hsin Kuo ◽  
Yun-Jhu Huang ◽  
Mu-Fong Chang ◽  
Jui-Yang Huang ◽  
...  
Keyword(s):  
Photoelectron Spectra ◽  
Condon Factors ◽  
Franck Condon

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.

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