Morse oscillator transition probabilities for molecular bond modes

Sage, Martin L.

doi:10.1016/s0301-0104(78)85253-7

Cited by 197 publications

(75 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…V, thesemiclassical matrix elements (i.e., Fourier components) were analytic and could be evaluated by the use of a hand calculator. The quantum mechanical Morse matrix elements of, for instance r or r, while analytic, 49 are more complicated to compute. The semiclassical techniques can therefore be particularly useful when one wishes to use relatively simple methods for comparison with experimental absorption spectra: In actual experiments, the rovibrational structure may only be partially resolved (e.g., Ref.…”

Section: Discussionmentioning

confidence: 99%

Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Voth

Marcus

1985

The Journal of Chemical Physics

View full text Add to dashboard Cite

Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two-state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch-bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two-state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method.

show abstract

Section: Discussionmentioning

confidence: 99%

Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Voth

Marcus

1985

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Schritt: Diagonalisierung der System-Hamiltonmatrix H S Bevor mit der eigentlichen Zeitpropagation der Redfield-Gleichung begonnen werden kann, muß der System-Hamiltonian H S diagonalisiert werden, um zur Eigenzustandsdarstellung für den Redfield-Formalismus zu gelangen. Der System-Hamiltonian ist eine N × N -Matrix, wobei die Größe von N auf S. 13 [126].…”

Section: A3 Anfangszustand Mit Initialem Impulsunclassified

Transient Spectral Features of a cis−trans Photoreaction in the Condensed Phase: A Model Study

Balzer

Stock

2004

J. Phys. Chem. A

View full text Add to dashboard Cite

A theoretical description to calculate transient absorption spectra of photoreactive systems in the condensed phase is developed. The formulation comprises a multidimensional model of nonadiabatic photoisomerization, a Redfield treatment of the environment within the secular approximation, and a doorway−window formulation to calculate transient pump−probe spectra. Employing the eigenstate representation and assuming Gaussian laser pulses, we derive explicit expressions for the doorway and window operators. The formalism scales with N 2 (N being the dimension of the system Hamiltonian matrix) and therefore allows us to handle multidimensional molecular models. Detailed computational studies of the dynamics and transient absorption are presented for various cis−trans photoisomerization models. It is shown that only the two-mode model involving a conical intersection yields short-time transients, as expected for a condensed-phase system. Problems in the interpretation of transient spectra associated with the competition (and cancellation) of the various spectroscopic contributions in a photoreaction are discussed in some detail. The computational studies demonstrate the need for theoretical modeling in order to achieve a microscopic interpretation of femtosecond experiments.

show abstract

“…(5) or with the analytical expressions [see ref 2 -9]. The deriving procedure of the analytical matrix elements can be divided into two parts [4]. The matrix elements of y λ are calculated first and then, the matrix elements of n q are calculated with the relationship:…”

Section: Displacement Matrix Elementsmentioning

confidence: 99%

“…However, the calculation with the numerical integration needs much more time than that with the analytical expressions. High accuracy is achieved in our expressions without the sign alternation in the summation, which causes the round off errors in previous expressions [4,5,7].…”

Section: Displacement Matrix Elementsmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of Displacement Matrix Elements for Morse Oscillators

Rong¹,

Cavagnat²,

Lespade³

2003

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Displacement matrix elements of the Morse oscillators are widely used in physical and chemical computation. Many papers have been published about the analytical expressions of the displacement matrix elements. People still use an integration method rather than the analytical expressions to calculate the displacement matrix elements. Analytical expressions of the diagonal and off diagonal displacement matrix elements with intermediate variables are derived, where v, m and n are non-negative integers and n • 6. Calculation with these expressions is superior to that with numerical integration in precision, calculation speed and convenience.

show abstract

Morse oscillator transition probabilities for molecular bond modes

Cited by 197 publications

References 10 publications

Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Transient Spectral Features of a cis−trans Photoreaction in the Condensed Phase: A Model Study

Calculation of Displacement Matrix Elements for Morse Oscillators

Contact Info

Product

Resources

About