Dipole matrix

What is the electric dipole matrix elements between the... 

The electric dipole matrix element between these two CSFs can be found, using the SC rules, to be... 

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

The second term in the above expansion of the transition dipole matrix element Za 3 if i/3Ra (Ra - Ra,e) can become important to analyze when the first term ifi(Re) vanishes (e.g., for reasons of symmetry). This dipole derivative term, when substituted into the integral over vibrational coordinates gives... 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

The subscript labels a, b,... (i, j,...) correspond to unoccupied (occupied) bands. The Mulliken notation has been chosen to define the two-electron integrals between crystalline orbitals. Two recent studies demonstrate the nice converging behaviour of the different direct lattice sums involved in the evaluation of these two-electron integrals between crystalline orbitals [30]. According to Blount s procedure [31], the z-dipole matrix elements are defined by the following integration which is only non zero for k=k ... 

Next, one introduces the electronic transition matrix element (which may be an electric dipole matrix element, but need not be so restricted for the development presented here)... 

The partial wave basis functions with which the radial dipole matrix elements fLv constructed (see Appendix A) are S-matrix normalized continuum functions obeying incoming wave boundary conditions. 

Vibrational Properties. Figures 4 and 5 show the variation of the energy Eg and the electric dipole moment p as a function of the relevant geometrical variables for H2O and NHg respectively. For the Internal variables, the curves corresponding to the Isolated molecules are also shown (dashed lines) for comparison lhe20Sclllatlon frequencies v and dipole matrix elements <1, sre also... 

Dipole matrix elements, one- vs. three-photon excitation, coherence spectroscopy, 163—166... 

The diagonal elements of the matrix A are af1 and the off-diagonal elements of Aij are Ty. Equation (9-21) determines how the dipoles are coupled to the static electric field. There are three major methods to determine the dipoles matrix inversion, iterative methods and predictive methods. 

FRET is a nonradiative process that is, the transfer takes place without the emission or absorption of a photon. And yet, the transition dipoles, which are central to the mechanism by which the ground and excited states are coupled, are conspicuously present in the expression for the rate of transfer. For instance, the fluorescence quantum yield and fluorescence spectrum of the donor and the absorption spectrum of the acceptor are part of the overlap integral in the Forster rate expression, Eq. (1.2). These spectroscopic transitions are usually associated with the emission and absorption of a photon. These dipole matrix elements in the quantum mechanical expression for the rate of FRET are the same matrix elements as found for the interaction of a propagating EM field with the chromophores. However, the origin of the EM perturbation driving the energy transfer and the spectroscopic transitions are quite different. The source of this interaction term... 

According to Equations (5.14) and (5.15), we see that the probability of a particular transition depends on the electric dipole matrix element /x, given by Equation (5.12). These transitions, which are induced by interactions of the electric dipole element with the electric field of the incident radiation, are called electric dipole transitions. Therefore, electric dipole transitions are allowed when p- 0. 

The dipole matrix element squared for channel in atomic units, M, is given by... 

In (15), the dependence on the energy of the exciting photon hv (at a given eigenvalue E,j) is stressed. A is a proportionahty factor containing fundamental constants. R] i and R)+i are radial dipole matrix elements ... 

Figure 3.3 The model five-level system studied by Etinski, Uiberacker, and Jakubetz. The dipole matrix elements coupling neighboring levels are displayed in the boxes (in a.u.). (From Ref. 51).

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

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