Energy transition moments

Linear response function approaches were introduced into the chemistry literature about thirty years ago Ref. [1,2]. At that time they were referred to as Green functions or propagator approaches. Soon after the introduction it became apparent that they offered a viable and attractive alternative to the state specific approaches for obtaining molecular properties as excitation energies, transition moments and second order molecular properties. 

Atomic core polarization e -p correlation Yamazaki and Ohtsuki [5] emphasized the important role of a special type of configuration mixing which contributes to a substantial reduction of the radiative transition rate. This effect is essentially the same as in the nuclear core polarization phenomena, where low energy transition moments are affected by the presence of high excitation mode (giant resonances). In the present case, the low energy El transitions ( 2 eV) are retarded by a factor of 3 by the existence of the hard electronic excitation ( 20 eV). 

Olsen J, Sanchez de Meras, Jensen HJAa, Jprgensen P (1989) Excitation energies, transition moments and dynamic polarizabilities for CH+ A comparison of multiconfigurational linear response and full configuration calculations. Chem Phys Lett 154 380-386. 

Although the valence ji-ji excitation spectra of benzene derivatives have been extensively studied over the past 65 years both experimentally and theoretically, much less is known about that of phenol, apart from its lowest excited state. In general, absorption and fluorescence spectroscopy of a benzene ring can be used to detect its presence in a larger compound and to probe its environment. While the relative constancy of the valence jt-n excitation spectrum allows a qualitative identification of spectral bands by a correspondence with those in free benzene, detailed quantitative differences could indicate the nature of substituents, ligands or medium. Key information on substituted benzene includes the excitation energies, transition moments and their direction, and electrostatic... 

Table 4. CT transitions Sig—energies, transition moments and occupation numbers. 

For a given rare gas atom, one can observe that the red shift increases by substitution in the benzene ring. The relationship existing between the red shift and the nature of the substituent results from numerous physical parameters involved in the complexation phenomenon such as polarizability, transition energies, transition moments, etc... No unique parameter characterizing the solute arises from the theory. However, it is well established that the nature of <— Sq electronic transition in... 

Here, (ATp) is the pth component of the electronic transition moment from state a to b,. and E j-are the energy... 

In turn, an expression for is obtained, which, in the frequency domain, consists of a numerator containing a product of (.s + 1) transition moment matrix elements and a denominator of. s complex energy... 

The fitting parameters in the transfomi method are properties related to the two potential energy surfaces that define die electronic resonance. These curves are obtained when the two hypersurfaces are cut along theyth nomial mode coordinate. In order of increasing theoretical sophistication these properties are (i) the relative position of their minima (often called the displacement parameters), (ii) the force constant of the vibration (its frequency), (iii) nuclear coordinate dependence of the electronic transition moment and (iv) the issue of mode mixing upon excitation—known as the Duschinsky effect—requiring a multidimensional approach. 

The poles con espond to excitation energies, and the residues (numerator at the poles) to transition moments between the reference and excited states. In the limit where cj —> 0 (i.e. where the perturbation is time independent), the propagator is identical to the second-order perturbation formula for a constant electric field (eq. (10.57)), i.e. the ((r r))Q propagator determines the static polarizability. 

Since the time of the quantum-mechanical calculations by Longuet-Higgins, many attempts have been made to calculate tt-electron densities, resonance energies, dipole moments, and optical transitions both by the LCAO-MO and the valence bond method.However, no agreement has been reached on the importance of pd-hybridization of the sulfur atom. This is considered by some workers an essential... 

Equation 17 can be viewed as the general form of a sum rule for an arbitrary one-electron operator O expressed in terms of the square of the transition moment of the operator and its excitation energies. 

In these dye-functionalized dendrimers, light absorbed by the numerous peripheral coumarin-2 units is funneled to the coumarin-343 core with remarkably high efficiency (toluene solution 98% for the first three generations 93% for compound 8). Given the large transition moments and the good overlap between donor emission and acceptor absorption, energy transfer takes place by Forster mechanism [34]. 

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

The vertical excited states of B2 symmetry, calculated at the Cl( level, are very high in energy. The first one, B2(3p) is already at 8.60 eV above the ground state (Table 12) with a transition moment of 0.16 a.u., probably too weak for the transition to be observed. 

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