Transition dipole moment electronic

Figure 5 shows a collection of S j -S0 R2PI spectra near the origin. The weak bands at low frequency are pure torsional transitions. We can extract the barrier height and the absolute phase of the torsional potential in S, from the frequencies and intensities of these bands. The bands labeled m7, wIq+, and are forbidden in the sense that they do not preserve torsional symmetry. In the usual approximation that the electronic transition dipole moment is independent of torsion-vibrational coordinates, band intensities are proportional to an electronic factor times a torsion-vibrational overlap factor (Franck-Condon factor). These forbidden bands have Franck-Condon factors m m") 2 that are zero by symmetry. Nevertheless, they are easily observed in jet-cooled spectra. They are comparably intense in many spectra, about 1-5% of the intensity of the allowed origin band. 

In general, only dye molecules with a large electronic transition dipole moment pS, Si] are considered in this account, which means that the S < So transition is of n < n type. 

Figure 1.20. (a) Angles 0 0y, and y, describing the relative orientation of the electronic transition dipole moments s between two dye molecules, (b) Relative orientations of the electronic transition dipole moments between two equal dye molecules in the channels of zeolite L. (c) Angular dependence of the orientation factor k2 under the anisotropic conditions (b) and averaged over y. 

K,y depends on the angles 0 0, and 4), describing the relative orientation of the electronic transition dipole moments shown in Figure 1.20(a). 

The electronic structure of fluorenes and the development of their linear and nonlinear optical structure-property relationships have been the subject of intense investigation [20-22,25,30,31]. Important parameters that determine optical properties of the molecules are the magnitude and alignment of the electronic transition dipole moments [30,31]. These parameters can be obtained from ESA and absorption anisotropy spectra [32,33] using the same pump-probe laser techniques described above (see Fig. 9). A comprehensive theoretical analysis of a two beam (piunp and probe) laser experiment was performed [34], where a general case of induced saturated absorption anisotropy was considered. From this work, measurement of the absorption anisotropy of molecules in an isotropic ensemble facilitates the determination of the angle between the So Si (pump) and Si S (probe) transitions. The excited state absorption anisotropy, rabs> is expressed as [13] ... 

Thus, the absorption to the excited electronic state depends on the electronic transition dipole moment, the Franck-Condon (EC) overlap between the vibrational wavefunctions in both electronic states and the vibrational excitation probability. Indeed, as seen from the schematic representation in Eigure 2.1b, the absorption spectrum represents the reflection of the wavefunction, but it is also dependent on the EC factors that lead to intensity alterations in the observed features. 

As mentioned above, the H photofragment yield depends on the SRS vibrational excitation probability, the FC overlap between the vibrational wavefunc-tions in the ground and excited electronic states, the electronic transition dipole moment and on the photodissociation channel. Since in the VMP process the combined SRS-I-UV excitation energies are in the -43,900-44,530 cm i range, the CH3NH2 A state is accessed from all the initially prepared vibrational states. It was therefore concluded [34, 81, 82] that the main player determining the H yield... 

In the simulations presented here, we assume that a pump laser excites the molecule to either the vibrationless, or specific vibrational levels of the Si electronic state. The diffraction pattern is measured by scattering the electron beam off the excited molecules on a time scale shorter than the rotational motion of the molecules, i.e. on a time scale less than about 10 ps. The diffraction pattern is measured in the plane perpendicular to the electron beam. The diffraction patterns shown here are for an excitation laser polarization parallel to the detector plane, and perpendicular to the electron beam. Since the electronic transition dipole moment of s-tetrazine is perpendicular to the aromatic ring, this pump-pulse polarization selects preferentially those molecules that are aligned with the aromatic plane parallel to the electron beam. 

As already mentioned, one of the main weaknesses of the simple reflection method is the fact that the electronic transition dipole moment, (or the transition dipole moment surface, TDMS for polyatomic molecules in Section 4) is assumed to be constant. This weakness will remain in the Formulae (12), (27) and (29) derived below. The average value of the square of the TDM (or TDMS) is then included in amplitude A and A = A /V. In Formulae (3), (3 ) and (3") the mass (or isotopologue) dependent parameters are p and the ZPE. In contrast, W and V., which define the upper potential, are mass independent. This Formula (3) is already known even if different notations have been used by various authors. As an example, Schinke has derived the same formula in his book [6], pages 81, 102 and 111. Now, the model will be improved by including the contribution of the second derivative of the upper potential at Re- The polynomial expansion of the upper potential up to second order in R - Re) can be expressed as ... 

Photodissociation involves electronic transitions initiated by the absorption of light. The key molecular property that mediates the interaction with light is the transition dipole moment. The electronic transition dipole moment between the jth and kth electronic state is defined by the integral over the electronic degrees of freedom for the operator where the dipole moment is sandwiched between the two electronic wave functions given by... 

The electronic transition dipole moment depends on the nuclear coordinates. Certain transitions are forbidden by symmetry, for example in CO2 and N2O. 

The TDSE requires an initial condition, i.e. one must specify the wave packet at f = 0. Based on the assumption that the nuclei do not move during an electronic transition but only the electrons, the photo-excitation can be described as a Franck-Condon transition where the wave packet is excited vertically to the excited electronic state. Here fixj is the electronic transition dipole moment of the transition between the ground state X and the th electronically excited state, whereas Xx is a wave function of the electronic groimd state, typically the lowest vibrational state. Assuming a vertical electronic transition the initial wave packet on the excited state PES is given by... 

In the following paragraphs we give selected examples of the use of our wavefunctions and potential curves to predict or confirm various spectroscopic features of the alkalis. We know of plans to observe Li2 spectra in at least two laboratories (23, 24) so some predictions regarding the spectra appear to be in order. Julienne (25) has used our wavefunctions for LI2 to calculate the electronic transition dipole moment function corres-... 

This means that the total emission intensity depends only on the purely electronic transition dipole moment. Thus, the electronic allowedness represents the source of intensity which is distributed according to the Franck-Condon factor to the different vibrational satelHtes. With respect to the symmetry of the Franck-Condon active vibrations, it is remarked that this factor can only be nonzero for totally symmetric modes (if it is referred to fundamentals), since the vibrational ground state n(v = 0) is totally symmetric (e.g.see [154,p. 113]). 

The electronic-transition dipole moment for the G E transition is defined by Mge = ( g A/ ge1 e> where the are the state wave functions and A/ ge is the dilference in dipole moment of the ground and excited states [22]. The intensity of the transition is proportional to Mge - The broad absorption bands usually observed in transition metal systems are composed of progressions in the vibrational modes that correlate with the differences in nuclear coordinates between the vibrationally equilibrated ground and excited state. Since the energy difference between the donor and acceptor is generally solvent-dependent, the distribution of solvent environments that is characteristic of solutions may also contribute to the bandwidth (see further discussion of this point in the sections below). If the validity of the Born Oppenheimer approximation is assumed, the intensity of each of these vibronic components is given by Eq. 11,... 

It has been shown recently by Kapturkiewicz and co-workers [14] that the analysis of the CT absorption CT <— So and the radiative and radiationless charge recombination processes CT So (Figure 4) in selected D-A n-n interacting systems sterically hindered to coplanarity (such as 9-anthryl and 9-acridyl derivatives of aromatic amines [14a,b], carbazol-9-yl derivatives of aromatic nitriles [14c] and ketones [14d] and D-A derivatives of indoles [14e] or phenoxazines and phe-nothiazines [14f]) in terms of the theory of photoinduced ET processes in absorption [52, 53] and emission [53-55] and Mulliken and Murrell models of molecular CT complexes [56, 57] leads to the determination of the quantities relevant for the rate of the radiative ET processes (exemplified by the CT absorption and emission) and to the estimation of the electronic structure and molecular conformation of the states involved in the photoinduced ET. A similar approach can be applied to describe the properties of the fluorescent singlet CT states and phosphorescent triplet CT states [58]. It should be pointed out that the relatively large values of the electronic transition dipole moments of the CT fluorescence indicate a non-... 

The electronic transition dipole moments Mabs corresponding to the CT absorption can be determined from an approximate expression [60]... 

The comparison of the Mfiu values with those of Mabs allows one to obtain information about the changes in the electronic structure and molecular conformation between the Franck-Condon excited state initially reached upon excitation and the solvent-equilibrated fluorescent state [14]. Electronic transition dipole moments are mainly determined by the direct interactions between the lowest CT state and the ground state (So), and by the contributions from the locally excited configurations [14, 54, 56, 57]. For example, for the fluorescent CT state one can obtain... 

---