Transition dipole moments, molecular

The molecular dipole moment (not the transition dipole moment) is given as a Taylor series expansion about the equilibrium position... 

The polarization properties of single-molecule fluorescence excitation spectra have been explored and utilized to detennine botli tlie molecular transition dipole moment orientation and tlie deptli of single pentacene molecules in a /7-teriDhenyl crystal, taking into account tlie rotation of tlie polarization of tlie excitation light by tlie birefringent... 

For large interchain separations (8 A < R < 30 A), the LCAO coefficients of a given molecular orbital are localized on a single chain, as intuitively expected. The lowest excited state of these dimers results from a destructive interaction of the two intrachain transition dipole moments, whereas a constructive interaction prevails for the second excited stale. This result is fully consistent with the molcc-... 

Tabic 6-2. Correlation diagram of the C2/, point group of the isolated T6 molecule (left column) with the C2i, factor group for solid T(, (right column) via the site symmetry C group (center). L, M, and N indicate the principal molecular transition dipole moments, while a, b, and c arc the crystalline axes. 

We have seen that the transition dipole moment occurring upon excitation of a molecule has a distinct orientation with regard to the molecular axis. This orientation can be determined by measuring the absorption of polarized light (oscillating in only one plane) by oriented single crystals,... 

The intermolecular interaction described above provides information about the magnitude of spectral shifts, but it does not explain why the absorption spectra of molecular aggregates usually have either an H- or J-band. The square of transition dipole moment (in Debye2 units) is usually termed the dipole strength and is related to the intensity of the absorption band as (van Amerongen et al. 2000)... 

Another important linear parameter is the excitation anisotropy function, which is used to determine the spectral positions of the optical transitions and the relative orientation of the transition dipole moments. These measurements can be provided in most commercially available spectrofluorometers and require the use of viscous solvents and low concentrations (cM 1 pM) to avoid depolarization of the fluorescence due to molecular reorientations and reabsorption. The anisotropy value for a given excitation wavelength 1 can be calculated as... 

The angular dependence of the polarized absorption spectra of LB films containing AMP deposited at lower (20 mN m1) and higher (43 or 50 mN m 1) surface pressures was studied to determine the molecular orientation of porphyrins as schematically shown in Figure 5. No polarization angle (a) dependence was observed at normal incidence. This indicates that the projections of the transition dipole moments of the porphyrins are statistically... 

The results presented here follow the analysis presented in Ref. 84. It is possible to define the functions (r, R, 9, t = 0) only when we have specified whether the electronic transition involved is perpendicular or parallel (i.e., whether the transition dipole moment is perpendicular to or lies in the molecular plane). 

In the case of flexible molecules all chiral conformers contribute to the observed CD spectrum. This usually leads to substantial reduction of the magnitude of the exciton Cotton effect. Nevertheless, if the conformation of the main contributor is established independently (e.g.. by molecular mechanics or NMR spectroscopy), its absolute configuration can be deduced from the exciton Cotton effect. Thus, for 3-(l-naphthalenyl)phthalide 5, the preferred conformation is 5 a. The negative couplet is in accordance with the left-handed screw between the phthalide 1 Ld and the naphthalene lBb transition dipole moment vectors, when the absolute configuration is R121. 

Transilion dipole moments are concerned with the dipole that exists in a molecular vibration when it adjusts itself to the frequency of the electromagnetic radiation with which it is in resonance (and about to undergo a transition). The values of such transition dipole moments can be calculated quantum mechanically (which is lengthy and approximate). If a bond is considered within a series of similar bonds for which reliably calculated transition dipole moments are available, an interpolation of the relevant value may be sufficient (Bockris and Carbajal, 1987)l... 

In addition, group theory can be used to assess when transition dipole moments must be zero. The product of the irreducible representations of the two wave functions and the dipole moment operator within the molecular point group symmetry must contain the totally symmetric representation for the matrix element to be non-zero (note that, if the molecule does not contain an inversion center, the operator r does not belong to any single irrep, except for the trivial case of Ci symmetry see Appendix B for more details). A consequence of this consideration is that, for instance, electronic transitions between states of the same symmetry are forbidden in molecules possessing inversion centers. 

Different types of chemical reactions involve different types of vibrational modes, e.g. dissociation reactions may be controlled by stretching vibrations, isomerizations by skeletal modes, and so on. The argument that infrared quanta are relatively energy-poor and infrared transitions generally have low absorption cross sections, especially if multiphoton excitation is required, limits the choice of suitable molecular transitions. With respect to these constraints the type of reaction chosen and described below was dissociation, involving molecules with maximal transition dipole moments, comparatively weak bonds to be broken, and vibrational excitation in the mid-infrared spectral range. 

In (5.10), (fa S+) is the expectation value of the instantaneous transition dipole moment variation of its value provides the means for controlling the molecular evolution. 

Active control of population transfer using the control relation displayed in Eq. (5.23) has been demonstrated experimentally by Sherer et al. [18]. In this experiment gaseous I2 was irradiated with two short (femtosecond) laser pulses the first pulse transfers population from the ground-state potential-energy surface to the excited-state potential-energy surface, thereby creating an instantaneous transition dipole moment. The instantaneous transition dipole moment is modulated by the molecular vibration on the excited-state surface. At the proper instant, when the instantaneous transition dipole moment expectation value is maximized, a second pulse is applied. The direction of population transfer is then controlled by changing the phase of the second pulse relative to that of the first pulse. 

Now to the problem of calculating the transition densities. We need these quantities in order to be able to compute transition properties like the transition dipole moment. When we use a common orthonormal set of molecular orbitals for both the electronic states, the formalism developed in chapter 3 can be applied. For a one-electron operator A the transition matrix element is obtained from the simple formula ... 

The polarization measurements showed that the Cl atoms and SnCl fragments had the same anisotropy factor 3 = 0.21 0.01, which, if the dissociation is fast compared with molecular rotation, suggests that there is a angle of 46.5 0.4° between the transition dipole moment and the dissociation direction. 

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