Oscillating charge

This yields 0.51 x 10 24 cm3 which agrees approximately with the value 0.58 xl0 24 ascribed to the double bond on an empirical basis. Also we may note that this / value corresponds to a transition dipole of 3.16xl0-18, if a one-dimensional charge oscillation is assumed, and that this dipole yields an apparent charge of 0,49 times the electronic charge for a C=C distance of 1.34 A. 

The usual multipole expansion is inappropriate for the treatment of London energies associated with the interatomic charge oscillation. However, London23 has given an appropriate method, known as the monopole method. Coulson and Davies7 and Haugh and Hirschfelder16 have applied the monopole method to the inter-... 

Fig. IX The calculated infrared absorption peak, assuming lifetime broadening and vibrational damping via local charge oscillations, (a) Fitted to the experimental spectrum in Fig. 11 for an ordered overlayer incorporating the dipole-dipole interaction, (b) The same calculation for a single adsorb molecule. (Reproduced by poTtassUm from Crljen and Langreth. )...

To conclude, even if there exist several processes that affect the vibrational line shape it seems probable that when most of them have been sorted out and with the good agreement between theory and experiment, the lifetime broadening for a chemisorbed CO molecule is of the order of a few cm, corresponding to a lifetime of a few ps. The main vibrational energy relaxation mechanism is creation of electron-hole pairs caused by the local charge oscillations between the metal and the 2n molecular resonance crossing the Fermi level. 

In Figure 6.2, the SPODS concept for control of photochemical reactions by the steering of electron dynamics is illustrated taking a fully nonperturbative approach including molecular dynamics into account. Experimental results obtained on charge oscillation-controlled molecular excitation are presented in Section 6.6. 

In order to relate the dressed state population dynamics to the more intuitive semiclassical picture of a laser-driven charge oscillation, we analyze the induced dipole moment n) t) and the interaction energy V)(0 of the dipole in the external field. To this end, we insert the solution of the TDSE (6.27) into the expansion of the wavefunction Eq. (6.24) and determine the time evolution of the charge density distribution p r, t) = -e r, f)P in space. Erom the density we calculate the expectation value of the dipole operator... 

The process starts in the ground state, where the electron is described by an Y-wave. For this highly symmetric charge distribution, the dipole moment, and hence the interaction energy, vanishes exactly indicating equal population of the dressed states. The weak pre-pulse serves to launch the coherent charge oscillation. Designed with a pulse area [92] of... 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

In order to switch the system into the upper target state 5) merely the sine-phase 0 has to be varied by half an optical cycle, that is, by A(p = n. In this case, the main pulse is phase-shifted by Af = -l- r/2 with respect to the pre-pulse and couples in antiphase to the induced charge oscillation. Hence, the interaction energy is maximized and the upper dressed state u) is populated selectively. Due to the energy increase, the system rapidly approaches the upper target state 5). The ensuing nonadiabatic transitions between the dressed states u) and 1 5) result in a complete population transfer from the resonant subsystem to the upper target state, which is selectively excited by the end of the pulse. 

Figure 44. Configuration of a nonrigid dipole formed by two charges oscillating along a straight line.

When the hopping frequency of the a-hole is equal to the resonance frequency of the jr-bond there are two equally important normal modes of the total system o-hole and 7r-bond, one where the hole and screening charge oscillate together in phase between the... 

Similar examinations of the CT spectra for bis(propylenedithio)-tetrathiafulvalene (BPDT-TTF) salts [36], BEDT-TTF salts [37], and bis-tetramethylenetetraselenafulvalene-(4,5-dimercapto-l,3-dithiole-2-thione)nickel [OMTSF-Ni(DMIT)2] salt [38] have been performed. The latter salts are examples of organic conductors that are almost isotropic in two dimensions. Thus only weak polarization dependence is found in the entire frequency range. The analysis of the spectra within a simple DA-charge oscillator model, which takes into account the coupling to intramolecular vibrational modes, demonstrates how IR and optical measurements can provide estimates for a number of physical parameters for lowdimensional organic conductors. 

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