Optical absorption linear response

The above theory is usually called the generalized linear response theory because the linear optical absorption initiates from the nonstationary states prepared by the pumping process [85-87]. This method is valid when pumping pulse and probing pulse do not overlap. When they overlap, third-order or X 3 (co) should be used. In other words, Eq. (6.4) should be solved perturbatively to the third-order approximation. From Eqs. (6.19)-(6.22) we can see that in the time-resolved spectra described by x"( ), the dynamics information of the system is contained in p(Af), which can be obtained by solving the reduced Liouville equations. Application of Eq. (6.19) to stimulated emission monitoring vibrational relaxation is given in Appendix III. 

Details of the picosecond pulse radiolysis system for emission (7) and absorption (8) spectroscopies with response time of 20 and 60 ps, respectively, including a specially designed linear accelerator (9) and very fast response optical detection system have been reported previously. The typical pulse radiolysis systems are shown in Figures 1 and 2. The detection system for emission spectroscopy is composed of a streak camera (C979, HTV), a SIT... 

As can be seen from Eq. (4.52), the dynamics of both population (i.e., time-resolved measurement and Eq. (4.52) can be applied to optical absorption and stimulated emission (SE). Furthermore, the ordinary linear response theory is recovered when au> — 0 and cru represents the Boltzmann distribution. 

Samples were irradiated by a 10 ps single or 2 ns electron pulse from a 35 MeV linear accelerator for pulse radiolysis studies (17). The fast response optical detection systems of the pulse radiolysis system for absorption spectroscopy (18) is composed of a very fast response photodiode (R1328U, HTV.), a transient digitizer (R7912, Tektronix), a computer (PDP-11/34) and a display unit. The time resolution is about 70 ps which is determined by the rise time of the transient digitizer. 

This is called the Kramers-Kronig (KK) relationship, from which the dielectric function e = ej + e2 can be derived [3.25]. Since e is also a linear response function, ej and 2 are again related by the KK relationship, thus the information contained in the dielectric function can be examined by concentrating on one of the two components of the dielectric function. We choose to work with 2(m) because it is what optical (X-ray) absorption spectroscopy measures and can be directly related to the atomic polarisability Im[a(o )] that appeared in (3.5). 

Often an instrumental method is employed in which y is not a linear function of [P]. For example, in optical absorption or potentiometric measurements, the output of a photomultiplier or an electrode is a logarithmic function of concentration. In such cases, the direct instrumental response can be written in a general form as... 

The linear term involving polarizability a describes the well known linear response such as the low-intensity refraction and absorption. The higher hyperpolarizability terms /3 and y describe the molecular nonlinear optical responses. 

The redox-switching of the linear optical absorption of self-assembled mono-layers and Langmuir-Schafer films of [Ru(NH3)5(4,4 -bipyridinium)] complexes [52-54] and a redox-switching of the NLO response of Langmuir-Blodgett thin films based on 5 were recently reported. Oxidation to Ru causes ca. 50% decrease of the intensity of the SHG, which is almost completely restored by reduction to Ru [55]. 

Both transition energies and oscillator strengths are needed for determination of optically allowed absorption spectra. In the multi-configuration version of the linear response theory (MCLR) one constructs an approximation to the exact linear response function by exposing the optimized (MC) SCF wavefunction 0> to a time-dependent perturbation. In this case the time-dependent wave function assumes the form... 

The most common time-dependent perturbation is a long-wavelength electric field, oscillating with frequency eo. In the usual situation, this field is a weak perturbation to the molecule, and one can therefore perform a linear response analysis. From the linear response, we can extract the optical absorption spectrum of the molecule due to electronic excitations. Thus, linear response TDDFT can be used to predict the transition frequencies to electronic excited states (along with many other properties), and this has been the primary use of TDDFT so far, with many applications to large molecules. 

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