Particle frequency response function

In terms of the set of KS orbitals / (r), 4>a(r) (we use indices i and j for occupied orbitals (occupation/ = 1) and indices a and b for virtual orbitals (occupation f = 0), respectively), the matrix elements for the single particle density response function induced by a perturbation with frequency co become... 

In this section we are going to develop a different approach to the calculation of excitation energies which is based on TDDFT [69, 84, 152]. Similar ideas were recently proposed by Casida [223] on the basis of the one-particle density matrix. To extract excitation energies from TDDFT we exploit the fact that the frequency-dependent linear density response of a finite system has discrete poles at the excitation energies of the unperturbed system. The idea is to use the formally exact representation (156) of the linear density response n j (r, cu), to calculate the shift of the Kohn-Sham orbital energy differences coj (which are the poles of the Kohn-Sham response function) towards the true excitation energies Sl in a systematic fashion. 

Figure 4 shows as examples of complete frequency coverage the dispersion and absorption curves of pure propylene carbonate (PC) and acetonitrile (AN). The maximum of e"( ) and the inflexion point of e (i/), situated at the same frequency, indicate the relsixation times r (PC) = 43 ps smd (AN) = 3.2 ps charsuiterizing the response function Fp of orientational polarization F" = > / V (/T,-, dipole moment of particle i V, volume... 

S/m (see Figure 19). The ER effect of the polyaniline particle of different conductivity dispersed into silicone oil was studied and the largest ER effect was found to occur in the suspension of polyanilinc particle of conductivity 10 S/m [621. Besides the influence on the ER effect, the particle conductivity also determines the current density of the whole suspension and the response time of the ER fluid. The current density of the oxidized polyacrylonitrile(OP)/silicone oil suspensions obtained at 2.5 kV/mm as a function of particle conductivity is shown in Figure 20 [61]. The current density almost linearly increases with the conductivity of particle. The response time was found to be inversely proportional to the particle conductivity both experimentally [63] and theoretically [64]. The response time can be determined from the relationship between the shear stress and the frequency of applied electric field. Such an example is shown in Figure 21, in which the shear stress of two aluminosilicate/silicone oil suspensions is plotted vs. frequency, fhe suspension with particle of conductivity 6.0 x 10 S/m displays a response time 0.6 ms, much shorter than that of the suspension of the particle conductivity 8.4 xlO S/m, 0.22s (42]. 

As far as the conversion of the analytical response is concerned, the most used detectors in GrFFF have been, until now, conventional ultraviolet (UV) detectors commonly used for HPLC. With this type of detector, the amount of particles with diameter di is proportional to the detector response at the zth point. With particulate samples, in fact, because of UV detector optics, the response is a turbidity signal read within an angle between the incident light and the photosensor (i.e., usually smaller than —10°) rather than the absorbance. This turbidity signal can be assumed to be directly proportional to the sum of all cross-sectional areas of the particulate sample components at any time. The validity of the above assumption, in the case of particles which are about 10-fold larger than the incident wavelength, is discussed elsewhere [6]. The mass frequency function can thus be expressed as [7]... 

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