Gaussian optical spectra

Figure 4. A) Room-temperature optical spectrum of a single crystal of plastocyanin obtained with light incident on the (0,1,1) face and polarized parallel (solid line) and perpendicular (dashed line) to a (from Ref. 11). B) Gaussian resolution of the 35 K visible absorption spectrum of a plastocyanin film with suggested assignments the symbols ( ) represent the experimental absorption spectrum. Right plastocyanin unit cell projected on the (0,1,1) plane, showing the positions of the four symmetry-related Cu atoms at their first coordination shells.

There has been considerable confusion in the literature about what the ET distance, the dab of Equations (2) and (3), actually represents. For transition metal-centered systems the metal-metal distance (estimated from model compounds such as a non-IV oxidation level of the compound of interest) was traditionally used as 7ab. However, as first pointed out clearly by Cave and Newton in their generalized Mullik-en-Hush theory,53,54 dab refers to the diabatic surfaces, while real molecules exist on adiabatic surfaces with electronic couplings intact, so it cannot be directly measured experimentally. Cave and Newton also pointed out that one can convert an ET distance measured on the adiabatic surface, a du value, to <2ab using the optical spectrum with Hush s Gaussian approximation of Equation (3), by employing the following equation ... 

Figure 8. The component optical bands of the spectrum of UV-irradiated KN3 at room temperature obtained by fitting the total optical spectrum to gaussian-shaped bands.

This equation holds only for an optical electric field which is Gaussian and which possesses an exponential autocorrelatitxi function, i.e., Eq. (66). If the field is non-Gaussian there is no simple relation between the optical spectrum lio)) and the power spectrum. Eq. (69) has three components (1) a shot noise term e(S ln which is independoit of the frequency (Le., white noise), (2) a d.a photocurrent 6(m) which is essentially infinite at extremely low fiequendes (i.e., d.c.) and a light beating spectrum which for an exponential autocorrelation function and Gaussian optical field is a Lorentzian of half width, IF. Fig. 4 shows the experimental data of Benedek et al with calculated points and observed line shape. What is not shown is the infinite d.c. photocurrent at ft)=0. These measurements were obtained by use of a spectrum analyzer which measures directly the power scattered at each frequency. 

Figure 3. The drawn curves represent the reduced absorption coefficient k/[Nap as a function of wavelength, calculated for 2000 K from Table III of Ref. 14, using Eq. 1, and adding 1050 cm to all transition frequencies. The spectrum has been folded with a Gaussian curve 7 nm wide (FWHM) to smooth the satellites. The four contributions from the four optically allowed Na ...

A detailed analysis of the UV-VIS spectrum of (spinach) plasto-cyanin in the Cu(II) state has been reported (56). A Gaussian resolution of bands at 427, 468, 535, 599, 717, 781, and 926 nm is indicated in Fig. 7. Detailed assignments have been made from low-temperature optical absorption and magnetic circular dichroic (MCD) and CD spectra in conjunction with self-consistent field Xa-scattered wave calculations. The intense blue band at 600 nm is due to the S(Cys) pvr transition, which is intense because of the very good overlap between ground- and excited-state wave functions. Other transitions which are observed implicate, for example, the Met (427 nm) and His (468 nm) residues. These bonds are much less intense. The low energy of the d 2 orbital indicates a reasonable interaction between the Cu and S(Met), even at 2.9 A. It is concluded that the S(Cys)—Cu(II) bond makes a dominant contribution to the electronic structure of the active site, which is strongly influenced by the orientation of this residue by the... 

Fig. 3.15 (Right) Time-gated fluorescence spectra of a film of polyfluorene PF2/6 after optical excitation at 3.35 eV at low temperature (15 K). The spectra were time integrated from 0-2, 8-10, 35-57, 134-136, 329-331, 822-824 and 1770-1850 ps, respectively. The arrow indicates the excitation energy. (Left) Low-temperature (80 l<) absorption spectrum of the film. The dashed line is a fit of a Gaussian curve to the red edge of absorption spectrum. Reprinted from [73], copyright 2001, with permission from Elsevier.

Figure 2.9 Residual optical absorption spectrum of y-irradiated sintered medical-grade Y-TZP (solid curve) and its Gaussian-Lorentzian deconvolution (dotted curves) (Dietrich, Heimann and Willmann, 1996).

Some interesting and important conclusions were drawn by separating the phonon spectrum in accordance with the polarization of the oscillations [15]. The whole spectrum was divided into six branches, each of which has an almost Gaussian form of the distribution curve g( ). For cubic crystals, these six branches consist of three acoustical branches (one branch of longitudinal and two branches of transverse waves) and three optical branches (one longitudinal and two transverse waves). The acoustical vibrations can be compared with the vibrations of atoms in a unit cell, and the optical vibrations with mutual oscillations of the sublattices in relation to one another. The curves of the density distribution of oscillations in each [Pg.180]

In actual spectrum measurement, the line spectrum is always broadened mainly due to a finite spectral resolution of an optical setup, where the line shape can be often approximated as Gaussian practically. When we introduce the spectral resolution as the full width of the half maximum (FWHM), the spectrum is finally written as follows ... 

Figure 14.13. The calculated emission spectrum for y = 1. The electronic gap is 2.1 eV, the optical phonon frequency 0.18 eV and a Gaussian lineshape with HWHM of 0.07 eV has been used (Reprinted with permission from ref 109).

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