Band positions calculation

A molecular orbital calculation of the ultraviolet spectrum of the quinolizinium cation has been made employing self-consistent field molecular orbitals of the parent hydrocarbon.34 Of the four band positions calculated on this basis, only two have been observed. The calculated and observed values are given in Table IV. 

The technique used for the band position calculation in luminescence spectra is very similar to that of photoelectron spectra (PHES). Thus, the energy of transitions from the ground to one of the excited states is calculated in both cases [2]. Therefore, such methods as TD-DFT, Cl or CASSCF [3] can be applied. The geometry optimization is necessary in both cases. 

Band positions calculated as explained in text, a assumed to be 45°, Relative values of rotational strength given on basis of mole of oligomer... 

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

Figure 6.33 gives an overview of the changes in d band position for monolayers of one metal on top of another, as calculated by N0rskov and co-workers [A.V. Ruban, B. Hammer, P. Stoltze, K.W. Jacobsen, H.L. Shriver and J.K. N0rskov, J. Mol. Catal. A115 (1997)... 

In this way it was shown that the opt values derived from data for MCl, MFi, and MFg species gave excellent correlations with the occupation number, q, and that the n -<-75 (ys) peak positions could be well reproduced using Eqs. 5 (7) and 5 (2), with spin-orbit corrections. In all cases the correlations were significantly better when the relativistic terms were included than when they were omitted, and in Table 30 we list the xopt and oPt values derived from the 5 d data for MFg, MFg, and MF6 complexes. In the Table we also show the observed and the calculated band positions using the corrected forms of Eqs. 5 (7) and 5 (2). Once again the xopt vs. q plots yield slopes in excellent agreement with the ( —ri) values deduced from these equations. Finally, in Figs. 16... 

TABLE 2. Observed band positions and calculated HMO ionization energies Iv- ca c for some polyenes... 

Natural minerals may contain simultaneously up to 20-25 luminescence centers, which are characterized by strongly different emission intensities. Usually one or two centers dominate, while others are not detectable by steady-state spectroscopy. In certain cases deconvolution of the liuninescence spectra may be useful, especially in the case of broad emission bands. It was demonstrated that for deconvolution of luminescence bands into individual components, spectra have to be plotted as a function of energy. This conversion needs the transposition of the y-axis by a factor A /hc (Townsend and Rawlands 2000). The intensity is then expressed in arbitrary imits. Deconvolution is made with a least squares fitting algorithm that minimizes the difference between the experimental spectrum and the sum of the Gaussian curves. Based on the presumed band numbers and wavelengths, iterative calculations give the band positions that correspond to the best fit between the spectrum and the sum of calculated bands. The usual procedure is to start with one or... 

Theoretical calculations indicate that the CD of parallel and antiparallel (3-sheets are quite similar. This conclusion is supported by the CD spectrum of pelC,[1011021 a protein that has a parallel (3-helix motif, 1031 and therefore is more than 30% parallel (3-sheet with no antiparallel (3-sheet. Moreover, the parallel (3-sheet has a rather small degree of twist. The band positions and relative amplitudes in the CD spectrum of this protein resemble those for poly(Lys) in the (3-sheet form, which is an antiparallel sheet that is expected to be only slightly twisted because of the linear side chains. 

Table 3. Observed band positions and calculated ligand-field parameters for some Cr + complexes (in cmr )...

Figure 4.4 shows the surface band positions of some typical semiconductors in aqueous electrolytes (pH 7), calculated from the experimentally determined C/ft, compared with the redox levels of some important redox reactions. It is known that the U for most semiconductors, such as n- and p-GaAs, n- and p-GaP, n- and p-InP, n-ZnO, n-Ti02, and n-Sn02, in aqueous electrolytes is solely determined by the solution pH and shifts in proportion to pH with a slope of -0.059 V/pH.3,4) This is explained by the adsorption equilibrium for H+ or OH- between the semiconductor surface and the solution, for example,... 

Fig. 4.4 Surface band positions of some semiconductors in an aqueous electrolyte (pH 7), calculated from experimentally determined U. ...

Note that the value of the anharmonicity constant can thus be derived from a comparison between the fundamental n = 0 to n = 1 absorption band frequency and the first and subsequent overtone band positions. Given the form of the Morse Curve, Xe can be calculated from De, and hence an estimate of the bond dissociation energy... 

If the A group is a saturated amine only three parameters remain eaA, a, and p. It should be possible to determine all three from the ligand field potential matrix, or directly from the spectroscopic fit. Our own experience with the ethylenediamine complex, [Cr(en)3]3+, revealed another problem [10] the effects of a and P on the ligand field potential matrix elements and on the calculated band positions, while not identical, are similar enough that they cannot be practically disentangled. It was, however, possible to determine a and P in [Cr(en)3]3+ by using circular dichroism spectra (see Sect. 7). 

The influence of the insulator crystal media on the matrix element Vtf is reduced to taking into account the dependence of Green s function on the position of the electron energy level in relation to the crystal electron energy bands. The calculation of Green s function is carried out using of its spectral representation. If the level of the bound electron is close to the minimum of the conductivity band or to the maximum of the valence band, the value of the tunneling exponent decreases noticeably. 

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