Transition intensities electronic structure calculations

In addition to experiments, a range of theoretical techniques are available to calculate thermochemical information and reaction rates for homogeneous gas-phase reactions. These techniques include ab initio electronic structure calculations and semi-empirical approximations, transition state theory, RRKM theory, quantum mechanical reactive scattering, and the classical trajectory approach. Although still computationally intensive, such techniques have proved themselves useful in calculating gas-phase reaction energies, pathways, and rates. Some of the same approaches have been applied to surface kinetics and thermochemistry but with necessarily much less rigor. 

Our interest in the photooxidation of Fe " in aqueous solution derives from our more general interest in the effects of solvents on electronic transitions, particularly those in which strong specific interactions with solvent molecules are present (42,45,46). We proceed by performing electronic structure calculations, hquid structure simulations, and spectroscopic calculations for mechanisms 1, 3, and 4, investigating the nature of the photochemical processes of aqueous Fe. In particular, we first require the gas-phase absorption frequencies and intensities of the Fe (H20)6 complex, using both ab initio and semi-empirical (INDO-MRSCI) techniques. Second, we need to determine the structure of water around the Fe " ion in solution. Third, we need to determine the solvent shifts of the absorption bands to evaluate transition energies in solution. This will lead to an estimation of relative importance of all but the charge transfer to solvent process (mechanism 2), calculation of which is beyond die capacity of our present computational facihties. The potential surfaces em-... 

A number of approximate VCD models are based on electronic structure calculations. The LMO modeH is a more accurate molecular orbital (MO) approach in evaluation of VCD intensities and has been implemented at the ab initio level. The nuclear and the electronic contributions to the dipole transition moments are treated completely separately in this model. The expressions of nuclear contributions are derived with full nuclear charges. For the expression of the electronic contributions, the BO approximation is invoked after the electronic part of the magnetic dipole operator is modified in such a way that the BO difficulty is avoided. Nonvanishing electronic contributions to the magnetic transition moments are thus obtained, which come from the displacements of the centroids of the localized MOs during vibrations. 

The PPV spectra of Fig. 16 show all the signatures of exciton absorption and emission, such as in typical molecular crystals. The existence of well-defined structure in the absorption spectrum is not so easily accounted for in a band-to-band absorption model. In semiconductor theory, the main source of structure is in the joint density of states, and none is predicted in one-dimensional band structure calculations (see below). However, CPs have high-energy phonons (molecular vibrations) which are known (see, e.g., RRS spectra) to be coupled to the electron states. The influence of these vibrations has not been included in previous theories of band-to-band transition spectra in the case of such wide bands [176,183]. For excitons, the vibronic structure is washed out in the case of very intense transitions, corresponding to very wide exciton bands, the strong-coupling case [168,170]. Does a similar effect occur for one-electron bands Further theoretical work would be useful. 

A wide variety of plasma diagnostic applications is available from the measurement of the relatively simple X-ray spectra of He-like ions [1] and references therein. The n = 2 and n = 3 X-ray spectra from many mid- and high-Z He-like ions have been studied in tokamak plasmas [2-4] and in solar flares [5,6]. The high n Rydberg series of medium Z helium-like ions have been observed from Z-pinches [7,8], laser-produced plasmas [9], exploding wires [8], the solar corona [10], tokamaks [11-13] and ion traps [14]. Always associated with X-ray emission from these two electron systems are satellite lines from lithium-like ions. Comparison of observed X-ray spectra with calculated transitions can provide tests of atomic kinetics models and structure calculations for helium- and lithium-like ions. From wavelength measurements, a systematic study of the n and Z dependence of atomic potentials may be undertaken. From the satellite line intensities, the dynamics of level population by dielectronic recombination and inner-shell excitation may be addressed. 

The minimal active space needed to describe the electronic structure of the NDI moiety includes the five occupied and five unoccupied 7t-orbitals of the naphthalene core and four lone pair orbitals of the carbonyl groups. The 57t[4n]57t active space contains 14 electrons and electronic transitions arise from seven states. Only two of the seven states, 1 1 B2u and 1 B3U, show transitions in the region of interest between 320 and 420 nm. Other transitions have no effect on the bands in this region and hence were not considered. The main features in the experimental absorbance spectrum were reproduced using the most intense Frank-Condon transitions (Fig. 15). The calculated spectrum (dashed lines) showed a red shift of 9 nm relative to the experiment, which may be due to the representation of each transition by only two charges, and also due to the neglect of other transitions. 

There are also properties for which the magnitude is dependent upon transition intensity and for which accurate results can be obtained only with perturbation theory examples occur in currently much studied areas like NMR spectroscopy (described in Chapter 2), but also involve other properties like magnetic susceptibilities and refractive indices, which are not much studied from an electronic structure point of view (although we would argue that, due to advances in theory, such experimental techniques are ripe for further exploration). Within a Hartree-Fock approach the perturbation of a molecule by electric or magnetic fields can be calculated at a number of levels of theory. Coupled Hartree-Fock perturbation theory (Lipscomb, 1966 Ditchfield, 1974), which arrives at a self-... 

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... 

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