Theoretical methods electronic spectra

Indazoles have been subjected to certain theoretical calculations. Kamiya (70BCJ3344) has used the semiempirical Pariser-Parr-Pople method with configuration interaction for calculation of the electronic spectrum, ionization energy, tt-electron distribution and total 7T-energy of indazole (36) and isoindazole (37). The tt-densities and bond orders are collected in Figure 5 the molecular diagrams for the lowest (77,77 ) singlet and (77,77 ) triplet states have also been calculated they show that the isomerization (36) -> (37) is easier in the excited state. 

Diels-Alder reactions, 4, 842 flash vapour phase pyrolysis, 4, 846 reactions with 6-dimethylaminofuKenov, 4, 844 reactions with JV,n-diphenylnitrone, 4, 841 reactions with mesitonitrile oxide, 4, 841 structure, 4, 715, 725 synthesis, 4, 725, 767-769, 930 theoretical methods, 4, 3 tricarbonyl iron complexes, 4, 847 dipole moments, 4, 716 n-directing effect, 4, 44 2,5-disubstituted synthesis, 4, 116-117 from l,3-dithiolylium-4-olates, 6, 826 electrocyclization, 4, 748-750 electron bombardment, 4, 739 electronic deformation, 4, 722-723 electronic structure, 4, 715 electrophilic substitution, 4, 43, 44, 717-719, 751 directing effects, 4, 752-753 fluorescence spectra, 4, 735-736 fluorinated derivatives, 4, 679 H NMR, 4, 731 Friedel-Crafts acylation, 4, 777 with fused six-membered heterocyclic rings, 4, 973-1036 fused small rings structure, 4, 720-721 gas phase UV spectrum, 4, 734 H NMR, 4, 7, 728-731, 939 solvent effects, 4, 730 substituent constants, 4, 731 halo... 

In principle, refined and relatively reliable quantum-theoretical methods are available for the calculation of the energy change associated with the process of equation 2. They take into account the changes in geometry, in electron distribution and in electron correlation which accompany the transition M(1 fio) — M+ (2 P/-), and also vibronic interactions between the radical cation states. Such sophisticated treatments yield not only reliable predictions for the different ionization energies 7 , 77 or 7 , but also rather precise Franck-Condon envelopes for the individual bands in the PE spectrum. However, the computational expenditure of these methods still limits their application to smaller molecules. We shall mention them later in connection with examples where such treatments are required. 

The failures of the Born-Oppenheimer separation of the electronic and nuclear motions show up in the spectra of molecules as homogeneous or heterogeneous perturbations in the spectra41. See, e.g. Ref. (42) for an example, a fully ab initio study of the spectrum of the calcium dimer in a coupled manifold of electronic states. Theoretical methods needed to describe the dynamics of molecules in nonadiabatic situations are being developed now. See Ref. (43) for a review. 

High-energy MES in the continuous electronic spectrum, especially those corresponding to the excitation of more than two electrons from the ground state, represent a rather exotic class of states, for which the available quantitative information as to their existence, their properties, and their role in processes, especially in molecules, is very limited. There are a number of theoretical and experimental reasons for this fact. The conventional wisdom that permeates the literature is that in order to understand the excitation by one photon of MES, one has to introduce electron correlation to high order. Indeed, this is the case if the determinants comprising the initial and the final wavefunctions consist of a single orthonormal basis set, as is normal in conventional methods. 

The other molecular properties to be considered include bond energies, electron distributions, the vibrational spectrum and the energies of various excited states. These properties are by no means an exhaustive list but they do represent some of the most frequently reported ones. They are subject to experimental verification and can therefore be used as yardsticks by which the quality of a given theoretical method can be judged. Furthermore, bond energies and electron distributions (along with the Molecular Orbitals (MOs) implied by the latter) provide the foundations for a discussion of chemical reactivity. 

We shall use the allyl radical to illustrate how one can treat planar unsaturated organic molecules using multiconfigurational methods. Some properties of the groimd state will be studied and, in addition, the electronic spectrum. The system has acmally been used as a example in a course given at the Department of Theoretical Chemistry in Lund called Quantum Chemistry at Work and a number of students have performed the calculations. We shall use their results. Some of them were recently published [69]. 

Several sets of theoretical calculations have been performed on the parent ring system. HMO calculations of total rr-electron densities and frontier electron densities successfully predicted that the nucleus would undergo electrophilic substitution at the 6- and 8-positions. Two groups, " have compared the electronic structure of indolizine and various aza derivatives using the SCF or semiempirical antisymmetric configuration interaction method. The results allowed interpretations of the electronic spectrum to be made which were in good agreement with experiment. 

Aldehydes and ketones are important chromophoric groups, which play a central role in many different areas of chemistry. Formaldehyde is the prototype molecule for these kinds of compounds. Its electronically excited states have therefore been investigated extensively both experimentally and theoretically (see Refs. 63-65 and references cited therein). Acetone is the simplest aliphatic ketone. It is probably the best experimentally studied system of this group of important organic systems. The interpretation of its electronic spectrum has been and remains a subject of experimental interest [66-73]. In contrast to formaldehyde, acetone has been much less studied theoretically, undoubtedly due to the larger size of the molecule. To our knowledge there exist only two previous ab initio studies [74, 75]. Formaldehyde, on the other hand, is frequently used for testing new theoretical methods developed to treat excited states, because of its apparent simplicity and the numerous studies available. 

As far as we know there has not been any earlier theoretical analysis of the electronic spectrum of PbO. Many of the methods used to study this molecule are such that they cannot be applied to excited states. The present approach, on the other hand, is constructed to be able to deal with complex open shell electronic structures. With the development of the RASSI... 

Cyanates and Related Species. Theoretical calculations of the electronic spectrum of a number of isocyanates HNCO, FNCO, CINCO, and LiNCO have been performed by means of serai-empirical MO methods. The NCO group is found to be non-linear, in agreement with recent experimental results. The results of these calculations have also been used to assign the u.v. photoelectron spectra of isocyanic acid (HNCO). A theoretical analysis of the vibrations of co-ordinated isocyanate (NCO ) and fulminate (CNO ) groups has been carried out the changes in the stretching vibrational frequency of these groups in metal co-ordination compounds have been explained. 

The u.v. spectrum of XeFj has been measured accurately in the photon energy range 6—35 eV, and assignments are consistent with the ionization potentials given in the literature/ Ab initio theoretical methods have been used to study the electronic structure of XeFj the bonding was found to conform quite closely with Coulson s model, viz. FXc F F Xe F. Liebman has discussed the evidence for the existence of the XeF ion. 

But in spite of all the advantages of the SEFS method as compared to both diffraction and spectroscopic methods of structure analysis, this technique has not yet been applied to analyze the local atomic structure of surfaces and thin films. This is explained by the diversity and complexity of the processes forming the secondary electron spectrum and the corresponding fine structures, and the resulting difficulties in their theoretical description and in the mathematical formalization of the problem of determining local atomic structure parameters from the experimental data. 

In addition, UV spectrum of the studied complexes was simulated by theoretical methods. The TD-DFT/B3PW91 approach was used to calculate the energies of electronic transitions in complexes VI and VII (Tables 10.7 and 10.8). 

The wide range of joinnals in which these publications appear is indicative of the broad spectrum of application areas in which perturbative correlation treatments are being exploited. Furthermore, we can expect there to be many more publications reporting work which exploited many-body perturbation theory methods which are not included in the above analysis simply because, quite rightly, other details of a particular study were considered more important when assigning keywords than the standard theoretical method used to approximate the electronic structure of the targeted system(s). 

The photoabsorption spectrum a(co) of a cluster measures the cross-section for electronic excitations induced by an external electromagnetic field oscillating at frequency co. Experimental measurements of a(co) of free clusters in a beam have been reported, most notably for size-selected alkali-metal clusters [4]. Data for size-selected silver aggregates are also available, both for free clusters and for clusters in a frozen argon matrix [94]. The experimental results for the very small species (dimers and trimers) display the variety of excitations that are characteristic of molecular spectra. Beyond these sizes, the spectra are dominated by collective modes, precursors of plasma excitations in the metal. This distinction provides a clear indication of which theoretical method is best suited to analyze the experimental data for the very small systems, standard chemical approaches are required (Cl, coupled clusters), whereas for larger aggregates the many-body perturbation methods developed by the solid-state community provide a computationally more appealing alternative. We briefly sketch two of these approaches, which can be adapted to a DFT framework (1) the random phase approximation (RPA) of Bohm and Pines [95] and the closely related time-dependent density functional theory (TD-DFT) [96], and (2) the GW method of Hedin and Lundqvist [97]. 

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