Electronic states theoretical background

II electronic states, 634-640 theoretical background, 625-626 triatomic molecules, 611-615 pragmatic models, 620-621 Ab initio multiple spawning (AIMS) conical intersection location, 491-492 direct molecular dynamics, 411-414 theoretical background, 360-361 Adiabatic approximation geometric phase theory ... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

Infinite-order sudden approximation (IOSA), electron nuclear dynamics (END), molecular systems, 345-349 Initial relaxation direction (IRD), direct molecular dynamics, theoretical background, 359-361 Inorganic compounds, loop construction, photochemical reactions, 481-482 In-phase states ... 

Among the many excited singlet and triplet levels, 5i and Ti have distinct properties. They are in general the only levels from which luminescence is observed (Kasha rule) also most photochemical reactions occur from Sr or Ti. Here we discuss the characterization of the lowest triplet state by electronic spectroscopy. First we treat the theoretical background that allows the absorption spectra of conjugated systems to be described, and then we discuss the routes that lead to phosphorescence emission and Ti- - Sq absorption intensity. Details of the experimental methods used to determine triplet-triplet and singlet-triplet absorption spectra, as well as phosphorescence emission spectra are given in Chapters III, IV, and V. Representative examples are discussed. 

The first attempt to explain the characteristic properties of molecular spectra in terms of the quantum mechanical equation of motion was undertaken by Born and Oppenheimer. The method presented in their famous paper of 1927 forms the theoretical background of the present analysis. The discussion of vibronic spectra is based on a model that reflects the discovered hierarchy of molecular energy levels. In most cases for molecules, there is a pattern followed in which each electronic state has an infrastructure built of vibrational energy levels, and in turn each vibrational state consists of rotational levels. In accordance with this scheme the total energy, has three distinct components of different orders of magnitude,... 

The theoretical background that will be needed to calculate the excited state distortions from electronic emission and absorption spectra is discussed in this section. We will use the time-dependent theory because it provides both a powerful quantitative calculational method and an intuitive physical picture [7-11]. In this section we will concentrate on the physical picture and on the ramifications of the theory. 

The theoretical background which will be needed to calculate the excited state distortions from electronic and Raman spectra is discussed in this section. We will use the time-dependent theory because it provides both a powerful quantitative calculational method and an intuitive physical picture [42,46-50]. The method shows in a simple way the inter-relationship between Raman and electronic spectroscopy. It demonstrates that the intensity of a peak in a resonance Raman spectrum provides detailed information about the displacement of the excited state potential surface along the normal mode giving rise to the peak [42,48]. It can also be used to calculate distortions from the intensities of vibronic peaks in electronic spectra [49]. For harmonic oscillators, the time-dependent theory is mathematically equivalent to the familiar Franck-Condon calculation [48]. 

After presenting the sample preparation in Sect. 5.2, we give an introduction to the theoretical background in Sect. 5.3. In Sect. 5.4, we briefly review the electronic influence on structure and phase stability of crystalline Hume-Rothery phases. In Sect. 5.5, we discuss the properties of non-magnetic amorphous alloys of the type just mentioned. The electronic influence on structure (5.5.1) and consequences for the phase stability (5.5.2) are also discussed. Structural influences on the electronic density of states are shown in 5.5.3. Electronic transport properties versus composition indicate additionally the electron-structure interrelation (5.5.4), and those versus temperature, the influence of low-lying collective density excitations (5.5.5). An extension of the model of the electronic influence on structure and stability was proposed by Hdussler and Kay [5.21,22] whenever local moments are involved as, for example, in Fe-containing alloys. In Sect. 5.6, experimental indications for such an influence are presented, and additional consequences on phase stability and magnetic properties are briefly discussed. 

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