Electronic spectra theory

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Figure 9. The measured momentum density of an aluminium film. In the left panel we show the measured momentum density near the Fermi level (error bars), the result of the LMTO calculations (dashed line) and the result of these calculations in combination with Monte Carlo simulations taking into account the effects of multiple scattering (full line). In the central panel we show in a similar way the energy spectrum near zero momentum. In the right panel we again show the energy spectrum, but now the theory is that of an electron gas, taking approximately into account the effects of electron-electron correlation (dashed) and this electron gas theory plus Monte Carlo simulations (solid line).

Mi CO). The first metal-metal bond to be characterized (35) is the formally single Mn-Mn bond in Mi CO). This compound has often been used as the model for developing electronic structure theories (1.18.36.37). Extremely efficient photofragmentation is responsible for the structureless electronic spectrum and the lack of emission following excitation of this molecule. This spectroscopic deficiency necessitates photofragmentation studies to obtain data to verify theoretical models. Most of the photochemical experiments in the past explored the reactions of the lowest excited singlet state in the near ultraviolet. 

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

Although the electronic spectrum of a molecule should be most directly correlated with theory, there are several other physical properties which can be related, if only qualitatively, to the bond theory of the molecule. We shall discuss some of these now. 

There have been a number of investigations of the electronic and IR spectra of chromates, and attempts to account for the electronic spectrum by molecular orbital theory.13061409... 

Basically there are two main nonequilibrium effects the electronic spectrum modification and excitation of vibrons (quantum vibrations). In the weak electron-vibron coupling case the spectrum modification is usually small (which is dependent, however, on the vibron dissipation rate, temperature, etc.) and the main possible nonequilibrium effect is the excitation of vibrons at finite voltages. We have developed an analytical theory for this case [124]. This theory is based on the self-consistent Born approximation (SCBA), which allows to take easily into account and calculate nonequilibrium distribution functions of electrons and vibrons. 

The electronic spectrum is yet another property which illustrates the similarities between the metallocenes and (7r-ollyl) metal compounds. In Table VI are listed some data for a series of Coin(absorption bands with the small extinction coefficients are probably two of the spin-allowed d-d transitions. Scott (34) has developed an approximate axial ligand field model for the carborane-transition metal complexes and has discussed the optical spectra in relation to this bonding theory. The actual assessment of bonding in the (7r-ollyl) metal compound as well as the metallocenes would be greatly aided by accurate assignments of the electronic spectra. 

Theories about the origin and nature of the universe have as test data the composition of stars and even of our own sun. The abundance of, say, boron in the atmosphere of the sun can be estimated from measurements of the BH electronic spectrum in the sun s emission coupled with known values of the oscillator strength of the transition. If the spectrum cannot be produced in the laboratory then only calculated values of the transition probability can be used. 

Figure 12-3. IR-UV double resonance spectrum of GC (structure C) in the mid-IR frequency range (recorded at the FELIX free electron laser facility), compared with three types of ab intio calculations. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces [30]...

Absorption of the X-ray makes two particles in the solid the hole in the core level and the extra electron in the conduction band. After they are created, the hole and the electron can interact with each other, which is an exciton process. Many-body corrections to the one-electron picture, including relaxation of the valence electrons in response to the core-hole and excited-electron-core-hole interaction, alter the one-electron picture and play a role in some parts of the absorption spectrum. Mahan (179-181) has predicted enhanced absorption to occur over and above that of the one-electron theory near an edge on the basis of core-hole-electron interaction. Contributions of many-body effects are usually invoked in case unambiguous discrepancies between experiment and the one-electron model theory cannot be explained otherwise. Final-state effects may considerably alter the position and strength of features associated with the band structure. 

Abramczyk H. (1991) Absorption spectrum of the solvated electron. 1. Theory. J Phys Chem 95 6149-6155. 

It is well known that the fine structure of the K absorption edge arises fiom the photoelectric effect of a Is orbital electron of an absorption atom. It is obvious that the peaks in the rising part on XANES spectra are ascribed to the electron transition fiom an inner shell orbital to higher molecular orbitals (called as Is electron transition in this rqrort). Therefore, to estimate the probabilities of the Is electron transition by an electronic dipole theory, theoretical XANES spectrum can be caloilated using molecular orbital calculations. ... 

The final two examples of the determination of excited state distortions are large bimetallic compounds whose electronic absorption spectra are broad and featureless. We must turn entirely to resonance Raman spectroscopy to measure the distortions because all of the information in the electronic spectrum is buried under the envelope. Fortunately, the resonance Raman profiles contain a great deal of information. These molecules were chosen as illustrative examples precisely because the resonance Raman spectra are so rich. The spectrum contains long overtone progressions and combination bands. Excitation profiles of not only the fundamentals but also of overtones and combination bands will be used to determine the distortions. The power of time-dependent theory from Section III.F and experimental examples of the effects of A on fundamentals, overtones, and combination bands are shown. The calculated distortions provide new insight about the orbitals involved in the electronic transition. 

The 320 nm electronic spectrum of naphthalene was the first for which the theory was developed in detail [67]. In the vapour spectrum there are two interpenetrating band systems. One system with oscillator strength f=0.0002 is very weakly electronically allowed and long-axis polarized. The other stronger (f=0.002) system is short axis polarized, and is induced by vibrational perturbation. In the crystal the effect of the crystal field on these systems is different. We had shown experimentally [66] that the origin transition on the one hand and the vibrationally induced transition on the other, were differently affected by crystal interactions. The origin band is split by 151 cmJl and the vibrational by less than 1 cm-1. 

Dogonadze, R.R., Ulstrup,)., and Kharkats, Y.l. (1972) Theory of electrode reactions through bridge transition states-bridges with a discrete electronic spectrum. Journal of Electroanalytical Chemistry, 39, 47-61. 

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