Electronic transition, definition

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

Light of definite energy and polarization has a selective power to exclusively excite dye molecules whose electronic transition energy and orientation match these parameters. Thus, if a dye is excited by polarized fight, its emission will also be highly polarized. Depolarization occurs only when the time correlation of these selectively excited species is lost due to their rotation or participation in some... 

These electronic transitions, shown as coloured arrows, correspond to lines with definite values of frequency and wavelength. The diagram is not to scale and the blue lines going back to the ground state should be much longer than the other lines because the difference between the r = 1 and n = 2 energy levels is by far the greatest, followed by the difference between n = 2 and r = 3. 

The parameter (v) is the average thermal velocity of an electron, Nc the density of states in the conduction band, g the degeneracy of the deep level, and A x = EQ — ET the electron transition energy. Equation (9) also relates the capture constant to the emission rate because of the definition... 

This is due to the comparative weakness of the electromagnetic interaction, the theory of which contains a small dimensionless parameter (fine structure constant), by the powers of which the corresponding quantities can be expanded. The electron transition probability of the radiation of one photon, characterized by a definite value of angular momentum, in the first order of quantum-electrodynamical perturbation theory mdy be described as follows [53] (a.u.) ... 

A number of ideas of the theory of electronic transitions were discussed in Chapter 4. In Part 6 we are going to consider this issue in more detail. Let us start with the definition of the main characteristics of electronic transitions, common for both electric and magnetic multipole radiation. 

The general definition of the electron transition probability is given by (4.1). More concrete expressions for the probabilities of electric and magnetic multipole transitions with regard to non-relativistic operators and wave functions are presented by formulas (4.10), (4.11) and (4.15). Their relativistic counterparts are defined by (4.3), (4.4) and (4.8). They all are expressed in terms of the squared matrix elements of the respective electron transition operators. There are also presented in Chapter 4 the expressions for electric dipole transition probabilities, when the corresponding operator accounts for the relativistic corrections of order a2. If the wave functions are characterized by the quantum numbers LJ, L J, then the right sides of the formulas for transition probabilities must be divided by the multiplier 2J + 1. 

The definitions of the 3n/-coefficients (6j-, 9j-, and 12j-) may be taken from Chapter 6. Analogous expressions for electronic transitions of types (25.3) and (25.4) follow from formulas describing transitions in the case of three open shells. The most important of them will be presented later in this chapter. 

Atomic spectral moments can be expressed in terms of the averages of the products of the relevant operators. Let Oi,C>2, --,Ok be the operators of interactions in definite shells or the operators of electronic transitions between definite shells in the second quantization form. The average of... 

In diatomic spectra, one distinguishes between individual bands each corresponding to a definite pair of quantum numbers v, v", and band systems, each composed of an ensemble of bands associated with a particular electronic transition. In polyatomic spectra, often (a), the individual bands of an electronic transition are so numerous and strongly overlapping that it is difficult or impossible to distinguish them individually, or (b), the electronic transition gives rise only to continuous absorption in both these situations the entire spectrum of an electronic transition is commonly called a band. IT IS RECOMMENDED (REC. 39) that the word band be reserved for definite individual bands, and that electronic transition or transition be used for the entire spectrum, whether discrete, pseudo-continuous, or strictly continuous, associated with an electronic transition or band system if the spectrum consists of discrete bands. ... 

The near IR spectra of the tetrakis(cumylphenoxy)phthalocyanines have not been reported before. The absorption in the Cu complex and one of the absorptions in the Co complex lie close to bands which have been tentatively assigned to trip-multiplet transitions in other phthalocyanines.(14) However, the other absorption bands shown in Table 1 have not been previously reported for phthalocyanines with no peripheral substitution. The small absorption cross sections of these bands in the cumylphenoxy phthalocyanines suggest that they are forbidden transitions. Possible assignments for these bands include a symmetry forbidden electronic transition (like the MLCT transitions in NiPc discussed above) becoming vibronically allowed, d-d transitions on the metal ion, or trip-multiplet transitions. Spectroscopic studies are in progress to provide a more definitive assignment of these absorptions. 

A most important concept that we will learn is that distinct wavelengths of light emitted from gaseous atoms result from electronic transitions between definite energy states within the atoms (Sections 4.2 and 4.4). 

We also conclude from our ab initio DF SCF calculations that the 5d, 6d and 5f DFAOs (and their associated electrons) are definitely involved (due to relativistic effects in the electronic structure and bonding of the diatomics of the heavy third-row transition elements and actinides, and they present the formidable dual challenge to quantum chemists of the accurate calculation of the relativistic and electron correlation effects for such systems. 

The first electronic transition in butadiene has been the subject of many experimental and theoretical studies.The absorption, which has a maximum at 2100 A., is strong and represents a tt tt transition from a ground singlet to an upper singlet state. Analysis of the spectrum, which shows very little structure, has not been carried out. Since no fluorescent radiation has ever been detected on excitation of any of the simple dienes even at low temperature, a definite assignment of the 0 — 0 band has not been made. The 0 — 0 band had been placed at 2300 A. (124 kcal./mole), at which point the absorption is only /so as intense as at its maximum. The oscillator strength is 0.53, which leads to a radiative lifetime of 10 sec. Since emission of radiation has not... 

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