Transition selective

Griesemer, J. R. (2000c), The units of evolutionary transition , Selection, 1, 67-80. 

This contribution will describe the manipulation of spin multiplets as a whole, and the word selective - or soft - will be used for multiplet-selective pulses, in contrast to band-selective, which refers to a broader bandwidth which may affect several spins, and to transition selective when only one line is affected. The discussion will be based on proton spectra, but all aspects are similar for other nuclei. Soft pulses use lower amplitudes and much longer irradiation times than non-selective hard pulses. Typical durations for soft pulses are of the order of 1 to 500 ms with a peak amplitude... 

The induced magnetic dipole moment has transformation properties similar to rotations Rx, Rt, and Rz about the coordinate axes. These transformations are important in deducing the intensity of electronic transitions (selection rules) and the optical rotatory strength of electronic transitions respectively. If P and /fare the probabilities of electric and magnetic transitions respectively, then... 

In the particular case of electric dipole radiation A/ = 1, i.e. El-transitions are permitted between configurations of opposite parity. For 2-transitions Al = 0, 2 (excluding transitions ns — n s), i.e. they are allowed between levels of one and the same configuration or between configurations of the same parity. M 1-transitions may take place only between levels of one and the same configuration. There are no restrictions on An for /c-transitions. Selection rules for J and M follow from the Clebsch-Gordan coefficient... 

This pulse sequence aims to transfer the y-DQ coherence into a transition-selective signal. This is achieved by converting one part of the y-DQ coherence into SQ AP coherence by a 45° pulse, which is later refocused generating the in-phase (IP) magnetisation. The other part of the DQ coherence, which does not evolve during the second spin echo, is converted into an AP magnetisation. When combined with the IP part, a transition selective signal is obtained. 

From such considerations the symmetry species of each wavefunction associated with an energy level is determined, and these are indicated at the right in Fig. 1. It is important to realize that this symmetry label is the correct one for the true wavefunction, even though it is deduced from an approximate harmonic-oscillator model. This is significant because transition selection rules based on symmetry are exact whereas, for example, the usual harmonic-oscillator constraint that An = 1 is only approximate for real molecules. 

Recently, we investigated the associative alkylation reaction of toluene with methanol catalyzed by an acidic Mordenite (see Figures 13 and 14) by means of periodic ab initio calculations." We observed that for this reaction some transition selectivity occurred, and induced sufficiently large differences in activation energies to explain the small changes in the para/meta/ortho distribution experimentally observed on large pore zeolites. Thepara isomer is the more valuable product as it is an important intermediate for terphthalic acid, an important polymer monomer." The steric constraints obtained for the transition state structures could be estimated from local intermediates for which the orientations of the toluene molecule were similar as the ones observed for the transition states (see Figure 14). 

For each L value, 2(2L- -1) electrons can be allocated 2 for L = 0, 6 for L=l, 10 for L = 2, 14 for L = 3, 18 for L = 4 and the remaining 10 for L = 5. The latter energy level would thus be only partly filled and the lowest energy absorption transition (selection rule AL=1) would involve an electron promotion from L = 4 to L — 5. The calculated wavelength from this model is 398 nm, which is in surprisingly good agreement with the experimental value, 404 nm (ref. 143). 

The atomic spectra of most elements originate from the transition of electrons from the ground state to the excited state, giving rise to what are commonly called resonance lines [4]. The diagrams in Figure 1.3 are transitions — selected fines for sodium and potassium and the wave-numbers associated with each transition. Some elements in the periodic table contain very complicated electronic structures and display several resonance lines close together. The widths of most atomic fines are extremely small (10 nm), and when broadened in various ways the width never exceeds 10 nm [5]. Fortunately, the modem optics available on the latest instruments can isolate lower bandwidths. 

XANES spectra of different systems have been interpreted with the band structure aproximation As an example for a transition metal we discuss here palladium absorption edges. The comparison between the K and Lj edge of Pd metal with the theoretical band approach is shown in Fig. 21. We can observe that the K and Li edges present the same spectral features and therefore contain identical information. In fact, the selection rule for electronic transitions selects the same I = 1 projected density of states. Because the L, edge occurs at lower energy a better instrumental energy resolution is obtained and the structures are better resolved. 

Molecular UV-vis spectroscopy is prevalent in the more advanced chemistry curriculum for undergraduates. It appears in Organic Chemistry in the analysis of organic compounds, and it can also be applied to Physical (or Quantum) Chemistry courses in discussions of molecular orbitals, electronic transitions between these orbitals, and also transition selection rules and microstates. It is also relevant to Inorganic Chemistry, as it is investigated in terms of transition metal complex color, crystal field theory, and molecular orbital diagrams and electronic transitions for a variety of inorganic compounds. 

The situation with asymmetric top rotors is rather more complex because of the wide range of transition selection rules followed, although similar comments apply. The more intense absorption lines will tend to occur at higher frequencies although the relative intensities of lines may vary because of symmetry considerations. Symmetric top spectra occur in clumps centred around 2B J + 1) and so from the quantitative analysis viewpoint differ hardly at all from those of linear molecules. Asymmetric top spectra are more scattered and it is rather easier to choose an accessible and discrete line from them. 

Fig. 6.6a can be understood with the help of Eq. (6.28). which shows us a model of the phenomena taking place. At room temperature, most of the molecules (Boltzmann law) are in their ground electronic and vibrational states k = 0, v = 0). IR quanta are unable to change quantum number k, but they have sufficient eneigy to change v and 7 quantum numbers. Fig. 6.6a shows what in fact has been recorded. From the transition selection rules (see above), we have An — 1 — 0=1 and either the transitions of the kind AJ = (7 + 1) — 7 = +l (what is known as the R branch, right side of the spectrum) or of the kind AJ = 7— (7 + 1) = —1 (the P branch, left side). 

The SFG technique probes the second-order nonhnear hyperpolarizability tensor this tensor includes the Raman and IR susceptibihty, which requires that the molecular vibrational modes are both Raman and IR active. Since Raman- and IR-dipole moment transition selection rules for molecules with a center of symmetry indicate that a vibrational mode is either Raman or IR active but not both, only molecules in a non-centrosymmetric environment on the surface interact with the electric fields molecules in the isotropic bulk phase show inversion symmetry where the third rank hyperpolarizability tensor goes to zero [25-27]. 

When the Ln ion is situated at a centrosymmetric site (i.e., with an inversion center), the pure electronic transitions between 4 levels are ED forbidden [10]. Magnetic dipole transitions (which are up to 10 times weaker than ED transitions) may then be allowed between states of the same parity in the solid if (8) is satisfied, since the magnetic dipole operator, Fq, is of even parity. The only way to destroy the centrosymmetry of Ln " and permit an ED transition between two electronic states is by motions of odd (ungerade) vibrations so that the electronic spectra of Ln " at an inversion center of a crystal are vibronic (vibrational-electronic) in nature. The transition selection rules then become ... 

A brief outline of basic information on the energy levels in atoms and molecules, as well as photon transitions/selection-rules (Chapter 2) a short... 

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