Electronic selection rules atoms

In the case of atoms (Section 7.1) a sufficient number of quantum numbers is available for us to be able to express electronic selection rules entirely in terms of these quantum numbers. For diatomic molecules (Section 7.2.3) we require, in addition to the quantum numbers available, one or, for homonuclear diatomics, two symmetry properties (-F, — and g, u) of the electronic wave function to obtain selection rules. 

For the orbital parts of the electronic wave functions of two electronic states the selection rules depend entirely on symmetry properties. [In fact, the electronic selection rules can also be obtained, from symmetry arguments only, for diatomic molecules and atoms, using the (or and Kf point groups, respectively but it is more... 

Just as with vibronically allowed transitions, in symmetry groups in which all Cartesian axes are not equivalent (noncubic groups), it is found that, in general, transitions will be allowed only for certain orientations of the electric vector of the incident light. One class of compounds in which this phenomenon has been studied both theoretically and experimentally consists of trischelate compounds such as tris(acetylacetonato)M(III) and tris(oxalato)M(III) complexes. In these complexes the six ligand atoms form an approximately octahedral array but the true molecular symmetry is only Dy Since there is no center of symmetry in these molecules, the pure electronic selection rules might be expected to be dominant. 

There are two other fairly common causes of apparent breakdown of the electronic selection rules. First, collisions with other atoms or molecules, or the presence of electric or magnetic fields, may invalidate selection rules based on state descriptions of the unperturbed species. Secondly, although the transition may be forbidden for an electric-dipole interaction, it may be permitted for the (much weaker) magnetic-dipole or electric-quadrupole transitions. 

The Parity Selection Rule Atomic Transitions and Electron Orbital Angular Momentum... 

Atoms have complete spherical synnnetry, and the angidar momentum states can be considered as different synnnetry classes of that spherical symmetry. The nuclear framework of a molecule has a much lower synnnetry. Synnnetry operations for the molecule are transfonnations such as rotations about an axis, reflection in a plane, or inversion tlnough a point at the centre of the molecule, which leave the molecule in an equivalent configuration. Every molecule has one such operation, the identity operation, which just leaves the molecule alone. Many molecules have one or more additional operations. The set of operations for a molecule fonn a mathematical group, and the methods of group theory provide a way to classify electronic and vibrational states according to whatever symmetry does exist. That classification leads to selection rules for transitions between those states. A complete discussion of the methods is beyond the scope of this chapter, but we will consider a few illustrative examples. Additional details will also be found in section A 1.4 on molecular symmetry. 

When you consider the selection rules, which are not particularly restrictive (see Section 7.1.6), governing transitions between these states arising from each configuration, it is not surprising that the electronic spectrum of an atom such as zirconium consists of very many lines. (Remember that the Laporte rule of Equation (7.33) forbids transitions between states arising from the same configuration.)... 

For atoms, electronic states may be classified and selection rules specified entirely by use of the quantum numbers L, S and J. In diatomic molecules the quantum numbers A, S and Q are not quite sufficient. We must also use one (for heteronuclear) or two (for homonuclear) symmetry properties of the electronic wave function ij/. ... 

The recombination should be governed by the same selection rules as spectroscopic transitions. Let us consider the recombination of an oxygen ion 2s2 2p3 4S°. When one p electron is added to the 4S ion we expect to obtain one of the states 5P and 3P. However, if the 2s2 2p4 state of the atom is obtained, it can only exist in the states 3P, lD, or lS. Thus the recombination can only give 2s2 2p4 3P. Sometimes the selection rules are not strictly valid. In this case, however, no transitions 2s2 2p3 4S° nx - 2s2 2p4 XD or lS have been observed by the spectros-copists (57) which shows that in this case the selection rules are strictly valid. 

Atomic spectra are much simpler than the corresponding molecular spectra, because there are no vibrational and rotational states. Moreover, spectral transitions in absorption or emission are not possible between all the numerous energy levels of an atom, but only according to selection rules. As a result, emission spectra are rather simple, with up to a few hundred lines. For example, absorption and emission spectra for sodium consist of some 40 peaks for elements with several outer electrons, absorption spectra may be much more complex and consist of hundreds of peaks. 

As a second example of the determination of selection rules from the properties of special functions, consider the hydrogen atom. At any given instant the dipole moment is ft = er, where r describes the position of the electron with respect to the proton and e is the electronic charge. The wavefiinctions for the hydrogen atom are given by... 

The ro-vibronic spectrum of molecules and the electronic transitions in atoms are only part of the whole story of transitions used in astronomy. Whenever there is a separation between energy levels within a particular target atom or molecule there is always a photon energy that corresponds to this energy separation and hence a probability of a transition. Astronomy has an additional advantage in that selection rules never completely forbid a transition, they just make it very unlikely. In the laboratory the transition has to occur during the timescale of the experiment, whereas in space the transition has to have occurred within the last 15 Gyr and as such can be almost forbidden. Astronomers have identified exotic transitions deep within molecules or atoms to assist in their identification and we are going to look at some of the important ones, the first of which is the maser. 

Polymer films were produced by surface catalysis on clean Ni(100) and Ni(lll) single crystals in a standard UHV vacuum system H2.131. The surfaces were atomically clean as determined from low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). Monomer was adsorbed on the nickel surfaces circa 150 K and reaction was induced by raising the temperature. Surface species were characterized by temperature programmed reaction (TPR), reflection infrared spectroscopy, and AES. Molecular orientations were inferred from the surface dipole selection rule of reflection infrared spectroscopy. The selection rule indicates that only molecular vibrations with a dynamic dipole normal to the surface will be infrared active [14.], thus for aromatic molecules the absence of a C=C stretch or a ring vibration mode indicates the ring must be parallel the surface. 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

So it is the number of electrons and not the number of atoms which determines the selection rule. Therefore, the selection rules for hydrogen migration in thermal sigmatropic shifts can be summarized as follows as given in the table ... 

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