Electronic selection mles

The electronic selection mles for linear molecules are as follows. AA = 0, + 1. A5 = 0. Again, these are really... 

The selection mle for vibronie states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection mles. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally S5mimetric. Transitions originating in that vibronie level must go to an excited state vibronie level whose S5mimetry is the same as one of the coordinates, x, y, or z. 

Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. 

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

Here, even and odd refer to the arithmetic sum over all the electrons and this selection mle is called the Laporte mle. An important result of this is that transitions are forbidden between states arising from the same configuration. For example, of the terms given in Equation (7.18) arising from the configuration of the carbon atom,... 

The total electron density contributed by all the electrons in any molecule is a property that can be visualized and it is possible to imagine an experiment in which it could be observed. It is when we try to break down this electron density into a contribution from each electron that problems arise. The methods employing hybrid orbitals or equivalent orbitals are useful in certain circumsfances such as in rationalizing properties of a localized part of fhe molecule. Flowever, fhe promotion of an electron from one orbifal fo anofher, in an electronic transition, or the complete removal of it, in an ionization process, both obey symmetry selection mles. For this reason the orbitals used to describe the difference befween eifher fwo electronic states of the molecule or an electronic state of the molecule and an electronic state of the positive ion must be MOs which belong to symmetry species of the point group to which the molecule belongs. Such orbitals are called symmetry orbitals and are the only type we shall consider here. 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

Indicate which of the following electronic transitions are forbidden in a diatomic molecule, stating which selection mles result in the forbidden character ... 

When M is an atom the total change in angular momentum for the process M + /zv M+ + e must obey the electric dipole selection mle Af = 1 (see Equation 7.21), but the photoelectron can take away any amount of momentum. If, for example, the electron removed is from a d orbital ( = 2) of M it carries away one or three quanta of angular momentum depending on whether Af = — 1 or +1, respectively. The wave function of a free electron can be described, in general, as a mixture of x, p, d,f,... wave functions but, in this case, the ejected electron has just p and/ character. 

Because two-photon selection mles are different from one-photon (electric dipole) selection mles, two-photon transitions may allow access to states which otherwise could not be reached. We shall consider just one example in detail - a two-photon electronic absorption specfrum. 

From the properties of the 6-j symbol in (11), the selection mles for electron transitions in this scheme are obtained [8],... 

Ceulemans paper of 1984 generalizes the work of Griffith [25,26] on particle-hole conjugation for the specific case of d" electrons split by an octahedral symmetry field. He relies on the use of matrices and determinants, in particular Laplace s expansion of the determinant in terms of complementary minors, for the analysis. He bases his selection mle analysis on the properties of a novel particle-hole conjugation operator... 

The mechanism for impact scattering at solids is rather complex as it involves the penetration of the incident electron into the adsorbed molecule the theoretical treatment requires a quantum mechanical formalism. The transfer of energy from the incident electron to a vibrational mode occurs, within a very short time, while the electron is inside the molecule. The dipole-scattering selection mles do not apply to impact scattering. Theoretical considerations have predicted, and experimental studies have confirmed, the following propensity mles for this mechanism" (i) Impact scattering... 

Doubly excited states of He of doublet symmetry have been observed in studies of electron impact on He [23]. In contrast, data on quartet states are sparse. Selection mles on photoexcitation from the P° ground state limit excited state production to those of S, P and symmetry. Recently, the He photodetachment cross section... 

One of the consequences of this selection mle concerns forbidden electronic transitions. They cannot occur unless accompanied by a change in vibrational quantum number for some antis5mimetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally S5mimetric they have no antisymmetric vibrations to make the transitions allowed. 

Electron energy-loss spectroscopy is used for obtaining spectroscopic data as a convenient substitute for optical spectroscopy, and, taking advantage of differences in selection mles, as an adjunct to optical spectroscopy. In addition, electron spectroscopy has many applications to chemical and stmctural analysis of samples in the gas phase, in the solid phase, and at the solid-gas interface. 

As discussed in [22], the spherical symmetry of is destroyed when these ions are situated in solids, so that a multiplet term level can be split up to 2/ + 1 crystal field levels for a non-Kramers ion. Due to the parity selection mle for pure electronic transitions in solids, the 41 (i) 4 (f) transition between states i and f is ED forbidden to first order. Parity describes the inversion behavior of the wavefunction of an electronic orbital, so that s,d... orbitals have even parity whereas p,f... orbitals are odd. The spectral feature representing the pure electronic transition is termed the electronic origin or the zero phonon line. An ED transition requires a change in orbital parity because the transition dipole operator (pe) is odd, and the overall parity for the nonzero integral involving the Einstein coefficient of spontaneous emission, A(ED) ... 

CARS can be resonantly-enhanced electronically when either the pump, Stokes or the CARS frequency Itself coincides with an electronic transition in the probed species. Stokes resonances are weighted by the excited vibrational state involved in the Raman resonance and this enhancement is generally weak even at flame temperatures. More typically one tries to achieve primary resonance with the pump laser. In so doing, Stokes resonances are automatically satisfied. The strength of the resonance scales as the product of the four dipole matrix elements Involved with each field in the wave mixing process. Thus only certain transitions tend to be enhanced leading in most cases to a simplification of the CARS spectrum. In the case of the combustion relevant OH molecule under study in our laboratory, a simple triplet spectrum is predicted since each Raman-resonant, downward Stokes transition must satisfy the appropriate dipole selection mles for strong electronic enhancement as shown in Fig. 10. ... 

In the case of a hydrogen atom, aU of the states are doublets, hi the case of multi-electron atoms, there may be different spin states. For light elements where the spin-orbit coupling is weak, the selection mles are as follows. 

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