Overlap selection rule

Figure 1.11. Schematic representation of the absorption spectrum of an organic molecule with some allowed transitions and some that are forbidden by spin, symmetry, or overlap selection rules (from left to right). The log e and/values of the ordinate are only meant to provide rough orientation. In particular, according to Equation (1.27), there is no simple relation between log e and/(by permission from Turro, 1978).

Overlap charge density. 26. 33 Overlap density. 14. 79. 125. 150. 209. 485 Overlap integral. 237. 362 Overlap selection rule, 32-33 Oxabicyclobuianc, 433 Oxacarbene, 386... 

In these terms, the electronic integrals such as (Mge)° and (Mge) a are constrained by the symmetry of the electronic states. While term I involves Frank-Condon overlap integrals, terms II and HI involve integrals of the form i Qa v) in the harmonic approximation, the integrals of this type obey the selection rule v = i + 1. Keeping these considerations in mind, we will next discuss how terms I, II and in contribute to distinct vibrational transitions. 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

The second factor is at the origin of the so called monopole selection rule. Symmetry requirements impose that the two W s must correspond to the same irreducible representation in order for the overlap integral not to vanish. 

With the selection rules AJ=0,1,2 an alternation of the recurrences is expected as the signal due to AJ=2 transitions overlaps with the AJ=1 recurrences. Neglecting the shape of the transient, which is comparable for neighbouring peaks the intensity alternation would be 1 2. In addition the spin statistics give rise to weak subrecurrences which will be treated in a later publication. 

The selection rules state that the total angular momentum quantum number may change by 1 or 0. Thus an element with several isotopes each with its own nuclear spin will present a line spectrum with a very complex and, under most experimental conditions, unresolved hyperfine structure. Nevertheless, as we shall see later, the overlap between the hyperfine components of a spectrum line is sufficiently incomplete to permit preferential excitation of one isotope in a mixture of isotopes by radiation from a lamp containing that same isotope. 

Laporte and spin-multiplicity selection rules ( 3.7) and have intensities 103 to 104 times higher than those of crystal field transitions (table 3.6), their absorption edges may extend well into the visible region and overlap crystal field spin-allowed and spin-forbidden peaks. 

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