Electronic frequently used notations

Most theoretical studies of the electronic properties of haems and haemoproteins have assumed that the chromophore has >4 symmetry. The consequences of the crystallographic results on earlier theoretical treatments have been discussed (9, 10) and the modifications which have to be made are not too serious. We shall frequently use notation, such as symmetry labels, which are appropriate to D 4 symmetry, although sometimes we shall have to consider the effects of a lower symmetry, such as Ci or C%v. It is important to appreciate that the extent of the displacement of the iron atom out of the haem plane is likely to determine the electronic properties of the group to some extent. Moreover, the exact position of the iron atom is likely to be dependent on the axial ligands. 

To date there is no accepted standard notation for electronic transitions. Without going into detail some of the frequently used notations will be discussed shortly. 

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

The notation used in this book is that normally encountered in the day-to-day work of a radiation chemist—eV, G value, and the like. For the hydrated electron, though, eh is used instead of the frequently employed notation e -, an equivalence the reader is urged to keep in mind. 

Figure 2.2 Demonstration of the two equivalent nomenclatures used for the description of inner-shell levels and X-ray transitions (also Auger transitions, see below). The vertical direction is regarded as the energy axis (but is not to scale here). On the left-hand side is given the notation which is frequently used in inner-shell spectroscopy, on the right-hand side the corresponding single-orbital quantum numbers with n, t and j being, respectively, the principal quantum number, the orbital angular momentum and the total angular momentum which includes the spin of the electron. Also shown are the main X-ray transitions with their spectroscopic notation (for a more complete plot which includes...

The most frequently used ansatz for the representation of molecular one-electron spinors is a basis expansion into Gauss-type spinors (where we have adopted the notation used in Quiney et al. (1998b))... 

The numbers in parentheses on the left-hand side of Eq. (5-1) symbolize the spatial coordinates of each of the n electrons. Thus, 1 stands for xi,> i,zi, or n, 6i, (j>i, etc. We shall use this notation frequently throughout this book. Since we are not here concerned with the quantum-mechanical description of the translational motion of the atom, there is no kinetic energy operator for the nucleus in Eq. (5-1). The index i refers to the electrons, so we see that Eq. (5-1) provides us with the desired kinetic energy operator for each electron, a nuclear electronic attraction term for each electron, and an interelectronic repulsion term for each distinct electron pair. (The summation indices guarantee that l/ri2 and l/r2i will not both appear in H. This prevents counting the same physical interaction twice. The indices also prevent nonphysical self-repulsion terms, such as l/r22, from occurring.) Frequently used alternative notations for the double summation in Eq. (5-1) are j 1/ 7. which counts each interaction twice... 

Clearly, it is inconvenient and tedious to write the structures of the contributing forms to show the structure of a resonance hybrid. A shorthand notation is therefore desirable. Frequently, dashed rather than full lines are used where the bonding electrons are expected to be delocalized over several atoms. For benzene, 16a or 16b is quite appropriate ... 

The braket notation has the electron indices (12 12) while the parenthesis notation has the order (11122). In many cases the integrals are written with only the indices given, i.e. XnXylXiSXs) = cixlPS). Since Coulomb and exchange integrals often are used as their difference, the following double bar notations are also used frequently. 

Fig. 1. Energy levels of trivaient lanthanides below 43000 cm (5.3 eV) arranged according to the number q of 4f electrons. Excited levels known frequently to luminesce are indicated by a black triangle. The excited levels corresponding to hypersensitive transitions from the ground state are marked with a square. For each lanthanide, J is given to the right (in the notation of atomic spectroscopy, ] is added to the Russell-Saunders terms as lower-right subscripts). When the quantum numbers S and L are reasonably well-defined, the terms are indicated to the left. It may be noted that the assignments and F< in thulium(lll) previously were inverted these two levels with 7 = 4 actually have above 60% of H and F character, respectively. Calculated 7-levels are shown as dotted lines. They are taken from Carnall et al. (1968) who also contributed decisively to the identification of numerous observed levels, mainly by using the Judd-Ofelt parametrization of band intensities.

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