Shell notation

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

A more detailed representation of the electron configuration of sodium is Na Is2 2s2 2p6 3s1 (subshell notation) instead of simply Na 2, 8, 1 (shell notation). 

Information box key. E represents the element s letter notation (for example, H = hydrogen), with the Z subscript indicating proton number. Orbital shell notations appear in the column on the left. For elements that are not naturally abundant, the mass number of the longest-lived isotope is given in brackets.The abundances (atomic %) are based on meteorite and solar wind data. The melting point (M.P.), boiling point (B.P.), and critical point (C.P.) temperatures are expressed in Celsius. Sublimation and critical temperatures are indicated by s and t. 

X-ray energy is far more energetic than that in the ultraviolet range. If an X-ray photon has an energy that exceeds the ionization energy of an electron, absorption of that photon can eject the electron outright. Furthermore, the ejected electrons are from core levels—those closest to the nucleus. In terms of quantum numbers, these levels correspond to n = 1,2, and 3, which are usually referred to with the older shell notation K, L, and M. When an inner-shell electron is ejected, an outer-shell electron "falls" to fill the vacancy and release X-ray photons (fluorescence) in the process as shown in Figure 5.44. 

Another family of basis sets, commonly referred to as the Pople basis sets, are indicated by the notation 6—31G. This notation means that each core orbital is described by a single contraction of six GTO primitives and each valence shell orbital is described by two contractions, one with three primitives and the other with one primitive. These basis sets are very popular, particularly for organic molecules. Other Pople basis sets in this set are 3—21G, 4—31G, 4—22G, 6-21G, 6-31IG, and 7-41G. 

Multiplying from the left by a specific basis function and integrating yields the Roothaan-Hall equations (for a closed shell system). These are the Fock equations in the atomic orbital basis, and all the M equations may be collected in a matrix notation. 

Give the notation for the valence-shell configuration (including the outermost (/-electrons) of (a) the alkali metals ... 

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 covalent bonding in organic compounds can be described by means of the electron dot notation (Chap. 5). The carbon atoms has four electrons in its outermost shell ... 

To represent the formation of bonds between atoms, it is convenient to use a system known as electron dot notation. In this notation, the symbol for an element is used to represent the nucleus of an atom of the element plus all of the electrons except those in the outermost (valence) shell. The... 

Using electron dot notation, the production of sodium fluoride, magnesium fluoride, and magnesium oxide may be pictured as follows A sodium atom and a fluorine atom react in a 1 1 ratio, since sodium has one electron to lose from its outermost shell and fluorine requires one more electron to complete its outermost shell. 

For simplicity of notation, we will here discuss the circumstance that the distinguished molecule is present at the lowest concentration. The occupants of the inner shell will be of one type only, solvent of type denoted by w w = H20 for example. Then our discussion can be more economical, though the ideas do have broader relevance. For a distinguished molecule of type a, we will encode the definition of the inner shell by an indicator function ba (k) which is one when the /cth solvent molecule occupies the defined inner shell, and zero otherwise. Then the PDT formula can be recast as... 

Here the notation [GC y indicates that the system to be treated is only the inner-shell volume, and the material enclosed is described by an ensemble of fluctuating composition - as with the grand canonical ensemble - under the influence of the molecular-field p. With longer-ranged interactions, a correction for those... 

In the case of a closed shell molecule, using Dirac notation the expression becomes... 

The label STO-3G (equivalent to 3-3G in the notation described above) denotes a minimal basis 3G set for both core and valence shells (nc = 3, nv = 3). 

The notation of Auger transitions uses the X-ray level nomenclature of Table 3.1. For example, KL L2 stands for a transition in which the initial core hole in the K-shell is filled from the L -shell, while the Auger electron is emitted from the L2-shell. Valence levels are indicated by V as in the carbon KVV transition. 

Table Al.l Electronic configuration of the elements. Elements in square brackets (e.g., [He]) imply that the electronic configurations of the inner orbitals are identical to those of the element in brackets. Thus silver (Ag, atomic number 47) has a configuration of [Kr]4(7105 1, which if written out in full would be s22s22p62s22p62d1QAs1Ap6Adw5>s1, giving 47 electrons in all. For the heavier elements (atomic number above 55), the alternative notation K, L, M is used to denote the inner shells corresponding to orbitals 1, 2 and 3 respectively. This notation is common in X-ray spectroscopy (see p. 33). (Adapted from Lide, 1990.)...

The term angular overlap model was first used in 1965 to describe a more general treatment, which may also be called the model (12,13). The relative energies of the orbitals in a partly-filled /-shell are expressed in terms of the parameters ex (X = a, rr, etc.), whose coefficients can be calculated from the geometry of the system. The eK model was developed from perturbation theory, but is equivalent to the E2 model when only a-overlap is considered, and to the Yamatera-McClure model for orthoaxial chromophores with linear ligators. The notation ex is often used, where ... 

Due to the presence of the several electron shells, a series of different X-lay lines are produced in cascades following inner shell ionizations. Notation of the lines corresponds to historical reasons (a is the strongest, P is the next strongest, etc.) and (in case of some minor lines) it is not always logical. The... 

The table shows the electronic configuration in spectroscopic and orbital box notation for the elements from scandium to zinc. [Ar] represents the electronic configuration of argon, which is Is 2s 2p 3s 3p . It is okay to use this shorthand here instead of writing out the full electron shells up to 3p. However, in the exam you should write out the spectroscopic notation for each element in full. 

For all results in this paper, spin-orbit coupling corrections have been added to open-shell calculations from a compendium given elsewhere I0) we note that this consistent treatment sometimes differs from the original methods employed by other workers, e.g., standard G3 calculations include spin-orbit contributions only for atoms. In the SAC and MCCM calculations presented here, core correlation energy and relativistic effects are not explicitly included but are implicit in the parameters (i.e., we use parameters called versions 2s and 3s in the notation of previous papers 11,16,18)). 

Figure P13 depicts the notation, number of electrons, and binding energy, which is the amount of energy required to remove (ionize) an electron from the inner shell...

We continue this chapter with a presentation of the basic concepts and notations relevant to D-functional theory (Section 111). We then review the fundaments of the NOF theory (Section IV) and derive the corresponding Euler equations (Section V). The Gilbert [15] and Pernal [81] formulations, as well as the relation of Euler equations with the EKT, are considered here. The following sections are devoted to presenting our NOF theory. The cumulant of the 2-RDM is discussed in detail in Section VI. The spin-restricted formulations for closed and open-shells are analyzed in Sections Vll and VIII, respectively. Section IX is dedicated to our further simplification in order to achieve a practical functional. In Section X, we briefly describe the implementation the NOF theory for numerical calculations. We end with some results for selected molecules (Section XI). 

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