Atoms with closed shells

In atomic spectroscopy, the energy levels in the atom are called terms or spectral terms. A term is described by a term symbol such as ic 

The letter in the term symbol is the letter code describing the value of L. The left superscript is the multiplicity of the state, 2S + 1, and is called singlet, doublet, triplet, quartet, and so on. The right subscript is the value of J. Sometimes the principal quantum number of the state is written before the term symbol. 

2S 1 = 2(j) +1 = 2. The terms are all doublets. Then J = L S = / + i- When I = 0, the only allowed value of J is J = there is only one state, which is therefore not a true doublet. In all the other cases we have two states with different values of J  

The simplest method for determining the possible terms corresponding to a given electron configuration is to calculate and M. From these values we can infer L and S. 

The values of Ml and Ms are determined by the relations in Eqs. (24.27) and (24.30). The first consequence of these rules is that a closed shell of electrons (a filled subshell) contributes neither orbital angular momentum nor spin angular momentum to an atom. In a closed shell the electrons all have paired spins. Thus, in the configurations s, p, values, and = — occur equally often. For any closed shell, 

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Atoms or ions with completely filled orbitals have J equal to zero, which means that atoms with closed shells have no magnetic moment. The only atoms that display a magnetic moment are those with incompletely filled shells. These are particularly found in the transition metals, with incompletely filled d shells, and the lanthanides and actinides, which have incompletely filled/shells. 

Lines, corresponding to different transitions from initial states with vacancy in the shells with the same n, compose a series of spectra, e.g. K-, L-, M-series etc. Main diagram lines correspond to electric dipole ( 1) transitions between shells with different n. The lines of 2-transitions also belong to diagram lines. Selection rules of 1-radiation as well as the one-particle character of the energy levels of atoms with closed shells and one inner vacancy cause, as a rule, a doublet nature of the spectra, similar to optical spectra of alkaline elements. X-ray spectra are even simpler than optical spectra because their series consist of small numbers of lines, smaller than the number of shells in an atom. The main lines of the X-ray radiation spectrum, corresponding to transitions in inner shells, preserve their character also for the case of an atom with open outer shells, because the outer shells hardly influence the properties of inner shells. 

The system of equations (1.8) is based on the central field approximation, and therefore its application to real atoms is entirely dependent on the existence of closed shells, which restore spherical symmetry in each successive row of the periodic table. For spherically symmetric atoms with closed shells, the Hartree-Fock equations do not involve neglecting noncentral electrostatic interactions and are therefore said to apply exactly. This does not mean that they are expected to yield exact values for the experimental energies, but merely that they will apply better than for atoms which are not centrally symmetric. One should bear in mind that, in any real atom, there are many excited configurations, which mix in even with the ground state and which are not spherically symmetric. Even if one could include all of them in a Hartree-Fock multiconfigura-tional calculation, they would not be exactly represented. Consequently, there is no such thing as an exact solution for any many-electron atom, even under the most favourable assumptions of spherical symmetry. 

Let us analyze some examples where this interaction is present. These examples establish a great affinity between gold atoms, which are as close as possible to each other and. generally, at distances even shorter than the ones found in metallic gold (2.88 A). We excluded gold clusters with formal metal-metal bonds and oxidation states between 0 and +i from the description. We will refer only to the interactions among atoms with closed-shell configurations. 

In closed-shell atoms, the nij dependence of the structure factors vanishes so that much simpler equations are obtained. The expectation value of the total ground-state energy can be written in cases of atoms with closed shells for the electronic state A as (cf. Refs. [126] and [57, p. 152]),... 

ABSTRACT. Predictions are presented of spectra for excitation of the van der Waals rovibrational modes in ArHCl, ArHCN, H2DF, ArOH and NeC2H4. For ArHCN, H2DF and ArOH the potential energy surfaces used in the spectral computations have been obtained from CEPA calculations with large basis sets. Comparisons with experiment illustrate the power and usefulness of ab initio methods in predicting spectra for van der Waals molecules. The results also demonstrate that predictions of spectra can now be made for van der Waals molecules more complicated than the complexes of atoms with closed-shell diatomics. 

Figure 11.5 Covalent bonding, (a) shows two isolated hydrogen atoms coming together to form a covalently bonded (di)hydrogen molecule, (b) shows a simple model of the bonding in a dihydrogen molecule, with the single Is orbital electron from each atom being shared by the molecule, to give each atom a closed shell.

There exist a number of methods to account for correlation [17, 45, 48] and relativistic effects as corrections or in relativistic approximation [18]. There have been numerous attempts to account for leading radiative (quantum-electrodynamical) corrections, as well [49, 50]. However, as a rule, the methods developed are applicable only for light atoms with closed electronic shells plus or minus one electron, therefore, they are not sufficiently general. 

Radicals react with closed-shell (diamagnetic) molecules via two pathways addition to a multiple bond (eq. 4.1) and atom abstraction (eq. 4.2). Thus, a suitable solvent for a radical reaction must not possess either abstractable atoms or reactive multiple bonds. Unfortunately, most of the solvents suitable for free-radical reactions (e.g., benzene, CC14) are damaging to the environment or carcinogenic. 

We need at least enough spatial MO s i// to accommodate all the electrons in the molecule, i.e. we need at least n ij/ s for the 2n electrons (recall that we are dealing with closed-shell molecules). This is ensured because even the smallest basis sets used in ab initio calculations have for each atom at least one basis function corresponding to each orbital conventionally used to describe the chemistry of the atom, and the number of basis functions

initio calculation on CH4, the smallest basis set would specify for C ... 

Ionic crystals are formed between highly electropositive and highly electronegative elements when electron transfer has occurred between the atoms, resulting in oppositely charged ions with closed shell (octet) electronic configurations. Ionic crystals such as potassium chloride... 

The third characteristic surface is found for molecules with closed-shell interactions, which in the present case are represented by molecules approaching the ionic limit the acceptor atom having orbital vacancies equal... 

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