Alkaline earth atoms valence electron states

In this chapter we have implicitly assumed the Rydberg atom to be a one electron-atom. In the perturbed Rydberg series of, for example, alkaline earth atoms, Rydberg states can have mixed valence-Rydberg character. In such states the black body effects are reduced by a factor equal to the fractional Rydberg character.14... 

The alkaline earth atoms—Be, Mg, Ca, Sr, and Ba—are the natural species to consider first. The important question here is whether the states of the two valence electrons are better described by collective, rotation-vibration quantization or by independent-particle quantization. Difficulties with the latter have been discussed.6,86,25 The new issue is whether moleculelike quantization is much more nearly free of its own problems. 

Figure 3. Conditional probability distributions for the valence electrons of the alkaline earth atoms in their ground states, for various values of the distance between the nucleus and one valence electron. The results are taken from calculations of Ref. 27.

In the preceding discussion of alkaline earth atom reactions, attention has been drawn to analogies with the corresponding alkali atom reactions, particularly in Section III.A. However, a still more revealing comparison might be anticipated with alkali dimer reactions, since both alkaline earth atoms A and alkali dimers M2 have two valence electrons in a totally symmetric orbital giving a singlet state of low ionization potential. 

The question addressed in this paper is, in its most general terms To what extent is it appropriate to describe a few-body system in terms of one quantization scheme or another Slightly more precisely, we ask Which simple model, among the choices we can invent, is the best starting approximation for any designated state of a given system As our vehicle to study this problem, we use the system of the two valence electrons in the helium and alkaline earth atoms. The models we consider and compare are the Hartree-Fock, independent-particle model and the collective model like that for a linear triatomic molecule. 

In the sodium atom pairs of 3/2 states result from the promotion of the 3s valence electron to any np orbital with n > 2. It is convenient to label the states with this value of n, as n P 1/2 and n f 3/2, the n label being helpful for states that arise when only one electron is promoted and the unpromoted electrons are either in filled orbitals or in an x orbital. The n label can be used, therefore, for hydrogen, the alkali metals, helium and the alkaline earths. In other atoms it is usual to precede the state symbols by the configuration of the electrons in unfilled orbitals, as in the 2p3p state of carbon. 

Symbol Ba atomic number 56 atomic weight 137.327 a Group llA (Group 2) alkaline earth element electronic configuration [Xejs valence state +2 ionic radius of Ba2+ in crystal (corresponding to coordination number 8) 1.42 A first ionization potential lO.OOeV stable isotopes and their percent abundances Ba-138 (71.70), Ba-137 (11.23), Ba-136 (7.85), Ba-135 (6.59), Ba-134 (2.42) minor isotopes Ba-130 (0.106) and Ba-132 (0.101) also twenty-two radioisotopes are known. 

Symbol Ca atomic number 20 atomic weight 40.078 a Group IIA (Group 2) alkaline-earth metaUic element ionic radius 1.06 A (Ca2+) electron configuration [Ar]4s2 valence state +2 standard electrode potential, E° = -2.87V stable isotopes and their abundance Ca-40 (97.00%), Ca-44 (2.06%) Ca-42 (0.64%), Ca-48 (0.18%), Ca-43 (0.145%), and Ca-46 (0.003%) also the element has six unstable isotopes of which Ca-41 has the longest half-life, l.lxlO yr (decay mode electron capture), and Ca-38 has shortest half life 0.66 sec (P-decay). 

The surface of states of equal energy in the reciprocal (i /X) space is only approximately spherical (see above). Before a zone is completely filled up to the corners, electrons with the same energy will already find a place in the next higher zone (Fig. 28 B). With the alkaline earth metals Ga, Sr (face-centred) and Ba (body-centred) the first zone can contain 2 electrons per atom so that the two valence electrons would just fill this zone. These metals, as a consequence of the overlap, are nevertheless conductors, in contrast to the above-mentioned linear molecule,... 

Alkaline earth metal atoms have fairly low ionization potentials, as have alkali metal atoms (e.g., 5.21 and 5.14 eV for barium and sodium, respectively [89]). Hence the reactions of alkaline earth metal atoms with oxidizing molecules are also expected to be initiated by an electron transfer and should follow the harpoon mechanism. However, alkali metal atoms are monovalent species, whereas alkaline earth metal atoms have two valence electrons. Hence peculiarities are to be expected in the alkaline earth metal reaction dynamics, especially when doubly charged products such as BaO are to be formed [90]. The second valence electron also opens up the possibility of chemiluminescent reactions, which are largely absent in alkali metal atom reactions [91, 92]. The second electron causes the existence of low-lying excited states in the product. 

Since alkaline earth metal atoms have two valence electrons, it is convenient to distinguish between reaction products, which have a single ionic bond such as BaCl (Ba+Cr) from products having a double ionic bond in the ground state such as BaO (BaO has the structure Ba +O in the ground state and Ba+O in the lowest excited states). 

To summarize this section one should say that an effective Hamiltonian treatment of the core electron effect faces a contradiction between the necessity to use extended valence basis sets for the extraction and the risk of appearance of core excited intruder states. One should also recognize that this approach leads to p-electron operators for atoms involving p valence electrons and seems much more difficult to handle than the monoelectronic core pseudopotentials extracted by simulation techniques and discussed in Section IV of the present contribution. As a counterpart one should mention that this core effective Hamiltonian would be much superior, since it would include for instance the core-valence correlation effects which play such an important role in alkali- or alkaline-earth-containing molecules. 

Metals. In simple metals such as the alkali and alkaline earth metals as well as A1 the valence electrons occupy only s and p levels. The rather extended shape of the atomic wave functions leads to a strong overlap and delocalization in the condensed phase. As a result, one obtains almost free-electron-like behavior for the electrons near the Fermi level and high electrical conductivity. Similarly, in the case of Cu and Ag, the electronic states at the Fermi level are derived from very delocalized s and p states, which explains the excellent electrical conductivity of these metals. Since the actual electrical conductivity of a material is strongly influenced by the scattering of the conduction electrons by impurities, lattice defects, and the thermal motion of the atomic nuclei, the quantitative prediction of electrical conductivity is difficult. 

The alkaline earth metals always exist in the +2 oxidation state in their compounds. Recall that atoms of the group 2 metals have an ns valence configuration and it is the ns electrons that are lost by these atoms when they combine with nonmetals to form compounds. The alkaline earth metals form primarily ionic compounds, but covalent bonding is evident in magnesium compounds and especially in beryllium compounds. 

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