The Ne Isoelectronic Series

There have been many calculations of a for neon itself at various levels of approximation. Some of these are summarized in Ref. [26] and a basis set analysis has been made in Ref. [25]. Of the electron-correlated results[42]-[47], there appears to be a consensus that the best value using coupled-cluster-single-doubles wavefunctions with a perturbational estimate of connected triplet excitations, CCSD(T), is 2.680-2.690 au[25],[44],[46],[47]. 

For the rest of the isoelectronic series, we will first look at F, since it has been very well studied[48]-[52]. The reason for this interest is the large amount of electron correlation present. In fact, the a value practically doubles upon its introduction. The HF value is 10.67 au[25] (or 10.62 au[48]) and the CCSD value was estimated by Kucharski etal.[51] to be from 18 to 20 au recently Woon and Dunning placed the CCSD(T) value at 17.15 au. Pauling s value of 7.05 is of similar size to the HF value but necessarily far from the correlated value. 

For the rest of the isoelectronic series there are far fewer results the CHF ones of McEachran et a/.[41], and the uncoupled HF ones of Yoshime and Hurst[53]. The former are the more reliable. There appear to be no electron-correlated values. From Ref. [41], for example, a(Na+) = 0.9454, a(Mg2+) = 0.4701, a(Al3+) = 0.2652 au. The corresponding Pauling values (see Table 1) are 1.216, 0.637 and 0.362 au. Density functional methods within the local density approximation have been applied to Na+ and Mg2+, they give a(Na+) = 1.07, a(Mg2+) = 0.51 au (see values quoted in Ref. [54]) - this is the closest we have so far come to accounting for correlation. 

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Fig. 5.5. Percentage deviation of the LDA for f[ ] from MBPT2 results [108] for the Ne isoelectronic series. For Ej the absolute value of the error has been plotted (note the take out scale)...

The inappropriate scaling of the RLDA with Z, and thus also with j6, becomes particularly obvious for fixed electron number. In Fig. 5.5 the percentage deviations of the RLDA for and Ej are shown for the Ne isoelectronic series. The error for the correlation energy in the RLDA shows little tendency to approach zero with increasing Z, indicating that the relativistic correction factor plotted in Fig. 4.4 is inadequate for electronic structure calculations. 

We will divide the survey into three parts (3.1) static dipole polarizabilities, (3.2) static dipole hyperpolarizabilities, and (3.3) dynamic dipole polarizabilities and hyperpolarizabilities. Within each part there will be sub-sections dealing with the three isoelectronic series He, Ne, and Ar. For (3.2) and (3.3) the hydrogen atom will also be included. 

Starting with the He isoelectronic series, we give the new pair functions needed as electrons are added one at a time until we reach Ne. As each electron is added not only do new ,., s appear, but the old ones are modified. 

Table 4.6 The sizes of a series of isoelectronic ions, with the [Ne] inert gas core...

Table 2 Roots of the ground state 7 -block of the interelectron repulsion matrix Tv, v for the N-like, O-like, F-like, and Ne-like isoelectronic series...

This effect increases as more 2p electrons are added (see C, N,. . Ne below). For the isoelectronic series 34 may... 

Notice the positions and atomic numbers of these elements in the periodic table. The nonmetal anions precede the noble gas Ne in the table. The metal cations follow Ne. Oxygen, the largest ion in this isoelectronic series, has the lowest atomic number, 8. Aluminum, the smallest of these ions, has the highest atomic number, 13. 

Systems are said to be isoelectronic (Greek isos, equal) if they have the same number of nuclei and the same munber of electrons. Thus, Na and F are isoelectronic with Ne, and the following constitutes an isoelectronic series ... 

Identify the isoelectronic series in the following group of species, and arrange them in order of increasing radius K Ne, Ar, Kr, F , and Cl. ... 

Molecules Isoelectronic with Neon.—Another set of molecules whose structure is typical of many standard chemical environments is the set of ten-electron first row hydrides Ne, HF, H20, NH3, and CH4. On p. 281 we saw how the outer electrons of the neon atom could be described either as being in the configuration (2s)2(2p)6 or, alternatively, as occupying four tetrahedral orbitals %2, %s, and y4 orientated relative to one another in a tetrahedral manner, the orientation of the tetrahedron in space being arbitrary. The electronic structures of the other molecules of the series can now be discussed in terms of this basic system if we imagine unit positive charges to be removed successively from the nucleus. 

The relative effect of increasing charge is also shown in the Fe, Fe and Fe series of Table 4.4. The relative effect of increasing atomic number, Z, is shown in the series of isoelectronic ions, i.e. with the same inert gas core of [Ne] (Table 4.6). 

The radius decreases rapidly with increase of positive charge for a series of isoelectronic ions such as Na, Mg ", Al +, aU of which have the electronic configuration [Ne]. Note that the real... 

Consider the following series of substances methane (CH4), ammonia (NH3), water (H2O), hydrofluoric acid (HF), and neon (Ne). These substances are all isoelectronic, i.e. they all have 10 electrons (hence also 10 protons — since the molecules themselves are electro-neutral). 

The size of an isolated ion cannot be specified readily, because its outer electron shell extends indefinitely around the inner ones and the nucleus. In a series of isoelectronic monatomic species, the sizes diminish, for example, 0 > F > Ne > Na > Mg, because of the increasing positive nuclear charge that puUs in the electrons. Nevertheless, radii for isolated monatomic ions, rf = r (r", ig) have been specified with the quantum-mechanical scaling principle relative to those of the noble gases (of known collision diameters), for example, Ne in the above series. 

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