Isoelectronic series

Sample Problem 7.8 shows how to identify members of an isoelectronic series and how to arrange them according to radins. 

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.  

Strategy fsoelectronic series are species with identical electron configurations but different nuclear charges. Determine the number of electrrxis in each species. The radii of isoelectrrxiic series members decreases with increasing nuclear charge. 

Solution The isoelectronic series includes K . Ar, P . S , and Cl. In order of increasing radius  

Practice Problem A Arrange the following isoelectronic series in order of increasing radius Se, Br . Kr. and Rb.  

Practice Problem B List all the common ions that are isoelectronic with Ne. 

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Comparative reactions of nitrogen compounds with the isoelectronic series, mercury(II), thal-lium(III) and lead(IV) acetates. Principles of oxidation reactions. R. N. Butler, Chem. Rev., 1984, 84, 249-276 (307). 

This approximation was denoted initially by the acronym IQG [34] and later on by IP (Independent Pairs) [35]. It gave satisfactory results in the study of the Beryllium atom and of its isoelectronic series as well as in the BeH system. The drawback of this approximation is that when the eigen-vectors are diffuse, i.e. there is more than one dominant two electron configuration per eigen-vector, the determination of the corresponding nj is ambiguous. In order to avoid this problem the MPS approximation, which does not have this drawback, was proposed. 

Wesendrup, R., Laerdahl, J.K and Schwerdtfeger, P. (1999) Relativistic Effects in Gold Chemistry. VI. Coupled Cluster Calculations for the Isoelectronic Series AuPt , Au2 and AuHg. Joumul of Chemical Physics, 110, 9457-9462. 

For the isoelectronic series S2, Cl, Ar, K+, and Sc3+, which species requires the least energy to remove an outer electron ... 

Such a peculiarity has also been observed in many other compounds with metal-carbon bonds, especially cobalt-carbon. As part of a study (using the above-mentioned extended CNDO method) of the AM(CO)3 isoelectronic series (AM from 772-C2H4Ni to rj6-C6H6Cr) it was shown that, in the t 3-C3HsCo derivative, the allyl group was linked to cobalt by means of the two C(H2) carbons and not predominantly by the C(H) carbon atom, despite the fact that Co—C(H2) = 2.10 A as compared with Co—C(H) = 1.98 A (55). 

In the isoelectronic series (butadiene)M( j8 — CgHg) (M = Ti, Zr, Hf), the Hf complex exhibits an NMR spectrum at > 30 °C consistent with an envelope flip (AG = 17.6 kcalmol-1). The same process can be detected for the Zr complex at > 40 °C only via magnetization transfer experiments (AG > 20 kcalmol-1). The Ti complex exhibits a static structure by NMR spectroscopy16. 

If an a-particle (4He nucleus) adds a d-quark, the energy difference should be almost 4 times the case of a proton. The first electron is bound (5/3)2 rydberg or 38 eV. The binding of the second electron can be extrapolated from the parabolic variation (20) in the isoelectronic series He, Li+, Be+2,... to be 13 eV, comparable with oxygen and chlorine atoms. Hence, the species He(d)-1/3 is not particularly reactive, though its proton adduct He(d)H+2/3 should be far less acidic than HeH+ (which is already stable toward dissociation in the gaseous state, but too strong a Br nsted acid to persist in any known solvent). 

The present contribution investigates compact wavefunctions for the He isoelectronic series from a more pragmatic viewpoint, with the goal of finding functional forms that are easy both to use and to understand. 

As indicated in Section 3.2, we settled on an optimized four-configuration wavefunction using the basis described in equation (2) as a standard highly compact function for extensive study. These wavefunctions, for the members of the He isoelectronic series from Z— (H" values given in Table 5. 

Calculations on the isoelectronic series Me(Ph)B , Me(Ph)C , and [Me(Ph)N ]+ show that the singlet-state geometries are different, reflecting differences in the orbital interactions between the hypovalent atom and the 7r-system. The high calculated barrier (21.5 kcal moP ) for [1,2]-H shift in the nitrenium ion is the result of migration using the orbital which is conjugated with the tt-system. 

Free-ion polarizabilities, arranged in isoelectronic series, are listed in table 1.7. A semilogarithmic plot of the listed values (figure 1.6) reveals a functional dependence on atomic number. This dependence, quite marked, allows us to estimate the free-ion polarizability for ions for which there are no precise experimental data (values in parentheses in table 1.7 estimates according to Viellard, 1982). 

Figure 1,6 Free-ion polarizability as a function of atomic number. Curves are drawn for isoelectronic series. Reprinted from Viellard (1982), Sciences Geologiques, Memoir n°69, Universite Louis Pasteur, with kind permission of the Director of Publication.

Table 1.7 Free-Ion polarizability (o ) arranged in isoelectronic series. Data in A. N = number of electrons (adapted from Viellard, 1982).

Figure 1.10 shows the relationship between bond strength and degree of covalence in cation-oxygen bonds for cations with 18, 36, and 54 electrons (note that in table 1.9 the parameters of equation 1.48 are identical for the three isoelectronic series). By combining equation 1.48 with a modified form of Donnay s (1969) equation ... 

Table 2 Correlation energies of the neon isoelectronic series Comparison ofE 2 tth the...

Table 2 Correlation energies of the neon isoelectronic series Comparison ofE 2 1- (4-6), with the corresponding second order Moller-Plesset (MP2) [30], RLDA [16] andPW91-GGA [8] results. In addition, AHF 1- is compared With the difference IaE, Eq. (4.9), between RHF [60] and x-only ROPM [16]...

It should be noted that in the case of the helium isoelectronic series (singlet GS of a two-electron system), because only one orbital is sufficient to construct the determinantal wave function and to obtain the density as n(r) — 2[t)r(r)], the minimization over n in Eq. (64) is equivalent to the minimization over ip in Eq. (28). Therefore the HF-KS and HF equations and their eigenfunctions are the same, ipir) = and consequently AT n =... 

A set of calculations on the beryllium atom and its isoelectronic series have been carried out [48]. The starting basis set used was dementi s double-zeta [82]. This basis was then transformed into the Hartree-Fock one, and the initial RDMs corresponded to Slater determinants built with this basis. Note that in... 

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