The He Isoelectronic Series

let us consider the hydride anion, H. This is a highly correlated system since electron correlation is the sole source of the binding of the second electron. A CHF treatment therefore gives a spurious result for a of 91.40 au[27]. Pauling s value, see Table 1, was 68.26 au. A more reliable value is obtained from Eq. (11) and using explicitly correlated wavefunctions (ECW)[28]. Since this method will be frequently used for two-electron systems, we will give the relevant details. 

The wavefunctions used in Ref. [28] were a generalization of those of Thakkar and Smith [29], [30]  

For the He atom there has been an extremely large number of calculations using all kinds of different methods. The most accurate value has, again, been found with the ECW-SOS method used for H and is a = 1.38319 au[33] (with the atomic unit based on a reduced electron mass appropriate for the He nucleus) the experimental value is 1.38320 0.00007 au[34]. Other accurate values are to be found in Refs. [27], [31], and [35]. We recall that Pauling s value, using his theoretically determined screening constant, was 1.343 au. 

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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. 

DPT has been applied to two kinds of explicitly correlated wave functions for the He-isoelectronic series [19, 10], the H2 molecule [10], and the H3-ion [96]. These calculations give some information on the coupling between relativistic and correlation effects. Only the leading relativistic corrections of 0(c ) were considered. For higher orders in 0(c ) problems arise if one wants to account for the correct behavior near ri2 = 0 (see section... 

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. 

Details of the numerical procedure are presented elsewhere A typical value for the integral of the absolute difference between the density 7(t) and the ground-state density coming from the solutions of the noninteracting Schrodinger one-particle equations with the effective potential Us([7(t)],r) is 10 for the He isoelectronic series, and 10 for the Li and Be sequences. 

Table 2.10. Correlation energies —Ec) of the He isoelectronic series LDA [29], PW91-GGA [30], CS [23], [18] and ISl [21] results (all energies obtained by...

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. 

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). 

I remember with great satisfaction my collaboration with J. S. Anderson in the Heidelberg Institute. In 1932 he made the volatile, previously unrecognized as such, dinitrosyldicarbonyliron by the action of pure nitric oxide on a solution of Fe3(CO)12 in iron pentacarbonyl (98). The complex Fe(CO)2(NO)2 was a deep red liquid at room temperature. With this compound the isoelectronic series Ni(CO)4, Co(CO)3NO, Fe(CO)2(NO)2 arose, and in this manner the field of carbonyl nitrosyls was opened up. The next member of this isoelectronic series, Mn(CO)(NO)3, predicted by us in 1932, was discovered recently (99). A study of the chemical behavior of the carbonyl nitrosyls, namely the ready substitution of the CO but not of the NO groups, was essentially established by Anderson (100), with the isolation of the derivatives Fe(NO)2py2, Fe(NO)2(o-phen), Co(NO)(CO)(o-phen), and Co(NO)(CO)(PR3)2, etc. 

The correlation energies for free (unconfined) H, He, Li+ and Be++ were well known at that time, and so Gimarc wanted to analyze, in particular, how the correlation energy changes as a function of the box radius for the confined helium atom isoelectronic series. Gimarc performed a number of variational calculations based on the following wave functions ... 

Indeed, the number of modifications of the Bom equation is hardly countable. Rashin and Honig, as example, used the covalent radii for cations and the crystal radii for anions as the cavity radii, on the basis of electron density distributions in ionic crystals. On the other hand, Stokes put forward that the ion s radius in the gas-phase might be appreciably larger than that in solution (or in a crystal lattice of the salt of the ion). Therefore, the loss in self-energy of the ion in the gas-phase should be the dominant contributor. He could show indeed that the Bom equation works well if the vdW radius of the ion is used, as calculated by a quantum mechanical scaling principle applied to an isoelectronic series centering around the crystal radii of the noble gases. More recent accounts of the subject are avail-able. ... 

In our laboratory a series of laser-microwave studies has been performed on metastable and short-lived excited states of heliumlike Li. Singly ionized lithium, like all members of the two-electron He isoelectronic sequence, belongs to the fundamental systems in atomic physics. Many of its spectroscopic and quantum-mechanical characteristics have been calcu-... 

The line integral method advsmced by van Leeuwen and Baerends [Phys. Rev. A 51, 170, (1995)] is applied to the calculation of correlation energies of the iso-electronic series terms with nuclear charge Z -f 1 from exact densities Peioct.Zi Pexact,z+i and the total energy of the term with nuclear charge Z. Numerical calculations are performed for He(Z = 1,2,3)-, Li(Z = 3,4,5,6,7,8,9)- and Be(Z = 4,5,6) isoelectronic series. 

In Section II, the basic formalism of the line integral method is described. In particular, we discuss the choice of integration path employed in the present work. In Section III, numerical results are presented for a few terms of the He-, Li- and Be-isoelectronic series. Finally, in Section IV we discuss the numerical results and assess their accuracy with respect to the exact values. The latter are obtained in the context of the Local Scaling Transformation (LST) DFT formalism. 

Table 1. "Exact correlation energies and those calculated by the line integral method for the path pexact,z Pexact,z+i for the He, Li and Be isoelectronic series (in Hartrees).

The principle of donor-acceptor interactions in noble gas cations is further exemplified by the theoretical study of Radom and coworkers [95a,c] on the series He C" . Figure 12 shows the optimized geometries for the four cations. The intriguing result of the theoretical studies is the rather short He,C bond length for the triply and quadruply charged species HejC and He4C . The latter molecule, which is isoelectronic with methane CH4, has also been calculated by Schleyer [90d]. and are explosive molecules with... 

Pauling considered a series of alkali metal halides, each member of which contained isoelectronic ions (NaF, KCl, RbBr, Csl). In order to partition the ionic radii, he assumed... 

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