Atoms with Two Valence Electrons

Szadz,L. and Brown,L. (1976), New formulation of the pseudopotential theory for atoms with two valence electrons , J.Chem.Phys. 65, 1393... 

By comparing experimental or accurate theoretical results with others based on approximate models, it is possible to determine which among those models offers the best approximate constants of the motion and quantum numbers to describe particular states. This approach is used to evaluate and compare the extent of validity of independent-particle, Hartree-Fock and collective, molecule-like descriptions of atoms with two valence electrons. The comparisons are made on the basis of overlaps, oscillator strengths, momentum correlation and quadrupole moments. The criterion for each evaluation is the extent of agreement with results obtained from well-converged Sturmian Configuration Interaction wave functions. 

The physical origin of the nonadiabatic correction is perhaps clearest in the earliest treatment of this problem by Van Vleck and Whitelaw/ who specifically addressed the problem of core polarization in atoms with two valence electrons. Here we outline their treatment. 

Using the formalism developed in section 20.4, we can analyze the behavior of the approximations to the valence spinors in the AIMP method. The purpose of this exercise is to determine whether the approximations to the one-electron Hamiltonian and the pseudospinors are likely to cause any undesirable behavior, such as collapse when a core spinor is mixed in. As before, the model we use is the simplest an atom with two valence electrons. We have three separate cases to consider. 

N = 2(8) + 4(2) + 8 = 32 (two carbon atoms with eight valence electrons each, plus four hydrogen atoms with two valence electrons each, plus an oxygen atom with eight valence electrons)... 

The reaction of magnesium, with two valence electrons, and chlorine, with seven valence electrons will produce magnesium chloride. The magnesium must donate one valence electron to each of two chlorine atoms. This leaves a magnesium ion and two chloride ions. All the ions have a complete octet. The ions form the ionic compound magnesium chloride, MgCl2. 

Lastly, one must occupy the MOs with the correct number of electrons. A neutral dicoordinated carbon atom has two valence electrons and a neutral uncoordinated oxygen atom has six, for a total of eight. Place electrons into the MOs two at a time. The HOMO is seen to be the higher nonbonding MO, no, and the LUMO is n 0. 

Carbenes are species which contain a dicoordinated carbon atom formally with two valence electrons. The possible electronic structures of the parent carbene, methylene CH2, are shown in Figure 7.5. The 2p orbital of the dicoordinated C atom is placed above a by about 0.25 fi in order to accommodate the lower electronegativity. 

Let us consider au atom with two s electrons, with different total quantum numbers for example, a beryllium atom with one valence electron in a 2s orbital and the other in a 3s orbital, in addition to the two electrons in the K shell. The orbital angular momenta of the two valence electrons are zero (h = 0, k = 0), and accordingly the resultant angular momentum is zero (L = 0). Each of the two electrons has spin quantum number (si = sz = ), and each spin angular mo-... 

The basic structural feature is boron icosahedra. In the unit cell, there are 50 boron atoms, with 150 valence electrons and 148 boron-boron nearest neighbors (bond positions). These 50 boron atoms form four nearly regular icosahedra plus two interstitial boron atoms in the unit cell. Within each B12 icosahedron, each B atom has five adjacent atoms at the distance 1.797 0.015 A. Each icosahedral B atom has an interstitial B atom lying 1.62 0.02 A from it. Furthermore, each of the interstitial B atoms has four nearest neighbors (icosahedral B atoms). This implies that the icosahedral B atoms have ligancy 6, and the interstitial B atoms have ligancy 4. 

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. 

Consider 1 as the central atom, with eight valence electrons. Two electrons form bonds to other I atoms, leaving three lone pairs, which prefer to occupy all three equatorial positions, leaving the bonding pairs in the axial positions. 

You will recall that the electron configuration for carbon is Is2 2s2 2p2, so each carbon atom, with four valence electrons, can make up to four single bonds. The suffix -ene tells us that there is a double bond between two of the carbon atoms. The carbon atoms involved in the double bond will use up two out of their four bonding electrons with that one double bond, and will only be able to make two additional single bonds. It doesn t matter between which two carbon atoms we show the double bond. 

Consider a diatomic, AB, interacting with a surface, S. The basic idea is to utilize valence bond theory for the atom-surface interactions, AB and BS> along with AB to construct AB,S For each atom of the diatomic, we associate a single electron. Since association of one electron with each body in a three-body system allows only one bond, and since the solid can bind both atoms simultaneously, two valence electrons are associated with the solid. Physically, this reflects the ability of the infinite solid to donate and receive many electrons. The use of two electrons for the solid body and two for the diatomic leads to a four-body LEPS potential (Eyring et al. 1944) that is convenient mathematically, but contains nonphysical bonds between the two electrons in the solid. These are eliminated, based upon the rule that each electron can only interact with an electron on a different body, yielding the modified four-body LEPS form. One may also view this as an empirical parametrized form with a few parameters that have well-controlled effects on the global PES. 

The hyperspherical close-coupling method is well adapted to atoms with two external electrons, but should also be capable of treating heavier systems such as the alkaline earths, in which the singly- and doubly-excited spectra interact strongly. So far, not much progress has been accomplished in extending it to systems in which interactions with the valence- or inner-shell spectra become important. 

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