HF electronic configuration

Here two electrons have been promoted, from the spin orbitals i//20 and i//2/j to ij/yy. and 1D,- and Dj represent promotion into virtual orbitals of one and two electrons, respectively, starting with the HF electronic configuration (Fig. 5.22). 

The closed shell HF electronic configuration for the ground state is obtained by occupying the bonding cr orbital with two electrons ... 

Here the a, are the LCAO coefficients, which have to be determined. The formulation of HF theory where we use the LCAO approximation is usually attributed to Roothaan (1951a). His formulation applies only to electronic configurations of the type 1/ 3,...,. Following the discussion of Chapter 5, the charge... 

This idea is readily extended to simple molecules of compounds formed by nonmetal atoms. An example is the HF molecule. You will recall that a fluorine atom has the electron configuration ls22s22p5. ft has seven electrons in its outermost principal energy level (n = 2). These are referred to as valence electrons, in contrast to the core electrons filling the principal level, n = 1. If the valence electrons are shown as dots around the symbol of the element, the fluorine atom can be represented as... 

As you can see, the fluorine atom owns six valence electrons outright and shares two others. Putting it another way, the F atom is surrounded by eight valence electrons its electron configuration has become ls22s22p6, which is that of the noble gas neon. This, according to Lewis, explains why the HF molecule is stable in contrast to species such as H2F, H3F,... none of which exist. 

The potential surfaces Eg, Hn, and H22 of the HF molecule are described in Fig. 1.6. These potential surfaces provide an instructive example for further considerations of our semiempirical strategy (Ref. 5). That is, we would like to exploit the fact that Hn and H22 represent the energies of electronic configurations that have clear physical meanings (which can be easily described by empirical functions), to obtain an analytical expression for the off-diagonal matrix element H12. To accomplish this task we represent Hn, H22, and Eg by the analytical functions... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Hamiltonian in the CSF basis. This contrasts to standard HF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond structures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

Multiplet structures are ignored completely and electronic configurations are defined only in terms of the occupation numbers of the various orbitals. Accordingly, the radial HFS wave equations for a free atom or ion are written in the form... 

Symbol Hf atomic number 72 atomic weight 178.49 a Group IV B (Group 4) transition metal element atomic radius 1.442A electron configuration [Xe]4/i45d26s2 common valence +4, also exhibits oxidation states +2 and -i-3 most abundant natural isotope Hf-180 isotopes and their natural abundances Hf-176 (5.21%), Hf-177 (18.56%), Hf-178 (27.10%), Hf-179 (13.75%), Hf-180 (35.22%), artificial isotopes 157, 158, 168, 173, 175, 181-183. 

In order to get good agreement between CASSCF and experimental results, it is often necessary to include correlation between the active electrons and the other valence electrons.This type of correlation, which is called dynamic correlation, can be added to a CASSCF wave function by using the equivalent of MP2 perturbation theory. However, in an MP2 calculation on an MC wave function, rather than including double excitations from a single HF reference configuration, excitations from all of the configurations must be included. 

Due to its 5t/-6.v- electron configuration, hafnium forms tctravalent compounds readily, although the Ilf1 ion docs not exist as such In aqueous solution except at very low pH values, Ihe common cation being HfO lor Hf OH)i ) and many of the tctravalent compounds are partly covalent. There are also less stable Hf(lll) compounds, There is close similarity in chemical properties to those of zirconium due to the similar outer electron configuration (4identical ionic radii (ZrJ is 0.80 A) the relatively low value for Hf being due lo the Lanthanide contraction. 

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