Hydrogen atom functions

There are several important points to stress about these hydrogenic atomic functions ... 

The wave functions (6.8) are known as atomic orbitals, for / = 0, 1,2, 3, etc., they are referred to as s, p, d, f, respectively, with the value of n as a prefix, i.e. Is, 2s, 2p, 3s, 3p, 3d, etc., From the explicit forms ofthe wave functions we can calculate both the sizes and shapes of the atomic orbitals, important properties when we come to consider molecule formation and structure. It is instructive to examine the angular parts of the hydrogen atom functions (the spherical harmonics) in a polar plot but noting from (6.9) that these are complex functions, we prefer to describe the angular wave functions by real linear combinations of the complex functions, which are also acceptable solutions of the Schrodinger equation. This procedure may be illustrated by considering the 2p orbitals. From equations (6.8) and (6.9) the complex wave functions are... 

A mixture of sodium dihydrogenphosphate, Na+H2PO and disodium hydrogenphosphate, (Na+)2HP04, will function as a buffer and control the pH to a value of approximately 7.0. In this example, the species with the greater number of available hydrogen atoms functions as the acid,... 

H2Ru6(CO),K, X-ray crystallography shows a distorted octahedral array of Ru atoms, with three terminal CO groups on each 30 the distortion of the octahedron is such as to suggest that the hydrogen atoms function as triple bridges on two opposite triangular faces. 

It was particularly the efforts to understand the spectrum of the hydrogen atom that led to the discovery of quantum mechanics. The wave functions of the hydrogen atom function as model orbitals in other atoms and molecules. 

One possibility as a basis set of functions to be used for/is the hydrogen-atom functions. As seen in the case of a helium atom, this is not a particularly good start. The hydrogen-atom wavefunctions do not account for shielding and other affects of the inter-electronic repulsion. A basis set of functions that take this into account is a much better starting point for the calculation. J. C. Slater created such a basis set of functions known as the Slater-type orbitals (STO). The functions have the following general form. 

The simplest example is that of tire shallow P donor in Si. Four of its five valence electrons participate in tire covalent bonding to its four Si nearest neighbours at tire substitutional site. The energy of tire fiftli electron which, at 0 K, is in an energy level just below tire minimum of tire CB, is approximated by rrt /2wCplus tire screened Coulomb attraction to tire ion, e /sr, where is tire dielectric constant or the frequency-dependent dielectric function. The Sclirodinger equation for tliis electron reduces to tliat of tlie hydrogen atom, but m replaces tlie electronic mass and screens the Coulomb attraction. 

Figure 8-6. Comparison of the radial distribution function of the ctiair, boat, and twist conformations of cyclohexane (hydrogen atoms are not considered).

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