Radial Behaviour of Atomic Orbitals

The basis functions used in constructing MOs are the AOs based on the hydrogen atom solutions of the Schrddinger equation discussed in Appendix 9, with the proviso that accurate energies will require flexibility in the radial decay constants. Before moving on to molecules more complex than H2, it is worth looking at the shapes of the AOs relevant for the first row of the periodic table. We have already used the shapes of s-, p- and d-functions to discuss the symmetry of particular AOs (e.g. the d-orbitals of the central metal atom in transition metal complexes were covered in Section 5.8). These shapes are based on the 

A 2p orbital has a radial part which is zero at r = 0 and has a maximum near to 1 A, with no radial node. In the angular function, as it must pass through zero to move between 

All three radial functions decay toward zero at large r, with the Is orbital approaching this limit more quickly than the 2s or 2p. This shows that electrons occupying these states would be localized by attraction to the positive atomic core, since the probability of finding an electron in such a state a long way from the nucleus will be vanishingly small. 

The Is function shows a peak at around 0.529 A this is known as the Bohr radius Aq and is the basic unit of distance used in the atomic units system discussed in Appendices 9 and 10. The same value was derived by Bohr as the radius for the orbit of the electron based on a classical physics analysis of the electrostatic interaction between the electron and nucleus in a hydrogen atom. 

This makes it easier to recognize why atoms from the same group of the periodic table, such as these examples, have similar chemical properties. 

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