Orbitals and the Periodic Table

The orbital concept and the Pauli exclusion principle allow us to understand the periodic table of the elements. An orbital is a one-electron spatial wave function. We have used orbiteils to obteiin approximate wave functions for many-electron atoms, writing the wave function as a Slater determinant of one-electron spin-orbitals. In the crudest approximation, we neglect all interelectronic repulsions and obtain hydrogenlike orbitals. The best possible orbitals are the Heu tree-Fock SCF functions. We build up the periodic table by feeding electrons into these orbitals, each of which can hold a pair of electrons with opposite spin. 

Orbital energies chemge with changing atomic number Z. As Z increases, the orbital energies decrease because of the increased attraction between the nucleus and the electrons. This decrease is most rapid for the inner orbitals, which eu e less well-shielded from the nucleus. 

To help explain the observed electron configurations of the transition elements and their ions, Vanquickenborne and co-workers calculated Hartree-Fock 3d and 4s 

For each of the atoms jH to jgK, Vanquickenbome and co-workers calculated the 3d average orbital energy 83 for the electron configuration in which one electron is removed from the highest-occupied orbital of the ground-state electron configuration and put in the 3d orbital they calculated 4, for these atoms in a similar manner. In agreement with Fig. 11.2, they found 3 84s for atomic numbers Z 6 and 84J 3 for Z = 7 to 19 for neutral atoms. 

Accurate representation of a many-electron atomic orbital (AO) requires a linear combination of several Slater-type orbitals. For rough calculations, it is convenient to have simple approximations for AOs. We might use hydrogenlike orbitals with effective nuclear charges, but Slater suggested an even simpler method to approximate an AO by a single function of the form (11.14) with the orbital exponent f taken as 

A lot of computation is required to perform a Hartree-Fock SCF calculation for a many-electron atom. Hartree did several SCF calculations in the 1930s, when electronic computers were not in existence. Fortunately, Hartree s father, a retired engineer, enjoyed numerical computation as a hobby and helped his son. Nowadays compnters have replaced Hartree s father. 

To help explain the observed electron configurations of the transition elanents and their ions, Vanquickenbome and co-workers calculated Hartree-Fock 3d and As orbital energies for atoms and ions for Z = 1 to Z = 29 [L. G. Vanquickenbome et al., Inorg. Chem., 28, 1805 (1989) /. Chem. Educ., 71,469 (1994)]. 

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In case the general reader might be wondering about the connection between atomic orbitals and the periodic table, let me address this issue briefly. As mentioned above, in the case of the first paper, the modern explanation for the periodic table is based entirely on the orbital model. It is only by ignoring the approximate nature of the model that the explanation for the periodic system might appear to be full and complete. 

Before estabiishing the connection between atomic orbitals and the periodic table, we must first describe two additionai features of atomic structure the Pauli exclusion principle and the aufbau principle. 

ATOMS, ISOTOPES, ELECTRON ORBITALS, AND THE PERIODIC TABLE... 

Atoms, isotopes, electron orbitals, and the periodic table 219... 

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