In this section we examine how the results of the various approximation methods considered in this chapter can be used to understand and predict the physical properties of multi-electron atoms. Our results include total electronic energies, orbital energies and single-electron wavefunctions that describe the spatial distribution of electron density. Physical properties that can be used to describe multi-electron atoms include total energies, atomic sizes and electron density distributions, ionization energies and electron affinities. Trends in these properties as Z increases form the basis of the periodic table and, as we see in Chapter 10, control chemical reactivity. Spectroscopic properties are considered in a link that includes a development of term symbols for multi-electron systems.
- 9.9.9A: Total Electronic Energies
- Using the results of variation calculations, perturbation theory, Hartree-Fock calculations, and/or configuration interaction, we can solve for the total energies of atoms with excellent accuracy.
- 9.9.9B: Orbital Energies
- Orbital energies are not physical properties. They are constructs that arise from our approximate approach to a true multi-electron wavefunction using products of single-electron wavefunctions called atomic orbitals. Nevertheless, a great deal can be learned by considering orbital energies.
- 9.9.9C: Atomic Sizes and Electron Density Distributions
- Knowledge of the relative sizes of atoms is important because their chemistry often correlates with size. For example, substituting one element for another in a crystal to modify the properties of the crystal often works if the two elements have essentially the same atomic size. Understanding electron density distributions is also important in understanding chemical properties.
- 9.9.9D: Ionization Potentials
- The energy it takes to remove an electron from an atom to infinity is called the ionization potential or the ionization energy.
- 9.9.9E: Electron Affinity
- The inverse of ionization, i.e. bringing an electron from infinity to occupy the lowest-energy vacancy in an atomic orbital, produces an energy change called the electron affinity.
Contributors and Attributions
David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski ("Quantum States of Atoms and Molecules")