General Principles of Electron Configurations

There are 78 known elements beyond the 36 we have considered. Let s survey the ground-state electron configurations to highlight some key ideas. 

Categories of Electrons The elements have three categories of electrons  

Inner (core) electrons are those seen in the previous noble gas and any completed transition series. They fill all the lower energy levels of an atom. 

Outer electrons are those in the highest energy level (highest n value). They spend most of their time farthest from the nucleus. 

Valence electrons are those involved in forming compounds. Among the main-group elements, the valence electrons are the outer electrons. Among the transition elements, the (n — 1 )d electrons are counted among the valence electrons because some or all of them are often involved in bonding. 

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General Principles of Electron Configurations Unusual Configurations Transition and Inner Transition Elements... 

A similar expansion can be made in practical finite-basis calculations, except that limitations of the basis set preclude the possibility that the exact wavefunction lies in the space spanned by the available ( ). However, it should be clear that the formation of linear combinations of the finite number of offers a way to better approximate the exact solution. In fact, it is possible to obtain by this means a wavefunction that exactly satisfies the electronic Schrodinger equation when the assumption is made that the solution must lie in the space spanned by the -electron basis functions ( ). However, even this is usually impossible, and only a select number of the are used. The general principle of writing -electron wavefunctions as linear combinations of Slater determinants is known as configuration interaction, and the resultant improvement in the wavefunction is said to account for electron correlation. The origin of this term is easily understood. Returning to helium, an inspection of the Hartree-Fock wavefunction... 

Conventional presentaticsis of DFT start with pure states but sooner w later encounter mixed states and d sities (ensemble densities is the usual formulation in the DFT literature) as well. These arise, for example in formation or breaking of chemical bonds and in treatments of so-called static correlation (situations in which several different one-electron configurations are nearly degenerate). Much of the DFT literature treats these problems by extension and generalization from pure state, closed shell system results. A more inclusively systematic treatment is preferable. Therefore, the first task is to obtain the Time-Dependent Variational Principle (TDVP) in a form which includes mixed states. 

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