Solid state physics Lecture 7 of 20

October 3, 2012 by Multimedia Publications and Printing Services

Lecturer: S. Scandolo, ICTP

lesson number 7(the problem of valence electrons and Chemical bonds)

In this lesson attention is made to the interaction between the electrons and nucleus and the interactions between atoms. Some concepts of atomics physics are recalled like the composition of an atom, the potential of interaction between the electron and the nucleolus, the concepts of valence electrons and core electrons. It is shown how the core electrons produce the so called shielding effect.

Then the Hamiltonian for the valence electrons of a single atom was written and it was emphasized the fact that interaction between the electrons is the term that introduces the major complexity to the problem, actually when you have more than two electrons the problem has not analytic solution jet, and for normal atoms it is not possible to solve the problem even numerically because the amount of memory needed to store the wave function is too large. For example for carbon with 6 electrons you need to store 1036 points for the wave function, not possible even in the near future. An approximation to this problem is to work with the density functional of electrons a functional that was demonstrated by Walter Kohn to exist and be unique, unfortunately this function is unknown jet. An approximation to this functional is obtained by an iterative method whiting the Density functional theory (DFT) formalism.

Finally some kinds of chemical bonds were introduced, the covalent bond that typically take place between atoms that are very similar and you will have accumulation of charge between the two nucleus. The Ionic bond, like the one in Na+Cl- , where we have a transference of 1,2,3… electrons from one atom to another. The Van der Waals bond a weak interaction between neutral charge densities at large distances very useful in glues for example and the hydrogen bond a kind of Ionic bond because its origin is electrostatic but there is not charge transfer between the atoms. The hydrogen bond is the main source of attraction in liquid water and is present in all biological objects.

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