Pseudo-potentials and basis sets

In this part of the lab you will gain experience in using larger basis sets and pseudo-potenitals, essential skills if you want to use computational chemistry to study inorganic systems, especially catalysis or main group metal containing compounds. This year you will be looking at GaBr3, Br is in the third row and has 35 electrons, with an electronic configuration of 1s22s22p63s23p63d104s24p5, at the level of quantum mechanics we are using, 35 electrons is a lot! Even worse, Gallium also has almost as many electrons, and both atoms exhibit relativistic effects which cannot be recovered by the standard Schrodinger equation. However, we can recover some of these relativistic effects by using a pseudo-potential. GaBr3 is important in the semi-conductor industry. For example, GaAs is used in the manufacture of light emitting diodes (LEDs), which are found in optical communications and watches. GaBr3 melts at 121 and boils at 279 degrees C. Pure semiconductors are grown via chemical vapour deposition and group-III halide precursors are used to provide the necessary In and Ga. Gallium is one of three elements that occur naturally as a liquid at room temperature, the other two being mercury and cesium, thus Ga can be used in high temperature thermometers.

Most of chemistry is based on the assumption that it is really the valence electrons that dominate in bonding interactions, and so we can safely model the core electrons of an atom by a special function called a pseudo-potential (PP) or an effective core potential (ECP), they are different names for the same thing, pseudo-potentials make calculations much easier.

Important PPs should ONLY be used on heavy atoms, definitely on atoms in the third row and below, and on second row atoms (Si, P, Cl etc) only if the situation warrents it (ie the calculation would otherwise take too long). Pseudo-potentials have been used for a long time and so we know they are accurate and do not effect the results significantly for heavy atoms (of course this all depends on the level of accuracy you want!).

When treating second row atoms and above, we also need to improve our basis set. Basis sets determine the number of functions used to descripe the electronic structure. I think showing you a simple example is the best way to get started.

Say I have a shape I want to descripe, for example a car as in the diagram. I could describe this shape with a single basis function (a circle). If I use only one basis function (a circle) of a given size, the shape of the car is not well reproduced. However, if I allow my circles to vary slightly in size, ie if I increase my basis set to two functions I get a better fit, and if I allow even more functions I can descripe the shape of the car very well! If we add too many basis functions the calculation will take too long, so we always have to balance computational difficulty vs the size of the baisis set.

In addition to adding more generic functions we can add functions that do specific things, for example, diffuse functions allow the electron density to extend out and away from the molecule, important when we are considering anions, or very soft elements. Polarization functions allow the electron density to become polarized to one side of a molecule. Both types of function are important for an accurate description of most inorganic molecules where the electron density is moving around and the basis sets must be good to accommodate this ebb and flow.

now lets move on to using larger basis sets and a pseudo potentials in our calculations

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