Gaussian Calculations - What is the Basis?

What am I actually changing when I click 631G(d) or 631G(d,p), etc. when I choose a "basis" in restricted Hartree Fock calculations? What is the difference between using an alternative basis? Many thanks. 




The [basis set](http://en.wikipedia.org/wiki/Basis_set_(chemistry)) is used to describe the molecular orbital wave functions.


I suggest reading through a number of links:


* [Wikipedia](http://en.wikipedia.org/wiki/Basis_set_(chemistry))
* [The Gaussian manual - Basis Sets](http://www.gaussian.com/g_tech/g_ur/m_basis_sets.htm) - a nice description of the different basis sets, if a bit technical at times.
* [Naming of quantum chemistry basis sets](https://chemistry.stackexchange.com/questions/2492/naming-of-quantum-chemistry-basis-sets?rq=1)
* [GAMESS Crash Course](https://chemistry.stackexchange.com/a/16537/5017) - applies to Gaussian or other packages


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