I am still a little confuse about diffuse function. How do we decide it is a smaller exponent?
A small exponent makes the orbital spatially more diffuse.
My question wasn't clear.
So in Lecture Note 26 you define: symbol + = Diffuse function = "adding function of smaller exponent". I don't really understand this.
Could you show me an example such as HW 13 number of basic function of 6-31G**+ for Benzene. What if it is 6-31**++?
so i think ++ means you add diffuse functions to heavy and light atoms?
so + means you add diffuse function to heavy atoms only? Do all heavy atoms have smaller exponent?
umm.. the diffuse functions added always have smaller exponents.. this means the spread of a gaussian is greater... so the diffuse functions always have smaller exponent than typical 'non diffuse' functions, regardless of the type of atom
Thank you! It starts to make sense now.
I am still not quite sure the number of basis functions for 6-31G**+ calculation, especially for the addition of diffuse function(+). Do we need to add diffuse functions for all the occupied orbitals or just some of them? (e.g. in homework 13 question2, should we add diffuse functions for both s and p orbitals (a total of 9 functions) or just for s or p orbitals?)
http://www.ccl.net/cca/documents/basis-sets/basis.html
Diffuse gaussians are usually of s and p type, however sometimes diffuse polarization functions are also used. Diffuse functions are necessary for correct description of anions and weak bonds (e.g. hydrogen bonds) and are frequently used for calculations of properties (e.g. dipole moments, polarizabilities, etc.). For the Pople's basis sets the following notaton is used: n-ij+G when 1 diffuse s-type and p-type gaussian with the same exponents are added to a standard basis set on heavy atoms. The n-ij++G are obtained by adding 1 diffuse s-type and p-type gaussian on heavy atoms and 1 diffuse s-type gaussian on hydrogens.
The first + indicates that one diffuse s function and one set of p functions are added to each heavy atom, even if the heavy atom has d orbitals. The second + indicates that a diffuse s function is added to hydrogen atoms.
For benzene C6H6, + means that for each C atom, you add one s-function, and one set of p functions, e.g, px, pz and pz. Hence, you add (1+3)*6 functions to your basis set.
The first * indicates that you add one polarizaiton function for each heavy atom. The second * indicates that you add a set of p functions for each hydrogen atom. Typically, the form of the polarization is given. For example, instead of the 6-31G** notation, you can see 6-31G(d,p). This means you add a set of d functions to all heavy atoms, and a set of p functions to all hydrogens.