This week's lecture is on LCAO and basis sets. Covers mostly Gaussian basis sets ( tiny bit on periodic planewave basis sets). More on planewave basis sets below.
Further reading:
http://molecularmodelingbasics.blogspot.dk/2015/06/a-brief-introduction-to-basis-sets.html
https://en.wikipedia.org/wiki/Basis_set_(chemistry)
https://www.shodor.org/chemviz/basis/teachers/background.html
http://www.ccl.net/cca/documents/basis-sets/basis.html
http://www.valeevgroup.chem.vt.edu/docs/basisset_notes.07032015.pdf
http://www.nwchem-sw.org/images/Pw-lecture.pdf
http://www.impmc.jussieu.fr/~seitsonen/Science/Presentations/Taiwan-juillet-2005/lectures/lecture-pw.pdf
Review articles on basis sets:
Grant Hill. Gaussian basis sets for molecular applications, Int. J. Quant. Chem 2012
Slater functions:
https://www.researchgate.net/publication/200710102_Molecular_Integrals_over_Slater-type_Orbitals._From_pioneers_to_recent_progress
Also:
EMSL Basis set Exchange Database of Gaussian-type basis sets.
Gaussian/Slater functions
Python code to plot Gaussian and Slater functions (requires Matplotlib):
import matplotlib.pyplot as plt
from numpy import *
# Slater/Gaussian exponent
zeta=0.5
#Increment of numbers
incr=0.00001
x1= arange(0.,10.,incr)
x2= arange(-10.,0.,incr)
#Gaussian
gy1=exp(-zeta*x1*x1)
gy2=exp(-zeta*x2*x2)
#Slater
sy1=exp(-zeta*x1)
sy2=exp(zeta*x2)
g1=plt.plot(x1,gy1,'b-')
g2=plt.plot(x2,gy2,'b-')
plt.plot((0, 0), (0, 1), 'k-')
s1=plt.plot(x1,sy1,'r-')
s2=plt.plot(x2,sy2,'r-')
plt.show()