This exercise teaches you about contracted Gaussian functions and the various different integrals that can be constructed. We start simple by exploring a single H atom which has a single electron.
Contacted Gaussian functions (CGFs) are a combination of Gaussian Type Orbitals (GTOs). One can build CGFs by specifying a series of coefficients that describe the GTOs. For example, for the 1s atomic orbital in H according to the STO-3g basis set, the following instructions build the CGF.
cgf1 = cgf([0.0, 0.0, 0.0])
cgf1.add_gto(0.154329, 3.425251, 0, 0, 0)
cgf1.add_gto(0.535328, 0.623914, 0, 0, 0)
cgf1.add_gto(0.444635, 0.168855, 0, 0, 0)To calculate the overlap, kinetic and nuclear attraction integral of this CGF with itself, an integrator object needs to be constructed, which is done via the following one-liner
integrator = PyQInt()This integrator class has the following methods to evaluate the integrals
s = integrator.overlap(<CGF1>, <CGF2>)
t = integrator.kinetic(<CGF1>, <CGF2>)
v = integrator.nuclear(<CGF1>, <CGF2>, <POSITION OF NUCLEUS>, <CHARGE OF NUCLEUS>)Calculate the overlap, kinetic and nuclear attraction integral of the 1s atomic orbital as represented by the STO-3g basis set. Use ex01_template.py to get started.
The solution is given in ex01_solution.py