Kimball Model of Methane

We will write a simple Mathematica version 10 code to study methane.

Our objective is to compute the groundstate energy of a tetrahedral structure.

We use the kinetic energy and screening constant parameters from the optimization with G3//6-311+G(d)

ab initio results. Here is the output of an optimization run whose results are used below.

Definitions

We define some arrays:

Electrical charges on the clouds and nuclei:

r Radii of clouds, exc excentricities of protons in CH-clouds, d1 distances of C,H nuclei, d2 distances of C-H clouds from C, n x,y,z coordinates of protons and w of clouds on the corners of cubes, defining tetrahedron; all lengths in (Bohr units):

Preparation of the interaction matrices and summation of terms within one cloud:

Kinetic energy of electrons, components of the potential energy, using matrix operations:

Minimization of the total energy

Results, extracted from the solution, above; all energies in [Eh] (Hartree)

3D Plot of the computed structure

Projection of Kimball spheres into diagonal plane through the C atom