Kimball Model of PenicillinV

We will write a simple *Mathematica* version 10 code to study PenicillinV. Our objective is to compute its energy components, given a 3D structure from the PDB library (ES 03 May 2013/04 October 2014). This is a HTML copy from the interactive notebook.

Input and Definitions

The coordinates have been read from the Wolfram *Mathematica* ChemicalData repository (in Å). We use atomic units here, the universally applied system of theoretical chemistry and (micro)physics, see NIST. Length data are in Bohr: 1 a0 = 0.52917721 Å = 52.917721 pm (the reciprocal of a0 is 1.889726 bohr/Å, used below), electric charges in ± electron charges, and energies in Hartrees: 1 Eh = 2 Rydberg = 627.5095 kcal/mol = 2625.50 kJ/mol.

Sort atom-array, show nuclear repulsion, charges, sorted atomstring, number of bonds

Compute Kimball radii from distance matrix

Select sigma bonded pairs by a distance criterion

Explanations of following transformations in EtAcetoAc_n1a.html

Compute kinetic energy terms, bonding clouds, core clouds:

Total kinetic energy except for Sulphur core, π-clouds and lone pairs

Determine connectivity matrix:

Localize double bonds and positions of π-clouds (PItrans.m)

Transform the triangle of every target atom with two of its neighbors into the xy-plane and attach π-clouds above and below the plane to the target. Then backtransform the triangle plus π-clouds into the molecular coordinate array.

Localize lone pairs, compute size and orientation:

Transform the triangle of every target atom with two of its neighbors into the xy-plane and attach lone pair(s). Then backtransform the triangle plus lone pair(s) into molecular coordinate array. One leg of the triangle is parallel to x-axis.

Bonding clouds : Atom pair, radius of cloud:

Plot of PenicillinV and its partial components

Preparation of interaction matrices (w-w, w-n, control size arrays):

Computation of energy components (control charges):

Add components of S[Ne](+6)

Results (energies in [Eh] Hartree)