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.

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

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Compute Kimball radii from distance matrix

Select sigma bonded pairs by a distance criterion

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Explanations of following transformations in EtAcetoAc_n1a.html

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Compute kinetic energy terms, bonding clouds, core clouds:

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

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Determine connectivity matrix:

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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.

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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.

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Bonding clouds : Atom pair, radius of cloud:

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Plot of PenicillinV and its partial components

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Graphics:PenicillinV

Graphics:Core skeleton

Graphics:bonded σ skeleton

Graphics:π clouds on skeleton

Graphics:Lone Pairs

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

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Computation of energy components (control charges):

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Add components of S[Ne](+6)

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Results (energies in [Eh] Hartree)

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Created with the Wolfram Language