Kimball Model of Saccharose

We will write a simple Mathematica version 10 code to study Saccharose “C12H22O11”

Our object is to compute its energy components, given a 3D structure, and to plot the different electronic constituents of its Lewis structure.

All computations are transparent. We only use basic elements of Mathematica, thus making it easy to understand at the level of highschool students. (ES 16 June 2013/10 December 2014).

Our run lasts 2 sec on one core of a i7-2600 CPU, 3.4 GHz, 16 GB of RAM, of which less than 1 GB are used.)

Input and Definitions

The coordinates are read in pm. 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 (whose reciprocal is 0.01889726 bohr/pm, used below) ; electric charges in ± electron charges, and energies in Hartrees : 1 Eh = 2 Rydberg = 627.5095 kcal/mol = 2625.50 kJ/mol.

Standard molecular formula without lone pairs

Analyze the atomic constituents of Saccharose

Analyze Lewis structure

Compute Kimball radii from atomic distance matrix, show core radii derived from CH4, NH3, H2O gauge molecules (cnofhydb.pas), (cnofhydb.ex_ to be renamed into runnable cnofhydb.exe after download).

Compute kinetic energy terms, bonding clouds, core clouds:

Total kinetic energy except for 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 back transform the π-clouds into the molecular coordinate array.

Localize lone pairs, compute size and orientation:

Subroutines: XOtrans.m XOYtrans.m CNCtrans.m LpyrNtrans.m

Transform the triangle of every target atom with two of its neighbors into the xy-plane and attach lone pair(s). Then back transform the lone pair(s) into the molecular coordinate array. See one of the subroutines. LpyrNtrans puts the base atoms of a pyramid into the xy plane and attaches LP's as needed, the moves these back into the molecule frame.

σ Bonding clouds: Connected atom pair, radius of cloud

Plot of Saccharose and its partial constituents

Add coordinates of π-clouds and lone pairs. Prepare interaction matrices:

Compute energy components

Interactions for i not j

Interactions for i = j

Kinetic energy of π clouds and lone pairs

Add components of Cl[Ne](+7) ; Politzerratio

Results (energies in [Eh] Hartree)