Quantitative electronic Lewis structure derived from nuclear coordinates of a molecule:
Formaldehyde


All computations are transparent and annotated. The run lasts about 1 sec on a i7-4690 CPU. (ES 16 June 2013/ 16 January 2017).
Structure from Wolfram ChemData.

Input and Definitions

The coordinates are read in pm. We are using atomic units, 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; electric charges in ± electron charges, and energies in Hartrees : 1 Eh = 2 Rydberg = 627.5095 kcal/mol = 2625.50 kJ/mol.

Normal Input for a structure given as a table with rows: |Atom_symbol  x  y  z|

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Normal Input for a structure downloaded from Wolfram ChemData repository

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Analyze the atomic constituents

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Unique nuclei         C H O
··· number                1    2    1
··· nuclear charge        6    1    8
··· core cloud charge   -2    0   -2
··· valence electrons    4    1    6
··· full Lewis shell      8    2    8
··· Core radii      0.26    0 0.178

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Analyze Lewis structure

Compute Kimball radii from 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), H excentricities, and number of σ bonds.

Distance Matrix :

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Nuclear repulsion

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Determine bonded pairs by a distance criterion

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Bonded atom pairs:  distances

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Subtract proton eccentricities

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Subtract core radii

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Show radii determined

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Summary of Lewis properties

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Compute kinetic energy terms, bonding clouds, core clouds:

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

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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, then moves these back into the molecule.

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σ Bonding clouds: Connected atom pair, radius of cloud

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Graphics:Cloud radii (bohr)

Plot molecule and its electronic partial constituents

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Graphics:Formaldehyde

Graphics:Core skeleton

Graphics:σ skeleton

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Graphics:Protons in CH-cloud

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

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Compute energy components

Interactions for i not j

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Interactions for i equals j

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Kinetic energy of π clouds and lone pairs

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Add components of Ne[10] cores; Politzerratio

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Results (energies in [Eh] Hartree)

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Created with the Wolfram Language