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


All computations are transparent and annotated. The run lasts about 1 sec on a i7-4690 CPU. (ES 16 June 2013/ 16 July 2017).
Structure from Wolfram ChemData. This is the neutral form of glycine in the gas phase. Associated with > 2 molecules of water the zwitterion NH3+CH2COO- becomes more stable.

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|

Glycine_sipi5_1.png

Normal Input for a structure downloaded from Wolfram ChemData repository

Glycine_sipi5_2.gif

Glycine_sipi5_3.gif

Glycine_sipi5_4.gif

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Glycine_sipi5_6.png

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Analyze the atomic constituents

Glycine_sipi5_8.png

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Glycine_sipi5_11.png

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 :

Glycine_sipi5_12.gif

Nuclear repulsion

Glycine_sipi5_13.gif

Glycine_sipi5_14.png

Determine bonded pairs by a distance criterion

Glycine_sipi5_15.gif

Glycine_sipi5_16.png

Bonded atom pairs:  distances

Glycine_sipi5_17.png

Glycine_sipi5_18.png

Subtract proton eccentricities

Glycine_sipi5_19.png

Glycine_sipi5_20.png

Glycine_sipi5_21.gif

Glycine_sipi5_22.png

Subtract core radii

Glycine_sipi5_23.gif

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Show radii determined

Glycine_sipi5_25.gif

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Summary of Lewis properties

Glycine_sipi5_27.gif

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Compute kinetic energy terms, bonding clouds, core clouds:

Glycine_sipi5_31.gif

Glycine_sipi5_32.png

Glycine_sipi5_33.png

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Total kinetic energy except for π - clouds and lone pairs

Glycine_sipi5_35.png

Glycine_sipi5_36.png

Glycine_sipi5_37.gif

Glycine_sipi5_38.png

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Determine connectivity matrix:

Glycine_sipi5_40.gif

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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.

Glycine_sipi5_42.png

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Glycine_sipi5_44.gif

Glycine_sipi5_45.png

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Glycine_sipi5_48.png

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Glycine_sipi5_50.png

Glycine_sipi5_51.png

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.

Glycine_sipi5_52.png

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Glycine_sipi5_56.gif

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Glycine_sipi5_62.png

Glycine_sipi5_63.png

σ Bonding clouds: Connected atom pair, radius of cloud

Glycine_sipi5_64.gif

Glycine_sipi5_65.png

Glycine_sipi5_66.png

Glycine_sipi5_67.png

Glycine_sipi5_68.png

Glycine_sipi5_69.png

Glycine_sipi5_70.png

Graphics:Cloud radii (bohr)

Plot molecule and its electronic partial constituents

Glycine_sipi5_72.gif

Graphics:Glycine

Graphics:Core skeleton

Graphics:σ skeleton

Graphics:π-clouds on skeleton

Graphics:Lone Pairs

Graphics:H atoms

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

Glycine_sipi5_79.png

Glycine_sipi5_80.png

Glycine_sipi5_81.png

Compute energy components

Interactions for i not j

Glycine_sipi5_82.gif

Interactions for i equals j

Glycine_sipi5_83.png

Kinetic energy of π clouds and lone pairs

Glycine_sipi5_84.png

Glycine_sipi5_85.png

Glycine_sipi5_86.png

Add components of Ne[10] cores; Politzerratio

Glycine_sipi5_87.png

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Results (energies in [Eh] Hartree)

Glycine_sipi5_89.png

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Glycine_sipi5_98.png

Glycine_sipi5_99.png

Glycine_sipi5_100.png

Glycine_sipi5_101.png

Glycine_sipi5_102.png

Created with the Wolfram Language