Quantitative electronic Lewis structure derived from nuclear coordinates of a molecule:
c-Propane


All computations are transparent. The run lasts < 1 sec on a i7-4790 CPU. (ES 22 May 2016).

c-propane is a famous case because the CCC angle in the ring is only 60 deg, far from the usual tetrahedral
angle of 109.47°.

c-butane forms a puckered ring and thus releases part of the tensions caused by a flat C-skeleton with CCC angles of
90°. Many cyclo-alkanes > C5 have a tetrahedrally relaxed C neighborhood.

It seems that Th. Förster in 1939 has proposed, for the first time, that the bonding electrons are not necessarily forced
to concentrate on the straight line - the not existing bonding stick ! - connecting two nuclei. They might relax the strain by yielding to the outside of the edges of the C3 ring. By this token the electron-electron repulsion and the high requirement for exchange corrections (because of Pauli forbidden overlaps within the ring) are lessened. We try to do this with Kimball’s free clouds.

You can manipulate the locations of the C-C bonding clouds by changing the factor bf in the first paragraph: bf=1 means straight bonds, bf > 1 makes the clouds shift their centers away from the symmetry center while maintaining touching bonding and core clouds. bf < 1 pushes the clouds towards the center of the molecule with bf ~0 a total collaps of three clouds onto one heap. Follow the changes in kinetic and total energy of the molecule while increasing or decreasing bf. Try to understand what you are doing. It is not difficult and gives you insight into important interactions. Perhaps, the most important being, that the chemists bonding stick is even more esoteric than the spherical electron clouds. “Bent bonds”, “banana bonds” and similar concepts reflect the macroscopic image of atoms holding together by sticks. Try to translate this archetypal “nonsense” into the quantitative nuclear-electron picture of modern chemistry. But, what would happen to the way organic chemists discuss their science if they could no more draw their imaginery molecular stick formulae? Hence, ‘bent bonds’ and friends as well as ‘strained bonds’ and ‘tension in rings’, will be with us and make heated scientific exchange for decades to come ... and some of this is fruitful for scientific progress even if the underlying concepts are obsolete.
Note: There is presently no exchange correction for cloud overlap in this notebook. The predefined bf = 1.78 presents a molecule with almost no overlap.

Input and Definitions


The structure is read in a0. We use 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 : Symbol, x, y, z

c-Propane_com2_1.gif

c-Propane_com2_2.png

c-Propane_com2_3.png

Normal Input for a structure downloaded from Wolfram ChemData repository

c-Propane_com2_4.png

Analyze the atomic constituents

c-Propane_com2_5.png

c-Propane_com2_6.png

c-Propane_com2_7.png

c-Propane_com2_8.png

c-Propane_com2_9.png

c-Propane_com2_10.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 :

c-Propane_com2_11.gif

c-Propane_com2_12.png

Nuclear repulsion

c-Propane_com2_13.gif

c-Propane_com2_14.png

c-Propane_com2_15.gif

c-Propane_com2_16.png

Select bonded pairs and their distances

c-Propane_com2_17.png

c-Propane_com2_18.png

Subtract proton eccentricities

c-Propane_com2_19.png

c-Propane_com2_20.png

c-Propane_com2_21.gif

c-Propane_com2_22.png

Subtract core radius

c-Propane_com2_23.gif

c-Propane_com2_24.png

Show radii determined

c-Propane_com2_25.gif

c-Propane_com2_26.png

Summary of Lewis properties

c-Propane_com2_27.gif

c-Propane_com2_28.png

c-Propane_com2_29.png

c-Propane_com2_30.png

Compute kinetic energy terms, bonding clouds, core clouds:

c-Propane_com2_31.gif

c-Propane_com2_32.png

c-Propane_com2_33.gif

Partial kinetic energy for cores and σ clouds

c-Propane_com2_34.png

c-Propane_com2_35.png

c-Propane_com2_36.gif

c-Propane_com2_37.png

c-Propane_com2_38.png

Determine connectivity matrix:

c-Propane_com2_39.gif

c-Propane_com2_40.png

σ Bonding clouds: Connected atom pair, radius of cloud

c-Propane_com2_41.gif

c-Propane_com2_42.png

c-Propane_com2_43.png

c-Propane_com2_44.png

c-Propane_com2_45.png

c-Propane_com2_46.png

c-Propane_com2_47.png

Graphics:Cloud radii (bohr)

Plot molecule and its partial constituents

c-Propane_com2_49.gif

Graphics:c-Propane: straight lines connecting cores,  bonding clouds yield

Graphics:Core skeleton, 'bent bonds'

Graphics:&sigma; skeleton, 'no sticks'

Graphics:C-C clouds on skeleton, 'no sticks!'

Graphics:H atoms, 'bent bonds'

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

c-Propane_com2_55.png

c-Propane_com2_56.png

c-Propane_com2_57.png

Compute energy components

Interactions for i not j

c-Propane_com2_58.gif

Interactions for i equals j

c-Propane_com2_59.png

Add components of Ne[10] cores; Politzerratio

c-Propane_com2_60.png

c-Propane_com2_61.png

Results (energies in [Eh] Hartree)

c-Propane_com2_62.png

c-Propane_com2_63.png

c-Propane_com2_64.png

c-Propane_com2_65.png

c-Propane_com2_66.png

c-Propane_com2_67.png

c-Propane_com2_68.png

c-Propane_com2_69.png

c-Propane_com2_70.png

c-Propane_com2_71.png

c-Propane_com2_72.png

c-Propane_com2_73.png

c-Propane_com2_74.png

c-Propane_com2_75.png

Created with the Wolfram Language