1. Energies, forces, bonds
- only shapes of atomic electron orbitals give us a hint of three-dimensional shapes of molecules
more quantitative treatment requires calculation of forces through which various atoms interact
amazingly Ludwig Seeber proposed already 1824 the concepts of repulsion, attraction and equilibrium without any evidence for the existence of atoms!

2. Is the potential between atoms, in case the corresponding force is central, it only repends in the interatomic distance, generally depends on angles (orientations)
As in mechanics, the force is negatice gradient of the potential
The force must be repulsive at short distances and attractive at the equilibrium distance and zero very far way.

3. Born-Mayer component is almost always present,
Naturally, different kinds of bonds also mean different potential shapes and strengths.
One component of interatomic potential is famous Max Born and Joseph Mayer (1932) potential describing the repulsion between atoms whose electrons are exclusively on completely filled orbitals.
Born-Mayer component is almost always present,
Since there closed shells even though actual bonding may take place between outermost electrons
= nm, for all closed shells !

5. Ionic interaction Can be + or - !
Decreases with increasing distance, but more or less linearly, not exponentially.

6. Covalent interaction
Never repulsive, always attractive,only empirical form exist,
no exact solution
Distance parameter
Coulomb interaction modulated by exponential decay, covalent bond always refers to a single orbital interaction
Comparison between covalent and ionig interaction with a single charge on each ion,
Covalent interaction dies away very rapidly

7. Metallic interaction
Inverse distance
…just for comparison...

8. Weak bonds, van der Waals
Attraction between filled orbitals, repulsion is trivial, since Pauli exclusion principle prohibits overlap of the orbitals belonging to the two atoms
Due to the instantaneous dipole-dipole interaction
The Buckingham potential function is
Born-Mayer van der Waals

9. However, in computer simulations, the Buckingham function is often replaced by a good approximation;
So called Lennard-Jones potential, which is faster to calculate

11. Bond energies:
Assume that essentially our body consists of C-C bonds.
5 x 1022 atoms per gram of tissue
in average maybe 3 bonds per atom
an adult would have appr. 4 x 1027 bonds
covalent bond energy is appr. 0.6 x J
total energy of all the bonds is appr. 2.4 x 109 J (0.6 x 109 cal)
= 250 times the daily intake of appr kcal

12. Hydrogen bond
No absolute universal acceptance of the form of the function
So called switching potential that takes the hydrogen bond to zero at distances greater than nm

13. Next example: glucose
Out of this energy mitochondria can produce 2 aJ of useful energy, so the efficiency is more than 50% ( a number that would be very good in industrial energy conversion).
A more detailed calculation would take into account non-covalent interactions. In addition, free energy is of relevance and it should take into account the changes in entropy.
6*0.82 aJ = 4.92 aJ *1.23 aJ *0.77 aJ= 9.24 aJ

14. Polyisoprene, 2 different molecular forms,
Demonstrates also the influence of weak interactions in molecules,
The exact calculation is exhaustive, since there are interactions between all atoms (exceeding thus the number of covalent bonds)
Methyl group and H on the same side of the double bond
Methyl group and H on opposite sides => no kink
Natural rubber gutta-percha
The difference is due to the non-bonded interactions, in practise about the rotation of the double bond.
The resistance of that rotation is called steric hindrance.

15. Twisting of polyethylene

16. Rotational energy function for twisting about one of the C-C bonds in polyethene.