Carbon and Graphene by RealQM

A carbon atom C has up to 4 valence electrons and forms a very large variety of compounds by connecting to 1 up to 4 other atoms as CO, CO2 and CH4... 

Graphene is a 2d hexagonal pattern of carbon atoms each atom connecting to 3 other atoms, thus involving 3 valence electrons.

We now let RealQM compute the energy of C in the following shell configurations:

• 2+4                     (2 electrons in 1st shell, 4 in 2nd shell)                                (code)
• 2+2+2                (2 electrons in 1st shell, 2 in 2nd shell and 2 in 3rd shell)    (code)
• 2+3+1                (2 electrons in 1st shell, 3 in 2nd shell and 1 in 3rd shell)    (code)

and get close to the a reference ground state value of -37.7 Hartree in all three cases. We also compute ionization energies in 2+2+1 (code) and 2+3 (code) configuration in agreement with a reference value of 0.4 Hartree.

Altogether, RealQM gives a picture of C with 3 possible ground states of about the same energy available to form molecules with 1-4 bonds.

The view of standard QM stdQM is that the ground state configuration of the C atom is $1s^22s^22p^2$ with 2 electrons in spherically symmetric orbits in 1st shell, 2 electrons in spherically symmetric orbits together with 2 electrons in p-states in 2nd shell, which suggests that 1-2 valence electrons are available, but the 3 in graphene.

To get 3 valence electrons in stdQM various hybrid sp-orbital states are introduced to give the following picture of the 2d hexagonal pattern of a graphene sheet with each carbon atom connected to 3 other atoms involving 3 sp2 valence electrons and the 4th electron hoovering above and under (or around) the sheet: 

We can connect the RealQM 2+3+1 configuration to this picture with 3 electrons centered in a plane and a 4th out-of-plane electron as 3d enclosure. 

RealQM approaches the electron distribution in atoms and molecules as a real physical packing problem in 3d. RealQM is ab initio. RealQM is computable at iPad power. 

StdQM uses a formal approach based on molecular orbits which have no real physical meaning. StdQM involves a set of ad hoc rules (Pauli, Hund's rules 1-3...) and is not ab initio. StdQM fills the books on Quantum Chemistry with a message that it works, even if stdQM itself is a mystery. StdQM is uncomputable on any thinkable digital computer.