A Quantum View of Bonding

Keep in mind that:

• When atomic orbital sets are filled, or half-filled they become completely symmetrical.

• We should expect orbitals in molecules to be different than those in atoms since the electrons are shared by two nuclei rather than distributed around a single nucleus.

• Orbitals are orbitals

  • Only two electrons can be accommodated in any orbital

  • No two electrons can have the same "address" (the same set of quantum numbers).

    • For a molecules the "address" becomes the molecule over which the electrons are shared rather than the atom.

  • We have conservation of orbitals - a molecule will have the same number of orbitals as the atoms which make up the molecule.

  • For our purposes we can also assume a conservation of orbital energy.

 

Electronic Energy Levels Review:

• n = the primary energy level, corresponding to the average radial distance of the electron from the nucleus. The lowest possible energy level is the ground state with n = 1.

• n also gives the # of nodes in each of the orbitals in that shell, with each shell having one node at infinity, where:

  • A node is a region of zero probability of finding an electron.

  • Nodes can have two general geometries:

    • radial (or spherical, a spherical shell at a specific radial distance from the nucleus), with each atom having at least one radial node at infinity;

    • angular (either planar, e.g. as in the planar p-node and diagonal d-nodes, or cone shaped, e.g. as in the cone-shaped nodes of the d_z² orbitals resulting in the donut shaped orbitals).

• Shells with n > 1 MAY have subshells which are different geometrical patterns of electron distribution:

  • The lowest energy pattern is spherical and given the designation s.

  • The next lowest energy distribution is bi-lobed with a planar symmetry. It is given the designation p.

  • The third lowest energy distribution has diagonal planes of symmetry and is designated d.

• The average energies of the different subshells are the energy of the shell, thus when subshells are present the energy of the shell is split. For example, in the n=2 shell the 2s orbital becomes lower in energy than the shell, while the 2p orbitals become higher in energy.

• The regions of electron occupancy in subshells are called orbitals.

  • For each shell there is one s orbital.

  • For each shell with n = 2 or greater there are three p orbitals: p_x, p_y, and p_z.

  • For each shell with n = 3 or greater there are five d orbitals: d_xz, d_yz, d_xy, d_{x²- y²}, and d_z²

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hybrid Orbitals for Tetrahedral Electronic Geometry

 

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© R A Paselk

Last modified 13 April 2015