Structural Biochemistry/Linear Combination of Atomic Orbitals

Linear Combination of Atomic Orbitals (LCAO) is the sum of atomic wave functions that lead to the formation of molecular orbitals.

Parameters
-The symmetry of the orbitals must have the same sign overlap

-The energy of the atomic orbitals must be smaller

-The distance between the atoms must be short enough to provide good overlap of the orbitals.



The Linear combination of atomic orbitals are essential for molecular orbital understanding and building the molecular orbital diagram. The Linear combination of atomic orbitals or LCAO are tools that have described groups of orbitals as linear combinations of basic functions. The LCAO helps us understand symmetry of a molecule and how the ligands surround the center.

s Orbital Bonding
s Orbital bonding is when their two electron clouds overlap and merge into a large molecular electron cloud. This results in a linear combination of the atomic orbitals. Bond order is defined by
 * $$\text{B.O.} = \frac{\text{number of bonding electrons} - \text{number of antibonding electrons}}{2}\ $$

This has to be positive in order for a stable bond to be created. The overall number of bonding and antibonding electrons determine the number of bonds

Bonding molecular orbital is where both atomic wave functions contribute, which has a lower energy than the original atomic orbitals Antibonding molecular orbital is the cancellation of waves functions, at a higher energy than the original atomic orbitals. Nonbonding molecular orbital is when the orbital of one atom has a symmetry that does not match the orbital of any other atoms

p Orbital Bonding
p Orbital bonding occurs when the two orbitals overlap, the overlapping regions have the same sign. As a result, the sum of the two orbitals has an increased electron probability in the overlap region. The overlap of two opposite signs leads to a node of zero electron density. As a result, the orbitals of Px, Py, and Pz are to be considered separately.

d Orbital Bonding
The transition metals bond in a similar way as p orbitals, but results in Dyz, Dz^2, Dyz, Dxz, Dx^2-y^2, and Dxy. The Dxz and Dyz orbitals form pie bonds. The Dx^2-y^2 and Dxy orbitals are collinear to the z axis and form delta bonds. The Dz^2 orbital forms a sigma bond.

Paramagnetic vs. Diamagnetic
Paramagnetic compounds are attracted by an external magnetic field due to one or more unpaired elections that are attracted to the magnetic field Diamagnetic compounds are not attracted by an external magnetic field because all the electrons are paired. This can have profound effects on metal compounds.

Reference
Miessler, Gary. Inorganic Chemistry. 4th Edition.