Linear Combination of Atomic Orbitals LCAO

Описание: According to Linear Combination of Atomic Orbitals (LCAO) when two atoms come close to one another, two atomic orbitals (one from each atom) having comparable energy, same symmetry and possessing large overlaps, combine to form two molecular orbitals. One of them has lower energy and the other has higher energy than the combining atomic orbitals. The molecular orbital with higher energy gives rise to a repulsive state and is called as antibonding molecular orbital (𝚿a), while molecular orbital with a lower energy gives rise to attractive state and is called as bonding molecular orbital (𝚿b).
As electrons have duel nature of particle and wave. They can be considered as moving in atom in the form of a wave represented as 𝚿.

Let us consider 𝚿A is the wave function of electron of atom A and 𝚿B is wave function of electron of atom B.

∴ wave function of Bonding molecular orbital will be given by 𝚿bonding = 𝚿A + 𝚿B

And wave function of Antibonding molecular orbital will be 𝚿antibonding = 𝚿A - 𝚿B
A wave has a crest and a trough, when crest of one wave combines with crest of other the amplitude of resulting wave increases.
The electron wave above the imaginary horizontal line is given a +ve sign while that below the line is -ve. In this case both the electron waves are on the same side(+ve side) i.e., the signs of the two wave functions are same. Such wave functions which may be regarded as in the same phase, when combine, give rise to larger resultant wave or molecular orbital. Such molecular orbital is called bonding molecular orbital (BMO). In this molecular orbital the region between the two nuclei is the place where there is overlap of the individual 1s orbitals and hence there is greater probability of electron density in center of two atoms.

When two waves are in the opposite direction. The wave functions of different signs, which may be regarded as out of phase, when combine, cancel each other and the probability of finding electron in this region is practically nil. Such a molecular orbital is known as antibonding molecular orbital

The electron density in an antibonding orbital tends to be greater in the corners of nuclei.

In the bonding molecular orbital, electron density between the two nuclei is increased. The nuclei are shielded from each other and there is greater attraction of the nuclei for the electrons. This results in lowering of energy.
In the antibonding molecular orbital, the electron density between the two nuclei is decreased. The nuclei are partially exposed to each other and there is greater nuclear repulsion. This results in an increase of energy.
The bonding orbital has a lower energy level than the isolated atoms by a quantity ▵E. Because of this ▵E, bonding orbital is more stable. On the other hand the antibonding orbital is at a higher energy level than the isolated atoms and is then destabilized by ▵E, The quantity ▵E is known as exchange energy.

Other Subjects:
Adult Education @ http://www.edmerls.com/index.php/Adul...
Analytical Chemistry @ http://www.edmerls.com/index.php/Anal...
Applied Physics @ http://www.edmerls.com/index.php/Appl...
Engineering Drawing @ http://www.edmerls.com/index.php/Engi...
English @ http://www.edmerls.com/index.php/Engl...
Environmental Studies @ http://www.edmerls.com/index.php/Envi...
General Medicine @ http://www.edmerls.com/index.php/Gene...
Mathematics @ http://www.edmerls.com/index.php/Math...
Organic Chemistry @ http://www.edmerls.com/index.php/Orga...
Physical Chemistry @ http://www.edmerls.com/index.php/Phys...
Patente B Italia @ http://www.edmerls.com/index.php/Pate...
Soft Skills @ http://www.edmerls.com/index.php/Soft...