Wavefunctions and their signs
What is a wavefunction? A wavefunction is a mathematical expression.
Atomic orbitals are graphs of 3-dimensional wavefunctions.
Two graphs of s-orbital wavefunctions
The phase sign for an s-orbital wavefunctions is always positive.
What happens when the orbitals overlap?
As the atoms approach one another, their valence atomic orbitals overlap.
Atomic orbitals are graphs of 3-dimensional wavefunctions.
y = sin x is an example of a 2-dimensional wavefunction.
Wavefunctions for orbitals may have both positive and negative regions just like sin x may be positive or negative. These mathematical phase signs have NOTHING to do with the presence or absence of electrons, but they are VERY important when considering overlap of atomic orbitals!
Wavefunctions for orbitals may have both positive and negative regions just like sin x may be positive or negative. These mathematical phase signs have NOTHING to do with the presence or absence of electrons, but they are VERY important when considering overlap of atomic orbitals!
Two graphs of s-orbital wavefunctions
The phase sign for an s-orbital wavefunctions is always positive.
The spherical representation of s-orbitals shows the region within which electrons are likely to be found. The top graph shows the probability of finding an electron in a 1s orbital plotted as a function of distance from the nucleus (vertical lines).
What happens when the orbitals overlap?
As the atoms approach one another, their valence atomic orbitals overlap.
According to molecular orbital theory, the two molecular orbitals resulting from overlap of atomic orbitals can be generated by linear combination (addition and subtraction) of wavefunctions for the overlapping atomic orbitals (1s in this case).
Addition gives an molecular orbital that has a lower energy than the orbitals on separated atoms (ADD on rollover) and subtraction (SUBTRACT on rollover) gives a higher energy molecular orbital.
Addition gives an molecular orbital that has a lower energy than the orbitals on separated atoms (ADD on rollover) and subtraction (SUBTRACT on rollover) gives a higher energy molecular orbital.