p electron atomic charge

The coefficients in the molecular orbitals reflect the charge distribution of an electron in that orbital.

y_i: Molecular orbital number ‘i’

f₁: atomic (p) orbital on atom 1

f₁: atomic (p) orbital on atom 1, etc.

In the coefficients c_ia

i ----- is the molecular orbital number

a ----- is the number of the atom and of corresponding atomic p-p orbital.

If there is an electron (just 1) in molecular orbital y_i the charge distribution corresponding to this electron is given by:

r(r): Charge distribution (electron density) -- this is a function of position r -- arises from 1 electron in M.O. “i”

The electron density is a function of the coordinates. Its value changes with position in space.

In the example above, c_i1² is a measure of the amount of charge on atom 1 - arising from 1 electron in MO i.

2c_i1c_i2 is a measure of the charge shared between atoms 1 and 2.

p electron charge on atom a (q_a):

n_i is the number of electrons in MO i.

If the occupied molecular orbitals all have 2 electrons in them then n_i=2 and the equation for the atomic charge becomes;

As you will see in the accompanying Theoretical Chemistry Class, the charges from Hückel Theory predict so-called ‘non-alternant’ hydrocarbons to be polar (have a dipole moment), while ‘alternant’ hydrocarbons are not, in agreement with experiment.

Next: p-bond order