Computational Chemistry

concept is clearly related to the dipole moment: in a diatomic (for simplicity)
molecule one expects the negative end of the dipole vector to point toward the
atom assigned the negative charge. However, there are two problems with the
concept: first, the charge on an atom in a molecule, unlike the dipole moment of
a molecule, cannot be (readily [ 254 ]) measured. Second, there is no unique, correct
theoretical method for calculating the charge on an atom in a molecule (devotees of
atoms-in-molecules (AIM) theory, to be discussed, may dispute this).
Both the measurement and calculational problems arise from the difficulty of
defining what we mean by “an atom in a molecule”. Consider the hydrogen chloride
molecule. As we move from the hydrogennucleusto the chlorinenucleus, where
does the hydrogen atom end and the chlorine atom begin? If we had a scheme for
partitioning the molecule into atoms (Fig.5.38a), the charge on each atom could be
defined as the net electric charge within the space of the atom, i.e. the algebraic sum
of the electronic and the nuclear charges. The electronic charge in the defined space
could be found by integrating the electron density (which can be calculated from the
wavefunction – seeSection 5.5.4.5) over that region of space.
Bond orderis a term with conceptual difficulties related to those associated with
atom charges. The simplest electronic interpretation of a bond is that it is a pair of
electrons shared between two nuclei, somehow [ 255 ] holding them together. From

A

B

C

A

B

C

a

b

A

B C

A

B C

A-B bonding

region?

Where does atom A end and B begin?

??

Fig. 5.38(a) In a molecule where does one atom end and another begin? How is the dividing
surface to be drawn? (b) How is the bonding region between two nuclei to be defined?

344 5 Ab initio Calculations