Lecture 30: Molecular interactions
Review
o Molecular orbitals
o Hybridization
Today
o Bonding in inorganic transition metals
o Geometric interactions
o Bond stretching/bending
o Intramolecular rotations
o Charge dependent nonspecific interactions
o Coulombic interactions
o Dipolar interactions
o London-Van-der Waal interactions
Bonding in inorganic complexes
Here we are mainly concerned with the geometric
disposition of ligands surrounding transition metal ion
focusing on how the d-orbitals interact with ligands.
Clearly, energies of degenerate orbitals will be enhanced or
depressed depending on the geometry of the complexes.
In addition, the extent of energy level splitting will depend
on the charge on metal ions and ligands. A series of ligands
are shown below rated according to the strength of binding.
The strength of ligand binding interaction has important
consequences in paramagnetic properties of the transition
metal ions.
What is the spin state iron in octahedral complexes?
Iron atom in octahedral geometry has its five d-orbitals
split as shown below.
The structure on the left has a lower splitting so the fiveelectron configuration is such that all the electrons occupy
separate orbitals. Of course, this involves an energy cost;
2E, but this compensated for by the reduction in the
electron-electron repulsion interactions. This is because
H2O is a weak ligand. On the other hand, if we consider a
strong ligand such as CN-, the splitting on the two sets of
energy levels is greater. Now the minimum energy
configuration of the system involves electron pairing as
shown in the right figure.
These simple energetic considerations have dramatic
influence on the magnetic properties of the complex. The
high spin complex, in the left figure, has all the spins
unpaired hence the Fe in this state exhibits strong
paramagnetism, which is directly related to the number of
unpaired electron present in a molecule.
Intra-molecular geometric interactions
As we discussed in the context harmonic oscillator problem,
stretching or compression of bonds can be energetic costly. If
we consider a simple Hooks law for stretching a single or a
double bond we find that for low quantum numbers. Similarly
Hooks law is a
good
approximation for
the bond bending in
a three-carbon atom
system as shown
below. However
energies involved
are much smaller.
Owing to zero point
energy the
contributions from
the vibrational
modes cannot be
simply ignored.
Rotation around a bond
Just as hooks law potential is a good approximation for the
bond bending/stretching, simple sine wave potential is a good
approximation for the rotation around single bond
Although the energy minima around carbon bond are shown
above to have identical energy at minimum, in reality, the trans
configuration generally has lower energy.
The structure of the potential also critically depends on pendent
groups attached.
Rotation around a double Bond
Similarly, rotation around a double bond can be considered.
Since the rotation requires breaking a pi bond the energies
needed to overcome the potential barriers are higher,
amides for example show:
This rotation is of importance for the geometric stability of
protein superstructure. Such empirical formulae for the
potential are extremely useful in the calculation of
minimum energy structures, for example in the molecular
mechanics calculations.
Non-covalent interactions: Coulomb interaction
Coulomb potential between two charges is given by:
As we have seen before, the molecular orbital method
allows us to calculate the probability density at a given
atom depending on which molecular orbitals are occupied.
As an example consider the following molecule:
Thus to calculate coulomb energy between to such
molecules we have to carry out a sum over all the binary
interactions between charges on both molecules. Peter
Debye who suggested we should also consider the dipole
moment of such a molecule introduced great simplification.
It is defined as q.r where q is the average positive charge
located at distance r from the average –ve charge. This dipole
moment accounts for the non-centro-symmetric distribution of
charges in molecules.
Dipoles
To calculate the net dipole moment of molecule we simply
evaluate sum of q.x,q.y,q.z for all atoms in molecule. For the
above molecule:
Since the dipole moment is a vector we can calculate the
magnitude and the orientation of the dipole moment from the
standard vector algebra:
   2x   y2 tan  
y
y
Fundamentally, dipole moment characterizes the polarity of
molecules. For centrosymmetric molecules the net dipole
moment vanishes, for example CH4 or CCl4. One advantage
of this concept is that the dipole moment can be
experimentally measured using a capacitance measurement
technique. The difficulty in applying such concept to real
biological molecules is the effect of solvent.
Dipole-dipole interactions.
The interaction between the two dipoles is given by:
Here, R12 is the distance between the two dipoles. Since the
dipoles are vectors we have to consider their dot products.
This is because the potential is a measure of energy, which is
a scalar quantity. The dipolar interaction decreases as the
distance between the dipoles is increased (-3 rd power law).
The contribution of the dipolar energy can be positive,
negative or zero, depending on the relative orientation of the
dipoles. Consider following examples:
London interaction: Induced dipole-dipole interaction
This is important where polarizable molecules (such as
benzene) are involved. Presence of a strong dipole in the
vicinity of a polarizable molecule leads to an induction of
dipole moment. This interaction is always negative and was
studied by London:
Notice the interaction is much shorter range than the dipoledipole interaction we considered previously; since it varies
inversely as the sixth power with respect relative separation of
molecules. Furthermore as r0 this interaction decreases
dramatically, suggesting a molecular fusion. It was van der
Waal who advocated an even a shorter-range repulsive
interaction with 1/r12 dependence to counter the effect of
London interaction. Thus, the net interaction, London+Van
der Waal, looks like as shown in the figure to the right. This is
the famous 6-12 potential. The position of the minimum gives
the Van der Waal radius of a molecule.