Polarization

One important limitation of current molecular mechanics methods is that the electrostatic properties cannot change in response to changes in the molecular environment, structure or interactions - the atomic charges are fixed and unchanging.

 

In reality, applying an electric field (e.g. due to surrounding molecules) will cause a change in the electronic distribution of a molecule - it will be polarized.

 

A dipole, m, will be induced, proportional to the induced field E:

m = aE

where a is the polarizability. 

 

·     One way to include polarizability effects is to allow induced dipoles on every atom, by associating a polarizability with each atom, and calculating the electric field at each atom. This incurs a considerable extra computational expense (particularly because all the dipoles should be calculated iteratively until they are self-consistent), but should provide a better model.

 

·     Development of polarizable MM potential functions is a very active area of current research - the next generation of organic/biomolecular potential functions will include polarization.

 

Many-body effects

The molecular mechanics potential function given above calculates the electrostatic and van der Waals energies as a sum of pairwise interactions, i.e. by adding together the interaction energies of all pairs of atoms.

 

·     However, in reality, the interaction energy of e.g. three molecules is not equal to the sum of the three separate interactions.

 

·     Many-body effects (due to the association of more than two molecules) should be included. Polarization, as described above, is an example.

 

·     Accurate calculations show that 3-body interactions also contribute to the dispersion energy, but this is a relatively small effect (e.g. 10% of the lattice energy of crystalline argon).

 

·     More importantly, including many-body effects would significantly increase the computer time required for a calculation - the calculation of non-bonded interactions is the most demanding part of a MM calculation on a large molecule, even with only pairwise interactions calculated (the number of pair interactions to be calculated is N(N-1)/2, where N is the number of atoms, e.g. 499500 interactions for a system of only 1000 atoms), and the introduction of three-body interactions would increase the computational requirements enormously.

 

MM parameterization