Developing a Force Field

Molecular Mechanics

Experimental One Dimensional PES

• Quantum mechanics tells us that vibrational energy levels are quantized, and that the energy separations between levels are dictated by the shape of the potential within which vibration takes place (i.e., the 1-D PES). By observing the allowed (above, with rotational information too) and forbidden (not shown) transitions of HCl and its isotopes of isomers (which have different vibrational energy levels by virtue of having different reduced masses) the shape of the PES can be deduced over a large range.

Result from lots of Experiments

Mathematically, how do we build the curve?

• Simplest idea is a polynomial function expanded about r (by the nature of the spectroscopy, we know most about the curve in the region of r)

Additional things to think about• Strain is a phenomenon associated with individual components of a

molecular geometry. • You can have many types of molecular strain, bond, angle, torsional

strain• Ideal values of bond lengths, angles and torsions depend on more

that just the atomic number, there are more than one “type” of the same atom. Think sp3 C vs sp2 C

• A force field is defined by its atom types, its functions for computing strain and the ideal constraints that appear in those functions

• Force fields can get very complicated very quickly (even though the calculations are “easy” given that the classification of atoms becomes more and more complex

Constants Needed!

• The more atom types, the better the force field can predict reality. – MM4 force field has over --- atom types

• Every atom type requires the definition of a force constant, and an equilibrium length between it and every other atom defined in the force field.

• The number of bond stretch parameters goes up as N2 where N is the number of atom types

• Assignment of parameters comes from experimental data or from high level QM calculations.

Bending

𝑈 (𝜃𝐴𝐵𝐶 )=12 𝑘𝐴𝐵𝐶¿

Torsion

Computer Power Rules

• Assign an atom type to all atoms• Assign which atoms are bonded to each other

(can be explicit, or based on some set distance algorithm)

• Look up force constants, equilibrium values, phase angles etc. for all bonds, angles and torsions (are we missing any?)

• Compute energy in a small fraction of a second on any decent computer

What about non-bonded interactions?

Electrostatics

Other Electrostatic Possibilities

Force Field Validation

• Collect experimental data (structural and energetic information is the more useful)

• Define an error function that balances what is tolerable for errors

• Vary the parameters and functional forms of the force field to minimize the error function

• Lock all the parameters and functional forms into stone (give it a name “MM3” “MMFF” and publish it (or sell it)

A word of Warning• Selection of a force field should be made based on how similar

your molecule is to those used to parameterize the force field.• Force fields are bad for reactions and good for structures and

energies– Once bonds are defined, they cannot break in a harmonic force field,

nor can new ones form• If you start with a bad guess structure, there is no guarantee

that the nearest minimum will be a chemically meaningful one– You must be smarter than your computer

• All of these issues can be corrected, and thus new force fields are being developed as we speak