## P=n.nn

The effect of an applied pressure on a solid can be simulated by P=n.nn, where n.nn is the pressure in Newtons per square meter, or P=n.nnGpa, where n.nn is the pressure in Gigapascals.

Typical bulk moduli are in the order of 10 - 700 GPa (gigapascals), and typical pressures should be n.nn = 1.D9 to n.nn =1.D10 NM-2. In general, solids are subjected to compression only, not tension, therefore the sign of n.nn should normally be positive, e.g. P=2.D9 or P=2.0GPa, however, for mechanically strong solids, negative pressures, even quite large pressures, can be used.

As the pressure rises, the calculated heat of formation will become more positive because energy must be used in generating the volume of the solid under pressure. Geometry optimization minimizes the total heat of formation =ΔHf of the solid + energy due to volume. The final geometry is then the optimized geometry at equilibrium with that pressure.

Bulk moduli, B, in Pascals, can be calculated from the change in unit cell volume at zero pressure (Vol(0)) to the unit cell volume under a pressure of P=n.nn (Vol(n.nn ) from:

B=n.nn*Vol(0)/(Vol(0)-Vol(n.nn))

For polymers, the applied strain is in units of Newtons per mole. That is, for one mole of polymer chains, stacked side by side, the applied force is n.nn Newtons. Suitable values for P=n.nn are in the order of 1013 Newtons. In general, polymers are subjected to tension only, not compression, therefore the sign of n.nn should normally be negative, e.g. P=-2.D13 .

Useful conversion factors are:

1 GPa = 109N.M-2 = 1010dynes.cm-2 = 1016erg.m-3

1 GPa = 6.0221367/(4.184*10)kcal.mol-1.Angstrom-3 = 0.14393kcal.mol-1.Angstrom-3.

so a unit cell of  100A3 under 1 GPa would have an energy equivalent of 14.39 kcal.mol-1.