Optimisation on crystals

The lattice energy of a crystal is given as a sum of repulsive, attractive, and Coulombic interactions. We have chosen not to optimise charge parameters on lattice observables. There are two main reasons for that. 

Firstly, the microscopic dielectric constant is always uncertain, so that the charge parameters would be uncertain. For example, Wil- 

Secondly, heteroatoms and different bond types would cause many difficulties. 

Therefore, when optimising on lattices observables, we have until now chosen to optimise only the parameters for repulsive and attractive interactions. To optimise on lattice energy, we use crystals 

In addition, in flexible molecules we have to take into account the difference of the strain energy in the crystalline and gas phases. This is usually small, and can be approximated by the difference calculated by the initial potential energy function. The goodness of this approximation is easily checked using the final potential energy function. 

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The next big step came in 1970 with optimisation on crystal pro-parties. The new potential energy function had the same form as the previous, and many parameters for intra-molecular interactions had changed very little- Angle-torsion cross terms were added, and a Lennard-Jones 9-6 form was used. For some interactions, different parameters were used for methyl and methylene groups. Altogether 29 parameters were employed. 

In optimisation on crystal properties, the first observables used were the unit cell dimensions, one to six data, which for technical reasons are concatenated to the conformational observables. Next, lattice energies were introduced, so far in a limited number. The use of other properties is being considered. 

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