The Prototype Molecule Approach

The prototype molecule (or cluster ) approach to the quantum chemical treatment of extended systems has proved to be a valuable tool, especially if the chemical phenomenon of interest is mainly of local character. The prototype molecule models were used e.g. in the quantum chemistry of silicates [58], zeolites [59] and enzymes [14]. In the solid state, quantum chemistry calculations on prototype molecules [60] represent an important alternative to crystal orbital type methods. Although these latter calculations may be very important as starting points even for the description of local phenomena which violate the exact translational symmetry, the cluster approaches have the advantage of providing a direct space representation of the wave function. 

Nevertheless, the prototype molecule models raise again the problem of the appropriate definition of a relevant part of the extended system. Moreover, if long-range electrostatic forces play an important role, their explicit consideration may also be unavoidable. 

As concerns the definition of the prototype molecule, at least two main cases can be distinguished. If the extended system consists of subsystems which are held together by nonbonded interactions (multipolar electrostatic forces, induction and dispersion interactions), it is possible to designate closed shell chemical subsystems without breaking covalent chemical bonds, and the prototype molecules can be the constituent molecules themselves. The situation becomes much more complicated, when the subunits are held together by covalent interactions, chemical bonds. In this case there are no natural frontiers for the representative subsystems, and it is unavoidable that a certain number of chemical bonds are broken. The prototype molecules are formed by saturating the broken (dangling) bonds by some appropriately selected atoms. 

In the context of semiempirical procedures several attempts have been made to use pseudoatoms which mimic the hybridization and electronegativity of the usually polyvalent atom at the frontier of the cluster [61-63]. 

Another possibility is to saturate dangling bonds of the representative cluster with hydrogen atoms. The prototype molecule thus obtained is relatively easy to handle with standard quantum chemical methods, and one can hope that the artefact effects are small or negligible, if the model system is sufficiently large. In a few cases, comparison of the electronic charge density maps in the finite models saturated by hydrogen atoms and the similar maps in accurate three-dimensional models confirm the use of prototype molecules [64]. 

---

In the prototype molecule approach the dangling bonds are usually saturated by hydrogen atoms. This procedure, although not without controversy, offers a simple recipe for obtaining closed shell model molecules, with well-defined electronic states, easily tractable with quantum chemical methods. 

---