The standard P-RFO optimisation method in DL-FIND requires a full Hessian calculation and is therefore not appropriate for systems with many degrees of freedom. The HDLCOpt implementation of P-RFO was more flexible in that a core region could be optimised to a saddle point while the environment was relaxed using the L-BFGS optimisation algorithm. This scheme is similar to microiterative minimisation, as the gradient of the environment must be optimised to zero after every P-RFO step [10].

In DL-FIND, microiterative P-RFO optimisation has been implemented by splitting the system into an inner region optimised by P-RFO and an outer region optimised by L-BFGS. The outer region is optimised using the routines established for microiterative minimisation. As in microiterative minimisation, an ESP fit can be used to relax the environment after each P-RFO step providing that the QM region is contained wholly within the inner region.

The P-RFO and Hessian evaluation routines were modified so that they operated on the subset of coordinates defined in the inner region. This differs from the minimisation scheme, where the macroiterative optimiser operates over the whole system, because in transition state optimisation the inner and outer regions are optimised differently. It is therefore important in the P-RFO case that the environment is fully optimised after each step, particularly towards the end of the optimisation, as the macroiteration steps will not be accurate otherwise [10]. In practice this means that a low maximum for the number of microiterations should not be used.

In standard P-RFO, `soft' modes are identified corresponding to rotations and translations of the system which are projected out so they do not hinder convergence. In microiterative optimisation, however, this is not appropriate as rotations or translations of the inner region with respect to the outer region may be necessary for correct convergence. The soft mode algorithms are therefore disabled for microiterative optimisation.

The microiterative P-RFO method was tested for correctness using the same solvated glycine system used for minimisation. In the P-RFO case the transition state between glycine and its zwitterionic form was optimised (Figure 3).

Figure 3: Optimised transition state of solvated glycine and its zwitterionic form.

The QM region was consisted of the glycine molecule and was calculated with MNDO using the AM1 Hamiltonian. The inner (macroiterative) region was defined to be equal to the QM region. The outer environmental region consisted of 62 water molecules described with the TIP3P force field, of which 13 were active. ESP fitting was used during the microiterations.

Although standard and microiterative transition state optimisations are not directly comparable (because the environment is part of the saddle point optimisation in the standard case), a well-chosen inner region should result in good agreement between the two, all other things being equal, because transition states are generally fairly localised. In the solvated glycine case there was an excellent agreement in optimised energies between the standard and microiterative runs, and between optimisation in Cartesian and HDLC coordinates, giving confidence that the implementation is correct.

Tom Keal 2013-06-04