Dimer method

The dimer method [11] is an alternative approach to transition state optimisation in DL-FIND which does not require evaluation of a Hessian and so is more suited to large-scale systems. A dimer optimisation involves the calculation of two close-lying points on the potential energy surface (the `dimer') separated by a fixed distance. In each optimisation cycle, the dimer is first rotated around its midpoint to minimise the sum of the energies of the endpoints, which aligns the dimer along the softest vibrational mode (the mode of the Hessian with the lowest eigenvalue). The dimer is then translated to maximise the energy along the direction of this mode while minimising the energy in all directions perpendicular to it.

In the standard dimer optimisation method implemented in DL-FIND, it is possible to weight individual coordinates when calculating the dimer vector and the rotational force on the dimer. By setting a weight of zero, coordinates can be excluded from the rotation step altogether, so that they are simply minimised during the translation step. The excluded coordinates act like an environment which is relaxed during the optimisation.

It is therefore natural to extend the weighting mechanism to implement a microiterative form of dimer optimisation. As in microiterative P-RFO, the system is divided into an inner region that is optimised to a saddle point and an outer region that is relaxed. The coordinates list is ordered first by image, then by region and finally by residue if applicable.

The dimer weights of the outer region coordinates are set to zero so that they take no part in the transition state optimisation. A macroiterative iteration consists of a rotation of the inner region dimer, followed by an inner region midpoint translation step. The microiterative loop then takes place, which relaxes the environment as in microiterative P-RFO. In total three L-BFGS optimisers are used (for dimer rotation, dimer translation and environment minimisation respectively) compared to two for the standard optimisation. The environment minimisation corresponds to the midpoint of the dimer and so only one set of coordinates is used in the microiterative cycles.

The microiterative dimer method was tested on the same solvated glycine transition state optimisation used for the P-RFO method. The same QM and MM setup was used and an ESP fit was used during the microiterations. Excellent agreement was seen for the optimised transition state energy between standard and microiterative dimer optimisations, between Cartesian and HDLC optimisations, and between microiterative dimer and microiterative P-RFO.