A Multi-Objective Approach to Force Field Optimization: Structures and Spin State Energetics of d6 Fe(II) Complexes

The next generation of force fields (FFs), regardless of the accuracy of the potential energy representation, will always have parameters that must be fitted in order to reproduce experimental and/or ab initio data accurately. Single objective methods have been used for many years to automate the obtaining of parameters, but this leads to ambiguity. The solution depends on the chosen weights and is therefore not unique. There have been few advances in solving this problem, which thus remains a major hurdle for the development of empirical FF methods. We propose a solution based on multi-objective evolutionary algorithms (MOEAs). MOEAs allow the FF to be tuned against the desired objectives and offer a powerful, efficient, and automated means to reparameterize FFs, or even discover the parameters for a new potential. Here, we illustrate the application of MOEAs by reparameterizing the ligand field molecular mechanics (LFMM) FF recently reported for modeling spin crossover in iron-(II)-amine complexes (Deeth et al. J. Am. Chem. Soc. 2010, 132, 6876). We quickly recover the performance of the original parameter set and then significantly improve it to reproduce the geometries and spin state energy differences of an extended series of complexes with RMSD errors in Fe-N and N-N distances reduced from 0.06 angstrom to 0.03 angstrom and spin state energy difference RMSDs reduced from 1.5 kcal mol(-1) to 0.2 kcal mol(-1). The new parameter sets highlight, and help resolve, shortcomings both in the non-LFMM FF parameters and in the interpretation of experimental data for several other Fe(II)N-6 amine complexes not used in the FF optimization.