Optimization of transition state structures using genetic algorithms

Geometry optimization of transition state structures (first order saddle points) has proven to be a challenging problem in theoretical chemistry. Despite many attempts, no method has been developed that can guarantee convergence to a transition structure. The well-known method of genetic algorithms (GA's) was adapted for this problem, and designed to seek points on a potential energy surface with a zero gradient norm and one negative eigenvalue in the Hessian. A description of genetic algorithms and the software written to optimize first order saddle points is given. The software developed was tested on a mathematical function having minima, maxima, and first order saddle points. The method was capable of finding all of the saddle points, as the results presented demonstrate. Optimization of various transition state structures was then attempted. Although the current genetic algorithm software requires long run times, the algorithm will preferentially seek first order saddle points, weeding out any other stationary points. Thus, the initial guess at the optimum is not as critical as with other methods, and as well, multiple saddle points can be found.