The Materials Computation Center, University of Illinois Duane Johnson and Richard Martin (PIs), NSF DMR OBJECTIVE: Accelerate Quantum Chemistry (QC) simulations of chemical and excited-states reactions by times by creating semi- empirical potentials approaching accuracy of high-level methods. APPROACH: Use machine-learning methods based upon efficient, Competent Genetic Algorithms (eCGA) and multi-objective optimization (MO). WHY IT MATTERS: With fast, but accurate semi- empirical potentials, we can search for new drugs or critical biological reactions 100 – 1000 times faster! Accurate Semi-Empirical Quantum Chemistry via Evolutionary Algorithms STRATEGY: Using a well-known empirical potential (MP3) we optimize two objectives (error of energy and energy-gradient) for ethylene from a few structures (excited-states) calculated from high- level QC (ab initio CASSCF) to make predictions of excited-states not in learning set. MP3 potential has 11 parameters just for Carbon. Pareto “nose” RESULT: (upper) Best solutions (circles) and their errors in energy and energy-gradient – the Pareto front. Figure (lower) shows 3 excited-state energies for the optimized MP3 potentials and “exact” answers (dashed lines), not used in fit! Excellent energies are found. The 11 parameters found for each solutions can be used in other molecules of carbon (transferability). * Awarded Silver Medal in Human Competitive Design at Genetic and Evolutionary Computation Conference 2006

The Materials Computation Center, University of Illinois Duane Johnson and Richard Martin (PIs), NSF DMR OUTLOOK: We are completing analysis for ethlyene and benzene and details of why “no-dominate” Pareto front and eCGA are necessary to do well, as opposed to standard GA’s being used in chemistry today. Our primary objectives are: to show utility of MO-GA using eCGA. to show potential transferability of potentials to show how well the cusp surfaces of the excited molecules are by semiempirical potentials compared to high-level QC. to show the importance of the “non-domininant Pareto fronts”, “crowding distances”, and “tournament selection” to set rank of solutions in getting good results from MO-GA. PUBLICATIONS : K Sastry, D.D. Johnson, Alexis L. Thompson, D.E. Goldberg, T.J. Martinez, J. Leiding, and Jane Owens, "Multiobjective Genetic Algorithms for Multiscaling Excited- State Dynamics in Photochemistry," GECCO (2006) *Silver Medal, Best Paper in real-world track. K. Sastry, D.D. Johnson, Alexis L. Thompson, D.E. Goldberg, "Optimization of Semiempirical Quantum Chemistry Methods via Multiobjective Genetic Algorithms: Accurate Photochemistry for Larger Molecules and Longer Time Scales" (invited) Materials and Manufacturing Processes (2006), to appear. K. Sastry, D.D. Johnson, and D.E. Goldberg, "Scalability of a Hybrid Extended Compact Genetic Algorithm for Ground State Optimization of Clusters,” (invited) Materials and Manufacturing Processes (2006), to appear. K. Sastry, D.D. Johnson, D.E. Goldberg, and P. Bellon, "Genetic programming for multitimescale modeling," Phys. Rev. B 72, (2005) K. Sastry, H.A. Abbass, D.E. Goldberg, D.D. Johnson, "Sub-structural Niching in Estimation of Distribution Algorithms," GECCO, (2005). PRINCIPAL INVESTIGATORS: D. D. Johnson (MSE), TJ. Martinez (Chemistry), D.E. Goldberg (IESE) Graduate Students: Kumara Sastry (IEE/MSE) and Alexis Thompson, Jeff Leiding, and Jane Owens (Chemistry)