Accurate Semi-Empirical Quantum Chemistry via Evolutionary Algorithms

1. Pareto “nose” Accurate Semi-Empirical Quantum Chemistry via Evolutionary Algorithms • 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). OBJECTIVE: Accelerate Quantum Chemistry (QC) simulations of chemical and excited-states reactions by +1000 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! STRATEGY:Using a well-known empirical potential (MP3) we optimize two objectives (error of energy and energy-gradient)for ethylenefrom 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. * Awarded Silver Medal in Human Competitive Design at Genetic and Evolutionary Computation Conference 2006

2. PUBLICATIONS 2005-2006: • • 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, 085438-9 (2005) • • K. Sastry, H.A. Abbass, D.E. Goldberg, D.D. Johnson, "Sub-structural Niching in Estimation of Distribution Algorithms," GECCO, 671-678 (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) • 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.