Multiobjective genetic algorithms for multiscaling excited state direct dynamics in photochemistry

This paper studies the effectiveness of multiobjective genetic and evolutionary algorithms in multiscaling excited state direct dynamics in photochemistry via rapid reparameterization of semiempirical methods. Using a very limited set of ab initio and experimental data, semiempirical parameters are reoptimized to provide globally accurate potential energy surfaces, thereby eliminating the need for full-fledged ab initio dynamics simulations, which are very expensive. Through reoptimization of the semiempirical methods, excited-state energetics are predicted accurately, while retaining accurate ground-state predictions. The results show that the multiobjective evolutionary algorithm consistently yields solutions that are significantly better---up to 230% lower error in the energy and 86.5% lower error in the energy-gradient---than those reported in the literature. Multiple high-quality parameter sets are obtained that are verified with quantum dynamical calculations, which show near-ideal behavior on critical and untested excited state geometries. The results demonstrate that the reparameterization strategy via evolutionary algorithms is a promising way to extend direct dynamics simulations of photochemistry to multi-picosecond time scales.

[1]  J. Stewart Optimization of parameters for semiempirical methods I. Method , 1989 .

[2]  Martin Pelikan,et al.  Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms , 2010, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[3]  David E. Goldberg,et al.  Genetic Programming for Multiscale Modeling , 2004 .

[4]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[5]  A. L. Thompson,et al.  Excited state direct dynamics of benzene with reparameterized multi-reference semiempirical configuration interaction methods , 2004 .

[6]  M. Dewar,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[7]  Todd J. Martínez,et al.  Ab Initio Quantum Molecular Dynamics , 2002 .

[8]  D. Goldberg,et al.  Modeling tournament selection with replacement using apparent added noise , 2001 .

[9]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[10]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[11]  Todd J. Martínez,et al.  Photochemistry from first principles and direct dynamics , 2005 .

[12]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.

[13]  Jane Michelle Owens Theoretical Studies of the Solvation, Dynamics, and Photochemistry of Ethylene, Retinal Protonated Schiff Base, Oligocellulose, and Gd(III) Clusters , 2004 .

[14]  David E. Goldberg,et al.  Genetic programming for multitimescale modeling , 2005 .

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  T. Martínez,et al.  Ab Initio Multiple Spawning: Photochemistry from First Principles Quantum Molecular Dynamics , 2000 .

[17]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[18]  J. Stewart Optimization of parameters for semiempirical methods. III Extension of PM3 to Be, Mg, Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi , 1991 .

[19]  Samir W. Mahfoud Population Size and Genetic Drift in Fitness Sharing , 1994, FOGA.

[20]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

[21]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[22]  Todd J. Martínez,et al.  Photodynamics of ethylene: ab initio studies of conical intersections , 2000 .

[23]  Ingolf V. Hertel,et al.  Internal conversion in highly excited benzene and benzene dimer: femtosecond time-resolved photoelectron spectroscopy , 1997 .

[24]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[25]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms: Motivation, Analysis, and First Results , 1989, Complex Syst..