Empirical valence bond models for reactive potential energy surfaces: a parallel multilevel genetic program approach.

We describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of one-dimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3-hydroxy-gamma-pyrone in gas phase and protic solvent.

[1]  N. Ernsting,et al.  Excited-state intramolecular proton transfer in 3-hydroxylflavone isolated in solid argon: fluoroescence and fluorescence-excitation spectra and tautomer fluorescence rise time , 1987 .

[2]  J. Pople,et al.  Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures , 1965 .

[3]  M. Robb,et al.  Excited States of Conjugated Hydrocarbons Using the Molecular Mechanics - Valence Bond (MMVB) Method: Conical Intersections and Dynamics , 2006 .

[4]  Richard Dawes,et al.  Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points. , 2007, The Journal of chemical physics.

[5]  A. Tebbe,et al.  The First Synthesis of a Daphnane Diterpene: The Enantiocontrolled Total Synthesis of (+)-Resiniferatoxin , 1997 .

[6]  A. Douhal,et al.  Tuning the mechanism of proton-transfer in a hydroxyflavone derivative , 2003 .

[7]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[8]  J. Porco,et al.  Enantioselective photocycloaddition mediated by chiral Brønsted acids: asymmetric synthesis of the rocaglamides. , 2006, Journal of the American Chemical Society.

[9]  A. Bader,et al.  Proton transfer in 3-hydroxyflavone studied by high-resolution 10 K laser-excited Shpol'skii spectroscopy , 2002 .

[10]  D. Mcmorrow,et al.  Intramolecular excited-state proton transfer in 3-hydroxyflavone. Hydrogen-bonding solvent perturbations , 1984 .

[11]  A. Mishra,et al.  Ground- and Excited-state Proton Transfer Reaction of 3-Hydroxyflavone in Dimyristoylphosphatidylcholine Liposome Membrane¶ , 2004 .

[12]  Jiali Gao,et al.  Potential energy functions for an intramolecular proton transfer reaction in the ground and excited state , 2007 .

[13]  Aaron Lefohn,et al.  A Multistate Empirical Valence Bond Approach to a Polarizable and Flexible Water Model , 2001 .

[14]  Titus V. Albu,et al.  Efficient Molecular Mechanics for Chemical Reactions: Multiconfiguration Molecular Mechanics Using Partial Electronic Structure Hessians , 2004 .

[15]  A. Demchenko,et al.  Electrochromic modulation of excited-state intramolecular proton transfer: the new principle in design of fluorescence sensors. , 2002, Journal of the American Chemical Society.

[16]  P. Barbara,et al.  The proton-transfer kinetics of 3-hydroxyflavone: solvent effects , 1985 .

[17]  Juan R. Rabuñal,et al.  Multilevel Genetic Algorithm for the Complete Development of ANN , 2001, IWANN.

[18]  Yang Song,et al.  Developing ab initio quality force fields from condensed phase quantum-mechanics/molecular-mechanics calculations through the adaptive force matching method. , 2008, The Journal of chemical physics.

[19]  Gregory A. Voth,et al.  Multistate Empirical Valence Bond Model for Proton Transport in Water , 1998 .

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

[21]  Dmitrii E. Makarov,et al.  FITTING POTENTIAL-ENERGY SURFACES : A SEARCH IN THE FUNCTION SPACE BY DIRECTED GENETIC PROGRAMMING , 1998 .

[22]  H. Schlegel,et al.  Accurate reaction paths using a Hessian based predictor-corrector integrator. , 2004, The Journal of chemical physics.

[23]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[24]  John R. Koza,et al.  Genetic Programming III: Darwinian Invention & Problem Solving , 1999 .

[25]  Donald G. Truhlar,et al.  Multiconfiguration molecular mechanics algorithm for potential energy surfaces of chemical reactions , 2000 .

[26]  H. Schlegel,et al.  Empirical valence bond models for reactive potential energy surfaces. II. Intramolecular proton transfer in pyridone and the Claisen reaction of allyl vinyl ether , 2007 .

[27]  G. Voth,et al.  Distributed Gaussian Valence Bond Surface Derived from Ab Initio Calculations. , 2009, Journal of chemical theory and computation.

[28]  Gregory A Voth,et al.  An improved multistate empirical valence bond model for aqueous proton solvation and transport. , 2008, The journal of physical chemistry. B.

[29]  H. Schlegel,et al.  Empirical Valence-Bond Models for Reactive Potential Energy Surfaces Using Distributed Gaussians. , 2006, Journal of chemical theory and computation.

[30]  Donald G. Truhlar,et al.  Molecular Mechanics for Chemical Reactions: A Standard Strategy for Using Multiconfiguration Molecular Mechanics for Variational Transition State Theory with Optimized Multidimensional Tunneling , 2001 .

[31]  Arieh Warshel,et al.  An empirical valence bond approach for comparing reactions in solutions and in enzymes , 1980 .

[32]  P. Matousek,et al.  Ultrafast measurements of excited state intramolecular proton transfer (ESIPT) in room temperature solutions of 3-hydroxyflavone and derivatives , 2001 .

[33]  L. Raff,et al.  Cis-->trans, trans-->cis isomerizations and N-O bond dissociation of nitrous acid (HONO) on an ab initio potential surface obtained by novelty sampling and feed-forward neural network fitting. , 2008, The Journal of chemical physics.

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

[35]  A. Bader,et al.  Excited State and Ground State Proton Transfer Rates of 3-Hydroxyflavone and Its Derivatives Studied by Shpol'skii Spectroscopy: The Influence of Redistribution of Electron Density† , 2004 .

[36]  Gregory A. Voth,et al.  A second generation multistate empirical valence bond model for proton transport in aqueous systems , 2002 .

[37]  John J. Grefenstette,et al.  Genetic algorithms and their applications , 1987 .

[38]  D. Mcmorrow,et al.  Proton-transfer spectroscopy of 3-hydroxychromones: extreme sensitivity to hydrogen-bonding perturbations , 1983 .

[39]  N. Ernsting,et al.  Excited-state intramolecular proton transfer in jet-cooled 3-hydroxyflavone. Deuteration studies, vibronic double-resonance experiments, and semiempirical (AM1) calculations of potential-energy surfaces , 1994 .

[40]  H. Metiu,et al.  Using Genetic Programming To Solve the Schrödinger Equation , 2000 .

[41]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[42]  Chris Walshaw,et al.  A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning , 2004, J. Glob. Optim..

[43]  B. Braams,et al.  Ab initio global potential-energy surface for H5(+) --> H3(+) + H2. , 2005, The Journal of chemical physics.

[44]  P. Barbara,et al.  Structural effects on the proton-transfer kinetics of 3-hydroxyflavones , 1985 .

[45]  J. Porco,et al.  A biomimetic approach to the rocaglamides employing photogeneration of oxidopyryliums derived from 3-hydroxyflavones. , 2004 .

[46]  Gregory A Voth,et al.  A linear-scaling self-consistent generalization of the multistate empirical valence bond method for multiple excess protons in aqueous systems. , 2005, The Journal of chemical physics.

[47]  H. Schlegel,et al.  Using Hessian Updating To Increase the Efficiency of a Hessian Based Predictor-Corrector Reaction Path Following Method. , 2005, Journal of chemical theory and computation.

[48]  P. Chou,et al.  Temperature-dependent study of the ground-state reverse proton transfer of 3-hydroxyflavone , 1989 .

[49]  John R. Koza,et al.  Routine human-competitive machine intelligence by means of genetic programming , 2004, SPIE Optics + Photonics.

[50]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

[51]  Kwang S. Kim,et al.  Theory and applications of computational chemistry : the first forty years , 2005 .

[52]  M. Malshe,et al.  Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feedforward neural networks. II. Numerical application of the method. , 2007, The Journal of chemical physics.

[53]  B. Schwartz,et al.  Direct observation of fast proton transfer: femtosecond photophysics of 3-hydroxyflavone , 1992 .

[54]  Jacob Cohen,et al.  A power primer. , 1992, Psychological bulletin.

[55]  Arieh Warshel,et al.  Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches , 1993 .

[56]  Jiali Gao,et al.  Combined Quantum Mechanical and Molecular Mechanical Methods , 1999 .

[57]  Jörg Homberger,et al.  A Parallel Genetic Algorithm for the Multilevel Unconstrained Lot-Sizing Problem , 2008, INFORMS J. Comput..

[58]  John R. Koza,et al.  Genetic Programming IV: Routine Human-Competitive Machine Intelligence , 2003 .

[59]  William H. Miller,et al.  An empirical valence bond model for constructing global potential energy surfaces for chemical reactions of polyatomic molecular systems , 1990 .