Finding Chemical Reaction Paths with a Multilevel Preconditioning Protocol

Finding transition paths for chemical reactions can be computationally costly owing to the level of quantum-chemical theory needed for accuracy. Here, we show that a multilevel preconditioning scheme that was recently introduced (Tempkin et al. J. Chem. Phys.2014, 140, 184114) can be used to accelerate quantum-chemical string calculations. We demonstrate the method by finding minimum-energy paths for two well-characterized reactions: tautomerization of malonaldehyde and Claissen rearrangement of chorismate to prephanate. For these reactions, we show that preconditioning density functional theory (DFT) with a semiempirical method reduces the computational cost for reaching a converged path that is an optimum under DFT by several fold. The approach also shows promise for free energy calculations when thermal noise can be controlled.

[1]  A. Warshel,et al.  Addressing open questions about phosphate hydrolysis pathways by careful free energy mapping. , 2013, The journal of physical chemistry. B.

[2]  G. Henkelman,et al.  Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points , 2000 .

[3]  Bo Qi,et al.  Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations. , 2014, The Journal of chemical physics.

[4]  G. Henkelman,et al.  A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives , 1999 .

[5]  Ioannis G Kevrekidis,et al.  Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations. , 2006, The Journal of chemical physics.

[6]  Eric Vanden-Eijnden,et al.  Revisiting the finite temperature string method for the calculation of reaction tubes and free energies. , 2009, The Journal of chemical physics.

[7]  E. V. Vetoshkin,et al.  Tunneling splittings in vibrational spectra of non-rigid molecules: IX. Malonaldehyde and its isotopomers as a test case for fully coupled multidimensional tunneling dynamics , 2000 .

[8]  Juan C. Meza,et al.  Motif-based Hessian matrix for ab initio geometry optimization of nanostructures , 2006 .

[9]  Marat Valiev,et al.  Phosphorylation reaction in cAPK protein kinase-free energy quantum mechanical/molecular mechanics simulations. , 2007 .

[10]  M. Karplus,et al.  Conjugate peak refinement: an algorithm for finding reaction paths and accurate transition states in systems with many degrees of freedom , 1992 .

[11]  Arieh Warshel,et al.  Why nature really chose phosphate , 2013, Quarterly Reviews of Biophysics.

[12]  V. Schramm,et al.  Transition Path Sampling Study of the Reaction Catalyzed by Purine Nucleoside Phosphorylase , 2008, Zeitschrift fur physikalische Chemie.

[13]  Dominik Marx,et al.  Mechanistic insights into the hydrolysis of a nucleoside triphosphate model in neutral and acidic solution. , 2012, Journal of the American Chemical Society.

[14]  Simone Morpurgo,et al.  Critical test of PM3-calculated proton transfer activation energies: a comparison with ab initio and AM1 calculations , 1998 .

[15]  M. Parrinello,et al.  Well-tempered metadynamics: a smoothly converging and tunable free-energy method. , 2008, Physical review letters.

[16]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

[17]  G. Henkelman,et al.  A climbing image nudged elastic band method for finding saddle points and minimum energy paths , 2000 .

[18]  Jan Almlöf,et al.  General methods for geometry and wave function optimization , 1992 .

[19]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

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

[21]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[22]  C. Tautermann,et al.  The optimal tunneling path for the proton transfer in malonaldehyde , 2002 .

[23]  R. O. Jones,et al.  ATP Hydrolysis in Water − A Density Functional Study , 2003 .

[24]  A. Laio,et al.  Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics. , 2006, The journal of physical chemistry. B.

[25]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[26]  Michele Parrinello,et al.  Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach , 2005, Comput. Phys. Commun..

[27]  W. Richards,et al.  Insights into Chorismate Mutase Catalysis from a Combined QM/MM Simulation of the Enzyme Reaction , 1995 .

[28]  H. Bernhard Schlegel,et al.  Estimating the hessian for gradient-type geometry optimizations , 1984 .

[29]  G. Henkelman,et al.  Optimization methods for finding minimum energy paths. , 2008, The Journal of chemical physics.

[30]  Daniel S. Katz,et al.  Swift: A language for distributed parallel scripting , 2011, Parallel Comput..

[31]  Albert C. Pan,et al.  Finding transition pathways using the string method with swarms of trajectories. , 2008, The journal of physical chemistry. B.

[32]  Vincenzo Barone,et al.  Proton transfer in the ground and lowest excited states of malonaldehyde: A comparative density functional and post‐Hartree–Fock study , 1996 .

[33]  Eric J. Bylaska,et al.  Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations. , 2013, The Journal of chemical physics.

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

[35]  Dennis R. Salahub,et al.  Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation , 1992 .

[36]  P. Ordejón,et al.  A DFT-Based QM-MM Approach Designed for the Treatment of Large Molecular Systems: Application to Chorismate Mutase , 2003 .

[37]  K. Fukui.  The path of chemical reactions - the IRC approach , 1981 .

[38]  E. Vanden-Eijnden,et al.  String method for the study of rare events , 2002, cond-mat/0205527.

[39]  J. Stewart.  Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements , 2007, Journal of molecular modeling.

[40]  Christopher B. Harrison,et al.  Quantum and classical dynamics simulations of ATP hydrolysis in solution. , 2012, Journal of chemical theory and computation.

[41]  Kendall N. Houk,et al.  Pericyclic Reaction Transition States: Passions and Punctilios, 1935-1995 , 1995 .

[42]  A. Dinner,et al.  Nonequilibrium umbrella sampling in spaces of many order parameters. , 2009, The Journal of chemical physics.

[43]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[44]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[45]  E. Vanden-Eijnden,et al.  On-the-fly string method for minimum free energy paths calculation , 2007 .

[46]  Carlo Adamo,et al.  Predicting proton transfer barriers with density functional methods , 1999 .

[47]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[48]  A. Mildvan.  Mechanisms of signaling and related enzymes , 1997, Proteins.

[49]  D. Herschlag,et al.  Mapping the transition state for ATP hydrolysis: implications for enzymatic catalysis. , 1995, Chemistry & biology.

[50]  Arieh Warshel,et al.  Quantifying the mechanism of phosphate monoester hydrolysis in aqueous solution by evaluating the relevant ab initio QM/MM free-energy surfaces. , 2013, The journal of physical chemistry. B.