Removing External Degrees of Freedom from Transition-State Search Methods using Quaternions.

In finite systems, such as nanoparticles and gas-phase molecules, calculations of minimum energy paths (MEPs) connecting initial and final states of transitions as well as searches for saddle points are complicated by the presence of external degrees of freedom, such as overall translation and rotation. A method based on quaternion algebra for removing the external degrees of freedom is described here and applied in calculations using two commonly used methods: the nudged elastic band (NEB) method for MEPs and the DIMER method for finding the minimum mode in minimum mode following searches of first-order saddle points. With the quaternion approach, fewer images in the NEB are needed to represent MEPs accurately. In both NEB and DIMER calculations of finite systems, the number of iterations required to reach convergence is significantly reduced. The algorithms have been implemented in the Atomic Simulation Environment (ASE) open source software.

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

[2]  Graeme Henkelman,et al.  Paths to which the nudged elastic band converges , 2011, J. Comput. Chem..

[3]  Andreas Pedersen,et al.  Simulated Annealing with Coarse Graining and Distributed Computing , 2010, PARA.

[4]  Andreas Pedersen,et al.  Geothermal model calibration using a global minimization algorithm based on finding saddle points and minima of the objective function , 2014, Comput. Geosci..

[5]  Karsten W. Jacobsen,et al.  An object-oriented scripting interface to a legacy electronic structure code , 2002, Comput. Sci. Eng..

[6]  K. Dill,et al.  Using quaternions to calculate RMSD , 2004, J. Comput. Chem..

[7]  Johannes Kästner,et al.  A Quadratically-Converging Nudged Elastic Band Optimizer. , 2013, Journal of chemical theory and computation.

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

[9]  Wolfgang Quapp,et al.  A comment to the nudged elastic band method , 2010, J. Comput. Chem..

[10]  Kari Laasonen,et al.  CO dissociation on iron nanoparticles: size and geometry effects. , 2013, The Journal of chemical physics.

[11]  Kurt Stokbro,et al.  Improved initial guess for minimum energy path calculations. , 2014, The Journal of chemical physics.

[12]  G. Henkelman,et al.  Comparison of methods for finding saddle points without knowledge of the final states. , 2004, The Journal of chemical physics.

[13]  A. Bell,et al.  Efficient methods for finding transition states in chemical reactions: comparison of improved dimer method and partitioned rational function optimization method. , 2005, The Journal of chemical physics.

[14]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[15]  Paul Sherwood,et al.  Superlinearly converging dimer method for transition state search. , 2008, The Journal of chemical physics.

[16]  Hannes Jónsson,et al.  Simulation of surface processes , 2011, Proceedings of the National Academy of Sciences.

[17]  K. Jacobsen,et al.  Real-space grid implementation of the projector augmented wave method , 2004, cond-mat/0411218.

[18]  N. A. Romero,et al.  Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[19]  Graeme Henkelman,et al.  EON: software for long time simulations of atomic scale systems , 2014 .

[20]  Pekka Koskinen,et al.  Structural relaxation made simple. , 2006, Physical review letters.

[21]  G. Henkelman,et al.  Basin constrained κ-dimer method for saddle point finding. , 2014, Journal of Chemical Physics.

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

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

[24]  H. Jónsson,et al.  Nudged elastic band method for finding minimum energy paths of transitions , 1998 .

[25]  Halim Kusumaatmaja,et al.  Exploring Energy Landscapes: Metrics, Pathways, and Normal-Mode Analysis for Rigid-Body Molecules. , 2013, Journal of chemical theory and computation.

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

[27]  Karsten Wedel Jacobsen,et al.  A semi-empirical effective medium theory for metals and alloys , 1996 .