Morse-Smale Analysis of Ion Diffusion in Ab Initio Battery Materials Simulations

Ab initio molecular dynamics (AIMD) simulations are increasingly useful in modeling, optimizing and synthesizing materials in energy sciences. In solving Schrodinger’s equation, they generate the electronic structure of the simulated atoms as a scalar field. However, methods for analyzing these volume data are not yet common in molecular visualization. The Morse-Smale complex is a proven, versatile tool for topological analysis of scalar fields. In this paper, we apply the discrete Morse-Smale complex to analysis of first-principles battery materials simulations. We consider a carbon nanosphere structure used in battery materials research, and employ Morse-Smale decomposition to determine the possible lithium ion diffusion paths within that structure. Our approach is novel in that it uses the wavefunction itself as opposed distance fields, and that we analyze the 1-skeleton of the Morse-Smale complex to reconstruct our diffusion paths. Furthermore, it is the first application where specific motifs in the graph structure of the complete 1-skeleton define features, namely carbon rings with specific valence. We compare our analysis of DFT data with that of a distance field approximation, and discuss implications on larger classical molecular dynamics simulations.

[1]  Deok-Soo Kim,et al.  Tunnels and Voids in Molecules via Voronoi Diagram , 2012, 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering.

[2]  H. Wolfson,et al.  MolAxis: Efficient and accurate identification of channels in macromolecules , 2008, Proteins.

[3]  H. Edelsbrunner,et al.  Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design , 1998, Protein science : a publication of the Protein Society.

[4]  Christopher Roland,et al.  Ab initio investigations of lithium diffusion in carbon nanotube systems. , 2002, Physical review letters.

[5]  B. Ouyang,et al.  Energetics and kinetics of li intercalation in irradiated graphene scaffolds. , 2013, ACS applied materials & interfaces.

[6]  Jaroslav Koca,et al.  CAVER: a new tool to explore routes from protein clefts, pockets and cavities , 2006, BMC Bioinformatics.

[7]  Seung Jin Chae,et al.  Diffusion mechanism of lithium ion through basal plane of layered graphene. , 2012, Journal of the American Chemical Society.

[8]  Jie Liang,et al.  CASTp: Computed Atlas of Surface Topography of proteins , 2003, Nucleic Acids Res..

[9]  Bernd Hamann,et al.  Segmenting molecular surfaces , 2006, Comput. Aided Geom. Des..

[10]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[11]  Jun Lu,et al.  Investigation of the Decomposition Mechanism of Lithium Bis(oxalate)borate (LiBOB) Salt in the Electrolyte of an Aprotic Li–O2 Battery , 2014 .

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

[13]  Talha Bin Masood,et al.  Extraction of Robust Voids and Pockets in Proteins , 2013, Visualization in Medicine and Life Sciences III.

[14]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[15]  Jean-Philip Piquemal,et al.  Characterizing Molecular Interactions in Chemical Systems , 2014, IEEE Transactions on Visualization and Computer Graphics.

[16]  Bernd Hamann,et al.  Topology-based simplification for feature extraction from 3D scalar fields , 2005, VIS 05. IEEE Visualization, 2005..

[17]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[18]  Daniel Baum,et al.  Dynamic channels in biomolecular systems: Path analysis and visualization , 2012, 2012 IEEE Symposium on Biological Data Visualization (BioVis).

[19]  Daniel Baum,et al.  Voronoi-Based Extraction and Visualization of Molecular Paths , 2011, IEEE Transactions on Visualization and Computer Graphics.

[20]  Sanket A. Deshmukh,et al.  Probing the evolution and morphology of hard carbon spheres , 2014 .

[21]  Valerio Pascucci,et al.  Computing Morse-Smale Complexes with Accurate Geometry , 2012, IEEE Transactions on Visualization and Computer Graphics.

[22]  Leila De Floriani,et al.  A primal/dual representation for discrete Morse complexes on tetrahedral meshes , 2013, Comput. Graph. Forum.

[23]  Herbert Edelsbrunner,et al.  The geometry of biomolecular solvation , 2005 .

[24]  H Edelsbrunner,et al.  Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins , 1998, Proteins.

[25]  Andrew Gillette,et al.  Topology Based Selection and Curation of Level Sets , 2009, Topology-Based Methods in Visualization II.

[26]  T. Sousbie.  The persistent cosmic web and its filamentary structure I: Theory and implementation , 2010, 1009.4015.

[27]  Jaroslav Koca,et al.  MOLE: a Voronoi diagram-based explorer of molecular channels, pores, and tunnels. , 2007, Structure.

[28]  Deok-Soo Kim,et al.  Three-dimensional beta-shapes and beta-complexes via quasi-triangulation , 2010, Comput. Aided Des..

[29]  R. Bader.  Atoms in molecules , 1990 .

[30]  R. Forman.  A USER'S GUIDE TO DISCRETE MORSE THEORY , 2002 .

[31]  Bernd Hamann,et al.  A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality , 2008, IEEE Transactions on Visualization and Computer Graphics.

[32]  Frédéric Chazal,et al.  Molecular shape analysis based upon the morse-smale complex and the connolly function , 2002, SCG '03.

[33]  Hans Hagen,et al.  Direct Feature Visualization Using Morse-Smale Complexes , 2012, IEEE Transactions on Visualization and Computer Graphics.

[34]  Peter Lindstrom,et al.  Topological Spines: A Structure-preserving Visual Representation of Scalar Fields , 2011, IEEE Transactions on Visualization and Computer Graphics.