Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals

Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localized orbitals in real space, rather than the delocalized eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential-energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from onetep, our linear scaling method based on localized orbitals in real space. The use of psinc functions for the underlying basis set and on-the-fly optimization of the localized orbitals results in smooth potential-energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimization to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimization algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.<br/

Adaptive Genetic Algorithm for Crystal Structure Prediction

We present a genetic algorithm (GA) for structural search that combines the speed of structure exploration by classical potentials with the accuracy of density functional theory (DFT) calculations in an adaptive and iterative way. This strategy increases the efficiency of the DFT-based GA by several orders of magnitude. This gain allows considerable increase in size and complexity of systems that can be studied by first principles. The method's performance is illustrated by successful structure identifications of complex binary and ternary inter-metallic compounds with 36 and 54 atoms per cell, respectively. The discovery of a multi-TPa Mg-silicate phase with unit cell containing up to 56 atoms is also reported. Such phase is likely to be an essential component of terrestrial exoplanetary mantles.Comment: 14 pages, 4 figure

Geometry Optimization of Crystals by the Quasi-Independent Curvilinear Coordinate Approximation

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. N\'emeth and M. Challacombe, J. Chem. Phys. {\bf 121}, 2877, (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexagonal boron-nitride, a (10,0) carbon-nanotube, hexagonal ice, quartz and sulfur at the $\Gamma$-point RPBE/STO-3G level of theory.Comment: Submitted to Journal of Chemical Physics on 7/7/0

Combining 2D2D synchrosqueezed wave packet transform with optimization for crystal image analysis

We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial information from atomic crystal images: crystal defects, rotations and the gradient of elastic deformation. The deformation gradient estimate is then improved outside the identified defect region via a variational approach, to obtain more robust results agreeing better with the physical constraints. The variational model is optimized by a nonlinear projected conjugate gradient method. Both examples of images from computer simulations and imaging experiments are analyzed, with results demonstrating the effectiveness of the proposed method