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Geometry optimization, including searching for transition states, accounts for most of the CPU time spent in quantum chemistry, computational surface science, and solid-state physics, and also plays an important role in simulations employing classical force fields. We have implemented a geometry optimizer, called DL-FIND, to be included in atomistic simulation codes. It can optimize structures in Cartesian coordinates, redundant internal coordinates, hybrid-delocalized internal coordinates, and also functions of more variables independent of atomic structures. The implementation of the optimization algorithms is independent of the coordinate transformation used. Steepest descent, conjugate gradient, quasi-Newton, and L-BFGS algorithms as well as damped molecular dynamics are available as minimization methods. The partitioned rational function optimization algorithm, a modified version of the dimer method and the nudged elastic band approach provide capabilities for transition-state search. Penalty function, gradient projection, and Lagrange-Newton methods are implemented for conical intersection optimizations. Various stochastic search methods, including a genetic algorithm, are available for global or local minimization and can be run as parallel algorithms. The code is released under the open-source GNU LGPL license. Some selected applications of DL-FIND are surveyed.

The structures of the polar surfaces of ZnO are studied using ab initio calculations and surface x-ray diffraction. The experimental and theoretical relaxations are in good agreement. The polar surfaces are shown to be very stable; the cleavage energy for the (0001)-Zn and ͑0001 ͒-O surfaces is 4.0 J͞m 2 comparable to 2.32 J͞m 2 for the most stable nonpolar (1010) surface. The surfaces are stabilized by an electronic mechanism involving the transfer of 0.17 electrons between them. This leads to 2D metallic surface states, which has implications for the use of the material in gas sensing and catalytic applications. DOI: 10.1103/PhysRevLett.86.3811 PACS numbers: 68.03.Cd, 68.35.Bs, 73.20.At The ionic model has provided the basis for our understanding of the very wide range of physical phenomena displayed by "ionic" crystals [1][2][3][4]. The model underpins our understanding of, for instance; cohesive properties, complex dielectric and optical response, and novel magnetic and electronic behavior including giant magnetoresistance and superconductivity [2]. One of the interesting consequences of the ionic model is that certain "polar" surfaces of ionic crystals will have a surface energy that diverges with sample size due to the generation of a macroscopic electrostatic field across the crystal. A definitive description of this behavior and the classification scheme which is now widely used were given by Tasker in 1979 [5]. Remarkably, a large number of naturally occurring materials have morphologies which display polar surfaces. In recent years a variety of stabilizing mechanisms have been demonstrated to operate at particular surfaces which typically involve the quenching of the macroscopic field either through the reconstruction of the surface, or the presence of adsorbates on the surface [3]. However, in some cases it appears that clean, unreconstructed surfaces are stable, at variance with Tasker's conclusions. A notable example is zincite (ZnO). A possible mechanism for the stability of these systems is a rearrangement of the electronic structure resulting in an effective charge transfer between the polar surfaces removing the macroscopic field which would otherwise be present. To date, no first principles investigation of such a phenomenon has been performed, although semiempirical calculations on SrTiO 3 indicate that such a mechanism might be operating [6,7]. Recently, similar effects have also been observed for thin film ionic materials grown on metallic substrates such as NaCl(111) on aluminum [8].ZnO crystallizes in the Wurtzite structure which does not have a center of inversion. Consequently, when the crystal is cleaved normal to the c axis in a manner which breaks the fewest interatomic bonds, two different polar surfaces are formed on opposite sides of the crystal, each having only one type of ion in its outermost plane. Thus, such a system may be considered to be a "slab" of material with the Zn cation outermost for the (0001)-Zn surface and the O anion outermost on the ͑0001͒-O surface. In orde...

Structure and stability of the (001) alpha-quartz surface Article (Published Version) http://sro.sussex.ac.uk Goumans, T P M, Wander, Adrian, Brown, Wendy A and Catlow, C Richard A (2007) Structure and stability of the (001) alpha-quartz surface. Physical Chemistry Chemical Physics, 9 (17). 2146 -2152 . ISSN 1463 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/48679/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.Structure and stability of the (001) The structure and surface energies of the cleaved, reconstructed, and fully hydroxylated (001) a-quartz surface of various thicknesses are investigated with periodic density functional theory (DFT). The properties of the cleaved and hydroxylated surface are reproduced with a slab thickness of 18 atomic layers, while a thicker 27-layer slab is necessary for the reconstructed surface. The performance of the hybrid DFT functional B3LYP, using an atomic basis set, is compared with the generalised gradient approximation, PBE, employing plane waves. Both methodologies give similar structures and surface energies for the cleaved and reconstructed surfaces, which validates studying these surfaces with hybrid DFT. However, there is a slight difference between the PBE and B3LYP approach for the geometry of the hydrogen bonded network on the hydroxylated surface. The PBE adsorption energy of CO on a surface silanol site is in good agreement with experimental values, suggesting that this method is more accurate for hydrogen bonded structures than B3LYP. New hybrid functionals, however, yield improved weak interactions. Since these functionals also give superior activation energies, we recommend applying the new functionals to contemporary issues involving the silica surface and adsorbates on this surface.