There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

The application of density functional theory to calculate adsorption properties, reaction pathways, and activation energies for surface chemical reactions is reviewed. Particular emphasis is placed on developing concepts that can be used to understand and predict variations in reactivity from one transition metal to the next or the effects of alloying, surface structure, and adsorbate-adsorbate interactions on the reactivity. Most examples discussed are concerned with the catalytic properties of transition metal surfaces, but it is shown that the calculational approach and the concepts developed to understand trends in reactivity for metals can also be used for sulfide and oxide catalysts.

Theoretical surface science and catalysis—calculations and concepts

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

We present a density functional theory study of the first step of CH4 adsorption on the Ni(111) surface, dissociation into adsorbed CH3 and H. The rupture of the C–H bond occurs preferentially on top of a Ni atom, with a dissociation barrier of about 100 kJ/mol (including zero point corrections). The transition state involves considerable internal excitation of the molecule. The active C–H bond is both stretched to 1.6 A and tilted relative to the methyl group. A normal mode analysis shows that the reaction coordinate is mainly a C–H stretch, while the orientation of the C–H bond relative to the surface is responsible for the highest real mode. Alloying the surface with gold also affects the reactivity of the Ni atoms on adjacent surface sites. The dissociation barrier is increased by 16 and 38 kJ/mol for a Ni atom with one or two gold neighbors, respectively. We attribute these changes to a shift in the local density of d states at the nickel atoms in the neighborhood of gold.

/pdf/a-theoretical-study-of-ch4-dissociation-on-pure-and-gold-2hqqoq56pp.pdf

A theoretical study of CH4 dissociation on pure and gold‐alloyed Ni(111) surfaces

We have studied the stability, the electronic, and the magnetic properties of Co2MnSi001 thin films for 15 different terminations using density functional theory calculations. The phase diagram obtained by ab initio atomistic thermodynamics shows that in practice the MnSi, pure Mn, or pure Si terminated surfaces can be stabilized under suitable conditions. Analyzing the surface band structure, we find that the pure Mn termination, due to its strong surface-subsurface coupling, preserves the half-metallicity of the system, while surface states appear for the other terminations. Heusler alloys are promising materials to be applied as spin injectors in the rapidly developing field of spin elec- tronics (spintronics) because they belong to the materials class of magnetic half-metals. As first evidenced by first- principles calculations (1), these systems are characterized by a metallic density of electronic states at the Fermi level (� F) for one spin channel, while the states for the other spin channel display a gap atF, leading to 100% spin-polarized metallic conductivity. Among this group, the intermetallic compound Co2MnSi, a so-called full-Heusler alloy, offers special advantages: it has the highest Curie temperature amongst the known Heusler alloys (Tc 985 K) (2) and a rather wide gap in the minority spin channel (3). However, the desired half-metallic properties can be lost near sur- faces or interfaces. While for spin injection the electronic structure of the half-metal-semiconductor interface is cru- cial (4), surfaces are more easily accessible experimentally than interfaces, and hence lend themselves to a systematic study of the factors governing the possible loss of half- metallicity. Moreover, recent interest in spin-polarized tunneling diodes and scanning tunneling microscopy (5) gives relevance to half-metallic surfaces as a research topic in its own right. Here, we present a comprehensive theoretical investiga- tion of the (001) surface of Co2MnSi. This surface is important for envisaged epitaxial growth of Co2MnSi on Ge(001) or GaAs(001), materials to which it is very closely lattice matched. So far, ab initio calculations have been performed only for the standard Co and MnSi terminations of Co2MnSi001 thin films (6). In these calculations, which did not take into account any structural relaxation, it was found that the (001) surface is no longer half- metallic, and that the spin polarization at the Fermi level is negligible. Experimental work on Co 2 MnSi thin films has so far mostly focused on preparation techniques and the crystallinity and magnetic properties of the films (7-9). Very recently two experimental groups reported a spin polarization of about 60% at low temperatures for Co2MnSi thin films (10,11). In this Letter, we present density functional theory (DFT) calculations demonstrating that it is possible to retain the half-metallicity of Co2MnSi by appropriate ter- mination at the (001) surface. Our results have been ob- tained by using the WIEN2K code, a full-potential linearized augmented-plane-wave code (12). In order to validate the appropriateness of the approximation to the exchange- correlation energy, we have calculated the bulk properties of Co2MnSi both in the local-density approximation (LDA) and in the generalized gradient approximation (GGA). We found that the theoretical lattice constant of the GGA (5.63 A ˚ ) agrees well with the experimental value

/pdf/preserving-the-half-metallicity-at-the-heusler-alloy-co2mnsi-2gykdvzsuo.pdf

Preserving the half-metallicity at the Heusler alloy Co2MnSi(001) surface: a density functional theory study.

The atomic arrangement of the technologically important As-rich $\mathrm{GaAs}(001)\ensuremath{-}(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructed surface is determined using bias-dependent scanning tunneling microscopy (STM) and first-principles electronic structure calculations. The STM images reveal the relative position and depth of the atomic-scale features within the trenches between the top-layer As dimers, which are in agreement with the $\ensuremath{\beta}2(2\ifmmode\times\else\texttimes\fi{}4)$ structural model. The bias-dependent simulated STM images reveal that a retraction of the topmost dangling bond orbitals is the novel electronic mechanism that enables the STM tip to image the trench structure.

/pdf/atomic-structure-of-the-gaas-001-2-4-surface-resolved-using-3evabasjs4.pdf

Atomic Structure of the GaAs ( 001 ) − ( 2 × 4 ) Surface Resolved Using Scanning Tunneling Microscopy and First-Principles Theory

We study the energetics of island formation in Stranski-Krastanow growth within a parameter-free approach. It is shown that an optimum island size exists for a given coverage and island density if changes in the wetting layer morphology after the 3D transition are properly taken into account. Our approach reproduces well the experimental island size dependence on coverage and indicates that the critical layer thickness depends on growth conditions. The present study provides a new explanation for the (frequently found) rather narrow size distribution of self-assembled coherent islands.

/pdf/formation-and-stability-of-self-assembled-coherent-islands-2ydqjqr5b8.pdf

Formation and Stability of Self-Assembled Coherent Islands in Highly Mismatched Heteroepitaxy

Three different clusters, Si9H12, Si15H16, and Si21H20, are used in density-functional theory calculations in conjunction with ab initio pseudopotentials to study how the energetics of H2 dissociative adsorption on and associative desorption from Si(001) depends on the cluster size. The results are compared to five-layer slab calculations using the same pseudopotentials and high quality plane-wave basis set. Several exchange-correlation functionals are employed. Our analysis suggests that the smaller clusters generally overestimate the activation barriers and reaction energy. The Si21H20 cluster, however, is found to predict reaction energetics, with Eades=56±3kcal/mol (2.4±0.1eV), reasonably close (though still different) to that obtained from the slab calculations. Differences in the calculated activation energies are discussed in relation to the efficiency of clusters to describe the properties of the clean Si(001)-2×1 surface.

/pdf/effect-of-the-cluster-size-in-modeling-the-h2-desorption-and-3drdqqeyfh.pdf

Peter Kratzer

Papers

A theoretical study of CH4 dissociation on pure and gold‐alloyed Ni(111) surfaces

Preserving the half-metallicity at the Heusler alloy Co2MnSi(001) surface: a density functional theory study.

Atomic Structure of the GaAs ( 001 ) − ( 2 × 4 ) Surface Resolved Using Scanning Tunneling Microscopy and First-Principles Theory

Formation and Stability of Self-Assembled Coherent Islands in Highly Mismatched Heteroepitaxy

Effect of the cluster size in modeling the H2 desorption and dissociative adsorption on Si(001)