Tight-binding Hamiltonians from Solids to Molecules

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1 Tight-binding Hamiltonians from Solids to Molecules D.A. Papaconstantopoulos Department of Computational and Data Sciences George Mason University, Fairfax Collaborators M.J. Mehl, NRL A. Shabaev, GMU M. Johannes, NRL N. Bernstein, NRL X. Sha, GMU E. N. Economou, FORTH Grant Support from DoE and ONR Wavepro Crete, Greece June 10, 2011

2 PHYSICAL REVIEW B VOLUME 26. NUMBER 7 loctober 1982 Effects of disorder on properties of 115 materials C. M. Soukoulis Corporate Research Science Laboratories, Exxon Research and En$ineeilng Company, Linden, New Jersey D. A. Papaconstantopoulos Naual Research Laboratory, Washington, D.C (Received 4 May 1982) We have calculated the effects of disorder on the density of states, Fermi velocity, and Drude plasma frequency for V and its,4 15 compounds VjX, with X:Al, Ga, Ge, Si, and Sn, and for Nb and its ll5 compounds Nb3X, with X:Al, Ga, Ge, Si, Sn, and Sb using the electron-lifetime model and the results of band-structure calculations. [n most cases the density of states and the superconducting transition temperature T. are found to decrease with increasing disorder, in qualitative agreement with experiment. Exceptions are Nb3Sb and Nb3Si, for which we have found a small increase in?'". We are also presenting calculations of the effects of disorder on the mean free path, BCS coherence length, London penetration depth, Ginzburg-Landau,(, and the temperature dependence of the upper critical field for the above materials. Comparison with the exisiting experimental data is made. z z i o z RESISTIvITY (p0 cm) t0amtmlar0 RESISTIvITY (p0 cn) FIG 8. Ginzburg-Landau r near?"" as a function of residual resistivity po 3 I! z z z 2 o J I fl E onb e Nb3Go I Nb:Sn + Nb35b I Nb3flL o Nb35L e Nb30e z o o vjgo o V3Sn + vssio VsGe 3' 02Dt0at0rm ra rao t RESISTIVITY (pq cm) o?0 r0 m E0 100 tm!0 160 ltr ao RtSISTIVtTY (p0 cnl FIG. 9. Calculated London penetration depth at 0 K in A as a function of residual resistivity p0.

4 NRL Tight-Binding Method Fit to DFT bands and total energies as a function of volume for high-symmetry structures. Calculate quantities accessible to standard DFT not fitted above, i.e., elastic constants, phonon spectra, and surface energies. Perform large scale simulations not practical via DFT, such as static calculations for the energetics of systems containing up to 10,000 atoms, or calculations for a very large number of k- points as needed for mapping Fermi surfaces and evaluating susceptibilities. Perform molecular dynamics simulations using up to 1,000 atoms and 5,000 MD time-steps, an impossible task for standard DFT codes.

5 NRL Tight-Binding Method: Applications We have applied the NRL-TB to the following materials: All transition metals (including the ferromagnets) Alkali, alkaline earth, and simple metals (Al-Pb) Semiconductors: C, Si, Ge Binary compounds: NiH, PdH, FeAl, CoAl, NiAl, NbC, VN, Cu 3 Au, SiC, MgB 2, FeNi, MgO Ternary compounds: Na x CoO 2, Sr 2 RuO 4, SrRuO 3, PbTiO 3 Molecules: C-H-O An improved Harrison-TB approach, inspired by the NRL-TB, was developed: Phys. Rev. B 70, (2004)

12 Vibrations in Amorphous Silicon using TB Feldman, Bernstein, Papa, Mehl, Phys. Rev. B 70, (2004); J. Phys.: Cond. Matter. 16, S5165 (2004). radial distribution se NRL-TB to relax structure, compute phonons et vibrational DOS, zero point motion static structure zero-point motion is significant (even for relatively heavy Si) asymmetry in 1st neighbor peak (influences analysis of coordination, defect concentration) with zeropoint motion

13 Palladium vacancy formation energy Double vacancies 2.52 ev 2.65 ev 2.67 ev 2.81 ev Single vacancy: 1.27 ev (experiment: 1.85 ev)

14 Formation energy (Ry) Pd (fcc) - TB Pd (fcc) - LAPW Pd (bcc) - TB Pd (bcc) - LAPW Pd (sc) - TB Pd (sc) - LAPW PdH (NaCl) - TB PdH (NaCl) - LAPW PdH (CsCl) -TB PdH (CsCl) -LAPW PdH 2 (Fluorite) - TB PdH 2 (Fluorite) - LAPW Pd 4 H 3 - TB Pd 4 H 3 - LAPW Pd 3 H - TB Pd 3 H - LAPW Volume (a.u.)

16 4 PdH Energy (ev) Distance (Å) Number of H atoms

17 0.7 FeAsO: TB /LAPW Band comparison (13 bands fit) TB LAPW Energy (Ry) ! " X Y M #! $ Z

18 TB and LAPW match well, even in orbital character

19 Local symmetry is tetrahedral Calcula?on shows: lower triplet, upper doublet t 2g (3) e g Expect: lower doublet, upper triplet (2) 3 2 Ques?on: Why does actual pseudogap occur with lower complex containing three states and upper complex containing two states? (i.e. opposite of expected ligand field configura?on) Elimina?ng all but nearest neighbor!)"" Fe As hopping in TB model:!!""!,-./ !(""!'""!&""!%""!$"" !E=F?./61 G@./6 " 9 HIJIK KH K $!H $ I $ Ligand filed configura?on is regained (as expected)!#""!"!"*&'!"*'!"*''!"*(!"*('!"*)!"*)'!"*+

First-principles calculations and tight-binding molecular dynamics simulations of the palladium-hydrogen system

First-principles calculations and tight-binding molecular dynamics simulations of the palladium-hydrogen system A. Shabaev and D. A. Papaconstantopoulos George Mason University, Fairfax, Virginia 22030,