Main contributor= Prof. K. Ohno

1. TOMBOTOhoku university all-electron Mixed-Basis Orbitals ab initio programstarted in 1990 byK. Ohno, Maruyama and Y. Kawazoe extended by M. Sluiter, S. Bahramy, U. Wagmhre, S. Ishii, J. Wu, T. M. Briere, T. Morisato, H. Adachi, Y. Liang, Vei Wang,M. Ikeoka, R. Kuwahara, Y. Noguchi, V. Belosludov, and R. Sahara Main contributor= Prof. K. Ohno

2. Plan of the TOMBO course at SUT • Introduction... What is TOMBO and computational materials science • Detailed description of TOMBO…Understand why all electron full potential is important with higher level of perturbation • New Fundions in TOMBO...How to make TOMBO faster, electron transport through conduction band • Training course… How to run TOMBO on your PC

3. Purpose of ACCMS • The Asian Consortium for Computational Materials Science (ACCMS) has been set up to nurture and promote research and developmental activities in computational materials science in Asian countries. • Utilize the human as well as computational resources existing in Asian region via collaboration and exchange programmes. • Establish Virtual Organization and Working Groups on some of the emerging areas of CMS Using our own computer programs : ex. TOMBO Realize advantages to work in Asian region

4. Short course: TOMBO on Windows First short course in Seoul for TOMBO Headed by Prof. Lee

5. Necessary time between Tokyo – Osaka hour Locomotive New materials change drastically the society Electric Shinkansen Nozomi with NdFeB superconductor year

6. No change in more than 25 years History of strength of magnet High Tc materials are the same 　　　　　　→ Theorists should contribute to change this situation!

7. In nanotechnology computer simulation is important to predict new materials!

8. Previous first-principled method１ • Pseudopotential （PAW） method Large Cutoff Energy for Plane WavesLack of core electron description Plane Waves rc

9. Previous first-principles method ２ • Linear Combination of Atomic Orbitals (LCAO) Overlap integrals require heavy computations. It cannot describe positive energy (PW) states. It has a Basis Set Superposition Error (BSSE). Incomplete basis → Limits in applications

10. Previous first-principles method ３ • Muffin-Tin Orbitals（LMTO, APW, KKR） It cannot handleisolated systems. Many combinationsbetween inner spherical waves and outer PWs.

11. To solve these problems, we can usea new first-principles method: All-electronmixed basis approach “TOMBO”

12. Explained by Kawazoe in 2000

13. Description of wave functions in all-electron mixed basis approach: Plane Wave (PW) Bloch Function of AO Atomic Orbital (AO)

14. Best in DFT+LDA • Present standard programs: • Planewave+pseudopotential(VASP, ABINIT… no core electrons • WIEN, FLAPW: heavy computation, no complete relaxation • All-electron full-potential mixed-basis formulation • Absolute energy evaluation • Core electron related physical properties such as hyperfine structure constant • Complete relaxation of atomic positions: no muffintin • High energy collisions of atoms • Fast : smaller number of plane waves (only 10,000 PWs for C60 ) • TOMBO(TOhokuUniversityMixedBasis Orbitalsab initio program) with GW approximation and Time dependent Schrödinger equation solver

15. C60 and C70on Cu(111) －bias HOMO +bias LUMO STM Expt. 15 15 All-electron mixed basis: Phys. Rev. Lett. 71, 2959 (1993) With Prof. Gu and Ohno.67papers with Gu Cutoff energy : 7 Ry in all-electron mixed basis approach 40 Ry in pseudopotential（PAW）approach

16. New additional features • Electron transport: Y.-Y. Liang the first program using real electron transport via excited states using Wannier function • Thermal transport: K. Esfarjani extension of phonon code including anharmonic terms • Van der Waals force estimation: V. Belosldov computing dipoler polarization and diple-dipole interaction

17. Advantages: • The exact treatment of electronic wavefunctions in the bonding regions as well as in the core regions, which makes fast atom collision process can be treated. • Calculations need fewer number of plane-waves as compared to other PW-based methods • Properties associated with core levels, e.g. hyperfine structure, NMR shift can be accurately and efficiently computed with the modest computational effort. • Phonon: we were the first to compute frozen phonon vibration frequencies: >500 citations

18. Fast atom collision process

19. Ease of use • program execution controlled by just 2 input files atomxyz.in and inputdeck.in • input files are documented and options are, as much as possible, intuitive. • default values for all input data are provided. atomicdata.in and defaults.in • in case of errors in the input, or certain errors during execution a verbose diagnostic message is written to the error.out file, and, if possible, a remedy is suggested. • the program produces just 4 human readable output files, log.out, trajectory.out, inputdeck.out, atomxyz.out • a hyperlinked manual in PDF and postscript formats is provided. http://www-lab.imr.edu/~marcel/tombo/tombo.html

20. Applications of TOMBO • Hydrogen storage material • Hyperfine structure constant • Absolute energy level estimation • Time dependent Schroedinger equation

21. Cleanest hydrogen carrier • Clathrate hydrates • Known for methane hydrate under sea • Apply clathrate hydrate for hydrogen storage

22. Hydrate Clathrate with H2 Molecules • Experimentally found in 2002 • X-ray, neutron experiments have difficulty to determine the atomic structure • TOMBO applied to analyze in 2002 • >700 atoms with structure optimization • Physico-chemical properties estimated • Stability studied Sluiter, Belosludov, Kawazoe

23. Surprising New Hydrates Until recently, always at most: 1 Guest to 1 Cage Therefore, very small atoms & molecules cannot stabilize hydrate clathrates…. BUT….. 1992, Londono et al.: Helium stabilizes Ice II 1993, Vos et al.: H2 stabilizes Ice II (called clathrate - but is misnomer!) 2002, Mao et al. True H2 Hydrate Clathrate discovered Ice II with H2 (from Vos et al PRL 71, 3150, 1993) H2 Hydrate Clat. Cubic 2 (2002)

24. hyperfine interaction • Astrophysics Determination of atomic properties of interstellar medium • Biochemistry Radicals: Identification of molecular radicals in solid, liquid and gaseous phases Transition metals: Study of their effect on living tissues • Solid state physics Defects: Identification of point-like defects in clusters and semiconductors Metal clusters: structural determination of the clusters

25. Problems of available codes • Not applicable:VASP • Applicable but not accurate:Gaussian • Accurate but unbearably time consuming:WIEN2K New method, applicable & accurate with minimal computational cost All-electron mixed-basis method TOMBO

26. Hyperfine parameters Hyperfine interaction in general contains two parameters: • Isotropic (Fermi contact): Comes from s-Orbitals • Anisotropic (Diplole): Comes from p-, d- and f-Orbitals

27. M(2) Structure of clusters. Pentagonal bipyramid D5h Hyperfine results for clusters M(5) Values are in MHz M. S. Bahramy et. al., Phys. Rev. B. 73, 045111 (2006). Experimental data from: D. A. Garland et al., J. Chem. Phys. 80, 4761 (1984); G. A. Thompson et al., J. Chem. Phys. 78, 5946 (1983); R. Arratia-Perez et al., Chem. Phys. Lett. 397, 408 (2004); S. B. H. Bach et al., J. Chem. Phys. 87,896 (1987).

28. Charge distribution in Cu7 cluster 63Cu7 pentagonal bipyramid cluster (top & bottom atom(2), 5-fold ring atom(5) rs > 0.010 e/A3 (white) rs > 0.005 e/A3 (green) rs > 0.001 e/A3 (red)

29. Comparison with others 63Cu7 pentagonal bipyramid cluster (top & bottom atom(2), 5-fold ring atom(5)

30. Molecualr model for deoxymyoglobin Hemoglobin (Heme part) Model for deoxymyoglobin

31. Fe in pure Pdwith G.P. Das • Strongly localized moment at the Fe site • A symmetric pattern of spin polarization around Fe. M. S. Bahramy et al., J. Mag. Mag. Mater. 2006

32. Present standard Ab initio calculation does not use experimental parameters but uses a big approximation. More sofisticated method than LDA is necessary. Our research

33. ＧＷ （quiasiparticle）approximation Louie group: crystal, pseudopotential VSSP ver. 5.11 also has GW cal. TOMBO: any structure, all-electron: absolute energy estimation Easy to be parallelized; similar time as DFT cal. Add this Feynman diagram to standard LDA photon electron

34. Prediction of photoemission（band gap value, relative） Standard LDA yellow？？ experiment narrow Blue color GW approximation Exact value！

35. All-electron abintioGW calculation to estimate for C60 Ionization potential, electron affinity in absolute values and obtained the HOMO-LUMO gap of C60 exactly … not relative values!!Ohno, Ishii, Adachi

36. DFT calculation（○） and GW by TOMBO（●）for diamond crystal エネルギー（eV) DFTis for the ground state ＧＷ approximation gives us the band gap value k

37. More than GWA (Applicable to Metal) GWA gives for metals、effective mass＞1, and narrow band width for alkali metals Λ＝１ in GWA：Applicable with band gap W photon Σ＝ More than GWA Σ＝Hedin, Yasuhara, only electron gas level Λ G electron

38. Time Dependent DFT • TDSE:　iΨj(x,t)/ t = H(t) Ψj(x,t) • normal pertubation: • Ψj(x,t+Δt) = Ψj(x,t) - iΔt H(t) Ψj(x,t) • 100 times heavier than CP:Δt =electronic motion • Modified method: • In LDA, Δρ « ρ→ΔH« H（Δt=small） • Ψj(x,t+Δt) = exp(-iΔt H(tc)) Ψj(x,t) • Δt is similar to CP.（Suzuki-Trotter method)

39. Institute for Materials Research, Tohoku University Dissociation of H2+ on Ni2- by one electron excitation: H H ↓↓ HOMO: H bonding LUMO: Ni anti bonding Ni dimer Figure: Trajectory of atomic motion. Ni dimer is perpendicularly positioned on the paper.

40. Heat Transport and thermoelectrics FP-DFT in a supercell Model Potential MD-GK Latt Dyn Thermal Properties

41. Thermal conductivity of ZrCoSbSimulations vs Experiments Sb Impurity scattering Co B=0 Zr B=9.1x10-44 B=3.6x10-43 Y. Xia et al., J. Appl. Phys. 88, 1952 (2000). T. Sekimoto et al., Jpn. J. Appl. Phys. 46, L673 (2007). Shiomi, Esfarjani, Chen, Phys. Rev. B 84, 104302 (2011)

42. How to get TOMBO? • Sales and Customer SupportHitachi Co. • TOMBO ver. 2.0 object code is free for academicians • Pls check our homepage

43. To have confidence • Catch phrase; from explanation to prediction! • How to realize this condition? • We should have good confidence to predict new materials without experimental observations.

44. Theoretical results should have quality assurance! • Our system= quantum many body electron and nucleus system interacted via Coulomb force • Coulomb force= geometrical force in 3D space • Virial theorem holds = a good measure for quality assurance (V/T=-2 for free system) :necessary condition

45. Is total energy minimization good enough in ab initio calculation？No!! Necessary condition = Virial theorem T and V are not independent ２Ｔ＋Ｖ＝３ＰΩ, for P=0 E=T+V=V/2=-T Sufficient condition＝solve accurately

46. quant. mech. Origin of ab initiocalulation variationl priciple Hohenberg-Kohn theory exact solution many body wavef(3N dim.) Charge density(3 dim.) density functional theory quantum chemistry Exchange-correlation potential(manybody effect) LDA, GGA HF, CI ab initio Monte Carlo method fundamentals in ab initio calculation From 3N dim to 3dim loses a lot! K-S wavefunction is for quasiparticle not electrons DFT is exact, but LDA, GGA are not Variational Mote Carlo (VMC) method Diffusion Monte Carlo (DMC) method

47. quantitative Computer cost △ N3 DFT ○ N6〜N! Full CI Quantum chemistry Computer cost ○ N3〜N4 Diffusion quantum MC DMC Electron N 20 electrons computing cost for ab initio methods →complete numerical calculation needed! Ab initio DMS seems to be a better method in future

48. H atom =Two body prob. →　exactly solvable How is for He atom? e 2 electrons in 1s states? He e It is a complex three body problem. Not easy to be solved!

49. Correlation energy in electron system ・He atom ・H2 molecule -1.1333 hartee -2.8616 hartree HF [6-311++G(3df,2pd)] 85.3% 94.5% -2.8975 Full CI [6-311++G(3df,2pd)] -1.1723 -1.1745 -2.9037 Exact(experimental) Exact(experimental) 100.0% 100.0% -1.1745(1) -2.9037 DMC （iinitial 6-311++G(3pd,2pf) ） DMC （initial 6-311++G(3pd,2pf)） Many body problem should be solved! By HF+CI difficult to reach … DFT also difficult… DMC=Diffusion Monte Carlo method is a candidate

50. Why ab initio simulation can predict new materials in nanoscale? • Objects of the materials research are many body system via Coulomb interaction • Si, steel, DNA all the same！ • Described by Schroedinger equation (Dirac eq.) • More than 50 years ago, Dirac already said that “All necessary equations are known, only to solve them!” But!!! • Many body problem is too much time consuming… difficult to be solved … many approximations and models have been invented and applied up to the present! • They could explain the experimental results… • And, many misunderstandings happened!!!