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TOMBO = TOhoku university all-electron Mixed-Basis Orbitals ab initio program started in 1990 by S. Bahramy, M. Sluiter, K. Ohno, Y. Maruyama, U. Wagmire, S. Ishii, T. M. Briere, H. Adachi, and Y. Kawazoe

TOMBO TOhoku university all-electron Mixed-Basis Orbitals ab initio program

started in 1990 by K. 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. OhnoPlan of the TOMBO course at SUTIntroduction... What is TOMBO and computational materials scienceDetailed description of TOMBOUnderstand 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 bandTraining course How to run TOMBO on your PC23Purpose of ACCMSThe 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 region3Short course: TOMBO on Windows

First short course in Seoul for TOMBOHeaded by Prof. LeeNecessary time between Tokyo Osaka

houryearLocomotiveShinkansenNozomi with NdFeBsuperconductorElectricNew materials change drastically the society

No change in more than 25 yearsHistory of strength of magnetHigh Tc materials are the sameTheorists should contribute to change this situation!

In nanotechnology computer simulation is important to predict new materials!Previous first-principled method Pseudopotential PAW method

rcLarge Cutoff Energy for Plane WavesLack of core electron description

Plane WavesPrevious first-principles method 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 applicationsPrevious first-principles method Muffin-Tin OrbitalsLMTO, APW, KKRIt cannot handleisolated systems.

Many combinationsbetween inner sphericalwaves and outer PWs.

To solve these problems, we can usea new first-principles method:All-electronmixed basis approachTOMBO

Explained by Kawazoe in 2000Description of wave functions in all-electron mixed basis approach:

Plane Wave (PW)Bloch Function of AO

Atomic Orbital (AO) Best in DFT+LDAPresent standard programs:Planewave+pseudopotential(VASP, ABINIT no core electronsWIEN, FLAPW: heavy computation, no complete relaxation

All-electron full-potential mixed-basis formulationAbsolute energy evaluationCore electron related physical properties such as hyperfine structure constantComplete relaxation of atomic positions: no muffintinHigh energy collisions of atomsFast : smaller number of plane waves (only 10,000 PWs for C60 )TOMBO(TOhoku UniversityMixed Basis Orbitals ab initio program) with GW approximation and Time dependent Schrdinger equation solver

1515C60 and C70 on Cu(111)

bias HOMO +bias LUMO

All-electron mixed basis: Phys. Rev. Lett. 71, 2959 (1993)With Prof. Gu and Ohno. 67papers with GuSTM Expt.Cutoff energy : 7 Ry in all-electron mixed basis approach 40 Ry in pseudopotentialPAWapproachNew additional featuresElectron transport: Y.-Y. Liang the first program using real electron transport via excited states using Wannier functionThermal transport: K. Esfarjani extension of phonon code including anharmonic termsVan der Waals force estimation: V. Belosldov computing dipoler polarization and diple-dipole interaction17Advantages:

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

17Fast atom collision process

19Ease of useprogram 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.html19Applications of TOMBO Hydrogen storage materialHyperfine structure constantAbsolute energy level estimationTime dependent Schroedinger equation

Cleanest hydrogen carrierClathrate hydratesKnown for methane hydrate under sea

Apply clathrate hydrate for hydrogen storage Hydrate Clathrate with H2 MoleculesExperimentally found in 2002X-ray, neutron experiments have difficulty to determine the atomic structureTOMBO applied to analyze in 2002>700 atoms with structure optimization Physico-chemical properties estimatedStability studiedSluiter, Belosludov, KawazoeSurprising New HydratesUntil recently, always at most: 1 Guest to 1 CageTherefore, very small atoms & molecules cannot stabilizehydrate clathrates. BUT..1992, Londono et al.: Helium stabilizes Ice II1993, 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 AstrophysicsDetermination of atomic properties of interstellar medium

BiochemistryRadicals: Identification of molecular radicals in solid, liquid and gaseous phasesTransition metals: Study of their effect on living tissues

Solid state physicsDefects: Identification of point-like defects in clusters and semiconductorsMetal clusters: structural determination of the clusters 2425Problems of available codesNot applicable: VASPApplicable but not accurate: GaussianAccurate but unbearably time consuming: WIEN2KNew method, applicable & accurate with minimal computational cost

All-electron mixed-basis methodTOMBO

2526

Hyperfine parametersHyperfine interaction in general contains two parameters:

Isotropic (Fermi contact): Comes from s-Orbitals

Anisotropic (Diplole): Comes from p-, d- and f-Orbitals

2627Hyperfine results for clustersclusterMethodM(2)M(5)Li7TOMBO100.05.1Exp.101.86.13Na7TOMBO325.516.7Exp.330.018.6K7TOMBO85.93.1Exp.85.55.0Cu7TOMBO1735.051.7Exp.174754Ag7TOMBO623.921.7Exp.685.025.0

M(5)M(2)Structure of clusters.Pentagonal bipyramidD5hValues are in MHzM. 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).27Virtual Materials Lab

Charge distribution in Cu7 cluster63Cu7 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)

Virtual Materials LabComparison with others63Cu7 pentagonal bipyramid cluster(top & bottom atom(2), 5-fold ring atom(5)

30Molecualr model for deoxymyoglobin

Hemoglobin (Heme part)Model for deoxymyoglobin3031Fe in pure Pdwith G.P. DasStrongly localized moment at the Fe siteA symmetric pattern of spin polarization around Fe.

M. S. Bahramy et al., J. Mag. Mag. Mater. 200631

Our researchPresent standardAb initio calculation does not use experimental parameters but uses a big approximation. More sofisticated method than LDA is necessary. quiasiparticleapproximationLouie group: crystal, pseudopotentialVSSP ver. 5.11 also has GW cal.TOMBO: any structure, all-electron: absolute energy estimationEasy to be parallelized; similar time as DFT cal.electronphotonAdd this Feynman diagram to standard LDAPrediction of photoemissionband gap value, relativenarrowExact valueexperimentGW approximationStandard LDABlue coloryellowAll-electron ab intio GW calculation to estimate for C60Ionization potential, electron affinity in absolute values and obtained the HOMO-LUMO gap of C60 exactly not relative values!!Ohno, Ishii, Adachi(eV)< m xc >< HLDA >< S x >< S c >E calcE expHOMO 14.06 6.61 14.900.01.0 7.5 7.6 aLUMO 11.18 5.26 7.80 0.71.0 2.6 2.6bDFT calculation and GW by TOMBOfor diamond crystal

keV)

DFT is for the ground state approximation gives us the band gap valueMore than GWA (Applicable to Metal)electronphoton in GWAApplicable with band gapWGGWA gives for metalseffective mass1, and narrow band width for alkali metalsMore than GWA Hedin, Yasuhara, only electron gas levelTime Dependent DFTTDSE:ij(x,t)/ t = H(t) j(x,t) normal pertubation: j(x,t+t) = j(x,t) - it H(t) j(x,t) 100 times heavier than CP:t =electronic motionModified method: In LDA, H H t=smallj(x,t+t) = exp(-it H(tc)) j(x,t)t is similar to CP.Suzuki-Trotter method)

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

Ni dimerHOMO: H bondingLUMO: Ni anti bondingNext I introduced Ni dimer and H2. Ni dimer is positioned at perpendicularly on the paper. HOMO is H bonding state and LUMO is Ni anti bonding state. In the case, H2 dissociate and comes to Ni dimer. If the charge transfer from H2 to Ni dimer occurs, this dissociation process occurred. Filally we can obtain the chemisorption of H on Ni dimer. 397/23/201340FP-DFT in a supercellModel PotentialThermal PropertiesMD-GKLatt DynHeat Transport and thermoelectrics40

Thermal conductivity of ZrCoSbSimulations vs ExperimentsB=3.6x10-43B=0B=9.1x10-44

Impurity scatteringY. Xia et al., J. Appl. Phys. 88, 1952 (2000).T. Sekimoto et al., Jpn. J. Appl. Phys. 46, L673 (2007).

CoZrSbShiomi, Esfarjani, Chen, Phys. Rev. B 84, 104302 (2011)

How to get TOMBO?Sales and Customer SupportHitachi Co.

TOMBO ver. 2.0 object code is free for academicians

Pls check our homepageTo have confidenceCatch phrase; from explanation to prediction!How to realize this condition?We should have good confidence to predict new materials without experimental observations.

Theoretical results should have quality assurance!Our system= quantum many body electron and nucleus system interacted via Coulomb forceCoulomb force= geometrical force in 3D spaceVirial theorem holds = a good measure for quality assurance (V/T=-2 for free system) :necessary condition44 Is total energy minimization good enough in ab initio calculation

No!!

Necessary condition = Virial theorem

T and V are not independent, for P=0 E=T+V=V/2=-T

Sufficient conditionsolve accurately 45fundamentals in ab initio calculation

variationl priciplequant. mech.Origin of ab initio calulation

quantum chemistry HF, CIab initio Monte Carlo methodExchange-correlation potential(manybody effect)density functional theoryLDA, GGA

Hohenberg-Kohn theorymany body wavef(3N dim.)

Charge density(3 dim.)

exact solutionVariational Mote Carlo (VMC) method Diffusion Monte Carlo (DMC) methodDFT is exact, but LDA, GGA are notFrom 3N dim to 3dim loses a lot!K-S wavefunction is for quasiparticle not electrons46HKHKLDAGGAcomputing cost for ab initio methodscomplete numerical calculation needed!Ab initio DMS seems to be a better method in futureComputer costquantitativeDFTN3Diffusion quantum MCN3N4DMCElectron NComputer costQuantum chemistryN6N!Full CI20 electrons47DMCDMCDMCHeeeIt is a complex three body problem. Not easy to be solved!H atom =Two body prob. exactly solvableHow is for He atom?2 electrons in 1s states?Correlation energy in electron system

-2.897585.3%-1.172394.5%Full CI[6-311++G(3df,2pd)]-2.9037100.0%DMCinitial 6-311++G(3pd,2pf)-1.1745(1)100.0%DMCiinitial 6-311++G(3pd,2pf) Many body problem should be solved!By HF+CI difficult to reach DFT also difficultDMC=Diffusion Monte Carlo method is a candidate -2.8616 hartree-2.9037-1.1333 hartee-1.1745HF[6-311++G(3df,2pd)]Exact(experimental)He atomH2 moleculeExact(experimental)49Full CIObjects of the materials research are many body system via Coulomb interactionSi, steel, DNA all the sameDescribed 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 resultsAnd, many misunderstandings happened!!!Why ab initio simulation can predict new materials in nanoscale?50Are LDA , GGA,(so called ab initio calculations) good enough? Computer simulationTM@Sin clusters

=ScTiVCrMnFeCoNiCustructureNormally within LDA, GGA good enough?

EgSinclustersSize dependencebulk

511.1eV

Cr@Sin clusters

GGA

B3PW91=good for organicspositive energy stablebut n=15(structural isomers GGA and B3PW91 give fundamentally different resultsn=12 clusterGGA and B3PW91 stable (magic) ok!more accurate method is necessary, and we have used DQMC to solve accurately with Exc and confirmed that GGA gives better solutionHongo, Kumar, Yasuhara, KawazoeMat. Trans. 200652nn=15GGAB3PW91Reliability in standard ab initio calculation

1. Ground state in iron???

2. hybrid model, LDA+U better than GGA?No! only a phenomenologygood for known materials, no power for prediction

53Accordingly!Better (than normal ab initio DFT) method is necessary to have confidence in our computational resultsBetween parallel spins, by the Paulis exclusion principle, electrons are separated, and they feel smaller Coulombic repulsion, and therefore the total energy reduces.Traditional explanation in the textbooks by Slater

Prof. J. C. SlaterJ. C. Slater, Phys. Rev. 34, 1293 (1929). THE THEORY OF COMPLEX SPECTRA, Using electron-electron interaction by perturbation, Hunds rule can be explained by the exchange energy. Explanation by perturbation theory by Slater55PauliSlater Slater

1. [10:31] 2. [10:42] 3. [10:55]Why traditional Slaters explanation is wrong?

J.C.Slater (1929)**

1 electron integralCoulomb integralexchange integralWrong!! becauseVirial theorem violated!!Same kinetic energy T Same electron-nucleus attractive potential VenElectron-electron energy Vee decreaces by the amount of exchange energy 2K12 ( Exchange energy )** J. C. Slater, Phys. Rev. 34, 1293 (1929)56Hund22Hund

Virial

StateEVenVeeT-V / TC (3P)-37.6886-88.1369

12.7596 37.6886

2.0000C (1D)-37.630212.81801.9985C (1S )-37.542612.90561.9961EX. Carbon atom; traditionally :orbitals for 3P is used also for 1D, 1SStateEVenVeeT-V / TC (3P)-37.6886-88.136912.759637.68862.000000004 C (1D)-37.6313-87.991012.728337.63132.000000004C (1S )-37.5496-87.766212.667037.54962.000000004Virial theorem satisfied : 3P, 1D, 1S each different orbitalstraditional explanation sets E =vee Unified interpretation of Hund's first and second rules for 2p and 3p atoms, JOURNAL OF CHEMICAL PHYSICS, 133[16] (2010) 164113, T. Oyamada, K. Hongo, Y. Kawazoe, and H. Yasuhara -V/T = completely wrong!Virial theorem : -V/T =2.00000057HFVirialEVenTVirialVirialVirialVirialVirial

CIEVenVeeT - V / TNi (3F)-1507.5054-3600.5174585.51071507.50142.000003Ni (1D)-1507.4424-3600.2551585.37321507.43952.000002Ni (3P)-1507.4333-3600.2018585.33771507.43082.000002Ni (1G)-1507.4017-3600.0737585.27481507.39722.000003Ni (1S)-1507.2621-3599.4583584.93631507.25982.000002E (3F)

0The interpretation of the stabilization mechanism of LS terms for the groundconfiguration of the Ni atom is the same as for the Ti atom. Results for [Ar]3d84s2 configuration of Ni atom: (Including correlation)The more stable LS term is due to the greater electron-nucleus attraction energy Ven that is gained at the cost of increasing the electron-electron repulsion energy Vee.Interpretation of Hunds 1st and 2nd rules (Relative stability of LS terms)This is MCHF results for 3d24s2 configuration of the titanium atom including correlation. We have obtained the following inequalities, which are consistent with the case of HF. The more stable LS term is due to the greater electron-nucleus attraction energy Ven that is gained at the cost of increasing the electron-electron repulsion energy Vee. The inclusion of correlation does not change the HF interpretation of the stabilization mechanism of LS terms for 3d24s2 configuration of the titanium atom.

58Perturbation methodEasy to understoodUsed long time

But.

Manybody problem is difficult Even dangarous sometimes!!Virial theorem satisfactionTheoryVirial theoremHatree-FockDensiy Functional TheoryHeitler-London ModelSlaters Perturbation Theory Hubbard ModelQunatum Monte CarloHatree-Fock with Conf. Int.Bardeen-Cooper-ShreeferLDA+UWe can compute what others can not!We should jump to a better paradigm, from only using ab initio calculation programs developed in Europe and US.Minimize amount of computation by PW+AOPlease join us to develop TOMBO together as an original software in Asia

No! You can not find me out!

WahYou find me out!

Carpet bombarding

Simulation study is easier to find necessary properties

No. of combination : binary= 3,000, ternary= 100 thousands

Limitaion of experimental study