new materials/electronic structure in 21 st century
DESCRIPTION
New materials/electronic structure in 21 st century. Typical features: - multi-component, hierarchies - 0-3D (dots, chains, layers ... ) - d- and f- elements - H: proton as a quantum part. - organic/inorganic/solid - bioinspired. Challenges: - lack of a "unifying" strategy - PowerPoint PPT PresentationTRANSCRIPT
New materials/electronic structure in 21st century
Typical features:- multi-component, hierarchies- 0-3D (dots, chains, layers ... ) - d- and f- elements - H: proton as a quantum part. - organic/inorganic/solid- bioinspired
H r1, r2, ... E r
1, r2,...
Solving these one-by-one, ie, by a postdoc focused on a class of materials for X years is ultimately inefficient
Unifying concept on which we all agree: Schrodinger equation
Solve it in the many-body framework (!)
Challenges: - lack of a "unifying" strategy - complexity - competition of mechanisms: quantum, temperature, etc - single electron/quantum effects important
H12i
i2
i,I
ZI
riI
i j
1
rij
Eionionwith the original Hamiltonian
Computational Materials Research
Key goals: - predict, design and optimize new materials for 21st century - complement, guide and/or replace experiment - new science frontier: from one-particle to many-bodyBroad application areas: - new energy sources: production/storage/processing of H - nanosystems based materials - bioinspired materials and processes: waste is nonexistentClear-cut example of previous impact: - 3rd most cited PRL in all physics and history is Ceperley/Alder Quantum Monte Carlo of homogeneous electron gasPossibilities/breakthroughs with 500-fold increase in compute power: - a few meV accuracy for energy differences - quantum effects, temperature, dynamics on the same footing - nanosystems in action, magnetism, supreconductivity in a wave function framework - H (bonded, solvated, ...): proton as a quantum particle
Quantum Monte Carlo: a unique strategy/opportunity for quantum
many-body problems
-sample the wave function by walkers in space -boost the efficiency with explicitly correlated trial functions -propagate the walkers while enforcing all required symmetries -evaluate the expectation values of interest
QMC: - new physics/paradigm: work directly on many-body effects - scalable, robust, highly efficient on parallel architectures - favorable scaling in # of particles: nominally ~ O( N3) and implentation with almost ~ O( N ) feasible - accurate: typically ~ 95% of correlation energy across systems 0.1 eV/1% accuracy/agreement with experiment - benchmarks for other methods, consistent results
R, t R exp H R' R', t d R'
Schrodinger equation in a propagator form
R r1, r2,..., r
N
QMC bottlenecks and advanatges: next 5-10 years
Scientific: - beyond the fixed-node approximation, very active research: obtain ~ 99% of correlation with polynomial scaling - spin and spatial degrees of freedom on the same footing - responses to external fields and spectral functions - from wave functions to density matrices (temperature)
Mix of Science and Algorithmic/Computational: - more efficient and accurate building of trial functions: eg, robust stochastic optimizations - efficient coupling and data exchange with one-particle approaches Hardware/ 1. processor speedSoftware: 2. parallelism 3. stability (QMC can test it real well) 4. memory, communication, etc, relevant but secondary
Qauntum Monte Carlo: typical run
System: 50 atoms, 200 electrons, desired accuracy ~ 0.1 - 0.2 eV Typical input: tens/hunderds of MB (initial/trial wave function)
Typical run: - tens of processors for days and weeks - MPI - 10-100s walkers in 3N-dim. space per processor - evolved for hundreds of steps (independently, or occasionally rebalanced) - accumulate statistics from processors Typical output: - most of the data reduced to simple physical quantities - current walker configurations stored (tens of MB per proc) - restartable
Materials with competing many-body effects: hexaborides CaB6,
LaxCa1-xB6 , ... 5% La-doped CaB6 is a weak magnet up to 900K (!) No d or f electrons: - genuine itinerant magnetism ? - promising spintronics material ?
Calculations inconclusive:DFT: band overlap 1 eV (Swiss,...)DFT: small gap (Japan)GW (DFT+ pert. corr.): 1 eV gap (NL)GW: small overlap (Japan)
Undoped CaB6 : insulator ? exitonic insulator ? metal ?
Experiments contardictory: ARPES: insulatorde Haas-van Alphen: metal Optical, etc: metal, insulator
Can we predict the correct gap before the experiment ?
CaB6 band structure in Hartree-Fock
Large gap of the order of 7 eV
CaB6 band structure in DFT - B3LYP
Gap is now only about 0.5 eV !
CaB6 band structure in DFT - PW91
1 eV overlap at the X point: d-states on Ca !
Fixed-node DMC gap:
1.3(3) eV
X G
Predict a "nanomagnet": caged transition elements TM@Si12 TM=Sc,
Ti, ... 3d, 4d, 5d
APS March Meeting in '94:L. M.: Electronic structure of Mn@Si12
- attempt to predict caged d-spin - no success, hybridized, unstable
Experiment in Japan in '01! W@Si12
Find the smallest stable "nanomagnet" made from silicon and a transition metal atom ...