Logo Quantum Monte Carlo simulations on silicate perovskite and … · 2014-08-17 · Quantum Monte...

Quantum Monte Carlo simulations on silicate perovskite and other high pressure phases

R E Cohen1,2 1Geophysical Laboratory, Carnegie Institution 2Dept. Earth Science, University College London

Cohen, 30 July, 2014 1 Quantum Monte Carlo in the Apuan Alps IX

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DFT, QMC, and DFT-DMFT Studies of some high pressure materials

•  SiO2 (CASINO) (Driver, Cohen, Wu, Militzer, Rios, Towler, Needs, &

Wilkins, PNAS 107, 9519 (2010). •  qmcpack on GPUs (Esler, Kim, Ceperley)

•  c-BN (qmcpack, GPU)(Esler, Cohen, Militzer, Kim, Needs, & Towler, PRL 104, 185702 (2010).

•  MgSiO3 (qmcpack, GPU) (Lin et al., submitted) •  FeSiO3 (DFT, xtalopt)(Cohen and Lin, submitted)

•  FeO (DFT-DMFT) (Ohta, Cohen, Hirose, Haule, Shimizu & Ohishi, PRL108, 026403, (2012)

Cohen, 30 July, 2014 Quantum Monte Carlo in the Apuan Alps IX 2

Beyond DFT: Quantum Monte Carlo Benchmark computations as standard

K. P. Driver, R. E. Cohen, Z. Wu, B. Militzer, et al., PNAS, 107, 9519-9524 (2010)

Boundary between Quartz and stishovite phases of SiO2

Boundary between CaCl2 and α-PbO2 phases of SiO2


Ken Esler (GL, Stone Ridge Technologies) Jeongnim Kim (NCSA, ORNL, Intel), Dave Ceperley (UIUC)

§  Ported the main functionality of a major QMC code to run fully on GPU clusters

§  In use for production simulations §  e.g. Phys. Rev. Lett. 104, 185702 (2010)

§  Achieves about 15x quad-core processor §  Some caveats (e.g. mixed precision vs. double §  CPU code is well optimized (SSE intrinsics, etc.)

§  Parallelized to run on MPI clusters of GPUs §  ~88% parallel efficiency with 256 GPUs


Why QMC on GPUs? § QMC consumes many cycles

§  e.g. ~70 million core hours on Jaguar in 2009 §  8k cores 24/7

§  It affords multiple levels for parallelization §  “Natural” Monte Carlo parallelism (walkers) §  Electrons, orbitals, ions, etc.

§ MPI communication requirements are low §  Primarily for load balancing

§ With GPUs §  Small problems are doable on a workstation §  Large problems are much cheaper


Why not QMC on GPUs? § Many kernels to port

§  No single major kernel §  Wave functions take many forms §  Subset of functionality: §  ~100 CUDA kernels, ~10k lines of kernel code

§ Algorithms and data need restructuring §  Need to utilize more parallelism than on CPUs

§ Debugging stochastic methods is hard § No libraries for the kernels we need


QMCPACK §  http://www.qmcpack.org

§  Paul Kent, ORNL (was Jeongnim Kim) §  https://groups.google.com/forum/#!forum/qmcpack

§  Open source C++ code (NCSA license) §  Hybrid OpenMP/MPI programming model

§  Scaled to > 200k cores with > 90% efficiency

§  Heavy use of template meta-programming §  At least as fast as any comparable code §  Kernels hand-tuned with SSE

§  Object-oriented style for extensibility


QMCPACK


•  Variational Monte Carlo •  Diffusion Monte Carlo •  Reptation •  Single and multi-determinant Slater Jastrow wavefunctions •  Wavefunction updates using optimized multi-determinant algorithm of Clark et al. •  Backflow wavefunctions •  One, two, and three-body Jastrow factors •  Excited state calculations via flexible occupancy assignment of Slater determinants •  All electron and non-local pseudopotential calculations •  Casula T-moves for variational evaluation of non-local pseudopotentials •  Wavefunction optimization using the “linear method” of Umrigar and co-workers, with arbitrary mix of variance and

energy in the objective function •  Gaussian, Slater, plane-wave and real-space spline basis sets for orbitals •  Interface and conversion utilities for plane-wave wavefunctions from Quantum Espresso (PWSCF) •  Interface and conversion utilities for Gaussian-basis wavefunctions from GAMESS •  Easy extension and interfacing to other electronic structure codes via standardized XML and HDF5 inputs •  MPI parallelism •  Fully threaded using OpenMP •  GPU (CUDA) implementation (limited functionality) •  HDF5 input/output for large data •  “Project Suite” advanced workflow tool to automate all aspects of QMC calculation from initial DFT calculations through

to final analysis •  Analysis tools for minimal environments (perl only) through to python-based with graphs produced via matplotlib. •  Although primarily used for electronic structure problems, within QMCPACK the Hamiltonian definition is very flexible

and also suited to some model systems.

Scaling with the number of GPUs

§  Higher throughput on GPUs puts greater demand on interconnect

§  Down to 88% efficiency on Lincoln at 256 GPUs

§  Newer clusters have faster interconnects and PCI-E bus (e.g. upcoming Cray XK6)

§  Direct GPU-to-GPU transfer now possible on one node

§  K. Esler, J. Kim, L. Shulenburger, and D. Ceperley, “Fully accelerating quantum Monte Carlo simulations of real materials on GPU clusters”, Computing in Science and Engineering doi: 10.1109/MCSE.2010.122 (2010)

§  Symposium on Application Accelerators in High Performance Computing http://saahpc.ncsa.illinois.edu/10/papers/paper_27.pdf

§  K. P. Esler, R. E. Cohen, B. Militzer, Jeongnim Kim, R. J. Needs, and M. D. Towler, “Fundamental High-Pressure Calibration from All-Electron Quantum Monte Carlo Calculations”, Phys. Rev. Lett. 104, 185702 (2010)


cBN as a pressure standard


Cubic boron nitride is an ideal pressure standard.

• Stable over wide pressure and temperature range

• Single Raman mode for calibration • Single lattice parameter

Equation of state of c-BN


Equation of state of c-BN: comparing PPs

About a 5% discrepancy at high pressure: not useful for an ab initio calibration!


All-electron QMC for solids •  Current QMC calculations on

solids use pseudopotentials (PPs) from Hartree-Fock or DFT

•  When different PPs give different results, how do we know which to use?

•  In DFT, decide based on agreement with all-electron calculation

•  We would like to do the same in QMC. Has only been done for hydrogen and helium.

•  LAPW is generally gold standard for DFT.

•  Use orbitals from LAPW calculation in QMC simulation.

•  Requires efficient evaluation methods and careful numerics

•  Use atomic-like representation near nuclei, plane-wave or B-splines in interstitial region:


Results §  After all-electron correction, EOS from 3 PPs in perfect

agreement §  Details in EPAS of Phys. Rev. Lett. 104, 185702 (2010)


cBN Raman Frequencies •  Within harmonic approx. DFT frequency is reasonable

•  But, cBN Raman mode is quite anharmonic

•  With anharmonic corrections, DFT frequencies are not so good.

•  Compute energy vs. displacement with DMC and do 4th-order fit. Solve 1D Schrodinger eq. to get frequency

•  Anharmonic DMC frequency is correct to within statistical error


cBN Raman Frequencies •  Raman frequencies are linear in 1/V •  When combined with EOS, data can be used

to directly measure pressure from the Raman frequency

•  There is some intrinsic T-dependent shift due to anharmonicity


MgSiO3, the Dominant Component of the Earth’s Lower Mantle

Inner core

Outer core

Lower mantle

Upper mantle

lithosphere

Core (iron with nickel and sulfur)

Mantle (silicate materials)

Crust (granitic and basaltic rocks)

Ocean MgSiO3Perovskite

MgSiO3Post-Perovskite

125GPa, 2500K

M. Murakami, K. Hirose, K. Kawamura, et al., Science, 304, 855-858 (2004) T. Litaka, K. Hirose, K. Kawamura, et al., Nature, 430, 442-445, (2004)

D”



1987

Cohen, 30 July, 2014 Quantum Monte Carlo in the Apuan Alps IX 24 Supported by NSF

MgSiO3Perovskite MgSiO3

Post-Perovskite

We obtained the QMC trial wavefunction from DFT calculations using PWSCF

( ) ( )∑ ↓↑=i

iii DDC φφψAS denotes a set of single-particle orbitals. are the up-(down-) spin Slater determinant. { }φ ( )↓↑ DD

We obtained the optimized one and two-body Jastrow factors using VMC calculations with a linear method

AS21T ψψ JJ= ( )⎥⎦

⎤⎢⎣

⎡−= ∑∑

0

1 expion

I

e

iIiabuJ Rr ( )⎥

⎦

⎤⎢⎣

⎡−= ∑∑

e

i

e

jjiabuJ rrexp2

A better set of Jastrow factors gives the smaller VMC energy and lower variance

QMC computations for MgSiO3 perovskite and post-perovskite

We obtained the total energies using DMC calculations with 0.001 steptime and 25,000 steps

https://code.google.com/p/qmcpack/


Finite Size Corrections and Infinite Size Energy Extrapolation QMC deals with isolated systems and without consideration of periodic boundary conditions

We used the 8 twists average to reduce the one-body finite size errors. To reduce the two-body finite size errors, we used the Model Periodic Coulomb (MPC) interaction to correct the potential energy and used the scheme of Chiesa, Ceperley and Martin (CCM) to correct the kinetic energy.

Einf


Pv: 40 atom supercell 2x1x1




QMC Equations of States of MgSiO3 Perovskite and Post-Perovskite

With the above procedures, we obtained the DFT and DMC energies at several volumes of MgSiO3 Perovskite and Post-Perovskite cells

Vinet energy and pressure equations

( )( ) ( )[ ] ( )( )⎥⎦

⎤⎢⎣

⎡ −−ʹ′−−−ʹ′+−ʹ′−−ʹ′

+= − 1123exp313512

14

002

00020

000 xKxxKKKV

KVKEE

( ) 3/10VVx =( ) ( )( )⎥⎦

⎤⎢⎣

⎡ −−ʹ′−⎥⎦

⎤⎢⎣

⎡ −= 11

23exp13

020 xKx

xKP PVEH +=


Thermal Equation of State Parameters, Pv


Thermal Equation of State Parameters, PPv


Pv-PPv Volume difference at 300K


Kamabayashi et al. EPSL 265, 515 (2008)


Thermal pressure from quasiharmonic lattice dynamics with DFT

Thermal Expansivity


Isotherm for Thermal Expansivity


MgSiO3 Perovskite and Post-Perovskite Phases Transition Pressure

Phases transition occurs at ΔG = 0


Oganov and Ono, Nature (2004)

MgSiO3 Perovskite and Post-Perovskite Phase Boundary


Post-perovskite The Last Mantle Phase Transition?



while children had detectable antibodies to PfSEA-1.These data suggest that anti–PfSEA-1 responsescould augment responses to other targets, suchas PfEMP-1, that may protect against severe ma-laria (24). Under conditions of natural exposure,only 6% of 1.5- to 3.5-year-old children in ourcohort had detectable antibodies to PfSEA-1. Thislow natural prevalence suggests that adjuvantedvaccination with PfSEA-1 could have a markedimpact on reducing severe malaria in youngchildren.In a second longitudinal Kenyan cohort, anti–

PfSEA-1 antibodies were associated with signif-icant protection against parasitemia in adolescentsand young adults. Individuals with detectableIgG anti–rPfSEA-1A antibodies had 50% lowerparasite densities over 18 weeks of follow-upcompared with individuals with no detectableIgG anti-rPfSEA-1A antibodies. It was noteworthythat the prevalence of detectable anti–rPfSEA-1Aantibodies in this age group (56%) was substan-tially higher than in our birth cohort, which sug-gests that natural exposure boosts anti–PfSEA-1 antibody levels.Together, our data validate our field-to-lab-to-

field-based strategy for the rational identifica-tion of vaccine candidates and support PfSEA-1as a candidate for pediatric falciparum malaria.By blocking schizont egress, PfSEA-1 may syn-ergize with other vaccines targeting hepatocyte(25) and RBC invasion (26).

REFERENCES AND NOTES

1. C. J. Murray et al., Lancet 379, 413–431 (2012).2. WHO, The World Malaria Report (WHO, Switzerland, 2012);

www.who.int/malaria/publications/world_malaria_report_2012/en/index.html.

3. S. Okie, N. Engl. J. Med. 353, 1877–1881 (2005).4. WHO, Malaria Vaccine Rainbow Tables (2012); www.who.int/

vaccine_research/links/Rainbow/en/index.html.5. A. N. Hodder, P. E. Crewther, R. F. Anders, Infect. Immun. 69,

3286–3294 (2001).6. A. Sabchareon et al., Am. J. Trop. Med. Hyg. 45, 297–308 (1991).7. J. D. Kurtis, D. E. Lanar, M. Opollo, P. E. Duffy, Infect. Immun.

67, 3424–3429 (1999).8. T. K. Mutabingwa et al., PLOS Med. 2, e407 (2005).9. R. Spaccapelo et al., Sci. Rep. 1, 39 (2011).10. N. D. Gómez et al., PLOS ONE 6, e25477 (2011).11. M. Kadekoppala, R. A. O’Donnell, M. Grainger, B. S. Crabb,

A. A. Holder, Eukaryot. Cell 7, 2123–2132 (2008).12. C. P. Nixon et al., J. Infect. Dis. 192, 861–869 (2005).13. M. Treeck, J. L. Sanders, J. E. Elias, J. C. Boothroyd,

Cell Host Microbe 10, 410–419 (2011).14. M. Manske et al., Nature 487, 375–379 (2012).15. J. D. Dvorin et al., Science 328, 910–912 (2010).16. A. Farrell et al., Science 335, 218–221 (2012).17. M. J. Blackman, H. G. Heidrich, S. Donachie, J. S. McBride,

A. A. Holder, J. Exp. Med. 172, 379–382 (1990).18. E. S. Bergmann-Leitner, E. H. Duncan, E. Angov, Malar. J. 8, 183

(2009).19. N. Ahlborg et al., Exp. Parasitol. 82, 155–163 (1996).20. I. D. Goodyer, B. Pouvelle, T. G. Schneider, D. P. Trelka,

T. F. Taraschi, Mol. Biochem. Parasitol. 87, 13–28 (1997).21. S. Yoshida et al., PLOS ONE 5, e13727 (2010).22. J. D. Kurtis, R. Mtalib, F. K. Onyango, P. E. Duffy, Infect. Immun.

69, 123–128 (2001).23. J. C. Beier et al., Am. J. Trop. Med. Hyg. 50, 529–536 (1994).24. P. C. Bull et al., J. Infect. Dis. 192, 1119–1126 (2005).25. RTS,S Clinical Trials Partnership, N. Engl. J. Med. 365,

1863–1875 (2011).26. C. Crosnier et al., Nature 480, 534–537 (2011).

ACKNOWLEDGMENTS

The authors thank the Mother Offspring Malaria Study projectstaff for their efforts in collecting clinical data, processing samples,and interpreting malaria blood smears, as well as the study

participants and their families. Ethical clearance was obtainedfrom the institutitional review boards of the Seattle BiomedicalResearch Institute and Rhode Island Hospital; the MedicalResearch Coordinating Committee of the National Institute forMedical Research, Tanzania; and the Kenyan Medical ResearchInstitute. We thank A. Muehlenbachs for assistance in interpretingthe electron microscopy images, B. Morrison for assistancewith data management, and D. Lanar for the LSA proteins. Thiswork was supported by grants from the U.S. National Institutesof Health (NIH) (grant R01-AI52059) and the Bill & MelindaGates Foundation (grant 1364) to P.E.D., the IntramuralResearch Program of the National Institute of Allergy andInfectious Diseases–NIH, and grants from NIH (grantR01-AI076353) and an internal Lifespan Hospital SystemResearch Pilot Award Grant to J.D.K., and grants fromNIH to J.D.D. (R01-AI102907 and DP2-AI112219). C.E.N.(grant T32-DA013911) and I.C.M. (grant 1K08AI100997-01A1)were supported by NIH. We also acknowledge researchcore services provided by the Rhode Island Hospital imagingcore (G. Hovanesian) and core services supported byLifespan/Tufts/Brown Center for Aids Research (P30AI042853)and Center for Biomedical Research Excellence (P20GM103421).The DNA sequence for PfSEA-1 is available in PlasmoDB(www.Plasmodb.org) as ID no. PF3D7_1021800. The work presentedin this manuscript has been submitted in partial support of patentapplication PCT/US12/67404 filed with the U.S. Patent Office. J.D.K.,

J.F.F., M.F., and P.E.D. designed the study; J.D.K., D.K.R., J.F.F.,M.F., and P.E.D. drafted the manuscript; M.F. and P.E.D.conducted the field-based sample and epidemiologic datacollection; C.P.N. conducted the differential screening; D.K.R,L.P., A.L., C.E.N., and L.C. performed the in vitro growth assays;D.K.R. and G.J. performed the immunolocalization; D.K.R.performed the gene knockout studies; C.G.D., E.A.M., S.A., andJ.D.D. performed the conditional gene knockdown studies; I.C.M.performed the single-nucleotide polymorphism detection; S.P.-T.,L.C., and H.-W.W. performed the antibody detection assays;S.P.-T. expressed and purified rPf SEA-1A and rPbSEA-1A; D.K.R.,C.E.N., and S.C. performed the vaccination studies; J.F.F., J.D.K.,and S.E.H. performed the statistical analyses; and J.D.K., J.F.F.,M.F., and P.E.D. supervised the study. The authors declare nocompeting financial interests.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/334/6186/871/suppl/DC1Materials and MethodsSupplementary TextTables S1 and S2Figs. S1 to S11References (27–41)

30 October 2013; accepted 25 April 201410.1126/science.1254417

DEEP EARTH

Disproportionation of (Mg,Fe)SiO3perovskite in Earth’s deeplower mantleLi Zhang,1,2* Yue Meng,3 Wenge Yang,1,4 Lin Wang,1,4 Wendy L. Mao,5,6 Qiao-Shi Zeng,5

Jong Seok Jeong,7 Andrew J. Wagner,7 K. Andre Mkhoyan,7 Wenjun Liu,8

Ruqing Xu,8 Ho-kwang Mao1,2

The mineralogical constitution of the Earth’s mantle dictates the geophysical andgeochemical properties of this region. Previous models of a perovskite-dominant lowermantle have been built on the assumption that the entire lower mantle down to thetop of the D″ layer contains ferromagnesian silicate [(Mg,Fe)SiO3] with nominally10 mole percent Fe. On the basis of experiments in laser-heated diamond anvil cells, atpressures of 95 to 101 gigapascals and temperatures of 2200 to 2400 kelvin, we foundthat such perovskite is unstable; it loses its Fe and disproportionates to a nearlyFe-free MgSiO3 perovskite phase and an Fe-rich phase with a hexagonal structure. Thisobservation has implications for enigmatic seismic features beyond ~2000 kilometersdepth and suggests that the lower mantle may contain previously unidentifiedmajor phases.

The conventional view of materials in Earth’slower mantle, which comprises the largestfraction of our planet (>55% by volume), hasevolved greatly in the past 10 years. High-pressure-temperature (P-T) experiments of

the past century suggested that the predominantphase was ferromagnesian silicate [(Mg,Fe)SiO3]with the orthorhombic perovskite (pv) structure,unchanging over the enormous P-T range from thebottom of the transition zone at 670 km depth(24 GPa) to the core-mantle boundary (CMB) at2900km (136GPa).However, laser-heated diamondanvil cell (DAC) technology coupled with x-rayspectroscopy (XRS) and x-ray diffraction (XRD)probes have led to two key discoveries: namely,the phase transition of (Mg,Fe)SiO3 pv to the

post-perovskite (ppv) structure (1–3) near the D″layer of the lower mantle, and the pressure-induced spin-pairing of the 3d electrons in Fe (4–6)

1Center for High Pressure Science and Technology AdvancedResearch (HPSTAR), Shanghai 201203, China. 2GeophysicalLaboratory, Carnegie Institution of Washington (CIW),Washington, DC 20015, USA. 3High Pressure CollaborativeAccess Team (HPCAT), Geophysical Laboratory, CIW, Argonne,IL 60439, USA. 4High Pressure Synergetic Consortium(HPSynC), Geophysical Laboratory, CIW, Argonne, IL 60439,USA. 5Geological and Environmental Sciences, StanfordUniversity, Stanford, CA 94305, USA. 6Photon Science, SLACNational Accelerator Laboratory, Menlo Park, CA 94025, USA.7Department of Chemical Engineering and Materials Science,University of Minnesota, Minneapolis, MN 55455 USA.8Advanced Photon Source, Argonne National Laboratory,Argonne, IL 60439, USA.*Corresponding author. E-mail: [email protected]

SCIENCE sciencemag.org 23 MAY 2014 • VOL 344 ISSUE 6186 877

RESEARCH | RESEARCH ARTICLES

while children had detectable antibodies to PfSEA-1.These data suggest that anti–PfSEA-1 responsescould augment responses to other targets, suchas PfEMP-1, that may protect against severe ma-laria (24). Under conditions of natural exposure,only 6% of 1.5- to 3.5-year-old children in ourcohort had detectable antibodies to PfSEA-1. Thislow natural prevalence suggests that adjuvantedvaccination with PfSEA-1 could have a markedimpact on reducing severe malaria in youngchildren.In a second longitudinal Kenyan cohort, anti–

PfSEA-1 antibodies were associated with signif-icant protection against parasitemia in adolescentsand young adults. Individuals with detectableIgG anti–rPfSEA-1A antibodies had 50% lowerparasite densities over 18 weeks of follow-upcompared with individuals with no detectableIgG anti-rPfSEA-1A antibodies. It was noteworthythat the prevalence of detectable anti–rPfSEA-1Aantibodies in this age group (56%) was substan-tially higher than in our birth cohort, which sug-gests that natural exposure boosts anti–PfSEA-1 antibody levels.Together, our data validate our field-to-lab-to-

field-based strategy for the rational identifica-tion of vaccine candidates and support PfSEA-1as a candidate for pediatric falciparum malaria.By blocking schizont egress, PfSEA-1 may syn-ergize with other vaccines targeting hepatocyte(25) and RBC invasion (26).

REFERENCES AND NOTES

1. C. J. Murray et al., Lancet 379, 413–431 (2012).2. WHO, The World Malaria Report (WHO, Switzerland, 2012);

www.who.int/malaria/publications/world_malaria_report_2012/en/index.html.

3. S. Okie, N. Engl. J. Med. 353, 1877–1881 (2005).4. WHO, Malaria Vaccine Rainbow Tables (2012); www.who.int/

vaccine_research/links/Rainbow/en/index.html.5. A. N. Hodder, P. E. Crewther, R. F. Anders, Infect. Immun. 69,

3286–3294 (2001).6. A. Sabchareon et al., Am. J. Trop. Med. Hyg. 45, 297–308 (1991).7. J. D. Kurtis, D. E. Lanar, M. Opollo, P. E. Duffy, Infect. Immun.

67, 3424–3429 (1999).8. T. K. Mutabingwa et al., PLOS Med. 2, e407 (2005).9. R. Spaccapelo et al., Sci. Rep. 1, 39 (2011).10. N. D. Gómez et al., PLOS ONE 6, e25477 (2011).11. M. Kadekoppala, R. A. O’Donnell, M. Grainger, B. S. Crabb,

A. A. Holder, Eukaryot. Cell 7, 2123–2132 (2008).12. C. P. Nixon et al., J. Infect. Dis. 192, 861–869 (2005).13. M. Treeck, J. L. Sanders, J. E. Elias, J. C. Boothroyd,

Cell Host Microbe 10, 410–419 (2011).14. M. Manske et al., Nature 487, 375–379 (2012).15. J. D. Dvorin et al., Science 328, 910–912 (2010).16. A. Farrell et al., Science 335, 218–221 (2012).17. M. J. Blackman, H. G. Heidrich, S. Donachie, J. S. McBride,

A. A. Holder, J. Exp. Med. 172, 379–382 (1990).18. E. S. Bergmann-Leitner, E. H. Duncan, E. Angov, Malar. J. 8, 183

(2009).19. N. Ahlborg et al., Exp. Parasitol. 82, 155–163 (1996).20. I. D. Goodyer, B. Pouvelle, T. G. Schneider, D. P. Trelka,

T. F. Taraschi, Mol. Biochem. Parasitol. 87, 13–28 (1997).21. S. Yoshida et al., PLOS ONE 5, e13727 (2010).22. J. D. Kurtis, R. Mtalib, F. K. Onyango, P. E. Duffy, Infect. Immun.

69, 123–128 (2001).23. J. C. Beier et al., Am. J. Trop. Med. Hyg. 50, 529–536 (1994).24. P. C. Bull et al., J. Infect. Dis. 192, 1119–1126 (2005).25. RTS,S Clinical Trials Partnership, N. Engl. J. Med. 365,

1863–1875 (2011).26. C. Crosnier et al., Nature 480, 534–537 (2011).

ACKNOWLEDGMENTS

The authors thank the Mother Offspring Malaria Study projectstaff for their efforts in collecting clinical data, processing samples,and interpreting malaria blood smears, as well as the study

participants and their families. Ethical clearance was obtainedfrom the institutitional review boards of the Seattle BiomedicalResearch Institute and Rhode Island Hospital; the MedicalResearch Coordinating Committee of the National Institute forMedical Research, Tanzania; and the Kenyan Medical ResearchInstitute. We thank A. Muehlenbachs for assistance in interpretingthe electron microscopy images, B. Morrison for assistancewith data management, and D. Lanar for the LSA proteins. Thiswork was supported by grants from the U.S. National Institutesof Health (NIH) (grant R01-AI52059) and the Bill & MelindaGates Foundation (grant 1364) to P.E.D., the IntramuralResearch Program of the National Institute of Allergy andInfectious Diseases–NIH, and grants from NIH (grantR01-AI076353) and an internal Lifespan Hospital SystemResearch Pilot Award Grant to J.D.K., and grants fromNIH to J.D.D. (R01-AI102907 and DP2-AI112219). C.E.N.(grant T32-DA013911) and I.C.M. (grant 1K08AI100997-01A1)were supported by NIH. We also acknowledge researchcore services provided by the Rhode Island Hospital imagingcore (G. Hovanesian) and core services supported byLifespan/Tufts/Brown Center for Aids Research (P30AI042853)and Center for Biomedical Research Excellence (P20GM103421).The DNA sequence for PfSEA-1 is available in PlasmoDB(www.Plasmodb.org) as ID no. PF3D7_1021800. The work presentedin this manuscript has been submitted in partial support of patentapplication PCT/US12/67404 filed with the U.S. Patent Office. J.D.K.,

J.F.F., M.F., and P.E.D. designed the study; J.D.K., D.K.R., J.F.F.,M.F., and P.E.D. drafted the manuscript; M.F. and P.E.D.conducted the field-based sample and epidemiologic datacollection; C.P.N. conducted the differential screening; D.K.R,L.P., A.L., C.E.N., and L.C. performed the in vitro growth assays;D.K.R. and G.J. performed the immunolocalization; D.K.R.performed the gene knockout studies; C.G.D., E.A.M., S.A., andJ.D.D. performed the conditional gene knockdown studies; I.C.M.performed the single-nucleotide polymorphism detection; S.P.-T.,L.C., and H.-W.W. performed the antibody detection assays;S.P.-T. expressed and purified rPf SEA-1A and rPbSEA-1A; D.K.R.,C.E.N., and S.C. performed the vaccination studies; J.F.F., J.D.K.,and S.E.H. performed the statistical analyses; and J.D.K., J.F.F.,M.F., and P.E.D. supervised the study. The authors declare nocompeting financial interests.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/334/6186/871/suppl/DC1Materials and MethodsSupplementary TextTables S1 and S2Figs. S1 to S11References (27–41)

30 October 2013; accepted 25 April 201410.1126/science.1254417

DEEP EARTH

Disproportionation of (Mg,Fe)SiO3perovskite in Earth’s deeplower mantleLi Zhang,1,2* Yue Meng,3 Wenge Yang,1,4 Lin Wang,1,4 Wendy L. Mao,5,6 Qiao-Shi Zeng,5

Jong Seok Jeong,7 Andrew J. Wagner,7 K. Andre Mkhoyan,7 Wenjun Liu,8

Ruqing Xu,8 Ho-kwang Mao1,2

The mineralogical constitution of the Earth’s mantle dictates the geophysical andgeochemical properties of this region. Previous models of a perovskite-dominant lowermantle have been built on the assumption that the entire lower mantle down to thetop of the D″ layer contains ferromagnesian silicate [(Mg,Fe)SiO3] with nominally10 mole percent Fe. On the basis of experiments in laser-heated diamond anvil cells, atpressures of 95 to 101 gigapascals and temperatures of 2200 to 2400 kelvin, we foundthat such perovskite is unstable; it loses its Fe and disproportionates to a nearlyFe-free MgSiO3 perovskite phase and an Fe-rich phase with a hexagonal structure. Thisobservation has implications for enigmatic seismic features beyond ~2000 kilometersdepth and suggests that the lower mantle may contain previously unidentifiedmajor phases.

The conventional view of materials in Earth’slower mantle, which comprises the largestfraction of our planet (>55% by volume), hasevolved greatly in the past 10 years. High-pressure-temperature (P-T) experiments of

the past century suggested that the predominantphase was ferromagnesian silicate [(Mg,Fe)SiO3]with the orthorhombic perovskite (pv) structure,unchanging over the enormous P-T range from thebottom of the transition zone at 670 km depth(24 GPa) to the core-mantle boundary (CMB) at2900km (136GPa).However, laser-heated diamondanvil cell (DAC) technology coupled with x-rayspectroscopy (XRS) and x-ray diffraction (XRD)probes have led to two key discoveries: namely,the phase transition of (Mg,Fe)SiO3 pv to the

post-perovskite (ppv) structure (1–3) near the D″layer of the lower mantle, and the pressure-induced spin-pairing of the 3d electrons in Fe (4–6)

1Center for High Pressure Science and Technology AdvancedResearch (HPSTAR), Shanghai 201203, China. 2GeophysicalLaboratory, Carnegie Institution of Washington (CIW),Washington, DC 20015, USA. 3High Pressure CollaborativeAccess Team (HPCAT), Geophysical Laboratory, CIW, Argonne,IL 60439, USA. 4High Pressure Synergetic Consortium(HPSynC), Geophysical Laboratory, CIW, Argonne, IL 60439,USA. 5Geological and Environmental Sciences, StanfordUniversity, Stanford, CA 94305, USA. 6Photon Science, SLACNational Accelerator Laboratory, Menlo Park, CA 94025, USA.7Department of Chemical Engineering and Materials Science,University of Minnesota, Minneapolis, MN 55455 USA.8Advanced Photon Source, Argonne National Laboratory,Argonne, IL 60439, USA.*Corresponding author. E-mail: [email protected]



coexisting MgSiO3 pv suggests an (Mg,Fe)SiO3

composition with Fe enrichment.We repeated the Fs15 experiments with Ne pres-

sure medium five times over the same P-T regionand were able to observe the disproportionationreaction and the formation of the H-phase re-peatedly (Fig. 1 and fig. S4).We found that theH-phase growsmore readily in theNemedium,whichprovides a quasi-hydrostatic environment that issuperior to that of other media. To eliminate thepossibility of any experimental artifacts intro-duced by Ne, we have also successfully repeatedthe observation of the disproportionation andappearance of the H-phase with SiO2 glass as thepressuremedia and insulation layers withoutNe.

Symmetry and Unit Cell Parametersof H-phase

In the two-phase mixed XRD pattern, the low-symmetry orthorhombic pv has many peaksinterfering with the H-phase peaks at the lowd-spacing region; only three peaks above 2.4 Åare specific to the H-phase. Moreover, powderXRD patterns only contain d-spacing information,and successful indexing of multiple peaks couldstill be inconclusive. The spottiness of the XRDpowder pattern may also introduce uncertaintyin peak intensity (fig. S8). On the other hand,single-crystal XRD contains three-dimensionalorientation and geometrical relationship in addi-tion to d-spacings and thus provides a moredefinitive characterization of the unit cell.We used a multigrain crystallography method

(22) to search and determine the orientationmatrices ofmultiple individual crystallites simul-taneously within the sample (20). We conductedprolonged laser-heating that promoted growthof a coarser-grained multiple-crystal aggregate,including MgSiO3 pv and H-phase crystals at101 GPa (Fig. 2A). By rotating the w (vertical) axisof the DAC holder to T21° at the steps of 0.1°,154 individual crystallites—each with 11 to 27reflections consistent with the H-phase—wereidentified within the x-ray beam spot of 6 by8 mm (Tables 1 and 2 and table S1). Six {101}diffraction reflections belonging to three Friedel’spairs from another crystallite further confirmthese results (Fig. 2B). With the stringent re-quirement that all reflections from each of the154 crystallites must satisfy the d-spacing, rota-tion angle w, and azimuthal angle h predicted byits particular orientation matrix, we confirmedthe symmetry and the basic unit cell of theH-phase. For comparison in the same sample at101 GPa using the same indexing procedure (20),we also identified and indexed 130 individualcrystallites of theMgSiO3 pv phase to the knownPbnm space group, with the maximum of 48reflections observed in a crystallite.To verify that all predicted reflections were in-

deed from the same single crystallite and not for-tuitously from the diffraction of another crystallitewithin the 6 by 8 mm x-ray spot, we were able tocover only about 10 crystallites by using the 0.3 by0.5 mm focused polychromatic and monochromaticx-ray beam (23). Thepolychromatic LaueXRDspotsof different Miller indices appear and disappear

Table 2. Single-crystal XRD data for the H-phase in Fs15 starting composition at 101 GPa.The unit-cell parameters of the H-phase are a = 5.096(2) Å, c = 2.862(3) Å; a = b = 90°, g = 120° at101 GPa.The single-crystal XRD data of one of the crystallites was obtained for the H-phase with anx-ray wavelength of 0.3738 Å. The Bragg angle 2q, rotation angle w, and azimuthal angle h arecalculated from the orientation matrix and observed as XRD spots.

h k l 2q (degrees) w (degrees) h (degrees) d (Å)

–1 0 1 8.93 –1.3 63.4 2.395–1 1 1 8.93 –16.2 32.8 2.3950 1 –1 8.93 –11.4 268.8 2.4011 –1 –1 8.95 0.3 212.8 2.3991 0 –1 8.95 8.7 243.2 2.402

–1 –1 1 11.29 3.0 87.4 1.8971 1 –1 11.27 14.3 267.3 1.902

–2 2 1 12.3 12.1 22.1 1.7410 –2 1 12.27 –12.4 105.9 1.7460 2 –1 12.25 0.3 285.7 1.751–1 –2 1 14.92 3.9 101.7 1.4361 0 –2 15.82 –4.1 240.6 1.358

–2 1 2 17.28 –12.4 47.6 1.242–1 –1 2 17.29 –15.6 75.8 1.2421 1 –2 17.22 2.3 255.7 1.2482 –1 –2 17.25 11.0 227.4 1.245

–2 0 2 17.97 –6.5 63.1 1.1942 –2 –2 17.95 8.6 211.9 1.1982 0 –2 17.93 13.7 242.9 1.199

–1 4 –1 19.04 0.5 304.4 1.129–1 –2 2 19.89 –12.1 88.0 1.0821 2 –2 19.79 7.8 267.9 1.0872 1 –2 19.81 16.8 256.4 1.086

–3 2 2 19.88 –3.1 38.2 1.0810 –4 1 20.94 –8.4 120.3 1.0290 4 –1 20.82 15.6 300.1 1.0330 3 –2 20.92 0.4 278.7 1.030

Fig. 2. Selection of MgSiO3 pv and H-phase individual single crystals using the multigrain method.(A) A representative spotty multiple-crystal XRD pattern of the H-phase and coexisting pv in Fs15 at101 GPa and after Tquench (x-ray wavelength of 0.3738 Å), and the marked Miller indices show some ofthe most intense diffraction spots. (B) Six {101} diffraction reflections at different rotation angle w andazimuthal angle h belonging to one selected crystallite of the H-phase at 101 GPa.



H-phase, a New Phase of Silicate in the Earth’s Mantle?

L. Zhang, et al. Science 344, 877 (2014)

Zhang et al., Science 2014, claim discovery of a new phase of (Mg,Fe)SiO3 they call the H phase based on X-‐ray powder diffraction.

They say the H-phase has hexagonal structure.

Atomic positions in the unit cell of H-phase are unknown.


Structure Evolution Algorithm in XtalOpt 1. Random Sampling

2. Genetic Algorithms

Given component atoms and ranges of lattice parameters

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

minmax

min1HHHHCp i

i 1=∑i

ip

pi, selection probability of structure i

Hi, DFT enthalpy of structure i

C normalization constant

Selection for Mating

Mating

Mutation

DFT Relaxation

Pool of Structures (Relaxed from DFT Calculations)

D. Lonie, and E. Zurek, Comp. Phys. Comm. 182, 372 (2011)


Mating and Mutation Operators

Crossover, Strain, Exchange, Ripple, and their hybrids

D. Lonie, and E. Zurek, Comp. Phys. Comm. 182, 372 (2011) Cohen, 30 July, 2014 Quantum Monte Carlo in the Apuan Alps IX 44

PPv-II Structure, Comparison with PPv

PPv-II, ChM PPv, Cecum


X-ray Diffraction Pattern, Comparison II

“The XRD peaks are almost for pure H-phase”

85GPa

Pv: MgSiO3

PPv-‐II: FeSiO3

PPv: FeSiO3

*Two main peaks of H-phase compare well with those of PPv-II FeSiO3. PPv-II has more peaks. Cohen, 30 July, 2014 Quantum Monte Carlo in the Apuan Alps IX 49

Phase Stability of Pv, PPv and PPv-II phases

Both Pv and PPv phases of FeSiO3 are more stable than PPv-II at T=0 K.

It is possible that PPv-II became stable at high temperature.


PPv-II continuous phase transition at lower pressures

At low pressures, Cmmm goes to C2/m via small displacements. Cohen, 30 July, 2014 Quantum Monte Carlo in the Apuan Alps IX 52

•  At ambient pressure FeO is an antiferromagnetic insulator with a rock salt structure

•  Iron 3d states partially filled, but localized

•  Borderline between charge transfer and Mott insulator

•  Difficult to make stoichiometric FeO in the lab at low pressures (vacancies yield Fe1-xO where x ~ 0.07) but stoichiometric under pressure

Background: FeO


The phase diagram as of 1994 (Fei and Mao, Science, 266, 1678, 1994)

Knittle and Jeanloz, JGR 1991

FeO wüstite is an insulator at ambient conditions

•  LDA/GGA etc. make it a metal

Cohen et al. (1998) High-Pressure Materials Research. Materials Research Society. 499.

• LDA+U does open a gap in AFM rhombohedral or lower symmetry FeO and predicts a metal insulator transition under pressure, but not a high-spin low-spin transition. (Gramsch, Cohen, and Savrasov, Am. Mineral., 88, 257 (2003). • LDA+U is a model, and how accurate it is unknown. • LDA+U cannot give a gap in paramagnetic FeO.


I N(M ) = 1

N(M ) = MΔε x

Extended Stoner model Increase in bandwidth causes spin collapse:


Magnetic collapse vs. High-spin low-spin transition vs. Orbital ordering in FeO


Moment 4μB

4 t2g 2 eg

Moment 0 6 t2g

t2g t2g

t2g

eg eg

Note: LDA+U cannot give an insualting state for cubic FeO

LDA-DMFT

Lattice Problem (DFT) LAPW

Atomic Problem (Many-body theory: DMFT)

H = h + tijciα† cjβ∑∑ Lattice Problem (contains geometry)

Simp = Satom + dt dt 'cα†∇(t − t ')∫ cβ∫

Impurity Model (CTQMC)

∇HDFT

Gimp

Σ

New density


Φ ρ,Gloc[ ] = EH ρ[ ] + ExcLDA ρ[ ] + Φ Gloc[ ]− ΦDC n[ ]

Fully self-consistent, finite temperature

DFT-DMFT


P ω + µ −HKS −Ε ′Σ( )−1 = ω − Eimp − Σ imp − Δ( )−1

G(k,iω ) = [(iω + µ)O(k

)−HKS (k

)− ′Σ (iω )]−1 Crystal problem

“Impurity” problem

Self-consistency condition Kristjan Haule DFT-DMFT code:

integrates wien2k LAPW code for Crystal with Continuous Time Quantum Monte Carlo (CTQMC) for impurity Fully self-consistent in charge density ρ, chemical potential μ, impurity levels Eimp, hybridization Δ, and self-energy Σ. Calculations are done on imaginary frequency ω axis, and analytically continued to real axis.

No down folding, fully self-consistent


Both Hubbard interaction and Hund’s coupling are included inCTQMC

HI =X

La,··· ,Ld ,m,��0

2lX

k=0

4⇡F k{l}

2k + 1hYLa |Ykm|YLc i

⇥ hYLd |Y⇤km|YLbi f

†La,�

f †Lb,�0 fLd ,�0 fLc�

YL are spherical harmonics

F k{l} are Slater integrals

F 0 is the Hubbard U, derived from cRPA, cLDA or GW

F 2, · · · ,F 6 are reduced by 30% of their atomic values due toscreening e↵ects


Haule

Continuous Time Quantum Monte Carlo (CTQMC)

QMC over Feynman diagrams Imaginary time (frequency)


Haule

GW: non-local interactions, no quantum fluctuations, bands have infinite lifetimes (widths)

DMFT: local interactions, quantum fluctuations, bands have widths (finite lifetimes)

CTQMC

β 0


Histogram of number of kinks on Feynman diagrams


300K

2000K

Number of kinks 1000 0 500

V/V0=1, High Spin

Experimental evidence of metallization at high P and T


Ohta, Cohen, et al., 2012 Kenji Ohta, Katsuya Shimizu, Osaka

University, Yasuo Ohishi, Japan Synchrotron Radiation Research Institute, Kei Hirose, Tokyo Institute of Technology

FeO d dos (Maximum entropy)


t2g

eg

13 GPa 62 GPa

88 GPa 157 GPa

230 GPa 250 GPa

3 GPa 45 GPa

68 GPa

FeO Density of States


Ohta et al., 2011

DC conductivity versus pressure


Magnetic state, complex phase diagrams, transitions with large density and elasticity changes, T-dependent electronic structure, sensitivity to defects, chemistry and strain (stress) state, metal-insulator transitions

Metal insulator transition (Hubbard model) Kotliar et al. RMP (2006)

Metallization is not like this in FeO:


DMFT orbital occupancy transition (HS-LS crossover)


Experimental equation of state: Fischer et al. EPSL 2011

Spectral Function A(k,ω)


V=405 au, V/V0=0.75, 68 GPa 300K V=405 au, V/V0=0.75, 88 GPa 2000K

Low spin insulator -> low spin metal

High spin at low P


V=540 au, V/V0=1

eg2 t2g4

HS

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 200 400 600 800 1000 1200

2000K300K

d5 d7

Spin fluctuations è metallization


0

0.05

0.1

0.15

0.2

0.25

0 200 400 600 800 1000 1200

2000 K300 K

V=405 au, V/V0=0.75, 68 GPa 300K V=405 au, V/V0=0.75, 88 GPa 2000K

eg0 t2g6

eg2 t2g4

LS

HS

More could be said…


•  SiO2 (CASINO) (Driver, Cohen, Wu, Militzer, Rios, Towler, Needs, &

Wilkins, PNAS 107, 9519 (2010). •  qmcpack on GPUs (Esler, Kim, Ceperley)

•  c-BN (qmcpack, GPU)(Esler, Cohen, Militzer, Kim, Needs, & Towler, PRL 104, 185702 (2010).

•  MgSiO3 (qmcpack, GPU) (Lin et al., submitted) •  FeSiO3 (DFT, xtalopt)(Cohen and Lin, submitted)

•  FeO (DFT-DMFT) (Ohta, Cohen, Hirose, Haule, Shimizu & Ohishi, PRL108, 026403, (2012)—now χ and TN with Peng Zhang

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