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GIPAW-NMR method
Transcript of GIPAW-NMR method
GIPAW-NMR method
apsi<[email protected]>
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Outline
● PART I: Introduction to NMR● Introduction to NMR● ChemicalShielding & ElectricFieldGradients
● PART II: GIPAW method● GIPAW for CS; extensions● (GI)PAW for EFG
● PART III: Applications of GIPAW method● Examples
● PART IV: Using the GIPAW module● Implementation● Input/output of GIPAW module
PART I: Introduction to NMR
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NMR spectroscopy
● Microscopic: Gives information about the
individual atoms (~ Å)
● Sensitive to the local environment of the atoms
● … but requires modelling/theoretical input
● Solids, amorphous, liquid, gaseous samples
● Time scale: ~ ms
Nuclear Magnetic Resonance
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Principles of MR spectroscopy
B
Induced orbital currents:● structure and chemical bonds● local electronic structure
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NMR technology
Two fields applied:● Static, homogeneous field: Align magnetic moments● Oscillating field: Excite between two (or two) magnetic energy
levels
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Response to magnetic field
The interaction depends on the local environment
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Spin-polarised nuclei
Isotopic enriching
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Spin-polarised nuclei
Isotopic enriching
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NMR Hamiltonian
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NMR Hamiltonian: Chemical shift
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Chemical shift
From the NMR Hamiltonian the shielding tensor is defined as:
It can be calculated via the response:
The chemical shift is then defined by
is a reference value in a well-characterised material
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Chemical shift: Linear response
The electronic structure does not depend explicitly on the magnetic field but implicitly through the wave functions. Their contribution can be calculated in perturbation theory:
GS wfcs perturbed wfcs
induced current
induced field
DFPT to magn. field
Biot-Savart
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Converse approach to chemical shielding
● Modern Theory of the Orbital Magnetisation
● Instead of direct approach
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Macroscopic shape
● The ring currents at the surface can lead to a notiseable signal● In anisotropic samples the effect can lead to a dependence on the
shape of the sample
Example: Haldane model:
From: T Thonhauser, Davide Ceresoli, David Vanderbilt & R Resta, Phys Rev Lett 95 (2005) 137205
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NMR Hamiltonian: Electric field gradient
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EFG: Electric Field Gradient
In quadrupolar nuclei; non-zero only when no cubic symmetry
Principal axis system: Eigenvectors and -values of
Convention:
Observables:● Quadrupolar coupling constant
● Asymmetry parameter
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NMR Hamiltonian: J coupling
PART II: GIPAW method
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Chemical shielding
● An external magnetic field leads to current leads to induced field:
● Task: Calculate the induced current via perturbation theory● Condensed phase – infinite systems● Reconstruct the wave functions and density close to the nucleus
due to the pseudo potential approach
Biot-Savart's law
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Magnetic field – gauge problem
● The result depends on the atomic coordinate
● One has to cure the gauge problem
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GIPAW method
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GIPAW method
● Introduce the gauge correction into the PAW scheme:
● The observables:
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GIPAW method
● First-order, perturbing potential:
● Perturbed orbitals:
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GIPAW method
● All-electron current operator:
● In GIPAW:
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GIPAW method● Expansion:
● Expectation value of first-order current:
● After regrouping:
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GIPAW method
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GIPAW method
● Trick: Replace
● In practise finite q: Too large, not accurate; too small, numerical problems
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GIPAW method
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● Collecting the terms, using on-site approximation:
Finally:
Biot-Savart:
GIPAW method
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Macroscopic shape
● The macroscopic shape appears via the susceptibility
where
In GIPAW
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Core relaxation
Core contribution has been shown to be to a large degree a constant, independent of the environment
Thomas Gregor, Francesco Mauri & Roberto Car, J Chem Phys 111 (1999) 1815
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(GI)PAW method: EFG
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(GI)PAW method: EFG
● This is evaluated using the PAW equations for the density
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GIPAW: Extensions
● Vanderbilt ultra-soft pseudo potentials ; Jonathan R Yates, Chris
J Pickard & Francesco Mauri, Phys Rev B 76 (2007) 024401
● Metals; Knight shift ; Mayeul d'Avezac, Nicola Marzari &
Francesco Mauri, Phys Rev B 76 (2007) 165122
● J coupling ; Sian A Joyce, Jonathan R Yates, Chris J Pickard &
Francesco Mauri, J Chem Phys 127 (2007) 204107
● EPR ; C J Pickard & F Mauri, Phys Rev Lett 88 (2002) 086403 ;
Davide Ceresoli, Uwe Gerstmann, apsi & Francesco Mauri,
arXiv.org:0904.1988
● NMR ; T Thonhauser, Davide Ceresoli, Arash A Mostoli, Nicola
Marzari, R Resta & David Vanderbilt, arXiv.org:0709.4429
PART III: Applications of GIPAW
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Applications using GIPAW: Molecules
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Applications using GIPAW: Molecules
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Applications using GIPAW: SiO2
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Applications using GIPAW: SiO2
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Applications using GIPAW: SiO2
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Applications using GIPAW: MgSiO3
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Applications using GIPAW: MgSiO3
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Applications using GIPAW: MgSiO3
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Applications using GIPAW: CNT
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Applications using GIPAW: CNT
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Applications using GIPAW: Metals
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Applications using GIPAW: Metals
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Applications using GIPAW: v-B2O3
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Applications using GIPAW: v-B2O3
Fraction of borons in boroxol rings:
• Experiments:• MD simulations:(Raman, NMR, inelastic diffusion…)(empirical potentials)
f = 6085 %f = 030 %
• molecular units:
OB
• boroxol rings:
firstprinciples MD?!
B B
B
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Applications using GIPAW: v-B2O3
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Applications using GIPAW: v-B2O3
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Applications using GIPAW: v-B2O3
Explanation for the former controversy:Explanation for the former controversy:
The simulations started from low concentration of The simulations started from low concentration of boroxyl, the quench did not allow for proper boroxyl, the quench did not allow for proper equilibrationequilibration
PART IV: Implementation of GIPAW in Q-E
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GIPAW implementations
● paratec
● CASTEP; commercial
● Quantum ESPRESSO
URL: http://www.gipaw.net/
The GIPAW module● General framework for computing magnetic resonance (MR)
spectra and more...
● Available for production in Espresso-4.1Credits: D. Ceresoli, A. P. Seitsonen, U. Gerstmann and F. Mauri
● Capabilities
Magnetic susceptibility NMR shielding tensors Electric Field Gradients (EFGs)
EPR g-tensor Hyperfine couplings
XAS (S. Fabris and Y. Yao) XANES (G. Gougoussis and M. Calandra)
● Simple input and nicely formatted output for calculated quantities
NMR
EPR
X-Ray
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GIPAW@Q-E: Limitations
● Only norm-conserving pseudo potentials currently
● The symmetry operations have to map coordinate axis to each
other, otherwise operation should be excluded!
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GIPAW pseudo potentials
● At the time of this school (July 2009), our GIPAW implementation works only with special norm-conserving PP's(eg. H.pbe-tm-gipaw.UPF)
● The PP's are generated according to existing (and well tested) NC-PP's
● They contain extra datasets, including:● core AE wfcs● valence AE and PS wfcs, 2 x angular momentum● AE and PS atomic potential
● They can be generated using the ld1.x code. A short guide is available at
http://www.impmc.upmc.fr/~software/gipaw/instructions.html
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Oxygen GIPAW pseudo potential &input title = 'O' prefix = 'O' zed = 8.0 rel = 1 config = '1s2 2s2 2p4 3s-1 3p-1 3d-1' iswitch = 3 dft = 'PBE' / &inputp pseudotype = 1 tm = .true. lloc = 2 file_pseudopw = 'O.pbe-tm-gipaw.UPF' lgipaw_reconstruction = .true. /32S 1 0 2.00 0.00 1.40 1.402P 2 1 4.00 0.00 1.40 1.403D 3 2 -1.00 -0.30 1.40 1.40 &test /42S 1 0 2.00 0.00 1.40 1.402P 2 1 4.00 0.00 1.40 1.403S 2 0 0.00 0.00 1.40 1.403P 3 1 0.00 -0.10 1.40 1.40
config.: 1s2 2s2 2p4
empty: 3s, 3p, 3d
PSEUDO: 1 proj x ang. mom.
GIPAW: 2 proj x ang. mom.3p unbound -> scattering state at -0.1 Ry
NC-PP lmax = 2, lloc = 2
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Oxygen GIPAW pseudo potential
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Oxygen GIPAW pseudo potential
NMR on benzene (C6H6)
FILE: benzene-relax.in
&control prefix = 'benzene' outdir = './scratch/'.../
&system.../
...
ATOMIC_SPECIESC 12.000 C.pbe-tm-gipaw.UPFH 2.000 H.pbe-tm-gipaw.UPF
ATOMIC_POSITIONS angstrom...
K_POINTS automatic1 1 1 0 0 0
FILE: benzene-nmr.in
&inputgipaw job = 'nmr' Prefix = 'benzene' tmp_dir = './scratch/' q_gipaw = 0.01 use_nmr_macroscopic_shape = .true./
FILE: benzene-efg.in
&inputgipaw job = 'efg' prefix = 'benzene' tmp_dir = './scratch/'/
pw.x -in benzene-scf.in > benzene-scf.outgipaw.x -in benzene-nmr.in > benzene-nmr.outgipaw.x -in benzene-efg.in > benzene-efg.out
benzene-nmr.out
Program GIPAW v.4.1 starts ... Today is 21Jul2005 at 8:52:20
Parallel version (MPI)
Number of processors in use: 4 R & G space division: proc/pool = 4
Planes per process (thick) : nr3 = 96 npp = 24 ncplane = 9216
Proc/ planes cols G planes cols G columns G Pool (dense grid) (smooth grid) (wavefct grid) 1 24 1377 82821 24 1377 82821 345 10373 2 24 1377 82819 24 1377 82819 344 10372 3 24 1377 82819 24 1377 82819 346 10374 4 24 1378 82820 24 1378 82820 346 10374 tot 96 5509 331279 96 5509 331279 1381 41493
init_gipaw_1: projectors nearly linearly dependent: ntyp = 1, l/n1/n2 = 0 2 1 0.99854824 init_gipaw_1: projectors nearly linearly dependent: ntyp = 1, l/n1/n2 = 1 2 1 0.99933412 init_gipaw_1: projectors nearly linearly dependent: ntyp = 2, l/n1/n2 = 0 2 1 0.99706935
NMR: species C, contribution to shift due to core = 200.510NMR: species H, no information on the core
benzene-nmr.out
f-sum rule: -29.9594 0.0000 0.0000 0.0000 -29.9594 0.0000 0.0000 0.0000 -29.9725
f-sum rule (symmetrized): -29.9594 0.0000 0.0000 0.0000 -29.9594 0.0000 0.0000 0.0000 -29.9725
chi_bare pGv (HH) in 10^{-6} cm^3/mol: -35.1776 0.0000 0.0000 0.0000 -35.1776 0.0000 0.0000 0.0000 -91.7273
chi_bare vGv (VV) in 10^{-6} cm^3/mol: -31.2502 0.0000 0.0000 0.0000 -31.2502 0.0000 0.0000 0.0000 -94.3768
benzene-nmr.out
NMR chemical bare shifts in ppm:
Atom 1 C pos: ( 0.131936 0.000000 0.000000) sigma: -100.1731 -181.7889 0.0000 0.0000 0.0000 -109.8400 0.0000 0.0000 0.0000 -8.8903
Atom 2 C pos: ( 0.065968 0.114260 0.000000) sigma: -100.1731 -127.8272 -31.1548 0.0000 -31.1548 -163.8017 0.0000 0.0000 0.0000 -8.8903
NMR chemical diamagnetic shifts in ppm:
Atom 1 C pos: ( 0.131936 0.000000 0.000000) sigma: 4.0081 4.0056 0.0000 0.0000 0.0000 4.0056 0.0000 0.0000 0.0000 4.0130
NMR chemical paramagnetic shifts in ppm:
Atom 1 C pos: ( 0.131936 0.000000 0.000000) sigma: -57.5707 -85.7823 0.0000 0.0000 0.0000 -59.3537 0.0000 0.0000 0.0000 -27.5761
benzene-nmr.out
Total NMR chemical shifts in ppm:
Atom 1 C pos: ( 0.131936 0.000000 0.000000) sigma: 46.7743 -63.0556 0.0000 0.0000 0.0000 35.3219 0.0000 0.0000 0.0000 168.0566
Symmetric tensor -63.0556 0.0000 0.0000 0.0000 35.3219 0.0000 0.0000 0.0000 168.0566
eigenvalue: 168.0566 eigenvector: 0.0000 0.0000 1.0000
eigenvalue: 35.3219 eigenvector: 0.0000 -1.0000 0.0000
eigenvalue: -63.0556 eigenvector: 1.0000 0.0000 0.0000
Anti-symmetric tensor 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
benzene-efg.out
Total EFG calculation:
C 1 efg -0.127585 0.000000 0.000000 C 1 efg 0.000000 -0.208497 0.000000 C 1 efg 0.000000 0.000000 0.336082
C 1 eig= 0.336082 -0.127585 -0.208497 C 1 Q= 1.00 10e-30 m^2 Cq= 0.7897 MHz eta= 0.24075
C 2 efg -0.188269 0.035036 0.000000 C 2 efg 0.035036 -0.147813 0.000000 C 2 efg 0.000000 0.000000 0.336082
C 2 eig= 0.336082 -0.127585 -0.208497 C 2 Q= 1.00 10e-30 m^2 Cq= 0.7897 MHz eta= 0.24075
benzene-efg.out
H 7 efg 0.276516 0.000000 0.000000 H 7 efg 0.000000 -0.129257 0.000000 H 7 efg 0.000000 0.000000 -0.147259
H 7 eig= 0.276516 -0.129257 -0.147259 H 7 Q= 1.00 10e-30 m^2 Cq= 0.6497 MHz eta= 0.06510
Acknowledgements
● Francesco Mauri
● Davide Ceresoli
Thibault Charpentier