A challenge to electronic structure theory from magnetic resonance experiments

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A challenge to electronic structure theory from
magnetic resonance experiments

• Seeing atoms with quantum mechanics

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Theory working with experiments
Diffraction spots
Quantitative theory
Solved structure
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Magnetic Resonance
NMR
EPR
Chemical shielding tensors Electric field
gradients J-coupling constants
g-tensors Hyperfine coupling constants
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What is nuclear magnetic resonance?
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What is special about solid state NMR?
Chemical shift anisotropy
Quadrupolar coupling
Dipolar coupling
Electronic structure and bonding
Internuclear proximities and distances
Motional processes
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Magic angle spinning (MAS)
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Why bother with a theory of SS-NMR?
To help experimentalists
To test our theories

• Comparison to accurate, repeatable experimentally
  determined parameters is an unforgiving test of
  theory
• There is a abundance of high quality NMR data
  available
• Disagreement with this data will force advances
  in theory

• NMR is a ubiquitous experimental technique
• Particularly in the solid state a lack of an
  empirical understanding of structure-spectra
  correlations
• Help the assignment of spectra, testing of
  hypotheses and design of experiments

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Chemical Shielding
Calculate the induced current in the
system Obtain the chemical shielding, s
Use perturbation theory
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The cluster approximation

• Need to choose as small a cluster as possible
• How the cluster is built is crucial to ensure
  rapid convergence with size
• How should the cluster be terminated in covalent
  systems?
• How should the electrostatics be dealt with in
  ionic systems?
• This seems like a lot of hard work why not use
  the translational symmetry of the crystal?

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The cluster approximation

• Need to choose as small a cluster as possible
• How the cluster is built is crucial to ensure
  rapid convergence with size
• How should the cluster be terminated in covalent
  systems?
• How should the electrostatics be dealt with in
  ionic systems?
• This seems like a lot of hard work why not use
  the translational symmetry of the crystal?

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A solid state pseudopotential theory of Nuclear
Magnetic Resonance
Solid state
Pseudopotential

• A naïve extension of the quantum chemical problem
  will fail
• This is due to the classic problem of
  perturbation operators proportional to r
• Mauri, Pfrommer and Louie solved this in 1996
• Take the long wavelength limit of a slowly
  varying B field instead

• It was not initially expected that a
  pseudopotential theory could exist
• The core contribution was thought to be dependent
  on the chemical environment
• Gregor, Mauri, Car showed that this was not true
• But there was still the problem of dealing with
  the pseudowavefunction near the nucleus

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Pseudopotentials are all-electron

• Ab initio pseudopotential calculations always
  were all-electron just not thought of that way
• This changed with Blöchls Projector Augmented
  Waves (PAW)

• The core electrons can be relaxed
• all-electron pseudopotentials
• And they are relativistic
• scalar relativistic by construction, and through
  ZORA for chemical shifts
• spin-orbit pseudopotentials

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The GIPAW method

• Theory
• Based on the plane wave pseudopotential approach
• Periodic boundary conditions
• All-electron results recovered using gauge
  including projector augmented waves (GIPAWs)

• Performance
• Results for single molecules same as Quantum
  Chemical approaches
• Same quality of results for infinite crystals
• Straightforward convergence with basis set

• Computational cost
• L-Glutamic Acid 84 atoms about 16hrs on a
  2.8GHz P4
• around 100 atoms on a PC
• around 200 atoms on a cluster
• up to 1000 atoms supercomputer

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Amino acids glutamic acid

• Oxygen-17 NMR
• a uniquely valuable probe of hydrogen-bonding
• few studies in organic compounds due to large
  quadrupolar interaction

• Using the GIPAW method
• we assign the spectra of L-Glutamic Acid.HCl
• find correlations between NMR parameters and
  hydrogen-bond strength

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A solid state theory for J-coupling

• First theory for extended systems
• No gauge origin problem
• Extreme test of accuracy
• All terms computed using PAW
• Systematic convergence with basis

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Hydrogen bonds in aminofulvene aldimines
H
Solution
N9
N1
2JN1N9 9.0 Hz 8.92 Hz
2JN1N9 8.0 Hz 8.48 Hz
Solid
H
N9
N1
2JN1N9 8.6 Hz 8.56 Hz
2JN1N9 7.2 Hz 8.06 Hz
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Challenge 1 DFT structures
P2 defect in silica two low T ( 18
EPR g-tensor allows identification
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Challenge 2 dynamics
25Mg chemical shift in MgO
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MgO and CaO

• MgO and CaO have the same structure
• But, Ca has upoccupied 3d states near the
  occupied states
• Mg-O is purely ionic
• Ca-O is iono-covalent (the Ca 3d can partially
  hybridise with the O 2p)

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Challenge 3 DFT response properties
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Theoretical context

• DFT-LDA/GGA does not give the correct excited
  state spectrum
• The band gap problem exists for all insulators
• But, we observe the chemical shifts to be
  generally good

• The situation can be more complex localised
  orbitals can be shifted relatively
• This can change the degree of hybridisation
• This changes the calculated response properties

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Comparison with GW results
GW data from Atsushi Yamasaki
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Solving structures

• Imagine we can meet the challenges
• We can calculate parameters for any configuration
  of atoms
• Even non-physical ones
• We could move the atoms until our theory matches
  experiment
• Solving the inverse problem
• Gradients of parameters can be evaluated using
  DFTPT
• We have first order wavefunctions with respect to
  ionic positions as well (phonons)

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Outlook

• We already have a useful technique to complement
  solid state magnetic resonance experiments
• Chemical shift tensors
• Quadrupolar coupling
• g-tensors
• Hyperfine parameters
• J-coupling
• There are still challenges
• DFT structures
• DFT response properties
• Temperature

• Modern electronic structure methods have a unique
  opportunity to revolutionise the interpretation
  of magnetic resonance experiments
• Can we develop a quantitative theory of solid
  state NMR to match that of diffraction based
  methods?

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First principles NMR
Porphyrins
Pharmaceutical polymorphs
1H 13C
1H, 13C, 19F
Tellurite glasses
Amino acids
Zirconates
17O 23Na 125Te
17O 31P
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Projects and collaborators

• Minerals and glasses
• Ian Farnan, Sharon Ashbrook, Laurent Le Polles,
  Etienne Balan, Stephanie Rossano minerals
• Bjoern Winkler, Ute Hantsch silicates
• Michele Warren Al/Si disorder
• Thibault Charpentier Na silicate glasses
• Magali Benoit, Mickael Profeta Ca silicate
  glasses

• Theoretical Developments
• Francesco Mauri
• Jonathan Yates chemical shifts
• Sian Joyce J-coupling constants
• Rachel Strong EPR g-tensor

• Molecular crystals
• Robin Harris, Phuong Ghi pharmaceutical
  polymorphism
• Ray Dupree, Cristel Gervais amino acids
• Steven Brown sugars and guanine ribbons,
  J-couplings

• Biological systems
• Itzam De Gortari, Matt Segall amyloid fibrils
• Melinda Duer, Helen Chappell hydroxyapatite
  and bone