Calculating the hyperfine coupling constant: Difference between revisions
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A second structural problem will come from the precise {{FILE|POSCAR}} that you use. Slightly different lattice parameters (10 mÅ) can change the hyperfine coupling constant by ~0.5 MHz. Make sure to use a [[Structure optimization|well-optimized structure]]. | A second structural problem will come from the precise {{FILE|POSCAR}} that you use. Slightly different lattice parameters (10 mÅ) can change the hyperfine coupling constant by ~0.5 MHz. Make sure to use a [[Structure optimization|well-optimized structure]]. | ||
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===PAW pseudopotentials=== | ===PAW pseudopotentials=== | ||
The choice of PAW | The choice of PAW pseudopotential can be important. GW pseudopotentials (i.e. _GW) underestimate the hyperfine coupling parameter with respect to experiment. With improved methods (i.e., HSE06), the difference is less significant. We recommend using standard pseudopotentials, though the use of GW should not be completely excluded. Additional valence electrons (i.e., _sv, _pv) should be considered for systems with heavier elements as they are likely important. | ||
REMOVE IF TO BE PUBLISHED: These are for CH3 radical and NV defect in diamond - it is not clear what the reason for this is | |||
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The | ===Hybrid functionals=== | ||
The calculated hyperfine coupling parameter is strongly influenced by the chosen method. PBE tends to underestimate the coupling constant relative to experiment. HSE06 and other [[:Category:Category:Hybrid functionals|hybrid functionals]] improve this, matching well with experiment {{Cite|szasz:prb:2013}}. Hybrid functional localize defect states, resulting in an improved description over GGA functionals. The {{FILE|INCAR}} tags are specified in for [[List of hybrid functionals|hybrid functionals]] and no additional tags are required. We found that the improvement for hybrid functionals is seen for both range-separated and unscreened hbrid functionals. | |||
* The PAW pseudopotential that you use should be considered. | * The PAW pseudopotential that you use should be considered. | ||
** Including additional electrons in the valence (i.e. _sv, _pv) can be important. | ** Including additional electrons in the valence (i.e. _sv, _pv) can be important. | ||
** GW pseudopotentials (i.e. _GW) can have a big effect on the hyperfine coupling parameter. | ** GW pseudopotentials (i.e. _GW) can have a big effect on the hyperfine coupling parameter. | ||
* Hybrid functionals give a better description than GGA. HSE06 can localize defect states, improving their description relative to PBE | * Hybrid functionals give a better description than GGA. HSE06 can localize defect states, improving their description relative to PBE. | ||
* We recommend using tightly converged settings: | * We recommend using tightly converged settings: | ||
{{TAG|PREC}} = Accurate | {{TAG|PREC}} = Accurate | ||
Revision as of 14:16, 5 March 2025
The hyperfine coupling constant (cf. hyperfine splitting) describes the interaction between the nuclear magnetic dipole moment and the magnetic field generated by the electrons (i.e. the nuclear spin-electron spin coupling. The hyperfine coupling constant is calculated using LHYPERFINE [1]. The hyperfine splitting often includes the interaction between the nuclear quadrupole moment and the electric field gradient (EFG), which is calculated separately using LEFG and the description in performing an EFG calculation. The hyperfine splitting can be measured using electron paramagnetic resonance (EPR), also called electron-spin resonance (ESR), and in atomic spectroscopy. The theory is covered in the NMR category page and LHYPERFINE page.
Step-by-step instructions
The hyperfine constant is calculated post-self-consistent field (SCF) using LHYPERFINE. A well-converged SCF calculation is therefore crucial. The hyperfine coupling constant is sensitive to several input parameters that must all be tested.
Step 1 (optional): Calculate the hyperfine constant using a previously converged calculation.
Since the hyperfine constant is calculated post-SCF, you can use a previously converged WAVECAR with ISTART = 1 and NELM = 1. The corresponding density, CHGCAR is calculated from the WAVECAR file before the first elementary step so need not be provided.
Step 2a: Define the nuclear gyromagnetic ratios
The hyperfine coupling constant depends on the nuclear gyromagnetic ratios defined in NGYROMAG. Since the defaults are set to 1, the gyromagnetic ratios must be defined to obtain meaningful coupling constants. Each species in your POSCAR file should be defined; there is no need to define each individual ion.
Step 2b (optional): Determine a suitable energetic break value
The break condition for the self-consistency step EDIFF does not strongly influence the coupling parameter for our test systems. However, it is important to confirm this for your system before performing more expensive convergence tests.
The hyperfine coupling constant depends on the nuclear gyromagnetic ratios defined in NGYROMAG. Since the defaults are set to 1, the gyromagnetic ratios must be defined to obtain meaningful coupling constants. Each species in your POSCAR file should be defined; there is no need to define each individual ion.
Step 3: Converge the plane-wave energy cutoff
The plane-wave basis can strongly influence the coupling constant. Unconverged values should not be compared to experiment. Perform multiple calculations while increasing the basis set size, as defined in ENCUT, incrementally (e.g., by 100 eV intervals). Convergence should be aimed to be within 0.1 MHz, although this will not be feasible for heavier elements.
Step 4: Converge the k point mesh
Similar to the basis, the k point mesh can strongly influence the coupling constant. The k point mesh should be increased incrementally, i.e., 1x1x1, 2x2x2, 3x3x3, until convergence to within 0.1 MHz is achieved.
Step 5: Compare to experiment
The purpose of these calculations is to compare to experiment. An example is given in Ref. [1]. It is important to include core contributions, as these can account for a significant portion of the Fermi contact term. The total coupling parameter can be compared to EPR.
Step 6 (optional): Perform hybrid calculations
In the literature, HSE06 has been shown to better localize defect states, which improves comparison to experiment relative to PBE [1]. Consider performing a hybrid calculation, if it is affordable.
Recommendations and advice
The hyperfine coupling constant requires tightly converged settings. The energetic break condition EDIFF and the plane-wave energy cutoff ENCUT impact the convergence of the hyperfine coupling constant. For solid-state systems, the choice of k-point mesh KPOINTS used can also be very important. Besides these input settings, the hyperfine coupling constant is influenced by several other factors, specifically structure, POTCAR, and method.
Structure
The structure defined in POSCAR will impact the hyperfine constant in two ways. The first and most important is that cells that are too small may converge to non-magnetic systems. For example, the NV-diamond defect cannot be properly described by a 15-atom supercell (based on a 2x2x2 cell from primitive diamond). As you increase the k-point mesh, the magnetization disappears due to coupling between neighboring defect sites. Be careful to use a large enough cell for your calculation, otherwise even converged settings will produce meaningless outputs. Sometimes, a non-magnetic solution is incorrectly found. If you are certain that it should be magnetic, then you can force this by using NUPDOWN to fix the number of unpaired electrons in your system during the calculation. Ensure that the energy of the magnetic state is lower than the non-magnetic state.
A second structural problem will come from the precise POSCAR that you use. Slightly different lattice parameters (10 mÅ) can change the hyperfine coupling constant by ~0.5 MHz. Make sure to use a well-optimized structure.