The ones of you who use QE-GIPAW for molecules in gas phases only would not know this but when you are dealing with solids be careful of this keyword:
use_nmr_macroscopic_shape
'Coz in solids, macroscopic shape really does matter. What do I mean?
When calculating chemical shifts (calculation='nmr') what we actually do is to assume that there is a tiny perturbative magnetic field affecting the electronic structure. Electrons respond to this field by inducing a current in the sample, and as every damn current, this induced current too, induces a magnetic field in the sample. We are only interested in the induced magnetic field at the nuclei positions.
Ok I have really over simplified the whole thing :) but lets continue. When you have a molecule, there is not much more to it, calculate the current, calculate the induced field and you are done. However a finite solid sample can sustain surface currents and your infinitely periodic unit cell does not know anything about it.
Depending on the strength of this surface current, one has to consider its affect on the chemical shifts. As it has everything to do with the surface ( therefore macroscopic shape of the sample ) you need to tell the code what this shape is. Say, if you are comparing to an experiment, check the shape they give in the article: slab? cylindrical? spherical? and supply this info using nmr_macroscopic_shape array.
here is for a spherical sample (default)
use_nmr_macroscopic_shape=.true.
nmr_macroscopic_shape(1:1)=2/3
nmr_macroscopic_shape(2:2)=2/3
nmr_macroscopic_shape(3:3)=2/3
And the code does add a shape correction proportional to the macroscopic susceptibility (chi) with
4*pi* nmr_macroscopic_shape(:,:) *chi_bare(:,:)
But where is this 2/3 coming from? why not 1/3, like in the normal depolarization coefficients of a sphere (n_depol)?
Well, 'coz the real equation is
B_total = B_induced - 4*pi*(1 − n_depol)*chi
but the code expects _you_ to do the (1-n) operation in your mind, duck face :)
So if you have a cylinder along z:
nmr_macroscopic_shape(1:1)=1/2
nmr_macroscopic_shape(2:2)=1/2
nmr_macroscopic_shape(3:3)=1
(For more theoretically inclined, another way of looking at this is shape contribution is solving for the magnetic field in the sample with boundary conditions that are set by the shape of the sample, unlike G=0 term vanishing in electric fields, here solve separately for infinite sample and add macroscopic susceptibility contribution. If there is any demand I will write down the equations otherwise go to your favorite Electromagnetism textbook, like Jackson chapter 5 )
use_nmr_macroscopic_shape
'Coz in solids, macroscopic shape really does matter. What do I mean?
When calculating chemical shifts (calculation='nmr') what we actually do is to assume that there is a tiny perturbative magnetic field affecting the electronic structure. Electrons respond to this field by inducing a current in the sample, and as every damn current, this induced current too, induces a magnetic field in the sample. We are only interested in the induced magnetic field at the nuclei positions.
Ok I have really over simplified the whole thing :) but lets continue. When you have a molecule, there is not much more to it, calculate the current, calculate the induced field and you are done. However a finite solid sample can sustain surface currents and your infinitely periodic unit cell does not know anything about it.
Depending on the strength of this surface current, one has to consider its affect on the chemical shifts. As it has everything to do with the surface ( therefore macroscopic shape of the sample ) you need to tell the code what this shape is. Say, if you are comparing to an experiment, check the shape they give in the article: slab? cylindrical? spherical? and supply this info using nmr_macroscopic_shape array.
here is for a spherical sample (default)
use_nmr_macroscopic_shape=.true.
nmr_macroscopic_shape(1:1)=2/3
nmr_macroscopic_shape(2:2)=2/3
nmr_macroscopic_shape(3:3)=2/3
And the code does add a shape correction proportional to the macroscopic susceptibility (chi) with
4*pi* nmr_macroscopic_shape(:,:) *chi_bare(:,:)
But where is this 2/3 coming from? why not 1/3, like in the normal depolarization coefficients of a sphere (n_depol)?
Well, 'coz the real equation is
B_total = B_induced - 4*pi*(1 − n_depol)*chi
but the code expects _you_ to do the (1-n) operation in your mind, duck face :)
So if you have a cylinder along z:
nmr_macroscopic_shape(1:1)=1/2
nmr_macroscopic_shape(2:2)=1/2
nmr_macroscopic_shape(3:3)=1
And a slab along z:
nmr_macroscopic_shape(1:1)=1
nmr_macroscopic_shape(2:2)=1
nmr_macroscopic_shape(3:3)=0
(For more theoretically inclined, another way of looking at this is shape contribution is solving for the magnetic field in the sample with boundary conditions that are set by the shape of the sample, unlike G=0 term vanishing in electric fields, here solve separately for infinite sample and add macroscopic susceptibility contribution. If there is any demand I will write down the equations otherwise go to your favorite Electromagnetism textbook, like Jackson chapter 5 )
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