mirror of https://gitlab.com/QEF/q-e.git
42 lines
1.6 KiB
Plaintext
42 lines
1.6 KiB
Plaintext
This example shows the use of th D3 code to calculate
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the third-order expansion coefficients with respect to
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atomic displacement for Silicon.
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First a normal self-consistent calculation is done.
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Then a phonon calculation for the Gamma point is performed.
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With these preliminary steps the coefficients C(0,0,0) are calculated.
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For the X-point a non self-consistent calculation of groundstate
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and the phonon calculation for this point is done.
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Afterwards C(0,X,-X) is calculated.
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By displacing one atom, one can get also these coefficients by a
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finite-difference mathod. We give first the values obtained by
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the 2n+1 method, then the values by the finite-differences.
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All units are in Ryd/(a_b)^3.
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tensor | 2n+1 | fin. dif.
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------------------------------------------------------------
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C_{x,y,z} (0,0,0|1,1,1) | 0.38314 | 0.38446
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------------------------------------------------------------
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C_{x,y,z} (0,X,-X|1,1,1) | 0.34043 | 0.34109
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C_{x,x,z} (0,X,-X|1,1,2) | -0.25316 | -0.25296
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C_{z,x,y} (0,X,-X|1,1,1) | 0.35781 | 0.35767
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C_{z,x,x} (0,X,-X|1,1,2) | -0.25706 | -0.25491
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C_{z,z,z} (0,X,-X|1,1,2) | -0.13133 | -0.12813
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The results of these calculations are also compared with the ones of
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Debernardi given in paranthesis, see Debernardi, PhD thesis (1995),
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page 81, available at
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http://www.sissa.it/cm/phd.php
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The units are in eV/(Angstrom)^3.
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B_xyz = -281.43 (-284.25)
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I_zaa = 225.82 (227.37)
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I_zbb = -37.00 (-37.64)
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I_zcc = 48.23 (49.91)
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I_xac = 436.01 (441.32)
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I_ybc = -64.10 (-63.91)
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