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JDFTx
1.1.2
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JDFTx
1.1.2
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We will first look at the lattice relaxation of silicon.
Here is the input file. It is essentially the same as the one in the Density of States tutorial page.
#---------------- Lattice Constant of Silicon ------------------
lattice \
0 0.5 0.5 \
0.5 0 0.5 \
0.5 0.5 0
latt-scale 10.77 10.77 10.77
ion-species Si.fhi
coords-type lattice
ion Si 0.250 0.250 0.250 0
ion Si 0.000 0.000 0.000 0
kpoint-folding 4 4 4
elec-ex-corr gga
dump-name silicon.$VAR
lattice-minimize \
nIterations 10 \
energyDiffThreshold 1e-6
electronic-minimize \
energyDiffThreshold 1e-7
The experimental (cubic) lattice constant of Silicon is 5.43 Angstroms, or roughly 10.26 bohrs. We run the calculation, starting from a 5 % strained initial state. (jdftx -i silicon.in -o silicon.out).
Just before the electronic minimization starts, you should see something like this:
--------- Lattice Minimization --------- Minimization of dimension 1 over strains spanned by: [ 0.57735 0 0 ] [ 0 0.57735 0 ] [ 0 0 0.57735 ]
This means that jdftx has detected the symmetries of your crystal and realized that there is only one lattice parameter. The basis matrices for the strain tensor are expressed in lattice coordinates, so a diagonal strain tensor corresponds to scaling all three fcc lattice vectors by the same constant. The normalization of the basis matrices is such that sum of all squares always add to 1 (i.e. 3 * 0.57734^2 = 1.0)
Calculations with lattice minimization tend to produce rather long output files, so it can be useful to use search tools (such as UNIX's grep) to look at them.
Lets grep the output file for lattice minimization iterations. grep LatticeMinimize silicon.out produces the following output:
LatticeMinimize: Iter: 0 Etot: -7.927814070374968e+00 |grad|_K: 1.940e-01 alpha: 1.000e+00 LatticeMinimize: Iter: 1 Etot: -7.937043278195619e+00 |grad|_K: 3.265e-02 alpha: 3.966e-01, linmin = -1.000e+00, cgtest = 1.000e+00 LatticeMinimize: Encountered beta<0, resetting CG. LatticeMinimize: Iter: 2 Etot: -7.937240053671994e+00 |grad|_K: 2.902e-04 alpha: 3.685e-01, linmin = 1.000e+00, cgtest = -1.000e+00 LatticeMinimize: Bad step direction: g.d > 0. LatticeMinimize: Undoing step. LatticeMinimize: Step failed: resetting search direction. LatticeMinimize: Iter: 3 Etot: -7.937240076434499e+00 |grad|_K: 2.798e-04 alpha: 0.000e+00 LatticeMinimize: Iter: 4 Etot: -7.937240091707153e+00 |grad|_K: 1.913e-04 alpha: 6.715e-01, linmin = 1.000e+00, cgtest = -1.000e+00 LatticeMinimize: Converged (|Delta Etot|<1.000000e-06 for 2 iters).
We see from that the lattice minimizer converged to 1 microHartrees in just 4 iterations.
Lets now grep for the strain tensor, i.e grep Strain -A 3 silicon.out. -A 3 just tells UNIX to report the 3 lines after finding the word Strain (case sensitive).
Strain Tensor = [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] -- Strain Tensor = [ -0.0444153 0 0 ] [ 0 -0.0444153 0 ] [ 0 0 -0.0444153 ] -- Strain Tensor = [ -0.0513619 0 0 ] [ 0 -0.0513619 0 ] [ 0 0 -0.0513619 ] -- Strain Tensor = [ -0.0513619 0 0 ] [ 0 -0.0513619 0 ] [ 0 0 -0.0513619 ] -- Strain Tensor = [ -0.0512534 0 0 ] [ 0 -0.0512534 0 ] [ 0 0 -0.0512534 ]
It seems that the crystal strained down by roughly 5.1 % from the initial size, i.e. almost back to the exprimental value. Lets look at the lattice vectors, grep "R = " -A 3 silicon.out
R = [ 0 5.385 5.385 ] [ 5.385 0 5.385 ] [ 5.385 5.385 0 ] -- R = [ 0 5.385 5.385 ] [ 5.385 0 5.385 ] [ 5.385 5.385 0 ] -- R = [ 0 5.14582 5.14582 ] [ 5.14582 0 5.14582 ] [ 5.14582 5.14582 0 ] -- R = [ 0 5.10842 5.10842 ] [ 5.10842 0 5.10842 ] [ 5.10842 5.10842 0 ] -- R = [ 0 5.10842 5.10842 ] [ 5.10842 0 5.10842 ] [ 5.10842 5.10842 0 ] -- R = [ 0 5.109 5.109 ] [ 5.109 0 5.109 ] [ 5.109 5.109 0 ]
The calculated lattice constant is 10.218 Bohrs (5.109x2), or 5.41 Angstroms, roughly 0.02 Angstorms off the experimental value.
1.8.11