Geometrical displacements
Geometrical displacements to be used during the search must be specified in a block starting with the
= GEO_DELTA
header flag, followed by a list of displacements for each of the atoms that one wants to move during the search.
Example:
= GEO_DELTA
O 1 z = -0.05 0.05 0.005 ! Oxygen atom 1 (and symmetry-equivalent atoms) will be displaced in z direction over the range [-0.05, 0.05] with step 0.005
Ir 2-11 z = -0.05 0.05 0.01 ! Iridium atoms 2-11 (and symmetry-equivalent atoms) will be displaced in z direction over the range [-0.05, 0.05] with step 0.01
O 1 [1 0] = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced along a over the range [-0.05, 0.05] with step 0.005
O 1 [0 1] offset = 0.02 ! Oxygen atom 1 displacements will additionally be offset by 0.02 A along b
The values on the right are interpreted as range of displacements in Ångström. How atoms are addressed on the left is described on the main DISPLACEMENTS page. However, The GEO_DELTA block contains one additional value on the left, which defines the direction of the displacement, as described below.
When multiple searches are executed consecutively or in a loop, the displacement ranges are centered around the optimized position from previous searches per default. If you define an offset for an atom, the optimized position from previous searches is discarded for this atom, and the offset is applied to its original position. If you want to center the displacement range around the original position of the atom, you can also clear the offset without specifying a direction:
O 1 offset = 0 ! center around original atom position, instead of the position resulting from previous searches
O 1 offset = clear ! equivalent
O 1 offset = original ! equivalent
Direction
Possible directions for displacements are:
zDisplacements along the direction orthogonal to the surface. Positive z values correspond to movements of the atoms away from the bulk.
O 1 z = -0.05 0.05 0.005 ! Oxygen atom 1 (and symmetry-equivalent atoms) will be displaced in z direction over the range [-0.05, 0.05] with step 0.005
ab[n1 n2](or just[n1 n2])In-plane displacements along the direction identified by the lattice vector with the whitespace-separated indices
n1(\(n_1\)) andn2(\(n_2\)). The first integer refers to the first vector \(\mathbf{a}\) in the POSCAR file. The displacement direction will be positive in the direction of the vector \(\mathbf{v} = n_1 \mathbf{a} + n_2 \mathbf{b}\).n1andn2accept floating point values. Notice that the direction vector will be normalized, so[1 3]and[9 27]correspond to the same direction.O 1 [1 0] = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced along a over the range [-0.05, 0.05] with step 0.005 O 1 ab[1 -1] = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced diagonally along (a-b) over the range [-0.05, 0.05] with step 0.005 ! Symmetry-equivalent atoms will be displaced such that the symmetry is preserved.
xy[m1 m2]
In-plane displacements along the vector \(\mathbf{v}\) = \(m1 \mathbf{x} + m2 \mathbf{y}\), where \(\mathbf{x}\) and \(\mathbf{y}\) are the unit vectors along the Cartesian axes. The direction vectors will be normalized.
O 1 xy[0 1] = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced along y over the range [-0.05, 0.05] with step 0.005 ! Symmetry-equivalent atoms will be displaced such that the symmetry is preserved.
azi(ab[c1 c2])In-plane displacement around a circular trajectory centered at a specified point \(C\). The same convention as in the previous commands is used to specify the center:
azi(ab[c1 c2])or justazi([c1 c2])means \(C = c_1 \mathbf{a} + c_2 \mathbf{b}\) andazi(xy[c3 c4])means \(C = c_3 \mathbf{x} + c_4 \mathbf{y}\).
The range on the right again defines a range of displacements in Ångström, in this case measured along the defined circular arc. Positive translations will translate to counterclockwise rotation as seen from vacuum. Zero displacement is the original position of the atom. Note that, since the displacement is given along the circular arc, the absolute displacement from the original position can be significantly smaller than for a linear displacement when the circle is small.
O 1 azi([0 0]) = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced along a circle centered on the origin by ±0.05 Å following the circular arc, with step 0.005 ! Symmetry-equivalent atoms will be displaced such that the symmetry is preserved.r(ab[c1 c2])In-plane displacement relative (radial) to a specified point C. The same convention as in the previous commands is used to specify the point of reference, i.e.,
r(ab[c1 c2])orr([c1 c2])means \(C = c_1 \mathbf{a} + c_2 \mathbf{b}\) andr(xy[c3 c4])means \(C = c_3 \mathbf{x} + c_4 \mathbf{y}\).
Positive values are interpreted as moving the atom away from point C, negative values move the atoms towards point C.
O 1 r([0 0]) = -0.05 0.05 0.005 ! Oxygen atom 1 will be displaced away from the origin over the range [-0.05, 0.05] with step 0.005 ! Symmetry-equivalent atoms will be displaced such that the symmetry is preserved.
Offset
In addition to displacement along a specific direction, an offset along a different direction can be defined. That offset will be added to the “neutral” position of the atom, i.e. apply to all points in the displacement range.
O 1 [0 1] offset = 0.02 ! Oxygen atom 1 displacements will be offset by 0.02 A along b
O 1 ab[0 1] offset = 0.02 ! same as above
O 1 xy[0 1] offset = 0.02 ! Oxygen atom 1 displacements will be offset by 0.02 A along y
Unlike the displacement ranges themselves, the offset flag allows multiple assignment, as long as one of the assignments is in-plane and the other one is out-of-plane:
! in-plane and out-of-plane offsets can be combined:
O 1 [0 1] offset = 0.02 ! Oxygen atom 1 displacements will be offset by 0.02 A along b ...
O 1 z offset = 0.03 ! ... and by 0.03 A along z
Note
If your input
start,stop, andstepvalues do not lead to an odd integer number of steps, the extremes of the interval will be extended in a symmetric fashion around the midpoint [= (start+stop)/2] (i.e.,stephas precedence).Displacements of atoms will be cross-checked for symmetry ** **conservation (unless you have turned off symmetry via SYMMETRY_FIX and/or The SYM_DELTA tag), and the program will throw an error if inconsistencies arise. In general: atoms at n-fold rotational axes cannot be displaced; atoms on mirror planes can be moved only along the planes. You can find which displacement directions conserve the symmetry of your structure input in the comments added to the POSCAR file. Refer to the relation between plane groups in the SYMMETRY_FIX page in case you required a lowering of the symmetry of your slab via SYMMETRY_FIX or The SYM_DELTA tag.
During one optimization run, an atom can only be displaced along one axis (so, for example, not sampling all in-plane directions at once). This is due to the way that the TensErLEED search is currently designed, with geometrical displacements being optimized along a 1D array of points only. Since LEED is much more sensitive to variations of the out-of-plane geometry of your sample (small \(k_{\textrm{par}}\)), it is a good idea to first run a few optimization runs on the z positions only, and treat in-plane displacements later as a refinement (unless your POSCAR model is very far off from the real structure).