Constraints for structure optimization

This block of the DISPLACEMENTS file allows you to define specific constraints other than symmetry for the structure-optimization routine. The commands are introduced by a header line of the form

= CONSTRAIN

The general syntax for a line in the CONSTRAIN block is (examples given below):

flag atoms[, more atoms] = value

  • flag is either geo, vib or occ, depending what type of parameter should be addressed (compare to the other blocks in the DISPLACEMENTS file).

  • The syntax for addessing atoms is the same as in the other blocks, i.e., by POSCAR element, chemical element, or site type, with optional further restriction by atom or layer number. Listing multiple sets of atoms in one line is also allowed using commas to separate them.

  • The value on the right is either linking to link parameters to each other, a floating point number to lock in a specific value from the displacements range, or ind(N), where N is an integer (counting from 1) giving an index in the displacement range that should be locked. See below for examples for each of these cases.

Linking parameters

The main function of CONSTRAIN blocks is to link parameters together, i.e., if one of them is at the Nth index of its displacement range, all of them will be. A simple example would be to keep all vibrational amplitudes for a given site type the same:

= VIB_DELTA
Ir_top = -0.05 0.05 0.01       ! vary vibrational amplitudes for all atoms in Ir_top sites over the range [-0.05, 0.05] with step 0.01
Ir_def = -0.03 0.03 0.01       ! vary vibrational amplitudes for all atoms in Ir_def sites over the range [-0.03, 0.03] with step 0.01

= CONSTRAIN
vib Ir_top = linked            ! keep the vibrational amplitudes of all Ir_top atoms the same at all times
vib Ir_def = linked            ! keep the vibrational amplitudes of all Ir_def atoms the same at all times

Note that for linking to work, the linked parameters have to have the same number of steps. In the above example, the following would not work, because the displacement ranges have different sizes:

= CONSTRAIN
vib Ir = linked                ! keep the parameter index for the vibrational amplitudes of all Ir atoms the same at all times

However, it can be made to work if the displacement ranges have the same size, i.e.,

= VIB_DELTA
Ir_top = -0.05 0.05 0.01     ! vary vibrational amplitudes for all atoms in Ir_top sites over the range [-0.05, 0.05] with step 0.01
Ir_def = -0.025 0.025 0.005  ! vary vibrational amplitudes for all atoms in Ir_def sites over the range [-0.025, 0.025] with step 0.005

= CONSTRAIN
vib Ir = linked              ! keep the vibrational amplitude index of all Ir_top atoms the same at all times

Note that while in this example, the indices for vibrational variation of Ir_top and Ir_def are tied together, that does in no way mean that the values have to be the same. Both the base values (defined in the VIBROCC file) and the actual values within the displacement ranges can differ.

You can also force atoms from different sites and/or elements to move in a concerted fashion by linking the respective parameters:

= GEO_DELTA
O L(1-2) z = -0.05 0.05 0.005     ! move oxygen atoms in layers 1 and 2 along z over range [-0.05, 0.05] with step 0.005
Ir L(1) z = 0.03 -0.03 0.003      ! move iridium atoms in layer 1 along z over range [0.03, -0.03] with step 0.003

= CONSTRAIN
geo O L(1-2), Ir L(1) = linked    ! link the indices for the displacement ranges above

In this example, all oxygen atoms in layers 1 and 2 would move in a concerted fashion, as would the iridium atoms in layer 1. Furthermore, by linking them in the same line, the movements of oxygen and iridium are coupled as given by the two ranges, so when oxygen moves up, iridium moves down (e.g., when O moves to +0.01 A, Ir moves to -0.006 A).

Freezing parameters

Apart from linking parameters, CONSTRAIN blocks can also be used to freeze a parameter to a specific value. This can be used to enforce an offset for a given value (within the limitations of tensor LEED) without having to re-do the reference calculation. It is also equivalent to giving a displacement range with only a single value.

Freezing parameters can be achieved by specifying a value from the displacements range, or by giving a specific index:

= VIB_DELTA
Ir_top = -0.05 0.05 0.02     ! vary vibrational amplitudes for Ir_top atoms over the range [-0.05, 0.05] with step 0.02

= CONSTRAIN
vib Ir_top = -0.03           ! although a displacement range is defined for Ir_top, fix it's value to -0.03 instead
vib Ir_top = ind(2)          ! same as the line before: Fix index to 2, i.e. the second entry in the displacement range

Note that in the ind(N) function, indices are counted starting at 1, not at 0, to keep them consistent with values in the SD.TL file.