Full-dynamic optimization

LEED-I(V) calculations require setting some parameters that cannot be (exactly) determined in experiment, but that are not accessible to variation within the tensor-LEED approximation. These include BEAM_INCIDENCE, V0_IMAG, and the exact dimensions of the unit cell. In order to fit these parameters, multiple full-dynamic (i.e., “reference”) calculations must be performed, instead.

Note

For performance reasons, Tensors are never output during a full-dynamic optimization.

To set up a full-dynamic optimization in viperleed.calc, set

RUN = 6

in the PARAMETERS file, and specify which quantity to vary with the OPTIMIZE parameter. Options to control the behavior of the optimization are also available via OPTIMIZE.

The algorithm for full-dynamic optimization calculates \(R\) factors for at least three values of the quantity under variation, then fits a parabola. If the minimum of the parabola is outside of the current scope (i.e., the points already known), then more points are added to expand the scope such that at least one point at either side of the minimum is present. Otherwise, the next calculation is performed at the parabola minimum. The parabola fit is repeated after obtaining any new data point. Convergence is reached when the new predicted minimum is within a given distance (defined via OPTIMIZE) of a point that was already calculated.

Note

The full-dynamic optimization can be slow, as an entire Reference calculation is executed for each of the values of the quantity under variation.

\(R\)-factor values corresponding to the calculated values of the quantity under variation are output to FD_Optimization.pdf and FD_Optimization.csv. FD_Optimization_beams.pdf plots the corresponding I(V) curves together with the experimental data.