Input and output

odatse-LEED module is a Solver which calculates the Rocking curve from atomic positions etc., using SATLEED, and returns the deviation from the experimental Rocking curve as \(f(x)\).

In this section, the input parameters, the input data, and the output data are explained. The input parameters are taken from the solver entry of the Info class. The parameters are specified in [solver] section when they are given from a TOML file. If the parameters are given in the dictionay format, they should be prepared as a nested dict under the solver key. In the following, the parameter items are described in the TOML format.

The input data consist of target reference data, and the bulk structure data. The output data consist of files containing the result of optimization. Their contents will be shown in this section.

Input parameters

Input parameters are specified in the solver section and the subsections (config, param, and reference).

  • name

    Format: string

    Description: The name of the direct problem solver. Optional.

  • dimension

    Format: integer

    Description: The number of parameters. If it is not specified, the dimension is taken from the [base] section.

[config] section

  • path_to_first_solver

    Format: string

    Description: Path to the solver satl1.exe. The default value is satl1.exe.

  • path_to_second_solver

    Format: string

    Description: Path to the solver satl2.exe. The default value is satl2.exe.

  • sigma_file_path

    Format: string

    Description: Path to the experimental data file. The default value is exp.d.

  • remove_work_dir

    Format: boolean

    Description: The output files of the solver program are stored in a directory LogXXXX_YYYY for each search point, in which XXXX denotes the step count and YYYY denotes the identifier such as replica number. When remove_work_dir is set to true, the directory is removed after the evaluation at the search point. The default value is false.

  • use_tmpdir

    Format: boolean

    Description: If it is true, the intermediate files are stored in a directory within /tmp or within the directory specified by the environment variable TMPDIR. The default value is false.

[param] section

  • string_list

    Format: list of strings

    Description: List of keywords embedded in the input template files.

[reference] section

  • path_to_base_dir

    Format: string

    Description: Path to the directory which stores exp.d, rfac.d, tleed4.i, tleed5.i.

  • rfactor

    Format: string or dictionary

    Description: Types of R-factor. The weighted average of multiple types of R-factors can be specified by a dictionary that relates the R-factor types and the relative weights. (For the latter, only the R-factor types r1 .. rpe are available.)

    The available types are described in the following section. The default value is rpe (Pendry R-factor).

  • rescale

    Format: boolean

    Description: If it is set to true, \(I_t\) is rescaled in the R-factor calculation. The default value is false.

  • smoothing factor

    Format: float

    Description: The smoothing parameter for I-V curve data. If it is set to 0.0, the smoothing is not applied. The default value is 0.0.

  • vi_value

    Format: float

    Description: The imaginary part of the inner potential needed to calculate the Pendry R-factor. The parameter value can be explicitly specified by vi_value, or it is obtained from the input file tleed5.i for SATLEED.

Types of R-factor

The types of R-factors available for the rfactor parameter are listed as follows.

The notation is summarized: \(\sum_b\) denotes the sum over the beams. \(\sideset{}{'}\sum_b = \sum_b w_b\) denotes the sum over that beams that takes account of the relative weight of energy ranges \(w_b = {\int dE}/{\sum_b \int dE}\). When rescale is set to true, \(c = {\int I_e dE}/{\int I_t dE}\), otherwise \(c=1\).

  • rsq

    \[R = \sqrt{ \dfrac{\sum_b \int \left(I_e - I_t\right)^2 dE}{\sum_b \int I_e^{\,2} dE} }\]

  • rsq_modified

    \[R = \sqrt{ \sideset{}{'}\sum_b \dfrac{\int \left(I_e - I_t\right)^2 dE}{\int I_e^{\,2} dE} }\]

  • r1

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left| I_e - c I_t \right| dE}{\int I_e dE}\]

  • r2

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left( I_e - c I_t \right)^2 dE}{\int I_e^{\,2} dE}\]

  • rp1

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left| I_e^\prime - c I_t^\prime \right| dE}{\int \left|I_e^\prime\right| dE}\]

  • rp2

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left( I_e^\prime - c I_t^\prime \right)^2 dE}{\int (I_e^\prime)^{2} dE}\]

  • rpp1

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left| I_e^{\prime\prime} - c I_t^{\prime\prime} \right| dE}{\int \left|I_e^{\prime\prime}\right| dE}\]

  • rpp2

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left( I_e^{\prime\prime} - c I_t^{\prime\prime} \right)^2 dE}{\int (I_e^{\prime\prime})^{2} dE}\]

  • rrzj (reduced Zanazzi-Jona R-factor)

    \[R = \sideset{}{'}\sum_b \dfrac{1}{0.027 \int I_e dE} \int \dfrac{\left| I_e^{\prime\prime} - c I_t^{\prime\prime} \right|\cdot\left| I_e^{\prime} - c I_t^{\prime} \right|}{\left|I_e^{\prime}\right| + {\rm max}\left|I_e^{\prime}\right|} dE\]

  • rmzj (modified Zanazzi-Jona R-factor)

    \[R = \sideset{}{'}\sum_b \dfrac{1}{\int I_e^{\prime\prime} dE} \int \dfrac{\left| I_e^{\prime\prime} - c I_t^{\prime\prime} \right|\cdot\left| I_e^{\prime} - c I_t^{\prime} \right|}{\left|I_e^{\prime}\right| + c\cdot{\rm max}\left|I_t^{\prime}\right|} dE\]

  • rpe (Pendry R-factor)

    \[R = \sideset{}{'}\sum_b \dfrac{\int \left(Y_e - Y_t\right)^2 dE}{\int Y_e^{\,2} + Y_t^{\,2} dE}, \quad Y = \dfrac{L}{1 + V_{0i}^{\,2} L^2}, \quad L = {\tilde I}^\prime / {\tilde I}.\]

    In the Pendry R-factor, \({\tilde I} = I_t + \kappa {\langle I \rangle}\), where \(\kappa\) is the parameter denoted by PERSH, and it is set to 0.05. \({\langle I \rangle}\) is the average over the peaks of \(I\). \(V_{0i}\) denotes the imaginary part of the inner potential.

    N.B. when RPE (the Pendry R-factor) is chosen in rfac.d for the R-factor (i.e. WR(10) is set to 1), the output of I-V curves contains \({\tilde I}\) instead of \(I\). Therefore, WR(10) must be set to 0 except when satleed is chosen for rfactor type.

  • satleed

    The value of R-factor is taken from the output (search.s) of satl2.exe.

Reference file for Solver

Target reference file

The file containing the data to be targeted to fit. Edit tleed4.i and tleed5.i in path_to_base_dir in the [reference] section.

The parameter values to be optimized are replaced by the keywords that depend on the types of parameters: The coordinates or the deviations of the coordinates are denoted by strings starting from opt. The inner potential is denoted by strings starting from IP. The Debye temperatures are denoted by strings starting from debye. The keywords are listed in the parameter solver.param.string_list in the input file. The number and the order of the keywords should be identical to those of the list of variables to optimize.

The keywords should be embedded in the templates according to the format of the parameters. In the following example, the parameter values corresponding to opt000 and opt001 (e.g. 0.23) are formatted by the format style (F7.4) (7 letters in total with 4 digits below the floating point) such as ␣0.2300.

Note that if IFLAG and LSFLAG are not set to 0, the satleed side is also optimized.

An example file is shown below.

 1  0  0                          IPR ISTART LRFLAG
 1 10  0.02  0.2                  NSYM  NSYMS ASTEP VSTEP
 5  1  2  2                       NT0  NSET LSMAX LLCUT
 5                                NINSET
 1.0000 0.0000                  1      PQEX
 1.0000 2.0000                  2      PQEX
 1.0000 1.0000                  3      PQEX
 2.0000 2.0000                  4      PQEX
 2.0000 0.0000                  5      PQEX
 3                                 NDIM
opt000 0.0000 0.0000  0           DISP(1,j)  j=1,3
 0.0000opt001 0.0000  0           DISP(2,j)  j=1,3
 0.0000 0.0000 0.0000  1           DISP(3,j)  j=1,3
 0.0000 0.0000 0.0000  0           DISP(4,j)  j=1,3
 0.0000  0                         DVOPT  LSFLAG
 3  0  0                           MFLAG NGRID NIV
 ...

Output file

In leed, the output files are stored in the subfolder LogXXXX_YYYY for each parameter value that is created in the folder with the rank number within the output_dir. Here, XXXX denotes the step count, and YYYY denotes the identifier such as the replica number.