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Analysing the basin-hopping results using Cluster

The //Cluster// program that is part of the //CamCASP// suite of codes can be used to perform an analysis of the results of the Basin-Hopping simulations. Here is a sample code:

reorient-analyse.clt

Title Re-orient and analyse clusters

Global
  Units Bohr Degrees kJ/mol
End

Orient
  Geom-File RDX_run1.geom
  Geom-File RDX_run2.geom  APPEND OFFSET 100
  Reorient  RDX2
  ! R-scalings 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.20 1.40 
  Sort
  Write  Format Orient All
  Analyse
    Sort
    Similarity  Moments  & Energy 
    Energy-Sigma 0.5 kJ/mol
    Moment-Sigma 40.0 AMU
    Similarity-cutoff 0.5
    Details
  End
End

Finish

In this example, the outputs of two Basin-Hopping simulations is analysed. Cluster uses the files containing the **minima**. These will be the files names with the command:

  minima  <filename>  

in the Basin-Hopping commands in the Orient command file. Here these are //RDX_run1.geom// and //RDX_run2.geom//. The **APPEND** command tells Cluster to append the contents of the second file after those of the first. The **OFFSET 100** command tells it to change the numbers of the minima in the second file by 100. This ensures that we have unique numbers to all minima. Of course, if your files contain more than 100 minima each then a larger offset will be needed.

Run this using

  $ cluster < reorient-analyse.clt > reorient-analyse-1.out  

It will run in a few seconds or so. The output will be fairly large, but the important parts are at the bottom and should be something like

partial output

Configuration statistics
! Config List name : CfgList-1
! Configs read from file : RDX_run1.geom
UNITS  BOHR DEGREE KJ/MOL AMU BOHR^2
! ----------------------------------------------------------------------------------------------------------------
! INDEX          ENERGY         I_XX           I_YY           I_ZZ           NUM-MOLS       NUM-SIMILAR    SYMMETRY

! ----------------------------------------------------------------------------------------------------------------
         9     -38.673719    4816.657600   26521.382000   29029.103000              2              2    C1
        13     -32.596392    5097.135300   25781.361000   28326.087000              2              4    C1
         8     -31.943536    7273.543700   15751.536000   16833.182000              2              2    C1
        12     -31.369167    6174.222300   21108.671000   24421.995000              2              2    C1
         1     -31.160460    6116.310500   20960.708000   24786.811000              2              2    C1
         6     -30.967247    5696.724600   24537.264000   27691.237000              2              2    C1
         4     -30.870978    5711.535600   24567.950000   27727.494000              2              2    C1
         5     -28.023902    6687.209600   16258.763000   18142.056000              2              2    C1
        20     -25.506775    7418.221300   17500.675000   18939.431000              2              2    C1
        15     -25.460627    8009.331400   14364.374000   15967.696000              2              2    C1
         3     -25.366652    8256.744300   15029.776000   15387.661000              2              2    C1
        18     -25.236796    5352.739300   25368.417000   27793.813000              2              4    C1
        17     -25.146462    7353.113400   17708.961000   19113.039000              2              2    C1
        21     -24.510071    6882.945500   20990.439000   22027.654000              2              2    C1
        14     -24.469602    6896.643800   20927.123000   21948.175000              2              2    C1
         7     -23.014142    6294.826700   22029.994000   25021.199000              2              4    C1
         2     -22.727332    6003.548700   24192.692000   28466.521000              2              4    C1
        16     -22.052672    7586.187000   20946.833000   21977.863000              2              2    C1

End

Finish
 Exiting program cluster_operations

This listing is a summary of the minima that Cluster considers as unique. The fields include:

• INDEX : the unique index of the minimum
• ENERGY: energy in units specified
• I_XX, I_YY, I_ZZ: moments of inertia in principle axes.
• NUM-MOLS: Number of molecules in the cluster. Here only 2 in each as we searched for only dimers.
• NUM-SIMILAR: Number of minima that Cluster considers to be similar. We expect to find 3-5 similar structures for each of the low-energy minima.
• SYMMETRY: At present the code does not find the point-group symmetry, so it prints out 'C1' for all.

The clustering is done using the commands in the ANALYSE block:

  Analyse
    Sort
    Similarity  Moments  & Energy 
    Energy-Sigma 0.5 kJ/mol
    Moment-Sigma 40.0 AMU
    Similarity-cutoff 0.5
    Details
  End

Here the structure similarity is based on the moments of inertia **and** the energies. Each quantity is given a tolerance set by a standard deviation. This defines a similarity probability as a normal distribution with the specified width. Structures are deemed to be similar to a probability. The cutoff level is set by **Similarity-cutoff**. Here it is $0.5$ so structures with a similarity probability $p \ge 0.5$ are deemed to be similar.

The clustering will depend on the standard deviations chosen. This needs to be tuned to the problem of interest. It is quite likely that the **Energy-Sigma** is too large in the example above, and quite likely that the **Moment-Sigma** is too small. You need to experiment to decide.

Configuration scan for a selected dimer

Computing the energy at a single dimer configuration is usually not very informative. Instead, more information may be gained by performing a suitable scan of geometries near the particular dimer (in configuration space). But configuration space for a pair of two rigid molecules is 6 dimensional, so we need to restrict the calculation to a scan along a particular direction, which is often chosen to be a radial direction.

The //Cluster// code can be used to generate radial scans for pairs of interacting molecules using the configuration previously read/analysed in the **Orient** block as described above. The commands are:

reorient-analyse-write-configs.clt

Orient
  Geom-File RDX_run1.geom
  Reorient  RDX2
  Sort
  Analyse
    Sort
    Similarity  Moments  & Energy 
    Energy-Sigma 0.5 kJ/mol
    Moment-Sigma 40.0 AMU
    Similarity-cutoff 0.5
    Details
  End
  !
  R-scalings 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.20 1.40 
  Write  Format GEOM  Config 9
  !
End

In this example, after the sorting and analysis has been done, one of the configurations, in this case, configuration 9, has been selected. Keeping the relative orientation of the dimer in this configuration fixed, the centre-of-mass separation between the two molecules is scaled using the **R-scalings* values to generate a set of configurations. When //Cluster// is run on the command file we get, at the end of the output:

config-9.geom

! CGF =     9
! Config List name : CfgList-1
! Configs read from file : RDX_run1.geom
! UNITS  BOHR DEGREE KJ/MOL
    1     -12.62296408      -3.31124455       5.26638266     180.61242241       0.50458282       0.02386497       0.86303339
    2     -13.41189934      -3.51819734       5.59553158     180.61242241       0.50458282       0.02386497       0.86303339
    3     -14.20083459      -3.72515012       5.92468050     180.61242241       0.50458282       0.02386497       0.86303339
    4     -14.98976985      -3.93210291       6.25382941     180.61242241       0.50458282       0.02386497       0.86303339
    5     -15.77870510      -4.13905569       6.58297833     180.61242241       0.50458282       0.02386497       0.86303339
    6     -16.56764036      -4.34600848       6.91212725     180.61242241       0.50458282       0.02386497       0.86303339
    7     -17.35657561      -4.55296126       7.24127616     180.61242241       0.50458282       0.02386497       0.86303339
    8     -18.93444612      -4.96686683       7.89957400     180.61242241       0.50458282       0.02386497       0.86303339
    9     -22.09018714      -5.79467797       9.21616966     180.61242241       0.50458282       0.02386497       0.86303339
  !

The (in this case) 9 configuration shown above are all based on configuration 9. Notice how only the radial separation vector $(R_x,R_y,R_z)$ changes. The angle and rotation axis are fixed. This set of configurations can be used in //Orient// and //Cluster// to compute energies as described on pages:

• Energy calculations using Orient.

• Energy scan using CamCASP.

If you wish to convert these angle-axis coordinates into an XYZ file then see this tutorial:

• Angle-axis to XYZ