Shortcut: ROPS

Module	crystdistrib
Description	Usage
Calculate the ROPS order parameter
output value	type
the values of the ROPS order parameters	vector

Details and examples

Calculate the ROPS order parameter

ROPS is a shortcut to calculate the Relative-Orientational Order Parameters that are described in the paper that is referenced below. As arguments, ROPS takes a list of atoms (corresponding to molecules), a vector of quaternions, a cutoff distance, and two kernel files detailing the means, variances, and normalization factors of the probability distributions. ROPS returns a vector of order parameters.

The DOPS kernel file has FIELDS height, mu, and sigma corresponding to the normalization factor, mean, and variance of the gaussian distributions used in the order parameters. The SET kerneltype is gaussian. The ROPS kernel file has FIELDS height, kappa, mu_w, mu_i, mu_j, and mu_k, which correspond to the normalization factor, reciprocal variance, and components of the mean quaternion frame of the Bipolar Watson distribution used in the order parameters. The SET kerneltype is gaussian.

ROPS returns one order parameter per atom given, evaluated over each atom's neighbors within the cutoff. The distribution defined by the kernel files, analogous to a radial distribution function, defined over all possible spatial orientations two molecules could take relative to one another. The domain is the set of all unit quaternions. The order parameter is obtained by evaluating the distribution at each neighbor's unit quaternion, and summing them.

This example file calculates the ROPS for a system of 3 molecules.

Click on the labels of the actions for more information on what each action computes

#SETTINGS INPUTFILES=regtest/crystdistrib/rt-rops-shortcut/kernels.dat,regtest/crystdistrib/rt-rops-shortcut/kernels2.dat
quatThe QUATERNION action with label quat calculates the following quantities:
 Quantity   
 Type   
 Description  
quat.w
vector
the real component of quaternion
quat.i
vector
the i component of the quaternion
quat.j
vector
the j component of the quaternion
quat.k
vector
the k component of the quaternion: QUATERNIONCalculate unit quaternions for molecules. More details ATOMS1the three atom that we are using to calculate the quaternion=1,2,3 ATOMS2the three atom that we are using to calculate the quaternion=4,5,6 ATOMS3the three atom that we are using to calculate the quaternion=7,8,9
bopsThe ROPS action with label bops calculates the following quantities:
 Quantity   
 Type   
 Description  
bops
vector
the values of the ROPS order parameters: ROPSCalculate the ROPS order parameter This action is a shortcut. More details ...
   SPECIESthe list of atoms for which the ROPS are being calculated and the atoms that can be in the environments=1,4,7 QUATERNIONSthe label of the action that computes the quaternions that should be used=quat CUTOFFcutoff for the distance matrix=100.0
   KERNELFILE_DOPSthe file containing the list of kernel parameters=
regtest/crystdistrib/rt-rops-shortcut/kernels.dat
 Click here to see an extract from this file.
  
  ×  
FILE: regtest/crystdistrib/rt-rops-shortcut/kernels.dat
    
#! FIELDS height mu sigma
#! SET kerneltype gaussian
2.26628554234 6.37235632777 0.17603354605920524374
2.26598891932 6.37243472055 0.17605658924421270294
2.83246817245 6.94118069019 0.14084616529226330342
2.23141032403 6.87945090447 0.178784814297  
2.26563347801 6.81645001966 0.17608420968
2.26829869206 6.37245683771 0.1758773136
2.26856314184 6.37237895273 0.175856811319
2.84313122015 6.94216988399 0.140317927493
2.21827805142 6.87753705648 0.17984322576
2.27474509536 6.81810643390 0.175378894635

  
   KERNELFILE_ROPSthe file containing the list of kernel parameters=
regtest/crystdistrib/rt-rops-shortcut/kernels2.dat
 Click here to see an extract from this file.
  
  ×  
FILE: regtest/crystdistrib/rt-rops-shortcut/kernels2.dat
    
#! FIELDS height kappa mu_w mu_i mu_j mu_k
#! SET kerneltype gaussian
 2.81566426485e-24  60.9517091737  0.999999935213 0.000323260605362 -3.54954971419e-05 0.000154325371938
 2.74313783032e-24  60.9784690136  -0.999999975104 -9.33618007376e-07 -0.000174903361291 0.000138561169562 
 0.0130950591427  7.87597632012  -0.00314335246277 0.331888328739 -0.504016340713 0.797375560746 
 0.0107350493097 8.12722630497  -0.0032553078902 0.272414440723 -0.417230695312 0.867005376192 
 0.0775451781009  5.47161569795  0.00999289453389 0.0115376130044 -0.00353037871082 0.999877273455
 8.41766101819e-25  62.1895764963 -0.999999978371 -6.76320959659e-05 0.000135881297839 0.000142199691495
 8.90283264343e-25  62.1321413047 0.999999916445 -0.000387459116169 6.61150331893e-06 0.000130162625944
 0.0133120880032 7.85508401972 -0.0033041458338 -0.332424752605 0.504900401912 0.796591771628 
 0.0099761880464 8.2193276117  -0.00312375550685 -0.271447650829 0.41694219092 0.867447764676 
 0.0794224100073  5.43643088621 0.0107636888243 -0.0116508635888 0.0021743879902 0.999871827995  






  
...
# PLUMED interprets the command:
# bops: ROPS ...
#    SPECIES=1,4,7 QUATERNIONS=quat CUTOFF=100.0
#    KERNELFILE_DOPS=regtest/crystdistrib/rt-rops-shortcut/kernels.dat
#    KERNELFILE_ROPS=regtest/crystdistrib/rt-rops-shortcut/kernels2.dat
# ...
# as follows (Click the red comment above to revert to the short version of the input):
bops_cmatThe DISTANCE_MATRIX action with label bops_cmat calculates the following quantities:
 Quantity   
 Type   
 Description  
bops_cmat
matrix
a matrix containing the weights for the bonds between each pair of atoms: DISTANCE_MATRIXCalculate a matrix of distances between atoms. More details  GROUPthe atoms for which you would like to calculate the adjacency matrix=1,4,7 CUTOFF ignore distances that have a value larger than this cutoff=100
bops_quatprodThe QUATERNION_PRODUCT_MATRIX action with label bops_quatprod calculates the following quantities:
 Quantity   
 Type   
 Description  
bops_quatprod.w
matrix
the real component of quaternion
bops_quatprod.i
matrix
the i component of the quaternion
bops_quatprod.j
matrix
the j component of the quaternion
bops_quatprod.k
matrix
the k component of the quaternion: QUATERNION_PRODUCT_MATRIXCalculate the outer product matrix from two vectors of quaternions More details MASKa matrix that is used to used to determine which elements of the output matrix to compute=bops_cmat ARGthe labels of the quaternion vectors that you are outer product of=quat.*,quat.*
bops_kfuncThe CUSTOM action with label bops_kfunc calculates the following quantities:
 Quantity   
 Type   
 Description  
bops_kfunc
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details MASKthe label for a sparse vector/matrix that should be used to determine which elements of the vector/matrix should be computed=bops_cmat ARGthe values input to this function=bops_cmat,bops_quatprod.* VARthe names to give each of the arguments in the function=x,w,i,j,k PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=2.26629*exp(-(x-6.37236)^2/(2*0.176034*0.176034))*2.81566e-24*exp(60.9517*(w*1+i*0.000323261+j*-3.54955e-05+k*0.000154325)^2)+2.26599*exp(-(x-6.37243)^2/(2*0.176057*0.176057))*2.74314e-24*exp(60.9785*(w*-1+i*-9.33618e-07+j*-0.000174903+k*0.000138561)^2)+2.83247*exp(-(x-6.94118)^2/(2*0.140846*0.140846))*0.0130951*exp(7.87598*(w*-0.00314335+i*0.331888+j*-0.504016+k*0.797376)^2)+2.23141*exp(-(x-6.87945)^2/(2*0.178785*0.178785))*0.010735*exp(8.12723*(w*-0.00325531+i*0.272414+j*-0.417231+k*0.867005)^2)+2.26563*exp(-(x-6.81645)^2/(2*0.176084*0.176084))*0.0775452*exp(5.47162*(w*0.00999289+i*0.0115376+j*-0.00353038+k*0.999877)^2)+2.2683*exp(-(x-6.37246)^2/(2*0.175877*0.175877))*8.41766e-25*exp(62.1896*(w*-1+i*-6.76321e-05+j*0.000135881+k*0.0001422)^2)+2.26856*exp(-(x-6.37238)^2/(2*0.175857*0.175857))*8.90283e-25*exp(62.1321*(w*1+i*-0.000387459+j*6.6115e-06+k*0.000130163)^2)+2.84313*exp(-(x-6.94217)^2/(2*0.140318*0.140318))*0.0133121*exp(7.85508*(w*-0.00330415+i*-0.332425+j*0.5049+k*0.796592)^2)+2.21828*exp(-(x-6.87754)^2/(2*0.179843*0.179843))*0.00997619*exp(8.21933*(w*-0.00312376+i*-0.271448+j*0.416942+k*0.867448)^2)+2.27475*exp(-(x-6.81811)^2/(2*0.175379*0.175379))*0.0794224*exp(5.43643*(w*0.0107637+i*-0.0116509+j*0.00217439+k*0.999872)^2)
bops_onesThe CONSTANT action with label bops_ones calculates the following quantities:
 Quantity   
 Type   
 Description  
bops_ones
vector
the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=3
bopsThe MATRIX_VECTOR_PRODUCT action with label bops calculates the following quantities:
 Quantity   
 Type   
 Description  
bops
vector
the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=bops_kfunc,bops_ones
# --- End of included input --- 

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
SPECIES	atoms	the list of atoms for which the ROPS are being calculated and the atoms that can be in the environments

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
SPECIES	input	none	the list of atoms for which the ROPS are being calculated and the atoms that can be in the environments
QUATERNIONS	compulsory	none	the label of the action that computes the quaternions that should be used
KERNELFILE_DOPS	compulsory	none	the file containing the list of kernel parameters
KERNELFILE_ROPS	compulsory	none	the file containing the list of kernel parameters
CUTOFF	compulsory	none	cutoff for the distance matrix

References

More information about how this action can be used is available in the following articles:

• E. E. Santiso, B. L. Trout, A general set of order parameters for molecular crystals. The Journal of Chemical Physics. 134 (2011)