Shortcut: NEMATIC_ORDER

Module	liquid_crystal
Description	Usage
Calculate the nematic order parameter.
output value	type
the modulus of the average vector	scalar

Details and examples

Calculate the nematic order parameter.

The nematic order parameter S characterizes the orientational order of molecules and ranges from S=0 (isotropic) to S=1 (all molecular axes are perfectly parallel). Most liquids are isotropic, as there is no preferred direction, and have an order parameter close to 0. In liquid crystals, membranes and solids, molecules tend to align giving rise to order parameters closer to 1.

$S$ is calculated from the distribution of the angles between the molecular axes ( $\hat{u}_i$ for $i=1,\ldots,N$ ) and the nematic director $\hat{n}$ , $S = \frac{1}{N} \sum_{i=1}^N \left(\frac{3}{2} \cos^2(\theta_i) - \frac{1}{2} \right),$ with $\cos(\theta_i) = \hat{n} \cdot \hat{u}_i$ .

The nematic director depends on the distribution of the molecular axes and is computed as the eigenvector belonging to the largest eigenvalue of the $3 \times 3$ nematic order tensor, $Q_{a,b} = \frac{1}{N} \sum_{i=1}^N \left(\frac{3}{2} u_{a,i} u_{b,i} - \frac{1}{2} \delta_{a,b} \right).$ Note that if only a single molecular axis is given (N=1), the nematic order parameter is always S=1.

By adding a bias to the nematic order parameter, one can drive a liquid crystal from the isotropic to the nematic phase.

The axis of a rod-like molecule is defined as the distance vector between two atoms, it points from the tail atom to the head atom.

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

# Assume there are three molecules with 20 atoms each.
# In the first molecule the molecular axis vector points from atom 1 to atom 20,
# in the second molecule it points from atom 21 to atom 40
# and in the third from atom 41 to atom 60.

# Compute nematic order parameter for the three molecules.
SThe NEMATIC_ORDER action with label S calculates the following quantities: Quantity    Type    Description  
S scalar the modulus of the average vector: NEMATIC_ORDERCalculate the nematic order parameter. This action is a shortcut. More details MOLECULE_STARTSThe atoms where the molecular axis starts=1,21,41 MOLECULE_ENDSThe atoms where the molecular axis ends=20,40,60
# PLUMED interprets the command:
# S: NEMATIC_ORDER MOLECULE_STARTS=1,21,41 MOLECULE_ENDS=20,40,60
# as follows (Click the red comment above to revert to the short version of the input):
S_dvalsThe DISTANCE action with label S_dvals calculates the following quantities: Quantity    Type    Description  
S_dvals vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,20 ATOMS2the pair of atom that we are calculating the distance between=21,40 ATOMS3the pair of atom that we are calculating the distance between=41,60
S_dvecsThe DISTANCE action with label S_dvecs calculates the following quantities: Quantity    Type    Description  
S_dvecs.x vector the x-component of the vector connecting the two atoms
S_dvecs.y vector the y-component of the vector connecting the two atoms
S_dvecs.z vector the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details COMPONENTS calculate the x, y and z components of the distance separately and store them as label  ATOMS1the pair of atom that we are calculating the distance between=1,20 ATOMS2the pair of atom that we are calculating the distance between=21,40 ATOMS3the pair of atom that we are calculating the distance between=41,60
S_duxThe CUSTOM action with label S_dux calculates the following quantities: Quantity    Type    Description  
S_dux vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=S_dvecs.x,S_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
S_duyThe CUSTOM action with label S_duy calculates the following quantities: Quantity    Type    Description  
S_duy vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=S_dvecs.y,S_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
S_duzThe CUSTOM action with label S_duz calculates the following quantities: Quantity    Type    Description  
S_duz vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=S_dvecs.z,S_dvals FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
S_uThe VSTACK action with label S_u calculates the following quantities: Quantity    Type    Description  
S_u matrix a matrix that contains the input vectors in its columns: VSTACKCreate a matrix by stacking vectors together More details ARGthe values that you would like to stack together to construct the output matrix=S_dux,S_duy,S_duz
S_uTThe TRANSPOSE action with label S_uT calculates the following quantities: Quantity    Type    Description  
S_uT matrix the transpose of the input matrix: TRANSPOSECalculate the transpose of a matrix More details ARGthe label of the vector or matrix that should be transposed=S_u
S_NThe CONSTANT action with label S_N calculates the following quantities: Quantity    Type    Description  
S_N scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUEthe single number that you would like to store=3
S_IdThe CONSTANT action with label S_Id calculates the following quantities: Quantity    Type    Description  
S_Id matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=3,0,0,0,3,0,0,0,3 NROWS the number of rows in your input matrix=3 NCOLS the number of columns in your matrix=3
S_uTuThe MATRIX_PRODUCT action with label S_uTu calculates the following quantities: Quantity    Type    Description  
S_uTu matrix the product of the two input matrices: MATRIX_PRODUCTCalculate the product of two matrices More details ARGthe label of the two matrices from which the product is calculated=S_uT,S_u
S_QsumThe CUSTOM action with label S_Qsum calculates the following quantities: Quantity    Type    Description  
S_Qsum 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 ARGthe values input to this function=S_uTu,S_Id FUNCthe function you wish to evaluate=((3*x-y)/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
S_QThe CUSTOM action with label S_Q calculates the following quantities: Quantity    Type    Description  
S_Q 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 ARGthe values input to this function=S_Qsum,S_N FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
S_diagThe DIAGONALIZE action with label S_diag calculates the following quantities: Quantity    Type    Description  
S_diag.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
S_diag.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities
S_diag.vals-2 scalar the eigevalues of the input matrix  This is the 2th of these quantities
S_diag.vecs-2 vector the eigenvectors of the input matrix  This is the 2th of these quantities
S_diag.vals-3 scalar the eigevalues of the input matrix  This is the 3th of these quantities
S_diag.vecs-3 vector the eigenvectors of the input matrix  This is the 3th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=S_Q
SThe CUSTOM action with label S calculates the following quantities: Quantity    Type    Description  
S scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=S_diag.vals-1,S_N FUNCthe function you wish to evaluate=x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details FILEthe name of the file on which to output these quantities=colvar ARGthe labels of the values that you would like to print to the file=S

# Add a bias to the nematic order parameter S.
The PRINT action with label  calculates somethingBIASVALUETakes the value of one variable and use it as a bias More details ARGthe labels of the scalar/vector arguments whose values will be used as a bias on the system=S

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
MOLECULE_STARTS	atoms	The atoms where the molecular axis starts
MOLECULE_ENDS	atoms	The atoms where the molecular axis ends

Full list of keywords

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

Keyword	Type	Default	Description
MOLECULE_STARTS	input	none	The atoms where the molecular axis starts
MOLECULE_ENDS	input	none	The atoms where the molecular axis ends

Quantity	Type	Description
S	scalar	the modulus of the average vector