View source for CV:PMOGT

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Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:PMOGT]]
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{{CVS}}
===Definition===
The selected principal moment of the mass weighted gyration tensor '''S''' calculated for the atom group '''A'''.

<center><math>\xi = \lambda_n^2</math></center>

where &lambda; is the selected principal moment of the gyration tensor. The mass weighted gyration tensor '''S''' is defined as

<center><math>S_{mn} \ = \frac {\sum_{i=1}^{N} m_i (x_{m}^{(i)} - x_{m}^{(\bold A)}) (x_{n}^{(i)} - x_{n}^{(\bold A)})}{\sum_{i=1}^{N} m_i} </math></center>

The eigenvalues of the tensor are <math>\lambda_{x}^2 \leq \lambda_{y}^2 \leq \lambda_{z}^2</math>:
<center><math>
\bold S = \begin{bmatrix}
\lambda_{x}^{2} & 0 & 0 \\
0 & \lambda_{y}^{2} & 0 \\
0 & 0 & \lambda_{z}^{2}
\end{bmatrix}
</math></center>

'''PBC note:''' The minimum-image convention is not used.


===Specification===
Section name: '''PMOGT'''
{|
| style="width: 5em;" | '''Key''' 
| style="width: 5em;" | '''Type'''
| style="width: 5em;" | '''Default'''
| '''Description'''
|-
|<hr/> || <hr/> || <hr/> || <hr/>
|-
| '''name'''
| string
|
| unique CV name
|-
| '''group_a'''
| [[Mask format|mask]]
|
| atoms specifying the group '''A'''
|-
| '''axis'''
| x,y,z
|
| principal moment axis
|}
''Keys in bold are mandatory.''