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Adaptive Biasing Force Method

2021-08-02T12:51:26Z

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Navigation: [[Documentation]] / [[Methods]] / [[Adaptive Biasing Force Method]]
----
__NOEDITSECTION__
<div style="float:right;">__TOC__</div>
==Chapters==
* [[Adaptive Biasing Force Method#Description|ABF:Description]]
* [[ABF:Controls]]
* [[ABF:Collective variables]]
* [[ABF:Post-processing]]
* [[ABF:Multiple walkers approach]]
* [[ABF:Examples]]

==Description==
===Free Energy from Unconstrained MD Simulations===
The Adaptive Biasing Force (ABF) method calculates the free energy as a function of selected collective variables from unconstrained molecular dynamics (MD) simulations. The method does not provide the free energy directly, but instead, it provides the free energy gradient <math>\frac{\partial G(\boldsymbol \xi)}{\partial \boldsymbol \xi}</math>, which must be integrated to get the free energy:

<center><math>\Delta G = G(\boldsymbol \xi_2) - G(\boldsymbol \xi_1) = \int_{\boldsymbol \xi_1}^{\boldsymbol \xi_2} \frac{\partial G(\boldsymbol \xi)} {\partial \boldsymbol \xi} \boldsymbol d \xi </math> ... (1)</center>

The free energy gradient is calculated as a mean of instantaneous collective force <math>\bold F_{ICF}</math>:

<center><math>\frac{\partial G(\boldsymbol \xi^{*})}{\partial \boldsymbol \xi} = - {\langle \bold F_{ICF} \rangle}_{\boldsymbol \xi=\boldsymbol \xi^{*}} </math> ... (2)</center>

with the instantaneous collective force calculated from the time evolution of the collective variable:<ref name="darve2008">Darve, E.; Rodríguez-Gómez, D.; Pohorille, A. Adaptive Biasing Force Method for Scalar and Vector Free Energy Calculations. ''J. Chem. Phys.'' '''2008''', ''128 (14)'', 144120. [https://doi.org/10.1063/1.2829861 doi:10.1063/1.2829861].</ref>

<center><math>\bold F_{ICF} = \frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right)</math> ... (3)</center>

where <math>\bold Z</math> is the matrix in the form:

<center><math>[Z]_{ij}=\sum_{k=1}^{N_{atoms}} \frac{1}{m_k} \frac{\partial \xi_i}{\partial \bold x_k} \frac{\partial \xi_j}{\partial \bold x_k}</math> ... (4)</center>

The analytical calculation of instantaneous collective force by Equation 3 requires the second derivatives of collective variables with respect to Cartesian coordinates. Since this can be prohibitive for complex collective variables such as the simple base-pair parameters, Equation 3 is evaluated numerically by a [[Adaptive Biasing Force Method#Instantaneous Collective Forces|finite-difference approach]].

===Sampling Space Discretization===
Due to numerical reasons, mean forces are collected on a regular grid. The averaging of instantaneous collective force is then done in small intervals centered at discrete CV values:

<center><math>\frac{\partial G(\boldsymbol \xi^{*})}{\partial \boldsymbol \xi} = - {\langle \bold F_{ICF} \rangle}_{\boldsymbol \xi=\boldsymbol \xi^{*} \pm \bold h/2} </math> ... (5)</center>

with the standard error:

<center><math>\sigma_e \left( \frac{\partial G(\boldsymbol \xi^{*})}{\partial \boldsymbol \xi} \right) = \sqrt{ \frac {N_{corr}} {N_b} } \sigma(\bold F_{ICF})_ {\boldsymbol \xi=\boldsymbol \xi^{*} \pm \bold h/2} </math> ... (6)</center>

where the standard deviation is given by:

<center><math>\sigma(\bold F_{ICF})_ {\boldsymbol \xi=\boldsymbol \xi^{*} \pm \bold h/2} = \sqrt { \frac{1}{N_b} \sum_{i=1}^{N_b} \left( F_{ICF}(\boldsymbol \xi_i) - \overline {F_{ICF}} \right)^2 \vert _{\boldsymbol \xi=\boldsymbol \xi^{*} \pm \bold h/2} }</math> ... (7)</center>

where <math>\bold h</math> is the interval size also called a bin, <math>N_b</math> is the number of samples collected in a bin centered at <math>\boldsymbol \xi^{*}</math>, and <math>N_{corr}</math> is a statistical inefficiency due to correlation in time series.

Therefore, each CV involved in ABF simulations must be discretized by specifying an interval in which the sampling is performed and the number of intervals (bins) for discretization, for further details, see [[ABF:Collective variables]]. The increasing number of bins improves the accuracy of Equation 5 and subsequently the quality of the integrated free energy (Equation 1) but it also increases the noise because of a smaller number of samples collected in a bin. A reasonable compromise is the number of bins, which leads to 0.1 Å or 1-2° bin widths.

===Adaptive Bias===
ABF introduces an adaptive bias, which improves the sampling of rare events. The bias removes barriers or higher free energy regions in the space described by predefined collective variables <math>\boldsymbol \xi</math>. As a result, the system evolves by free diffusion alongside these collective variables. The bias is derived from the free energy, which is projected in the form of biasing force <math>\bold F_{bias}</math> to the Cartesian space and removed from force <math>\bold F_{pot}</math> originated from inter-atomic interaction potential <math>V(\bold R)</math>. The application of the bias thus leads to the modified equations of motions:

<center><math>m_{i} \frac { d^2 \bold r_i }{dt^2} = \bold F_{pot,i}(\bold r_i) - \bold F_{bias,i}(\bold r_i) = - \frac{\partial V(\bold R)} {\partial \bold r_i} + \frac{\partial G(\boldsymbol \xi)}{\partial \boldsymbol \xi} \frac{\partial \boldsymbol \xi}{\partial \bold r_i}</math> ... (8)</center>

where <math>m_i</math> is mass of atom i, <math>\bold r_i</math> is atom position, and <math>t</math> is time.

Since the biasing force is not known prior to the simulation, it is calculated during the simulation and adaptively applied. To accelerate sampling, the biasing force is applied even if an inadequate number of samples is collected in a bin. In this case, the biasing force is scaled in the early stages to avoid artifacts from applications of overestimated biasing forces. The biasing force can also be smoothed to decrease noise in collected data. For further details, see feimode in [[ABF:Controls]].

===Instantaneous Collective Forces===
PMFLib implements two algorithms to calculate Equation 3: simplified and original ABF algorithms. The original ABF algorithm is theoretically more accurate than the simplified one but it works only for MD without constraints. Therefore, the simplified algorithm is the default one as it is numerically more robust at all MD setups.

====Simplified ABF Algorithm====
The simplified ABF algorithm (fmode=1) uses the result of the product rule for derivatives applied on Equation 3 leading into the two distinct contributions into the instantaneous collective forces:

<center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) \big|_{(t)} = \left( \bold Z^{-1}(t) \nabla \boldsymbol \xi (t) \right) \cdot \bold a(t) + \frac{d}{dt} \left( \bold Z^{-1}(t) \nabla \boldsymbol \xi (t)) \right) \cdot \bold v(t) = \bold F_{ICF,pot}(t) + \bold F_{ICF,kin}(t)</math> ... (9)</center>

The potential contribution <math>\bold F_{ICF,pot}(t)</math> is given:

<center><math>\bold F_{ICF,pot}(t) = \left( \bold Z^{-1}(t) \nabla \boldsymbol \xi (t) \right) \cdot \frac{\bold v(t+dt/2) - \bold v(t-dt/2)}{dt}</math> ... (10)</center>

It employs the accelerations <math>\bold a(t)</math> calculated back from the velocities:

<center><math>\bold a(t) = \frac{\bold v(t+dt/2) - \bold v(t-dt/2)}{dt}</math> ... (11)</center>,

which ensures that effect of SHAKE and other constraints on acceleration is properly counted (see [[Molecular_Dynamics_Algorithms|the leap-frog integration algorithm]] for further details).

The kinetic contribution <math>\bold F_{ICF,kin}(t-dt/2)</math> is calculated from numerical differentiation:

<center><math>\bold F_{ICF,kin}(t-dt/2) = \frac {\bold Z^{-1}(t) \nabla \boldsymbol \xi (t) - \bold Z^{-1}(t-dt) \nabla \boldsymbol \xi (t-dt)}{dt} \bold v(t-dt/2) </math> ... (12)</center>

Finally, to get <math>\bold F_{ICF,kin}</math> at the same time as <math>\bold F_{ICF,pot}</math>, two values are averaged:

<center><math>\bold F_{ICF,kin}(t) = \frac {\bold F_{ICF,kin}(t+dt/2) + \bold F_{ICF,kin}(t-dt/2) }{2}</math> ... (13)</center>

The algorithm uses a history of values collected in two consecutive time steps. But, the first result is available from the fourth time step to be compatible with the original algorithm.

====Original ABF Algorithm====
The original ABF algorithm (fmode=2) implements the algorithm presented by Darve ''at al''.<ref name="darve2008"/><ref name="darve2007">Darve, E. Thermodynamic Integration Using Constrained and Unconstrained Dynamics. In Free Energy Calculations Theory and Applications in Chemistry and Biology; Springer Series in CHEMICAL PHYSICS; Springer: Berlin, 2007; Vol. 86, pp 119–170.</ref>. This algorithm should not be used when SHAKE is enabled because the accelerations entering into the calculations are not corrected for constraints. The algorithm uses a history of values collected in four consecutive time steps. Thus, the first result is available from the fourth time step.

<center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) \big|_{(t)} = \frac{1}{2} \left( \frac{\bold p^+_{\xi}(t+dt) - \bold p^+_{\xi}(t) } {dt} + \frac{\bold p^-_{\xi}(t+dt) - \bold p^-_{\xi}(t) } {dt} \right)</math> ... (14)</center>

where

<center><math>\bold p^+_{\xi}(t) = \bold Z^{-1}(t) \nabla \boldsymbol \xi(t) \cdot \left[ \bold v(t+dt/2) - \frac{dt}{6} \bold a(t+dt) \right]</math> ... (15)</center>

<center><math>\bold p^-_{\xi}(t) = \bold Z^{-1}(t) \nabla \boldsymbol \xi(t) \cdot \left[ \bold v(t-dt/2) + \frac{dt}{6} \bold a(t-dt) \right]</math> ... (16)</center>

==References==
<references />

ABF:Controls

2021-08-02T10:20:27Z

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Navigation: [[Documentation]] / [[Methods]] / [[Adaptive Biasing Force Method]] / [[ABF:Controls]]
----
__NOEDITSECTION__ __NOTOC__
The behavior of the ABF method is controlled by the setup provided in the [abf] and eventually [abf-walker] sections. Both sections belong to the {PMFLIB} group.

==[abf]==
{| style="width: 100%;"
| style="width: 10em;" | '''Key'''
| style="width: 10em;" | '''Default value'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|- style="vertical-align: top; background-color: #f6f6f6;"
| fmode
| 0
| [[Control key types|integer]]
| The mode of the ABF method:<br/>0 - the method is disabled<br/> 1 - the standard ABF implementation is used (four points)<br/> 2 - less accurate implementation is used (two points)<br/>If the method is enabled then at least one collective variable must be provided in the {ABF} group. The collective variable specification is described in [[ABF:Collective variables]].
|- style="vertical-align: top;"
| fapply_abf
| on
| [[Control key types|logical]]
| Determine if the collected mean force is applied as a bias.
|- style="vertical-align: top; background-color: #f6f6f6;"
| feimode
| 1
| [[Control key types|integer]]
| The extrapolation/interpolation mode for ABF forces:<br/>0 - disabled<br/>1 - linear ramp with bottom limit<br/>2 - Gaussian kernel smoothing<br/>This option triggers further setup, which is optional and described below.
|- style="vertical-align: top;"
| fsample
| 5000
| [[Control key types|integer]]
| Every <i>fsample</i> MD steps, the actual information about collective variable values will be printed to the ABF output file. The name of the output file is provided in the [[General setup|[files]]] section.
|- style="vertical-align: top; background-color: #f6f6f6;"
| frestart
| off
| [[Control key types|logical]]
| Disable/Enable restarting the ABF simulation from the previous run. The name of the restart file is provided in the [[General setup|[files]]] section. If the restart is enabled but no restart file exists, then warning is raised and the simulation continues.
|- style="vertical-align: top;"
| frstupdate
| 5000
| [[Control key types|integer]]
| Every <i>frstupdate</i> MD steps, the actual ABF force and other data will be printed to the ABF restart file. The name of the restart file is provided in the [[General setup|[files]]] section.
|- style="vertical-align: top; background-color: #f6f6f6;"
| ftrjsample
| 0
| [[Control key types|integer]]
| Every <i>ftrjsample</i> MD steps, the actual ABF acumulator and other data will be printed to the ABF trajectory file. The name of the trajectory file is provided in the [[General setup|[files]]] section. Zero interval disables the ABF trajectory writing.
|- style="vertical-align: top;"
| fapply_mask
| off
| [[Control key types|logical]]
| Disable/Enable ABF force weights (mask). The name of file with the ABF weights is provided in the [[General setup|[files]]] section. The ABF mask is suitable for difficult free energy surfaces containing high energy regions, which is not necessary/appropriate to sample.
|- style="vertical-align: top; background-color: #f6f6f6;"
| fenthalpy
| off
| [[Control key types|logical]]
| If enabled, data for enthalpy calculation are collected.
|- style="vertical-align: top;"
| fentropy
| off
| [[Control key types|logical]]
| If enabled, data for entropy (-TdS) calculation are collected.
|- style="vertical-align: top; background-color: #f6f6f6;"
| fepotoffset
| 0.0
| [[Control key types|real]]
| A constant, which is added to the potential energy (affect the enthalpy calculation).
|- style="vertical-align: top;"
| fekinoffset
| 0.0
| [[Control key types|real]]
| A constant, which is added to the kinetic energy (affect the entropy calculation).
|}

===Linear ramp===
If the feimode option is equal to 1 then the following options change behavior of the linear ramp.
{| style="width: 100%;"
| style="width: 10em;" | '''Key'''
| style="width: 10em;" | '''Default value'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|- style="vertical-align: top; background-color: #f6f6f6;"
| fhramp_min
| 100
| [[Control key types|integer]]
| Bottom limit for number of samples in a bin. If the actual number of samples in a bin is lower than this number no ABF force is applied.
|- style="vertical-align: top;"
| fhramp_max
| 200
| [[Control key types|integer]]
| Top limit for number of samples in a bin. If the actual number of samples in a bin is higher than this number then estimated ABF force is applied fully otherwise it is scaled down by the linear ramp.
|}
The linear ramp has the following form:
<center><math>\bold F_{applied} = \frac{N_k - fhramp\_min}{fhramp\_max-fhramp\_min}\bold F_{estimated}</math>, if <math>N_k < fhramp\_max</math>,</center>
otherwise the full force is applied:
<center><math>\bold F_{applied} = \bold F_{estimated}</math>,</center>
where <math>N_k</math> is the number of samples in the bin <i>k</i>.

===Gaussian kernel smoothing===
If the feimode option is equal to 2 then the following option changes behavior of the Gaussian kernel smoothing. This filter requires an additional parameter (wfac) specified for each CV.
{| style="width: 100%;"
| style="width: 10em;" | '''Key'''
| style="width: 10em;" | '''Default value'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|- style="vertical-align: top; background-color: #f6f6f6;"
| fsmoothupdate
| 5000
| [[Control key types|integer]]
| The value determines how often (in MD steps) the smoothed mean forces are updated.
|}
The relationships between the sampled instantaneous collective and smoothed forces is given:
<center><math>\bold F_{aplied}(\boldsymbol \xi_i) = \frac{ \sum\limits_{j=1}^{N_{bins}} K(\boldsymbol \xi_i,\boldsymbol \xi_j)\bold F_{estimated}(\boldsymbol \xi_j)} {\sum\limits_{j=1}^{N_{bins}} K(\boldsymbol \xi_i,\boldsymbol \xi_j) }</math></center>,
with the Gaussian smoothing kernel defined as:
<center><math>K(\boldsymbol \xi_i,\boldsymbol \xi_j) = exp\left( - \frac {1}{2} \sum\limits_{k=1}^{N_{CVS}} \frac { (\xi_{i,k} - \xi_{j,k})^2} { w_{k}^2 h_{k}^2 } \right)</math></center>,
where <math>h_{k}^2</math> is a bin width and <math>w_{k}^2</math> is an user provided factor (wfac), see [[ABF:Collective variables]].

==[abf-walker]==
The optional section [abf-walker] provides information about access to the MWA server. The MWA extension is described in [[ABF:Multiple walkers approach]].
{| style="width: 100%;"
| style="width: 10em;" | '''Key'''
| style="width: 10em;" | '''Default value'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|- style="vertical-align: top; background-color: #f6f6f6;"
| fserverkey
|
| [[Control key types|string]]
| The name of a file with a server key. The server key contains information about the server name, the port number, and the server password. The file is generated by the mwa-server utility when the MWA server is started.
|- style="vertical-align: top;"
| fserverupdate
| 20000
| [[Control key types|integer]]
| The number of MD steps between exchanges of data with the MWA server. Since data are exchanged in a connect/send/receive/disconnect mode, exchanges should not occur too often.
|- style="vertical-align: top; background-color: #f6f6f6;"
| fabortonmwaerr
| on
| [[Control key types|logical]]
| Should the running of a walker (client) abort when MWA server communication failure occurs?
|- style="vertical-align: top"
| fconrepeats
| 0
| [[Control key types|integer]]
| The number of consecutive failed exchanges with the server that will lead to premature client termination. The zero means that no failures are allowed and the client is terminated at the first failed exchange.
|}

CV:ORAD2

2021-07-26T08:23:17Z

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__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:ORAD2]]
----
{{CVS}}
===Definition===
The radial distance of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_{x} = \sqrt{{A'}_{com,y}^2 + {A'}_{com,z}^2}</math></center>
<center><math>\xi_{y} = \sqrt{{A'}_{com,x}^2 + {A'}_{com,z}^2}</math></center>
<center><math>\xi_{z} = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''ORAD2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:ORAD2

2021-07-26T08:21:42Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:ORAD2]]
----
{{CVS}}
===Definition===
The radial distance of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_{x} = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>
<center><math>\xi_{y} = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>
<center><math>\xi_{z} = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''ORAD2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-26T08:19:20Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_{x} = A_{com,x}^'</math></center>
<center><math>\xi_{y} = A_{com,y}^'</math></center>
<center><math>\xi_{z} = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:ORAD2

2021-07-21T14:02:14Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:ORAD2]]
----
{{CVS}}
===Definition===
The radial distance of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''ORAD2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:56Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:47Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi x = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:30Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:22Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi x_a = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:16Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi _a = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:01:02Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:00:49Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>{\xi} = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:00:41Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\{xi} = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:00:33Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:00:25Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_{a} = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T14:00:15Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:59:28Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi = A_{com,x}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:59:14Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_{x} = A_{com,x}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:58:51Z

Durnik:

CV:OPOS2

2021-07-21T13:58:31Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure. Any axis of the superimposed coordinate system can be selected.

<center><math>\xi_x = A_{com,x}^'</math></center>
<center><math>\xi_y = A_{com,y}^'</math></center>
<center><math>\xi_z = A_{com,z}^'</math></center>

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:57:08Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure.

<center><math>\xi = A_{com,z}^'</math></center>

Any axis of the superimposed coordinate system can be selected.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:ORAD2

2021-07-21T13:55:49Z

Durnik: Created page with "__NOEDITSECTION__ Navigation: Documentation / Collective Variables / CV:ORAD2 ---- {{CVS}} ===Definition=== The radial distance of the point from z-axis of re-orie..."

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:ORAD2]]
----
{{CVS}}
===Definition===
The radial distance of the point from z-axis of re-oriented coordinate system along principal moments of the tensor inertia '''I'''.

<center><math>\xi = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>

The z-axis can be reoriented to any axis of the re-oriented coordinate system.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''ORAD2'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:53:26Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure.

<center><math>\xi = A_{com,z}^'</math></center>

Any axis of the superimposed coordinate system can be selected.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:52:13Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along a selected axis of the superimposed coordinate system of a reference structure.

<center><math>\xi = A_{com,z}^'</math></center>

The z-axis can be reoriented to any axis of the re-oriented coordinate system.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:50:21Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along z-axis of re-oriented coordinate system along principal moments of the tensor inertia '''I'''.

<center><math>\xi = A_{com,z}^'</math></center>

The z-axis can be reoriented to any axis of the re-oriented coordinate system.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''reference_a'''
| string
|
| name of the file with the reference structure in the XYZ format, the structure must have the same number of atoms as the group '''group_a'''
|-
| '''group_b'''
| [[Mask format|mask]]
|
| atoms specifying the point '''B'''
|-
| '''direction'''
| x, y, z
|
| select axis in the superimposed coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:45:47Z

Durnik:

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:OPOS2]]
----
{{CVS}}
===Definition===
The absolute position of the point along z-axis of re-oriented coordinate system along principal moments of the tensor inertia '''I'''.

<center><math>\xi = A_{com,z}^'</math></center>

The z-axis can be reoriented to any axis of the re-oriented coordinate system.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''OPOS'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''z_direction'''
| [[Mask format|mask]]
|
| single atom specifying the end of approximate z-direction vector of the re-oriented coordinate system. The vector origin is in '''A'''<sub>com</sub>. The atom must be member of the group '''A'''.
|-
| '''direction'''
| x, y, z
|
| determine direction of z-axis in the re-oriented coordinate system
|}
''Keys in bold are mandatory.''

CV:OPOS2

2021-07-21T13:44:21Z

Durnik: Created page with "__NOEDITSECTION__ Navigation: Documentation / Collective Variables / CV:ORAD ---- {{CVS}} ===Definition=== The radial distance of the point from z-axis of re-orien..."

__NOEDITSECTION__
Navigation: [[Documentation]] / [[Collective Variables]] / [[CV:ORAD]]
----
{{CVS}}
===Definition===
The radial distance of the point from z-axis of re-oriented coordinate system along principal moments of the tensor inertia '''I'''.

<center><math>\xi = \sqrt{{A'}_{com,x}^2 + {A'}_{com,y}^2}</math></center>

The z-axis can be reoriented to any axis of the re-oriented coordinate system.

The relation between re-oriented (') and native coordinate system is given by the transformation matrix '''T''':

<center><math>\bold A_{com}^' = \bold T \bold A_{com}</math></center>

===Specification===
Section name: '''ORAD'''
{|
| 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 point '''A'''
|- style="vertical-align: top;"
| '''z_direction'''
| [[Mask format|mask]]
|
| single atom specifying the end of approximate z-direction vector of the re-oriented coordinate system. The vector origin is in '''A'''<sub>com</sub>. The atom must be member of the group '''A'''.
|-
| '''direction'''
| x, y, z
|
| determine direction of z-axis in the re-oriented coordinate system
|}
''Keys in bold are mandatory.''

Template:CVS

2021-07-21T13:41:55Z

Durnik:

__NOTOC__
<div style="float:right; border-style: solid; border-width: 1px; border-color: #aaaaaa; background-color: #f6f6f6; margin-left: 10px; padding: 0px; width: 10em;">
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Distance</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:DD|DD]], [[CV:DIS|DIS]], [[CV:MDIS|MDIS]], [[CV:MDISG|MDISG]], [[CV:ODIS|ODIS]], [[CV:OPOS|OPOS]], [[CV:OPOS2|OPOS2]], [[CV:ORAD|ORAD]], [[CV:ORAD2|ORAD2]], [[CV:POS|POS]], [[CV:RAD|RAD]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Angle</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:ANG|ANG]], [[CV:ANG2|ANG2]], [[CV:AXANG|AXANG]], [[CV:AXANG2|AXANG2]], [[CV:DIH|DIH]], [[CV:DIH2|DIH2]], [[CV:PANG|PANG]], [[CV:PVANG|PVANG]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Coordination</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:CNFF|CNFF]], [[CV:CNGFF|CNGFF]], [[CV:CNSW|CNSW]], [[CV:CNGSW|CNGSW]], [[CV:CNRF|CNRF]], [[CV:CNGRF|CNGRF]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Shape</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:ACYL|ACYL]], [[CV:ASPH|ASPH]], [[CV:EVEC|EVEC]], [[CV:PMGTD|PMGTD]], [[CV:PMOGT|PMOGT]], [[CV:PLANE|PLANE]], [[CV:RGYR|RGYR]], [[CV:RMSDT|RMSDT]], [[CV:SANIS|SANIS]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">[[Nucleic Acids]]</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:NASBPP|NALBPP]], [[CV:NASBPP|NASBPP]], [[CV:NASBPPOLD|NASBPPOLD]], [[CV:NALSTP|NALSTP]], [[CV:NASSTP|NASSTP]], [[CV:NASSTPOLD|NASSTPOLD]], [[CV:NASBO|NASBO]], [[CV:NAPBO|NAPBO]], [[CV:NABEND|NABEND]]
</div>

<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">[[Ring Puckering|Puckering]]</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:PUCK6Q|PUCK6Q]], [[CV:PUCK6P|PUCK6P]], [[CV:PUCK6T|PUCK6T]], [[CV:PUCK5Q|PUCK5Q]], [[CV:PUCK5P|PUCK5P]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Special</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:WORMPOS|WORMPOS]], [[CV:WORMANG|WORMANG]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Energy</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:POT|POT]], [[CV:EGAP|EGAP]]
</div>
<p style="margin:2px 2px 0px 2px; border: none; background-color: #87cefa; text-align: center; font-size: 1.0em; color: blue; padding: 2px;">Algebra</p>
<div style="margin: 5px; font-size: 0.8em;">
[[CV:ADD|ADD]], [[CV:SUB|SUB]], [[CV:MULT|MULT]], [[CV:DIV|DIV]], [[CV:FSWITCH|FSWITCH]], [[CV:RSWITCH|RSWITCH]]
</div>
</div>

Collective Variables

2021-07-21T13:39:50Z

Durnik:

Navigation: [[Documentation]] / [[Collective Variables]]
----
{{CVS}}__NOEDITSECTION__

Collective variables (CVs) define a subset of configuration space in which free energy is being calculated.

The CV definition can be read either from the input file or from an external file. The mode will depend on configuration in the [[General setup|[files]]] section. If the value of the fcvsdef key contains the name of the group (e.g. string starting with the "{" character) then the CV definition will be read from this group in the input file. Otherwise, the CV definition will be read from a file with the name provided by the fcvsdef key. In the latter case, the CV definition must be in the {MAIN} group (which is implicit and can be omitted in the file).

The group or file can contain several collective variables. Each collective variable is specified in a single section. The name of the section defines a type of CV. The section contains the name key containing a unique CV name and other keys specific to a given CV type.

Extra documentation:
* [[Nucleic Acids]]
* [[Ring Puckering]]
* [[Macrocycle Threading]]

===Supported Types===
{| style="width: 80%;"
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Distance'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:DD|DD]]
| distance difference
| [[CV:DIS|DIS]]
| distance between two points
|-
| [[CV:MDIS|MDIS]]
| minimum value of atom pair distances
| [[CV:MDISG|MDISG]]
| minimum distance between two atom groups
|-
| [[CV:ODIS|ODIS]]
| distance between plane and point
| [[CV:OPOS|OPOS]]
| absolute position in the oriented coordinate system
|-
| [[CV:ORAD|ORAD]]
| radial distance in the oriented coordinate system
| [[CV:POS|POS]]
| absolute position
|-
| [[CV:ORAD2|ORAD2]]
| radial distance in the superimposed coordinate system
| [[CV:OPOS2|OPOS2]]
| absolute position in the superimposed coordinate system
|-
| [[CV:RAD|RAD]]
| radial distance
|
|
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Angle'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:ANG|ANG]]
| angle among three points
| [[CV:ANG2|ANG2]]
| angle between two vectors defined by four points
|-
| [[CV:AXANG|AXANG]]
| angle between two principal axes
| [[CV:AXANG2|AXANG2]]
| angle between two reference axes
|-
| [[CV:DIH|DIH]]
| dihedral angle among four points
| [[CV:DIH2|DIH2]]
| dihedral angle among three vectors defined by six points
|-
| [[CV:PANG|PANG]]
| angle between two planes
| [[CV:PVANG|PVANG]]
| angle between plane and vector
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Coordination Numbers'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|- valign="top"
| [[CV:CNFF|CNFF]]
| coordination number atom-atom using Fermi like function
| [[CV:CNGFF|CNGFF]]
| coordination number point-atom using Fermi like function
|- valign="top"
| [[CV:CNSW|CNSW]]
| coordination number atom-atom using switch function
| [[CV:CNGSW|CNGSW]]
| coordination number point-atom using switch function
|- valign="top"
| [[CV:CNRF|CNRF]]
| coordination number atom-atom using rational function
| [[CV:CNGRF|CNGRF]]
| coordination number point-atom using rational function
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Shape'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:ACYL|ACYL]]
| acylindricity
| [[CV:PMGTD|PMGTD]]
| difference of two principal moments of gyration tensor

|-
| [[CV:ASPH|ASPH]]
| asphericity
| [[CV:PMOGT|PMOGT]]
| principal moment of gyration tensor
|-
| [[CV:SANIS|SANIS]]
| relative shape anisotropy
| [[CV:RMSDT|RMSDT]]
| root-mean square deviation to target structure
|-
| [[CV:RGYR|RGYR]]
| radius of gyration
| [[CV:PLANE|PLANE]]
| root-mean-square deviation from the plane
|-
| [[CV:EVEC|EVEC]]
| projection into essential vector
|
|
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''[[Nucleic Acids]]'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:NALBPP|NALBPP]]
| local base-pair parameters
| [[CV:NALSTP|NALSTP]]
| local base-pair step parameters
|-
| [[CV:NASBPP|NASBPP]]
| simple base-pair parameters
| [[CV:NASSTP|NASSTP]]
| simple base-pair step parameters
|-
| [[CV:NASBPPOLD|NASBPPOLD]]
| simple base-pair parameters
| [[CV:NASSTPOLD|NASSTPOLD]]
| simple base-pair step parameters
|-
| [[CV:NASBO|NASBO]]
| simple base-pair opening
| [[CV:NAPBO|NAPBO]]
| primitive base-pair opening
|-
| [[CV:NABEND|NABEND]]
| nucleic acid bending

|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''[[Ring Puckering]]'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:PUCK6Q|PUCK6Q]]
| total puckering amplitude of six-membered ring
| [[CV:PUCK5Q|PUCK5Q]]
| total puckering amplitude of five-membered ring

|-
| [[CV:PUCK6P|PUCK6P]]
| puckering azimuthal angle of the six-membered ring
| [[CV:PUCK5P|PUCK5P]]
| puckering azimuthal angle of the five-membered ring
|-
| [[CV:PUCK6T|PUCK6T]]
| puckering polar angle of the six-membered ring
|
|
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Special'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:WORMPOS|WORMPOS]]
| parametrical position of an axle inside a macrocycle
| [[CV:WORMANG|WORMANG]]
| orientation of an axle inside a macrocycle
|-
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Energy'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:POT|POT]]
| potential energy
| [[CV:EGAP|EGAP]]
| energy gap between two resonance states
|-
| colspan="4" style="text-align: center; background-color: #CCCCFF;" | '''Algebra'''
|-
| style="width: 5em;" | '''Type'''
| '''Description'''
| style="width: 5em;" | '''Type'''
| '''Description'''
|-
| [[CV:ADD|ADD]]
| sum of two collective variables
| [[CV:SUB|SUB]]
| difference between two collective variables
|-
| [[CV:MULT|MULT]]
| product of two collective variables
| [[CV:DIV|DIV]]
| ratio of two collective variables
|-
| [[CV:FSWITCH|FSWITCH]]
| Fermi-like switch function
| [[CV:RSWITCH|RSWITCH]]
| rational switch function
|}