Trajectory Analysis

analysis is a standalone program that performs analysis of molecular dynamics trajectories created with AMS. It can produce histograms and radial distribution functions. It is used under the hood in AMSmovie (MD Properties menu bar).

New in Trajectory Analysis-2023

  • Intra- and inter-molecular radial distribution functions

  • Properties used to compute autocorrelation or mean square displacement can be stored to file

  • Manual selection of coordinate unwrapping for autocorrelation or mean square displacement functions

General Input Options

This example computes the oxygen-oxygen radial distribution function of a MD simulation using the analysis utility program:

Task RadialDistribution

TrajectoryInfo
    Trajectory
        KFFilename ams.results/ams.rkf
        Range 1 1000 2
    End
End

RadialDistribution
    NBins 1000
    AtomsFrom
        Element O
    End
    AtomsTo
        Element O
    End
End
eor

The analysis program reads one or more trajectory files (filename.rkf) from an AMS molecular dynamics (MD) or a Grand Canonical Monte Carlo (GCMC) simulation. The file information is supplied in the TrajectoryInfo input block. In this block, a separate Trajectory subblock needs to be supplied for each trajectory file. The Trajectory subblock contains a mandatory keyword KFFilename, and an optional keyword Range. The latter contains the initial frame to be read, the final frame to be read, and optionally the stepsize. By default all frames on the trajectory file are read.

TrajectoryInfo
   NBlocksToCompare integer
   Trajectory
      KFFilename string
      Range integer_list
      StepSize integer
   End
End
TrajectoryInfo
Type

Block

Description

All the info regarding the reading of the trajectory files.

NBlocksToCompare
Type

Integer

Default value

1

Description

Get an error estimate by comparing histograms for NBLocks time blocks of the trajectory.

Trajectory
Type

Block

Recurring

True

Description

All info regarding the reading of a single trajectory file.

KFFilename
Type

String

Default value

ams.rkf

Description

The name of the AMS trajectory file.

Range
Type

Integer List

Description

One or two values: start frame, and optionally end frame. By default the first and last frame are read.

StepSize
Type

Integer

Default value

1

Description

The step size at which frames are read from the RKF (default 1, every frame is read).

All tools in the analysis program provide an option to obtain information on the equilibration of the simulation. If the optional keyword NBlocksToCompare in the TrajectoryInfo block is set to a value \(N\) higher than 1, the trajectory is divided into \(N\) blocks, and the analysis results for each block are compared. The variation in the analysis result is provided as a standard deviation.

Radial Distribution Function (RDF)

The Analysis tool computes radial distribution functions \(g(r)\) if the Task keyword is set to RadialDistribution.

Task [RadialDistribution | Histogram | AutoCorrelation | MeanSquareDisplacement | AverageBinPlot]
Task
Type

Multiple Choice

Options

[RadialDistribution, Histogram, AutoCorrelation, MeanSquareDisplacement, AverageBinPlot]

Description

The analysis task.

Further details on the radial distribution functions are then set in the RadialDistribution block. If more than one RadialDistribution block is present in the input, more than one radial distribution function will be computed. The result is printed to output as text, as well as stored in a binary file (plot.kf).

Description

A radial distribution function \(g(r)\), or pair correlation function, is a density of distances between particles, relative to the average distance density. The x-axis variable represents a distance \(r\), while the y-axis represents the relative density of that distance. For a complete homogeneous system of particles the \(g(r)\) values for the distances between all particles equals 1 everywhere.

Two sets of atoms \(\mathbb{S}_{\textrm{from}}\) and \(\mathbb{S}_{\textrm{to}}\), of length \(n_{\textrm{from}}\) and \(n_{\textrm{to}}\) respectively, are specified with the keywords AtomsFrom and AtomsTo in the RadialDistribution block. As a result the program computes \(n_{\textrm{from}}*n_{\textrm{to}}\) distances \(r_{ij}^s\) between atom \(i\) in \(\mathbb{S}_{\textrm{from}}\) and atom \(j\) in \(\mathbb{S}_{\textrm{to}}\) for each trajectory frame \(s\) out of a total of \(n_{\textrm{frames}}\) frames.

A normalized histogram is then computed from these distances, resulting in a function \(N(r)\).

\(N(r)=\frac{1}{n_{\textrm{frames}}} \sum_{s=1}^{n_{\textrm{frames}}} \sum_{i=1}^{n_{\textrm{from}}}\sum_{j=1}^{n_{\textrm{to}}} \delta(r_{ij}^s-r)\).

This histogram is converted to a density, by dividing all values \(N(r)\) with the volume \(V(r)= 4 \pi r^2 dr\) of a sphere-slice at radius \(r\) with thickness \(dr\).

The density is further converted to a relative density by dividing with the total density of the system \(\rho_{\textrm{tot}} = \frac{n_{\textrm{from}}*n_{\textrm{to}}}{V_{\textrm{tot}}}\), yielding the final radial distribution function \(g(r)\).

\(g(r) = \frac{N(r)}{V(r)*\rho_{\textrm{tot}}}\)

Options

Non-periodic systems The above equation assumes that the volume \(V_{\textrm{tot}}\) of the system is a well-defined quantity. This assumption is correct for systems with 3D periodicity, where the \(V_{\textrm{tot}}\) is defined as the volume of the periodic cell. In such a system the value of \(r\) can be no larger than \(r_{\textrm{max}}\), the radius of the largest sphere that can be placed inside the periodic cell.

If a system is non-periodic in one or more direction, then the program still computes a \(g(r)\), only if the radius \(r_{max}\) is supplied by the user with the Range keyword in the RadialDistribution block. The radius is the second value supplied.

RadialDistribution
   Range float_list
End
RadialDistribution
Type

Block

Recurring

True

Description

All input related to radial distribution functions.

Range
Type

Float List

Description

Either one, two, or three real values. If one it is the stepsize. If two, it is the minimum value and the maximum value. If three, it is the minimum value, the maximum value, and the stepsize. The stepsize overrides NBins.

In this case the volume \(V_{\textrm{tot}}\) is assumed to be the volume of a sphere with radius \(r_{\textrm{max}}\).

NPT simulations The above equation further assumes that the volume \(V_{\textrm{tot}}\) is constant throughout the simulation. The \(g(r)\) of the trajectory from an NPT simulation can still be computed, and in this case \(V_{\textrm{tot}}\) is the average value of the volume of the periodic cell.

Simulations with varying numbers of atoms The above equation also assumes that \(n_{\textrm{from}}\) and \(n_{\textrm{to}}\) remain constant throughout the simulation. However, in a Molecular Gun simulation particles can be added to the system, and in a GCMC simulation particles can be both added and removed from the system. Nonetheless, the program still computes a \(g(r)\) in these situations.

If the AtomsFrom and AtomsTo blocks contain element names (supplied with the recurring Element keyword), then every time atoms are added to or removed from the system, the sets of atoms \(\mathbb{S}_{\textrm{from}}\) and \(\mathbb{S}_{\textrm{to}}\) are re-evaluated.

If the AtomsFrom and AtomsTo blocks contain atom numbers (supplied with the recurring Atom keyword), these numbers are updated in the sets \(\mathbb{S}_{from}\) and \(\mathbb{S}_{to}\) every time atoms are added to or removed from the system. If one of the atoms from the set disappears, the number of distances contributing to the \(g(r)\) decreases.

Note: Currently, the values of \(n_{from}\) and \(n_{to}\) in the normalization factor are taken from the last frame of the simulation.

Warning: If multiple trajectories are supplied, and the number of atoms changes between the end of one trajectory and the beginning of another, this may result in an error in the atom numbers used by the program internally.

Inter- or intra-molecular atom-pairs By default, all \(n_{\textrm{from}}*n_{\textrm{to}}\) distances are included. Sometimes it can be convenient to view exclusively the distances between atoms within a molecule, or those between different molecules. This can be controlled with the keyword DistanceTypeSelection in the RadialDistribution block.

RadialDistribution
   DistanceTypeSelection [All | InterMolecular | IntraMolecular]
End
RadialDistribution
Type

Block

Recurring

True

Description

All input related to radial distribution functions.

DistanceTypeSelection
Type

Multiple Choice

Default value

All

Options

[All, InterMolecular, IntraMolecular]

Description

Select only a certain type of interatomic distances.

Histogram

The Analysis program computes histograms if the Task keyword is set to Histogram.

Task [RadialDistribution | Histogram | AutoCorrelation | MeanSquareDisplacement | AverageBinPlot]
Task
Type

Multiple Choice

Options

[RadialDistribution, Histogram, AutoCorrelation, MeanSquareDisplacement, AverageBinPlot]

Description

The analysis task.

Further details on the histogram need to be specified in the Histogram block. If more than one Histogram block is present in the input, more than one histogram will be computed. The result is printed to output as text, as well as stored in a binary file (plot.kf). By default the histogram contains the number of occurrences of a certain value, but the normalized occurrence is provided if the keyword Normalized in the Histogram block is specified.

Histogram
   Normalized Yes/No
End
Histogram
Normalized
Type

Bool

Default value

No

Description

Give the normalized histogram.

Histograms can be computed for every quantity stored on the molecular dynamics trajectory file (ams.rkf) in the section History. Example quantities are PotentialEnergy, KineticEnergy, TotalEnergy, Temperature. In the histogram block, this quantity is selected with the keyword Variable in the Axis subblock. If more than one Axis subblock is present, the dimensionality of the histogram is increased: Three Axis subblocks result in a 3D histogram.

For each histogram axis, the number of bins can be selected with the NBins keyword in the Axis block, in which case the range of values along each axis is automatically determined. The default NBins value is 100.

Alternatively, a range and a stepsize can be selected with the keyword Range in the Axis subblock. The keyword Range can contain one, two, or three values: 1: Only a stepsize. 2: A smallest value and a largest value. 3: A smallest value, a largest value, and the stepsize.

Histogram
   Axes
      Axis
         NBins integer
         Range float_list
         Variable string
      End
   End
End
Histogram
Type

Block

Recurring

True

Description

All input related to histograms.

Axes
Type

Block

Description

Specifications for the histogram axes.

Axis
Type

Block

Recurring

True

Description

Specifications for a single histogram axis.

NBins
Type

Integer

Default value

100

Description

The number of bins along the histogram axis.

Range
Type

Float List

Description

Either one, two, or three real values. If one it is the stepsize. If two, it is the minimum value and the maximum value. If three, it is the minimum value, the maximum value, and the stepsize. The stepsize overrides NBins.

Variable
Type

String

Description

The quantity along the histogram axis.

Autocorrelation Functions

The Analysis program computes autocorrelation functions (ACF) if the Task keyword is set to AutoCorrelation.

Task [RadialDistribution | Histogram | AutoCorrelation | MeanSquareDisplacement | AverageBinPlot]
Task
Type

Multiple Choice

Options

[RadialDistribution, Histogram, AutoCorrelation, MeanSquareDisplacement, AverageBinPlot]

Description

The analysis task.

Further details need to be specified in the AutoCorrelation block. If more than one AutoCorrelation block is present in the input, more than one ACF will be computed. The result is printed to output as text, as well as stored in a binary file (plot.kf).

AutoCorrelation
   Atoms
      Atom integer
      Element string
   End
   DataReading [Auto | AtOnce | BlockWise]
   InputValues
      Values float_list
   End
   MaxFrame integer
   NPointsHighestFreq integer
   PerElement Yes/No
   Property [Velocities | DipoleMomentFromCharges | InputValues | DiffusionCoefficient | 
             DipoleDerivativeFromCharges | PressureTensor | Viscosity]
   TimeStep float
   UnwrapCoordinates [Auto | Yes | No]
   UseAllValues Yes/No
   VecElements
      Index integer
   End
   WritePropertyToKF Yes/No
End
AutoCorrelation
Atoms
Type

Block

Description

Relevant if Property is set to Velocities, DipoleMomentFromCharges, DipoleDerivativeFromCharges, or DiffusionCoefficient. Atom numbers or elements for the set of atoms for which the property is read/computed. By default all atoms are used.

Atom
Type

Integer

Recurring

True

Description

Atom number.

Element
Type

String

Recurring

True

Description

Element Symbol Atom.

DataReading
Type

Multiple Choice

Default value

Auto

Options

[Auto, AtOnce, BlockWise]

Description

The KF data can be read in and handled once, or blockwise. The former is memory intensive, but mostly faster. If Auto is selected, the data is read at once if it is less than 1 GB, and blockwise if it is more.

InputValues
Type

Block

Description

Relevant if Property is set to InputValues. All input values (a vector on each line) need to be provided in this block, using the keyword Values (possibly multiple times).

Values
Type

Float List

Recurring

True

Description

The values at each step (on a single line)

MaxFrame
Type

Integer

Description

The maximum number of frames for which the autocorrelation function will be computed. The default is half of the number of provided frames.

NPointsHighestFreq
Type

Integer

Default value

4

Description

The number of points (timesteps) used for the highest frequency displayed in spectrum. This determines up to which frequency the spectrum is displayed. If the spacing between time-steps used for the ACF is 1 fs, then by default the maximum frequency displayed is 0.25 fs-1 (or 8339 cm-1). This corresponds to a (default) value of NPointsHighestFreq of 4. A higher number selected here, will result in a lower maximum frequency returned by the program. The lowest possible value (spectrum up to highest possible frequency) is 2.

PerElement
Type

Bool

Default value

No

Description

Compute ACF for all elements in the system. Any other settings in the block will be used.

Property
Type

Multiple Choice

Default value

DipoleDerivativeFromCharges

Options

[Velocities, DipoleMomentFromCharges, InputValues, DiffusionCoefficient, DipoleDerivativeFromCharges, PressureTensor, Viscosity]

Description

Compute the ACF either from velocities (from rkf), the dipole moment (from coordinates and atomic charges in rkf), the dipole moment derivative (from velocities and atomic charges in rkf), from the pressure tensor (from rkf), or from values specified in input. Selecting DiffusionCoefficient is equivalent to selecting Velocities. The default, DipoleDerivativeFromCharges, results in the computation of an IR spectrum.

TimeStep
Type

Float

Description

Relevant if Property is set to InputValues. The time separating the entries (in fs). If Property is set to any of the other quantities, it can be read from an RKF file, and the timestep is read from the RKF file as well. The read value then overrides this keyword.

UnwrapCoordinates
Type

Multiple Choice

Default value

Auto

Options

[Auto, Yes, No]

Description

If the coordinates are involved in the requested property, those coordinates are wrapped into the box at each time step. If set to true, this keyword unwraps those coordinates so that the trajectory is continuous. If not provided the code uses automatic defaults.

UseAllValues
Type

Bool

Default value

No

Description

By default the same number of values are used for each t-step in the ACF. This has the advantage that all values in the ACF are equally reliable, but it does mean that for the smaller timesteps much of the data is not used. To switch this off and use all data, UseAllValues can be set to true

VecElements
Type

Block

Description

A set of indices referring to a subset of the property vector. Works in combination with the atoms block. For example, in combination with the property Velocities, the Atoms block allows the selection of a subset of atoms, while the VecElelements block allows the selection of a subset of vector elements (e.g. 1 and 2 for the elements x and y). Currently not implemented with InputValues.

Index
Type

Integer

Recurring

True

Description

Element of the property vector.

WritePropertyToKF
Type

Bool

Default value

No

Description

Write the selected property to the KF files for every requested frame

Description

An autocorrelation function \(C(t)\) describes the average correlation (overlap) of a (vector) property \(\textbf{A}\) with itself as a function of time.

\(C(t) = \langle \textbf{A}(0) \cdot \textbf{A}(t)) \rangle\)

The average runs over all time-intervals \(\left( t_{0}, t_{0}+t \right),\left( t_{1}, t_{1}+t \right),...,\left( t_{N}, t_{N}+t \right)\), with \(t_{N} = t_{n} - t_{m}\). Here \(n\) is the total number of frames read from the trajectory (as determined in the block TrajectoryInfo), and \(m\) is the number of discrete \(t\) values for which \(C(t)\) is computed. The value \(m\) can be set with the keyword MaxFrame, and defaults to half the total number of frames read. As stated above, the default average runs over the same number of time intervals for each value of \(t\). If UseAllValues is selected, the average runs over all available time intervals for each value of \(t\), which is large for small \(t\), and smallest (\(N\)) for \(t_{m}\).

The normalized autocorrelation function \(c(t)\) describes the decorrelation of the property with time, and always starts at 1.0 at \(t=0\).

\(c(t) = \frac{\langle \textbf{A}(0) \cdot \textbf{A}(t)) \rangle}{\langle \textbf{A}(0) \cdot \textbf{A}(0)) \rangle}\)

In most cases short timescale fluctuations are important, so frequent storage of the desired property is required (when preparing the molecular dynamics simulation, set the Frequency keyword in the Trajectory block of the MolecularDynanimcs settings low, preferably to 1).

A power spectrum is automatically computed by Fourier transform of the autocorrelation function, and provides information on the frequencies of the signal. When the selected property is the dipole moment or the dipole moment derivative, the power spectrum matches the IR spectrum.

Properties

Autocorrelation functions can be computed for different simulation properties: 1) Dipole moments from coordinates and atomic charges 2) Dipole moment derivatives from velocities and atomic charges 3) Velocities 4) The pressure tensor 5) User provided values. Selecting 6) Diffusion coefficient is equivalent to selecting Velocities.

AutoCorrelation
   Property [Velocities | DipoleMomentFromCharges | InputValues | DiffusionCoefficient | 
             DipoleDerivativeFromCharges | PressureTensor | Viscosity]
End
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Property
Type

Multiple Choice

Default value

DipoleDerivativeFromCharges

Options

[Velocities, DipoleMomentFromCharges, InputValues, DiffusionCoefficient, DipoleDerivativeFromCharges, PressureTensor, Viscosity]

Description

Compute the ACF either from velocities (from rkf), the dipole moment (from coordinates and atomic charges in rkf), the dipole moment derivative (from velocities and atomic charges in rkf), from the pressure tensor (from rkf), or from values specified in input. Selecting DiffusionCoefficient is equivalent to selecting Velocities. The default, DipoleDerivativeFromCharges, results in the computation of an IR spectrum.

Some of the properties for which an autocorrelation function can be computed are simply read as is from the trajectory RKF file, but others are quite complex. For example, the dipole moment is a property obtained by reading the coordinates and the atomic charges, multiplying each atomic position vector with the corresponding charge, and then summing over all atoms. With the keyword WritePropertyToKF in the AutoCorrelation block, the user can choose to store not only the autocorrelation function, but also the property used to produce it.

AutoCorrelation
   WritePropertyToKF Yes/No
End
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

WritePropertyToKF
Type

Bool

Default value

No

Description

Write the selected property to the KF files for every requested frame

If a property involves atomic coordinates, then this generally means atomic coordinates wrapped into the periodic box at every time step. As a result, coordinates can make seemingly big jumps from one side of the box to another between two consecutive frames. The code is able to unwrap the coordinates, so that all atoms follow a continuous trajectory. For the DipoleMoment property, the wrapped coordinates will be used by default, but an experienced user can determine whether the wrapped or unwrapped coordinates are used with the keyword UnwrapCoordinates in the AutoCorrelation block.

AutoCorrelation
   UnwrapCoordinates [Auto | Yes | No]
End
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

UnwrapCoordinates
Type

Multiple Choice

Default value

Auto

Options

[Auto, Yes, No]

Description

If the coordinates are involved in the requested property, those coordinates are wrapped into the box at each time step. If set to true, this keyword unwraps those coordinates so that the trajectory is continuous. If not provided the code uses automatic defaults.

Options

With the keyword MaxFrame the number of values \(m\) in the autocorrelation function (\(t = [0,t_{1},t_{2},....,t_{m}]\)) can be set. The default value is half of the total number of frames \(n\) read from the trajectory.

A subset of atoms for which the property \(\textbf{A}\) should be selected/computed can be provided in the block Atoms. The block can contain element names (recurring keyword Element), or individual atom numbers (recurring keyword Atom).

AutoCorrelation
   Atoms
      Atom integer
      Element string
   End
End
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Atoms
Type

Block

Description

Relevant if Property is set to Velocities, DipoleMomentFromCharges, DipoleDerivativeFromCharges, or DiffusionCoefficient. Atom numbers or elements for the set of atoms for which the property is read/computed. By default all atoms are used.

Atom
Type

Integer

Recurring

True

Description

Atom number.

Element
Type

String

Recurring

True

Description

Element Symbol Atom.

A subset of vector elements can be provided with the subblock VecElements. By default all vector elements found on the RKF file will be used.

AutoCorrelation
   VecElements
      Index integer
   End
End
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

VecElements
Type

Block

Description

A set of indices referring to a subset of the property vector. Works in combination with the atoms block. For example, in combination with the property Velocities, the Atoms block allows the selection of a subset of atoms, while the VecElelements block allows the selection of a subset of vector elements (e.g. 1 and 2 for the elements x and y). Currently not implemented with InputValues.

Index
Type

Integer

Recurring

True

Description

Element of the property vector.

Mean Square Displacement

The Analysis program computes mean square displacements (MSD) if the Task keyword is set to MeansSquareDisplacement.

Task [RadialDistribution | Histogram | AutoCorrelation | MeanSquareDisplacement | AverageBinPlot]
Task
Type

Multiple Choice

Options

[RadialDistribution, Histogram, AutoCorrelation, MeanSquareDisplacement, AverageBinPlot]

Description

The analysis task.

Further details need to be specified in the MeanSquareDisplacement block. If more than one MeanSquareDisplacement block is present in the input, more than one MSD will be computed. The result is printed to output as text, as well as stored in a binary file (plot.kf).

MeanSquareDisplacement
   Atoms
      Atom integer
      Element string
   End
   DataReading [Auto | AtOnce | BlockWise]
   InputValues
      Values float_list
   End
   MaxFrame integer
   PerElement Yes/No
   Property [Coords | InputValues | DiffusionCoefficient]
   StartTimeSlope float
   TimeStep float
   UnwrapCoordinates [Auto | Yes | No]
   UseAllValues Yes/No
   VecElements
      Index integer
   End
   WritePropertyToKF Yes/No
End
MeanSquareDisplacement
Atoms
Type

Block

Description

Relevant if Property is set to any quantity that is available per atom (Coords, DiffusionCoefficient). Atom numbers or elements for the set of atoms for which the property is read/computed are provided here. By default all atoms are used.

Atom
Type

Integer

Recurring

True

Description

Atom number.

Element
Type

String

Recurring

True

Description

Element Symbol Atom.

DataReading
Type

Multiple Choice

Default value

Auto

Options

[Auto, AtOnce, BlockWise]

Description

The KF data can be read in and handled once, or blockwise. The former is memory intensive, but mostly faster. If Auto is selected, the data is read at once if it is less than 1 GB, and blockwise if it is more.

InputValues
Type

Block

Description

Relevant if Property is set to InputValues. All input values (a vector on each line) need to be provided in this block, using the keyword Values (possibly multiple times).

Values
Type

Float List

Recurring

True

Description

The values at each step (on a single line)

MaxFrame
Type

Integer

Description

The maximum number of frames for which the mean square displacement function will be computed. The default is half of the number of provided frames.

PerElement
Type

Bool

Default value

No

Description

Compute MSD for all elements in the system. Any other settings in thie block will be used.

Property
Type

Multiple Choice

Default value

Coords

Options

[Coords, InputValues, DiffusionCoefficient]

Description

Compute the MSD from the property selected here (from rkf). Selecting DiffusionCoefficient is equivalent to selecting the property Coords.

StartTimeSlope
Type

Float

Default value

0.0

Description

The MSD has a nonlinear regime at short timescales, and a linear regime at long timescales. To determine the slope, the starting point for the linear regime has to be determined. This keyword sets the starting time in fs. If set to zero, the starttime will be automatically determined.

TimeStep
Type

Float

Description

Relevant if Property is set to InputValues. The time separating the entries (in fs). If Property is set to any of the other quantities, it can be read from an RKF file, and the timestep is read from the RKF file as well. The read value then overrides this keyword.

UnwrapCoordinates
Type

Multiple Choice

Default value

Auto

Options

[Auto, Yes, No]

Description

If the coordinates are involved in the requested property, those coordinates are wrapped into the box at each time step. If seti to true, this keyword unwraps those coordinates so that the trajectory is continuous. If not provided the code uses automatic defaults.

UseAllValues
Type

Bool

Default value

No

Description

By default the same number of values are used for each t-step in the MSD. This has the advantage that all values in the MSD are equally reliable, but it does mean that for the smaller timesteps much of the data is not used. To switch this off and use all data, UseAllValues can be set to true

VecElements
Type

Block

Description

A set of indices referring to a subset of the property vector. Works in combination with the atoms block. For example, in combination with the property Coords, the Atoms block allows the selection of a subset of atoms, while the VecElelements block allows the selection of a subset of vector elements (e.g. 1 and 2 for the elements x and y). Currently not implemented with InputValues.

Index
Type

Integer

Recurring

True

Description

Element of the property vector.

WritePropertyToKF
Type

Bool

Default value

No

Description

Write the selected property to the KF files for every requested frame

Description

The mean square displacement \(MSD(t)\) describes the average change of a (vector) property \(\textbf{A}\) over time. This property is usually a set of atom coordinate vectors, but the implementation is entirely general.

\(MSD(t) = \langle [\textbf{A}(0) - \textbf{A}(t)]^2 \rangle\)

The average runs over all time-intervals \(\left( t_{0}, t_{0}+t \right),\left( t_{1}, t_{1}+t \right),...,\left( t_{N}, t_{N}+t \right)\), with \(t_{N} = t_{n} - t_{m}\). Here \(n\) is the total number of frames read from the trajectory, and \(m\) is the number of discrete \(t\) values for which \(MSD(t)\) is computed. The value \(m\) can be set with the keyword MaxFrame, and defaults to half the total number of frames read from the trajectory. As stated above, the default average runs over the same number of time intervals for each value of \(t\). If UseAllValues is selected, the average runs over all available time intervals for each value of \(t\), which is large for small \(t\), and smallest (\(N\)) for \(t_{m}\).

The most common use of the mean square displacement is for the computation of the diffusion coefficient, in which case the selected property is the set of atom coordinates (Coords). The diffusion coefficient is proportionate to the slope of this mean square displacement function, and therefore this slope is automatically computed. The function \(MSD(t)\) becomes linear only after an initial time interval, and the user can set this initial time with the keyword StartTimeSlope. If not provided, this start time is automatically determined. To allow the user to determine if the linear regime has been sufficiently sampled, the slope of \(MSD(t)\) as a function of \(t\) is computed as well. If the slope has not converged to a stable value, the user should select a larger value of \(t_m\) or continue the molecular dynamics simulation for a longer time.

Properties

Autocorrelation functions can be computed for different simulation properties: 1) Coordinates 2) User provided values. Option 3) Diffusion coefficient is equivalent to option 1).

MeanSquareDisplacement
   Property [Coords | InputValues | DiffusionCoefficient]
End
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Property
Type

Multiple Choice

Default value

Coords

Options

[Coords, InputValues, DiffusionCoefficient]

Description

Compute the MSD from the property selected here (from rkf). Selecting DiffusionCoefficient is equivalent to selecting the property Coords.

When read from file, the atomic coordinates will be wrapped inside the periodic box at every time step. As a result, coordinates can make seemingly big jumps from one side of the box to another between two consecutive frames. By default, the coordinates are unwrapped before the computation of the mean square displacement, so that all atoms follow a continuous trajectory. For the experienced users, the option exist to manually determine whether the wrapped or unwrapped coordinates are used with the keyword UnwrapCoordinates in the MeanSquareDisplacement block.

MeanSquareDisplacement
   UnwrapCoordinates [Auto | Yes | No]
End
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

UnwrapCoordinates
Type

Multiple Choice

Default value

Auto

Options

[Auto, Yes, No]

Description

If the coordinates are involved in the requested property, those coordinates are wrapped into the box at each time step. If seti to true, this keyword unwraps those coordinates so that the trajectory is continuous. If not provided the code uses automatic defaults.

Since the coordinates used to compute the mean square displacement often differ from the coordinates as read from the trajectory (they will be unwrapped, so that the trajectory becomes continuous). With the keyword WritePropertyToKF in the MeanSquareDisplacement block, the user can choose to store not only the mean square displacement results, but also the property used to produce it.

MeanSquareDisplacement
   WritePropertyToKF Yes/No
End
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

WritePropertyToKF
Type

Bool

Default value

No

Description

Write the selected property to the KF files for every requested frame

Options

A subset of atoms for which the property \(\textbf{A}\) should be selected/computed can be provided in the block Atoms. The block can contain element names (recurring keyword Element), or individual atom numbers (recurring keyword Atom).

MeanSquareDisplacement
   Atoms
      Atom integer
      Element string
   End
End
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Atoms
Type

Block

Description

Relevant if Property is set to any quantity that is available per atom (Coords, DiffusionCoefficient). Atom numbers or elements for the set of atoms for which the property is read/computed are provided here. By default all atoms are used.

Atom
Type

Integer

Recurring

True

Description

Atom number.

Element
Type

String

Recurring

True

Description

Element Symbol Atom.

A subset of vector elements can be provided with the subblock VecElements. By default all vector elements found on the RKF file will be used.

MeanSquareDisplacement
   VecElements
      Index integer
   End
End
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

VecElements
Type

Block

Description

A set of indices referring to a subset of the property vector. Works in combination with the atoms block. For example, in combination with the property Coords, the Atoms block allows the selection of a subset of atoms, while the VecElelements block allows the selection of a subset of vector elements (e.g. 1 and 2 for the elements x and y). Currently not implemented with InputValues.

Index
Type

Integer

Recurring

True

Description

Element of the property vector.

AverageBinPlot

The Analysis program can plot two arbitrary properties, present on the RKF file, against each other averaged over each bin if the Task keyword is set to AverageBinPlot.

Task [RadialDistribution | Histogram | AutoCorrelation | MeanSquareDisplacement | AverageBinPlot]
Task
Type

Multiple Choice

Options

[RadialDistribution, Histogram, AutoCorrelation, MeanSquareDisplacement, AverageBinPlot]

Description

The analysis task.

Further details need to be specified in the AverageBinPlot block. If more than one AverageBinPlot block is present in the input, more than one AverageBinPlot will be computed. The result is printed to output as text, as well as stored in a binary file (analysis.kf).

AverageBinPlot
   Nbins integer
   Property
      Axis float_list
      Name string
      Region string
      Vector string
   End
   Timestep integer
End
AverageBinPlot
Nbins
Type

Integer

Default value

10

Description

Number of bins that are plotted

Property
Type

Block

Recurring

True

Description

Property 1

Axis
Type

Float List

Description

If defined the dot_product along this axis will be taken

Name
Type

String

Description

Name of the property

Region
Type

String

Description

Name of the atom region among which the forces will be averaged

Vector
Type

String

Description

is it a vector? yes/no

Timestep
Type

Integer

Default value

1

Description

Timestep used for the plotting

Viscosity

The viscosity can be computed from an equilibrated Molecular Dynamics run as the integral over the pressure tensor autocorrelation function.

\(\eta = \frac{1}{10T} \int_{t=0}^{t=t_{max}} \langle \P_ij(0) \cdot \P_ij{v}(t)) \rangle dt\)

The viscosity is computed if the task AutoCorrelation is selected, and if in the AutoCorrelation block Viscosity is selected as the Property.

$AMSBIN/analysis <<eor
   Task AutoCorrelation
   AutoCorrelation
      Property Viscosity
   End
eor
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Property
Type

Multiple Choice

Default value

DipoleDerivativeFromCharges

Options

[Velocities, DipoleMomentFromCharges, InputValues, DiffusionCoefficient, DipoleDerivativeFromCharges, PressureTensor, Viscosity]

Description

Compute the ACF either from velocities (from rkf), the dipole moment (from coordinates and atomic charges in rkf), the dipole moment derivative (from velocities and atomic charges in rkf), from the pressure tensor (from rkf), or from values specified in input. Selecting DiffusionCoefficient is equivalent to selecting Velocities. The default, DipoleDerivativeFromCharges, results in the computation of an IR spectrum.

Again, a subset of atoms can be selected with the sublock Atoms.

The value of the viscosity is written to the output, as well as to the KF file.

Diffusion Coefficient

The diffusion coefficient can be computed from a molecular dynamics trajectory in two ways.

  1. As the integral over the velocity autocorrelation function.

  2. As the slope of the mean square displacement of the atomic coordinates.

The latter is more commonly used, as the former requires trajectory information to be stored at very short time intervals. Note that the obtained values for the diffusion coefficients correspond to the temperature of the molecular dynamics simulation.

From Velocity Autocorrelation

The diffusion coefficient can be defined as an integral over the velocity autocorrelation function.

\(D = \frac{1}{d} \int_{t=0}^{t=t_{max}} \langle \textbf{v}(0) \cdot \textbf{v}(t)) \rangle dt\)

The factor \(\frac{1}{d}\) corrects for the dimension of the system, which we assume to equal the length of the provided vector \(\textbf{v}\). The dimension \(d\) equals 3, unless specified otherwise in the subblock VecElements. In a system that is periodic in less than 3 dimensions, it may make sense to provide only the vector elements along the periodic dimensions. By default, however, all vector elements provided are used.

The diffusion coefficient is computed if the task AutoCorrelation is selected, and if in the AutoCorrelation block DiffusionCoefficient is selected as the Property. The result is completely equivalent to selecting the task AutoCorrelation with Velocities as the Property keyword.

$AMSBIN/analysis <<eor
   Task AutoCorrelation
   AutoCorrelation
      Property DiffusionCoefficient
   End
eor
AutoCorrelation
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Property
Type

Multiple Choice

Default value

DipoleDerivativeFromCharges

Options

[Velocities, DipoleMomentFromCharges, InputValues, DiffusionCoefficient, DipoleDerivativeFromCharges, PressureTensor, Viscosity]

Description

Compute the ACF either from velocities (from rkf), the dipole moment (from coordinates and atomic charges in rkf), the dipole moment derivative (from velocities and atomic charges in rkf), from the pressure tensor (from rkf), or from values specified in input. Selecting DiffusionCoefficient is equivalent to selecting Velocities. The default, DipoleDerivativeFromCharges, results in the computation of an IR spectrum.

From Mean Square Displacement

The mean square displacement becomes linear with time, after an initial time interval. We can therefore define the linear part of the function as follows.

\(MSD(t) = {\langle \textbf{r}(0) - \textbf{r}(t)) \rangle} = at + b\),

with \(a\) as the slope of the function. The diffusion coefficient is proportional to the slope \(a\).

\(D = \frac{1}{2d} a\)

Here, \(d\) is the dimensionality of the system, or the length of the provided vector \(\textbf{r}\). The dimension \(d\) equals 3, unless specified otherwise in the subblock VecElements. In a system that is periodic in less than 3 dimensions, it may make sense to provide only the vector elements along the periodic dimensions. By default, however, all vector elements provided are used.

The diffusion coefficient is computed if the task MeanSquareDisplacement is selected, and if in the MeanSquareDisplacement block DiffusionCoefficient is selected as the Property. The result is completely equivalent to selecting the task MeanSquareDisplacement with Coords as the Property keyword.

$AMSBIN/analysis <<eor
   Task MeanSquareDisplacement
   MeanSquareDisplacement
      Property DiffusionCoefficient
   End
eor
MeanSquareDisplacement
Type

Block

Recurring

True

Description

All input related to auto correlation functions.

Property
Type

Multiple Choice

Default value

Coords

Options

[Coords, InputValues, DiffusionCoefficient]

Description

Compute the MSD from the property selected here (from rkf). Selecting DiffusionCoefficient is equivalent to selecting the property Coords.

In both cases, a subset of atoms can be selected with the sublock Atoms, and a subset of vector elements (in this case elements 1=X, 2=Y, 3=Z for the Cartesian coordinates) can be selected with the subblock VecElements.

The value of the diffusion coefficient is written to the output, as well as to the KF file.