List of analysis types

AreaPerMolecule

Computes the area per molecule.

The area per molecule is computed by simply dividing the surface of one of the simulation box faces (ab, bc or ac) by the number of molecules with a given name. This property should be a constant unless the simulation performed was in the NPT ensemble. This analysis is relevant for oriented structures like lipid membranes.

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AverageStructure

Outputs a structure file of the atom positions averaged over time.

This analysis only makes sense for crystalline systems where atoms remain within a finite distance around their equilibrium positions.

Please run Mean Square Displacement or Root Mean Square Displacement analysis on your trajectory to make sure that the atoms remain around their equilibrium positions. Otherwise the time-averaged atom positions will be meaningless. If your system consists of a crystalline material with migrating guest atoms, you can output just the crystalline part using a corresponding atom selection.

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CenterOfMassesTrajectory

Outputs a trajectory where molecules have been replaced by artificial particles.

Creates a trajectory from the centre of masses for selected groups of atoms in a given input trajectory. The resulting trajectory will not include the internal vibrations of molecules or the rotational modes.

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CoordinationNumber

Calculates the coordination number for pairs of atom types.

The Coordination Number is computed from the pair distribution function. It describes the total number of neighbours, as a function of distance, from a central atom, or the centre of a group of atoms.

Please not the the Coordination Number results are not symmetrical. That is, the number of B atoms around an A atom is not equal to the number of A atoms around a B atom.

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CurrentCorrelationFunction

Computes the current correlation function for a set of atoms.

The transverse and longitudinal current correlation functions are typically used to study the propagation of excitations in disordered systems. The longitudinal current is directly related to density fluctuations and the transverse current is linked to propagating ‘shear modes’.

For more information, see e.g. ‘J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (3rd ed., Elsevier), chapter 7.4: Correlations in space and time.’

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Density

Computes the atom and mass densities for a given trajectory.

These are time dependent if the simulation box volume fluctuates.

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DensityOfStates

Calculate the vibrational density of states of the trajectory.

The Density Of States describes the number of vibrations per unit frequency. In MDANSE the DOS calculation returns the Fourier transform (FT) of the weighted Velocity Correlation Function (vcf). With an atomic mass weighting scheme the MDANSE DOS result is proportional to the actual vibrational DOS. The partial DOS corresponds to selected sets of atoms or molecules.

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DipoleAutoCorrelationFunction

Calculates the Dipole Autocorrelation Function of a system.

Partial charges need to be defined in the system for this analysis to produce non-zero results.

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DynamicCoherentStructureFactor

Computes the dynamic coherent structure factor \(S_{\text{coh}}(\mathbf{q}, \omega)\) for a set of atoms.

It can be compared to experimental data e.g. the energy-integrated, static structure factor \(S_{\text{coh}}(q)\) or the dispersion and intensity of phonons.

The coherent part is derived from correlations between pairs of atoms. This analysis requires the \(\mathbf{q}\)-vectors to be commensurate with the reciprocal lattice of the simulation box.

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DynamicIncoherentStructureFactor

Computes the dynamic incoherent structure factor \(S_{\text{inc}}(\mathbf{q},\omega)\) for a set of atoms.

It can be compared to experimental data e.g. the quasielastic scattering due to diffusion processes.

This property is derived from the self-correlation of individual atoms over time. While it does not require the \(\mathbf{q}\)-vectors to be commensurate with the simulation box reciprocal lattice, a “lattice” vector generator should be chosen if you intend to combine the result with the coherent part into the total dynamic structure factor.

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Eccentricity

Computes the eccentricity of a selected set of atoms.

The eccentricity is calculated from the principal moments of inertia via the equation \(\sqrt{\text{pm3}^{2} - \text{pm1}^{2}} / \text{pm3}\) where \(\text{pm1}\) and \(\text{pm3}\) are the smallest and largest principal moments of inertia respectively. Therefore, for a spherically symmetric molecule its eccentricity will be 0 while for an aspherical molecule like CO2 its eccentricity will be 1. This job follows the equations used in rdkit which was itself taken from https://doi.org/10.1002/9783527618279.ch37.

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ElasticIncoherentStructureFactor

Calculates the Elastic Incoherent Structure Factor of a trajectory.

The Elastic Incoherent Structure Factor (EISF) is defined as the limit of the incoherent intermediate scattering function for infinite time.

The EISF appears as the incoherent amplitude of the elastic line in the neutron scattering spectrum. Elastic scattering is only present for systems in which the atomic motion is confined in space, as in solids. The Q-dependence of the EISF indicates e.g. the fraction of static/mobile atoms and the spatial dependence of the dynamics.

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GaussianDynamicIncoherentStructureFactor

Computes the dynamic incoherent structure factor in the Gaussian approximation.

Gaussian approximation is exact for a system of free particles and a system of particles undergoing brownian motion. The results of this analysis will be close to the Dynamic Incoherent Structure Factor analysis in the limits of very short \(\mathbf{q}\) and very long \(\mathbf{q}\), and will differ from it for intermediate \(\mathbf{q}\) values.

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Infrared

Calculates the infrared spectrum of a system of molecules.

The infrared spectrum is calculated as the autocorrelation of the derivative the molecular dipole moments.

This analysis requires molecules to be defined in the system, and partial charges to be set to non-zero values.

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MeanSquareDisplacement

Calculates the mean square displacement (MSD) of atoms in the trajectory.

The MSD is a representation of diffusion in the system. The motion of an individual atom or molecule does not follow a simple path since particles undergo collisions. The path is to a good approximation to a random walk.

Mathematically, a random walk is a series of steps where each step is taken in a completely random direction from the one before, as analyzed by Albert Einstein in a study of Brownian motion. The MSD of a particle in this case is proportional to the time elapsed:

\[\langle d^{2}(t) \rangle = 6Dt + C\]

where \(\langle d^{2}(t) \rangle\) is the MSD and \(t\) is the time. \(D\) and \(C\) are constants. The constant \(D\) is the so-called diffusion coefficient.

More generally the MSD reveals the distance or volume explored by atoms and molecules as a function of time. In crystals, the MSD quickly saturates at a constant value which corresponds to the vibrational amplitude. Diffusion in a volume will also have a limiting value of the MSD which corresponds to the diameter of the volume and the saturation value is reached more slowly. The MSD can also reveal e.g. sub-diffusion regimes for the translational diffusion of lipids in membranes.

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MolecularTrace

Maps the volume occupied by atoms over time.

A Molecular Trace is a time-integrated trace of selected atoms coordinates.

  • the minimal and maximal coordinates from the selected atomic trajectories are computed.

  • based on these min/max and a spatial resolution, a cartesian grid is constructed.

  • for each atom and for each frame of the selected trajectories, a histogram of presence, called the spatial density, is constructed.

The molecular trace can reveal anisotropic vibrations and diffusion pathways.

Acknowledgement and publication: Gael Goret, PELLEGRINI Eric

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NeutronDynamicTotalStructureFactor

Combines the coherent and incoherent dynamic structure factors.

The partial results need to be calculated before using the Dynamic Coherent/Incoherent Structure Factor jobs with the same \(\mathbf{q}\)-vector settings.

The partial results will be scaled by neutron scattering lengths, producing a total result with coherent and incoherent parts on the same scale, directly comparable to each other.

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PairDistributionFunction

Calculates a histogram of interatomic distances.

The Pair-Distribution Function (PDF) is an example of a pair correlation function, which describes how, on average, the atoms in a system are radially packed around each other. This is a particularly effective way of describing the average structure of disordered molecular systems such as liquids. Also in systems like liquids, where there is continual movement of the atoms and a single snapshot of the system shows only the instantaneous disorder, it is essential to determine the average structure.

The PDF can be compared with experimental data from x-ray or neutron diffraction. It can be used in conjunction with the inter-atomic pair potential function to calculate the internal energy of the system, usually quite accurately. Finally it can even be used to derive the inter-atomic potentials of mean force.

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PositionCorrelationFunction

Calculates the position correlation function.

Like the velocity correlation function, but using positions instead of velocities.

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PositionPowerSpectrum

Calculates the position power spectrum.

Power spectrum (using Fast Fourier Transform) of atomic trajectories calculated from the Positional correlation Function (PCF). The calculation result is similar to the density of states, which is calculated from the velocity correlation function. In fact, PPS and DOS may show the same features in systems where position and velocity are strongly correlated (i.e. solids).

This calculation is used by TrajectoryFilter to create a preview of the spectrum, so that a desired range of atomic vibrational modes can be isolated.

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RadiusOfGyration

Calculates the radius of gyration of selected atoms.

The Radius of Gyration can be used, for example, to determine the compactness of a molecule. It is calculated as a root (mass weighted) mean square distance of the atoms of a molecule relative to its centre of mass. ROG can be used to follow the size and spread of a molecule during the molecular dynamics simulation.

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ReorientationalTimeCorrelationFunction

Correlation of molecule’s orientation in time.

The result is a reorientational time-correlation function, which describes the change in orientation of a specific direction axis within a molecule. For one index, the axis will be defined by the positions of the atom with that index and the molecule’s centre of mass. For two indices, the axis will be the vector between the atoms with these indices. If no indices are given, the shortest axis of the moment of inertia (pm1) will be used in the calculation. This will not be tied to specific atoms and will be sensitive to changes in the molecule’s shape.

In principle, reorientational time-correlation functions can be Legendre polynomials of different order. At the moment, this analysis will calculate all the orders up the maximum Legendre polynomial order specified as one of the input parameters.

Angle at time \(t\) is calculated as the following:

\[\hat{\mathbf{n}}(t) = \frac{\mathbf{r}_{i}(t) - \mathbf{r}_{j}(t)}{\vert \mathbf{r}_{i}(t) - \mathbf{r}_{j}(t) \vert}\]
\[\phi(t = t_{1}-t_{0}) = \arccos( \hat{\mathbf{n}}(t_{1}) \cdot \hat{\mathbf{n}}(t_{0}))\]

The general result is \(C_{l}(t) = \langle P_{l}[\cos(\phi(t))] \rangle\), where \(P_{l}[x]\) is the Legendre polynomial of the order \(l\).

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RootMeanSquareDeviation

Calculates the Root Mean Square Deviation of the selected atoms.

The Root Mean-Square Deviation (RMSD) is one of the most popular measures of structural similarity. It is a numerical measure of the difference between two structures. Typically, the RMSD is used to quantify the structural evolution of the system during the simulation. It can provide essential information about the structure, if it reached equilibrium or conversely if major structural changes occurred during the simulation.

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RootMeanSquareFluctuation

Calculates the Root Mean Square Fluctuation of atom positions.

The root mean square fluctuation (RMSF) for a set of atoms is similar to the square root of the mean square displacement (MSD), except that it is spatially resolved rather than time resolved. It reveals the dynamical heterogeneity of the molecule over the course of an MD simulation.

As opposed to most analysis types, the result is a single number per atom index.

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ScatteringLengthDensityProfile

Produces the time-averaged scattering length density profile.

The main result, named ‘sldp’ in the output file, is the time-averaged coherent scattering length density profile in units of 10^-6 / Ang^2, as used in neutron reflectometry calculations.

You may want to export the ‘sldp’ dataset as text file using the MDANSE_GUI plotter, and load it into your preferred neutron reflectometry software.

Additionally, the following other profiles are provided in the output:

  • ‘dp_{atom_type}’, numeric density profiles (number of atoms per volume)

  • ‘dp_total’, numeric density profile for all atoms

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SolventAccessibleSurface

Calculates the accessible surface of the selected atoms.

Please keep in mind that the atoms outside of the selection are still considered to be blocking the accessible surface. If you are interested in the total surface of a group of atoms, please remove the other atoms from the trajectory.

Solvent Accessible Surface is calculated using the ‘rolling ball’ algorithm developed by Shrake & Rupley in 1973.

  • Shrake, A., and J. A. Rupley. JMB (1973) 79:351-371.

This algorithm uses a sphere (of solvent) of a particular radius to ‘probe’ the surface of the molecule.

It involves constructing a mesh of points equidistant from each atom of the molecule and uses the number of these points that are solvent accessible to determine the surface area. The points are drawn at a water molecule’s estimated radius beyond the van der Waals radius, which is effectively similar to ‘rolling a ball’ along the surface. All points are checked against the surface of neighboring atoms to determine whether they are buried or accessible. The number of points accessible is multiplied by the portion of surface area each point represents to calculate the SAS.

The choice of the ‘probe radius’ has an effect on the observed surface area - using a smaller probe radius detects more surface details and therefore reports a larger surface. A typical value is 0.14 nm, which is approximately the radius of a water molecule. Another factor that affects the result is the definition of the VDW radii of the atoms in the molecule under study.

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StaticStructureFactor

Computes the static structure factor for a set of atoms.

The static structure factor is calculated as a Fourier transform of the partial pair distribution function (following the Faber-Ziman definition).

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StructureFactorFromScatteringFunction

Computes the static structure factor from the results of another analysis.

The static structure factor is calculated from the intermediate scattering function of the dynamic coherent scattering function calculation results.

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Temperature

Calculates the temperature of the system for every selected frame.

Computes the time-dependent temperature for a given trajectory. The temperature is determined from the kinetic energy i.e. the atomic velocities which are in turn calculated from the time-dependence of the atomic coordinates.

Note that the velocity calculated from atom positions will be underestimated and the error in the results will be larger for trajectories with a large step between (saved) frames compared to the actual time step of the MD simulations (~fs).

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TrajectoryEditor

Write out a modified version of the input trajectory.

At the moment, the main applications include:

  • molecule detection,

  • setting unit cell parameters,

  • setting partial charges,

  • removing or transmuting atoms,

  • removing frames.

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TrajectoryFilter

Design and apply a filter for the atomic trajectories.

This job outputs a new trajectory, where part of the vibrational spectrum of atoms has been removed. Effectively, this allows to separate the high- and low-frequency vibrational modes, also in disordered systems where lattice-dynamics analysis would be difficult.

The filter is applied in the standard signal-processing approach, where the positions of atoms as a function of time are Fourier-transformed (producing a position power spectrum), the filter is applied to the spectrum, and the modified spectrum is Fourier-transformed back into positions.

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VanHoveFunctionDistinct

Calculates the distinct van Hove function.

The van Hove function is related to the intermediate scattering function via a Fourier transform and the dynamic structure factor via a double Fourier transform. The van Hove function describes the probability of finding a particle (j) at a distance r at time t from a particle (i) at a time t_0. The van Hove function can be split into self and distinct parts. The self part includes only the contributions from only the same particles (i=j) while the distinct part includes only the contributions between different particles (i≠j). This job calculates a distinct part of the van Hove function, spherically averaged and normalised so that G(r,t)=1 as r→∞ or t→∞ for liquid or gaseous systems and G(r,0)=PDF(r).

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VanHoveFunctionSelf

Calculates the self part of the van Hove function.

The van Hove function is related to the intermediate scattering function via a Fourier transform and the dynamic structure factor via a double Fourier transform. The van Hove function describes the probability of finding a particle (j) at a distance r at time t from a particle (i) at a time t_0. The van Hove function can be split into self and distinct parts. The self part includes only the contributions from only the same particles (i=j) while the distinct part includes only the contributions between different particles (i≠j). This job calculates a self part of the van Hove function.

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VelocityCorrelationFunction

Calculates the velocity correlation function of the selected atoms.

The Velocity Correlation Function (VCF) is a property describing the dynamics of a molecular system. It reveals the underlying nature of the forces acting on the system. Its Fourier Transform gives the cartesian density of states for a set of atoms.

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Voronoi

Performs the Voronoi analysis of available volume per atom.

Computes the volume of each Voronoi cell and corresponding ‘neighbourhood’ statistics for 3d systems. Vornoi diagram and Delaunay tesselation are used as implemented in scipy.spatial module. Replicas of atoms from the simulation box will be included in the calculation within a finite distance from the box wall (given in nm).

Voronoi analysis is another commonly-used, complementary method for characterising the local structure of a system.

Acknowledgement: Gael Goret, PELLEGRINI Eric

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XRayStaticStructureFactor

Computes the X-ray static structure for a set of atoms.

Computes the X-ray static structure from the pair distribution function for a set of atoms, taking into account the atomic form factor for X-rays.

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