Coordination numbers

Computing radial distribution functions
Overview of the solvent and solute properties

Computing radial distribution functions

The distributions returned by the mddf function (the mddf and rdf vectors), are normalized by the random reference state. This is equivalent to a site count based on the numerical integration of the volume corresponding to each minimum-distance to the solute.

If, however, the solute is defined by a single atom (as the oxygen atom of water, for example), the numerical integration of the volume can be replaced by a simple analytical spherical shell volume, reducing noise. The ComplexMixtures.gr function returns the radial distribution function and the KB integral computed from the results, using this volume estimate:

g, kb = ComplexMixtures.gr(R)

By default, the single-reference count (rdf_count) of the Result structure will be used to compute the radial distribution function. The function can be called with explicit control of all input parameters:

g, kb = ComplexMixtures.gr(r,count,density,binstep)

where:

Parameter	Definition	Result structure output data to provide
`r`	Vector of distances	The `d` vector
`count`	Number of site counts at each r	The `rdf` or `mddf` vectors
`density`	Bulk density	The `density.solvent_bulk` or `density.solvent` densities.
`binstep`	The histogram step	The `options.binstep`

Example:

...
R = mddf(trajectory_file, solute, solvent, options)
g, kb = ComplexMixtures.gr(R.d,R.rdf_count,R.density.solvent_bulk,R.options.binstep)

ComplexMixtures.gr — Method

gr(r::AbstractVector{<:Real}, count::AbstractVector{<:Real}, density::Real, binstep::Real)

Computes the radial distribution function from the count data and the density.

This is exactly a conventional g(r) if a single atom was chosen as the solute and solvent selections.

Returns both the g(r) and the kb(r)

source

ComplexMixtures.gr — Method

gr(R::Result) = gr(R.d,R.rdf_count,R.density.solvent_bulk,R.files[1].options.binstep)

If a Result structure is provided without further details, use the rdf count and the bulk solvent density.

source

Overview of the solvent and solute properties

The output to the REPL of the Result structure provides an overview of the properties of the solution. The data can be retrieved into a data structure using the overview function. Examples:

...

julia> results = mddf(trajectory_file, solute, solvent, Options(bulk_range=(8.0, 12.0)))

julia> results
--------------------------------------------------------------------------------
MDDF Overview - ComplexMixtures - Version 2.0.8
--------------------------------------------------------------------------------

Solvent properties:
-------------------

Simulation concentration: 0.49837225882780106 mol L⁻¹
Molar volume: 2006.532230249041 cm³ mol⁻¹

Concentration in bulk: 0.5182380507741433 mol L⁻¹
Molar volume in bulk: 1929.6151614228274 cm³ mol⁻¹

Solute properties:
------------------

Simulation Concentration: 0.002753437894076249 mol L⁻¹
Estimated solute partial molar volume: 13921.98945754469 cm³ mol⁻¹

Bulk range: 8.0 - 12.0 Å
Molar volume of the solute domain: 34753.1382279134 cm³ mol⁻¹

Auto-correlation: false

Trajectory files and weights:

   /home/user/NAMD/trajectory.dcd - w = 1.0

Long range MDDF mean (expected 1.0): 1.0378896753018338 ± 1.0920172247127446
Long range RDF mean (expected 1.0): 1.2147429551790854 ± 1.2081838161780682

--------------------------------------------------------------------------------

In this case, since solute and solvent are equivalent and the system is homogeneous, the molar volumes and concentrations are similar. This is not the case if the molecules are different or if the solute is at infinite dilution (in which case the bulk solvent density might be different from the solvent density in the simulation).

To retrieve the data of the overview structure use, for example:

julia> overview = overview(results);

julia> overview.solute_molar_volume
657.5051512801567