Atomic Interactions -

Loading in Forcefield Files#

Lennard-Jones forcefield parameters are stored in comma-separated-value format in PorousMaterials.PATH_TO_FORCEFIELDS.

Interaction of an adsorbate with the framework is modeled as pair-wise additive and with Lennard-Jones potentials of the form:

V(r) = 4 * epsilon * [ x ^ 12 - x ^ 6 ], where x = sigma / r

The Lennard Jones force field input files, e.g. UFF.csv contain a list of pure (i.e. X-X, where X is an atom) sigmas and epsilons in units Angstrom and Kelvin, respectively. Note that, e.g., in the UFF paper, the Lennard Jones potential is written in a different form and thus parameters need to be converted to correspond to the functional form used in PorousMaterials.jl.

using PorousMaterials

ljff = LJForceField("UFF.csv")

PorousMaterials will the output information about the forcefield file you just loaded:

    Force field: UFF.csv
    Number of atoms included: 106
    Cut-off radius (Å) = 14.0

This also prints all of the atoms included in the loaded forcefield with their given ϵ and σ. This was excluded because it would use too much space on this page.

Building Blocks of PorousMaterials: Lennard-Jones forcefields#

# read in Lennard-Jones force field parameters from the Universal Force Field
forcefield = LJForceField("UFF.csv", cutoffradius=14.0, mixing_rules="Lorentz-Berthelot")

# access the Lennard-Jones epsilon & sigma for Xe
forcefield.pure_ϵ[:Xe] # K
forcefield.pure_σ[:Xe] # Å

# access the Lennard-Jones epsilon & sigma for Xe-C interactions
forcefield.ϵ[:Xe][:C] # K                                                                 
forcefield.σ²[:Xe][:C] # Å (store σ² for faster computation)

Building Blocks of PorousMaterials: Potential energies#

First, set the fractional coordinates of the molecule in the context of some unit cell box.

# molecule in a framework
set_fractional_coords!(molecule, framework.box)

# molecule in a 10 by 10 by 10 cube
box = Box(10.0, 10.0, 10.0, π/2, π/2, π/2) # make a box
set_fractional_coords!(molecule, box)

Potential Energies: Van der Waals#

What is the van der Waals potential energy of a Xe adsorbate inside SBMOF-1 at [0.0, 1.0, 3.0] Cartesian coordinates using the UFF as a molecular model?

using PorousMaterials

framework = Framework("SBMOF-1.cif")

forcefield = LJForceField("UFF.csv")

molecule = Molecule("Xe")
set_fractional_coords!(molecule, framework.box)

translate_to!(molecule, [0.0, 1.0, 0.0], framework.box) # need box b/c we're talking Cartesian

energy = vdw_energy(framework, molecule, forcefield) # K

Potential Energies: Electrostatics#

What is the electrostatic potential energy of a CO₂ adsorbate inside CAXVII_clean at [0.0, 1.0, 0.0] Cartesian coordinate?

using PorousMaterials

framework = Framework("CAXVII_clean.cif") # has charges

molecule = Molecule("CO2")
set_fractional_coords!(molecule, framework.box)

translate_to!(molecule, [0.0, 1.0, 0.0], framework.box) # need box b/c we're talking Cartesian

rotate!(molecule, framework.box) # let's give it a random orientation

# this is for speed. pre-compute k-vectors and allocate memory
eparams, kvectors, eikar, eikbr, eikcr = setup_Ewald_sum(12.0, framework.box)

energy = electrostatic_potential_energy(framework, molecule, eparams, kvectors, eikar, eikbr, eikcr)

Potential Energies: Equations of state#

Calculate fugacity of methane at 298 K and 65 bar using the Peng-Robinson EOS:

fluid = PengRobinsonFluid(:CH4)
props = calculate_properties(fluid, 298.0, 65.0) # dictionary of PREOS properties
props["fugacity coefficient"] # 0.8729

Calculate compressibility factor of hydrogen at 300 K and 50 bar using van der Waals EOS:

fluid = VdWFluid(:H2)
props = calculate_properties(fluid, 300.0, 50.0) # dictionary of VdW properties
props["compressibility factor"] # 1.03511

Pass eos=:PengRobinson to gcmc_simulation to automatically convert pressure to fugacity using the Peng-Robinson equation of state.

Forcefields#

# PorousMaterials.LJForceField — Type.

Data structure for a Lennard Jones forcefield.

Attributes

name::String: name of forcefield; correponds to filename
pure_σ::Dict{Symbol, Float64}: Dictionary that returns Lennard-Jones σ of an X-X interaction, where X is an atom. (units: Angstrom)
pure_ϵ::Dict{Symbol, Float64}: Dictionary that returns Lennard-Jones ϵ of an X-X interaction, where X is an atom. (units: K)
σ²::Dict{Symbol, Dict{Symbol, Float64}}: Lennard Jones σ² (units: Angstrom²) for cross-interactions. Example use is sigmas_squared[:He][:C]
ϵ::Dict{Symbol, Dict{Symbol, Float64}}: Lennard Jones ϵ (units: K) for cross-interactions. Example use is epsilons[:He][:C]
cutoffradius_squared::Float64: The square of the cut-off radius beyond which we define the potential energy to be zero (units: Angstrom²). We store σ² to speed up computations, which involve σ², not σ.

Loading in Forcefield Files#

Building Blocks of PorousMaterials: Lennard-Jones forcefields#

Building Blocks of PorousMaterials: Potential energies#

Potential Energies: Van der Waals#

Potential Energies: Electrostatics#

Potential Energies: Equations of state#

Forcefields#

Potential Energy#

Nearest Image Conventions#

Electrostatics Energy#

Van der Waals Energy#