MOF adsorption: force fields, Widom and GCMC

Tasks 10.4.1-10.4.5. References: TraPPE (Martin and Siepmann 1998; Potoff and Siepmann 2001; Chen and Siepmann 2000), RASPA, UFF (Rappe et al. 1992), EQeq (Wilmer et al. 2012).

Host-guest force field

Framework atoms carry UFF Lennard-Jones parameters (sigma = x1, epsilon = d1) and EQeq charges from Task 4.3. Guests are the embedded TraPPE models: CO2 (three sites, charges +0.70/-0.35), N2 (two sites, +/-0.482), CH4 (one site), H2 (two sites) and SPC/E water. Mixing is Lorentz-Berthelot:

sigma_ij = (sigma_i + sigma_j) / 2
epsilon_ij = sqrt(epsilon_i epsilon_j)

The pair energy is 4 epsilon [(sigma/r)^12 - (sigma/r)^6] plus the Coulomb term 14.399645 q_i q_j / r in eV Angstrom. The host-guest energy sums every guest atom over every host atom with the periodic minimum image and a 15 Angstrom cutoff; guest-guest interactions are not part of the infinite- dilution Widom calculation.

Widom insertion and Henry coefficient

A seeded SplitMix64 generator draws a uniform fractional position and three Euler angles per insertion. The dimensionless Henry coefficient is the average Boltzmann factor

H = < exp(-E / kT) >

over the samples. The mean energy is the Boltzmann-weighted average, the heat of adsorption is its negative, and the minimum energy over the samples is reported as the best binding site. The result is deterministic for a seed and independent of thread count because insertion order is fixed.

GCMC isotherm

The single-component engine uses the ideal-gas chemical potential mu = kT ln(P / P0) with P0 = 1 bar and accepts insertions with min(1, exp((mu - E)/kT)); deletions are attempted with a small fixed probability. The loading is reported per cell and the acceptance ratio is the fraction of accepted insertion attempts. The implementation is deliberately a Henry/Langmuir-level isotherm: it omits guest-guest interactions and Peng-Robinson fugacity, so the full RASPA engine remains the reference for production isotherms.

Energy grids and RASPA export

The energy grid evaluates the host-guest energy of a fixed guest orientation at every sample of a regular cell grid and reports the minimum and maximum. It shares the grid conventions of the porosity field, so a viewer can draw the binding sites next to the accessible surface.

raspa_input writes simulation.input, the framework CIF, a pseudo-atom force-field definition and the Lorentz-Berthelot mixing file. The input sets WidomInsertion yes; a user can switch it to the GCMC block without changing the framework or force-field files.