Dataset DOI: 10.5061/dryad.44j0zpcwk

Description of the data and file structure

The data associated with all figures presented in the manuscript, “Molecular Simulation and Multistate Analysis for Efficient Property Estimation in Polymeric Systems: A Case Study on PIM-1,” are available here.

Files and variables

File: fig01.zip

Description

Figure 1: pVT Relationship of Molten Isotactic Polypropylene

Figure 1 presents the pressure–volume–temperature (pVT) relationship of isotactic polypropylene (i-PP) in the molten state. Molecular dynamics (MD) results obtained at selected temperature–pressure conditions are compared with experimental data and predictions from the Tait equation.

The calculations included in this folder evaluate the pVT behavior of molten i-PP using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at sampled thermodynamic states, post-processing of the MD log files, MBAR calculations, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input templates and initial system data required to perform the simulations.

• 21step.in0: LAMMPS input template for performing the 21-step relaxation protocol used to prepare the i-PP system.
• eq_prod.in0: LAMMPS input template for performing the NPT equilibration and production simulations at the specified temperature–pressure conditions.
• pack.lmps: LAMMPS data file containing the initial atomic coordinates, molecular topology, atom types, and force-field parameters for the i-PP system.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm³
  Volume = ų

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include properties evaluated at the sampled and/or reweighted thermodynamic states used to generate Figure 1.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig02.zip

Description

Figure 2: Density of PIM-1 as a Function of Polymer Chain Composition

Figure 2 presents the simulated and skeletal densities of PIM-1 as a function of the number of monomers in the polymer chains and the total number of chains in the system.
The calculations included in this folder evaluate the density and pore-volume behavior of PIM-1 polymer systems using molecular dynamics simulations across multiple system configurations with varying chain lengths and chain populations. The dataset includes LAMMPS production simulations at different polymer chain compositions, LAMMPS post-processing calculations to extract thermodynamic properties, and complementary Poreblazer analysis to quantify micropore volumes and skeletal densities.

Input Files

The input folder contains the LAMMPS input templates, initial system data, and force-field parameters required to perform the simulations of PIM-1 polymer systems.

• 21-step.in: LAMMPS input template for performing the multi-step relaxation and equilibration protocol used to prepare the PIM-1 polymer system prior to production simulations.
• pack.lmps: LAMMPS data file containing the initial atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system.
• poreblazer/CustomFF.atoms: Custom force-field file containing atomic parameters for poreblazer analysis used to calculate micropore volumes and skeletal density.
• poreblazer/defaults.dat: Default parameters and settings for poreblazer calculations.

Output Files

The output folder is organized by system composition (chain count and monomer count combinations). Each composition folder contains multiple independent configurations and post-processing results.

System Configurations

Five distinct system compositions are analyzed:

• 01.10chainsx10monomers: 10 chains with 10 monomers each
• 02.15chainsx10monomers: 15 chains with 10 monomers each
• 03.20chainsx10monomers: 20 chains with 10 monomers each
• 04.15monomerx7chains: 7 chains with 15 monomers each
• 05.20monomerx5chains: 5 chains with 20 monomers each

Configuration Folders

Each system composition directory contains five independent simulation configurations (config01 through config05) and a postprocessing folder.

LAMMPS Production Simulation Files

• config0X/log.lammps: LAMMPS log file from the production simulation of configuration X. The log file contains thermodynamic quantities recorded during the simulation, including temperature, pressure, volume, density, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

• config0X/prod.data: LAMMPS final configuration snapshot from the production simulation of configuration X, containing final atomic coordinates and system information.

Post-Processing Analysis

The postprocessing folder within each system composition contains aggregated data from the corresponding simulations and supplementary analysis.
lammps_averages.dat: Ensemble-averaged thermodynamic properties extracted from LAMMPS log files across all five configurations of that system composition. This file includes bulk density, volume, pressure, and energy-related quantities with corresponding statistical uncertainties. Units are the same as showed in the log files.
poreblazer_averages.dat: Pore-structure analysis results calculated using poreblazer for all five configurations of that system composition. This file contains skeletal density (accounting for micropore volume), accessible pore volume, and related structural properties. Units are listed in the file.

File: fig03.zip

Description

Figure 3: Configurational Energy Uncertainties of PIM-1 Between 0.1 MPa and 2.0 MPa, and 283.15 K and 313.15 K

Figure 3 presents configurational energy uncertainties of PIM-1 calculated with the Multistate Bennett Acceptance Ratio (MBAR) method using two different sampling densities: 4 independent simulations and 35 independent simulations.
The calculations included in this folder evaluate how the number of sampled thermodynamic states affects the accuracy of configurational energy uncertainty estimates obtained through MBAR reweighting. The dataset includes simulations at sampled thermodynamic states across the temperature–pressure grid, post-processing of the MD log files, MBAR calculations, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the thermodynamic state points sampled in both the 4_states and 35_states analyses.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data. Results are organized into two subdirectories corresponding to different sampling strategies: 4_states (minimal sampling with 4 thermodynamic state points) and 35_states (enhanced sampling with 35 thermodynamic state points distributed across the temperature–pressure grid).

LAMMPS Log Files

The log_files folders (within each state directory) contain the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point. For the 4_states folder, XX ranges from 01 to 04. For the 35_states folder, XX ranges from 01 to 35. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, configurational energy, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic property uncertainties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables and their uncertainties estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include configurational energy uncertainties evaluated at the sampled and reweighted thermodynamic states used to generate Figure 3.
• STD_results.dat: Contains conventional single-state ensemble-average estimates and uncertainties calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates. 

File: fig04.zip

Description

Figure 4: Configurational Energy Uncertainties of PIM-1 Calculated with Standard Ensemble Averaging Between 0.1 MPa and 2.0 MPa, and 283.15 K and 313.15 K

Figure 4 presents configurational energy uncertainties of PIM-1 calculated using conventional single-state ensemble averaging with two different sampling densities: 35 and 279 independent simulations.

The calculations included in this folder evaluate configurational energy uncertainties obtained through conventional ensemble averaging without multistate reweighting, and demonstrate how uncertainty estimates converge as the number of sampled thermodynamic states increases. The dataset includes simulations at sampled thermodynamic states across the temperature–pressure grid, post-processing of the MD log files, and conventional single-state ensemble calculations used for comparison with MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the thermodynamic state points sampled in both the 35_states and 279_states analyses.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data. Results are organized into two subdirectories corresponding to different sampling densities: 35_states (sparse sampling with 35 thermodynamic state points) and 279_states (dense sampling with 279 thermodynamic state points distributed across the temperature–pressure grid).

LAMMPS Log Files

The log_files folders (within each state directory) contain the log files generated during the production MD simulations.=

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point. For the 35_states folder, XX ranges from 01 to 35. For the 279_states folder, XX ranges from 01 to 279. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, configurational energy, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic property uncertainties using conventional single-state ensemble averages. The resulting uncertainty estimates and interpolated data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the uncertainty analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

Statistical Results

The results folders contain the primary outputs of the single-state ensemble averaging analysis.

• STD_results.dat: Contains conventional single-state ensemble-average estimates and uncertainties calculated directly from the simulation data without multistate reweighting. The file header identifies each variable and its corresponding unit. These results represent the primary data used to generate Figure 4 and demonstrate configurational energy uncertainties as a function of thermodynamic state and sampling density.

File: fig05.zip

Description

Figure 5: Volume Expansivity of PIM-1 and Configurational Energy Distributions Across Temperature States

Figure 5 presents the volume expansivity of PIM-1 calculated across seven temperature states ranging from 283.15 K to 313.15 K.

The calculations included in this folder evaluate the volume expansivity of PIM-1 using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method across a temperature range. The dataset includes simulations at seven sampled temperature states, post-processing of the MD log files, MBAR calculations that enable interpolation to 24 additional unsampled temperatures, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled temperature states.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature conditions at constant pressure. This template is used for each of the seven temperature states sampled in the analysis.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/temperature state, ranging from 01 to 07. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, configurational energy, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol). This file is also used to generate the probability density distributions shown in the bottom panel of Figure 5.
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different temperature states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include volume expansivity evaluated at both the 7 sampled temperature states and the 24 additional unsampled intermediate states.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig06.zip

Description

Figure 6: Density of PIM-1 Across Temperature–Pressure Space

Figure 6 presents the density of PIM-1 as a function of temperature and pressure for a total of 279 thermodynamic states.

The calculations included in this folder evaluate the density behavior of PIM-1 using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at 35 sampled thermodynamic states, post-processing of the MD log files, MBAR calculations that enable interpolation to 244 additional unsampled states, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the 35 thermodynamic state points sampled in the analysis.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point, ranging from 01 to 35. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, density, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include density evaluated at both the 35 sampled thermodynamic states and the 244 additional unsampled intermediate states, for a total of 279 states used to generate the smoothed surface representation.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig07.zip

Description

Figure 7: Density of PIM-1 Across Temperature–Pressure Space at Different Simulation Durations

Figure 7 presents the density of PIM-1 as a function of temperature and pressure, demonstrating convergence with respect to simulation duration.

The calculations included in this folder evaluate how configurational sampling duration affects the accuracy and convergence of density estimates obtained through molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at three different equilibration and production time durations across 35 sampled thermodynamic states, post-processing of the MD log files for each duration, MBAR calculations that enable interpolation to 244 additional unsampled states, and comparison of results across simulation lengths to assess convergence.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is adapted for each simulation duration (0.5 ns, 1.0 ns, or 2.0 ns equilibration and production times) and is used for each of the 35 thermodynamic state points sampled.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data. Results are organized into three subdirectories corresponding to different simulation durations: 0.5ns (0.5 ns equilibration and 0.5 ns production), 1.0ns (1.0 ns equilibration and 1.0 ns production), and 2.0ns (2.0 ns equilibration and 2.0 ns production).

LAMMPS Log Files

The log_files folders (within each duration directory) contain the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point, ranging from 01 to 35. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, density, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include density evaluated at both the 35 sampled thermodynamic states and the 244 additional unsampled intermediate states, for a total of 279 states used to generate the smoothed surface representation in Figure 7 for each simulation duration.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig08.zip

Description

Figure 8: Volume Expansivity of PIM-1 Across Temperature–Pressure Space

Figure 8 presents the volume expansivity of PIM-1 as a function of temperature and pressure.

The calculations included in this folder evaluate the volume expansivity behavior of PIM-1 using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at 63 sampled thermodynamic states, post-processing of the MD log files, MBAR calculations that enable interpolation to additional unsampled states, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the 63 thermodynamic state points sampled in the analysis.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point, ranging from 01 to 63. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include volume expansivity evaluated at both the 63 sampled thermodynamic states and additional unsampled intermediate states used to generate the smoothed surface representation.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig09.zip

Description

Figure 9: Isothermal Compressibility of PIM-1 Across Temperature–Pressure Space

Figure 9 presents the isothermal compressibility of PIM-1 as a function of temperature and pressure.

The calculations included in this folder evaluate the isothermal compressibility behavior of PIM-1 using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at 63 sampled thermodynamic states, post-processing of the MD log files, MBAR calculations that enable interpolation to additional unsampled states, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the 63 thermodynamic state points sampled in the analysis.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point, ranging from 01 to 63. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, and energy-related quantities.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy minus the internal molecular energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include isothermal compressibility evaluated at both the 63 sampled thermodynamic states and additional unsampled intermediate states used to generate the smoothed surface.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig10.zip

Description

Figure 10: Chemical Potential of CH₄ and CO₂ in PIM-1 as a Function of Pressure

Figure 10 presents the chemical potential of methane (CH₄) and carbon dioxide (CO₂) adsorbed in PIM-1 as a function of pressure.

The calculations included in this folder evaluate the chemical potential of CH₄ and CO₂ in PIM-1 using Monte Carlo simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes grand canonical Monte Carlo (GCMC) simulations at sampled pressure and temperature conditions for each gas species, post-processing of the MC output files, MBAR calculations, and conventional single-state ensemble averages used for comparison with the MBAR results.

CH4 Folder

• ch4.lmps: LAMMPS data file containing the molecular structure and force-field parameters for methane.
• props.inp: Configuration file specifying simulation parameters for CH₄ adsorption, including temperature, pressure points, and Monte Carlo simulation settings.
• run_pysimm.py: Python script using the pysimm library to prepare and manage the CH₄ molecular structure and force-field assignments for the grand canonical Monte Carlo simulations.

CO2 Folder

• CO2.lmps: LAMMPS data file containing the molecular structure and force-field parameters for carbon dioxide.
• props.inp: Configuration file specifying simulation parameters for CO₂ adsorption, including temperature, pressure points, and Monte Carlo simulation settings.
• run_pysimm.py: Python script using the pysimm library to prepare and manage the CO₂ molecular structure and force-field assignments for the grand canonical Monte Carlo simulations.

Output Files

The output folder contains the Monte Carlo simulation results and analysis scripts organized by gas species. Results for CH₄ (14 simulated states) and CO₂ (10 simulated states) are presented in separate subdirectories.

GCMC Log Files

The log_files folders contain the log files generated during the grand canonical Monte Carlo simulations.

• XX_result.out.log: Monte Carlo log file corresponding to one simulation. The numerical prefix (XX) identifies the individual simulation/state point (pressure and temperature combination). The log files contain records of Monte Carlo moves, energy evaluations, and accumulated statistics from the GCMC simulations.

Property Files

The prp_files folders contain property output files from the Monte Carlo simulations.

• XX_result.out.prp: Monte Carlo property file containing detailed output from the simulation, including adsorbed molecule counts, system energies, and thermodynamic quantities. These files are used in conjunction with log files for data extraction.

  Units:
  energy = kJ/mol
  pressure = bar
  Volume = ų

Post-Processing Scripts

• data.py: Python script that reads the Monte Carlo log files and property files in the log_files and prp_files folders and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the Monte Carlo output files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• chempot.dat: Contains the chemical potential values corresponding to each simulated state, reported in kilocalories per mole (kcal/mol).
• Nmols.dat: Contains the average number of adsorbed molecules in the system for each state.
• pressure.dat: Contains the pressure values associated with the simulations, reported in pascals (Pa) or bar.
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy of the adsorbate–framework and adsorbate–adsorbate interactions. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the framework volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include chemical potential evaluated at sampled and reweighted thermodynamic states across the temperature range (273.15 K to 308.15 K).
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig11.zip

Description

Figure 11: Simulated Sorption Isotherms of CH₄ in PIM-1

Figure 11 presents simulated sorption isotherms of methane (CH₄) in PIM-1 across multiple temperatures.

The calculations included in this folder evaluate the methane sorption behavior in PIM-1 using grand canonical Monte Carlo (GCMC) simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations across 5 independent polymer configurations at 18 sampled pressure conditions for each of two temperature states (293.15 K and 308.15 K), post-processing of the MC output files, MBAR calculations, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the molecular structure file, equilibration configuration, simulation parameters, and script required to prepare the system for grand canonical Monte Carlo simulations.

• CH4.lmps: LAMMPS data file containing the molecular structure and force-field parameters for methane.
• eq_adj.lmps: LAMMPS data file containing an equilibrated PIM-1 polymer framework configuration used as the starting point for GCMC simulations.
• props.inp: Configuration file specifying simulation parameters for CH₄ adsorption in PIM-1, including temperature, pressure points, Monte Carlo settings, and system parameters.
• run_pysimm_time_limit.py: Python script using the pysimm library to prepare and manage the CH₄ molecular structure, force-field assignments, and framework configuration for the grand canonical Monte Carlo simulations with optional time limits.

Output Files

The output folder contains the Monte Carlo simulation results and analysis scripts organized by temperature state and independent polymer configuration. Results are organized into two temperature directories: 293K and 308K, each containing 5 independent polymer configurations (config01 through config05).

Temperature and Configuration Organization

Each temperature directory contains results from 5 independent polymer configurations, allowing for assessment of configuration-dependent variability in sorption behavior:

• 293K: GCMC simulations at 293.15 K with 5 independent polymer configurations
• 308K: GCMC simulations at 308.15 K with 5 independent polymer configurations

GCMC Log Files

The log_files folders contain the log files generated during the grand canonical Monte Carlo simulations.

• XX_result.out.log: Monte Carlo log file corresponding to one simulation. The numerical prefix (XX) identifies the individual simulation/pressure state, ranging from 01 to 18. The log files contain records of Monte Carlo moves, energy evaluations, and accumulated statistics from the GCMC simulations.

Property Files

The prp_files folders contain property output files from the Monte Carlo simulations.

• XX_result.out.prp: Monte Carlo property file containing detailed output from the simulation, including adsorbed molecule counts, system energies, chemical potentials, and thermodynamic quantities. These files are used in conjunction with log files for data extraction.

  Units:
  energy = kJ/mol
  pressure = bar
  Volume = ų

Post-Processing Scripts

• data.py: Python script that reads the Monte Carlo log files and property files in the log_files and prp_files folders and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates adsorption properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the Monte Carlo output files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• chempot.dat: Contains the chemical potential values corresponding to each simulated pressure state, reported in kilocalories per mole (kcal/mol).
• Nmols.dat: Contains the average number of adsorbed methane molecules in the system for each pressure state.
• loadings_m.dat: Contains the gas loading expressed on a mass basis (mass of gas per unit mass of adsorbent), reported in mmol/g.
• loadings_v.dat: Contains the gas loading expressed on a volume basis (moles of gas per unit volume of adsorbent), reported in cm³/cm³.
• nominal_pressure.dat: Contains the nominal pressure targets specified for each GCMC simulation state in megapascals (MPa).
• pressure.dat: Contains the average pressure values during the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the adsorbate–framework and adsorbate–adsorbate interaction energies. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the framework volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different pressure states.
• MBAR_results.dat: Contains adsorption properties estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include gas loading, chemical potential, and related quantities evaluated at sampled and reweighted pressure states across the temperature range.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig12.zip

Description

Figure 12: Simulated Sorption Isotherms of CO₂ in PIM-1

Figure 12 presents simulated sorption isotherms of carbon dioxide (CO₂) in PIM-1 across multiple temperatures.

The calculations included in this folder evaluate the carbon dioxide sorption behavior in PIM-1 using grand canonical Monte Carlo (GCMC) simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations across 5 independent polymer configurations at 46 sampled pressure conditions for 293.15 K and 19 sampled pressure conditions for 308.15 K, post-processing of the MC output files, MBAR calculations, and conventional single-state ensemble averages used for comparison with the MBAR results.

Input Files

The input folder contains the molecular structure file, equilibration configuration, simulation parameters, and script required to prepare the system for grand canonical Monte Carlo simulations.

• CO2.lmps: LAMMPS data file containing the molecular structure and force-field parameters for carbon dioxide.
• eq_adj.lmps: LAMMPS data file containing an equilibrated PIM-1 polymer framework configuration used as the starting point for GCMC simulations.
• props.inp: Configuration file specifying simulation parameters for CO₂ adsorption in PIM-1, including temperature, pressure points, Monte Carlo settings, and system parameters.
• run_pysimm_time_limit.py: Python script using the pysimm library to prepare and manage the CO₂ molecular structure, force-field assignments, and framework configuration for the grand canonical Monte Carlo simulations with optional time limits.

Output Files

The output folder contains the Monte Carlo simulation results and analysis scripts organized by temperature state and independent polymer configuration. Results are organized into two temperature directories: 293K and 308K, each containing 5 independent polymer configurations (config01 through config05).

Temperature and Configuration Organization

Each temperature directory contains results from 5 independent polymer configurations, allowing for assessment of configuration-dependent variability in sorption behavior:

• 293K: GCMC simulations at 293.15 K with 5 independent polymer configurations and 46 sampled pressure states
• 308K: GCMC simulations at 308.15 K with 5 independent polymer configurations and 19 sampled pressure states

GCMC Log Files

The log_files folders contain the log files generated during the grand canonical Monte Carlo simulations.

• XX_result.out.log: Monte Carlo log file corresponding to one simulation. The numerical prefix (XX) identifies the individual simulation/pressure state, ranging from 01 to 46 for 293K configurations and 01 to 19 for 308K configurations. The log files contain records of Monte Carlo moves, energy evaluations, and accumulated statistics from the GCMC simulations.

Property Files

The prp_files folders contain property output files from the Monte Carlo simulations.

• XX_result.out.prp: Monte Carlo property file containing detailed output from the simulation, including adsorbed molecule counts, system energies, chemical potentials, and thermodynamic quantities. These files are used in conjunction with log files for data extraction.

  Units:
  energy = kJ/mol
  pressure = bar
  Volume = ų

Post-Processing Scripts

• data.py: Python script that reads the Monte Carlo log files and property files in the log_files and prp_files folders and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates adsorption properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the Monte Carlo output files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• chempot.dat: Contains the chemical potential values corresponding to each simulated pressure state, reported in kilocalories per mole (kcal/mol).
• Nmols.dat: Contains the average number of adsorbed methane molecules in the system for each pressure state.
• loadings_m.dat: Contains the gas loading expressed on a mass basis (mass of gas per unit mass of adsorbent), reported in mmol/g.
• loadings_v.dat: Contains the gas loading expressed on a volume basis (moles of gas per unit volume of adsorbent), reported in cm³/cm³.
• nominal_pressure.dat: Contains the nominal pressure targets specified for each GCMC simulation state in megapascals (MPa).
• pressure.dat: Contains the average pressure values during the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the adsorbate–framework and adsorbate–adsorbate interaction energies. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the framework volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different pressure states.
• MBAR_results.dat: Contains adsorption properties estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include gas loading, chemical potential, and related quantities evaluated at sampled and reweighted pressure states across the temperature range.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: fig13.zip

Description

Figure 13: Simulated Isosteric Heats of Sorption of CH₄ and CO₂ in PIM-1

Figure 13 presents simulated isosteric heats of sorption for methane (CH₄, blue circles) and carbon dioxide (CO₂, orange squares) in PIM-1.

The calculations included in this folder evaluate the isosteric heats of sorption for both CH₄ and CO₂ in PIM-1 using grand canonical Monte Carlo (GCMC) simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations across 5 independent polymer configurations at 18 sampled pressure conditions for CH₄ and 46 sampled pressure conditions for CO₂, post-processing of the MC output files to extract configurational energies and loadings, MBAR calculations, and conventional single-state ensemble averages used to calculate isosteric heats via the Clausius-Clapeyron equation.

Input Files

The input folder contains gas-specific subdirectories for CH₄ and CO₂, each containing molecular structure files, equilibration configurations, simulation parameters, and scripts.

CH4 Folder

• CH4.lmps: LAMMPS data file containing the molecular structure and force-field parameters for methane.
• eq_adj.lmps: LAMMPS data file containing an equilibrated PIM-1 polymer framework configuration used as the starting point for GCMC simulations.
• props.inp: Configuration file specifying simulation parameters for CH₄ adsorption in PIM-1, including temperature, pressure points, Monte Carlo settings, and system parameters.
• run_pysimm_time_limit.py: Python script using the pysimm library to prepare and manage the CH₄ molecular structure, force-field assignments, and framework configuration for the grand canonical Monte Carlo simulations.

CO2 Folder

• CO2.lmps: LAMMPS data file containing the molecular structure and force-field parameters for carbon dioxide.
• eq_adj.lmps: LAMMPS data file containing an equilibrated PIM-1 polymer framework configuration used as the starting point for GCMC simulations.
• props.inp: Configuration file specifying simulation parameters for CO₂ adsorption in PIM-1, including temperature, pressure points, Monte Carlo settings, and system parameters.
• run_pysimm_time_limit.py: Python script using the pysimm library to prepare and manage the CO₂ molecular structure, force-field assignments, and framework configuration for the grand canonical Monte Carlo simulations.

Output Files

The output folder contains the Monte Carlo simulation results and analysis scripts organized by gas species and independent polymer configuration. Results for CH₄ and CO₂ are presented in separate subdirectories, each containing 5 independent polymer configurations (config01 through config05).

Gas-Specific Organization

• CH4: GCMC simulations for methane with 5 independent polymer configurations and 18 sampled pressure states
• CO2: GCMC simulations for carbon dioxide with 5 independent polymer configurations and 46 sampled pressure states

GCMC Log Files

The log_files folders contain the log files generated during the grand canonical Monte Carlo simulations.

• XX_result.out.log: Monte Carlo log file corresponding to one simulation. The numerical prefix (XX) identifies the individual simulation/pressure state (01 to 18 for CH₄, 01 to 46 for CO₂). The log files contain records of Monte Carlo moves, energy evaluations, and accumulated statistics from the GCMC simulations.

Property Files

The prp_files folders contain property output files from the Monte Carlo simulations.

• XX_result.out.prp: Monte Carlo property file containing detailed output from the simulation, including adsorbed molecule counts, system energies, chemical potentials, potential energies, and thermodynamic quantities. These files are used in conjunction with log files for data extraction.

  Units:
  energy = kJ/mol
  pressure = bar
  Volume = ų

Post-Processing Scripts

• data.py: Python script that reads the Monte Carlo log files and property files in the log_files and prp_files folders and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates adsorption properties using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folders contain quantities extracted from the Monte Carlo output files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis and isosteric heat calculations.

• chempot.dat: Contains the chemical potential values corresponding to each simulated pressure state, reported in kilocalories per mole (kcal/mol).
• Nmols.dat: Contains the average number of adsorbed gas molecules in the system for each pressure state.
• loadings_m.dat: Contains the gas loading expressed on a mass basis (mass of gas per unit mass of adsorbent), reported in mmol/g.
• loadings_v.dat: Contains the gas loading expressed on a volume basis (moles of gas per unit volume of adsorbent), reported in cm³/cm³.
• nominal_pressure.dat: Contains the nominal pressure targets specified for each GCMC simulation state in megapascals (MPa).
• poteng.dat: Contains the potential energy of adsorbate–framework and adsorbate–adsorbate interactions for each state, reported in kilocalories per mole (kcal/mol).
• pressure.dat: Contains the average pressure values during the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational energy, defined as the total potential energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the framework volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folders contain the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different pressure states.
• MBAR_results.dat: Contains adsorption properties estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include gas loading, chemical potential, potential energy, and related quantities evaluated at sampled and reweighted pressure states used to calculate isosteric heats.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

File: figS01-S05.zip

Description

Figure S1: Total Energy Relaxation During Final Equilibration Step Across Timestep Values

Figure S1 presents the total energy as a function of simulation time during the final relaxation step for five independent simulations at each of five different timestep values.

The calculations included in this folder evaluate the energy relaxation behavior of PIM-1 during the final step of a multi-step equilibration protocol using molecular dynamics simulations. The dataset includes log files from the 21-step relaxation procedure conducted with five different timestep values, with five independent simulations performed for each timestep, and post-processing analysis to extract and compare energy convergence behavior.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the multi-step relaxation protocol.

• 21step.in: LAMMPS input template for performing the 21-step relaxation protocol used to prepare the PIM-1 system. This template is adapted for each of the five timestep values (0.1 fs, 0.2 fs, 0.5 fs, 1.0 fs, and 2.0 fs) to generate the trajectories shown in Figure S1.
• pack.lmps: LAMMPS data file containing the initial atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all relaxation simulations.

Output Files

The output folder contains LAMMPS log files from the relaxation protocol conducted at each of the five timestep values, and post-processing analysis results.

LAMMPS Log Files

Five independent configuration directories (config01 through config05) correspond to the five different timestep values examined:

• config01: Results from simulations using 0.1 fs timestep (Panel a in Figure S1)

• config02: Results from simulations using 0.2 fs timestep (Panel b in Figure S1)

• config03: Results from simulations using 0.5 fs timestep (Panel c in Figure S1)

• config04: Results from simulations using 1.0 fs timestep (Panel d in Figure S1)

• config05: Results from simulations using 2.0 fs timestep (Panel e in Figure S1)

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Each configuration directory contains:

• log.lammps_21step: LAMMPS log file from the 21-step relaxation protocol. This file contains thermodynamic quantities recorded at each timestep during the final relaxation step, including total energy, potential energy, kinetic energy, temperature, and pressure. The log file tracks the energy evolution across five independent simulations performed at the specified timestep value.

Post-Processing Analysis

The post-processing folder contains aggregated data from the relaxation simulations.

• lammps_averages.dat: Ensemble-averaged thermodynamic properties extracted from the log files across all five timestep configurations. This file contains statistical summaries of energy relaxation behavior, including average total energies, kinetic energies, potential energies, and related quantities for comparison across the different timestep values. Units are the same as showed in the log files.

File: figS06-S11.zip

Description

Figure S2: Thermodynamic Quantities for Derivative Property Calculations Across Temperature–Pressure Space

Figure S2 presents standard NPT ensemble averages and MBAR estimates of thermodynamic quantities entering Equation (S1) for the calculation of derived properties. The six panels display: (a) ⟨H_conf⟩ (conformational enthalpy), (b) ⟨V⟩ (volume), (c) ⟨H_conf V⟩ (product of conformational enthalpy and volume), (d) ⟨H_conf⟩⟨V⟩ (product of individual averages), (e) the numerator of Equation (S1) (equivalent to the covariance of H_conf and V), and (f) the denominator of Equation (S1).

The calculations included in this folder evaluate the thermodynamic quantities required for calculating derived properties (such as isothermal compressibility or other second-order derivatives) using molecular dynamics simulations and multistate reweighting with the Multistate Bennett Acceptance Ratio (MBAR) method. The dataset includes simulations at 63 sampled thermodynamic states, post-processing of the MD log files, MBAR calculations that enable interpolation to additional unsampled states, and conventional single-state ensemble averages used to decompose property derivatives.

Input Files

The input folder contains the LAMMPS input template and initial system data required to perform the simulations at the sampled thermodynamic state points.

• prod.in0: LAMMPS input template for performing NPT production simulations at the specified temperature–pressure conditions. This template is used for each of the 63 thermodynamic state points sampled in the analysis.
• step21.data: LAMMPS data file containing the equilibrated atomic coordinates, molecular topology, atom types, and force-field parameters for the PIM-1 system used as the starting point for all production simulations.

Output Files

The output folder contains the LAMMPS simulation log files and scripts used to extract, process, and analyze the simulation data.

LAMMPS Log Files

The log_files folder contains the log files generated during the production MD simulations.

• XX_log.lammps: LAMMPS log file corresponding to one production simulation. The numerical prefix (XX) identifies the individual simulation/state point, ranging from 01 to 63. The log files contain the thermodynamic quantities recorded during the simulations, including temperature, pressure, volume, configurational (conformational) energy, potential energy, kinetic energy, and total energy.

  Units:
  time = femtoseconds
  energy = kcal/mol
  temperature = Kelvin
  pressure = atmospheres
  density = g/cm^dim

Post-Processing Scripts

• data.py: Python script that reads the LAMMPS log files in the log_files folder and extracts the relevant simulation data. The extracted quantities are organized into separate files in the processed_data folder.
• run_mbar.py: Python script that reads the processed simulation data and calculates thermodynamic properties and their derivatives using both conventional single-state ensemble averages and MBAR reweighting. The resulting MBAR and conventional-average data are written to the results folder.

Processed Data

The processed_data folder contains quantities extracted from the LAMMPS log files and organized by variable type. These files serve as intermediate input to the subsequent MBAR analysis.

• mass.dat: Contains the number of atoms in the system and the corresponding total system mass. Masses are reported in atomic mass units (amu) and kilograms (kg).
• pressure.dat: Contains the pressure values associated with the simulations, reported in megapascals (MPa).
• temperature.dat: Contains the simulation temperatures, reported in kelvin (K).
• uconf.dat: Contains the configurational (conformational) enthalpy, defined as the total potential energy. Values are reported in kilocalories per mole (kcal/mol).
• volume.dat: Contains the simulation-cell volumes, reported in cubic angstroms (ų).

MBAR and Statistical Results

The results folder contains the primary outputs of the multistate analysis and the corresponding conventional single-state calculations.

• f_k.dat: Contains the dimensionless reduced free-energy estimates (f_k) obtained for the simulation states during the MBAR calculation. These values are used to determine the relative statistical weights of configurations sampled from the different thermodynamic states.
• MBAR_results.dat: Contains thermodynamic observables and their derivatives estimated using MBAR reweighting. The file header identifies each variable and its corresponding unit. These results include the six quantities displayed in Figure S2: ⟨H_conf⟩, ⟨V⟩, ⟨H_conf V⟩, ⟨H_conf⟩⟨V⟩, the covariance of H_conf and V, and related derivatives, evaluated at both the 63 sampled thermodynamic states and additional unsampled intermediate states used to generate the smoothed surface representation.
• STD_results.dat: Contains conventional single-state ensemble-average estimates calculated directly from the simulation data, without MBAR reweighting. The file header identifies each variable and its corresponding unit. These results provide a reference for comparison with the MBAR estimates.

Code/software

LAMMPS: 29 August 2024 release
CASSANDRA: 1.3.1 release
PYSIMM: v1.1
Python: 3.8

Python modules:
pyMBAR v4.0.3
pyMBAR v2.0beta
Uncertainties v3.2.2