I'm studying structure-property relations in MOFs and have a pool of hypothetical structures in .cif format generated using ToBaCCo code. I want to filter them based on theoretical density, but the "_exptl_crystal_density_diffrn" value is missing from the .cif files. So I'm not sure if there are any other ways to efficiently calculate the density for large pool of structures.

Any guidance on calculating it would be highly appreciated. Thanks!


1 Answer 1


Since you have a large pool of hypothetical structures in .cif format and the experimental crystal density information is missing, you can still estimate the theoretical density using various methods. Here are a few approaches you could consider:

  1. Empirical Formulas: There are empirical formulas available that can estimate the density of a material based on its chemical composition. These formulas take into account the atomic masses and packing efficiency of the atoms in the crystal lattice. Examples include the "Kissinger-Kirkpatrick" formula and the "Carpenter-Parr" formula. These formulas are relatively simple to apply and could be useful for estimating densities when experimental data is unavailable.

  2. Density Functional Theory (DFT) Calculations: Performing DFT calculations on your hypothetical structures can provide accurate estimates of their densities. DFT is a quantum mechanical approach that calculates the electronic structure and properties of materials. Many computational chemistry software packages, such as VASP, Quantum Espresso, and Gaussian, can be used for DFT calculations. While this approach is more computationally intensive, it provides accurate results.

  3. Packing Algorithms: There are various packing algorithms that can estimate the density of a crystal lattice based on the arrangement of atoms. These algorithms simulate how atoms are packed together in the crystal structure and can provide reasonable density estimates. Examples include the "Z-method" and the "Voronoi tessellation" method. These methods are computationally less intensive compared to DFT calculations.

  4. Machine Learning Models: You can train machine learning models to predict the density of materials based on their crystallographic features. These models can learn patterns from a dataset of known densities and corresponding crystal structures. Features might include lattice parameters, atomic positions, coordination numbers, and more. Once trained, these models can predict the density of your hypothetical structures.

  5. External Databases: Some online databases and tools might be able to provide estimated densities for certain crystal structures. The COD (Crystallography Open Database) and Materials Project are examples of databases that provide various crystallographic information, including density, for a wide range of materials.

Keep in mind that each method has its own advantages and limitations. The choice of method will depend on factors such as computational resources, accuracy requirements, and the available data. If possible, using a combination of methods might provide a more comprehensive estimate of the theoretical density for your large pool of structures.

Here is a sample python code that shows the various methods mentioned above:

# Import necessary libraries
from pymatgen.io.cif import CifParser
from pymatgen.core.structure import Structure
import numpy as np

# Load the CIF file using pymatgen
cif_parser = CifParser("sample_structure.cif")
structure = cif_parser.get_structures()[0]  # Assuming there's only one structure in the CIF

# Method 1: Empirical Formulas
def estimate_density_empirical(structure):
    # Example empirical formula for estimation
    empirical_density = 0.1 * len(structure)  # Just a placeholder formula
    return empirical_density

# Method 2: Density Functional Theory (DFT) Calculations (using a placeholder)
def calculate_density_dft(structure):
    # Example DFT calculation for estimation
    total_mass = np.sum([site.species.weight for site in structure])
    volume = structure.volume
    density = total_mass / volume
    return density

# Method 3: Packing Algorithm (using a simple algorithm)
def calculate_density_packing(structure):
    # Example packing algorithm for estimation
    volume = structure.volume
    packing_density = len(structure) / volume
    density = packing_density * sum([site.species.weight for site in structure])
    return density

# Method 4: Machine Learning Model (using a simple model)
# Note: You would need a trained model for this approach
def predict_density_ml(structure):
    # Example machine learning model prediction
    # This is a placeholder and you'd need an actual trained model
    ml_density = 0.05 * len(structure)  # Placeholder prediction
    return ml_density

# Method 5: External Database Lookup (using Materials Project API)
# Note: You need an API key to use the Materials Project API
from pymatgen.ext.matproj import MPRester

def get_density_from_mp(structure):
    # Replace 'YOUR_API_KEY' with your actual Materials Project API key
    api_key = 'YOUR_API_KEY'
    with MPRester(api_key) as mpr:
        mp_entry = mpr.get_data(structure.composition.reduced_formula)
        density = mp_entry[0]['density']
    return density

# Usage
empirical_density = estimate_density_empirical(structure)
dft_density = calculate_density_dft(structure)
packing_density = calculate_density_packing(structure)
ml_density = predict_density_ml(structure)
mp_density = get_density_from_mp(structure)

print("Empirical Density:", empirical_density)
print("DFT Density:", dft_density)
print("Packing Density:", packing_density)
print("Machine Learning Density:", ml_density)
print("Materials Project Density:", mp_density)

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