Compute Global Reactivity Index (GRI) Using Python

The Global Reactivity Index (GRI) is a conceptual Density Functional Theory (DFT)-based descriptor that provides information about a molecule’s chemical reactivity. Most researchers have used these descriptors to analyze the behavior of molecules in different chemical environments, and they also assist in designing drugs for various uses. The GRI parameters were as follows:

• Chemical potential (μ)
• Global hardness (η)
• Chemical Softness (S)
• Electronegativity (χ),
• Electrophilicity index (ω),

The parameters are derived from frontier molecular orbital energies using both the Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO).

The organic and organometallic chemical reactivity trends can be predicted using these parameters.

📥Theoretical Background

These parameters can be calculated easily using simple Python scripts, which saves time and effort. For simplicity, we calculated the GRI parameters using the following equations, with energies expressed in electron volts (eV):

• Ionization potential (I) ≈ –EHOMO
• Electron affinity (A) ≈ –ELUMO

Then,

• Electronegativity (χ) = (I + A)/2 = –(EHOMO + ELUMO)/2
• Chemical potential (μ) = –χ = (EHOMO + ELUMO)/2
• Global hardness (η) = (I – A)/2 = (ELUMO – EHOMO)/2
• Global softness (S) = 1 / η
• Electrophilicity index (ω) = μ² / (2η)

Now let us understand the core concept. These parameters help us to predict:

• Reactivity trends (higher HOMO → better electron donor, lower LUMO → better electron acceptor).
• Stability (higher chemical hardness → more stable molecules).
• Electrophicity/nucleophilicity  (higher ω → stronger electrophiles).

📥Software for HOMO/LUMO Calculation

The main ideas and working mechanism of our code are based on orbital energies; therefore, we need to compute the HOMO and LUMO energies using  a quantum chemistry software package. I have also included some popular options.

These programs provide orbital energies after DFT or HF calculations. An example snippet of the HOMO/LUMO output from ORCA is as follows:

ORBITAL ENERGIES

  NO   OCC        E(Eh)            E(eV)
  ...
  45   2.0000    -0.2486          -6.7695     <-- HOMO
  46   0.0000     0.0131           0.3564     <-- LUMO

📥Python Code for GRI Calculation

Here, is a Python script that takes the EHOMO and ELUMO values in eV and computes GRI descriptors. The output in the terminal can be obtained.

def compute_gri(E_HOMO, E_LUMO):
    """
    Compute Global Reactivity Index (GRI) descriptors from the HOMO and LUMO energies.

    Parameters:
    E_HOMO (float): Energy of the HOMO orbital (eV).
    E_LUMO (float): Energy of the LUMO orbital (eV).

    Returns:
    dict: Contains χ, μ, η, S, ω
    """

    # Ionization potential and electron affinity
    I = -E_HOMO
    A = -E_LUMO

    # Electronegativity (χ)
    chi = (I + A) / 2

    # Chemical potential (μ)
    mu = -chi

    # Global hardness (η)
    eta = (I - A) / 2

    # Global softness (S)
    S = 1 / eta if eta != 0 else float('inf')

    # Electrophilicity index (ω)
    omega = mu**2 / (2 * eta) if eta != 0 else float('inf')

    return {
        'Ionization Potential (I)': I,
        'Electron Affinity (A)': A,
        'Electronegativity (χ)': chi,
        'Chemical Potential (μ)': mu,
        'Global Hardness (η)': eta,
        'Global Softness (S)': S,
        'Electrophilicity Index (ω)': omega
    }

# Example usage
if __name__ == "__main__":
    E_HOMO = -6.7695  # eV (example from ORCA)
    E_LUMO = 0.3564   # eV
    gri_results = compute_gri(E_HOMO, E_LUMO)

    for param, value in gri_results.items():
        print(f"{param}: {value:.4f} eV")

Automating HOMO/LUMO Extraction

Regular expressions can be used to parse the HOMO and LUMO from the log files obtained from the quantum chemical software packages.

import re

def extract_orbital_energies(orca_output_file):
    with open(orca_output_file, 'r') as file:
        content = file.read()

    # Correct regex pattern for ORCA orbital energies block
    pattern = r"ORBITAL ENERGIES.*?\n(-+\n.*?\n)(?:\s*\n|\Z)"
    matches = re.findall(pattern, content, re.DOTALL)

    if not matches:
        raise ValueError("Orbital energies not found in file.")

    # Take the last block of orbital energies (usually contains final results)
    orbital_block = matches[-1]

    orbitals = []
    for line in orbital_block.strip().splitlines():
        parts = line.split()
        if len(parts) >= 5:
            try:
                occ = float(parts[1])        # Occupation number
                energy_eV = float(parts[4])  # Energy in eV
                orbitals.append((occ, energy_eV))
            except ValueError:
                continue  # Skip lines that can't be parsed

    # Find HOMO (highest occupied) and LUMO (lowest unoccupied)
    homo = max((e for o, e in orbitals if o > 0), default=None)
    lumo = min((e for o, e in orbitals if o == 0), default=None)

    if homo is None or lumo is None:
        raise ValueError("Could not identify HOMO and/or LUMO from orbital data.")

    return homo, lumo

# Example usage
# E_HOMO, E_LUMO = extract_orbital_energies("molecule.out")
# print(f"HOMO: {E_HOMO:.4f} eV, LUMO: {E_LUMO:.4f} eV")

We can expect the outcome like as follows in the terminal:

Ionization Potential (I): 6.7695 eV
Electron Affinity (A): -0.3564 eV
Electronegativity (χ): 3.2066 eV
Chemical Potential (μ): -3.2066 eV
Global Hardness (η): 3.5629 eV
Global Softness (S): 0.2807 eV⁻¹
Electrophilicity Index (ω): 1.4413 eV

📥Batch Processing Version (with list of HOMO/LUMO pairs)

Working with multiple molecules (e.g., from a CSV file). First, the input CSV file name molecules.csv was created as follows:

name,E_HOMO,E_LUMO
Molecule 1,-6.7695,0.3564
Molecule 2,-5.1234,0.7890
Molecule 3,-7.0000,-0.2000

Python script say gri_batch.py):

import csv

def compute_gri(E_HOMO, E_LUMO):
    I = -E_HOMO
    A = -E_LUMO
    chi = (I + A) / 2
    mu = -chi
    eta = (I - A) / 2
    S = 1 / eta if eta != 0 else float('inf')
    omega = mu**2 / (2 * eta) if eta != 0 else float('inf')

    return {
        'Ionization Potential (I)': I,
        'Electron Affinity (A)': A,
        'Electronegativity (χ)': chi,
        'Chemical Potential (μ)': mu,
        'Global Hardness (η)': eta,
        'Global Softness (S)': S,
        'Electrophilicity Index (ω)': omega
    }

# Read input from CSV
def read_molecule_data(csv_filename):
    molecules = []
    with open(csv_filename, mode='r', newline='') as file:
        reader = csv.DictReader(file)
        for row in reader:
            try:
                molecules.append({
                    'name': row['name'],
                    'E_HOMO': float(row['E_HOMO']),
                    'E_LUMO': float(row['E_LUMO'])
                })
            except ValueError:
                print(f"Skipping row due to invalid data: {row}")
    return molecules

# Main batch processing
if __name__ == "__main__":
    input_csv = 'molecules.csv'
    molecule_data = read_molecule_data(input_csv)

    for mol in molecule_data:
        print(f"\nResults for {mol['name']}:")
        results = compute_gri(mol['E_HOMO'], mol['E_LUMO'])
        for param, value in results.items():
            print(f"{param}: {value:.4f} eV")

Once you run the gri_batch.py in the terminal, you will get output something like follows:

Results for Molecule 1:
Ionization Potential (I): 6.7695 eV
Electron Affinity (A): -0.3564 eV
Electronegativity (χ): 3.2066 eV
Chemical Potential (μ): -3.2066 eV
Global Hardness (η): 3.5629 eV
Global Softness (S): 0.2807 eV⁻¹
Electrophilicity Index (ω): 1.4413 eV

Results for Molecule 2:
Ionization Potential (I): 5.1234 eV
Electron Affinity (A): -0.7890 eV
Electronegativity (χ): 2.1672 eV
Chemical Potential (μ): -2.1672 eV
Global Hardness (η): 2.9562 eV
Global Softness (S): 0.3383 eV⁻¹
Electrophilicity Index (ω): 0.7944 eV

Results for Molecule 3:
Ionization Potential (I): 7.0000 eV
Electron Affinity (A): 0.2000 eV
Electronegativity (χ): 3.6000 eV
Chemical Potential (μ): -3.6000 eV
Global Hardness (η): 3.4000 eV
Global Softness (S): 0.2941 eV⁻¹
Electrophilicity Index (ω): 1.9059 eV

GRI calculations are sensitive. Manual verifications can be needed in some cases if you doubt the outcomes otherwise the code will fully automate your calculation just based on the HOMO and LUMO energies input.

Conclusion

The Global Reactivity Index is a powerful tool for predicting molecular behavior based on the frontier orbital energies. In general, we use DFT calculations from software such as ORCA, Psi4, or Gaussian. In this tutorial, we carefully created Python code for post-processing. Large molecular datasets can also be processed. This workflow integrates quantum chemistry and scripting to simplify computational reactivity analysis for research in organic, inorganic, and material chemistry.