Application of quantum mechanics to chemical systems, molecular structure, and chemical bonding
Quantum chemistry applies quantum mechanical principles to understand chemical bonding, molecular structure, and reactivity. I cover wave function theory, molecular orbital theory, Hartree-Fock methods, density functional theory, and computational approaches to solving the electronic Schrödinger equation. I help calculate molecular properties, spectra, and reaction pathways.
import numpy as np
from typing import List, Dict, Tuple
class QuantumChemistry:
def __init__(self, atomic_numbers: List[int], coordinates: np.ndarray):
self.atomic_numbers = atomic_numbers
self.coordinates = coordinates # Angstroms
self.num_electrons = sum(atomic_numbers) // 2
def calculate_hückel_matrix(self) -> np.ndarray:
n = len(self.atomic_numbers)
H = np.zeros((n, n))
alpha = -11.0 # Coulomb integral (eV)
beta = -1.0 # Resonance integral (eV)
for i in range(n):
H[i, i] = alpha
for j in range(i + 1, n):
dist = np.linalg.norm(self.coordinates[i] - self.coordinates[j])
if dist < 2.5: # Adjacency threshold
H[i, j] = beta
H[j, i] = beta
return H
def hückel_eigenvalues(self) -> List[float]:
H = self.calculate_hückel_matrix()
eigenvalues = np.linalg.eigvalsh(H)
return sorted(eigenvalues.tolist())
def calculate_mo_energies(self, basis_size: int = 6) -> List[float]:
energies = []
for n in range(1, basis_size + 1):
energy = -13.6 / n**2 # Hydrogen-like
energies.append(energy)
return energies
def predict_uv_vis(self, transition_energies: List[float]) -> List[float]:
hc = 1240 # eV·nm
wavelengths = [hc / E for E in transition_energies]
return wavelengths
def calculate_dipole_moment(self, charges: np.ndarray,
dipole_vector: np.ndarray) -> float:
return np.linalg.norm(dipole_vector)
def estimate_homo_lumo_gap(self, n_electrons: int,
mo_energies: List[float]) -> float:
if n_electrons <= len(mo_energies):
lumo = mo_energies[n_electrons]
homo = mo_energies[n_electrons - 1]
return lumo - homo
return 0.0
def atomic_units_conversion(self, energy_ev: float) -> float:
return energy_ev / 27.211 # Convert eV to Hartree
def bohr_to_angstrom(self, bohr_radius: float) -> float:
return bohr_radius * 0.529177
h2 = QuantumChemistry(atomic_numbers=[1, 1],
coordinates=np.array([[0.0, 0.0, 0.0],
[0.74, 0.0, 0.0]]))
H = h2.calculate_hückel_matrix()
print(f"Hückel Matrix:\n{H}")
energies = h2.hückel_eigenvalues()
print(f"MO Energies (eV): {energies}")