physical-chemistry

# Physical Chemistry ## What I Do I provide comprehensive physical chemistry tools including quantum chemistry calculations, molecular orbital theory, spectroscopic analysis, chemical kinetics, surface chemistry, and electrochemistry for chemistry research applications. ## When to Use Me - Molecular structure calculations - Quantum chemistry simulations - Spectroscopic interpretation - Reaction rate predictions - Surface science analysis - Electrochemical systems ## Core Concepts - **Quantum Chemistry**: Hartree-Fock, DFT, post-HF methods - **Molecular Orbitals**: Hückel, ab initio, basis sets - **Spectroscopy**: IR, UV-Vis, NMR, Raman - **Chemical Kinetics**: Rate laws, Arrhenius equation - **Surface Chemistry**: Adsorption, catalysis - **Electrochemistry**: Redox, Nernst equation - **Statistical Mechanics**: Partition functions - **Thermodynamics**: Free energy, equilibria ## Code Examples ### Molecular Orbital Calculations ```python import numpy as np def huckel_method(hamiltonian_matrix): eigenvalues, eigenvectors = np.linalg.eigh(hamiltonian_matrix) return eigenvalues, eigenvectors def build_huckel_matrix(adjacency_matrix, alpha=0, beta=-1): n = len(adjacency_matrix) H = np.full((n, n), alpha) for i in range(n): for j in range(n): if adjacency_matrix[i, j] == 1: H[i, j] = beta return H adjacency_butadiene = np.array([ [0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0] ]) H = build_huckel_matrix(adjacency_butadiene) eigenvalues, eigenvectors = huckel_method(H) print(f"MO energies (β units): {eigenvalues}") ``` ### Spectroscopic Calculations ```python def vibrational_frequency(mass_reduced, force_constant): k = force_constant mu = mass_reduced return (1 / (2 * np.pi)) * np.sqrt(k / mu) def ir_intensity(dipole_derivative, reduced_mass): return (dipole_derivative**2) / reduced_mass def electronic_transition_energy(HOMO_LUMO_gap): return HOMO_LUMO_gap def uv_vis_wavelength(nm): hc = 1239.84 # eV·nm return hc / nm def calculate_extinction_coefficient(molar_absorptivity, path_length=1): return molar_absorptivity * path_length mu = 1.673e-27 # kg (proton mass) k = 500 # N/m freq = vibrational_frequency(mu, k) print(f"Vibrational frequency: {freq:.2e} Hz") wavelength = 200 # nm energy = uv_vis_wavelength(wavelength) print(f"Energy: {energy:.2f} eV") ``` ### Chemical Kinetics ```python def arrhenius_rate(k0, Ea, T): R = 8.314 # J/mol·K return k0 * np.exp(-Ea / (R * T)) def rate_law_concentration(order, k, concentrations): rate = k for i, conc in enumerate(concentrations): rate *= conc**order[i] return rate def integrated_rate_law(t, k, initial_conc, order): if order == 0: return initial_conc - k * t elif order == 1: return initial_conc * np.exp(-k * t) elif order == 2: return initial_conc / (1 + k * t * initial_conc) def activation_energy(t1, t2, k1, k2): return np.log(k2 / k1) / (1/t1 - 1/t2) * 8.314 T1, T2 = 298, 308 k0, Ea = 1e10, 50000 k298 = arrhenius_rate(k0, Ea, T1) k308 = arrhenius_rate(k0, Ea, T2) print(f"Rate constants: k298={k298:.4e}, k308={k308:.4e}") ``` ### Electrochemistry ```python def nernst_equation(E0, n, Q, T=298): R = 8.314 F = 96485 return E0 - (R * T / (n * F)) * np.log(Q) def butler_volmer(i0, alpha_a, alpha_c, eta, n, T=298): R = 8.314 F = 96485 i = i0 * (np.exp(alpha_a * n * F * eta / (R * T)) - np.exp(-alpha_c * n * F * eta / (R * T))) return i def electrochemical_impedance(Rct, Cdl, omega): Z = Rct + 1 / (1/Rct + 1j * omega * Cdl) return Z def diffusion_limited_current(D, n, A, C_bulk, delta): return n * F * A * D * C_bulk / delta E0, n, Q = 0.76, 2, 1 E = nernst_equation(E0, n, Q) print(f"Nernst potential: {E:.3f} V") ``` ### Statistical Thermodynamics ```python from scipy.special import spherical_jn def partition_function_translational(V, m, T): R = 8.314 h = 6.626e-34 return V * (2 * np.pi * m * R * T / h**2)**1.5 def partition_function_vibrational(theta_v, T): return 1 / (1 - np.exp(-theta_v / T)) def partition_function_rotational(theta_r, T, symmetry_number=1): return T / (symmetry_number * theta_r) def calculate_free_energy(G, H, S): return H - T * S def calculate_entropy(S_trans, S_rot, S_vib, S_elec): return S_trans + S_rot + S_vib + S_elec theta_v = 2260 # K for N2 T = 298 q_vib = partition_function_vibrational(theta_v, T) print(f"Vibrational partition function: {q_vib:.4f}") ``` ## Best Practices 1. **Convergence**: Check SCF and geometry convergence 2. **Basis Set**: Choose appropriate basis set 3. **Solvent Effects**: Include implicit solvent models 4. **Temperature**: Consider thermal corrections 5. **Method Validation**: Benchmark against experiments ## Common Patterns ```python # Geometry optimization def gradient_descent_geometry(forces, step_size=0.01): return step_size * forces # Transition state search def nudged_elastic_band(images, energies, forces): return new_images ``` ## Core Competencies 1. Quantum chemistry methods 2. Molecular orbital theory 3. Spectroscopic interpretation 4. Chemical kinetics 5. Electrochemical systems