Фізика молекулярної та хімічної динаміки

🔬 Молекулярна динаміка

Рівняння руху

Ньютон: F_i = -∇_i V(R₁,...,R_N). N atoms: 3N coupled ODEs. Numerical integration: Verlet, velocity Verlet.

Потенціальні функції

Force fields: V = bonds + angles + dihedrals + nonbonded. Lennard-Jones, Coulomb. Parameterized.

Timescales

Vibrations: ~10 fs. Rotations: ~1 ps. Diffusion: ns-μs. MD: femtosecond-picosecond. Long simulations: parallel computing.

Applications

Protein folding, drug design, materials. Solvation, conformational changes. Molecular trajectories.

⚗️ Кінетика реакцій

Arrhenius law

k = A·exp(-E_a/(RT)). Activation energy E_a. Pre-exponential A. Temperature dependence.

Transition state theory

k = (k_B T/h)·exp(-ΔG†/(RT)). Gibbs activation. Eyring equation. Rate-limiting step.

Reaction mechanisms

Elementary steps. Kinetic equations: d[A]/dt. Steady-state, equilibrium approximations.

Collision theory

Hard-sphere collisions. σ: cross section, v: relative speed. k ~ σv exp(-E_a/(RT)).

🔬 Потенціальні поверхні

Born-Oppenheimer

V(R): electronic energy vs nuclear coordinates. Adiabatic separation. Ground-state surface.

Transition states

Saddle points: maximum along reaction, minimum perpendicular. E_a barrier. Imaginary frequency.

Reaction paths

Minimum energy pathways. Intrinsic reaction coordinate (IRC). Dynamics on surface.

Computational methods

DFT, CCSD(T): electronic structure. Transition state search. NEB: nudged elastic band.

💡 Фотохімія

Jablonski diagram

Ground (S₀) → Excited (S₁, S₂...). Spin multiplicity: singlet, triplet. Fluorescence, phosphorescence.

Deactivation processes

Internal conversion (S₂→S₁), intersystem crossing (S₁→T₁), fluorescence (S₁→S₀), phosphorescence (T₁→S₀).

Quantum yields

Φ_i = k_i/Σk_j. Radiative: fluorescence Φ_f, phosphorescence Φ_p. Non-radiative: quenching.

Applications

Photovoltaics, photocatalysis, sensors, lasers. Sunscreen, photodynamic therapy.

⚗️ Каталіз

Heterogeneous

Surface catalysts: Pt, Pd, Ni. Activation, adsorption, reaction, desorption. Industrial processes.

Homogeneous

Solvent-phase: organometallic, enzymes. Mechanisms. Selectivity, turnover frequency.

Enzyme catalysis

Michaelis-Menten: v = V_max[S]/(K_M + [S]). Lock-and-key, induced fit. Specificity.

Mechanisms

Acid-base, redox, coordination. Ligand effects, alloying. Structure-activity relationships.

🔬 Spectroscopy

IR spectroscopy

Vibrational transitions: ν ~ √(k/μ). Fingerprint region: functional groups. Anharmonicity.

UV-VIS

Electronic transitions: π → π*, n → π*. Chromophores. Beer's law: A = εlc.

NMR

Nuclear spin: magnetic field. Chemical shift δ, coupling J. ¹H, ¹³C NMR. Structure determination.

Mass spectrometry

m/z: mass-to-charge. Fragmentation patterns. Isotopes. Identification, quantification.

📊 Графіки та діаграми

Arrhenius plot

ln(k) vs 1/T:

Linear: Arrhenius behavior. Non-linear: temperature-dependent E_a, tunneling.

Jablonski diagram

Energy levels:

Singlet-triplet splitting. Spin-orbit coupling. Quantum yields.

ln(k) = ln(A) - E_a/(RT) Slope: -E_a/R Intercept: ln(A) E_a ~ 20-100 кДж/моль

🧪 Практичні приклади

Приклад 1: Protein folding

MD simulations: microseconds. Folding pathways, intermediates. Force fields: AMBER, CHARMM.

Приклад 2: Haber-Bosch

N₂ + 3H₂ → 2NH₃. Fe catalyst. E_a ~ 335 кДж/моль. Industrial: 150°C, 200 atm.

Приклад 3: Photosynthesis

Chlorophyll: S₀→S₁, energy transfer. Charge separation. Quantum efficiency ~95%.

Приклад 4: Enzyme kinetics

Catalase: H₂O₂ → H₂O + O₂. V_max huge, K_M ~ mM. Specificity.

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Молекулярна динаміка: рух молекул

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