Фізика молекул та міжмолекулярних взаємодій

⚛️ Молекулярна структура

Born-Oppenheimer

Electronic + nuclear separation. V(R): potential energy surface. Ground-state electronic structure.

Bond lengths

C-C ~ 1.54 Å, C-H ~ 1.09 Å, O-H ~ 0.96 Å. Covalent radii, hybridization.

Bond angles

Tetrahedral ~109°, trigonal ~120°, linear 180°. VSEPR theory, geometry.

Electronic structure

MO theory, hybridization. HOMO, LUMO. Ionization energies, electron affinities.

🌊 Vibrational modes

Harmonic oscillator

ν = (1/2π)·√(k/μ). Normal modes: symmetry. 3N-6 (nonlinear), 3N-5 (linear).

IR spectroscopy

800-4000 см⁻¹ range. Fingerprint region. Functional groups. Beer's law: A = εlc.

Anharmonicity

Morse potential: V = D_e(1-e^(-a(r-rₑ)))². Overtones, combination bands, Fermi resonance.

Raman

Inelastic scattering. Symmetry selection. Complementary IR. Polarizability changes.

🔬 Rotational spectra

Rigid rotor

E_J = J(J+1)ℏ²/(2I). Microwave: pure rotation. J = 0,1,2... quantum number.

Rotational constant

B = ℏ²/(2I). Bond length determination. Isotopic substitution. Reduced mass μ.

Selection rules

ΔJ = ±1, ΔM_J = 0,±1. Permanent dipole moment required. Frequency spacing.

Nuclear statistics

Bosonic vs fermionic nuclei. H₂: ortho-para ratios. Nuclear spin coupling.

🔗 Intermolecular forces

Van der Waals

London dispersion: V ~ -C/r⁶. Temporary dipole-induced dipole. ~0.1-10 кДж/моль.

Dipole-dipole

V ~ -μ₁μ₂/(r³). Permanent dipoles. ~1-50 кДж/моль. Alignment dependence.

Hydrogen bonding

H...X (X=O,N,F). ~10-50 кДж/моль. H₂O, DNA, proteins. Directional.

Aggregation

Liquids, solids formation. Cohesive energy. Intermolecular distance optimization.

🔗 Polymers

Chain conformations

Random walk, Gaussian coil. R_g ~ N^(3/5) good solvent, N^(1/2) Θ. Self-avoidance.

Transitions

Glass transition T_g, melting T_m. Crystalline, amorphous phases. DSC.

Viscoelasticity

Relaxation times, modulus. Storage G', loss G''. Frequency-dependent behavior.

Molecular weight

Distribution M_n, M_w. Polydispersity M_w/M_n. Size exclusion chromatography, light scattering.

🔬 Electronic spectroscopy

UV-VIS

Electronic transitions: π→π*, n→π*. Chromophores, conjugation. Beer's law.

Fluorescence

S₁→S₀ emission. Stokes shift. Quantum yield Φ. Lifetime τ ~ ns. FRET.

Phosphorescence

T₁→S₀ emission. τ ~ ms-s. Spin-forbidden, weak. Enhanced heavy atoms.

Photochemistry

Excitation, energy transfer, electron transfer. Quantum yields, mechanisms.

📊 Графіки та діаграми

Morse potential

V(r) для vibrations:

Anharmonicity: asymmetry, overtones. Morse: realistic bond potential.

Rotational spectrum

E_J spacing:

Pure rotation: ΔJ=±1. Spectroscopic constant B.

V(r) = D_e(1 - e^(-a(r-rₑ)))² V_harmonic ≈ k(r-rₑ)²/2 а ≈ 0.1-1 Å⁻¹ Dissociation D_e

🧪 Практичні приклади

Приклад 1: Water molecule

O-H ~ 0.96 Å, angle ~104°. Hydrogen bonding: lattice. Ice structure, liquid properties.

Приклад 2: CO₂ molecule

Linear: O=C=O. Symmetric stretch ν₁ (Raman), asymmetric ν₃ (IR). Greenhouse gas.

Приклад 3: DNA helix

Hydrogen bonding: A-T, G-C pairs. Double helix stability. Melting temperature T_m.

Приклад 4: Polyethylene

-(CH₂-CH₂)_n-. T_g ~ -120°C, T_m ~ 130°C. Crystalline, amorphous. MW distribution.

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Молекули: динаміка та спектроскопія

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