Physics / advanced
Molecular motion and quantum bonding
Separate and reconnect electronic, vibrational, and rotational molecular dynamics, emphasizing symmetry, spectroscopy, and the limits of Born-Oppenheimer reasoning.
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Module 01 advanced
Molecular motion and quantum bonding
Separate and reconnect electronic, vibrational, and rotational molecular dynamics, emphasizing symmetry, spectroscopy, and the limits of Born-Oppenheimer reasoning.
- 01
Born–Oppenheimer separation and potential surfaces
Construct nuclear potential surfaces from clamped electronic states and identify the mass, gap, and derivative-coupling assumptions behind a single-surface description.
27 min - 02
The hydrogen molecular ion and bonding
Use a nonorthogonal two-orbital variational model to explain one-electron bonding while comparing total molecular energy with a declared dissociation threshold.
27 min - 03
Molecular orbitals and electronic symmetry
Use molecular symmetry to organize orbital mixing and distinguish one-electron labels, many-electron states, and qualitative bond-order counts.
26 min - 04
Rigid-rotor levels and rotational spectra
Relate reduced mass and bond length to rotational energies, track frequency versus wavenumber units, and identify electric-dipole and Raman probes.
26 min - 05
Anharmonic vibrations and Morse potentials
Use the Morse model to separate local force constants, decreasing vibrational spacings, dissociation thresholds, and isotope-dependent zero-point energy.
28 min - 06
Rovibrational selection rules
Connect dipole and polarizability matrix elements to IR and Raman activity, then calculate elementary P and R branches within stated electronic symmetry.
27 min - 07
Franck–Condon factors and electronic transitions
Factor electronic and nuclear transition amplitudes, derive a displaced-oscillator progression, and separate overlap weights from complete measured intensities.
27 min - 08
Conical intersections and nonadiabatic coupling
Resolve a two-surface degeneracy in its branching plane and distinguish adiabatic energies, diabatic couplings, and actual nuclear transition dynamics.
28 min - 09
Molecular spin statistics and identical nuclei
Enforce total nuclear exchange symmetry, count symmetric and antisymmetric spin states, and connect allowed rotations to spin-isomer populations.
28 min - 10
Van der Waals forces and long-range potentials
Derive the attractive nonretarded dispersion tail from virtual dipole coupling, distinguish energy from force scaling, and interpret empirical short-range models cautiously.
28 min