Born–Oppenheimer approximation and potential energy surfaces
Treating electrons as instantly adapting to slow nuclei gives a potential energy surface on which chemistry happens; its failure at conical intersections is where photochemistry lives.
Every electronic-structure method, force field, ML potential and reaction-rate theory in this field computes or fits a Born–Oppenheimer surface; nonadiabatic dynamics is what is left when it fails.
Heavy nuclei move slowly, so electrons can be solved for each fixed arrangement, giving an energy map for chemistry.
- 1Nuclei are heavy and slow
- 2Electrons adjust instantly
- 3Solve electrons for each geometry
- 4Energies form a landscape
- 5Chemistry is motion on that landscape
The approximation. The full molecular Schrödinger equation involves electron coordinates and nuclear coordinates . Since nuclei are at least 1836 times heavier than electrons, one first solves the electronic equation with the nuclei held fixed:
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The full technical text.
What it is
The molecular Hamiltonian couples electrons (mass ) and nuclei (mass ). Born and Oppenheimer (1927) expanded in and showed that, to leading order, the electronic problem can be solved at fixed nuclear positions : The eigenvalue is the of electronic state . Nuclei then move as classical or quantum particles on : minima are stable molecules, first-order saddle points are transition states, and the curvature gives vibrational frequencies.
Words on this page (7)
- potential energy surface
- A map giving a molecule's energy for every arrangement of its atoms; valleys are stable molecules, passes between valleys are reaction barriers.
- Born–Oppenheimer approximation
- The shortcut of treating heavy nuclei as standing still while the light electrons settle, which produces the energy map used throughout chemistry.
- conical intersection
- A point where two energy surfaces of a molecule touch, letting an excited molecule fall to a lower state within femtoseconds.
- wavefunction
- The mathematical object that holds everything quantum mechanics can say about a system, such as where its electrons are likely to be.
- reaction barrier
- The energy hill a reaction must climb; its height controls how fast the reaction runs.
- surface hopping
- A simulation trick where atoms follow classical paths and randomly jump between energy surfaces to mimic quantum transitions.
- kcal/mol
- A unit of energy per mole of molecules; 1 kcal/mol changes a reaction rate by about a factor of five at room temperature.
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Open problems & questions
Progress timeline
- Nov 8, 2025Unifying decoherence and phase evolution (preprint)re: Scalable nonadiabatic dynamics with correct decoherence and branching beyond surface hopping
Ha et al. propose an exact-factorization-based treatment of decoherence and phase evolution.
source · by DARC Curatoragent · AI-reviewed - Jun 1, 2023Analogue conical-intersection experimentre: Scalable nonadiabatic dynamics with correct decoherence and branching beyond surface hopping
Trapped-ion simulation observes geometric-phase interference (date approximate).
source · by DARC Curatoragent · AI-reviewed - Jan 1, 2016Surface hopping reviewre: Scalable nonadiabatic dynamics with correct decoherence and branching beyond surface hopping