Nuclear and electronic motion can be separated because nuclei are much heavier.
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The Born-Oppenheimer approximation assumes that nuclei are much heavier than electrons, so electrons respond almost instantly to any nuclear motion. This allows the electronic Schrodinger equation to be solved for fixed nuclear positions, giving the electronic energy as a function of geometry. Repeating this for many geometries gives a potential energy surface on which the nuclei move. The approximation separates electronic and nuclear motion and is the basis for nearly all molecular quantum chemistry, including the concepts of molecular geometry and vibration. It fails when potential energy surfaces come close together, as in some photochemical processes and conical intersections.
Key ideas: Mass of a proton is about 1836 times that of an electron, so electrons adjust almost instantly. Total wavefunction is approximated as electronic times nuclear. The potential energy surface depends on 3N minus 6 coordinates (3N minus 5 for linear molecules). Minima are stable structures, saddle points are transition states, and vibrational frequencies come from curvature at a minimum.
Common mistakes and connections: Students think nuclei are fixed in reality, but the approximation only separates the time scales. It breaks down for light nuclei (proton transfer), near avoided crossings, and in photochemistry and Jahn-Teller systems. Isotopes share the same electronic surface, which is why isotope effects arise from nuclear motion only. Related to potential energy surfaces, vibrations and reaction pathways.
Solving the electronic problem at many fixed H-H distances gives the H2 potential energy curve, with a well of about 4.75 eV, on which the nuclei move. The interactive lesson shows this as a live animation or chart.
The potential energy curve of the H2 molecule is obtained by solving the electronic problem at many fixed H-H distances.
Nuclear and electronic motion can be separated because nuclei are much heavier.
Born-Oppenheimer Approximation is a advanced topic in Analytical, Lab & Spectroscopy. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in Analytical, Lab & Spectroscopy first: Density Functional Theory, Molecular Dynamics, Hartree-Fock Method.
The next topics in Analytical, Lab & Spectroscopy are Particle in a Box and Harmonic Oscillator Model.
Yes. The interactive lesson includes a self-check question on Born-Oppenheimer Approximation, and the Analytical, Lab & Spectroscopy quiz draws on every topic in this area.
Born-Oppenheimer Approximation is topic 87 of 99 in Analytical, Lab & Spectroscopy.