Electronic energy as a function of nuclear coordinates — the foundation of molecular quantum chemistry
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Born-Oppenheimer: Nuclei are 1000x heavier than electrons, so electrons relax instantly as nuclei move. The electronic energy E(R) as a function of nuclear coordinate R is the Potential Energy Surface (PES). Nuclei move on the PES via quantum mechanics — vibrational levels are quantized by ℏω(n+½). Molecular bonding, dissociation, and chemical reactions are governed by PES topology.