The Born-Oppenheimer approximation separates electronic and nuclear motion. At leading order, fixed nuclear positions and electric charges specify an electronic potential energy curve, on which the atomic nuclei move with their own masses.
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The Born-Oppenheimer approximation is a fundamental concept in molecular quantum mechanics that simplifies the study of molecular systems by decoupling the motion of nuclei and electrons. The core idea is based on the significant difference in mass between nuclei (which are heavy) and electrons (which are much lighter). This mass difference leads to different time scales for their motions.
