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The original equation that describes the motion of electrons and ions is complicated to solve. Exact and analytical solutions can be found for only simple systems like a hydrogen atom. Even numerical solutions are very challenging to find for small systems. Today’s most powerful supercomputer cannot even solve the Schrödinger equation for a sodium (Na) atom with 11 electrons. We need to introduce approximations to overcome this challenge. Born-Oppenheimer approximation is often used to decouple the motion of electrons and ions since electrons move much faster than ions. Then, we can put the coordinates of ions as parameters of the electron’s wavefunctions.

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First-Principles Methods and Atomistic Simulations

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  • 发表日期：

    2026年

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  • Zongrui Pei

摘要

The original equation that describes the motion of electrons and ions is complicated to solve. Exact and analytical solutions can be found for only simple systems like a hydrogen atom. Even numerical solutions are very challenging to find for small systems. Today’s most powerful supercomputer cannot even solve the Schrödinger equation for a sodium (Na) atom with 11 electrons. We need to introduce approximations to overcome this challenge. Born-Oppenheimer approximation is often used to decouple the motion of electrons and ions since electrons move much faster than ions. Then, we can put the coordinates of ions as parameters of the electron’s wavefunctions.