The Born-Oppenheimer approximation states that as the motion of electrons in orbitals are much quicker than the nuclear vibrational motions, the electrons can immediately change their distribution according to the slow movement of nuclei. This assumption can be used to mathematically treat the nuclei and the electrons independently.
This also means that we can calculate the electronic energy at whatever nuclear configuration. This is a great approximation when the system is a stable organic molecule in its ground state with zero or little interaction with its excited states. When there are two or more states of the same energy with the same nuclear geometry, there is resonance in the wavefunctions and the Born-Oppenheimer approximation is no longer effective.
Unraveling the Enigma: Zero-Knowledge Proofs in Blockchain
Security and privacy have emerged as critical concerns in the rapidly growing realm of blockchain technology. The concept of Zero-Knowledge Proofs (ZKPs) is one…