Path integral study of the correlated electronic states of Na₄–Na₆

Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na₄–Na₆. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results show that the electrons are localized, rather than delocalized as previous workers have concluded from examination of the single‐particle orbitals. We find that the best picture of these clusters is that they contain three‐center, two‐electron bonds.