Fig. 2.

Radial probability density distributions ρ(r) = 4πr²|ψ|² for (A) the two lowest-energy S (ℓ = 0) eigenstates in an idealized 3 nm radius spherical CdSe nanocrystal and (B) the lowest-energy eigenstates in 3 nm radius CdSe and PbSe nanocrystals, calculated according to the method described by Brus (17). The discontinuity in the first derivative of the probability density at the nanocrystal surface arises from different effective masses of the electron inside and outside the nanocrystal core. The wave functions of higher-energy eigenstates extend farther beyond the nanocrystal surface, facilitating strong electronic coupling to neighboring nanocrystals or bulk semiconductor substrates.