The band gaps, band structure, and excited-state (exciton) energies of CdS, GaAs, and GaP semiconductor clusters are calculated using pseudopotentials. In addition, the sensitivity of the exciton energies to the size, shape, crystal structure, and lattice constant of the unit cell are investigated. The calculated exciton energies of CdS clusters are in excellent agreement with experiment over a wide range of cluster sizes. Also, the exciton states of small CdS clusters are sensitive to whether their crystal structure is zinc blende or hexagonal. Such a sensitivity is absent in large CdS clusters. Furthermore, small GaAs clusters are shown to exhibit anomalous redshift of their absorption spectra, in sharp contrast to CdS and large GaAs clusters whose spectra always shift to blue with decreasing cluster size. Finally, the lowest-energy non-Franck–Condon transition in GaP clusters always shifts to blue with decreasing cluster size, whereas the higher-energy Franck–Condon transition in small clusters exhibits the anomalous redshift. These novel findings reveal that (1) the optical spectroscopy of semiconductor clusters is strongly material and crystal structure dependent; (2) the spectroscopy of small clusters is dramatically different from those of large clusters and bulk; and (3) these effects cannot be explained, even qualitatively, using the effective-mass approximation.

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Theoretical methods are developed for determining the collective vibrational excitation spectra of quantum clusters, and applied to clusters of 4He. A quantum liquid drop model gives excitation energies in terms of two-point ground state density correlations, which are evaluated from microscopic calculations of the ground state wave functions. An alternative approach based on a Bijl–Feynman ansatz for the excited states also yields excitation energies in terms of ground state correlations, without the imposition of a sharp liquid surface. These methods are applied to the calculation of the excitation spectra of 4HeN , N=20, 70, and 240 clusters. The relationship between the collective spectra of these clusters and that of bulk fluid He II, and the significance of an observed roton minimum in the spectrum for N≥70 are discussed.

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The ground and several l=0 breathing mode vibrational excited state wave functions of HeN clusters are determined for N=3–5, 20, 70, and 240, using the variational Monte Carlo method. These wave functions incorporate one-, two-, and three-particle correlation effects and give binding energies, density profiles, and vibrational excitation energies accurately. The larger clusters have liquid-like structure, characterized by a pair distribution function showing approximately two coordination shells. The smallest clusters (N=3, 4) have extensively delocalized structures, which on average are equilateral triangular and tetrahedral, respectively. The N=5 cluster has a totally symmetric average structure, which can only be described in terms of a quantum liquid. No molecular structure, whether rigid or floppy can be assigned in this case. The relative importance of various correlation effects in clusters of different sizes is analyzed and discussed. These wave functions are completely analytical and are convenient as importance functions in diffusion and Green’s function Monte Carlo calculations.