(Hyper)polarizabilities of GaN, GaP, and GaAs Clusters:  An Ab Initio Time-Dependent Hartree−Fock Study

Abstract

The (hyper)polarizabilities of GaN, GaP, and GaAs clusters have been calculated using an ab initio timedependent Hartree-Fock method and an even-tempered Gaussian basis set. The geometries of the clusters used in the study were optimized by ab initio Hartree-Fock calculations using the same basis set. The clusters used in this calculation are of the type Ga m X n (m ) 1, 3, 4 and n ) 1, 3, 4) where X ) N, P, or As. The Ga m X n clusters are in a charge neutral (q ) 0) state for m ) n and in an appropriately charged state for m * n. All of the clusters studied are stable in a nearly tetrahedral geometry. The magnitude of the calculated (hyper)polarizabilities appears to depend on the size of the cluster. The cluster-size dependence of calculated (hyper)polarizabilities is more pronounced for the first hyperpolarizability, β, than for the polarizability, R. The calculated frequency-dependent polarizability, R(ω), exhibits a small but finite dispersion with the frequency of the optical field. The magnitude of the calculated β(-ω σ ;ω 1 ,ω 2 ) corresponding to various second-order effects shows the expected trend of β(-2ω;ω,ω) > β(-ω;0,ω) > β(0;0,0).

Size-dependence of the Linear and Nonlinear Optical Properties of GaN Nanoclusters

“…This suggests that the computed value of the linear polarizability computed at the DZP(1p,1d) level for m=17 should be a reasonable estimate of the polarizability one would obtain from a larger calculation. The values we compute for the dipole moments and linear polarizabilities for m=1 and 4(o) are in rough agreement with the results obtained by Korambath et al [7] who noted that the polarizability of clusters depended in an approximately linear fashion on the number of GaN units in the cluster. Our value for the polarizability per GaN unit is slightly larger however.…”

“…An important issue in a bottom-up approach to fabricating nanoclusters for future technological applications is an understanding of the evolution of their response properties with cluster size and shape. Theoretical work on atomic clusters of III-V semiconductors have examined the electronic structure and stability of small clusters using density functional theory [4,5] and their linear and non-linear optical properties using the ab initio time dependent HartreeFock formalism [6,7,8] as well as time-dependent density functional theory [9]. Work by Kandalam et al suggests that as cluster sizes increase a transition from low energy planar to bulk-like 3-D structures occurs in some nitrides [4].…”

Surface bonding effects in compound semiconductor nanoparticles: II

“…In these cases, the bond around the metal angle is less acute than that around the X atom with the M-M distance being the closest homonuclear distance. In contrast, Ga 2 N 2 is also a rhombus, but the situation is reversed with the N-Ga-N angle being most acute, and the In contrast, for the M 3 X 3 cluster, a buckled six-membered ring with alternating M and X atoms appears to be the most stable configuration not only for Zn 3 S 3 , Zn 3 Se 3 , Cd 3 S 3 and Cd 3 Se 3 but also for Ga 3 N 3 (10,11,28). Ga 3 As 3 shows a different structure, however.…”

“…GaAs clusters have been modeled by various groups including Chelikowsky and coworkers (15,16) and others (17)(18)(19)(20)(21)(22)(23)(24)(25). GaN clusters have also been studied by Pandey and coworkers (26)(27)(28) as well as others (29)(30)(31)(32). AlP has also been studied by a number of investigators (33)(34)(35)(36)(37).…”

Charge-Transfer Induced Large Nonlinear Optical Properties of Small Al Clusters: Al4M4 (M = Li, Na, and K)

“…Also, there have been previous efforts to calculate the NLO coefficients in inorganic clusters like GaN, GaP and GaAs [32]. These systems have higher gap than the Al 4 M 4 clusters so the NLO coefficients are smaller.…”