J. Phys. Chem. C 2008, 112, 20413–20417
20413
Density Functional Study of Surface Passivation of Nonpolar Wurtzite CdSe Surfaces Istvan Csik,*,† Salvy P. Russo,† and Paul Mulvaney‡ Applied Physics, School of Applied Sciences, RMIT UniVersity, Melbourne, Australia, and School of Chemistry, UniVersity of Melbourne, Melbourne, Australia ReceiVed: June 09, 2008; ReVised Manuscript ReceiVed: October 30, 2008
The reconstructed geometries, surface energies, surfactant adsorption energies, and work function have been calculated for the nonpolar (101j0) and (112j0) surfaces of wurtzite CdSe. This study was undertaken in the framework of ab initio density functional theory. Passivation with an amine or phosphine group lowers the surface energy of both nonpolar surfaces. However, thiol passivation of (101j0) increases its surface energy. Both (101j0) and (112j0) tend to maintain their bulklike structure more so when passivated. The surface work function of (101j0) and (112j0) decreased with amine and phosphine passivation; amine had a more marked effect. Thiol passivation, on the other hand, increased the work function of both surfaces studied. Introduction Cadmium selenide, in the bulk, is a type II-VI ionic semiconductor. It can exist as wurtzite, zinc blende, or rock salt phases, which are found at atmospheric pressures, thin film, and higher pressures, respectively.1 Recently, there has been a strong interest in CdSe colloidal nanocrystals and their application as biological markers,2 in quantum-dot lasers,3 and in quantum-dot light-emitting diodes.4 Despite this strong interest, the surface chemistry and growth mechanisms of colloidal semiconductor nanocrystals remain poorly understood. Of major interest is the synthesis of nanocrystals with high quantum efficiency and photoluminescence. To prevent further growth of the individual nanocrystals the surface must be passivated to remove dangling bonds. This passivation is also important to enhance the optical properties for the given application. For highly symmetric cubic structures, such as zinc blende and rock salt, the growth rate of facets is generally not biased toward a particular direction, yielding nanocrystals with no particular direction of growth.5 However, lower symmetry structures, such as hexagonal wurtzite, have a unique polar axis in the [0001] direction.6 CdSe nanocrystals, which often occur in this phase, can be coerced into growing in a number of shapes, including spherical and rodlike.7 Popular methods of surface passivation include capping with trioctylphosphine (TOP) and trioctylphosphine oxide (TOPO),8 alkyl amines, such as octylamine,9 and overcoating the nanocrystals with another semiconductor material.10 In these cases, surface passivation with TOPO usually yields spherical nanocrystals, quantum dots (QDs), whereas passivation with less bulky alkyl amines can promote anisotropic growth, nanorods. Passivation with thiolated molecules improves nanocrystal water solubility and biocompatibility, as well as maintaining smallsized nanocrystals. However, thiolated molecules cause a reduction in nanocrystal quantum yield.11-13 Theoretical studies of CdSe nanocrystals have been carried out with density functional theory (DFT) using the local density approximation (LDA) scheme in order to better understand the * Corresponding author. E-mail:
[email protected]. † RMIT University. ‡ University of Melbourne.
size-dependent properties of nanocrystals.14 For this study cluster sizes in the range of 32-166 atoms were used. Studies of the electronic properties using an empirical pseudopotential method15 for clusters have also been published. The study found that clusters have a strong dipole moment in the c-axis. Semiempirical tight-binding models have been used to study the relaxation of the facets of CdSe nanocrystals up to about 30 Å in radius, which contain approximately 850 atoms.16 These relaxations have been shown to be similar to bulk surface relaxations. The work also found that cluster surface reconstruction removed most of the unphysical surface states from the band gap region, which were present for the unrelaxed systems. The work presented here uses this finding to make various studies of bulk surface reconstructions in the presence of prototypical ligands used for surface passivation of nanocrystals. Passivation studies using a pseudopotential DFT method include thermochemical studies of the growth of nanocrystal facets with the adatom adsorption of Se and Cd on (0001) and (112j0).17 It was found the Se-terminated polar (0001) surface was the primary direction of growth. Alkyl phosphonic acid and methylamine adsorption on the bulk surface (0001), (112j0), and (101j0), in the framework of plane-wave expansion DFT, found that full-coverage passivation decreased the surface energies in all cases. In this work we study the adsorption on the nonpolar (101j0) and (112j0) surfaces in the framework of DFT-GGA (generalized gradient approximation). In particular, we study how the nonpolar (101j0) and (112j0) surfaces of wurtzite CdSe reconstruct when passivated with either the surfactants NH2, PH2, or SH. The primary goal was to determine how the amine, phosphine, and thiol functional groups affect the surface energies, adsorption energies, and the work functions of the surfaces studied as a function of ligand coverage. Methods DFT Calculations. All calculations were performed using the program VASP.19-22 VASP uses a pseudopotential planewave expansion of ab initio DFT. The core electrons for Cd, Se, P, and S were described by ultrasoft pseudopotentials (USPP)23 parametrized for the Perdew-Wang exchange-correlation functional.24 US-PPs were used to remain consistent with our
10.1021/jp805074b CCC: $40.75 2008 American Chemical Society Published on Web 12/03/2008
20414 J. Phys. Chem. C, Vol. 112, No. 51, 2008 previous studies in CdSe. The US-PP method was used previously by the researchers to determine a number of surface properties of CdSe and was found to be in good agreement with experiment.28 The projector-augmented plane-wave (PAW) method was tested against the US-PP method used in this paper. For a number of adsorption system runs tested the geometryoptimized energies obtained using PAWs were comparable to within a few millielectronvolts of the US-PP method. For the Cd (4d105s2), Se (4s24p4), P (3s23p3), and S (3s23p4) ions the outer 12, 6, 5, and 6 valence electrons, respectively, were expressed as truncated plane-wave expanded basis sets. The Cd 4d electrons were treated explicitly as valence electrons, as previous pseudopotential calculations for CdSe found that the Cd 4d electrons made a significant contribution to the band structure.25 Plane-wave kinetic energy cutoff is determined by the pseudopotentials; a 25% increase in default cutoff was used, in the range of about 400 eV. For the lighter ions, N and H, all electron plane-wave basis sets were used. Sampling of the reciprocal k-space was performed using a Monkhorst-Pack mesh.26 An 8 × 8 × 1 reciprocal space mesh was used, which resulted in 64 irreducible k-points. Tests were performed to ensure sufficient total energy convergence for k-point sampling 4 × 4 × 1 and 2 × 2 × 1. The Kohn-Sham wave function was calculated self-consistently in an iterative fashion using an RMMS method. Surfaces. Periodic boundary conditions (PBC), perpendicular to the surface, were used to create an infinite slab for the (101j0) and (112j0) surfaces. Both surface slabs were made up of 10 monolayers so that internal layers exhibited bulklike properties, i.e., negligible ionic reconstruction. Energy convergence was within approximately 7 meV for larger slabs. A 2 × 2 supercell was used for the (101j0) surface passivation, as the surface primitive unit cell contains one surface Cd and one surface Se atom. However, the lower symmetry (112j0) surface contains four atoms, two Cd and two Se; therefore, a 1 × 1 cell was used for this surface. For all simulation slabs, both the top and bottom monolayers were passivated so as not to have to differentiate between them. It is experimentally understood that surfactants bond preferentially with electron-poor Cd surface sites as opposed to electron-rich Se surface sites;5 this has also been theoretically observed.18 Therefore, only passivation of Cd (cation) sites has been studied. For surfaces with two passivation sites (Cd sites) per simulation cell it is only possible to study zero-, half-, and full-coverage passivation. For additional coverage fractions, simulation cells containing slabs of larger surface would be required. As ab initio DFT calculation time is proportional to N3 with the number of electrons in the system, increasing the simulation cell size thereby increasing the number of electrons would have unnecessarily inflated the computational intensity required for the simulations. The surfaces were fully reconstructed in the presence of the surfactants. A three-step optimization/relaxation scheme was used to aid in the convergence of the surface/surfactant system. Initially, the internal bond lengths of the surfactants NH2, PH2, and SH were optimized independently of the surface. For molecules (and atoms) the Bloch theorem does not apply; therefore, a single Γ-centered k-point was used and an energy convergence of 1 × 10-5 eV. An iterative conjugate gradient (CG)27 scheme was used to calculate the ionic relaxation optimization of the surface/ surfactant systems from the ideal surface. For systems which undergo significant relaxation/reconstruction, such as the surfaces studied here, the CG optimization scheme, which optimizes
Csik et al. the expectation value of the Hamiltonian, is an efficient method of optimization if the initial starting guess (surface) is not close to the optimized surface. In this case, the surfaces were relaxed from the ideal surface structure. For each ionic optimization step the ground-state charge density and wave functions are minimized. The surfactants were attached to the surface, at the Cd dangling bond sites, and their height (in the Z-direction) was optimized while the XY freedom was fixed. Second, the surfacelayer atoms, including surfactants, were allowed to relax in the three spacial degrees of freedom (XYZ) and the Hellman-Feynman force minimized in all three directions. For each ionic step the charge density was minimized with a convergence of 1 × 10-5 eV. The nomenclature of the systems studied is the surface with the surfactant subtended; for example, the (101j0) surface passivated with NH2 would be (101j0)-N. Surface Energies. The work function (Φ) for a given surface of a semiconductor such as CdSe is defined as the amount of energy required to remove an electron from the Fermi level (εF) to vacuum (Evac) (infinity)
Φ ) Evac - εF
(1)
For a metal this is equivalent to the electron affinity of the surface. Surface energies, including Φ and εF, can be evaluated from the output of the SCF total energy calculations. The slab method was used to calculate surface energies. The sum of the surface energies (σ) for the top and bottom layers or a relaxed slab is given by
σtop + σbottom ) (Eslab,rlx - nCdSeEbulk)/A
(2)
Eslab,rlx is the total energy of the relaxed slab and A is the area of the slab. For the nonpolar (101j0) and (112j0) surfaces a slab can be created where there is an equal number of species in a layer, nCd ) nSe, giving nCdSe, the total number of CdSe units in the slab. The top and bottom layers become equivalent, i.e., σtop ) σbottom. This equivalence also extends to the passivated systems, as the surfactants were attached symmetrically to the top and bottom surfaces. Therefore, it is not necessary to distinguish between the top and bottom surfaces. Equation 2 can then be simplified to
2σ ) (Eslab,rlx - nCdSeEbulk)/A
(3)
To further elaborate on how these simplifications are derived, Manna et. al18 describe a method to calculate the surface energy using
σtop + σbottom ) Eslab,rlx - nCdµCd - nSeµSe
(4)
where µCd and µSe are the chemical potentials of the two particle reservoirs for Cd and Se, respectively. CdSe is a stable ionic crystal; if it were not, Cd or Se atoms would flow into their respective particle reservoirs yielding bulk Cd and bulk Se. Therefore, one can assume the particle reservoirs are in thermal equilibrium with the bulk CdSe. The chemical potentials can be combined to yield
µCd + µSe ) Ebulk
(5)
For a slab of equal ratio of Cd to Se, nCd ) nSe, this reduces to eq 2. After the surface-surfactant systems were ionically relaxed, the surfactants were removed and the electronic structure of the bare slab was optimized to calculate Eslab,rlx and σ for each of the systems studied.
Surface Passivation of Wurtzite CdSe Surfaces
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20415 TABLE 2: XY Displacement of Cd Atoms Relative to Bulk Atoms in the Same Vertical Axis, i.e., Having the Same Initial (Preionic Relaxation) XY Coordinatesa HCP (101j0)-N (101j0)-P (101j0)-S (112j0)-N (112j0)-P (112j0)-S
HCUP
FC
X
Y
X
Y
X
Y
0.27 0.31 0.29 0.15 0.20 0.27
0.00 0.00 0.00 0.17 0.21 0.38
0.43 0.44 0.40 0.33 0.32 0.27
0.00 0.00 0.00 0.42 0.42 0.19
0.19 0.26 0.19 0.08 0.14 0.18
0.00 0.00 0.00 0.17 0.22 0.38
a Full-coverage (FC) and passivated (HCP) Cd and unpassivated (HCUP) Cd of half-coverage systems. All values in angstroms.
Figure 1. Side (A) and top (C) view of (101j0)-NH2 of the halfcoverage system; also, the side (B) and top (D) view of the respective (112j0)-NH2 system. Cd is the lighter shade, and Se is the darker shade. Note the smaller inward relaxation of the passivated Cd cation (A).
TABLE 1: Z-Direction Displacement (Relaxation) between Surface First-Layer Se and Passivated Cd Atoms for Full-Coverage (FC) and Passivated (HCP) Cd and Unpassivated (HCUP) Cd of Half-Coverage Systemsa (101j0)-N (101j0)-P (101j0)-S (112j0)-N (112j0)-P (112j0)-S a
FC
HCP
HCUP
0.14 0.26 0.02 0.16 0.22 0.06
0.29 0.35 0.27 0.25 0.32 0.25
0.75 0.72 0.61 0.61 0.60 0.72
All values in angstroms.
The calculation of the adsorption energy, Eads, of the surfactant being attached to the system is similar to the calculation of the surface energy and is defined by
Eads ) Eslab+L - Eslab,rlx - EL,gas
(6)
where Eslab+L is the ionically relaxed energy of the slab/surfactant system and EL,gas is the energy of the surfactants. Results Surface/Surfactant Reconstruction. Bond length conserving reconstruction is observed for unpassivated wurtzite CdSe (101j0) and (112j0) surfaces.6,28 Similar reconstruction is observed for the all passivated systems studied here. However, the passivated Cd cations, which relax inward toward the bulk, are pulled outward due to the presence of the surfactants. In other words, passivation has the ability, to a degree, of conserving the ideal nonpolar surface, i.e., maintaining the bulklike structure of the nonpolar surface. Figure 1 shows the (101j0)-N with 50% coverage, where the inward relaxation of the unpassivated Cd is noticeably larger. Table 1 shows the Z-direction displacement, parallel to the surface, of the isolated Cd-Se dimer, included is the Z-displacement for the full-coverage (FC) systems, as well as the Z-displacement of the passivated (HCP) and unpassivated (HCUP) Cd-Se surface dimer.
For FC systems, the presence of S has a more pronounced effect in maintaining the bulklike structure of both the (101j0) and (112j0) surfaces; see Table 1. The PH2 and NH2 surfactants have a reduced effect. Full passivation maintains the bulklike structure more so than half-coverage. This is represented by a smaller Z-displacement shown in Table 1. However, for (112j0)S the unpassivated dimer shows a higher relaxation than for the other respective systems. As mentioned previously, all surfactant-surface systems were allowed to relax in three degrees of freedom. This allows for any reconstruction in the XY plane of the surface atoms. As with the bare surfaces,28 reconstruction in XY is still significant for all the passivated surfaces studied. This reconstruction can be seen in Figure 1, parts C and D, for (101j0) and (112j0), respectively. Reconstruction is visually represented by a transverse movement of the surface atoms with respect to the bulk atoms in the same vertical axis (same XY coordinates), thus slightly exposing the bulk atoms. The (101j0) surface undergoes reconstruction in one degree of freedom in the X-direction, referring to the coordinate system in Figure 1C. For the half-coverage (HC) systems, the passivated Cd atoms (HCP) actually undergo visibly less reconstruction than the unpassivated Cd atom (HCUP). The relative reconstructions are shown in Table 2. The N-, P-, and S-passivated (101j0) systems show comparative X reconstruction. For the HC (101j0) systems, P-passivated Cd atoms show 14% and 6.9% more reconstruction than N- and S-passivated Cd atoms, respectively. Also, for the FC (101j0) systems P-passivated Cd shows 37% more reconstruction than both N- and S-passivated Cd atoms; refer to Table 2. The lower symmetry (112j0) surface undergoes a reconstruction in both X and Y. This is seen graphically in Figure 1D by a slight displacement in both X and Y of surface atoms exposing bulk atoms. Again, the half-coverage surfaces undergo significantly more reconstruction than the FC systems. As with Z-direction relaxation of the (112j0) surface, the systems passivated with S undergo the considerably more reconstruction than the other comparative systems. For the HC (112j0) systems, S passivation of Cd sites shows 100% and 61% more reconstruction than N- and P-passivated sites, respectively. Also, for the FC (112j0) systems S-passivated sites show 2.2 and 1.5 times more reconstruction than both N- and P-passivated Cd atoms, respectively; refer to Table 2. Surface Energies. The surface energies for the passivated systems calculated using eq 3 are shown graphically in Figure 2. In general, passivation at half-coverage significantly reduces the surface energies for both (101j0) and (112j0). Half-coverage systems passivated with N showed a reduction in surface energy for (101j0) and (112j0) of 69% and 36%, respectively. In comparison to the N-passivated systems, half-coverage systems
20416 J. Phys. Chem. C, Vol. 112, No. 51, 2008
Csik et al.
Figure 2. Surface energies, for increasing coverage, for the passivated systems in meV/Å2. The zero surface coverage (unpassivated) surface energies are from Csik et al. (ref 28). Note the increase in surface energy for the (101j0) system.
TABLE 3: Adsorption Energies for the Passivated Systems in eVa (101j0)-N (101j0)-P (101j0)-S (112j0)-N (112j0)-P (112j0)-S
HC
FC
-1.08 -3.01 -3.21 -0.93 -2.90 -3.02
-1.12 -2.98 -3.19 -0.96 -2.81 -2.94
a Note that larger negative values represent a “stronger” adsorption. Note the insignificant change in adsorption energy with increasing coverage.
passivated with P showed a higher reduction in surface energy. In the case of (112j0) and (101j0) passivated with P, passivation reduced the surface energy by approximately 50% and 40%, respectively. However, (101j0) showed a slight increase when passivated with S; this was most likely due to the lack of sufficient Z-direction relaxation of (101j0) in the presence of S. It is known that surface reconstruction reduces the surface energy.28 Interestingly, complete (full-coverage) passivation had the effect of increasing surface energy. This increase in surface energy with passivation was previously reported for polar (0001), where the surface was passivated with methylamine and methyl phosphonic acid.18 This characteristic was attributed to the final attached surfactant putting too much electronic density into the bond. However, in the case of the nonpolar (101j0) and (112j0) surfaces, the lack of surface reconstruction for the fully passivated systems can be most likely attributed to the increase in surface energy. Adsorption Energies. The adsorption energies for all passivated systems were calculated using the method described in the Surface Energies section. For each of the surfactants, N, P, and S, adsorption onto (101j0) surfaces was approximately 15-19% “stronger” or higher than on the equivalent (112j0) surfaces; refer to Table 3. The adsorption energy also increases with atomic mass of the surfactant species. For example, S is approximately 3 times more strongly bonded to the surface than N and is approximately 7% more strongly bound than P. Increasing passivant coverage, from 50% to 100%, does not significantly change the adsorption energy of the surface; the change is less than 2.5%. This is a verification of work by Manna et al.,18 who assumed that for nonpolar facets (surfaces)
Figure 3. Change in work function, in eV, from the ideal surface, to the relaxed (real) surface, to the half-coverage (HC), to full coverage (FC) of the six systems studied. Note the increase in work function for the S-passivated systems.
the adsorption energy, or in their case the removal energy, is independent of surface coverage. This was explained by the electron counting rule, where removing one surfactant and in turn creating one Cd dangling bond does not significantly redistribute surface electrons. Work Function. The work function was calculated for all systems studied. Figure 3 shows the change in work function, Φ, from the ideal (unreconstructed), Φi, to the reconstructed surface, Φi,28 then from half-coverage to fully passivated for all six systems studied. For (101j0), the work function increases as the surface is reconstructed, from 5.15 to 5.79 eV. Passivation with N and P decreases the work function, with increasing surface coverage. For (101j0), 50% NH2 and PH2 passivation decreases the work function to 5.16 and 5.40 eV, respectively. This corresponds to a decrease of 0.64 and 0.39 eV, for N and P passivation, respectively. Full surface passivation with N and P further decreases the surface work function to 5.01 and 5.30 eV, respectively. Similarly, the (112j0) undergoes an increase in work function as the unpassivated surface reconstructs, from 5.30 to 5.89 eV. This increase is proportional to the change in (101j0). Passivation of the (112j0) with N and P leads to a greater decrease in surface work function; see Figure 3. The work function of (112j0) decreases with increasing surface passivation with N and P, at 50% coverage to 5.14 and 5.33 eV, respectively. Full passivation of (112j0) with N and P further decreases the work function to 4.83 and 5.23 eV, respectively. This corresponds to a decrease of 0.31 and 0.10 eV for N and P, respectively. Passivation with the amine group, for both surfaces studied, has a more marked effect on reducing the surface work function than the phosphine group. Passivation with a thiol group, however, actually increases the surface work function. For halfcoverage systems, this increase is 0.33 and 0.07 eV for (101j0) and (112j0), respectively. Increasing coverage of (112j0) with S does not increase the surface work function. However, passivation with the thiol group further increases the surface work function, with increasing surface coverage, of (101j0) by 0.14 eV. The reduction in surface work function cannot be solely attributed to the reduction in surface reconstruction in the presence of surfactants, as passivation with S of (101j0) shows similar XY reconstruction and higher Z relaxation relative to the N- and P-passivated systems.
Surface Passivation of Wurtzite CdSe Surfaces Discussion and Conclusions To better understand surfactant adsorption on nanocrystal facets, a computational study of the (101j0) and (112j0) surfaces was made using PBCs in the framework of ab initio DFT. The adsorption with NH2, PH2, and SH onto electron-poor Cd sites showed bond length conserving reconstruction for both surfaces studied. Cd adsorption sites underwent less reconstruction than corresponding unpassivated Cd sites. S adsorption showed the most bulklike conservation for both (101j0) and (112j0). For most systems studied, surface passivation reduces the nonpolar surface energy. However, increasing surface passivation sees a slight increase in surface energy. This is likely due the lack of energy-lowering reconstruction in the fully passivated systems. Also, it could be attributed to the second adsorbed surfactant putting too much electronic density into the bond.18 Passivation with P for both (101j0) and (112j0) showed the highest reduction in surface energy, then followed by N. This trend could start to shed light on the experimental observations that phosphine and amines tend to produce QDs and nanorods, respectively, since, phosphine has a higher ability to reduce surface energies, thereby producing lower energy structures, i.e., QDs. One must remember, however, the ligands used in this study are only primitive rudiments of TOPO and octylamine. Further studies incorporating all the prototypical surfaces of both morphologies would have to be made before making any concrete conclusions about this. However, for (101j0) S passivation increased the surface energy. This errant result was mostly likely due to the lack surface reconstruction shown by the (101j0)-S system. Increasing surface passivation, 50% to 100% coverage, slightly increased the surface energy. The observations that thiolated molecules reduce quantum yield11 could be associated with this observed increase in surface energy. However, the 101j0 surface is one of several prototypical facets associated with QDs. The adsorption energy increased with the atomic mass of the adsorption species. Also, increasing surface coverage had no significant effect on the adsorption energy. It is assumed the addition of an extra surfactant does significantly redistribute the nonpolar surface electronic density, thereby not affecting the adsorption energy. The work function of (112j0) is approximately 3% higher than for (101j0). When the unpassivated surface undergoes reconstruction the surface work function increases; both surfaces show a similar increase. As the surfaces are passivated, at 50% coverage, with N and P, the surface work function decreases. Passivation with P has a more marked effect in reducing the surface work function than N. Increasing surface coverage with N and P also further decreases the surface work function for both (101j0) and (112j0). On the other hand, S adsorption
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20417 increases the surface work function, in the case of (101j0) increasing the S surface coverage further increased the work function. As discussed above with regard to surface energy, the increase in work function could be associated with an observed reduction in quantum yield and photoluminescence found experimentally with nanocrystals passivated with thiolated molecules. Acknowledgment. This work was supported by the Australian Centre of Advanced Computing (APAC) and Victorian Centre of Advanced Computing (VPAC). References and Notes (1) Zakharov, O.; Rubio, A.; Cohen, M. L. Phys. ReV. B 1995, 51, 4926–4930. (2) Parak, W. J.; Gerion, D.; Pellegrino, T.; Zanchet, D.; Micheel, C.; Williams, S. C.; Boudreau, R.; Gros, M. A. L.; Larabell, C. A.; Alivisatos, A. P. Nanotechnology 2003, 14, R15-R27. (3) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H. J.; Bawendi, M. G. Science 2000, 290, 314–317. (4) Coe, S.; Woo, W. K.; Bawendi, M.; Bulovic, V. Nature 2002, 800– 803. (5) Lee, S. M.; Jun, Y. W.; Cho, S. N.; Cheon, J. J. Am. Chem. Soc. 2002, 124, 11244. (6) Wang, Y. R.; Duke, C. B. Phys. ReV. B 1988, 37, 6417. (7) Peng, Z. A.; Peng, X. G. J. Am. Chem. Soc. 2002, 124, 3343– 3353. (8) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706–8715. (9) Mulvaney, P.; Bullen, C. Langmuir 2006, 22, 3007–3013. (10) Dabbousi, B. O.; Rodriguez-Viejo, J.; Mikulec, F. V.; Heine, J. R.; Mattoussi, H.; Ober, R.; Jensen, K. F.; Bawendi, M. G. J. Phys. Chem. B 1997, 101, 9463–9475. (11) Breus, V. V.; Heyes, C. D.; Nienhaus, G. U. J. Phys. Chem. C 2007, 111, 18589–18594. (12) Reiss, P.; Bleuse, J.; Pron, A. Nano Lett. 2001, 2, 781. (13) Chan, W. C.; Nie, S. Science 1998, 281, 2016. (14) Sarkar, P.; Springborg, M. Phys. ReV. B 2003, 68, 235409–7. (15) Rabani, E.; Hetenyi, B.; Berne, B. J.; Brus, L. E. J. Chem. Phys. 1999, 110, 5355–5369. (16) Leung, K.; Whaley, K. B. J. Chem. Phys. 1999, 110, 11012–11022. (17) Rempel, J.; Trout, B.; Bawendi, M.; Jensen, K. J. Phys. Chem. B 2005, 109, 19320–19328. (18) Manna, L.; Wang, L. W.; Cingolani, R.; Alvisatos, A. P. J. Phys. Chem. B 2005, 109, 6183–6192. (19) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, RC558. (20) Kresse, G. Ph.D. Thesis, Technische Universita¨t Wien, 1993. (21) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15–50. (22) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (23) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (24) Perdew, J. P.; Wang, Y. Phys. ReV. B 1989, 40, 3399. (25) Schroer, P.; Kruger, P.; Pollmann, J. Phys. ReV. B 1993, 48, 18264– 18267. (26) Pack, J. D.; Monkhorst, H. J. Phys. ReV. B 1977, 16, 1748. (27) Meter, M. P.; Payne, M. C.; Allan, D. C. Phys. ReV. B 1989, 40, 12255. (28) Csik, I.; Russo, S. P.; Mulvaney, P. Chem. Phys. Lett. 2005, 414, 322.
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