PHYSICA E

Volume 41, Issue 7, Pages: 1151–1156, 2009

Preprint

Opto-

germ

�

DOI: http://dx.doi.org/10.1016/j.physe.2008.12.021

Opto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

Farah Marsusi a, Kavoos Mirabbaszadeh b,�, G. Ali Mansoori ca Department of Physics, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iranb Department of Physics & Nanotechnology Research Center, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran

ngineer

ic pr

0H16perti

Our 16 are positive. Electronic properties and optical gaps resulting from hybrid

ment with quantum Monte Carlo results.

c Departments of Bio & Chemical E

Keywords:

Abstract:We present the opto-electron

and germa-adamantane (Si1shown that the electronic proaffected by hydrogen atoms.

those of Si10H16 and Ge10H

functionals are in close agree

electronic properties, Adama

a-adamantane Electron affini

Corresponding author. Tel.: +98216

+982166419506.

Email addresses: marsusi@aut.ac.ir (F. Mars

mirabbas@aut.ac.ir (K. Mirabbamansoori@uic.edu (G.A. Man

ing and Physics, University of Illinois at Chicago, Chicago, IL 60607-7052, USA

operties of adamantane (C10H16) compared to hydrogen-terminated sila- and Ge10H16) as calculated by the density functional theory. We have es of adamantane in comparison to sila- and germa-adamantane are morecalculations show that the electron affinity of C10H16 is negative, while

ntane, Hydrogen-terminated sila-adamantane Hydrogen-terminated ty, Hybrid functionals, Nanoelectro-mechanical systems

1. Introduction

Diamondoids were first discovered and isolated from petro-leum in 1933. They have diamond-like fused-ring structures. Therigidity, strength, and assortment of their three-dimensionalshape make them valuable molecular building blocks fornanotechnology. Adamantane (C10H16) is the simplest of thesepolycyclic diamondoids. The unique structure of adamantane isreflected in its highly unique physical and chemical properties,which can have many applications in nanotechnology [1–3].Recently, theoretical simulations of quantum conductance ofC10H16 have shown that it is electronically an insulator. However,its derivatives have interesting electronic properties, which makethem useful for building nanoelectro-mechanical systems (NEMS)and other nanoscale logic units [4].

4542585; fax:

usi), szadeh), soori)

1151

Small semiconductor nanoclusters exhibit quite differentoptical properties, including luminescence, optical gap, andoscillator strength from those of bulk size. Confinement of asystem into three dimensions results in a blue shift of thecharacteristic transition energy such as exciton binding energy(Eex) [5]. Experimentally, deposited Si [6] and Ge [7] nanocrystalswith sizes above 1 nm exhibit clear, theoretically confirmedquantum confinement (QC) effects. But recent experimentalinvestigations have shown that contradictory to other group IVsemiconductors, diamondoids do not exhibit a size-dependentblue shift as expected within the QC model [8]. On the other hand,theoretical studies of the size-dependent QC and some other opto-electronic properties such as electron affinities (EA) of diamond-oids have produced contradictory results. Raty et al. [9] concludedthat the QC disappears in diamondoids with sizes larger than1 nm. In contrast, McIntosh et al. [10] predicted that for particlesranging in size between 0.5 and 2 nm the bandgaps are at least0.8 eV above the gap of bulk diamond. Additionally, in anothertheoretical study of diamondoids positive EAs were reported [11].However, in some other works negative values have been obtained[12,13]. The negative EA of a functionalized diamondoid wasrecently verified experimentally, and highly monochromaticphotoelectron emissions from tetramantane-6-thiol film on theAu substrate were obtained [14].

In this paper, we have analyzed the opto-electronic propertiesof adamantane with the density functional theory (DFT) method.

F. Marsusi, K. Mirabbaszadeh, G.A. MansooriOpto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

PHYSICA E 41(7): 1151–1156, 2009

For a more comprehensive study, we have compared theseproperties to their corresponding H-terminated sila- (Si10H16)and germa-adamantane (Ge10H16). H-terminated sila- and germa-adamantane are tricyclic cage-shaped Si10 and Ge10 lattices withthe same structure as adamantane and can be considered to bethe smallest repeated unit of crystallized silicon and germanium,respectively [15]. In contrast to silicon nanoclusters, which havebeen extensively studied both experimentally and computation-ally, for germanium nanoclusters theoretical studies have beenlimited. Optical properties of both Si and Ge nanoclusters aresignificantly affected by their QC effects [6,7]. Visible lightemissions from porous silicon [16] and photoluminescence inthe near-infrared region from Ge nanoclusters [17] result fromtheir QC effect.

We have investigated the effects of functionals and basis setson the gaps between the highest occupied molecular orbital(HOMO) and the lowest unoccupied molecular orbital (LUMO) ofthese molecules. We also compared our DFT results with thequantum Monte Carlo (QMC) outcomes from previous works. Ithas been seen that the experimental relative bandgaps ofdiamondoids are in good agreement with the QMC results [18].In this article, the anomalous electronic properties of C10H16 arehighlighted in comparison to those of Si10H16 and Ge10H16. Such amethodology can help us to explain distinct characteristicproperties of diamondoids with more reliable theoretical schemesat a rather low computational effort. We compare the HOMO–LUMO gaps and the EAs of these nanoparticles. Besides, thesequantities along with the calculated Eexs of adamantane andsila-adamantane are compared to the corresponding results ofQMC. According to our calculations the electronic gaps obtainedfrom hybrid functionals are in good agreement with QMC. Wehave also found that, compared to Si and Ge nanoparticles oneshould take care of the basis set in DFT calculations of diamond-oids. Our calculations confirmed that in contrast to Si10H16

and Ge10H16, C10H16 has negative EA, which corresponds to thedifferent nature of dipole moment of charge distribution onits surface.

Table 1Calculated bond lengths (A) at the various levels of the theory and from Aug-cc-

pVDZ basis sets for C10H16, Si10H16, and at B3LYP/6-31+G** for Ge10H16.

Bond length B3LYP PBE1 BLYP PBE LDA

C–C 1.543 1.533 1.555 1.544 1.523

C–H (for CH) 1.100 1.100 1.107 1.109 1.109

C–H (for CH2) 1.101 1.101 1.108 1.110 1.106

Si–Si 2.373 2.356 2.389 2.367 2.334

Si–H (for SiH) 1.498 1.502 1.507 1.512 1.510

Si–H (for SiH2) 1.501 1.510 1.511 1.515 1.512

Ge–Ge 2.412

Ge–H (for Ge–H) 1.587

Ge–H (for GeH2) 1.537

2. Computational method

We used the graphical user interface Gauss view [19] for theinitial structure of molecules. The DFT calculations with variousfunctionals are performed using the GASSIAN03 package [20].These are local density approximation (LDA), generalized gradientapproximation (GGA), and hybrid functionals. The BLYP and PBE,those of the most popular GGA approximation, are used in ourcalculations. BLYP is Becke’s 1988 exchange functional [21] withLYP functional of Lee et al. [22] for correlation. PBE is Perdew,Burke, and Ernzerhof functional [23]. Finally, the calculations arecompleted with the hybrid PBE1PBE and Becke’s three-parameterB3LYP [24] functionals, which are mixed in some fraction withexact exchange.

In order to analyze the effect of the basis sets on the calculatedbandgap of each particle, we employed different Gaussian-typefunctions. These bases were the polarized (6-31G**) [25], furtherenlarged (6-311G**) double diffused (6-31++G(d,p)), (6-311++G(d,p)), Dunning’s correlation-consistent double-z basis(cc-pVDZ) [26], and augmented Dunning’s double-z basis (Aug-cc-pVDZ). The geometrical optimizations of C10H16 and Si10H16 areperformed at every level of calculation and are used to calculateHOMO–LUMO gaps, but in the case of Ge10H16 (with Z ¼ 32 forGe) the optimized structure at the B3LYP/6-31+G** level isemployed through all calculations of HOMO–LUMO gaps. Thenatural bond orbital (NBO) [27] calculations are done at theB3LYP level.

11

3. Results and discussion

3.1. Optimized structure, HOMO–LUMO gaps, and the quantum

confinement effect

The ground state of all three molecules showed Td symmetry.The calculated bond lengths of C10H16 and Si10H16 differ a littleusing different functionals, see Table 1. However, LDA-predictedC�C and Si�Si bonds length are a bit smaller than the resultsobtained from other functionals. We report the optimizedgeometries of C10H16 and Si10H16 carried out at the B3LYP/Aug-cc-pVDZ level in Fig. 1. The bond length values could be comparedwith the experimental results of 1.54 A for C–C, 1.12 A for C–H [28]and about 2.36 A for Si–Si bond lengths in sila-adamantane [15].The Ge–H and Ge–Ge bond lengths are also in good agreementwith those of in Ref. [29]. In Tables 2–4, we see that the resultingbandgaps of Si10H16 and Ge10H16 against basis sets are nearlymonotonic, while for C10H16 it varies and gradually converges asthe more diffuse basis sets are added. For Si10H16 and Ge10H16 themaximum variations in the bandgap against basis sets are fromthe B3LYP functional with 0.57 and 0.51 eV, respectively. ForC10H16, it is significantly larger and about 2.25 eV from PBE1. Thecalculated gaps from hybrid functionals are close to the QMCresults, but those from the GGA and LDA are nearly the same andunderestimated. In Fig. 2, the energy values of the HOMO andLUMO states of C10H16 and Si10H16 molecules from the B3LYPfunctional against basis sets have been plotted. We observe thatthe energy of the HOMO state in both cases is nearly steady but incontrast to Si10H16, the LUMO of C10H16 is very sensitive to thechoice of the selected basis sets. Its magnitude varies untilconvergence is established by adding the more diffused basis. Thesame results could also be obtained from other functionals. Inorder to understand how H-terminated C atoms in the sp3

structure respond to QC, we have calculated the HOMO–LUMOeigenvalues of some hydrogenated C and Si clusters. The resultsare compared in Fig. 3. We observe different behaviors for C atomsfamily versus Si. As the size of particle in the C clusters decreases,the HOMO states obtain red shift, but the LUMOs show nearly noshift in the blue range. This phenomenon was also experimentallyconfirmed by recent soft X-ray emission and absorption spectro-scopy [18,8]. They discovered that the lowest unoccupied statesare relatively fixed in energy. So an increase in HOMO–LUMO gapby reducing size stems only from the occupied states of thediamondoids family. In contrast, QC affects both LUMO and HOMOstates in the Si family. Isosurface plots of HOMO and LUMO statesof these particles also help us to better understand the differentnature of these molecules. According to Fig. 4(a), HOMO states ofthese particles are nearly localized over bonds. While LUMOisosurfaces of sila- and germa-adamantane resemble each other,the LUMO isosurface of C10H16 has a completely distinct config-uration. It has been diffused over the hydrogen atoms, and looks

52

Table 2Calculated DFT (HOMO�LUMO) gap for C10H16 at B3LYP, PBE1PBE, BLYP, PBE, and

LDA levels of the theory using different basis sets along with previous calculated

DMC optical gap taken from Ref. [13].

Basis set B3LYP PBE1 BLYP PBE LDA QMC

7.61

6-31G** 9.32 9.78 7.50 7.50 7.30

6-311G** 8.37 8.81 6.70 6.72 6.59

cc-pVDZ 8.63 9.10 6.90 6.92 6.76

6-31++G** 7.18 7.57 5.70 5.76 5.85

6-311++G** 7.22 7.60 5.75 5.80 5.93

Aug-cc-pVDZ 7.15 7.53 5.69 5.75 5.86

DE 2.17 2.25 1.81 1.75 1.45

The variation of the energy bandgap in each level is shown with DE, (all in eV).

Table 3Calculated DFT (HOMO�LUMO) gap for Si10H16 at B3LYP, PBE1PBE, BLYP, PBE, and

LDA levels of the theory using different basis sets, along with previous calculated

QMC optical gap taken from Ref. [36].

Basis set B3LYP PBE1 BLYP PBE LDA QMC

6.0

6-31G** 6.87 7.14 5.44 5.30 5.226-311G** 6.50 6.75 5.11 4.97 4.89

cc- pVDZ 6.57 6.79 5.16 5.01 4.93

6-31++G** 6.30 6.57 4.94 4.84 4.74

6-311++G** 6.31 6.56 4.94 4.83 4.74

Aug-cc-pVDZ 6.32 6.57 4.95 4.84 4.77

DE 0.57 0.58 0.50 0.47 0.48

The variation of energy bandgap in each level is shown with DE, (all in eV).

d2 = 1.543 d2 = 2.373

α1 = 109.76α1 = 109.65

d1 = 1.501

d3 = 1.101

d1 = 1.100

α5 = 109.61α5 = 109.55

C10H16 Si10H16

α4 = 109.38

α2 = 110.05α3 = 106.93 α3 = 107.94

α4 = 109.33

α2 = 109.78

d3 = 1.498

Fig. 1. (color on line) The ground-state structure of C10H16 and Si10H16 molecules at the B3LYP level of theory using an Aug-cc-pVDZ basis set. Optimized lengths are in A

and bond angles are in degree. Both structures show a Td symmetry.

Table 4Calculated DFT (HOMO�LUMO) gaps for Ge10H16 at B3LYP, PBE1PBE, BLYP, PBE,

and LDA levels of the theory using different basis sets, along with the previous

calculated QMC optical gap taken from Ref. [35].

Basis set B3LYP PBE1 BLYP PBE LDA QMC

6.4

6-31G** 6.78 7.07 5.39 5.35 5.28

6-311G** 6.56 6.88 5.18 5.16 5.10

cc- pVDZ 6.66 6.97 5.26 5.25 5.18

6-31++G** 6.32 6.65 5.01 5.01 4.96

6-311++G** 6.28 6.60 4.96 4.96 4.92

Aug-cc-pVDZ 6.27 6.59 4.96 4.95 4.92

DE 0.51 0.48 0.40 0.36 0.43

The variation of energy bandgap in each level is shown with DE, (all in eV). The

optimized geometry from B3LYP/6-31+G** level was employed through all

calculations.

6-31G** cc-pVDZ 6-31G** 6-31++G** 6-311++G** Aug-cc-pVDZ-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

Basis set

Eig

enva

lue

(eV

)

LUMO(C10H16)

LUMO(Si10H16)

HOMO(C10H16)

HOMO(Si10H16)

Fig. 2. DFT HOMO and LUMO eigenvalues (eV) calculated using B3LYP functional

with different basis sets for C10H16 along with those of Si10H16. The HOMO of

Si10H16 is almost superimposed by the HOMO of C10H16 in each point.

F. Marsusi, K. Mirabbaszadeh, G.A. MansooriOpto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

PHYSICA E 41(7): 1151–1156, 2009

like as if it is dominated by the H-terminated surface. Also, thecalculated natural atomic charges represent a nearly uniformamount of electronic charge density, which is transferred fromhydrogen to carbon in C–H compound (see Table 5). Compared toSi10H16 and Ge10H16, the delocalized regions of the LUMO state inC10H16 are much more stretched over CH sites. In contrast, a littledensity is presented over the CH2, SiH2, and GeH2 bonds. This isdue to the special property of mirror planes that bisect the H–C–H,Si–H–Si, and H–Ge–H compounds. The special diffused feature ofthe LUMO state of adamantane is a general nature of diamond-oids, and matches well with the corresponding scanning tunnel-

1153

ling microscopy (STM) image taken from tetramantane at +2.0 V[30], Fig. 4(b). The different behavior we report in Figs. 2 and 3results from this distinct nature and it implies that diffuse basis

XH4 X2H6 X5H12 X10H16 X14H20-12

-10

-8

-6

-4

-2

0

Ene

rgy

(eV

)

HOMO(X~C)

LUMO(X~C)

HOMO(X~Si)

LUMO(X~Si)

Fig. 3. Calculated HOMO and LUMO eigenvalues (eV) at the B3LYP/6-311++G(d,p)

level of the theory for some sp3 structures of C and Si family with H-terminated

surfaces. The horizontal labels are: X ¼ C: CH4, C2H6, C5H12, C10H16, C14H20. X ¼ Si:

SiH4, Si2H6, Si5H12, Si10H16, Si14H20.

LUMO(C10H16)

LUMO(Si10H16)

LUMO(Ge10H16)

HOMO(C10H16)

HOMO(Si10H16)

HOMO(Ge10H16)

Fig. 4. (color online) (a) The isosurfaces plot of HOMO and LUMO states from

B3LYP/Aug-cc-pVDZ for C10H16, Si10H16 and B3LYP/6-31+G** for Ge10H16 with

isodensity value ¼ 0.02 a.u. The electron accumulation is indicated with dark gray

(red) and the charged depletion with light gray (green) colors. The figure was

produced using the Gauss view program [19] and (b) positive-bias (V ¼ +2.0 V)

STM images of tetramantane (C22H28) molecules in [10 0] molecular orientations.

The image was taken from Ref. [30]. (For the interpretation of references to color in

this figure legend, the reader is referred to the web version of this article.)

F. Marsusi, K. Mirabbaszadeh, G.A. MansooriOpto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

PHYSICA E 41(7): 1151–1156, 2009

sets are utilized in the theoretical investigations of the opto-electronic behaviors of diamondoids.

3.2. Electron affinity, quasiparticle, and binding energy

The adiabatic electron affinity (AEA) and ionization potential(IP) are defined as

AEA ¼ Eneutral � Eanion

IP ¼ Ecation � Eneutral

where Eneutral is the total energy of the neutral molecule at itsoptimized geometry. Eanion and Ecation are the total energy of thecorresponding anion and cation calculated at their optimizedgeometry. According to our calculations, all anionic structureshave Td symmetry, but adamantane and sila-adamantane havelost their symmetry in order to find a minimum energy point. Wehave also evaluated zero-point vibrational energies (ZPVE) forthe purpose of correcting the AEA and IP. Our results are listed inTable 6. The calculated AEAs of adamantane using differentfunctionals are negative. This is in agreement with Drummond etal. [13], Qian-shu et al. [12], and also the experimental results ofYang et al. [14]. However, in another work this quantity [11] wasreported as a positive value (about 3.3 eV). The inconsistency inthe latter study [11] originates from using smaller basis 6-31G(d)in their DFT calculations. We have clarified before that thisbasis cannot indicate the surface nature of LUMO in C10H16.However, the calculated AEAs of Si10H16 and Ge10H16 are positive(see Table 6), and its value for germa-adamantane is less than sila-adamantane. The zero-point (ZP)-corrected AEAs from GGA (PBEfunctional, which are not shown in Table 6) are greater than thoseof hybrid functionals (�0.24 eV for C10H16 and 0.7 eV for Si10H16).Applying ZP correction in the calculation of AEA and for a largermolecule is more important than IP, and could change its value upto more than 100%. The negative EA value for C10H16 and thepositive value for two other particles indicate that the conductionband edge of C10H16 is above, and those of Si10H16 and Ge10H16 arebelow the vacuum level. Two factors affect the EA: first, thesurface dipole moment and second the charge occupation onthe surface. In semiconductors the inter-atomic force that bindsthe atoms together is mainly from the electron-pair in covalentbonds, but there is a slight ionic force as the valence electrons arenot evenly shared by the two host atoms. The NBO-calculated

115

natural charges in Table 5 show that for C10H16 atomic charges areproduced so that a fraction of negative charge as much as d istransferred almost uniformly from hydrogen to carbon, which canbe represented by C�d�H+d. The surface character of the LUMOstate in this molecule could be a result of this uniform chargedistribution over hydrogen atoms. The negative EA of adamantane

4

agreement with the QMC results of Refs. [13,34], and predicts a

Table 5Calculated natural atomic charge distribution (NBO analysis).

Molecule At X (XH) At H (XH) At X (XH2) At H (XH2)

C10H16 �0.265 0.232 �0.430 0.226

Si10H16 0.011 �0.097 0.289 �0.116

Ge10H16 �0.005 �0.070 0.223 �0.087

The calculations were performed at B3LYP/Aug-cc- pVDZ for C10H16, Si10H16, and

B3LYP/6-31+G** for Ge10H16.

Table 6DFT calculated adiabatic electron affinity with ZPVE correction (AEA) and without

it (AEA*), ionization potential with ZPVE correction (IP) and without it (IP*), all in

eV.

Molecule B3LYP PBE1PBE

AEA AEA* IP IP* AEA AEA* IP IP*

C10H16 �0.33 �0.37 8.87 9.21 �0.39 �0.42 8.86 9.19

Si10H16 0.41 0.20 8.47 8.40 0.46 0.27 9.26 9.07

Ge10H16 0.27 0.08 0.26 0.08

Calculations were performed at the B3LYP/Aug-cc-pVDZ, and PBEPBE/Aug-cc-

pVDZ levels for C10H16, Si10H16 and B3LYP/6-31+G** for Ge10H16.

Table 7DFT calculated optical gap, quasiparticle gap, and exciton binding energy

using B3LYP and PBE1 hybrid functionals along with the QMC results taken from

Refs. [13] and [35], all in eV.

Molecule B3LYP/AUG-cc-pVDZ PBE1PBE/AUG-cc-pVDZ QMC

Eopt Eqp Eex Eopt Eqp Eex Eex

C10H16 6.52 9.20 2.68 6.63 9.25 2.65 2.67a

Si10H16 5.41 8.06 2.65 5.41 8.80 3.39 3.6

a This value is resulted from Table 1 of Ref. [13].

F. Marsusi, K. Mirabbaszadeh, G.A. MansooriOpto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

PHYSICA E 41(7): 1151–1156, 2009

can be described by the production of small dipole on C–H bonds.According to the description in Ref. [31], the net effect of thissmall dipole on the surface layer of C10H16 is the creation of apotential step, Dv, perpendicular to the surface over a distance ofthe order of C–H bond length. This potential step implies that thevacuum level is lowered relative to conduction band by eDv, sothat this band lies above the vacuum level together with areduction in EA by �eDv. In contrast to the positive value of AEAfor Si10H16, a theoretical study of methyl-terminated sila-ada-mantane, (Si14C24H72) made of an adamantine-like Si10 corerepresents negative EA [32], which could again be stemmed fromC–H surface dipoles in this molecule. As an application, thenegative EA of molecules make the possibility of coating surfaceswith them to produce electron emission devices.

While there is no significant difference in the calculated IP ofadamantane from both functionals, PBE1 results in a greater valuefor sila-adamantane. To this end, we have compared thequasiparticle gap (Eqp) and Eex of C10H16 and Si10H16. For anN-electron system, the Eqp is defined as the difference betweenionization potential and electron affinity of their ground states

Eqp¼ EðN þ 1Þ þ EðN � 1Þ � 2EðNÞ ¼ Eopt

þ Eex

where Eopt is the optical gap of ground state, and Eex arises fromthe electron–hole interaction. Both Eex and Eqp are different fromtheir bulk value. By decreasing molecular size, QC causes anincrease in the Eqp gap, resulting in the blue shift of the Eopt.However, the increase in the exciton binding energy gives it a redshift. The Eopt is determined as the total energy differencebetween the ground-state (Egs) configuration and an excited-stateconfiguration (Eexc):

Eopt¼ Eexc

� Egs

As excited state, we have restricted our DFT variational space tothe N-electrons system, which is in the triplet spin state. Ourresults are compared to the QMC results in Table 7. The calculatedEopt from both functionals for sila-adamantane are in goodagreement with the values of 5.45 eV from B3LYP/Aug-cc-pVQZand 5.49 eV from PBE0/Aug-cc-pVQZ given in Ref. [33] and alsowith the 5.9 eV estimated experimental excitation threshold [33].The calculated trend of Eex results from PBE1 is in better

1155

smaller value for adamantane than sila-adamantane. The QMC and GW-BSE calculations have established that the Eex is dramatically enhanced at the nanoscale due to the increased overlap of the electron and the hole [34]. However, the delocalized surface behavior of LUMO state in admantane causes an increase in screening, resulting in a smaller Eex compared to Si10H16.

4. Conclusions

We studied the opto-electronic properties including HOMO–LUMO gaps, quantum confinement effects, electron affinities of adamantane (C10H16), hydrogen-terminated sila- (Si10H16) and germa-adamantane (Ge10H16). Quasiparticle and exciton binding energies of C10H16 and Si10H16 are also computed and the results are compared to the corresponding quantities of the QMC results taken from previous studies. The obtained optical properties using hybrid functionals are in good agreement with the QMC results due to the cancellation of self-interaction errors. The LUMO state of C10H16 has a very distinct configuration compared to those of Si10H16 and Ge10H16. This could be a result of the almost uniform charge transfer from hydrogen to carbon in C–H and H–C–H compounds. It brings about a dipole moment, resulting in a potential step that causes a conduction band that lies below the vacuum level and therefore a negative electron affinity. This delocalized LUMO also causes an increase in the screening, resulting in a smaller exciton binding energy compared toSi10H16. The electron affinity of Si10H16 is larger than Ge10H16, while both are positive.

Acknowledgment: We would like to thank Mr. Mehdi Gambarian for his helpful discussion on details of the GAUSSIANpackage.

Abbreviations: DFT, density functional theory; EA, electron affinities; Eexc, excited-state configuration total energy;Egs, ground-state total energy;Eopt, optical gap of ground state;Eqp, quasiparticle gap;Eex, exciton binding energy;HOMO, highest occupied molecular orbital; IP, ionization potential; GGA, generalized gradient approximation; LDA, local density approximation; LUMO, unoccupied molecular orbital; NBO, natural bond orbital; NEMS, nanoelectro-mechanical systems; QC, quantum confinement; ZPVE, zero-point vibrational energies

F. Marsusi, K. Mirabbaszadeh, G.A. MansooriOpto-Electronic Properties of Adamantane and Hydrogen-Terminated Sila- and Germa-Adamantane: A Comparative Study

PHYSICA E 41(7): 1151–1156, 2009

[12] Qian-shu Li, Xue-jun Feng, Y. Xie, H.F. Schaefer, J. Phys. Chem. A 109 (2005)1454.

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