7
First principles study of the structure, electronic state and stability of Al n As C m cations Ling Guo * , Hai-shun Wu School of Chemistry and Material Science, Shanxi Normal University, Linfen 041004, China Received 30 August 2005; accepted 12 October 2005 Available online 3 February 2006 Abstract Structural and electronic properties of semiconductor binary microclusters Al n As C m cations have been investigated using the B3LYP-DFT method in the ranges of nZ1, 2 and mZ1–7. Full structural optimization, adiabatic ionization potentials calculation and frequency analysis are performed with the basis of 6-311CG(d). The charged-induced structural changes in these cations have been discussed. The strong As–As bond is also favored over Al–As bonds in the Al n As C m cations in comparison with corresponding neutral cluster. With As m forming the base, adding Al atom(s) in different positions would find the stable structures of Al n As C m cations quickly and correctly. AlAs C 2 , AlAs C 4 , and AlAs C 6 are predicted to be species with high stabilities and possible to be produced experimentally. q 2006 Elsevier B.V. All rights reserved. Keywords: Al n As CC m cluster; Density functional theory; Stability 1. Introduction The III–V semiconductor clusters have been the topic of many experimental and theoretical studies [1–3]. A primary driving force behind such studies is that III–V materials are of great technological importance as they find applications in the fabrication of fast microelectronic devices, small devices, and light-emitting diodes. Consequently, a detailed study of the properties of such clusters as a function of their sizes could provide significant insight into the evolution from the molecular level to the bulk. Despite the numerous experimental investigations on the GaAs, InAs, InP, and more recently, the AlP and GaP clusters, the literature contains very little on the AlAs clusters. While ab initio calculations on properties of Al x As y clusters have been carried out by several groups [4–10]. Andreoni [4] calculated the structures, stability, and melting of (AlAs) n (nZ2–5) using the Car-parrinello method. Quek et al. [5] had reported tight binding molecular dynamics studies of the structures of Al m As n (mCn%13). Tozzini et al. [6] presented extensive theoretical calculations of the geometric and electronic properties of neutral and ionized AlAs fullerene- like clusters of the type Al x As xC4 with a number of atoms up to 52, on the basis of density functional theory. Costales et al. [7] used density functional theory (DFT) to explore structural and vibrational properties for (AlAs) n clusters up to six atoms, finding the same behavior as in the Aluminum nitride clusters. Archibong et al. [8] calculated the low-lying electronic states of Al 3 As, AlAs 3 , and the corresponding anions at the B3LYP and CCSD(T) levels using the 6-311CG(2df) one-particle basis set. The adiabatic electron affinities, electron detachment energies and harmonic vibrational frequencies of both the anions and the neutral molecules are presented and discussed. Feng et al. [9] reported MRSDCI study of the ground and several low-lying excited states of Al 2 As 3 , Al 3 As 2 , and their ions. Recently, Zhu [10] studied the spectroscopic properties for Al 2 As, AlAs 2 , and their ions using density functional theory (DFT:B3LYP) and complete active space multiconfiguration self-consistent field (CASSCF) calculations. Since the properties of clusters are unique, it is expected that cluster assembled materials can have uncommon properties. Studies on the electronic and geometric structures of clusters are necessary. Theoretical calculations have been performed on aluminum arsenide clusters by a number of methods for some time. While most studies were devoted to the small neutral clusters and theoretical investigations on cationic clusters are few. In this work, we present a density function theory study for semiconductor binary systems AlAs C m and Al 2 As C m with mZ1–7. We aim to provide more reliable ground-state geometries and electronic states, relative orbital and total energies, HOMO– LUMO gaps and theoretically calculated IR vibration frequen- cies at the corresponding optimum structures. With As m forming Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173 www.elsevier.com/locate/theochem 0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.10.060 * Corresponding author. E-mail address: [email protected] (L. Guo).

First principles study of the structure, electronic state and stability of cations

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First principles study of the structure, electronic state and stability

of AlnAsCm cations

Ling Guo *, Hai-shun Wu

School of Chemistry and Material Science, Shanxi Normal University, Linfen 041004, China

Received 30 August 2005; accepted 12 October 2005

Available online 3 February 2006

Abstract

Structural and electronic properties of semiconductor binary microclusters AlnAsCm cations have been investigated using the B3LYP-DFT

method in the ranges of nZ1, 2 and mZ1–7. Full structural optimization, adiabatic ionization potentials calculation and frequency analysis are

performed with the basis of 6-311CG(d). The charged-induced structural changes in these cations have been discussed. The strong As–As bond is

also favored over Al–As bonds in the AlnAsCm cations in comparison with corresponding neutral cluster. With Asm forming the base, adding Al

atom(s) in different positions would find the stable structures of AlnAsCm cations quickly and correctly. AlAsC2 , AlAsC4 , and AlAsC6 are predicted to

be species with high stabilities and possible to be produced experimentally.

q 2006 Elsevier B.V. All rights reserved.

Keywords: AlnAsCCm cluster; Density functional theory; Stability

1. Introduction

The III–V semiconductor clusters have been the topic of

many experimental and theoretical studies [1–3]. A primary

driving force behind such studies is that III–V materials are of

great technological importance as they find applications in the

fabrication of fast microelectronic devices, small devices, and

light-emitting diodes. Consequently, a detailed study of the

properties of such clusters as a function of their sizes could

provide significant insight into the evolution from the

molecular level to the bulk. Despite the numerous experimental

investigations on the GaAs, InAs, InP, and more recently, the

AlP and GaP clusters, the literature contains very little on the

AlAs clusters. While ab initio calculations on properties of

AlxAsy clusters have been carried out by several groups [4–10].

Andreoni [4] calculated the structures, stability, and melting of

(AlAs)n (nZ2–5) using the Car-parrinello method. Quek et al.

[5] had reported tight binding molecular dynamics studies of

the structures of AlmAsn (mCn%13). Tozzini et al. [6]

presented extensive theoretical calculations of the geometric

and electronic properties of neutral and ionized AlAs fullerene-

like clusters of the type AlxAsxC4 with a number of atoms up to

52, on the basis of density functional theory. Costales et al. [7]

0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2005.10.060

* Corresponding author.

E-mail address: [email protected] (L. Guo).

used density functional theory (DFT) to explore structural and

vibrational properties for (AlAs)n clusters up to six atoms,

finding the same behavior as in the Aluminum nitride clusters.

Archibong et al. [8] calculated the low-lying electronic states

of Al3As, AlAs3, and the corresponding anions at the B3LYP

and CCSD(T) levels using the 6-311CG(2df) one-particle

basis set. The adiabatic electron affinities, electron detachment

energies and harmonic vibrational frequencies of both the

anions and the neutral molecules are presented and discussed.

Feng et al. [9] reported MRSDCI study of the ground and

several low-lying excited states of Al2As3, Al3As2, and their

ions. Recently, Zhu [10] studied the spectroscopic properties

for Al2As, AlAs2, and their ions using density functional theory

(DFT:B3LYP) and complete active space multiconfiguration

self-consistent field (CASSCF) calculations.

Since the properties of clusters are unique, it is expected that

cluster assembled materials can have uncommon properties.

Studies on the electronic and geometric structures of clusters are

necessary. Theoretical calculations have been performed on

aluminum arsenide clusters by a number of methods for some

time. While most studies were devoted to the small neutral

clusters and theoretical investigations on cationic clusters are

few. In this work, we present a density function theory study for

semiconductor binary systems AlAsCm and Al2AsCm with mZ1–7.

We aim to provide more reliable ground-state geometries and

electronic states, relative orbital and total energies, HOMO–

LUMO gaps and theoretically calculated IR vibration frequen-

cies at the corresponding optimum structures. With Asm forming

Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173

www.elsevier.com/locate/theochem

Fig. 1. Ground state structures of AlnAsCm cations.

L. Guo, H.-s. Wu / Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173168

the base, adding Al atom(s) in different position would shed

useful insight into the similarities and differences between the

binary system and corresponding elemental clusters. To our

knowledge, this is the first time to study the ground state

geometries of AlnAsCm (nCmO5) clusters.

2. Methodology

The B3LYP/6-311CG(d) method has been employed to

optimize the geometries of AlAsCm and Al2AsCm (mZ1–7)

cations. Frequency analysis are also performed at the same

Fig. 2. Substate structure

theoretical level to check whether the optimized structures are

transition states or true minima on the potential energy surfaces

of corresponding clusters. Density functional theory (DFT)

[11,12] has evolved into a widely applicable computational

technique, while requiring less computation effort than

convergent quantum mechanical methods such as coupled

cluster theory. The application of density functional theory has

been shown to be effective for many species in groups III and V

such as the GaxPy, GaxAsy, AlxNy, and InxNy systems [13–15].

The initial input structures are taken either from published

results for Asm [16] clusters by adding Al atoms in different

s of AlnAsCm cations.

Table 1

Geometric parameters and electronic states of AlnAsCm clusters

Molecule Type L (A)

1A’ 1–2 2.867

2–3 2.1302A2 1–2 2.395

1–4 2.724

2–4 2.3981A’ 1–2 2.454

2–3 2.513

2–4 2.964

3–4 2.9712A’’ 1–2 2.569

L. Guo, H.-s. Wu / Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173 169

positions, or the results reported for other III–V semiconductor

clusters, or arbitrarily constructed and fully optimized via the

Berny algorithm. For AlnAsCm clusters, the ground-state

structures are either relaxed within the geometries of

corresponding neutrals or distorted into new structures with

lower energies and much lower symmetries due to Jane–Teller

distortions. To determine the stability of the optimized

structures, harmonic vibration frequencies are further calcu-

lated with B3LYP functional. Some optimized geometries,

although low in energies, are found to be first order or even

higher order stationary points. All calculations are performed

with the GAUSSIAN 98 suite of programs [17].

1–3 2.485

1–5 2.541

2–3 2.893

2–4 2.540

2–6 2.507

3–4 2.3831A’ 1–2 2.679

1–3 2.499

1–6 2.490

3–4 2.352

AlAsC7 ð2AÞ 1–4 2.396

1–5 2.510

3. Results and discussion

3.1. Geometry

The ground state and metastable state geometric sketch

figures of AlnAsCm (nZ1, 2; mZ1–7) optimized by B3LYP

method are shown in Figs. 1 and 2, respectively. Geometric

parameters are listed in Table 1.

1–8 2.472

2–3 2.456

2–4 2.523

2–6 2.573

3–4 2.555

3–5 2.544

5–7 2.500

6–7 2.510

6–8 2.443

Al2AsC(3B2) 1–3 2.3912B1u 1–2 2.569

2–3 2.3801A’1 1–2 2.499

2–3 2.655

Al2AsC4 ð2AÞ 1–3 2.513

1–6 2.583

2–3 2.582

1–4 2.5121A’ 1–2 2.376

1–3 2.764

2–3 2.547

2–4 2.591

3–5 2.429

3–7 2.547

4–7 2.591

5–6 2.2592B1 1–2 2.447

1–3 2.558

3–4 2.510

4–8 2.478

3.1.1. AlAsCmAlAsC. The optimized bond length of neutral AlAs is

2.33 A, somewhat shorter than the Costales’ result of 2.57 A

[7] at the GGA level of theory in conjunction with a double

numerical basis set supplemented with d polarization func-

tions. And the vibrational frequency (349 cmK1) is higher than

Costales’ result (282 cmK1) [8]. For the cationic case, the

ionize electron comes out from a bonding orbital predicting its

instability relative to the neutral monomer by 7.70 eV. It is also

manifested in an increase in the internuclear distance (2.54 A)

and a decrease in the frequency value (233 cmK1) indicating

that the bond in cationic state is weaker than the corresponding

one in the neutral monomer.

AlAsC2 . The present calculations predict an isosceles

triangles (C2v,2B2) ground state 1(a) for the equilibrium

geometry of AlAs2 molecule. Geometric sketch shows it to

be acute triangle with aAs–Al–AsZ47.28 and the Al–As, As–As

bond lengths are 2.749 and 2.202 A, which compare well with

Zhu’s values [10] of 48.68, 2.706 and 2.226, respectively,

optimized by the CASSCF calculation. The ground state of

AlAsC2 is the Cs (1A 0) geometry 1(a). The structure 2(a)

(C2v,1A1), which has the same geometry as the neutral AlAs2

cluster, is now a transition state with an imaginary frequency at

56i cmK1 and lying only 0.08 eV higher in energy.

AlAsC3 . A near degeneracy is found by previous ab initio and

density functional study [8] between the 1A1(C2v) and the1A 0(Cs) lowest states for AlAs3. The present calculation leads to

the same conclusion. The distorted tetrahedron 2(b) with Cs

symmetry is the ground state of neutral AlAs3. The local

minimum rhomboidal structure 1(b) with C2v symmetry and

another Cs (1A 0) structure with imaginary frequency lie 0.03

and 0.47 eV, respectively, higher in energy. The energy

ordering is different in the cations. Removing an electron

stabilizes the C2v (2A2) structure 1(b) with respect to the Cs

(2A 00) and Cs (2A 0) 2(b) form and their energy differences are

0.005 and 0.03 eV, respectively.

AlAsC4 . The most stable AlAs4 isomer is a tetrahedral As4

structure [16] with a two-fold Al atom bond to it. The structure

is very similar to 2(c). While the lowest-energy structure we

found for AlAsC4 is a distorted trigonal bipyramid (Cs) 1(c),

which can be derived from a tetrahedral As4 structure by

L. Guo, H.-s. Wu / Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173170

capping an additional Al atom between atoms (2, 3, 5). At the

same time, bonding a two-fold Al atom to the tetrahedral As4

form, we obtain a substable isomer of AlAsC4 2(c) with C2v

symmetry lying 0.03 eV above the ground state, which has the

very similar geometry as that of the neutral AlAs4. Both AlAs4

and its cation have the same geometry as that of the AlP4 [18]

and GaAs4 [19], which is attributed to the fact that both of them

take a similar valence structure due to the same family in the

periodic table.

AlAsC5 . The ground state of neutral AlAs5 (C5v,1A1) 2(d) is

derived from the As5 [16] cluster by placing a five-fold Al atom

on the top. In the procession, the geometry of As5 is nearly

maintained and the five same As–As bond lengths are only

elonged by 0.6%. Removing an electron from the neutral

molecule yields a cationic AlAsC5 (C5v,2A1), which has the

same geometry as the neutral AlAs5. The distorted triangle

prism 1(d) lying only 0.03 eV below the 2(d) is a ground state

structure with Cs (2A 00) symmetry, which is built from

substitution of an As atom by an Al atom in the triangle

prism As6.

AlAsC6 . The face-capped triangle prism 2(e) is the ground

state of the neutral AlAs6 (C2v,2A2) in our present optimization.

It can be viewed as capping an additional Al atom on the square

face of the triangle prism As6. The As2–As4 and As6–As7 bonds

are broken in the capping procession. Removing an electron

produces the ground state structure of cationic AlAsC6 (Cs,1A 0)

1(e), which is different from the neutral isomer and derived

from a boat-shape As6 by adding of one two-fold Al atom

between atoms (1,5). Model 2(e) of AlAsC6 (C2v,1A1) is now a

transition state lying 0.39 eV above the ground state.

Removing an electron results that the four same Al–As bonds

(2.510 A) of 2(e) are elonged compared to the corresponding

Al–As bond lengths (2.490 A) in the neutral isomer, while the

average As–As bond length is contracted by about 0.41%. The

numbers of As–As bonds in 2(e) are less than those of 1(e),

which may be the reason for its less stable and indicates that the

As–As bonds play a more decisive role than the Al–As bonds in

the determination of the geometry and energy of AlAsC6 .

AlAsC7 . The present calculations consider a cuneane

structure 1(f) as the ground state of neutral AlAs7, which can

be derived from a square-face-capped triangle prism As7 by

adding an additional three-fold Al atom. The symmetry of As7

is changed from C2v to lower Cs (1A 0) symmetry of AlAs7 in the

procession. AlAsC7 with lower C1 (2A) symmetry takes the

similar geometry 1(f) as the neutral. Another Cs isomer 2(f) of

cationic AlAsC7 with the same electronic state as 1(f) lies

0.72 eV above the ground state, which contains a one-fold Al

atom.

3.1.2. Al2AsCm clusters

Al2AsC. The 2B2 state of triangle prevails as the ground state

of Al2As with the Al–As–Al apex angle of 92.18, and the Al–As

and Al–Al bond lengths of 2.351 and 3.384 A agree well with

Zhu’s [10] results. This global minimum exhibits the same

symmetry as that of the cationic Al2AsC (C2v,3B2) 1(g).

The comparison of geometries of the neutral and cation reveals

that the Al–Al (3.549 A) bond lengths in Al2AsC are elongated

with a more open Al–As–Al (95.88) bond angle, implying that

the Al–Al bond is further weaken upon ionization. The Al–As–

Al linear configuration of Al2AsC 2(g) is 0.21 eV less stable

than 1(g).

Al2AsC2 . Costales et al. [7] have investigated four different

linear configurations and a rhombic structure of Al2As2 at the

GGA/DNP level of theory, and we have calculated both the

singlet and triplet states of these and other isomers. We support

their prediction that the 1Ag electronic state with rhombus

equilibrium structure 1(h) is the ground state of Al2As2.

The As–As bond length is 2.308 A and is much shorter than the

Al–Al bond length of 4.793 A resulting in an acute As–Al–As

bond angle of 51.48 in the rhombus structure. Removing an

electron from it produces a cationic Al2AsC2 (2B1u) 1(h), which

has the same geometry as the neutral. In the rhombus cationic

dimmer, the loss of an electron results in the decrease of the

Al–As (from 2.660 to 2.569 A) bond distance, with a

corresponding increase in the As–As distances (from 2.308 to

2.380 A). The next lowest energy isomer is a trapezoidal form

2(h) with C2v (2A2) symmetry, which has an imaginary

frequency lying 0.79 eV above the ground state. The mode of

imaginary frequency shows a tendency for the rhombic ground

state.

Al2AsC3 . Balasubramanian et al. [9] studied different isomers

of neutral Al2As3 cluster. We have considered these and other

structures and support their results that the most

stable configuration is trigonal bipyramid geometry 1(i) with

D3h;ð2AÞ symmetry. The next structure in the energetic

ordering is the C2v (2A1) isomer 2(i) lying 0.42 eV above the

ground state. The ground state structure of Al2AsC3 ðD3h;1A

0

1)

1(i) is the same as that of the neutral molecular. The As–As

(2.655 A) bond length in the Al2AsC3 is elonged, while the Al–

Al (3.947 A) and Al–As (2.499 A) bond lengths are contracted

compared to the corresponding bond lengths of Al–Al

(4.213 A), Al–As (2.572 A) and As–As (2.557 A) in the

neutral ground state. Next low-lying Al2AsC3 isomer in the

energy ordering possesses (C2v1A1) geometry 2(i). This

structure is a transition state with imaginary frequency lying

0.63 eV above the ground-state structure discussed above.

Al2AsC4 . The lowest energy Al2As4 isomer is a slightly

distorted square bipyramid 2(j) with C2v (1A1) symmetry,

which is very similar to D4h point group. It can be derived from

the optimal structure of Al2As3 isomer 1(i) by capping an As

atom between two adjacent As atoms. The structure of the

Al2AsC4 1(j) is different from its neutral molecule. This global

minimum of Al2AsC4 (C1) can be obtained from the minimum

structure of neutral AlAs4 2(c) by capping an additional Al

atom between As3 and As5 atoms. The C2v (2B1) square

bipyramid 2(j) in the cationic isomers is now a transition state

lying only 0.06 eV higher in energy.

Al2AsC5 . The present calculations predict the Cs (2A 0) ground

state 1(k) for neutral Al2As5. Another Cs isomer 2(k) with the

same electronic state is located at 0.50 eV above the ground

state, which can be derived from the substable structure of

AlAs5 1(d) by capping an additional Al atom between atoms

(1,6). The energy ordering is preserved in the cation. Removing

an electron makes the Cs (1A 0) structure 1(k) still the global

Table 2

Vibrational frequencies of AlnAsCm

Molecule V (cmK1) I (km molK1)

AlAsC2 46 (a 0) 5

149 (a 0) 73

AlAsC3 32 (a 00) 2

169 (a 0) 46

AlAsC4 60 (a 0) 3

169 (a 0) 93

AlAsC5 51 (a 00) 0

295 (a1) 22

AlAsC6 37 (a 00) 3

113 (a 0) 10

AlAsC7 61 (a 0) 0

156 (a 00) 4

Al2AsC 73 (a1) 1

322 (b2) 64

Al2AsC2 96 (b3u) 2

164 (b2u) 9

Al2AsC3 156 (e 0) 0

250 (e 0) 6

Al2AsC4 92 (a 0) 0

227 (a 00) 8

Al2AsC5 57 (a 00) 0

215 (a 0) 22

Al2AsC6 88 (a1) 0

247 (b2) 16

L. Guo, H.-s. Wu / Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173 171

minimum. The local minimum 2(k) with the same symmetry

and electronic state is now 0.19 eV higher in energy.

Al2AsC6 . The fully optimized ground-state structure of

Al2As6 is a distorted cube structure with C2v (1A1) symmetry,

which is obtained by substitution of two As atoms by two Al

atoms in the cube As8 [16] cluster and similar to the cationic

Al2AsC6 (C2v,2B1) 1(l) in shape. In the two lowest-energy

structures of Al2As6 and Al2AsC6 , both Al and As atoms adopt

the three-fold coordination. The As–As (2.510 A) bond length

in the Al2AsC6 is contracted, while the two different Al–As bond

lengths (2.478 and 2.447 A) are elonged compared to the

corresponding bond lengths of As–As (2.580 A) and Al–As

bond lengths (2.461 and 2.445 A) in the neutral ground state.

Table 3

Calculated electronic energies Et (Hartree/particle), zero point energy ZPE (kJ molK

standard entropy S2 (J molK1 KK1) for AlAsCm

Molecule Symmetry Et ZPE

AlAsC CNv K2477.9930 1.44

AlAsC2 Cs K4713.9614 3.73

AlAsC2 C2v K4713.9583 3.30

AlAsC3 C2v K6949.8722 8.44

AlAsC3 Cs K6949.8720 6.53

AlAsC4 Cs K9185.8288 10.52

AlAsC4 C2v K9185.8277 12.69

AlAsC5 Cs K11421.7111 14.78

AlAsC5 C5v K11421.7101 14.62

AlAsC6 Cs K13657.6594 17.89

AlAsC6 C2v K13657.6451 17.61

AlAsC7 Cs K15893.5608 20.94

AlAsC7 Cs K15893.5345 18.05

The substable structure of Al2AsC6 is also with the C2v (2B2)

symmetry 2(l). We can very roughly decompose this structure

into two interacting entities: structure 2(a) and 2(c) are bridged

with Al–Al bond. It is located at 1.18 eV higher in energy.

The energy surface of a large molecule can be rather

complex and there could be other stable minimums corre-

sponding to geometries that are unexplored. Although, the

isomers of AlnAsCm have been studied extensively and reported

in this letter, there can be no guarantee that other possible

minima do not exist. Our results of geometry optimization are

only predictions, and it would be of great interest to see more

experimental studies being done on the system.

3.2. Vibrational frequency analysis

A vibrational frequency calculation is important to

predicting molecular stability. To determine the ground state

of clusters, we tried at least five different initial configurations

with low total energies and then calculated vibrational

frequencies for these clusters. We reported the lowest

vibrational frequencies and the highest infrared spectra

intensity of the ground states for each cluster in Table 2. It

can be clearly seen that they are actually equilibrium states

without imaginary frequencies. The symmetry vibrational

models are also given in the parentheses.

3.3. Energy and thermodynamical property

The total energies, zero point energies, HOMO–LUMO

energy gaps, heat capacity, and standard entropy of AlnAsCm are

tabulated in Tables 3 and 4. The zero point energy, Cv and S2

are nearly in portion to increased n their average enhancement

are 3.25 kJ molK1, 22.48 and 44.89 J molK1 kK1 for AlAsCmcations, respectively, and those are 3.87 kJ molK1, 22.72 and

35.22 J molK1 kK1 for Al2AsCm cations, respectively. Except

for AlAsC4 , the zero-point energy of other ground-state

structures is greater than that of their substable isomers, and

the energy gap of the other ground-state structures is greater

than that of their substable structures, which can be thought to

be the ways for judging a ground state correctly.

1), HOMO–LUMO energy gaps Egap (eV), heat capacity Cv (J molK1 KK1) and

Egap Cv S2

243 28.32 250.13

3.57 47.25 326.68

3.48 39.01 302.90

3.01 69.46 354.74

2.36 71.40 374.19

4.39 94.00 403.88

3.35 91.95 379.35

2.92 116.27 442.09

2.31 116.82 425.51

3.90 139.23 482.84

2.74 131.07 457.93

3.32 163.21 519.49

3.06 157.20 527.34

Table 4

Calculated electronic energies Et (Hartree/particle), zero point energy ZPE (kJ molK1), HOMO–LUMO energy gaps Egap (eV), heat capacity Cv (J molK1 KK1) and

standard entropy S2 (J molK1 KK1) for Al2AsCm

Molecule Symmetry Et ZPE Egap Cv S2

Al2AsC C2v K2720.4994 4.15 3.43 47.19 313.37

Al2AsC DNh K2720.4915 2.67 3.23 36.03 267.51

Al2AsC2 D2h K4956.4435 7.61 2.49 70.59 345.16

Al2AsC2 C2v K4956.4143 7.43 1.04 61.79 342.25

Al2AsC3 D3h K7192.3760 13.09 2.89 91.76 360.94

Al2AsC3 C2v K7192.3527 7.72 1.92 78.80 385.69

Al2AsC4 C1 K9428.2857 14.60 2.74 116.88 433.52

Al2AsC4 Cs K9428.2834 13.12 2.30 109.38 421.60

Al2AsC5 CS K11664.2107 19.25 2.69 137.66 470.93

Al2AsC5 CS K11664.2037 17.69 2.60 140.07 470.74

Al2AsC6 C2v K13900.1412 23.52 2.50 160.81 489.46

Al2AsC6 C2v K13900.0980 19.84 2.28 145.29 513.95

L. Guo, H.-s. Wu / Journal of Molecular Structure: THEOCHEM 760 (2006) 167–173172

To test the stability of cluster further, the following energy

variation of reaction is considered:

2ðAlnAsCm Þ/ ðAlnAsCmC1ÞC ðAlnAsCmK1Þ

We define the energy variation in formula as

D2EmZEmC1CEmK1K2Em, the second difference in energy

for AlnAsCm. Hence, we obtain the curves shown in Fig. 3

corresponding to the energy variations in formulae as number

of total atoms. The larger the D2Em is, the more stable the

cluster corresponding to cluster size is. Therefore, from Fig. 3,

it is clear that the D2Em is larger as odd total number of atoms

and lower as even total number of atoms, which indicates that

those AlnAsCm clusters corresponding to odd total number of

-2

-1

0

1

2

3

2 3 4 5 6 7 8

total number of atoms

∆2E

m/e

V

Al AsmAl 2Asm

Fig. 3. Relationships between D2Em and number of total atoms for AlnAsmC.

66.2

6.46.6

6.87

7.2

7.47.6

7.88

1 2 3 4 5 6 7 8 9

total number of atoms

IP/e

V

Al Asm

Al 2Asm

Fig. 4. Relationships between IP and number of total atoms for AlnAsm.

atoms are more stable, so that the ‘magical number’ regularity

of AlnAsCm is that the total atom number should be odd.

Especially, AlAsC2 , AlAsC4 and AlAsC6 are predicted to be

species with high stabilities and possible to be produced

experimentally.

3.4. Adiabatic ionization energy

The adiabatic ionization energy (IP) of AlAsm and Al2Asmare plotted as a function of cluster size in Fig. 4. The IP values

of AlAsm (mZ1, 3, 5, 7) are the peak values, which

corresponding to relatively stable neutral state. No experiments

are available for AlnAsm clusters at present hence, it would be

of great interest to see more experimental studies being done on

them to validate our conclusions.

4. Conclusions

Structural and electronic properties of semiconductor binary

microclusters AlnAsCm cations have been investigated using the

B3LYP-DFT method in the ranges of nZ1, 2 and mZ1–7. Full

structural optimization, adiabatic ionization potentials calcu-

lation and frequency analyses are performed with the basis of

6-311CG(d). The charged-induced structural changes in these

cations have been discussed. The strong As–As bond is also

favored over Al–As bonds in the AlnAsCm cations in comparison

with corresponding neutral cluster. With Asm forming the base,

adding Al atom(s) in different positions would find the stable

structures of AlnAsCm cations quickly and correctly. Both

AlAsC2 , AlAsC4 and AlAsC6 are predicted to be species with high

stabilities and possible to be produced experimentally.

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