First principles study of the structure, electronic state

and stability of AlnPmþ cations

Ling Guoa,b,*, Hai-shun Wub, Zhi-hao Jina

aSchool of Material Science and Engineering, Xi’an Jiaotong University, Xi’an 710049,People’s Republic of ChinabInstitute of Material Chemistry, Shanxi Normal University, Linfen 041004, People’s Republic of China

Received 7 September 2003; accepted 7 May 2004

Abstract

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

method in the ranges of n ¼ 1; 2 and m ¼ 1–7: Full structural optimization, adiabatic ionization potentials calculation and frequency analysis

are performed with the basis of 6-311G(d). The charge-induced structural changes in these cations have been discussed. The strong P–P bond

is also favored over Al–P bonds in the AlnPmþ cations in comparison with corresponding neutral cluster. With Pm forming the base, adding Al

atom(s) in different positions would find the stable structures of AlnPmþ cations quickly and correctly. Both AlP4

þ and AlP6þ are predicted to be

species with high stabilities and possible to be produced experimentally.

q 2004 Elsevier B.V. All rights reserved.

Keywords: AlnPmþ 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. AlP clusters are

attractive targets of study compared to III–V clusters with

heavier atoms because they have higher vibrational

frequencies, facilitating the observation of vibrational

progressions in their photoelectron spectra [4]. In addition,

the smaller number of electrons makes them more amenable

to electronic structure calculations. Under the high vacuum

condition, laser ablation of a mixture of aluminum and red

phosphorus powders can generate aluminum phosphide

clusters. And a series of AlnPm [4,5] clusters had already

been observed. Ab initio calculations on properties of AlxPy

clusters have been carried out by several groups [6–14].

Raghavachari [8] calculated minimum-energy structures for

(AlP)n using Hartree–Fock (HF) and fourth-order Moller–

Plesset perturbation theory, followed by quadratic configur-

ation interaction QCISD(T). Tomasulo and Ramakrishna

[10] used density functional theory (DFT) to explore

structures for (AlP)n clusters up to 12 atoms, finding

significantly different structures than those for Si2n clusters

for n $ 3: Feng and Balasubramanian [11,12,14,15] per-

formed higher-level ab initio calculations on a series of

AlxPy neutral and charged clusters with four or fewer atoms.

Archibong et al. [13] calculated structures and detachment

energies for AlP22, Al2P2

2, and their neutral counterparts

at the DFT and coupled cluster singles and doubles

(CCSD (T)) levels of theory.

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. However, Time-of-

flight mass spectrum experiment shows the existence of

charged clusters, so it is important to carry out investigation

of ionic AlnPm species. Theoretical calculations have been

performed on aluminum phosphide clusters by a number of

methods for a long time. While most studies were devoted to

the small neutral clusters and theoretical investigations on

0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2004.05.008

Journal of Molecular Structure (Theochem) 680 (2004) 121–126

www.elsevier.com/locate/theochem

* Corresponding author. Tel.: þ86-357-2053306.

E-mail addresses: gl-guoling@163.com (L. Guo), wuhs@dns.sxtu.edu.

cn (H. Wu).

cationic clusters are few. In this work, we present a density

function theory study for semiconductor binary systems

AlPmþ and Al2Pm

þ with m ¼ 1–7: 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 frequencies at the

corresponding optimum structures. With Pm forming 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 AlnPmþ ðn þ m . 5Þ clusters.

2. Methodology

The B3LYP/6-311G* method has been employed to

optimize the geometries of AlPmþ and Al2Pm

þ ðm ¼ 1–7Þ

cations. Frequency analysis is also performed at the same

theoretical level to check whether the optimized structures

are transition states or true minima on the potential energy

surfaces of corresponding clusters. The choice of DFT has

been fully justified for semiconductor systems studied due

to the fact that it is an ab initio tool and it includes the

electron correlation effect which has been found necessary

for aluminum and phosphorous clusters at relatively low

computational cost. The initial input structures are taken

either from published results for Pm by adding Al atoms in

different position, or the results reported for other III–V

semiconductor clusters, or arbitrarily constructed and

fully optimized via the Berny algorithm. For AlnPmþ cations,

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 Jahn–Teller distortions. To determine

the stability of the optimized structures, harmonic vibration

frequencies are further calculated 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 carried out using the GAUSSIAN

98 program on a SGI/O2 workstation.

3. Results and discussion

3.1. Geometry

The ground state and metastable state geometric sketch

figures of AlnPmþ ðn ¼ 1; 2;m ¼ 1–7Þ optimized by B3LYP

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

parameters are listed in Table 1.

3.1.1. AlPmþ

AlPþ. The electronic state is 3S for the neutral monomer,

and 2S for cation. The optimized bond length of neutral AlP

is 0.2229 nm, somewhat shorter than the bulk Al–P bond

length of 0.2360 nm [8] and the vibrational frequency

(437 cm21) is higher than Allaham’s result (381 cm21)

obtained using HF/6-31G*. For the cationic case, the ionize

electron comes out from a bonding orbital predicting its

instability relative to the neutral monomer by

766.65 kJ mol21. It is also manifested in an increase of

the internuclear distance (0.2429 nm) and a decrease of the

frequency value (303 cm21) indicating that the bond in

cationic state is weaker than the corresponding one in the

neutral monomer.

Fig. 1. Ground state structures of AlnPmþ cations.

L. Guo et al. / Journal of Molecular Structure (Theochem) 680 (2004) 121–126122

AlP2þ. The present calculations predict a C2v(

2B2) ground

state for AlP2 molecule. Geometric sketch shows it to be

acute triangle with aP–Al–P ¼ 44:48 and the Al–P, P–P

bond lengths are 0.2617 and 0.1979 nm, which compare

well with Archibong’s values [13], indicating strong P–P

bonding in the case. Feng and Balasubramanian [14] has

predicted the ground state of AlP2þ is also an acute isosceles

triangle structures 2(a) with a closed-shell 1A1 state, which

has the same symmetry as that of the neutral AlP2 and the

removed electron is from the singly occupied 2b2 HOMO of

the neutral X 2B2 state. While the present calculations find it

a transition state indeed with an imaginary frequency at

78i cm21. This results from two types of different

theoretical methods (CASSCF and B3LYP), and the finally

optimized linear C1v(1S) geometry 1(a), which is

14.18 kJ mol21 lower in energy than 2(a), is confirmed to

be the ground state of AlP2þ without imaginary frequency.

The P–P bond length of the 1S state of this isomer is only

0.1896 nm, which is the shortest one among all AlP clusters

discussed and nearly equal to the P –P triple bond

(0.1893 nm) found in the P2 dimmer [14].

AlP3þ. In good agreement with previous calculations [13],

the minimum-energy structure found for neutral AlP3 is a

rhomboidal C2v(1A1) structure and a Cs(

1A0) structure 1(b)

with imaginary frequency lies 59.34 kJ mol21 higher in

energy. Distortion of 1(b) in the direction of the a00 mode

having the imaginary frequency results in another Cs(1A0)

structure 2(b), which is 9.71 kJ mol21 higher in energy than

the ground state. The energy ordering is significantly

different in the cations. Removing an electron stabilizes

the Cs(2A0) structure 1(b) with respect to the C2v(

2B2) and

Cs(2A00) 2(b) form and their energy differences are 119.99

and 8.9 kJ mol21, respectively.

AlP4þ. The most stable AlP4 isomer is a tetrahedral P4

structure [18] with a two-fold Al atom bond to it. While the

lowest-energy structure we found for AlP4þ is a distorted

trigonal bipyramid (Cs) 1(c), which can be derived from a

tetrahedral P4 structure by capping an additional Al atom

Fig. 2. Substate structures of AlnPmþ cations.

Table 1

Geometric parameters and electronic states of AlnPmþ clusters

Molecule Type L/nm Molecule Type L/nm

AlP2þ(1S) P1–Al2 0.2958 Al2Pþ3B2) Al1–P2 0.2269

P1–P3 0.1896

AlP3þ(2A0) Al1–P2 0.2689 Al2P2

þ(2B1u) P1–Al2 0.2453

P2–P3 0.2195 P1–P3 0.2135

P3–P4 0.2051

AlP4þ(1A0) P1–P2 0.2208 Al2P3

þ(1A01) Al1–P2 0.2377

P1–P3 0.2210 P2–P3 0.2400

P2–P3 0.2253 Al1–Al5 0.3862

P2–Al4 0.2860

P3–Al4 0.2886

AlP5þ(2A1) Al1–P2 0.2570 Al2P4

þ(2A1) Al1–P3 0.2859

P2–P3 0.2166 Al2–P4 0.2427

P4–P5 0.2256

P3–P5 0.2217

AlP6þ(1A0) P1–P2 0.2260 Al2P5

þ(1A0) Al1–P2 0.2273

P1–P3 0.2235 P2–Al3 0.2426

P2–P3 0.2243 P2–P4 0.2320

P1–Al4 0.2240 Al3–P5 0.2325

P2–P6 0.2506 P5–P6 0.2013

P3–P7 0.2463 P4–P6 0.2607

AlP7þ(2A00) Al1–P4 0.2349 Al2P6

þ(2B1) P1–Al2 0.2341

Al1–P5 0.2296 P1–P3 0.2308

P2–P3 0.2239 Al2–P4 0.2360

P2–P4 0.2268

P2–P6 0.2294

P3–P5 0.2328

L. Guo et al. / Journal of Molecular Structure (Theochem) 680 (2004) 121–126 123

between atoms (2,3,5). At the same time, bonding a two-

fold Al atom to the tetrahedral P4 form, we obtain a

substable isomer of AlP4þ 2(c) with C2v symmetry lying

10.76 kJ mol21 above the ground state, which has the very

similar geometry as that of the neutral AlP4. While the

distance between two neighboring P atoms (1,4) of the

cationic AlP4þ is contracted, resulting there exists a single

bond between the two P atoms. The common feature of the

two low-lying AlP4þ species is that they have the same P–P

bond numbers, while the numbers of Al–P bond are three

and two, respectively. Both AlP4 and its cation have the

same geometry as that of the GaAs4 [17], which agrees best

with the prediction of Gomez et al. [4] prediction. This is

attributed to the fact that both of them take a similar valence

structure due to the same family in the periodic table.

AlP5þ. The ground state of neutral AlP5 (C5v,

1A1) 1(d) is

derived from the P5 [16] cluster by placing a five-fold Al

atom on the top. In the procession, the geometry of P5 is

nearly maintained and the five same P–P bond lengths are

only elonged by 0.6%. Removing an electron from the

neutral molecule yields a cationic AlP5þ(2A1), which has the

same geometry as the neutral AlP5. The distorted triangle

prism 2(d) lying 40.96 kJ mol21 above the ground state is a

substable structure with Cs(2A00) symmetry, which is built

from substitution of a P atom by an Al atom in the triangle

prism P6.

AlP6þ. The face-capped triangle prism 2(e) is the ground

state of the neutral AlP6(C2v,2A2) in our present optimiz-

ation. It can be viewed as capping an additional Al atom on

the square face of the triangle prism P6. The P2–P4 and

P6–P7 bonds are broken in the capping procession.

Removing an electron produces the ground state structure

of cationic AlP6þ(Cs,

1A0) 1(e), which is different from the

neutral isomer and derived from a boat-shape P6 by adding

of one two-fold Al atom between atoms (1,5). Model 2(e) of

AlP6þ(C2v,1A1) is now a local minimum lying

12.08 kJ mol21 above the ground state. Removing an

electron results in the four same Al–P bonds (0.2384 nm)

of 2(e) are elonged compared to the corresponding Al–P

bond lengths (0.2362 nm) in the neutral isomer, while the

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

number of P–P bonds in 2(e) are less than those of 1(e),

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

the P–P bonds play a more decisive role than the Al–P

bonds in the determination of the geometry and energy of

AlP6þ.

AlP7þ. The present calculations consider a cuneane

structure 1(f) as the ground state of neutral AlP7, which

can be derived from a square-face-capped triangle prism P7

by adding an additional three-fold Al atom. The symmetry

of P7 is changed from C2v to lower Cs(1A0) symmetry of

AlP7 in the procession. AlP7þ(2A0) takes the same geometry

1(f) as the neutral. Another Cs isomer 2(f) of cationic AlP7þ

with the same electronic state as 1(f), lies 47.00 kJ mol21

above the ground state, which contains a one-fold Al atom.

3.1.2. Al2Pmþ clusters

Al2Pþ. The 2B2 state of triangle prevails as the ground

state of Al2P with the Al–P–Al apex angle of 96.78, and the

Al–P and Al–Al bond lengths of 0.2239 and 0.3347 nm

agree very well with Feng and Balasubramanian [14]

results. This global minimum exhibits the same symmetry

as that of the cationic Al2Pþ (C2v,3B2) 1(g). The comparison

of geometries of the neutral and cation reveals that the

Al–Al (0.3369 nm) bond lengths in Al2Pþ are elongated

with a more open Al–P–Al (97.08) bond angle, implying

that the Al–Al bond is further weaken upon ionization. The3Sg state of the linear configuration of Al2Pþ 2(g) is

11.03 kJ mol21 less stable than 1(g). The energy difference

between the two low-lying isomers is similar to Feng’s

result [14].

Al2P2þ. Feng and Balasubramanian [12] have investi-

gated T-shaped, linear, trapezoidal and rhombic structures

of Al2P2 at the CASSCF and MRSDCI levels, and we have

calculated both the singlet and triplet states of these and

other isomers. We support their prediction that the

rhombus (D2h) equilibrium structure 1(h) with 1Ag

electronic state is the ground state of Al2P2. Removing

an electron from it produces a cationic Al2P2þ(2B1u) 1(h),

which has the same geometry as the neutral. In the

rhombus cationic dimer, the loss of an electron results in

the decrease of the Al–P (from 0.2538 to 0.2453 nm) bond

distance, with a corresponding increase in the P–P

distances (from 0.2076 to 0.2135 nm). These bond lengths

agree very well with the calculations of Feng and

Balasubramanian [12]. The next lowest-energy isomer is

a trapezoidal form 2(h) with C2v(2A2) symmetry, which has

an imaginary frequency lying 82.44 kJ mol21 above the

ground state. The mode of imaginary frequency shows a

tendency for the rhombic ground state.

Al2P3þ. Balasubramanian and Feng [15] studied different

isomers of neutral Al2P3 cluster. We have considered these

and other structures and support their results that the most

stable configuration is regular trigonal bipyramid with

D3h(2A200) symmetry. The ground state structure of Al2P3

þ

(D3h,1A01) 1(i) is the same as that of the neutral Al2P3. The

P–P (0.2400 nm) bond length in the Al2P3þ is elonged, while

the Al–Al (0.3862 nm) and Al–P (0.2377 nm) bond lengths

are contracted compared to the corresponding bond lengths

of Al– Al (0.4089 nm), Al– P (0.2442 nm) and P – P

(0.2313 nm) in the neutral ground state. Next low-lying

Al2P3þ isomer in the energy ordering possesses C2v(

1A1)

geometry 2(i). This structure is a local minimum on the

potential energy surface of Al2P3þ, lying 23.89 kJ mol21

above the true ground state structure discussed above.

Al2P4þ. The lowest-energy Al2P4 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 Al2P3 isomer 1(i) by capping a

P atom between two adjacent P atoms. The structure of the

Al2P4þ 1(j) is different from its neutral molecule. This global

minimum of Al2P4þ (C2v,

2A1) can be obtained from

L. Guo et al. / Journal of Molecular Structure (Theochem) 680 (2004) 121–126124

the minimum structure of neutral AlP4 2(c) by capping an

additional Al atom between P2 and P3 atoms. The C2v(2B1)

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

transition state lying only 3.68 kJ mol21 higher in energy.

Al2P5þ. The present calculations predict the Cs(

2A0)

ground state 1(k) for neutral Al2P5. Another Cs isomer

2(k) with the same electronic state is located at

69.31 kJ mol21 above the ground state, which can be

derived from the substable structure of AlP5 2(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(1A0) structure 1(k) till the global minimum.

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

electronic state is now 38.59 kJ mol21 higher in energy.

Al2P6þ. The fully optimized ground state structure of Al2P6

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

is obtained by substitution of two P atoms by two Al atoms in

the cube P8 [19] cluster and similar to the cationic Al2P6þ (C2v,

2B1) 1(l) in shape. In the two lowest-energy structures of

Al2P6 and Al2P6þ, both Al and P atoms adopt the three-fold

coordination. The P–P (0.2308 nm) bond length in the Al2P6þ

is contracted, while the two different Al–P bond lengths

(0.2341 and 0.2360 nm) are elonged compared to the

corresponding bond lengths of P–P (0.2318 nm) and Al–P

bond lengths (0.2331 and 0.2345 nm) in the neutral ground

state. The substable structure of Al2P6þ is also with the

C2v(2B2) symmetry 2(l). We can very roughly decompose

this structure into two interacting entities: structures 2(a) and

2(c) are bridged with Al– Al bond. It is located at

93.99 kJ mol21 higher in energy.

The energy surface of a large molecule can be rather

complex and there could be other stable minimums

corresponding to geometries that are unexplored. Although,

the isomers of AlnPmþ 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 in

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 AlnPmþ are

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

are nearly in portion to increased n; their average enhance-

ment are 5.30 kJ mol21, 19.89 and 18.71 J mol21 k21 for

Table 2

Vibrational frequencies of AlnPmþ

Molecule V (cm21) I (km mol21) Molecule V (cm21) I (km mol21)

AlP2þ 7(P) 6 Al2Pþ 46(P) 5

143(a0) 107 250(su) 307

AlP3þ 32(e) 3 Al2P2

þ 32(Pu) 9

426(b1) 173 203(a0) 187

AlP4þ 33(b1) 0 Al2P3

þ 62(a2) 0

156(a1) 111 301(b1) 226

AlP5þ 68(a0) 3 Al2P4

þ 28(a00) 0

179(a0) 45 581(b1u) 117

AlP6þ 24(b1) 1 Al2P5

þ 11(a00) 2

148(a0) 89 160(a0) 99

AlP7þ 44(a0) 0 Al2P6

þ 7(a2) 0

177(a0) 19 217(a0) 125

Table 3

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

(kJ mol21), HOMO–LUMO energy gaps Egap (eV), heat capacity Cv

(J mol21 K21) and standard entropy SQ (J mol21 K21) for AlPmþ

Molecule Symmetry Et ZPE Egap Cv SQ

AlPþ C1v 2583.4546 1.81 2.76 27.74 236.89

AlP2þ C1v 2924.9164 5.69 4.48 48.11 327.36

AlP2þ C2v 2924.9110 5.37 4.17 35.86 282.98

AlP3þ Cs 21266.2916 10.28 3.69 65.71 346.46

AlP3þ Cs 21266.2882 10.10 3.18 66.29 339.94

AlP4þ Cs 21607.7266 17.30 4.94 84.25 359.03

AlP4þ C2v 21607.7225 17.43 4.35 83.88 377.03

AlP5þ C5v 21949.0807 23.71 3.39 105.00 358.44

AlP5þ Cs 21949.0651 23.27 2.28 105.42 374.87

AlP6þ Cs 22290.4870 28.47 4.22 125.27 412.71

AlP6þ C2v 22290.4824 28.46 2.79 125.21 409.10

AlP7þ Cs 22631.8679 33.62 3.04 147.07 430.92

AlP7þ Cs 22631.8500 30.99 2.01 149.28 461.23

Table 4

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

(kJ mol21), HOMO–LUMO energy gaps Egap (eV), heat capacity Cv

(J mol21 K21) and standard entropy SQ (J mol21 K21) for Al2Pmþ

Molecule Symmetry Et ZPE Egap Cv SQ

Al2Pþ C2v 2825.9730 5.44 3.74 45.20 297.72

Al2Pþ D1h 2825.9688 4.14 1.95 52.43 304.31

Al2P2þ D2h 21167.3903 10.17 2.45 66.94 319.31

Al2P2þ C2v 21167.3589 9.30 1.06 58.80 316.08

Al2P3þ D3h 21508.7884 17.96 2.83 85.00 322.79

Al2P3þ C2v 21508.7793 12.66 2.19 89.54 386.39

Al2P4þ C2v 21850.1763 20.03 3.28 108.38 400.85

Al2P4þ C2v 21850.1749 19.38 2.83 100.61 376.58

Al2P5þ CS 22191.5753 27.60 2.78 126.73 408.05

Al2P5þ CS 22191.5606 26.19 2.46 129.02 409.33

Al2P6þ C2v 22532.9827 35.27 2.70 145.84 408.85

Al2P6þ C2v 22532.9469 30.01 1.51 148.16 515.46

L. Guo et al. / Journal of Molecular Structure (Theochem) 680 (2004) 121–126 125

AlPmþ cations, respectively, and those are 5.97 kJ mol21,

20.33 and 22.39 J mol21 k21 for Al2Pmþ cations, respectively.

Except for AlP4þ, 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.

To test the stability of cluster further, the following

energy variation of reaction is considered:

2ðAlPþmÞ! ðAlPþ

mþ1Þ þ ðAlPþm21Þ

We define the energy variation in formula as D2Em ¼

Emþ1 þ Em21 2 2Em; the second difference in energy for

AlPmþ. 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 theD2Em is larger as odd m and lower as even m;

which indicates that those AlPmþ clusters corresponding to m

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

AlPmþ is that the total atom number m should be odd. So, both

AlP4þ and AlP6

þ 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 AlPm and Al2Pm

are plotted as a function of cluster size in Fig. 4. The IP

values of AlP4, AlP6 are the peak values, which correspond

to enhanced stability and are in good consistent with the

D2Em values discussed above. So, it approves furthermore,

the stability of these clusters.

4. Conclusions

Structural and electronic properties of semiconductor

binary microclusters AlnPmþ cations have been investi-

gated using the B3LYP–DFT method in the ranges of

n ¼ 1; 2 and m ¼ 1–7: Full structural optimization,

adiabatic ionization potentials calculation and frequency

analyses are performed with the basis of 6-311G(d). The

charge-induced structural changes in these cations have

been discussed. The strong P–P bond is also favored

over Al–P bonds in the AlnPmþ cations in comparison

with corresponding neutral cluster. With Pm forming the

base, adding Al atom(s) in different positions would find

the stable structures of AlnPmþ cations quickly and

correctly. Both AlP4þ and AlP6

þ are predicted to be

species with high stabilities and possible to be produced

experimentally.

Acknowledgements

This work was supported by the National Science

Foundation of China (20341005).

References

[1] C.C. Arnold, D.M. Nermark, J. Chem. Phys. 99 (1994) 3353.

[2] C.C. Arnold, D.M. Nermark, J. Chem. Phys. 100 (1994) 1797.

[3] G.R. Burton, C. Xu, C.C. Arnold, J. Chem. Phys. 104 (1996) 2757.

[4] H.Gomez,T.R.Taylor,D.M.Neumark,J.Phys.Chem.A105(2001)6886.

[5] Z.Y. Liu, C.R. Wang, R.B. Huang, Int. J. Mass Spectrom. Ion

Processes 141 (1995) 201.

[6] P.J. Bruna, F.J. Grein, Phys. B: At. Mol. Opt. Phys. 22 (1989) 1913.

[7] U. Meier, S.D. Peyerimhoff, P.J. Bruna, Chem. Phys. 130 (1989) 31.

[8] M.A. Allaham, G.W. Trucks, K.J. Raghavachari, J.Chem. Phys. 96

(1992) 1137.

[9] P. Rodriguez-Hernandez, A. Munoz, Semiconduct. Sci.Technol. 7

(1992) 1437.

[10] A. Tomasulo, M.V. Ramakrishna, J. Chem. Phys. 105 (1996) 10449.

[11] P.Y. Feng, K. Balasubramanian, Chem. Phys. Lett. 301 (1999) 458.

[12] P.Y. Feng, K. Balasubramanian, J. Phys. Chem. A 103 (1999) 9093.

[13] E.F. Archibong, R.M. Gregorius, S.A. Alexander, Chem. Phys. Lett.

321 (2000) 253.

[14] P.Y. Feng, K. Balasubramanian, Chem. Phys. Lett. 318 (2000) 417.

[15] K. Balasubramanian, P.Y. Feng, J. Phys.Chem. A 105 (2001) 11295.

[16] M.D. Chen, R.B. Huang, Chem. Phys. Lett. 325 (2000) 22.

[17] P. Piquini, S. Canuto, A. Fazzio, Nanostruct. Mater. 10 (1998) 635.

[18] H.K. Quek, Y.P. Feng, C.K. Ong, Z. Phys. D 42 (1997) 309.

[19] M.D. Chen, R.B. Huang, L.S. Zheng, J. Mol. Struct. (Theochem) 499

(2000) 195.

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

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

L. Guo et al. / Journal of Molecular Structure (Theochem) 680 (2004) 121–126126