Ab initio investigation of structures and stability of AlnPm clusters

Ab initio investigation of structures and stability of AlnPm clusters

Ling Guoa,b,*, Hai-shun Wua,*, Zhi-hao Jinb

aSchool of Chemistry and Material Science, Shanxi Normal University, Linfen 041004, ChinabSchool of Material Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 28 February 2004; accepted 21 June 2004

Available online 23 August 2004

Abstract

Various structural possibilities for AlnPm (nCmZ3–6) neutral and anionic isomers were investigated using the density functional method

of Becke’s three-parameter hybrid exchange functional with the nonlocal correlation of Lee, Yang, and Parr. Berny structural optimization

and frequency analyses are performed with the basis of 6-311CG(d) for both the neutrals and anions. The calculations predicted the

existence of a number of previously unknown isomers. The calculation results show that the singlet structures have higher symmetries than

those of doublet structures. The adiabatic electron affinities and vertical detachment energies calculated at the optimized ground-state

structures agree satisfactorily with recent experimental values.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Density functional method; Aluminum phosphides; AlnPm clusters

1. Introduction

The chemistry and physics of the compounds formed

by the elements in groups III and V is extraordinarily

rich and their usefulness in the semiconductor industries

has been a motivation for the numerous experimental and

theoretical studies [1–6]. Among them, the aluminum

phosphides have received considerable attention, as they

have higher vibrational frequencies (due to lower

masses), and, thus, as noted by Gomez et al. [7], could

result in vibrational progressions in the spectra compared

to heavier clusters. In addition, the smaller number of

electrons makes them more amenable to electronic

structure calculations. There have been some previous

theoretical studies on AlnPm cluster. Aurora Costales

et al. [8] have theoretically investigated the structure,

stability, and vibrational properties of the (AlP)n (nZ1–

3) using both gradient-corrected (GGA) Becke exchange

functional [9] and Perdew and Wang [10] correlation

functional. Archibong et al [11,12] have reported the

equilibrium geometries, harmonic vibrational frequencies

and electron detachment energies of the neutral

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

doi:10.1016/j.theochem.2004.06.038

* Corresponding author. Tel./fax: C86-357-2051375.

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

and anion AlP2, Al2P2, Al3P, and AlP3 performed at

density functional theory (B3LYP, BP86 and BPW91-

DFT) and ab initio methods [MP2 and CCSD (T)]. Ping

Yi Feng and Balasubramanian [13–15] have also studied

the structures and potential energy curves of a number of

electronic states of Al3P, AlP3 and its positive ions,

Al2P3, Al3P2 and their ions using the complete active

space self-consistent field (CASSCF) method followed

by multireference singles and doubles configuration

interaction (MRSDCI), and found the C3v structure to

be the global minima of AlP3, which is different

from Archibong [12] prediction. Other theoretical studies

on AlnPm and AlnPKm have been also published [16–20].

Gomez et al., [7] reported the experimental adiabatic

electron affinity and vertical detachment energy of AlnPm.

The theoretical prediction of AlnPm electron

detachment energy and electron affinities is found in

the 2000–2002 study of Archibong and Feng et al. [11,

12,15,20]. In the present study, we performed calcu-

lations on AlnPm (nCmZ3–6) neutral and anionic

species with standard B3LYP/6-311CG(d) method to

provide more reliable ground-state geometries and

relative stability. The charge-induced structural change

in these clusters will be discussed. It is to be noted here

that the reliability of the present calculations will be

Journal of Molecular Structure (Theochem) 684 (2004) 67–73

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L. Guo et al. / Journal of Molecular Structure (Theochem) 684 (2004) 67–7368

verified by a comparison of the theoretical results and

photoelectron spectra.

2. Computational methods

Initial geometrical optimizations were performed at the

B3LYP/6-31G(d) level without any symmetry constraints,

except for those needed to maintain a particular geometry.

These minimized AlnPm structures were further optimized

using the B3LYP/6-311CG(d) method. The second-order

Moller–Plesset (MP2) energy was evaluated to determine the

most stable isomers. Harmonic frequencies were evaluated

(at B3LYP/6-311CG(d)) to characterize the stationary

points as minima or transition-state structures on the

potential energy surfaces of corresponding clusters. All of

the obtained most stable charged and neutral AlnPm clusters

were characterized as energy minima without imaginary

frequencies. Partial charges were given with Mulliken

atomic charges. The first electron affinities of various

clusters were calculated with the adiabatic approximation.

All calculations were carried out using the GAUSSIAN 98

program [21] on SGI/O2 workstations in our laboratory.

3. Results and discussion

Geometric parameters of the lowest energy neutral and

anionic species are listed in Tables 1 and 2, respectively.

Several equilibrium geometries for energetically low-lying

isomers are presented in Figs. 1–6, and the respective

‘bonds’ are shown for internuclear separations of less than

3.30 (Al–Al), 3.00 (Al–P) and 2.50 A (P–P). Total energies

are reported in Table 3 for neutral and anionic clusters.

Table 1

Distances between two atoms (L/A) in AlnPm neutral clusters

Symmetry Type L

Al2P C2v 1–3 2.242

AlP2 C2v 1–2 2.622 A

2–3 1.980

Al3P D3h 1–2 2.362 A

AlP3 C2v 1–2 2.106

1–3 2.471

2–3 2.299

Al2P2 D2h 1–2 2.539

2–3 2.078

Al4P C2v 1–2 2.408 A

1–3 2.472

2–3 2.845 A

3–5 2.638

AlP4 C2v 1–2 2.371 A

2–3 2.279

3–5 2.182

Al3P2 C2v 1–2 2.313

1–3 2.525 A

3.1. AlnPm (nCmZ3) clusters

3.1.1. Al2P

The neutral Al2P can adopt C2v and DNh structures with

comparable energy, the C2v (2B2) isomer being 0.16 eV

more stable than the linear. The linear molecule with an

imaginary bending-mode frequency shows the tendency of

the phosphorus atom to vibrate along the radial direction

into the triangle, 1(a). Feng and Balasubramanian [14]

reported a theoretical bond length of 2.250 A at the

MRSDCICQ level of theory with the RECPSC3s3p basis

sets. Our B3LYP result of 2.242 A is close to their result.

Their energy ordering is preserved in the anion. The C2v

(1A1) configuration is more stable than the linear configur-

ation by 0.10 eV.

A comparison between neutral and anionic triangular

species shows an increase of 3.8% in the Al–P–Al bond

angle. This may be ascribed to the increase in electrostatic

force between Al atoms because the net charge of Al atoms

is increased significantly upon charging (Table 4).

3.1.2. AlP2

The present calculations predict a C2v (2B2) ground state

with a bond angle of qPAlPZ45.88 for AlP2 molecule. Feng

and Balasubramanian [14] reported a theoretical bond

lengths of 2.599 and 1.989 A for Al–P and P–P bonds and

a bond angle of 45.08 at the MRSDCICQ level of theory

with relativistic effective core potentials (RECPS) and 3s3p

valence basis sets. Achibong et al. [11] have optimized the

geometry with rAl–PZ2.603 A, rp–pZ1.985 A, qPalPZ44.88

at the BPw91 level, and rAl–PZ2.580 A, rp–pZ1.990 A,

qPalP Z45.48 at the CCSD(T) level with the 6-311CG(2df)

one-particle basis set. Our B3LYP results are close to

the earlier MRSDCICQ and CCSD(T) results. A bent

chain (Cs,2A 00) 1(d) is 0.65 eV less stable. Its imaginary

Symmetry Type L

1–5 2.495

l2P3 D3h 1–2 2.445

2–3 2.317

l5P Cs 1–3 2.549

1–5 2.381

2–3 2.940

2–5 2.581

3–4 2.551

3–6 2.761

lP5 C5v 1–4 2.914

1–2 2.130

l2P4 C2v 1–2 2.189

1–3 2.787

l4P2 C2v 1–2 2.523

2–4 2.441

2–6 2.384

3–4 2.616

l3P3 D3h 1–2 2.226

Table 2

Distances between two atoms (L/A) in AlnPKm anions

Symmetry Type L Symmetry Type L

Al2P C2v 1–3 2.259 1–5 2.363

AlP2 C2v 1–2 2.440 3–4 2.640

2–3 2.073 2–5 2.610

Al3P C2v 1–2 2.731 4–5 3.260

1–3 2.529 AlP5 Cs 1–2 2.195

2–3 2.341 1–4 2.553

AlP3 Cs 1–2 2.182 1–5 2.231

2–3 2.466 2–3 2.116

2–4 2.341 Al2P4 Cs 1–3 2.332

Al2P2 C2v 1–2 2.442 1–4 2.292

2–3 2.247 1–5 2.712

Al4P C4v 1–5 2.395 2–3 2.259

AlP4 C4v 1–2 2.180 2–5 2.539

1–5 2.682 3–6 2.345

Al3P2 D3h 1–2 2.468 Al4P2 C2v 1–2 2.592

1–5 2.396 1–3 2.494

Al2P3 D3h 1–2 2.539 1–4 2.320

2–3 2.261 2–3 2.835

Al5P Cs 1–3 2.470 Al3P3 D3h 1–2 2.244

1–4 2.570

L. Guo et al. / Journal of Molecular Structure (Theochem) 684 (2004) 67–73 69

bending-mode frequency shows the tendency of the

vibrating middle phosphorus atom along the radial direction

into the ground state 1(c).

The C2v (1A1) anionic conformer 1(c) is also an

energetically most favourable configuration, which is

consistent with previous calculations [11]. It is 0.77 eV

more stable than Cs (3A 00) isomer 1(d). A comparison of the

triangle shows that the P–P bond in the anion is longer than

those in the neutral isomer by about 3.9%. This may be

linked to the increase in electrostatic repulsive force

between P and P atoms because the net charge of P atoms

is increased upon charging.


3.2.1. Al3P

Archibing [20] investigated five different neutral and

anionic isomers at the B3LYP, MP2, and CCSD(T) levels of

theory using the 6-311CG(2df) one-particle basis set. We

support their prediction that the energetically most favourable

isomer is the planar D3h (1A10) isomer 2(b). A rhomboidal

(C2v,1A1) structure 2(a) is 0.37 eV less stable. Another

low-lying isomer is Cs (1A 0) structure 2(c) at 1.05 eV.

The energy ordering is partially changed in the anion. C2v

(2B2) rhombus 2(a) in the anion is the energetically most

favourable isomer. Archibing et al. [20] reported the

Al1–Al2, Al1–P3 and Al2–P3 bond distances as 2.750,

2.468 and 2.338 A at the MP2/6-311CG(2df) level,

and 2.716, 2.512 and 2.343 A at the CCSD(T) level,

Fig. 1. Low-lying isomers of (a,b) Al2P- and (c,d) AlPK2 anions.

respectively. Our B3LYP method predicts the 2.731, 2.529

and 2.341 A for the Al1–Al2, Al1–P3 and Al2–P3 bonds,

giving the most reliable bond lengths for comparison with

the MP2 and CCSD(T). D3h anion does not converge at all.

And Cs (2A 0) isomer 2(c) is 0.76 eV less stable.

3.2.2. AlP3

The geometry of the ground state of AlP3 is displayed in

Fig. 2(f). AlP3 is a stable clusters, and many experimental and

theoretical studies have been reported. Liu et al. [22] have

observed the AlPK3 cluster in TOF. Gomez et al. [7] reported

the experimental adiabatic electron affinity (2.06G0.05 eV)

and vertical detachment energy (2.58G0.025 eV) for AlP3.

The previous theoretical studies of the AlP3 geometry

include the 1999 work by Feng and Balasubramanian [13]

at the ab initio CASSCF/MRSDCI level of theory with

Fig. 2. Low-lying isomers of (a–c) Al3PK, (d–f) AlP3K and (g–i) Al2PK

2

anions.

Fig. 5. Comparison between the calculated adiabatic electron affinities

(circles) and corresponding experimental values (squares) of AlnPm.

Fig. 3. Low-lying isomers of (a–c) Al4PK, (d–f) AlP4K, (g–i) Al2PK

3 and

(j–l) Al3PK2 anions.

Fig. 4. Low-lying isomers of (a–c) Al5PK, (d–f) AlPK5 ; (g–i) Al2PK

4 ; (j–l)

Al4PK2 and (m–o) Al3PK

3 anions.


the RECPsC3s3p basis sets, and the 2002 work by

Archibong, Goh, and Marynick [12] with the B3LYP-DFT,

MP2 and CCSD (T) methods. Feng’s studies appeared to

have established the ground state geometry of AlP3 to be

the pyramidal C3v (3A2) structure. They reported the Al–P and

P–P bond distances and the P–Al–P bond angle to be 2.780,

2.165 A and 45.88, respectively. While Archibong et al.

gave the different conclusion. They found two singlet states

(1A1–C2v and 1A 0–Cs) were nearly degenerate and lower in

energy by at least 0.5 eV than the triplet (3A2–C3v) state

previously predicted by Feng et al. as the ground electronic

state of AlP3, and predicted the C2v structure to be the ground

state of AlP3. Our optimized AlP3 ground state is consistent

with Archibong’s results. Two Cs (1A 0) isomers 2(d) and 2(e)

lie 0.08 and 0.57 eV above the 2(e) isomer, respectively.

The energy ordering differs in the anion. The lowest-

energy state is found to be 3D distorted tetrahedron structure

2(d) with Cs (2A 0) symmetry. Next in the energy ordering is

(Cs,2A 00) isomer 2(e), located 0.10 eV above the ground

state. Their energy difference and ordering is similar to

those of previous calculations [12] on the anions. The third

is the planar C2v (2A1) isomer 2(f) lying 0.13 eV above the

ground state.

Fig. 6. Comparison between the calculated vertical detachment energies

(circles) and corresponding experimental values (squares) of AlnPm.

Table 3

Total energy (au/B3LYP) for neutral and anionic clusters

Neutral Sym-

metry

Energy Anion Sym-

metry

Energy

Al2P C2v 826.2453 Al2PK C2v 826.3358

AlP2 C2v 925.1782 AlPK2 C2v 925.2510

Al3P D3h 1068.7375 Al3PK C2v 1608.7938

AlP3 C2v 1266.5764 AlPK3 Cs 1266.6475

Al2P2 D2h 1167.6605 Al2PK2 C2v 1167.7308

Al4P C2v 1311.1864 Al4PK C4v 1311.2552

AlP4 C2v 1607.9743 AlPK4 C4v 1608.0705

Al3P2 C2v 1410.1184 Al3PK2 D3h 1410.2194

Al2P3 D3h 1509.0660 Al2PK3 D3h 1509.1584

Al5P Cs 1553.6495 Al5PK Cs 1553.7235

AlP5 C5v 1949.3832 AlPK5 Cs 1949.4469

Al4P2 C2v 1652.6045 Al4PK2 C2v 1652.6810

Al2P4 C2v 1850.4512 Al2PK4 Cs 1850.5335

Al3P3 D3h 1751.5487 Al3PK3 D3h 1751.6421


Because the broad envelop of the photoelectron spec-

troscopy [7] indicates significant geometrical reorganization

in the neutral, the neutral and anionic AlP3 species having

the different geometrical structure should be reasonable.

3.2.3. Al2P2

The equilibrium structure of the 1Ag ground state of

neutral Al2P2 is displayed in Fig. 2(h). For the D2h Al2P2

structure, the optimized Al–P, P–P bond lengths and P–Al–P

bond angle are 2.539, 2.078 A and 44.48, respectively.

Costales et al. [8] reported a theoretical Al–P and P–P bond

lengths of 2.530 and 2.080 A and a bond angle of 488 at

the GGA/DNP level of theory. Al-Laham et al. [16] using

HF/6-31G(d) theory reported 2.530, 2.040 A and 488, their

work seems to underestimate the P–P distance due to neglect

of electron correlation. Our B3LYP results are close to the

earlier GGA/DNP and HF results. The energy of (Cs,1A 0)

trapezoid 2(i) is 0.47 eV above rhombus 2(h).

The energy ordering of the anions differs from that of the

neutral cluster. The anionic Al2PK2 is found to have a no

Table 4

Lowest vibrational frequencies (cmK1) for neutral and anionic ground-state

clusters

Neutral Sym-

metry

v Anion Sym-

metry

v

Al2P C2v 66.1 Al2PK C2v 67.1

AlP2 C2v 146.4 AlPK2 C2v 286.1

Al3P D3h 51.2 Al3PK C2v 75.0

AlP3 C2v 191.9 AlPK3 Cs 151.9

Al2P2 D2h 95.4 Al2PK2 C2v 54.7

Al4P C2v 38.8 Al4PK C4v 67.9

AlP4 C2v 79.3 AlPK4 C4v 153.4

Al3P2 C2v 57.7 Al3PK2 D3h 101.1

Al2P3 D3h 176.5 Al2PK3 D3h 146.3

Al5P Cs 82.7 Al5PK Cs 42.9

AlP5 C5v 131.7 AlPK5 Cs 15.5

Al4P2 C2v 21.8 Al4PK2 C2v 64.6

Al2P4 C2v 76.9 Al2PK4 Cs 92.6

Al3P3 D3h 86.1 Al3PK3 D3h 120.1

planar C2v(2B1) distorted tetrahedron ground state (‘butter-

butterfly’ structure 2(g)), which is different from Feng’s [19]

prediction of D2h geometry, and in agreement with the results

of Archibong [11] and Gomez [7]. Next in the energy

ordering is the D2h (2B1g) rhombus 2(h), located only 0.01 eV

above the ground state. Their energies should be evaluated

with MP2 because of their near degeneracy. It is found that

2(g) is 0.05 eV more stable than 2(h), which is in agreement

with the density functional calculation. The third is the planar

Cs(2A 00) isomer 2(i), which is 0.47 eV higher in energy.

A noticeable point is that the charge is equally distributed

(0.075 e per aluminum and K0.075 e per phosphorus) in a

neutral molecule whereas a P atom bears a K0.3 e charge in

the rhombic anion. A comparison between neutral and anionic

rhombus species shows an increase of 8.4% in the P–P bond

length. This may be link to the increase in electrostatic

repulsive force between P and P atoms upon charging.

Because the existence of a sharp peak among the broad

peaks in the photoelectron spectroscopy [7] indicates the

coexistence of several isomers in the neutral cluster, the

small energy difference in 2(g) and 2(h) anionic isomers is

compatible with the observed complicated spectrum.


3.3.1. Al4P

The lowest-energy Al4P isomer is a planar C2v (2A1)

structure 3(b), which can be derived from the minimum-

energy structure of Al5 [23] by replacing the central Al atom

with a P atom. Next in the energy ordering is the C2v (2B2)

isomer 3(c), located only 0.05 eV above the ground state.

Their energies should be evaluated with MP4(SDTQ)

because of their near degeneracy. It is found that 3(b) is

0.08 eV more stable than 3(c). The third is a square

pyramidal C4v (2B1) isomer 3(a) with an imaginary

frequency, which is located 0.31 eV higher in energy.

The energy ordering of the anion differs from that of the

neutral cluster. An additional electron makes the planar C2v

(1A1) 3(b) and the C4v (1A1) square pyramid 3(a) nearly

degenerate. We found that 3(a) is 0.17 eV more stable than

3(b) at MP2/6-311CG(d) level, which is in agreement with

the density functional calculation. Another planar C2v (1A1)

isomer is 0.10 eV less stable.

Because the existence of a sharp peak among the broad

peaks in the photoelectron spectroscopy [7] indicates the

coexistence of several isomers in the neutral cluster, the

small energy difference in 3(a) and 3(b) anionic isomers is

compatible with the observed complicated spectrum.

3.3.2. AlP4

The ground state of the AlP4 molecule is found to be the

3D (C2v,2A1) isomer 3(f), which can be seen as a tetrahedral

P4 with a two-fold Al atom bond to it. It is similar to the

valence-isoelectronic GaAs4 reported by Piquini [24], and

this similarity proves the Gomez’s prediction [7] that small

AlP clusters can adopt the two- and three-dimensional


characteristic of GaxAsy clusters. Planar C2v (2B1) form 3(e)

can be considered to replace a P atom in an apical position

with an Al atom in the structure of P5 (a planar D5h

pentagon). It lies 0.24 eV higher in energy. Structure 3(d)

(C4v,2A1) lies 0.77 eV higher in energy.


energy state is found to be the square pyramidal C4v (1A1)

structure 3(d). Two C2v (1A1) isomers 3(e) and 3(f) are 0.26

and 0.77 eV less stable relative to 3(d), respectively.

The existence of a broad envelop of the photoelectron

spectroscopy [7] of the AlP4 anion indicates significant

geometrical reorganization in the neutral. Our calculated

results are consistent with such experimental observations.

3.3.3. Al2P3

Both Al2P3 neutral and anion have the same D3h trigonal

bipyramidal structure, which is given in Fig. 3(g).

Balasubramanian and Feng [15] studied the Al2P3 structure.

They reported the Al–P and P–P distances to be 2.434 and

2.300 A, respectively, using the CASSCF/MRSDCI level of

theory with the RECPsC3s3p basis sets. Our B3LYP bond

distances 2.445 and 2.317 A are close to the their

predictions. Structure 3(h) (C2v,2A1) is 0.39 eV higher in

energy than the 3(g) and 0.43 eV below the C1 (2A) 3(i).

The additional electron has no effect on the relative

stability of the anionic isomers. For the 1A10 ground state

of Al2PK3 ; the symmetry dose not change, but the P–P

bond lengths are shorter than those of the neutral species

by K0.056 A, and the Al–P bond lengths are longer by

K0.094 A. This may be link to the different change of

electrostatic force among Al–P atoms and P–P atoms because

transverse equatorial Al atoms reverse the sign of their

charge upon charging. Balasubramanian and Feng [15] also

optimized the anionic Al2PK3 structure, predicting the bond

distances to be 2.523 A (Al–P) and 2.263 A (P–P) at the

CASSCF level. Their bond lengths are in good agreement

with our B3LYP bond distances. Two low-lying isomers are

the C2v (1A1) form 3(h) and C1 (1A) structure 3(i), located

0.28 and 0.83 eV above the 3(g), respectively.

3.3.4. Al3P2

Balasubramanian et al. [15] investigated Al3P2 neutral

and charged isomers. We support their results that the most

stable configuration is the distorted bipyramid (C2v,2A1)

[quite similar to 3(j)]. Next in the energy ordering, located

0.11 eV above the 3(j), is a C2 (2A) form 3(k). The third is a

Cs (2A 0) form 3(l) obtained by replacing a P atom in a

equatorial position with an Al atom in configuration 3(h),

which is located 0.23 eV above the ground state.

The trigonal bipyramid (D3h, 1A10) 3(j) is the energeti-

cally most favourable form in the anion, which agrees well

with the calculation [15]. The symmetry of the neutral

structure (C2v) is changed to D3h symmetry upon charging.

The (C2, 1A) anion 3(k) is 0.05 eV above the ground state

3(j) and 0.41 eV below Cs (1A 0) isomer 3(l).


3.4.1. Al5P

The Cs symmetry structure of the 1A 0 ground state for the

neutral Al5P is shown in Fig. 4(a), which is derived from

the substitution of an Al atom in an apical position by a P

atom in the Al6 octahedron [23]. The next structure in the

energy ordering is Cs (1A 0) structure 4(b) with an imaginary

frequency, which is located 0.28 eV above the ground state.

The third is a planar (Cs,1A 0) isomer 4(c) built from capping

an Al atom over atoms (1,5) in structure 3(b) lying 0.49 eV

above the ground state.

The energy ordering is preserved in the anion. Cs (2A 0)

anion 4(b) lies 0.17 eV above isomer 4(a) and 0.40 eV

below the 4(c) isomer.

The addition of an electron to the neutral ground state

4(a) results in an increase in the separation among atoms

Al–Al and a reduction in the separation among atoms Al–P

in the anion. This may be linked to the different change of

electrostatic force among Al–Al atoms and Al–P atoms

because the net charge of Al atoms is increased upon

charging.

3.4.2. AlP5

AlP5 takes a pentagonal pyramid (C5v,1A1) 4(d) as its

ground-state structure, which is obtained by adding an Al

atom over the minimum-energy structure of P5 pentagon.

The (Cs,1A 0) structure 4(e) lies 1.05 eV higher in energy. It

is obtained by replacing a P atom in an apical position with

an Al atom in structure of P6 (a trigonal prism). Another

low-lying isomer is Cs (1A 0) isomer 4(f) at 1.61 eV.

Their energy ordering is preserved in the anion. Cs (2A 0)

form 4(d) in the anion is the energetically most favourable

isomer. The symmetry of the neutral structure (C5v) is

lowered to Cs symmetry upon charging. Cs (2A 0) structure

4(e) is 0.54 eV higher in energy than isomer 4(d) and

0.45 eV below Cs (2A 00) isomer 4(f).

The addition of an electron to the neutral C5v isomer

results in symmetry lowering. It results from the change in

electrostatic force between Al–P atoms because of three P

atoms (2,3,6) reverse the sign of their charge upon charging.

3.4.3. Al2P4

The ground state of the Al2P4 molecule is found to be C2v

(1A1) octahedron 4(i), which is obtained by the substitution

of two apical P atoms by Al atoms in the P6 octahedron.

Two low-lying Cs (1A 0) isomers 4(h) and 4(g) are located

0.54 and 0.69 eV above the 4(g), respectively.


energy state is found to be 3D Cs(2A 0) structure 4(g), which

is 0.56 and 2.24 eV more stable than the 4(h) and 4(i),

respectively.

3.4.4. Al4P2

The global minimum of Al4P2 is an edge-capped trigonal

bipyramid (C2v,1A1) 4(k), which is built by capping an Al


atom over atoms (4, 5) in anion 3(j). C2v (1A1) isomer 4(j)

and CS (1A 0) isomer 4(l) lie 0.17 and 0.24 eV above the

ground state, respectively.

The energy ordering of the anion is partially changed.

The energetically most stable structure is the distorted

octahedron (C2v,2A1) 4(j), which is 0.02 and 0.08 eV more

stable than the (C2v,2B1) isomer 4(k) at B3LYP/6-311C

G(d) and MP2/6-311CG(d) levels of theory, respectively.

The third is the (Cs,2A 00) isomer 4(l) with an imaginary

frequency, which is 0.2 eV above the ground state.

3.4.5. Al3P3

Raghavachari et al. [16] performed a calculation on the

eleven geometric structure of Al3P3 and obtained the

lowest-energy isomer to be D3h structure 4(m). Our present

results support their predictions that the (D3h, 1A10) structure

as the ground state of the Al3P3 molecule, which is derived

from the three phosphorus’ edge capping the Al3 triangle.

This is followed by a capped trigonal bipyramid Cs (1A 0)

structure 4(o), lying 0.33 eV above the 4(m). It is build from

capping an Al atom over atoms (1,3,4) in configuration 3(g).

Another low-lying isomer is Cs (1A 0) structure 4(n), which is

0.61 eV less stable.

The energy ordering is partially changed in the anion.

The planar D3h (2A10) hexagon 4(m) is also the energetically

most favourable form. Two Cs isomers 4(n) and 4(o) lie 1.09

and 1.65 eV above the 4(m) isomer, respectively.

A comparison between neutral and anionic hexagon

shows an increase in the separation of atoms 1–2 by about

1.8%, which is linked to the P atoms reverse the sign of their

charge upon charging.

The calculated adiabatic electron affinities (AEAs) and

vertical detachment energies (VDEs) are compared with

recent experimental values in Figs. 5 and 6. As can be seen

from Fig. 5, Our calculated AEAs generally agree well with

experimental AEAs, reproducing all the variations of the

AEA values observed in experiments. The AEA values of

Al3P, AlP3 and Al2P2 are smaller values, which correspond

to relatively stable neutral state. As for vertical detachment

energies, our calculated VDEs also agree satisfactorily with

photoemission experiments (see Fig. 6). The measured

maximum at (n, m)Z(1, 4), the minimum at (n, m)Z(3, 1),

and the decreasing at Al4P2 are all reproduced. No

photoelectron measurements are available for the Al5P,

AlP5 and Al2P4 clusters at present, hence it would be of

great interest to see more experimental studies being done

on them.

4. Summary

In summary, we have presented a comprehensive

DFT-B3LYP study for AlnPm cluster neutrals and anions

in the size range of nCmZ3–6. The calculations predicted

the existence of a number of previously unknown isomers.

The calculation results show that the singlet structures have

higher symmetry than those of doublet structures. The DFT

AEAs and vertical detachment energies agree well with

experiments.

Acknowledgements

This work was supported by the National Science

Foundation of China (20341005).

References

[1] W. Andreoni, Phys. Rev. B. 45 (1992) 4203.

[2] L. Lou, L. Wang, L. Chibante, R.T. Laaksonen, P. Nordlander,

R.J. Smalley, Chem. Phys. 94 (1991) 8015.

[3] K.R. Asmis, T.R. Taylor, D.M. Neumark, J. Chem. Phys. 111 (1999)

8838.

[4] K.R. Asmis, T.R. Taylor, D.M. Neumark, J. Chem. Phys. 111 (1999)

10491.

[5] T.R. Taylor, K.R. Asmis, C.S. Xu, D.M. Neumark, Chem. Phys. Lett.

297 (1998) 133.

[6] K. Balasubramanian, Chem. Phys. Lett. 171 (1990) 58.

[7] H. Gomez, T.R. Taylor, D.D.J. Neumark, Phys. Chem. A 105 (2001)

6886.

[8] A. Costales, A.K. Kandalam, R. Franco, R. Pandey, J. Phys. Chem. B

106 (2002) 1940.

[9] A.D. Becke, Phys. Rev. A 38 (1988) 3098.

[10] Y. Wang, J.P. Perdew, Phys. Rev. A 43 (1991) 8911.

[11] E.F. Archibing, R.M. Gregorius, S.A. Alexander, Chem. Phys. Lett.

321 (2000) 253.

[12] E.F. Archibing, S.K. Goh, D.S. Marynick, Chem. Phys. Lett. 361

(2002) 214.

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

[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.A. Al-Laham, G.W. Trucks, K. Raghavachari, J. Chem. Phys. 96

(1992) 1137.

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

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

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

[20] E.F. Archibing, A. St-Amant, J. Phys. Chem. A 106 (2002) 5932.

[21] M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al. GAUSSIAN 98, Revision

A.6, Gaussian, Inc., Pittsburgh PA, 1998.

[22] Z.Y. Liu, C.R. Wang, R.B. Huang, Int. J. Mass Spectrom. 4 (1995) 201.

[23] B.K. Rao, P. Jena, J. Chem. Phys. 111 (1999) 1890.

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

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Ab initio investigation of structures and stability of AlnPm clusters