A density functional study of the Ni5Sn and Ni6Sn clusters

Journal of Molecular Structure (Theochem) 634 (2003) 171–179 www.elsevier.com/locate/theochem

A density functional study of the Ni5Sn and Ni6Sn clusters M. Finettia, E.E. Ottavianellia, R. Pis Diezb, A.H. Jubertb,* a

CIUNSa, Consejo de Investigacio´n UNSa Departamento de Quı´mica, Facultad de Ciencias Exactas, UNSa Buenos Aires 177, 4400 Salta, Argentina b CEQUINOR, Centro de Quı´mica Inorga´nica (CONICET, UNLP) Departamento de Quı´mica, Facultad de Ciencias Exactas, UNLP C. C. 962, B1900AVV La Plata, Argentina Received 6 February 2003; accepted 30 April 2003

Abstract A systematic study of the geometric, electronic, and vibrational properties of the Ni5Sn and Ni6Sn clusters using both the local and the gradient-corrected approximations to the density functional theory is presented in this work. The ionisation potentials and electron affinities are also calculated for the stable neutral clusters. Population analyses are used to investigate charge transfer process within the neutral and ionised clusters. Moreover, the changes in the sp and d populations of the nickel atoms are used to discuss the possible catalytic behaviour of the neutral clusters towards capture and dissociation of dihydrogen. The results are compared with the well-known lack of activity towards the activation of the H –H bond in H2 undergone by Ni– Sn bimetallic catalysts. q 2003 Elsevier B.V. All rights reserved. Keywords: Density functional theory; Local spin density approximation; Generalized gradient approximation; NiSn clusters

1. Introduction A systematic study of NinSn clusters, with n ¼ 1 2 4; was recently accomplished by us to get a deeper understanding of their properties. In particular, both the structural, electronic, magnetic, and vibrational properties [1] and the ionisation potentials and electron affinities [2] of those clusters were studied within the framework of the local and gradient-corrected approximations to the density functional theory. The potential catalytic activity of those aggregates was also investigated since it is a well-known fact that * Corresponding author. Tel.: þ54-221-4-259-485; fax: þ 54221-4-259-485. E-mail address: [email protected] (A.H. Jubert).

bimetallic catalysts such as Ni –Sn are less active than the corresponding transition metal-based monometallic systems in the H –H bond activation process [3]. Although no direct determination of the catalytic activity of the NinSn clusters was achieved in [1] or in [2], interesting results were obtained concerning possible electronic effects attributed to Sn. It was found in [1] that those nickel atoms located farther from the tin atom undergo a charge rearrangement that would lead to a decrease in the H – H bond activation in H2. On the other hand, the ionisation processes investigated in [2] were considered as ideal charge transfer processes involving both the d and sp orbitals of the nickel atoms and the s and sp molecular orbitals of an imaginary H2 molecule. It was found that the electronic population changes

0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00339-7

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undergone by the orbitals of the nickel atoms suggest that those nickel atoms located further from the tin atom would be less active in the charge transfer process mentioned above thus decreasing their ability to weaken the H – H bond. It can then be seen that the findings in [1] and [2] are in good agreement. In the present work we extend our investigations to Ni5Sn and Ni6Sn. Our aim is again twofold. The structural, electronic, magnetic, and vibrational properties as well as the ionisation potentials and electron affinities of those aggregates are calculated on the one hand to help in their characterization. On the other hand, the potential catalytic role of Ni5Sn and Ni6Sn is investigated in terms of charge rearrangements and changes in the electronic populations of the atomic orbitals of nickel atoms.

2. Computational details The local spin density approximation (LSDA) to the density functional theory (DFT) [4] is used to study the Ni5Sn and Ni6Sn clusters. The ADF2000.02 package [5] is employed to carry out the calculations. This code is based on Slater type orbitals (STO) instead of the usual gaussian functions. Moreover, it takes advantage of a set of auxiliary STO to fit the electronic density in order to get a faster evaluation of the Coulomb potential. The local correlation functional due to Vosko, Wilk, and Nusair [6] is used for geometry and spin multiplicity optimisations of the neutral and ionised bimetallic clusters. The triple-zeta basis set of STO available as set IV in the package is used. The basis sets include an additional set of p and d functions for nickel and tin, respectively, playing the role of polarization functions. The frozen core approximation up to the 3p and 4p orbitals (included) is utilized for Ni and Sn, respectively. The geometries and spin multiplicities of Ni5Sn and Ni6Sn are optimised with convergence thresholds of 1026 au for the energy, 5 £ 1024 au for the gradients, and 1026 au for the self consistent cycle. The integration accuracy parameter is set to 6.0 (see) [5.c] for details about the numerical integration technique. Those point groups with the higher possible symmetries are considered as starting points for

the geometry optimisation of each cluster size. The optimisations are symmetry-constrained in all cases unless otherwise explicitly stated. Harmonic vibrational frequencies are calculated for the optimised geometries to confirm that these are true minima on the potential energy surface of the corresponding aggregate. In those cases in which a given conformer becomes a saddle point on the potential energy surface, the imaginary frequencies are used to allow distortions in the original cluster to achieve a true minimum after further optimisations. Frequency calculations are accomplished using default convergence and accuracy thresholds. The equilibrium geometries of the stable neutral clusters are considered as starting points for the geometry optimisation of the ionised aggregates. However, no symmetry constrains are imposed in those cases. The generalized gradient approximation (GGA) [7] is self-consistently applied to the LSDA geometries of neutral and ionised clusters to achieve a better description of binding energies, ionisation potentials, and electron affinities. The electron smearing technique is used in those cases in which difficulties in the convergence of the self-consistent cycle are found. Ionisation potentials are calculated as the total energy difference between the positively charged cluster and the neutral one, IP ¼ ET ðNin Snþ Þ 2 ET ðNin SnÞ: Electron affinities are obtained in a similar way, that is, as the total energy difference between the neutral aggregate and the negatively charged cluster, EA ¼ ET ðNin SnÞ 2 ET ðNin Sn2 Þ: 3. Results and discussion 3.1. Neutral clusters The starting symmetries for Ni5Sn are the D5h planar structure and the C5v and C4v 3D structures. The ground state of the planar structure is found to be a 3A200 state. The vibrational study leads to a set of three imaginary frequencies along the A200, E100, and E200 modes indicating that the conformer is a third-order

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179

saddle point on the potential energy surface of Ni5Sn. The non-degenerate nature of the ground state suggests that the conformer is subjected to secondorder Jahn –Teller deformations [8]. Further geometry and spin multiplicity optimisations along the A200 mode yield a non-symmetric species characterized by a quintet state. The corresponding vibrational analysis shows that this aggregate is a true minimum on the potential energy surface of Ni5Sn. Unfortunately, the optimisation along the degenerate modes exhibits severe convergence problems, which prevent the corresponding species from a proper characterization. The ground state for the C5v symmetry is found to be a 5A2 state. The vibrational analysis, however, shows an imaginary frequency along the E2 mode. Further optimisation along that mode leads to a non-symmetric conformer in a quintet electronic state, which agrees with the conformer, found from distortion of the D5h planar structure mentioned above. Finally, the ground state for the C4v symmetry is found to be a 5B1 state. A set of real vibrational frequencies indicates that this is a true minimum on the potential energy surface of Ni5Sn and, moreover, it becomes the lowest-energy conformer of Ni5Sn according to the present calculations. It is characterized by the following valence electronic configuration 1e41 1a21 1b21 1b22 2a21 3a21 2e41 4a21 2b22 3e41 2b21 5a21 3b22 4e41 6a21 5e41 3b21 6e41 4b22 7a21 4b21 7e41 1a22 2a12 ð"Þ5b11 ð"Þ8e21 ð"Þ The starting symmetries for Ni6Sn are the D6h planar structure and the Oh ; C6v ; and D3d 3D structures. A 3A2u state is found to be the ground state for the planar structure of Ni 6Sn. The corresponding vibrational analysis leads to two imaginary frequencies along the A2u and B1g modes suggesting the presence of second-order Jahn – Teller effects. Further distortion along the B1g mode leaves the conformer in plane thus leading to no new structures. Further optimisation along the A2u mode, on the other hand, yields a C6v conformer, which turns out a true minimum after the corresponding vibrational analysis. The aggregate is characterized by a 3B1 ground state and presents the following valence electronic configuration 1e41 1e42 1a21 2a21 2e41 3a21 1b22 2e42 3e41 4a21 2b21 3e42 4e41 5a21 5e41 4e42 6e41 5e42 6e42 6a21 1b22 2b22 7e41 3b12 ð"Þ1a12 ð"Þ

173

A different starting geometry for the C6v symmetry leads to a 5E2 ground state. The degenerate nature of that state allows to predict first-order Jahn – Teller effects [8]. This is confirmed by the presence of two imaginary frequencies along the B1 and E2 modes according to the vibrational analysis. Further distortion along the B1 mode is not completed due to severe convergence problems. Geometry and spin multiplicity optimisations along the E2 mode yield a non-symmetric species characterized by a quintet electronic ground state. This new conformer proves to be a true minimum on the potential energy surface of Ni6Sn according to the vibrational analysis. The ground state for the D3d symmetry is found to be a 5A1u state. The calculation of the vibrational frequencies leads to two imaginary frequencies along the A1u and Eu modes. Distortion along the A1u mode produces a non-symmetric aggregate characterized by a quintet electronic ground state. A close inspection to its geometrical parameters indicates that it is the same species obtained by distortion along the E2 mode of the C6v 5 5E2 ground state discussed above. Further optimisation along the Eu mode is also accomplished obtaining a cluster which is described by a 5A00 ground state and belongs to the Cs point group. Unfortunately, convergence problems during the vibrational analysis prevent its proper characterization on the potential energy surface of Ni6Sn. It should be noted, however, that this conformer becomes the lowest-energy Ni6Sn aggregate found in the present work both at the LDA and self-consistent-only GGA levels of theory. Finally, the spin multiplicity and geometry optimisation processes lead to a 5T2u ground state for the Oh symmetry. The degenerate nature of the ground state indicates that this conformer is not a true minimum on the potential energy surface of Ni6Sn and it will undergo first-order Jahn –Teller distortions. Unfortunately, severe convergence problems during the vibrational analysis preclude the proper characterization of that conformer. The binding energies of the ground states and some low-lying excited states of the different symmetries of Ni5Sn and Ni6Sn are shown in Table 1. The vibrational frequencies of the stable conformers are also shown in that table. The equilibrium geometries of the stable conformers are depicted in Fig. 1 and the more relevant equilibrium bond distances are listed in Table 2.

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Table 1 Binding energies (BE, in eV/at) of the ground state and some low-lying excited states of the Ni5Sn and Ni6Sn clusters in different symmetries. Vibrational frequencies (ve, in cm21) of the corresponding stable ground states are also shown. S is the total electronic spin Ni5Sn

Ni6Sn

Symmetry

S

BE

D5h b

0 1 2 0 1

2.53 2.66 2.50 2.98 3.04

2 3 0 1 2

3.11 2.85 3.15 3.20 3.26 (2.61)c

3 2

3.15 3.24 (2.57)c

C5v b

C4v

C1

ve

a

Symmetry

S

BE

D6h b

0 1 2 0 1

2.80 2.90 2.85 2.87 2.99 (2.30)c

2 3 0 1 2

3.02 2.95 2.63 2.67 2.95

3 0

2.63 2.20

1 2 3 1 2 2

2.21 2.32 2.21 3.32 3.34 (2.62)d 3.29 (2.57)c

C6v

D3d b 102 (e1) 106 (b2) 110 (a1) 147 (b1) 178(b1) 195 (e1) 244 (a1) 263 (e1) 326 (a1) 38 97 131 157 166 195 199 216 223 248 313 318

Oh b

Cs b C1

a b c d

ve a

32 (e2) 55 (e1) 76 (e2) 87 (b2) 126 (a1) 155 (b2) 243 (a1) 250 (e1) 302 (e2) 305 (b1)

11 44 80 115 130 134 169 195 199 204 211 249 290 303 315

Symmetry assignment of frequencies is given in parenthesis. No stable conformers exist for this symmetry. GGA values in parenthesis. Vibrational frequencies are not reported due to convergence problems. See text.

It is worth noting that the binding energies for NinSn, with n ¼ 1 2 4; show a continuous increase from 1.52 eV/at in NiSn to 2.45 – 2.57 eV/at in Ni4Sn as it is reported in [1]. It is found in the present work that the binding energies of Ni5Sn exhibit a small increase with respect to Ni4Sn up to 2.57 –2.61 eV/at. Ni 6Sn, however, shows no further increase in their binding energy values (even including the lowest-energy conformer of Cs symmetry). Thus, these findings suggest that Ni5Sn, and Ni6Sn perhaps, would be a local maximum in the curve describing how the binding energy depends on the NinSn cluster size. Table 3 shows the atomic charges for the stable neutral clusters calculated using both the Mulliken population analysis [9] and the Voronoi charge

analysis [10]. The sp and d populations on the nickel atoms evaluated from the Mulliken analysis are also indicated in the table. It can be seen that both analyses predict a charge transfer process from tin to the nickel atoms in the four stable neutral clusters found for the Ni5Sn and Ni6Sn species. It can also be noted that for all the clusters listed in Table 3 both the Voronoi and Mulliken atomic charges tend to be smaller, that is, less negative for those nickel atoms located more distantly from the tin atom. This findings are completely in line with the results reported in [1]. A relationship was proposed in reference [1] between the lack of activity for the H –H bond activation of the H2 molecule by bimetallic systems with respect to monometallic catalysts as pure nickel,

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179

175

atom. On the other hand, atom Ni5 of the C1 Ni5Sn aggregate and atoms Ni5 and Ni6 of the C1 Ni6Sn conformer exhibit the more significant decrease in their d populations with respect to the d9 s1 electronic configuration of the isolated atom. It is clear then that atom Ni5 of the C1 Ni5Sn conformer and atoms Ni5 and Ni6 of the C1 Ni6Sn cluster fulfil simultaneously both conditions and should be less active to capture and dissociate dihydrogen, thus evidencing the lack of activity mentioned above. Again, these results agree well with those reported in [1]. These results are complemented below with additional data obtained from the ionised aggregates.

4. Ionised clusters

Fig. 1. Equilibrium geometries of neutral and ionised Ni5Sn and Ni6Sn clusters. White and light grey circles represent nickel and tin atoms, respectively. The numbers used to label the nickel atoms indicate proximity to tin, the lower the number, the nearer the nickel atom is to tin. See Table 2 for bond distances. Note that the three nickel atoms without numbers in Ni5Sn –C4v are equivalent to Ni1 and the six nickel atoms in Ni6Sn– C6v are equivalent one another.

Ionisation potentials (IP) and electron affinities (EA) of the stable conformers found for each cluster size are also calculated in the present work. Even though the calculations are performed without symmetry constrains only small departures from the symmetries of the neutral clusters are found after ionisation. Thus, ionised clusters are characterized using the symmetry of the corresponding neutral cluster. It should be mentioned that no frequency calculations are accomplished for the ionised clusters. The ground state of the C4v Ni5Snþ cluster is found to be a 6E1 state and the calculated IP is 6.52 and 6.32 eV at the LSDA and GGA levels of theory, respectively. Its valence electronic configuration is

and the simultaneous increase in the sp population and decrease in the d population of the nickel atoms with respect to an isolated nickel atom in its ground state after the formation of the bimetallic clusters (see [1] for further details). Following the same argument, it can be seen in Table 3 that atoms Ni2 and Ni5 of the C1 Ni5Sn conformer and atoms Ni5 and Ni6 of the C1 Ni6Sn cluster show the more pronounced increase in their sp populations with respect to an isolated nickel

Table 2 ˚ ) of the stable neutral clusters and their ionised conformers studied in this work. See Fig. 1 for atom Ni–Sn equilibrium bond lengths (r; in A labels Ni5Sn

Ni6Sn C1

C4v

r(Sn –Ni1) r(Sn –Ni2) r(Sn –Ni3) r(Sn –Ni4) r(Sn –Ni5) r(Sn –Ni6)

C6v

C1

Neutral

Cation

Anion

Neutral

Cation

Anion

Neutral

Cation

Anion

Neutral

Cation

Anion

2.51 3.39

2.55 3.53

2.50 3.39

2.49 2.51 2.52 2.61 2.87

2.51 2.52 2.54 2.59 3.22

2.49 2.51 2.53 2.61 2.73

2.63

2.67

2.60

2.47 2.48 2.57 2.58 2.75 2.78

2.49 2.50 2.58 2.59 2.79 2.81

2.48 2.48 2.59 2.60 2.70 2.71

the following 1e41 1a21 1b21 1b22 2a21 3a21 2e41 2b22 4a21 3e41 2b21 5a21 3b22 4e41 6a21 5e41 3b21 6e41 4b22 1a22 7e31 ð"Þ4b21 7a21 2a12 ð"Þ5b11 ð"Þ8e21 ð"Þ For the C4v Ni5Sn2 species a 4E1 ground state is found, the EA is 1.70 and 1.63 eV at the LSDA and GGA levels of theory, respectively, and it is characterized by the following valence electronic configuration 1e41 1a21 1b21 1b22 2a21 3a21 2e41 4a21 2b22 3e41 2b21 5a21 3b22 4e41 6a21 5e41 6e41 3b21 4b22 7a21 7e41 1a22 4b21 2a12 ð"Þ5b11 ð"Þ8e31 ð"Þ The Ni – Sn bond lengths become fairly enlarged when the cation is formed whereas these are almost unaltered when the neutral cluster gains an additional electron. These findings are consistent with the fact that an electron is removed from the rather deep 7e1 bonding molecular orbital of the neutral aggregate. On the other hand, the additional electron that comes into the neutral cluster to form the anion occupies the 8e1 molecular orbital having mainly a non-bonding character. In the case of the C1 Ni5Sn aggregate a quartet electronic state is obtained both when one electron is added to the system and when an electron is removed from it. The IP is 6.65 and 6.54 eV at the LSDA and GGA levels of theory, respectively, whereas the EA is 1.72 and 1.64 eV, respectively. The variation in the bond lengths is significant only for the largest Ni– Sn distance, which shows a very important enlargement when the cation is formed, and an appreciable shortening when the anion is obtained. The ground state of the C6v Ni6Snþ cluster is found to be a 6B1 state. The IP is 6.13 and 5.78 eV at the LSDA and GGA levels of theory, respectively, and it presents the following valence electronic configuration

c

d

a

C4v symmetry. C1 symmetry. C6v symmetry. C1 symmetry.

1e41 1e42 1a21 2a21 3a21 2e41 1b21 2e42 3e41 2b21 4a21 3e42 4e41 5a21 5e41

b

sp d sp Q Q

Q

sp

d

Q

sp

d

Q

sp

d

Ni4 Ni3 Ni2 Ni1 Sn

48 (25) 1.05 8.92 Ni5Sna 560 (391) 2152 (2104) 1.15 8.96 Ni5Snb 577 (434) 2155 (2111) 1.11 9.00 2128 (2124) 1.18 8.95 2154 1.07 9.01 2111 (277) 1.13 8.95 229 1.18 8.86 (286) (236) Ni6Snc 660 (666) 2110 (2111) 1.11 9.00 Ni6Snd 664 (510) 2131 (285) 1.01 9.08 2130 (284) 1.00 9.08 2129 1.15 8.95 2127 (2103) 1.15 8.95 277 1.17 8.90 270 1.17 8.89 (2103) (272) (263)

Q Q

d

Ni6 Ni5

sp

d

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179 Table 3 Atomic charges (Q) of nickel and tin atoms calculated according to the Voronoi analysis and the Mulliken analysis (in parentheses), both in lel £ 103. Mulliken sp and d populations on the nickel atoms, also in lel, are also shown. See Fig. 1 for atom labels.

176

4e42 6e41 5e42 6e42 7e21 ð"Þ1a12 ð"Þ1b22 2b22 3b12 ð"Þ2a12 ð"Þ6a21 On the other hand, the C6v Ni6Sn2 anionic system is characterized by a 4B2 ground state, an EA of 1.97 and 2.32 eV at the LSDA and GGA levels of theory, respectively, and the following valence electronic

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179

configuration 1e41 1e42 1a21 2a21 2e41 3a21 1b21 4a21 2e42 3e41 2b21 3e42 4e41 5a21 5e41 4e42 6a21 6e41 5e42 6e42 7e41 1b22 2b22 3b12 ð"Þ1a12 ð"Þ2a12 ð"Þ The Ni –Sn bond distance becomes slightly enlarged when the Ni6Snþ cluster is formed. On the other hand, a small shortening in the Ni –Sn bond length is observed when an electron is added to the neutral aggregate. It is interesting to note that an important rearrangement takes place when the cation is formed. The rather deep 7e1 bonding molecular orbital loses two electrons, one of them is actually lost by the neutral cluster but the other one occupies the 2a2 molecular orbital, mainly non-bonding in character. On the other hand, the additional electron gained by the neutral aggregate to form the anion occupies the 2a2 molecular orbital and no additional rearrangements take place. These facts would explain the changes in the bond lengths mentioned above. The C1 Ni6Sn ionised species are characterized by a sextet state and a quartet state in the case of the cationic and the anionic systems, respectively. The IP is 6.31 and 6.12 eV at the LSDA and GGA levels of theory, respectively, whereas the EA is 1.81 and 1.74 eV, respectively. In the case of Ni6Snþ, the equilibrium bond distances slightly increased their values. For Ni6Sn2, on the other hand, the change in the equilibrium bond lengths is characterized by small enlargements in the case of the shorter Ni– Sn bonds and by non-negligible shortenings for the larger Ni– Sn bonds. The equilibrium geometries of the ionised aggregates derived from the Ni5Sn and Ni6Sn neutral species is depicted in Fig. 1. The more important equilibrium bond lengths are shown in Table 2. Table 4 shows the change in the atomic charges of Sn and the nickel atoms of the stable Ni5Sn and Ni6Sn clusters as well as the change in the sp and d populations of the nickel atoms after the ionisation processes take place. Those properties are calculated using the Voronoi and the Mulliken population analyses. It can be seen from the table that the change in the Voronoi atomic charges suggests that the ionisation processes involve molecular orbitals mainly located on the nickel atoms, except for the C4v Ni5Snþ and Ni5Sn2 species and the C1 Ni5Snþ

177

aggregate for which both the additional and the removed electrons are almost equally localized on each atom of the cluster irrespective of its nature. On the other hand, the change in the Mulliken atomic charges shows that those molecular orbitals involved in the ionisation processes of the two Ni5Sn clusters and in the C1 Ni6Snþ aggregate are mainly localized on the Sn atom. In the case of the C6v Ni6Sn conformers and the C1 Ni6Sn2 cluster, on the other hand, the Ni atoms play a slightly dominant role. The change in the sp and d populations of the nickel atoms clearly indicates that the ionisation processes mainly involve their sp atomic orbitals. These results are in line with the findings reported in [2] for NinSn clusters, with n ¼ 1 2 4: It was proposed in reference [2] to take the ionisation processes as ideal charge donation (in the case of the electron affinity) and back-donation (in the case of the ionisation potential) processes involving the bimetallic clusters under study and an imaginary dihydrogen molecule. Those charge transfer processes seem to be the main steps in the overall mechanism towards the activation of the H – H bond in H2 (see [2] for a more detailed discussion). It was then suggested that those nickel atoms showing simultaneously the lowest increase in the sp population after the corresponding anionic system is formed and the lowest decrease in their d population after the corresponding cation is formed should be candidates to lack their activity towards the H – H bond activation of the H2 molecule. Following those arguments, it can be seen in Table 4 that atoms Ni2 and Ni5 of the C1 Ni5Sn conformer and atoms Ni2 of the C4v Ni5Sn species on the one hand, and atoms Ni1 to Ni4 of the C1 Ni6Sn aggregate and all the atoms in the of the C6v Ni6Sn cluster on the other hand, show the lowest increase in their sp population after the anion is formed. Moreover, it can be seen that only atom Ni2 of the C1 Ni5Sn conformer evidences an increase in its d population when the cation is formed, although a small decrease is observed for atoms Ni3 to Ni5 of that same conformer and atom Ni1 of the C1 Ni6Sn aggregate. Thus, it is concluded that atoms Ni2 and Ni5 of the C1 Ni5Sn conformer and atom Ni1 of the C1 Ni6Sn cluster fulfil simultaneously both conditions mentioned above. Putting together these results and the ones reported for neutral clusters it is possible to argue that atom Ni5

178

Ni5Snþa Ni5Sn2a Ni5Snþb 2b

Ni5Sn

Ni6Snþc 2c

Ni6Sn

Ni6Snþd 2d

Ni6Sn a b c d

Sn

Ni1

Q

Q

sp

d

Q

sp

d

174 (275) 2160 (2 252) 163 (236) 2138 (2 208) 80 (118) 268 (2 93) 116 (208)

170 (140) 2179 (2 157) 175 (165) 2192 (2 169) 153 (147) 2155 (2 151) 123 (131) 2126 (2 123)

20.08

20.07

2 0.11

2 0.05

0.14

0.01

0.12

0.01

20.11

20.06

2 0.18

0.01

0.13

0.04

143 (166) 2 160 (2121) 148 (151) 2 156 (2127)

0.11

0.01

20.10

20.05

0.11

0.04

20.09

20.03

2 0.09

2 0.04

0.12

0.01

123 (130) 2 119 (2113)

0.12

0.00

2100 (2 134)

C4v symmetry. C1 symmetry. C6v symmetry. C1 symmetry.

Ni2

Ni3

Ni4

Ni5

Ni6

Q

sp

d

Q

sp

d

Q

sp

d

Q

165 (138) 2205 (2193)

20.11

20.03

20.11

2 0.02

20.03

0.04

0.15

0.00

189 (179) 2 136 (2140)

2 0.15

0.16

160 (131) 2174 (2 163)

0.11

0.03

143 (110) 2148 (2126)

20.06

20.04

20.06

2 0.04

20.06

0.01

0.12

0.01

177 (157) 2 181 (2190)

2 0.09

0.12

142 (109) 2146 (2 125)

0.19

0.01

176 (155) 2189 (2 189)

sp

d

20.10

20.06

0.18

0.01

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179

Table 4 Change in Voronoi and Mulliken (in parentheses) atomic charges (Q) of nickel and tin atoms, both in lel £ 103. Changes in Mulliken sp and d populations of the nickel atoms, in lel, are also shown. Negative values indicate loss of electronic charge with respect to the neutral conformer, whereas positive values denote earning of electronic charge with respect to the neutral conformer. See Fig. 1 for atom labels

M. Finetti et al. / Journal of Molecular Structure (Theochem) 634 (2003) 171–179

of the C1 Ni5Sn conformer is a good candidate to exhibit a lack of catalytic activity towards the activation of the H – H bond in the H2 molecule. This result is consistent with the findings reported in [1] and [2] suggesting that those nickel atoms located farther from Sn in a given cluster should evidence the lack of activity just mentioned.

179

ionised clusters are formed reveals that the nickel atom located farthest from the tin atom in the nonsymmetric Ni5Sn conformer should be a good candidate to show a lack of activity towards the activation of the H –H bond in H2.

Acknowledgements 5. Conclusions A density functional study of the properties of neutral and ionised Ni5Sn and Ni6Sn clusters is accomplished in this work. Two stable conformers are found for Ni5Sn, the lowest-energy one belonging to the C4v point group and the other characterized by a non-symmetric structure. Two stable conformers are also found for Ni6Sn. In this case, a non-symmetric structure is the lowest-energy conformer, whereas a C6v cluster lies a little higher in energy. Geometric parameters, electronic configurations, and vibrational frequencies are provided to completely characterize their electronic states. The optimised geometries of the ionised clusters show that the bond lengths increase their values when the cations are formed. When the neutral clusters accept an additional electron, however, the equilibrium bond distances are almost unaltered or become slightly shortened. A few exceptions are observed for this behaviour, though. The IP and the EA follow the expected trend with the cluster size, that is, a decrease is observed in the IP from Ni5Sn to Ni6Sn whereas the opposite behaviour is noticed for the EA. It is found that when the neutral clusters are formed a charge transfer from tin to the nickel atoms takes place. The charge transfer, however, occurs to a lesser extent for those nickel atoms located more distant from tin. Finally, the analysis of the change in sp and d populations of the nickel atoms after the neutral and

The authors thanks CIUNSa and Fundacio´n Antorchas for financial support. EEO and RPD are members of the Scientific Research Career of CONICET. AHJ is member of the Scientific Research Career of CICPBA.

References [1] M. Finetti, E.E. Ottavianelli, R. Pis Diez, A.H. Jubert, Comp. Mat. Sci. 20 (2001) 57. [2] M. Finetti, E.E. Ottavianelli, R. Pis Diez, A.H. Jubert, Comp. Mat. Sci. 25 (2002) 92. [3] G.F. Santori, Ph. D. Thesis, Departamento de Ingenierı´a Quı´mica, Facultad de Ingenierı´a, Universidad Nacional de La Plata, March 2000. [4] (a) P. Hohenberg, W. Kohn, Phys. Rev. 136B (1964) 864. (b) W. Kohn, L.J. Sham, Phys. Rev. 140B (1965) 1133. (c) R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, New York (1989). [5] (a) E.J. Baerends, D.E. Ellis, P. Ros, Chem. Phys. 2 (1973) 41. (b) L. Versluis, T. Ziegler, J. Chem. Phys. 322 (1988) 88. (c) G. te Velde, E.J. Baerends, J. Comp. Phys. 99 (1992) 84. (d) C. Fonseca Guerra, J.G. Snijders, G. te Velde, E.J. Baerends, Theor. Chem. Acc. 99 (1998) 391. [6] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [7] K. Burke, J.P. Perdew, Y. Wang, in: J.F. Dobson, G. Vignale, M.P. Das (Eds.), Electron Density Functional Theory: Recent Progress and New Directions, Plenum, New York, 1997. [8] I.B. Bersuker, The Jahn– Teller Effect and Vibronic Interactions in Modern Chemistry, Plenum, New York, 1984. [9] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [10] The Voronoi charge analysis is based on assigning the density in a given point in space to the nearest atom. Then, atomic charges are obtained by means of numerical integration of the charge density on each atom.