Theoretical Study of [Ni (H2O) n] 2+(H2O) m (nâ¤ 6, mâ¤ 18)

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Theoretical Study of [Ni (H2O)n]2þ(H2O)m (n e 6, m e 18) Marcía Bustamante,†,‡ Israel Valencia,‡ and Miguel Castro*,‡ † ‡

Instituto de Materiales y Reactivos de la Universidad de la Habana, Cuba, San Lazaro s/n, Vedado CP 10400, Ciudad de la Habana, Cuba Departamento de Física y Química Teorica, DEPg, Facultad de Química, Universidad Nacional Autonoma de Mexico, C.P. 04510, Mexico D. F., Mexico

bS Supporting Information ABSTRACT: The [Ni(H2O)n]2þ(H2O)m (n e 6, m e 18) complexes were studied by means of first-principles all-electron calculations performed with the BPW91 gradient corrected functional and the 6-311þG(d,p) basis sets for the H, O, and Ni atoms. Triplet states were found as low-lying states for each (n, m) combination. The estimated Ni2þ(H2O)n binding energies (112.857.4 kcal/mol for the first layer and 52.023.0 kcal/mol for the second one) decreases and the Ni2þOH2 bond lengths lengthen as n þ m increases. With six H2O moieties the Ni2þ ion furnishes its first coordination sphere of octahedral geometry. Further water addition renders the formation of the second layer. The effect of Ni2þ on the (H2O)n 3 3 3 (H2O)m hydrogen bond formation for several “n” and “m” combinations was studied, revealing an enhancement of this kind of bonding, which is of key importance for the stabilization and growth of the clusters. For some n þ m isomers the second layer appears before the first octahedral layer is fully formed. For example, the square planar Ni2þ(H2O)4 core originates twodimensional 4 þ 2 and 4 þ 4 isomers, where each outer water molecule accepts two H-bonds, lying 2.0 kcal/mol above the 6 and 6 þ 2 ground states. The clusters were also studied by IR spectra; the OH stretching vibrational frequencies allowed us to identify the outer solvation shells by the presence of red-shifted hydrogen bond regions.

1. INTRODUCTION Transition metal (TM) cations in aqueous solutions have been extensively studied due to their importance in several chemical and biological processes. The energetics and the type of growing structures for the solvation of TM cations by water involve complicated electrostatic and covalent contributions that are quite difficult to describe and understand at a molecular level. Solvated TM ions have been the subject of experimental13 and theoretical47 studies. More recently it has been found that insights into the hydration of ions in solution can be also obtained by studying hydrated clusters in the gas phase. For instance, recently improved electrospray ionization (ESI) methods have made possible the synthesis of hydrated dications for a wide variety of metal ions,8,9 which are characterized by infrared photodissociation (IRPD) spectroscopy, blackbody infrared radiative dissociation, and density functional theory. In the case of Cu2þ(H2O)n, n = 68, coordination numbers (CN) of 4 were indicated, although contributions from a higher CN cannot be ruled out; for n = 1012, the presence of water molecules that accept two hydrogen bonds and donate one H-bond as well as single H-bond acceptors was revealed, indicating the formation of a third solvent layer at a relatively small cluster size.8 Using laser vaporization for cluster formation and IRPD spectroscopy, Duncan et al. have explored small cationwater clusters.10,11 For Niþ(H2O)n, n e 25, it was possible to follow the progressive solvation of a TM ion for the first time; specifically, they found evidence that essentially all of the water molecules are in a hydrogen bond network in a size of n = 10. r 2011 American Chemical Society

Lisy et al., using IRPD, studied the solvation behavior of alkali metal ion species with water.12 They found a smaller hydration shell (4) of Naþ in the gas phase than that in solution (6); the formation of the second shell was inferred by the H-bonded OH stretching. Similar results were found by Stace et al. for Mn2þ.13 It was pointed out that more studies are needed on other metals with different CNs and charge states to get deeper insight on the nascent solvation process.11 Nickel is one of the TM atoms essential for all forms of life, because it is present at the active centers of several important enzymes such as urease,14 NiFe hydrogenases,1518 methyl coenzyme M reductase,19 carbon monoxide dehydrogenase,20 acetyl coenzyme A synthase,21 and nickel superoxide dismutase (NiSOD).22 In most of these systems, nickel has an oxidation number of 2, Ni(II), and it is bonded directly to either the oxygen or nitrogen atoms of the nucleophilic moieties. A deep understanding of the catalytic behavior of these enzymes needs knowledge of the electronic (electrostatic and covalent contributions) and structural properties of the Ni2þO and Ni2þN interactions. With water, Ni2þ shows several possibilities of coordination, 4 or 6, in square, tetrahedral, or octahedral structures, among others. The hydrated structure of Ni(II) has been well analyzed using experimental methods.1,2 Most of those studies have determined Received: September 6, 2010 Revised: March 22, 2011 Published: April 08, 2011 4115

dx.doi.org/10.1021/jp108503e | J. Phys. Chem. A 2011, 115, 4115–4134

The Journal of Physical Chemistry A

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Figure 1. Low-lying states for Ni2þ(H2O)n, n e 6, with all water molecules in the first layer. Equilibrium bond lengths (in angstroms), bond angles, atomic charges, and dipole moments are indicated.

that the Ni2þ ion is bonded to six water molecules in an octahedral coordination sphere. Experimental NiO distances are considered to be 2.0022 and 2.060 Å.23 From a theoretical point of view, classical molecular dynamics (MD), classical Monte Carlo (MC),24 and combined quantum mechanical/molecular mechanical (QM/ MM) MD simulations were carried out to investigate the hydrated structure of Ni(II) in water.23,25 The exchange process between hydration shells of Ni(II) and heteroligands, such as ammonia, have been analyzed using QM/MM MD simulations.26 Some first-row TM ions, including Ni(II), have been investigated by a similar computational procedure, using liquid ammonia as solvent. The exchange of ligands (L), H2O by NH3, was also analyzed in those studies.23,27 However, taking into account the importance and complexity of Ni2þH2O and Ni2þNH3 sys-

tems in chemical and biological processes, their experimental and theoretical study is still scarce. The goal of this research work is to study, by means of density functional theory (DFT) based methods, the low-lying states of Ni(II) interacting with water molecules in the gas phase. In the absence of solvent effects, such as those in the liquid, we will address the growth of the first layers, Ni2þ(H2O)n, n e 6, emphasizing the structural and electronic effects. Further, the stability and growth of the outer solvation shells is depicted through the analysis of the hydrogen bond formation for several n þ m isomers. It is shown that the outer m molecules form one or two H-bonds, stabilizing the second shell and promoting its growth even before the first octahedral shell is formed. The results obtained are discussed with available experimental and theoretical data. 4116

dx.doi.org/10.1021/jp108503e |J. Phys. Chem. A 2011, 115, 4115–4134


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Figure 2. Low-lying states for the n = 3, 4, 3 þ 1, 4 þ 1, and 3 þ 2 isomers of Niþ(H2O)n.

2. COMPUTATIONAL PROCEDURE In this research work, the geometry and electronic structure for the ground states (GSs) of Ni2þ(H2O)n(H2O)m, with n e 6 and m e 18 (n and m are labels for the number of water molecules in the first and second layers of solvation, respectively), were studied by means of all-electron calculations performed with the B3LYP28,29 and BPW9130,31 functionals; 6-31G(d, p) and 6-311þG(d,p) basis sets were chosen for the H, N, O, and Ni atoms.3234 The Gaussian 03 quantum chemistry software was employed.35 The optimized structures were confirmed as local minima, on the potential energy surface (PES), by estimating their vibrational frequencies within the harmonic approximation with the following computational

procedure. Strict convergence was required for the total energy, minimized up to 108 au, while the geometries were optimized choosing a 105 au threshold for the root-mean-square forces. An ultrafine grid was used for these steps. These tight tolerances are needed for a correct GS estimation, because in most of these clusters several low-lying states are contained within a very small energy range. Several candidate structures of different CNs were chosen for each cluster for full optimization, without imposing symmetry constrains. Once the GS of the “n” cluster was located, one water moiety was added to this structure for the GS searching of the n þ 1 parent. The states in Figures 112 are true minima on the PES as they have positive frequencies. Despite the limitations 4117



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Figure 3. Estimated IR spectra for (a) Ni2þ(H2O)3 and (b) Niþ(H2O)3.

of the widespread Mulliken electron population analysis,36 such as its sensitive to the basis set and crude partition of the bonding electrons between two different atomic sites,37 gross atomic charge distributions with this method were obtained for a qualitative rationalization of the exhibited trends of binding energies and equilibrium distances. The structures and molecular orbitals (MOs) were visualized with the Gauss View package. Specifically, HOMO (highest occupied MO) and LUMO (lowest unoccupied MO) are useful frontier orbitals for the characterization of some key electronic properties of these clusters. The BPW91 GS wave function, Ψ, allows knowledge of the total electron density F = |Ψ|2 of the cluster. Though dependent on the accuracy of F, the theory of atoms in molecules, AIM,38 yields insight into the metalligand and hydrogen bonds through the F and Laplacian (r2F) values for the bond critical points (BCPs) along the NiO and OH 3 3 3 H paths. AIM was used to depict this type of bond in Ni2þ(H2O)n; the AIM analysis was

carried out with the AIM2000 code.39 The B3LYP method gave a similar picture, to that found with BPW91, for Ni2þ(H2O)n, n e 6. For this reason the B3LYP and the AIM results were moved to the Supporting Information. The structural parameters are quoted in Tables 13. The structural changes of H2O in Ni2þ(H2O)n are referred to the isolated water molecule in section 3. The vibrational frequencies and shifts to the red for the OH stretches are contained in Table 4. Including zero-point energy (ZPE) for the GSs of Ni2þ(H2O)n and H2O, the adiabatic binding energies (BE), estimated by the difference of total energies [Et(Ni2þ) þ n[Et(H2O)] Et[Ni2þ(H2O)n] are contained in Table 5.

3. RESULTS AND DISCUSSION [NiH2O]2þ. The BPW91/6-311þG(d,p) GS of Ni2þH2O,

shown in Figure 1, is a triplet (M = 2S þ 1 = 3, where S is the total spin), defining a planar structure, since the HONiH dihedral 4118



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Figure 4. Geometries for Ni2þ(H2O)3H2O, Ni2þ(H2O)4H2O, and Ni2þ(H2O)3(H2O)2.

angle is 180. Using multiconfiguration quasi-degenerate perturbation theory, Iuchi et al.25 found a value of about 1.900 Å for the NiO distance in Ni2þH2O, in good agreement with our result. The OH distances and the HOH angle present enlargements of 0.030 Å and 4.0, implying considerable distortion on the water moiety, due to the strong Ni2þH2O bonding. Indeed, a high value was found for the BE, 112.8 kcal/mol, which was consistent with the short NiO separation, 1.892 Å, and with big red shifts, 361 and 412 cm1, for the symmetric and asymmetric OH stretches. The former has a stronger band (659) than the latter (502); the intensities are shown in parentheses. Besides, the bending is blue-shifted, which can be viewed as a mechanical effect: Ni2þ impedes the movement of the H atoms, increasing the bending frequency to a higher value. These changes (Tables 1 and 4), can be rationalized in terms of the transference of electrons (e), 0.61 e, from H2O to Ni2þ in Ni2þH2O, because the frontier MOs of water, HOMO (at 7.2 eV) and HOMO 1 (the lone pair at 9.3 eV), from which the electrons are removed, show partial bonding character between the OH atoms. Thus, weaker bonding on the water moiety leads to lower frequency vibrations, accounting for the estimated red shifts in Ni2þH2O and those observed in NiþH2O.11 Indeed, our calculations show that one electron deletion from H2O produces enlargements of 0.044 Å and 4.4 for the bond lengths and angle of H2Oþ, which are in concordance with the results, 0.030 Å and

4.0, when less than one electron, 0.69, is deleted from H2O. They show also red shifts, 466 and 519 cm1, for the symmetric and asymmetric OH stretches of H2Oþ, in accordance with those (361 and 412 cm1) of Ni2þH2O, and with the measured shifts,40 >400 cm1, for H2Oþ. The red shifts of NiþH2O were also explained by the polarization effects of Niþ on the lone pair of H2O.11 Smaller charge donations from each H2O to Ni2þ produce smaller changes of the OH lengths and HOH angles and smaller red shifts in Ni2þ(H2O)n; see below. [Ni(H2O)2]2þ. The M = 3 GS of Ni2þ(H2O)2 shows planar geometry with the ONiO sites lying on the molecular axis. This and the shortest NiO distances (Figure 1) imply high stability for this adduct, and it is confirmed by its high BE, 98.0 kcal/mol/H2O. The OH bond lengths and the HOH angles have enlargements of 0.020 Å and 4, revealing small but sensitive structural changes of the attached water molecules, which are reflected by the red shifts, 250 and 276 cm1, suffered by the symmetric and asymmetric OH stretches. These changes are smaller than those of Ni2þH2O. Likewise, it was found by Duncan et al.11 that the red shifts for these stretches in Niþ(H2O)2 (of highest intensity in the mass spectrum of Niþ(H2O)n, and tentatively also of high stability, probably similar to that of Ni2þ(H2O)2) are smaller than those of NiþH2O, and they are clearly smaller than in Ni2þ(H2O)1,2. In fact, red shifts of 34 and 64 cm1 were found for NiþH2O.11 The effect of the charge on the metal on the IR 4119



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Figure 5. IR spectra of (a) Niþ(H2O)4, (b) Niþ(H2O)3H2O, (c) Ni2þ(H2O)4, and (d) Ni2þ(H2O)3H2O. 4120



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Figure 6. IR spectra for (a) Niþ(H2O)4H2O, (b) Niþ(H2O)3(H2O)2, and (c) Niþ(H2O)3(H2O)2.

spectra of Ni1þ,2þ(H2O)1,2 is shown by these results and those of ref 11. The IRPD spectrum of Ni2þ(H2O)1,2 is needed to confirm this trend. Ni2þ(H2O)2 has bigger blue shift for the bending than Ni2þH2O, due to the shorter NiO bond. [Ni(H2O)3]2þ. The GS of Ni2þ(H2O)3 shows a triangular pyramidal geometry, as the Ni atom lies 12.2 above the plane defined by the oxygen sites (Figure 1). The short NiO distances and the BE, 83.0 kcal/mol/H2O, reflect significant NiO bonding, producing enlargements of 0.0130.014 Å and 3.7 for the OH distances and HOH angles, which are smaller than those of Ni2þ(H2O)2.

We have also addressed the interaction of three water molecules with the Niþ cation, since the IRPD spectrum reveals the absence of H-bonded water molecules for this cluster.11 A triangular planar GS was found for Niþ(H2O)3, with longer NiO distances than those of Ni2þ(H2O)3, mainly due to the fact that the single positive charge produces smaller electrostatic attractions and smaller transference of charge: 0.51 e in Niþ (H2O)3 versus 1.17 e in Ni2þ(H2O)3. In Niþ(H2O)3 (Figure 2) two water moieties have their H atoms opposite each other and out of the ONiþO plane, while the third molecule has its H atoms near this plane; a similar structure was found by Duncan 4121



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Figure 7. IR spectra for the (a) n = 5, (b) 4 þ 1, (c) 3 þ 2, and (d) 3 þ 2 isomers of Ni2þ(H2O)5. 4122



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Figure 8. Low-lying states for the (a) n = 5 þ 1, (b) 4 þ 2, and (c) 3 þ3 of Ni2þ(H2O)6.

et al.11 The BPW91/6311þG(d,p) spectrum for Niþ(H2O)3 presents two bands centered at 3692 and 3779 cm1 (Figure 3b) for the symmetric and asymmetric OH stretching vibrations, which are red-shifted, by about 30 and 52 cm1, referred to the bare water molecule; the bands are separated by 87 cm1. These results agree well with the experimental IR spectrum, which shows two bands at 3619 and 3700 cm1, separated by 81 cm1 and indicating also red shifts, 38 and 56 cm1, for the symmetric and asymmetric OH stretches, respectively.11 The calculated spectrum using the B3LYP method is also in agreement with the experiment.11 It is interesting to compare these results with the estimated IR spectrum of Ni2þ(H2O)3 (Figure 3a), which also possess two bands, at 3561 and 3645 cm1, separated by about the same value, 84 cm1, as in the Niþ case. They correspond also to the symmetric and asymmetric OH stretching

vibrations but suffer bigger red shifts, 161 and 186 cm1, than those of Niþ(H2O)3, signifying that Ni2þ perturbs more strongly the electron density of water, weakening the OH bonds more markedly and producing stronger NiO bonds, which is indicated by the shorter (longer) Ni2þO (OH) distances compared to those of Niþ(H2O)3. Thus, Niþ(H2O)3 and Ni2þ(H2O)3 present similar IR spectra, though bigger red shifts occur in the latter, which is mainly due to the direct coordination of the water units with the Ni cation in both cases, with the OH groups lying away from the metal so that they vibrate freely.11 The importance of the charge state of the metal on the structural, bonding, and vibrational properties of Ni1þ, 2þ(H2O)3 is illustrated by these results. Experimental values for the BEs of Ni2þ(H2O)n are scarce. The measured BEs for NiþH2O are 39.7,41 36.5,42 and 43.9 kcal/mol.43 4123



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Figure 9. IR spectra for the (a) n = 6, (b) 5 þ 1, (c) 4 þ 2, and (d) 3 þ 3 isomers of Ni2þ(H2O)6.

Thus, the BE of Ni2þH2O is much bigger than those of NiþH2O, which is mainly due to bigger electrostatic attractive interactions in Ni2þH2O and to different bonding capabilities of the valence electrons of Ni2þ (4s13d6) and Niþ (4s13d7). The BE

per H2O for n = 2 and 3 (Table 5) is reduced by ≈15 kcal/mol from n = 1 to 2 and from 2 to 3, accounted for by the following: (1) the bond of Ni2þ is divided among more water moieties and (2) the bigger H2O to Ni2þ total transference of charge reduces the 4124



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Figure 10. Lowest energy BPW91/6-311þG(d,p) states for [Ni(H2O)6]2þ(H2O)m, m = 1, 2. The A coordination forms a single H-bond, whereas in B two H-bonds are formed.

metalligand attractions. This BE trend is reflected by the symmetric and asymmetric OH stretches, which have smaller shifts to the red for n = 2 and 3, with the former showing bigger intensity than the latter in both clusters; see Table 4. The experimental BEs for Niþ(H2O)n, n e 3, show a different trend: the values for n = 1 and 2 of refs 41 and 42 show small increases, 0.91.5 kcal/mol, and a reduction of 3.7 kcal/mol was found by Armentrout et al.43 From n = 2 to 3 a huge decrease, 24.0 kcal/mol, was found.43 Our calculated BE, 43.9 kcal/mol, for NiþH2O agrees well with the measured value43 and with the results at the MCPF, 41.1 kcal/mol,44 and B3LYP, 45.0 kcal/mol,45 levels of theory. [Ni(H2O)4]2þ. At the BPW91/6-311þG(d,p) level, Ni2þ (H2O)4 presents square planar geometry, which is a preferred

structure of Ni2þL4 compounds. BPW91/6-31G(d,p) yields a tetrahedron for n = 4. The importance of basis sets for accurate studies of these clusters is revealed by Ni2þ(H2O)4. The plot of HOMO, in the Supporting Information, shows signatures on the H2O units implying nucleophilic character of these sites. LUMO, placed on the Ni2þ and H atoms, reveals that these are the reactive sites of Ni2þ(H2O)4 against donors of charge species. Then, further addition of water units could occur either at Ni2þ continuing with the growth of the first shell or at the H sites, raising a second layer. It was found that the 3 þ 1 isomer is 11.8 kcal/mol more stable than the n = 4 one-layer cluster. Thus, as in the Niþ ion,11 also in the Ni2þ(H2O)4 cluster in the gas phase appears the formation 4125



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Figure 11. Geometries for the 5 þ 2, 4 þ 3, 4 þ 4, and 6 þ2 isomers of Ni2þ(H2O)7,8 clusters.

of a second layer at this small cluster size. The Ni2þO bond lengths of the 3 þ 1 GS are markedly shorter than those of Ni2þ(H2O)4. They are also shorter than those of Ni2þ (H2O)3 and Niþ(H2O)3(H2O) (see Figure 4 and Table 1), implying a huge weakening of the OH bonds, mainly for the water molecule involved in the H-bond. Effectively, the H atom forming this bond lies between the oxygen sites with O 3 3 3 H distances of 1.235 and 1.194 Å, implying major rupture of the

OH bond of that inner molecule in such way that the H atom is nearer the outer O site. The O 3 3 3 H 3 3 3 O angle, 177, suggests strong H-bonding. In Niþ(H2O)3H2O the H atom forming the H-bond shows shorter OH, 1.005 Å, and O 3 3 3 H distances, 1.629 Å; see Figure 2. Thus, compared with Niþ(H2O)3H2O, a different IR spectrum for Ni2þ(H2O)3 H2O is expected. Referred to n = 3, the n = 4 square planar isomer shows a decrease of 14.8 kcal/mol in its BE, 68.2 kcal/mol/H2O, whereas 4126



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Figure 12. IR spectra for the (a) 6 þ 1, (b) 5 þ 2, and (c) 4 þ 3 isomers of Ni2þ(H2O)7.

the BE for the 3 þ 1 GS shows a smaller decrease, 11.9 kcal/mol. Thus, adding the fourth water molecule in the outer shell yields a bigger BE, which is in line with the shorter NiO distances in the 3 þ 1 GS, mainly for the molecule, 1.846 Å, forming the H-bond, with the more opened angle of this moiety, 110, and with the big dissociation energy (DE), 35.3 kcal/mol, of the outer ligand, roughly obtained through a total energy difference: Et[Ni2þ (H2O)3H2O] [Et(Ni2þ(H2O)3) þ Et(H2O)]. The DE, 23.5 kcal/mol, for the square planar isomer is smaller than that of the 3 þ 1 GS. Then, hydrogen bonding contributes greatly to the

formation of a two-layer GS at n = 4. The 3 þ 1 GS records even smaller red shifts than the n e 3 clusters, with stronger intensity for the symmetric stretch; see Table 4. However, in this case the strongest band is for bending modes, at 1036 cm1 (3047), of the water units forming H-bonds. The GS of Niþ(H2O)4 shows square planar geometry with longer NiþO distances than those of Ni2þ(H2O)4. We have found that Niþ(H2O)3H2O is isoenergetic with Niþ(H2O)4 (Figure 2). This is different from the quoted picture for the Ni2þ case, where 3 þ 1 is clearly the GS. The BPW91 estimated IR 4127



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Table 1. Equilibrium Bond Lengths Re (NiO and OH), in angstroms, and Bond Angles — (HOH, NiOH, and ONiO), in degrees, for the Lowest Energy States of the Small Ni2þ(H2O)n, n e 4, Clusters in the Gas Phase system

Re(NiO)

— (HOH)

Re(OH)

— (NiOH)

— (ONiO)

0.969

104.2

Ni2þH2O Ni2þ(H2O)2

1.892 1.867

0.999 0.989

108.4 108.2

125.8 125.9

180.0

Ni2þ(H2O)3

1.931

0.9820.983

107.9

126.0

119.0

Ni2þ(H2O)3H2O, GS

1.8461.958

0.9781.235

108.0110.0

125.4125.7

110.0129.0

H2O

118.8130.9 Ni2þ(H2O)4

1.990

0.978

108.2

126.0

90.0

Table 2. Equilibrium Bond Lengths Re (NiO and OH), in angstroms, and Bond Angles — < (HOH, NiOH, and ONiO), in degrees, for the Lowest Energy States of the Ni2þ(H2O)n, n = 5 and 6, Isomers in the Gas Phase system Ni (H2O)5, GS I 2þ

Re(NiO) 2.0232.079

Re(OH) 0.975

— (HOH)

— (NiOH)

107.2108.1

122.7128.2

— (ONiO) 86.791.3 102.6

Ni2þ(H2O)4H2O, II Ni2þ(H2O)3H2OH2O, III

1.9662.017 1.8741.966

0.9761.005 0.9751.111

105.1107.8

122.2128.1

110.4

118.8128.1

107.4107.9

125.8

109.5109.8

120.4129.8

89.4102.9 113.8123.7

Ni2þ(H2O)3H2OH2O, IV

1.8311.964

0.9741.068 1.4321.444

107.0107.9 112.1

125.4126.1 122.4125.3

Ni2þ(H2O)6, GS I

2.093

0.974

107.3

85.993.9

120.3

Ni2þ(H2O)5H2O, II

2.0112.088

0.9750.977

105.7107.4

86.0104.0

120.3

0.9730.997

108.2109.8

Ni2þ(H2O)4(H2O)2, III

1.9781.982

0.9740.974

105.0

0.9961.001

110.1110.4

Ni2þ(H2O)3(H2O)3, IV

Ni2þ(H2O)3(H2O)3, V

1.8941.900

1.8481.978

0.9730.974

107.0

1.0661.074 1.4171.427

109.3109.7

0.9730.976

106.5107.2

1.0441.077

109.7111.5

108.6130.3

126.9 89.0105

119.1128.0

121.3128.3

117.0121.0

123.0127.4

112.0130.0

1.4031.494

spectrum for Niþ(H2O)3H2O, shown in Figure 5, fits well with the experimental IRPD results,11 because it shows a resonance at 3099 cm1, assigned to the OH stretching of the H2O unit involved in the H-bond; the experiment records this band at 3180 cm1. The bands at 3678, 3685, and 3723 cm1 are for the symmetric OH stretches, free of H-bonds, of the B, C, and D moieties. The experiment locates these bands at 3624 cm1. For A, the OH stretching of the H atom not forming an H-bond was found at 3760 cm1. The bands positioned at 3769, 3784, and 3822 cm1 belong to the asymmetric OH stretching of C, B, and D; IRPD reveals these bands at 3700 cm1.11 The symmetric OH stretches of B and C are red-shifted by 44 and 37 cm1, but D exhibits a negligible change, as this molecule is not bonded directly to Niþ. The asymmetric OH stretches of B and C are also red-shifted, by 62 and 47 cm1, whereas a smaller shift, 9 cm1, was found for D. These results agree with the IRPD spectrum, Figure 5 of ref 11, showing red shifts of 33 and 56 cm1, for those symmetric and asymmetric modes. Analogous results for the IR spectrum of this cluster were found through the B3LYP method.11 The IR spectrum for Niþ(H2O)4, Figure 5, shows two signals, at 3676 and 3768 cm1, for the symmetric and asymmetric OH stretches. Moving now to Ni2þ(H2O)4,

these bands are located at smaller frequencies, 3617 and 3709 cm1, pointing bigger red shifts for this isomer. Notably, the IR spectrum of the Ni2þ(H2O)3(H2O) GS, Figure 5d, is empty of bands in the H-bond region, which is due to the longer OH distance, 1.235 Å, signifying major rupture of the OH bond, quenching the OH stretching. Lastly, the symmetric and asymmetric OH stretches in Ni2þ(H2O)3H2O (see Table 4) have bigger red shifts than those in Niþ(H2O)3H2O, 3744 and 4762 cm1. [Ni(H2O)5]2þ. The GS of Ni2þ(H2O)5 has a square pyramidal geometry with long NiO distances (Table 2) and small enlargements, 0.006 Å and 3.4, for the OH distances and HOH angles. Adding the fifth water molecule in the outer layer yields Ni2þ(H2O)4H2O, located 4.1 kcal/mol above the GS, with the outer molecule accepting two H-bonds, forming a sixmember ring; see Figure 4. The water moieties free of H-bonds are placed out of the plane defined by this ring. We have also studied the 3 þ 2 isomers, which may be viewed as emerging from the 3 þ 1 GS. Here, the addition of two outer water molecules on different (the same) inner ones produces a structure located 7.7 kcal/mol (11.8 kcal/mol) above the GS; these isomers are reported 4128



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Table 3. Equilibrium Bond Lengths Re (NiO and OH), in angstroms, and Bond Angles — (HOH, NiOH, and ONiO), in degrees, for the Low Lying States of Ni2þ(H2O)6(H2O)m, m = 1, 2 system Ni (H2O)6H2O, B GS 2þ

Ni2þ(H2O)6H2O, A II

Re(NiO) 2.0772.110

2.0412.107

— (HOH)

— (NiOH)

— (ONiO)

0.974

106.4107.8

115.7127.1

84.587.9

0.982 0.975

106.8108.7 104.7

116.8125.9

0.973

107.5

115.7128.1

1.0171.603

108.3

118.0128.6

Re(OH)

85.394.7

105.2 Ni2þ(H2O)5(H2O)2, III

2.0352.055

0.9740.976

105.0107.0

115.0121.6

0.9940.976

107.3109.0

120.2126.9

1.7921.815 Ni2þ(H2O)4(H2O)3, IV

1.9352.006

Ni2þ(H2O)6(H2O)2, B GS

2.0862.117

90.0105.0

121.1

0.976 0.9931.007

105.0 108.5114.2

116.6125.9

91.097.0

88.595.6

1.6831.949 0.9730.972

104.7107.2

118.5122.3

0.992

106.8109.3

115.5125.1

1.8201.837 Ni2þ(H2O)6(H2O)2, A II

Ni2þ(H2O)6(H2O)2, C III

Ni2þ(H2O)4(H2O)4, D IV

2.0502.111

2.0802.123

1.9312.015

0.9730.974

105.1107.4

118.7130.6

1.0121.012

107.8108.7

113.9127.8

1.6211.628 0.975

105.0

113.0123.0

0.9900.993

106.7106.9

113.0125.6

1.8211.874

106.0108.4

0.975

105.0

0.9850.998

111.2114.2

120.0122.9

88.294.7

84.095.0

90.6

1.7551.935

in Figure 4. Thus, in the gas phase, the n = 5 one-layer cluster is of higher stability than the two-layer ones. In 4 þ 1, the DE of the last molecule is 43.1 kcal/mol. However, the n = 5 GS shows a bigger DE of 47.2 kcal/mol. Thus, direct metalligand bonding (one layer) is favored at n = 5 over hydrogen bonding (two layers). From n = 4 to n = 5, the BE shows a smaller decrease than from 3 to 4, due to the stability of the 3 þ 1 GS; see Table 5. At n = 5 smaller red shifts than for the n e 4 clusters also occur, but the asymmetric OH stretch has a bigger intensity than the symmetric mode; see Table 4. The present BPW91/6-311þG(d,p) study for Niþ(H2O)5 shows that the Niþ monocation is not able to keep five water moieties in the first layer; instead, 4 þ 1 and 3 þ 2 isomers were found as the low-lying states of this cluster. On 4 þ 1, the outer water molecule accepts two H-bonds, as in the Ni2þ case, but it is more planar since all oxygen sites and the metal atom are contained in the same plane. As expected, its NiO bond lengths are longer than those of Ni2þ(H2O)4 H2O. The 3 þ 2 cluster, with the outer molecules bonded with different inner moieties, is isoenergetic with 4 þ 1, whereas the 3 þ 2 isomer with the outer molecules bonded on the same inner moiety is also close in energy, 1.6 kcal/mol, to the GS. Figure 2 shows the structures of these clusters. These findings are in agreement with the experimental IRPD spectrum and with B3LYP/6-311þG(d,p) results for Niþ(H2O)5.11 Effectively, the bands observed at 3195, 3357, and 3520 cm1, Figure 6 of ref 11, reveal the existence of H-bonded water molecules in these clusters. The last resonance comes from the 4 þ 1 complex; it was predicted at 3516 cm1 using B3LYP11 and at 3525 cm1 in our BPW91 calculations. For the 3 þ 2 GS isomer, its spectrum, Figure 6, exhibits two

resonance signals, 3181 and 3196 cm1, for the OH stretching vibrations of the two internal molecules forming H-bonds, which matches the observed band at 3195 cm1. Lastly, the other 3 þ 2 isomer shows two bands, 3268 and 3300 cm1, for the OH stretches of the inner moiety forming H-bonds; we judge that they correspond to the 3357 cm1 measured signal. It was concluded that the spectrum reflects signatures of 4 þ 1 and 3 þ 2 isomers, signifying that they are present in the sample.11 Indeed, as shown above, they differ by less than 2 kcal/mol. These BPW91 results and the B3LYP ones account for the observed Niþ(H2O)5 spectrum.11 The IR spectra for the 5, 4 þ 1, and 3 þ 2 isomers of Ni2þ(H2O)5 are reported in Figure 7. The GS has two higher frequency bands for the symmetric and asymmetric free OH stretches. In 4 þ 1, the former is slightly red-shifted to 36433649 cm1, and the latter exhibits a doublet; whereas the H-bond stretch appears at smaller values than those of Niþ(H2O)4H2O, implying weaker OH bonds in Ni2þ (H2O)4H2O, which is confirmed by its longer OH distances, ≈1.0 Å; see Figure 4. In the 3 þ 2 isomers the H-bond regions fall at even smaller values, as depicted in Figure 7. Remarkably, as in Niþ(H2O)4H2O,11 the 4 þ1 isomer has the highest H-bond OH stretching frequency, which is for a H-bond pattern with higher connectivity than in other structures, as the double acceptor configuration of the outer moiety furnishes a sixmember ring in 4 þ 1. This is also true for the 5 þ1 and 4 þ 2 structures, of higher connectivity than the 3 þ 3 ones; see below. This is the prediction for the IR spectrum of Ni2þ (H 2 O)5 : major contributions are expected from the 5 and 4 þ 1 isomers; still, the 3 þ 2 higher energy states may also 4129



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Table 4. Vibrational Frequencies and Shifts to the Red, in cm1, for Symmetric and Asymmetric OH Stretchesa system

symmetric OH str

shift

asymmetric OH str

shift

μ

H2O

3722 (6)

3831 (45)

2.14

Ni2þH2O

3361 (659)

361

3419 (502)

412

2.03

Ni2þ(H2O)2

3472 (1505)

250

3555 (811)

276

0.0

Ni2þ(H2O)3

3561 (690)

161

3645 (619)

186

0.98

Ni2þ(H2O)3H2O

36143633 (400)

89108

36973716 (294)

115134

8.0

Ni2þ(H2O)4

3617 (714)

105

3709 (885)

122

0.0

Ni2þ(H2O)5

36573668 (281)

5465

37443751 (337)

8188

1.31

Ni2þ(H2O)4H2O

36433649 (292)

7379

37053709 (458) 37183733 (262)

123127 99114

5.0

4297

3719 (252)

112

3.1

37553757(219)

7476

37113713 (303) 37663771 (218)

118120 6065

H-bonds at 3086 (618) and 3272 (1530) Ni2þ(H2O)3H2OH2O

36353680 (326) H-bonds at 1742 (4389) and 1843 (1235)

Ni2þ(H2O)3H2OH2O

36273634 (349) 36763684 (311)

8895 3846

H-bonds at 2118 (3092) and 2238 (3069) Ni2þ(H2O)6, I

36693672 (245)

5053

3763 (362)

68

0.0

Ni2þ(H2O)5H2O, II

36543665 (160)

5768

37253753 (205)

78106

5.70

69

3728 (264)

103

0.32

3641

37703774 (201)

5761

4.30

2.26

H-bonds at 3212 (130) and 3307 (1823) Ni2þ(H2O)4(H2O)2, III 4 þ 2

3653 (132) H-bonds at 3164 (877) and 32903308 (3028)

Ni2þ(H2O)3(H2O)3, IV 3 þ 3

36813686 (152) H-bonds at 2058 (5351), 2118 (5527), and 2221 (1148)

Ni2þ(H2O)6 H2O, B GS

Ni2þ(H2O)5 (H2O)2, III 5 þ 2

3666 (61)

56

3742 (159)

89

36683677 (146)

4554

37583771 (172)

6073

H-bonds at 3308 (141) and 3380 (1429) 36633671 (126)

5159

37403762 (194)

6991

1.10

5860

37393742 (216)

8992

5.60

1.86

H-bond band centered at 3338 (3050) Ni2þ(H2O)4 (H2O)3, IV 4 þ 3

36623664 (72) H-bonds at 3060 (1395), 3199, 3272, 3353 (1715), 3406 (757), and 3492 (1003)

Ni2þ(H2O)5(H2O)2, B I 6 þ 2

36713672 (55)

5051

3749 (172)3750 (159)

8182

36763681 (92) H-bonds at 3317 (176), 3357,

4146

37683779 (158)

5263

3390 (1566), and 3002 (853) Ni2þ(H2O)6 (H2O)2, A II 6 þ 2 A

36723682 (103)

4050

37643779 (142)

5267

36953698 (66)

2427

3780 (183)

51

1.57

H-bonds at 2982 (2875) and 3002 (853) Ni2þ(H2O)6 (H2O)2, C III 6 þ 2 C

36713672 (151)

5051

37493750 (173)

8182

3689 (83)

33

37623783 (156)

48

5051

3751 (626)

80

3.70

H-bonds at 3318 (311), 3340, 3401 (2309), and 3411 (149) Ni2þ(H2O)4 (H2O)4, D IV 4 þ 4 D

36713672 (61)

2.08

H-bonds at 3181 (1399), 3269 (2915), 3443 (999), and 3528 (2202)

Values in parentheses are for the intensities in kilometers per mole (km/mol); the dipole moment, μ, is reported in debyes (D) . The H-bond region is also indicated for some isomers. a

4130



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Table 5. Binding Energies, BE, per Water Molecule, for Ni2þ(H2O)n, n e 24, and Dissociation Energies, DE, for Elimination of the Last H2O cluster BE (kcal/mol)

DE

1

Ni H2O

112.8

112.8

2

Ni2þ(H2O)2

98.0

83.0

3

Ni2þ(H2O)3

83.0

53.1

4

Ni2þ(H2O)3H2O

71.1

35.3

5 6

Ni2þ(H2O)5 Ni2þ(H2O)6

63.9 57.4

47.2 24.7

7

Ni2þ(H2O)6H2O

52.0

19.6

8

Ni2þ(H2O)6(H2O)2

48.0

19.6

9

Ni2þ(H2O)6(H2O)3

44.6

17.6

10

Ni2þ(H2O)6(H2O)4

41.5

13.8

11

Ni2þ(H2O)6(H2O)5

39.0

14.2

12

Ni2þ(H2O)6(H2O)6

36.8

12.9

16 18

Ni2þ(H2O)6(H2O)10 Ni2þ(H2O)6(H2O)12

30.0 27.7

7.0 10.7

20

Ni2þ(H2O)6(H2O)14

25.9

7.9

24

Ni2þ(H2O)6(H2O)18

23.0

9.8

2þ

contribute. In general, the bands of Ni2þ(H 2 O)5 are different and more red-shifted than those observed for Niþ(H 2 O)5 . 11 [Ni(H2O)6]2þ. The calculated GS for Ni2þ(H2O)6 presents an octahedral geometry with NiO distances, 2.093 Å, which are slightly longer than the experimental values of 2.002,2 2.060,23 and 2.056 Å46 determined in the liquid for the coordination of the Ni2þ ion with six water molecules. Our NiO results are shorter than the obtained values of 2.250, 2.210, and 2.140 Å by classical MD,24 classical MC,24 and combined QM/MM MD23,25 simulations, respectively. Then, explicit inclusion of quantum effects reduces the NiO distances, suggesting stronger bonds. Indeed, we have found a BE of 57.4 kcal/mol/H2O for Ni2þ (H2O)6. These properties indicate high stability for Ni2þ(H2O)6, which is inferred also by the large, 6.8 eV, HOMOLUMO gap. Such stability accounts for the fact that [Ni(H2O)6]2þ has also been observed in the crystal phase. Varadwaj et al. have found significant interligand hydrogen bonding in the determined Ni2þ(H2O)6 octahedron using UX3LYP/6-311þþG(d,p).47 Such a bond occurring between the H atom of one ligand and the O atom of a neighboring water unit has a O 3 3 3 H distance of 2.670 Å. In our study, Ni2þ(H2O)6 does not show an interligand H-bond, as the O 3 3 3 H contact, 2.750 Å, is larger than the sum of the van der Waals (vdW) radii of the O (1.520 Å) and H atoms (1.200 Å). Neither AIM indicates a bond critical point along the O 3 3 3 H path. Note that the value, 2.670 Å, of Varadwaj et al. is shorter than our result, by 0.080 Å, and shorter than the sum of the H and O vdW radii. With six water molecules the Ni2þ ion furnishes its first octahedral coordination sphere. The HOMO and LUMO drawings for this cluster are shown in the Supporting Information; LUMO presents signatures on the hydrogen atoms suggesting that they could be considered as favorable sites for reaction with nucleophilic species such as water, with a second shell then emerging at this cluster size. Adding one water unit to the pyramidal GS Ni2þ(H2O)5 renders a 5 þ 1 isomer, placed 1.2 kcal/mol over the Ni2þ

(H2O)6 GS; with similar NiO distances as those of the n = 5 parent, the pyramid is kept and two H-bonds appear with O 3 3 3 H distances and OH 3 3 3 H angles marking moderate hydrogen bonding. Further, lying 3.1 kcal/mol over the GS, the 4 þ 2 isomer presents a nonplanar geometry with each outer molecule accepting two H-bonds of medium strength, as implied by the OH 3 3 3 O angles. These isomers are shown in Figure 8. On this path of growth, the NiO distances of 4 þ 2 are near those of the 4 þ 1 parent, from which it is originated. Continuing with the 3 þ 3 isomer, IV, with each outer molecule bonded with different inner moieties, shows 8.1 kcal/mol over the GS. Another 3 þ 3 isomer, V, also in Figure 8, was located 10.9 kcal/mol above the GS. In these isomers, the OH 3 3 3 O angles, 177178, suggest strong H-bonds. The IR spectrum of Ni2þ(H2O)6 shows two bands for the symmetric and asymmetric OH stretches; see Figure 9. They are red-shifted by small quantities, 5053 and 68 cm1, with the latter band showing bigger intensity (362) than the former (245). The results for n = 6 are similar to those of n = 5; both clusters, absent of H-bonds, are the ones with more water moieties in the first shell. They also present NiO distances longer than 2.0 Å (Table 2) compared to the ones, 8 clusters, and a table containing the structural parameters for the Ni2þ(H2O)n, n > 8, clusters studied in this work. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors are thankful for the financial support from Project PAPIIT IN-102308, DGAPA-UNAM. The authors express their deep thanks for access to the supercomputer KanBalam at DGSCA-UNAM. A research grant from CONACyT-Mexico, Project 60894-CB, is deeply appreciated. Valuable comments on the IR spectra of these clusters by one of the reviewers are strongly appreciated. ’ REFERENCES

4. CONCLUSIONS The Ni2þ(H2O)n, n e 24, clusters were studied with the BPW91/6-311þG(d,p) method, revealing the growth of outer layers even before the first coordinated octahedral shell is formed. Effectively, isomers with two layers appear at the n = 4, 5, and 6 small clusters; they are mainly promoted by strong hydrogen bonding with the outer waters accepting one and two H-bonds. They constitute the GS in some cases, but in general several single-layer isomers, absent of H-bonds, and two-layer isomers fall within a short energy range, ≈10 kcal/mol; such competition greatly complicates the assignment of the true GS and the analysis of the structural and vibrational properties. This is in agreement with IR spectroscopic experimental results for Niþ (H2O)n and Cuþ(H2O)n revealing the presence of symmetric and asymmetric free OH stretching vibrational bands, as well as red-shifted hydrogen bond regions, signifying clearly the formation of second layers at small cluster sizes of n e 8. The present findings show how the structural and vibrational patterns of the Niþ and Cuþ ions may also occur in small Ni2þ(H2O)n clusters in the gas phase. Coordination of water molecules with the Ni2þ ion produces small but significant increases of the OH distances and HOH angles which are reflected by considerable red shifts, even bigger than those of Niþ(H2O)n, of the OH stretch vibrational bands determined for these small clusters as

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