Theoretical Studies of Boron−Water Cluster Ions B+(H2O)n and

Growth dynamics and intracluster reactions in Ni[sup +](CO[sub 2])[sub n] complexes via infrared spectroscopy. N. R. Walker , R. S. Walters , G. A. Gr...
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J. Phys. Chem. 1996, 100, 3377-3386

3377

Theoretical Studies of Boron-Water Cluster Ions B+(H2O)n and Aluminum-Water Cluster Ions Al+(H2O)n: Isomers and Intracluster Reactions Hidekazu Watanabe†,‡,§ and Suehiro Iwata*,†,‡ Institute for Molecular Science, Okazaki, 444 Japan, Department of Chemistry, Faculty of Science and Technology, Keio UniVersity, Hiyoshi, Kohoku, Yokohama, Japan, and Graduate UniVersity for AdVanced Studies, Okazaki, 444 Japan ReceiVed: August 25, 1995; In Final Form: NoVember 14, 1995X

With ab initio molecular orbital calculations, structures of the singly positive charged boron-water clusters B+(H2O)n and aluminum-water clusters Al+(H2O)n are determined. The insertion reaction products HBOH+(H2O)n-1 and HAlOH+(H2O)n-1 are also investigated. Structures of the dimer-core clusters [M+(H2O)2](H2O)n-2 are similar to each other for M ) B and Al. In contrast, the stability and structures of [B+(H2O)](H2O)n-1 and [Al+(H2O)](H2O)n-1 are quite different. The monomer-core boron clusters [B+(H2O)](H2O)n-1 do not have stable local minima; the spontaneous proton transfer reaction takes place to form BOH(H3O)+(H2O)n-2. In other words, the acid-base reaction takes place in such small clusters. In the larger clusters, the reaction further proceeds and the clusters isomerize to the linear type HBOH+(H2O)n-1. On the other hand, in the clusters [Al+(H2O)](H2O)n-1, no such reaction takes place. The cis-form hydrated products of the insertion reaction HMOH+(H2O)n-1 are more reactive, and the acid-base reaction is seen for both M ) B and Al.

1. Introduction Boron and aluminum belong to group 3 and have three valence-electrons. In inorganic chemistry, they have both similarities and differences in chemical properties. Their compounds are often amphoteric. In acidity, boron is somewhat stronger than aluminum. In the neutral solution, boric acid, H3BO3, is a weak acid, and on the other hand, H3AlO3 shows weak basicity. In H3BO3, boron atoms form sp2 hybridization, as the other atoms in the second period. The most interesting series of compounds of boron are boranes. For the boranes, (BH3)n, there are a tremendous amount of investigations in both experimental and theory.1,2 Many people are enchanted with the wonderful chemistry of borane. In recent years, cluster chemistry of waters has flourished both experimentally and theoretically. In particular, the detailed spectroscopic studies of the hydrated clusters X(H2O)n are reported. For aluminum-water clusters, for example, Fuke and his co-workers studied experimentally the photoionization and the photodissociation spectra of Al(H2O)n and Al+(H2O)n.3 Bauschlicher and his co-workers investigated theoretically the structures of the cation Al+(H2O)n.4,5 We also reported the theoretical studies of the cation Al+(H2O)n and neutral Al(H2O)n clusters6 and elucidated the experimental results of Fuke’s group.3,7,8 The reactions of an aluminum atom (ion) with water clusters are also reported. Hrusˇa´k et al. examined the insertion reaction of Al+ to H2O.9 In the neutral Al-H2O complex, the insertion reaction is discussed by several groups.10-12 Sakai studied the structures of the various kinds of hydrides and neutral aluminum complexes and their insertion reactions.13 In contrast, there are very few studies for X ) B and B+. One of reasons is the high ionization energy of the boron atom. It makes the experiment of boron’s clusters difficult. In the present paper, we investigate the singly positive charged boron-water cluster (B+(H2O)n) and their insertion products †

Institute for Molecular Science. Keio University. § Graduate University for Advanced Studies. X Abstract published in AdVance ACS Abstracts, January 15, 1996. ‡

0022-3654/96/20100-3377$12.00/0

(HBOH+(H2O)n-1) from the theoretical side. We also study the aluminum-water clusters (Al+(H2O)n and HAlOH+(H2O)n-1) for comparison. At first, we will show geometric structures of the hydrated clusters B+(H2O)n and Al+(H2O)n. Their stabilities are also discussed. In particular, the stability of [B+(H2O)](H2O)n-1, in which one water molecule is directly bonded to a boron cation, is carefully examined. The intracluster reaction without a barrier is found in the clusters [B+(H2O)](H2O)n-1 and discussed in the subsequent subsection. The products of the intracluster reaction are HBOH+(H2O)n-1. The acidity of the cluster HBOH+(H2O)n-1 is stronger than that of the cluster B+(H2O)n. Their structures, stabilities, and other intracluster reactions are discussed in the next subsection. The corresponding clusters HAlOH+(H2O)n-1 of Al are also examined there. Finally, we will discuss the incremental hydration energies of B+(H2O)n and Al+(H2O)n and their BSSE correction. 2. Method The geometric structures of the boron cation-water clusters B+(H2O)n and aluminum cation-water clusters Al+(H2O)n are optimized with the ab initio molecular orbital method. The geometric parameters are first optimized with the closed shell restricted self-consistent-field (RHF) methods, and then they are refined with the frozen core second-order Mo¨ller-Plesset (MP2) method. The basis sets used are 6-31G*. (Several structures are determined only with the MP2 (frozen core) method.) The harmonic frequencies at all optimized structures are evaluated to confirm the true energy minimum or the transition state. The hydration energies and the energy difference among the isomers of clusters are evaluated at the MP2(frozen core)/6-31G* level. The full geometric parameters and calculated harmonic frequencies are supplied on request through e-mail.14 The program used in the computation is GAUSSIAN 92.15 The computation was carried out on our local network of workstations and on the computer system at the computer center of the Institute for Molecular Science. © 1996 American Chemical Society

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Figure 1. Optimized structures of B+(H2O), Al+(H2O), their isomers, and the transition state of reactions 1 and 2. The geometric parameters are evaluated with the MP2(frozen core) approximation. The parameters are given in angstroms and degrees. In the following figures, the true stability (saddle point) of the optimized structures are confirmed by evaluating the harmonic frequencies.

Figure 4. Optimized structures of the dimer- and trimer-core Al+(H2O)n. The side view is shown of Al+(H2O)2 (4-2). For three isomers of n ) 5, the MP2 structures are shown.

Figure 2. Natural population analysis of B+(H2O), Al+(H2O), their isomers, and their transition states of reactions 1 and 2. The values are evaluated with the MP2 method.

Figure 5. Optimized structures of the proton-transferred isomers BOH(H3O+)(H2O)n-2. The stable structures are found only with the SCF approximation for 5-3a and 5-4.

Figure 3. Optimized structures of the dimer- and trimer-core B+(H2O)n. The numbers in parentheses are determined with the SCF method, and those outside of parentheses are with the MP2(frozen core) method. The side view is shown of B+(H2O)2 (3-2).

3. Results Figure 1 shows the optimized structures of the clusters B+(H2O) and Al+(H2O) and their isomers. The natural populations of these clusters are shown in Figure 2. The optimized structures of larger hydrated clusters (B+(H2O)n and Al+(H2O)n) and inserted clusters (HBOH+(H2O)n-1 and HAlOH+(H2O)n-1) are shown in Figures 3-10. Figures 11 and 12 shows the natural populations of B+(H2O)n, Al+(H2O)n, HBOH+(H2O)n-1,

and HAlOH+(H2O)n-1. The names to the left of the molecular structures in Figures 3-9 are used in the text, tables, and Figures 11 and 12. Some of the geometric parameters of each structure are given in the figures; they are determined with the frozen core MP2 (SCF) methods. Only MP2(frozen core) parameters are given in some clusters. In all clusters, there is little difference between the parameters of the SCF and MP2 methods except for the water-water hydrogen bonds. The relative energy in kJ/mol among the isomers of B+(H2O)n and Al+(H2O)n is summarized in Tables 1-3. The isomerization energies between structures are in most cases as large as 40 kJ/mol, or in some cases larger than 400 kJ/mol. Thus, the present calculation level is precise enough for the following discussion. In the previous studies6,16 we classified the hydrated metal

Boron-Water and Aluminum-Water Cluster Ions

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Figure 6. Optimized structures of the monomer-core isomers of Al+(H2O)n.

Figure 9. Optimized structures of the sp2 type HBOH+(H2O)n-1. The MP2 parameters are given.

Figure 7. Optimized structures of linear sp type HBOH+(H2O)n-1.

Figure 8. Optimized structures of linear sp type HAlOH+(H2O)n-1. For n ) 3, we find a significant difference in structure between SCF and MP2 methods. The MP2 structure of n ) 3 is shown in 8-3, and SCF is shown in 8-3′, respectively.

clusters as monomer-core [X(H2O)](H2O)n-1, dimer-core [X(H2O)2](H2O)n-2, and trimer-core [X(H2O)3](H2O)n-3, depending on how many waters are directly bonded to the central metal. As is seen in the figures, however, some of the clusters are the products of the intracluster oxidation-reduction, or proton transfer, reactions. Therefore, in the present paper, we classify the isomers according to the central structures of the clusters. 3.1. The Structures of B+(H2O), Al+(H2O) and Their Isomers. The optimized structures of B+(H2O), Al+(H2O), and their isomers are shown in Figure 1. The complexes B+(H2O) and Al+(H2O) have very similar structures. All four atoms lie on a plane, and the complexes have C2V symmetry. The bond

Figure 10. Optimized structures of the sp2 type HAlOH+(H2O)n-1. Only MP2 parameters are given.

length of B+-O is shorter than that of Al+-O by 0.555 Å because of the very small ionic radius of B+. The clusters HBOH+ and HAlOH+ are the products of the insertion reactions 1 and 2.

B(H2O) f HBOH+

(1)

Al(H2O) f HAlOH+

(2)

The cations B+ and Al+ insert in an OH bond of a water. The structures of HBOH+ and HAlOH+ are also similar; the stable structures are linear. But the reaction energies are quite

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Figure 11. Natural population analyses of B+(H2O)n, HBOH+(H2O)n-1, and their isomers. The values are evaluated with the MP2(frozen core) method. But in clusters BOH(H3O+)(H2O) and BOH(H3O+)(H2O)2, the values of the SCF method are given because only with SCF are stable structures found (in parentheses).

different, as is given in Table 1. The total energy of the product HBOH+ is 324.40 kJ/mol below that of the complex B+(H2O). In contrast, the energy of HAlOH+ is 49.36 kJ/mol above that of Al+(H2O) with the MP2/6-31G* approximation. The transition states of the insertion reactions 1 and 2 are also shown in Figure 1. Both transition states have a triangle form. In the transition state of the aluminum complex, all four atoms lay in a plane, and it has Cs symmetry, while the transition state of the boron complex does not. The barrier height of the insertion reaction 1 is 140.92 kJ/mol with the MP2(frozen core) method, and that of reaction 2 is 283.87 kJ/mol. The insertion reaction takes place more easily in B+(H2O) than in Al+(H2O). The insertion product HBOH+ is more stable because of sp hybridization of B+. Hrusˇa´k, Sto¨ckigt, and Schwarz also studied insertion reaction 2.9 Their evaluated energy barrier is 266.94 kJ/mol and the reaction energy is 35.98 kJ/mol with the QCISD(T)/6-3111+G**(2df)//MP2(all electrons)/6-31G** approximation. Our results are in agreement with their more elaborate calculations. Figure 2 shows the natural populations of the complexes in Figure 1. The natural charge of B+ in B+(H2O) is +0.8, and Al+ in Al+(H2O), +0.9; the positive charge is localized on the central ion in both complexes. The charge distribution of the

HAlOH+ cluster is remarkable. The natural charge of Al becomes +1.90, and the complex (HAlOH)+ becomes almost HAl2+OH-. In other words, an aluminum is oxidized in the (HAlOH)+ complex. In the transition state of reaction 2, the natural charge of Al is +1.34; the aluminum is already half oxidized in the transition state. In contrast, although the geometric structures are similar, the charge localization in the boron complex is not so drastic as in the aluminum complex. The natural charge of B in (HBOH)+ is +1.19, and at the transition state of reaction 1, it is +0.84. Another possible isomer of [BH2O]+ is the H2BO+ complex, in which two hydrogen atoms are directly bonded to a boron atom as +

H B

O

H

In the optimized structure H2BO+, the distance of two hydrogen atoms is 0.856 Å, and the two B-H distances are 1.325 Å with the MP2/6-31G* approximation. In other words, this isomer is an ion complex of BO+ with H2. The energy of H2BO+ is less stable by 4.98 kJ/mol than the B+(H2O) complex with the MP2(frozen core)/6-31G* approximation. For the neutral

Boron-Water and Aluminum-Water Cluster Ions

J. Phys. Chem., Vol. 100, No. 9, 1996 3381

Figure 12. Natural population analyses of Al+(H2O)n, HAlOH+(H2O)n-1, and their isomers. The values are evaluated with MP2(frozen core) method. For the cluster HAlOH+(H2O)2 (sp), both the MP2 and SCF values are given because a significant difference is seen in the electric correlation effect. (The SCF parameters are in parentheses.)

TABLE 1: Symmetries and Relative Energies of B+(H2O) and Al+(H2O) and Their Isomersa M+(H2O)

transition state

M ) B C2V +0.00 M ) Al C2V +0.00 Cs

HMOH+

H2MO+

+140.92 C∞V -324.39 C2V +4.98 +283.87 C∞V +49.36 C2V +441.68

a Units are given in kJ/mol. The energies are estimated with the MP2(frozen core)/6-31G* approximation.

complex, on the other hand, Mains found that the most stable neutral isomer is H2BO.1 We also examine the cation aluminum complex H2AO+. The cluster H2AlO+ also has a structure similar to H2BO+. The energy of H2AlO+ is 441.68 kJ/mol less stable than that of Al+(H2O) (see also Table 1). In H2AlO+, the natural charge on the Al atom is +1.62, but the charge on B in H2BO+ is hardly changed from that of B+(H2O).

3.2. Structures of B+(H2O)n and Al+(H2O)n (Dimer- and Trimer-Core). The optimized geometries of B+(H2O)n and Al+(H2O)n are shown in Figures 3 and 4, respectively. Structures 3-1 and 4-1 are already shown in Figure 1. Generally speaking, the geometric structures of dimer-core [B+(H2O)2](H2O)n-2 are very similar to structures of [Al+(H2O)2](H2O)n-2. The angles of H2O-M+-OH2 (M ) Al and B) are nearly 90°. They are “surface” type structures named by Hashimoto et al.18,19 The “surface” cluster is the solvated cluster in which the central atom is on the solvating molecular clusters. In contrast, the “interior” cluster is the solvated cluster in which the central atom is surrounded by the solvating molecules. In the cluster Mg+(H2O)2, the angle of O-Mg+-O is also nearly 90°,5,16,20,21 while in the cluster Na+(H2O)2, the structure of O-Na+-O is linear.22 The cluster Mg+(H2O)2 is a surface type, and the cluster Na+(H2O)2 is an interior type.

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TABLE 2: Symmetries and Relative Energies of Isomers of B+(H2O)n and HBOH+(H2O)n-1a n)1

n)2

B+(H2O)n

3-1 C2V

+0.00

BOH(H3O+)(H2O)n-2 HBOH+(H2O)n-1

7-1 C∞V

-324.39

3-2 C2 5-2 Cs 7-2 C2V 9-2 Cs

n)3 +0.00

3-3a C2V 3-3b C3 5-3b 7-3 Cs 9-3a Cs 9-3b

-59.26 -245.28 -431.77

n)4 +0.00 +43.34 -35.65 -170.38 -433.87 -442.41

+0.00

3-4 Cs

-136.52 -451.96 -455.75 -470.84

7-4 9-4a 9-4b Cs 9-4c

a The structures of the isomers (such as 3-3b) are given in Figures 3, 5, 7, and 9 (as 3-3b in Figure 3). Units are given in kJ/mol. The energy’s standard is set in dimer-core isomers. The energies are estimated with the MP2(frozen core)/6-31G* approximation.

TABLE 3: Symmetries and Relative Energies of Al+(H2O)n and HAlOH+(H2O)n-1a n)1 +

Al (H2O)n

HAlOH+(H2O)n-1

4-1 C2V

8-1 C∞V

n)2 +0.00

+49.36

n)3

4-2 C2

+0.00

6-2 Cs

+8.89

8-2 C2V 10-2 Cs

+113.49 -82.93

4-3a C2V 4-3b C3 6-3a 6-3b C2V 8-3 10-3a Cs 10-3b

+0.00 +12.24 +46.43 +28.82 +119.39 -86.14 -89.06

n)4 4-4a Cs 4-4b Cs 6-4 10-4a 10-4b 10-4c

n)5 +0.00 -0.64 +39.28

4-5a C2V 4-5b 4-5c

+0.00 -16.40 -5.10

-87.00 -110.01 -116.32

a Units are given in kJ/mol. The energy’s standard is set in dimer-core isomers. The energies are estimated with the MP2(frozen core)/6-31G* approximation.

Bauschlicher explained the smallness of the angle by the sp2 hybridization of Mg+. The nonbonding orbitals of waters are intracting with the vacant sp2 hybrid orbitals.21 The complex M+(H2O)2, having two waters directly bonded (dimer-core structure), has similar geometric structures for both B+ and Al+; two watrs are equivalent and do not lie on a plane, having C2 symmetry, as shown in the side view (3-2 and 4-2). Recently, in the neutral Na(H2O)2, Hashimoto et al. found a similar complex in which two water molecules also are directly bonded to Na.17,19 But there is a substantial difference; the cluster Na(H2O)2 forms a Na-O-H-O four-membered ring and has Cs symmetry. This was attributed to the smaller Na-O distance (RNa-O ) 2.177). A boron ion B+ has a small ionic radius (RB+-O ) 1.526), but the complex has no such ring structure. The geometric structures of the dimer-core complexes of M+(H2O)3 are also shown in 3-3a of Figure 3 and in 4-3a of Figure 4. In the dimer-core structures [M+(H2O)2](H2O), the third water molecules are bound to two water molecules in the first shells with the hydrogen bondings, forming a six-membered ring. Six atoms in the ring lie nearly in a plane, and the clusters for both M ) B and Al have a symmetric plane, belonging to the C2V point group. The six-membered ring is very stable and has been found in several metal-water clusters.5,6,16,17 The sixmembered ring consists of two pairs of water dimers and the B+ (Al+) ion. The trimer-core isomers B+(H2O)3 and Al+(H2O)3 are shown in 3-3b and 4-3b. All three water molecules are equivalent, having C3 symmetry. In both B+(H2O)3 and Al+(H2O)3, the dimer-core isomers are more stable. The six-membered ring stabilizes the dimer-core structure very much. In particular, the energy difference between isomers [B+(H2O)2](H2O) and B+(H2O)3 is 43.34 kJ/mol. With the larger basis set MP2(frozen core)/6-31+G*, the trimer-core B+(H2O)3 is 45.56 kJ/mol higher than the dimer-core [B+(H2O)2](H2O). The energy difference between trimer-core Al+(H2O)3 and the dimer-core [Al+(H2O)2](H2O) is +12.24 kJ/mol with the MP2(frozen core)/6-31G* method and +15.49 kJ/mol with the MP2(frozen core)/6-31+G* method. The addition of the diffuse functions does not change the trends of the relative energies between isomers of M+(H2O)3. The large destabilization in the trimer-core B+(H2O)3 is due to the repulsion among the coordinating water molecules. The

bond lengths of B+-O with the MP2 approximation are 1.615 Å for n ) 2 and 1.734 Å for the trimer-core isomer. The B+-O distance in the trimer-core isomer is longer by more than 0.1 Å. In contrast, the ionic radius of Al+ is large enough, and the repulsion interaction among the water molecules does not destabilize the trimer-core structure much. The distance of Al+-O with the MP2 approximation is 2.119 Å for n ) 2 and 2.168 Å for the trimer-core isomer; the lengthening of the bond is not so drastic. The cluster Mg+(H2O)3 provides us with a different example from B+(H2O)3 and Al+(H2O)3. In both dimer- and trimercore isomers, the structure of Mg+(H2O)3 is very similar to those of B+(H2O)3 and Al+(H2O)3. Although the dimer-core [Mg+(H2O)2](H2O) has a stable six-membered ring, the trimercore Mg+(H2O)3 is more stable than [Mg+(H2O)2](H2O).16 The difference of the stability among the isomers results from the binding energy difference between the metal-water bondings of water-water bondings. With the MP2(frozen core)/6-31G*/ /SCF/6-31G* level of approximation, the hydration energy of Mg+(H2O) is 1.725 eV,16 while that of Al+(H2O) is 1.466 eV. For the Mg+-water clusters, the stabilization due to the sixmembered ring is smaller than that of Mg+-H2O bond formation. Only the dimer-core isomer is found for a stable structure of B+(H2O)4 (shown in structure 3-4). We failed to locate a B+(H2O)4 of the trimer-core. On the other hand, in Al+(H2O)4, both dimer- and trimer-core structures are found; structure 4-4a is similar to structure 3-4. The relative energy ordering of 4-4a and 4-4b is not definitive; in the SCF method, structure 4-4a is more stable by 4.66 kJ/mol, but in the MP2 method, structure 4-4b is slightly more stable than 4-4a (see also Table 3). The complex Mg+(H2O)4 has two types of isomers also similar to Al+(H2O)4. But the most stable isomer in Mg+(H2O)4 is trimercore [Mg+(H2O)3](H2O).16 The reason that the cluster B+(H2O)4 cannot form is again attributed to the small ionic radius of B+. The strong repulsion of water molecules prevents the third water molecule from being directly bonded to the B+ ion. The tetramer-core isomer in which all four water molecules are directly bonded to a metal ion is found for Mg+, but not for Al+.16 Even in Mg+(H2O)4, however, the most stable isomer is the trimer-core isomer.16 Interestingly, the B-O distance in 3-4 is shortest among 3-2, 3-3a, 3-3b, and 3-4. The bond

Boron-Water and Aluminum-Water Cluster Ions lengths of M+-water become shorter because of the increase of the Lewis basicity of the water dimer. Despite the structural similarity of dimer- and trimer-core B+(H2O)n and Al+(H2O)n, the charge distribution is different in the corresponding B+(H2O)n and Al+(H2O)n complexes, as shown in Figures 11 and 12. For n ) 1, the natural population of B in B+(H2O) is +0.81. But the natural charges on B in the clusters B+(H2O)n for n g 2 are about +0.5 to +0.6 (see Figure 11). Especially, in the trimer-core B+(H2O)3, the charge of boron is as small as +0.38. The positive charges are delocalized on the hydrogens of waters. In contrast, the charges of aluminum atoms in aluminum cation-water clusters are about +0.77 to +0.9. For the aluminum-water clusters, we examine the structures of Al+(H2O)5, shown in structures 4-5a, 4-5b, and 4-5c in Figure 4. Only MP2 parameters are written in the figure. There should exist more stable isomers. Structure 4-5a is a dimer-core isomer, and structures 4-5b and 4-5c are trimer-core isomers. Structure 4-5a has Cs symmetry, and the planar symmetry of 4-5b is slightly broken. The isomer 4-5b has a new type of eightmembered ring. To make the eight-membered ring formed, the six-membered ring in structure 4-5b is substantially deformed. Structure 4-5c has two six-membered rings, and it is a little less stable than structure 4-5b. For n e 4, the most stable isomers of Al+(H2O)n are the dimer-core structures [Al+(H2O)2](H2O)n-2. On the other hand, for n ) 5, the trimercore isomers [Al+(H2O)3](H2O)2 4-5b and 4-5c become more stable (see Table 3) than 4-5a, because the hydrogen bond network of waters formed in the second (and third) shell stabilizes the cluster a great deal. The view from above of structure 4-5c suggests that the cluster is regarded as the complex of the metal ion with two pairs of water dimers and a water. In the above M+(H2O)n clusters the M+ ion lies on top of the water clusters, but they are not like the “surface” clusters discussed by Hashimoto and his co-workers, because M+-O interaction determines the geometric structure of the cluster, not the water networks. 3.3. Intracluster Reactions of B+H2O(H2O)n-1 (MonomerCore). In the present subsection we examine the clusters [M+H2O](H2O)n-1 (M ) B, Al) having only one oxygen attached to an M+ ion. It turns out that the optimized structures of the B+ ion clusters are very different from the Al+ ion (and other previously studied atomic ion) clusters. As shown in Figure 6, the clusters of Al+ are simply the complexes of an atomic ion with a cluster of waters. On the other hand, we cannot locate the similar types of water clusters of B+. As shown in Figure 5, in B+H2O(H2O)n-1 a proton (H+) of the water hydrating the boron atom moves spontaneously to the second-shell water molecule, forming a complex containing an oxonium ion, BOH(H3O+)(H2O)n-2. As shown in Figure 11, the positive charge moves to the oxonium ion, and the moiety BOH becomes a neutral species. This intracluster proton transfer reaction, which is nothing but the acid-base reaction, takes place with no barrier. Similarly for n ) 3 and 4, we found the products of the proton transfer reaction as shown in structures 5-3a, 5-3b, ad 5-4 in Figure 5. But isomrs 5-3a and 5-4 are stable only with the SCF approximation. It turns out that when the MP2 approximation is used in the geometry optimization, structures 5-3a and 5-4 are no longer stable and the reaction proceeds further. Structure 5-3b, a branch type isomer, is found stable with both SCF and MP2 methods. In any case, an oxonium ion H3O+ is spontaneously formed. For n ) 3, when we begin with structure 5-3a for the optimization procedure with the MP2 approximation, we end

J. Phys. Chem., Vol. 100, No. 9, 1996 3383

Figure 13. Geometric optimization process of the monomer-core B+(H2O)3 with the MP2(frozen core) method. Schemes II and III are neither the intermediate products nor transition states.

up with structure 7-3 in Figure 7; the apparent insertion reaction of a B+ ion into the O-H bond takes place spontaneously! To examine the reactions, we scrutinize the intermediate structures during the geometry optimization. Figure 13 shows two intermediate schemes, II and III. The boron atom in BOH(H3O+)(H2O) (scheme I) attracts the hydrogen atom H(c), the proton is transferred further from O(2) to O(3), and a water molecule and oxonium ion form a cyclic structure (scheme II). After another proton transfer, as in scheme III, eventually the cluster becomes (HBOH)+(H2O)2 (scheme IV). The positive charge center moves through the chain of water molecules in this sequential barrierless reaction. In schemes III and IV, the positive charge returns to the boron atom of HBOH. It must be noted that schemes II and III are neither transition states nor intermediate products. A similar reaction is also found for n ) 4. In other words, the apparent insertion reaction [B+(H2O)](H2O)n-1 into (HBOH)+(H2O)2 take place for n g 3. The reaction is a kind of solventassisted reaction. The characteristics of the clusters (HBOH)+(H2O)n-1 are discussed in the next subsection. The products of the intracluster reaction 5-2 and branch type 5-3b are stable with both approximations, which is confirmed by evaluating the harmonic frequencies. The reaction shown in Figure 13 is induced by the increase of the Lewis basicity (proton affinity) in the water dimer. These types of reactions are not found for the Al+-water clusters. All four clusters in Figure 6 are at a stable local minimum with both SCF and MP2 methods. But there is no stable local minimum for the clusters AlOH(H3O+)(H2O)n-2; if we start the optimization at a structure AlOH(H3O+)(H2O)n-2, the clusters return to the structure [Al+(H2O)](H2O)n-1. No proton-transferred clusters [Al+(H2O)](H2O)n-1 have local minima for the monomer-core isomers, although the relative energy is higher than the other dimer- and trimer-core isomers. 3.4. Clusters (HBOH)+(H2O)n-1 and (HAlOH)+(H2O)n-1. In Figures 7 and 9, the structures of the hydrated products of the insertion reaction (HBOH)+(H2O)n-1 are shown. If a water is attached to the H atom side, as in Figure 7, the core H-B+O-H is almost linear, and the boron atom is sp hybridized. These isomers are the direct product of the reaction of B+ and water clusters for n g 3, as described above. On the other hand, if a water directly hydrates the B atom, the core H-B+-O-H becomes the cis-form 9-2 in Figure 9, and the boron becomes sp2 hybridized. The linear type isomers in which a hydrating water bonds to a hydrogen of HO-B are not found; they become

3384 J. Phys. Chem., Vol. 100, No. 9, 1996 the cis-type isomers without barriers. The structures of the similar clusters (HAlOH)+(H2O)n-1 are shown in Figures 8 and 10. The natural populations of the HBOH+ and HAlOH+ cores are kept almost unchanged in the clusters (HBOH)+(H2O)n-1 and (HAlOH)+(H2O)n-1. The positive charge is also strongly localized on aluminum in the linear type (sp) clusters. Even in the cis type (sp2) clusters, aluminum is strongly oxidized, and their charges are more than +1.8 (compare Figures 11 and 12). The clusters (HBOH)+(H2O)n-1 (sp) are more stable than B+(H2O)n, but the clusters (HBOH)+(H2O)n-1 (sp2) are even more stable than (HBOH)+(H2O)n-1 (sp). On the other hand, in the aluminum cation-water clusters, (HAlOH)+(H2O)n-1 (sp) are less stable than Al+(H2O)n clusters. But the isomers (HAlOH)+(H2O)n-1 (sp2) are more stable than any other aluminum cation-water clusters, but not so significant as (HBOH)+(H2O)n-1, (sp2), as given in Tables 2 and 3. This is due to the difference in the hybridization of B and Al atoms; the boron atom is as easy to hybridize as the carbon atom. The new B-O bond between the boron atom and the oxygen of water is strong, and the bond length is much shorter than those at the B-O distance in the other clusters. The charge transfer from the oxygen to B is slightly noticed in Figure 11. The spontaneous proton (H+) transfer reaction is also found in several clusters of the products of insertion reaction. In structure 9-3b, (HBOH)+(H2O)2, a proton moves to the outer water molecule, and the cluster becomes H[B(OH)2]‚H3O+. A oxonium ion, H3O+, is bonded to both oxygen atoms in H[B(OH)2], which makes a small six-membered ring. The symmetry is slightly broken from Cs. The complex 9-4c of HB(OH2) and H5O2+ has a large eight-membered ring. In structure 9-4a, (HBOH)+(H2O)3, the proton transfer is also seen. Structure 9-4a is less stable than 9-4c, because the H5O2+ ion is bonded to only one -OH group. But in structure 9-4b the proton transfer does not take place. The difference between 9-4b and 9-4a is explained again by a Lewis basicity of the water dimer, as in BOH(H3O+)(H2O)n-2. Such proton transfer is not seen in structure 10-3b, (HAlOH)+(H2O)2, although a hydrogen atom at the end of the chain is attracted to the oxygen of the HAlOH+ core. In contrast, in structure 10-4c the proton transfer reaction takes place to form H[Al(OH)2]‚H5O2+. The isomer 10-4a, the corresponding isomer of 9-4a, gives us an interesting example; a hydrogen somewhat moves to an outer water shell, but the proton transfer is not completed. The Lewis basicity of (H2O)2 is strong enough to neutralize a HAl+OH core in 10-4c, but not enough in 104a. It is well-known that in free H5O2+ the central hydrogen is exactly at the middle of two water molecules.24-26 But in clusters 9-4c and 10-4c, a proton is more or less localized to one of water (H2O) moieties, forming an oxonium ion. A moiety HB(OH)2 in 9-3b and 9-4c is almost neutral, as is seen in Figure 11, and was investigated by Mains under different contexts.1 It should be noted that the intracluster reaction does not proceed to form boric acid, B(OH)3, because all three valence electrons of the boron (aluminum) atom are used up for bonding to O and H atoms in 9-2. In contrast, in BOH(H3O+)(H2O)n-2, in Figure 5, only one of three valence electrons in the boron atom is used for bonding to a oxygen atom, and the boron atom draws a proton of the last water of the chain with two valence electrons. To form boric acid, B(OH)3, in the intracluster reaction, the hydrogen is to be replaced with a OH; at least a trimer of waters is required to form [B(OH)3](H3O+)3.

Watanabe and Iwata

Figure 14. Incremental hydration energies of the monomer- and dimercore B+(H2O)n and Al+(H2O)n. The energies are calculated with the MP2(frozen core) method. The solid lines and square plots are those of the dimer-core structures [M+(H2O)2](H2O)n, and the broken lines and circle plots are those of monomer core [M+(H2O)](H2O)n-1. For n ) 1, we use the same structure for the monomer-core isomers and the dimer-core isomers. See text for details. The energies of the monomer-core boron-water clusters are for n ) 2.

In the intracluster proton transfer reaction, the boron ionwater complexes are always more reactive than the corresponding clusters of the aluminum ion because a boron is more nonmetallic. Interestingly, on the other hand, in (HAlOH)+(H2O)2 (sp), structure 8-3, a proton is transferred from the Al atom to the water molecule, but not in the (HBOH)+(H2O)2 (sp) complex, 7-3. The reasons for the difference might result from a weak bond of Al-H; the hydrogen bonded to the hydration water has a negative charge. In contrast, the charge of the hydrogen bonded to the water is almost zero in (HBOH)+(H2O)2 (sp) (see also Figures 11 and 12). The proton transfer reaction of (HAlOH)+(H2O)2 (sp), 8-3, is found only with the MP2 optimization. Structure 8-3′ is the SCF structure in which no proton transfer reaction takes place. We cannot find any stable structures of sp type HAl+OH(H2O)3; they isomerize without barrier to sp2 type isomers. 3.5. Hydration Energies. The size dependence of the hydration energies of monomer-core and dimer-core clusters (B+(H2O)n and Al+(H2O)n) is summarized in Figure 14. The energy is evaluated with the MP2(frozen core) approximation. The hydration reaction is given as

M+(H2O)n-1 + H2O f M+(H2O)n (M ) B or Al) (3) The incremental hydration energy - ∆EM+,x(n) (M ) B or Al) is defined as

-∆EM+,x(n) ) -[EM+,x(n) - {EM+,x(n - 1) + E(H2O)}] (4) where EM+,x(n) is the total energy of B+(H2O)n or Al+(H2O)n, and E(H2O) is the total energy of H2O. The suffix x of ∆EM+,x(n) and EM+,x(n) refers to the x-mer-core clusters. The solid lines are for the dimer-core (x ) 2) isomers, and the broken lines are for the monomer-core (x ) 1) isomers. For n ) 1, we use structures 3-1 and 4-1 for both monomer- and dimercore isomers. Because no stable local minimum structures are found for [B+(H2O)](H2O)n-1 (n ) 2, 3) with MP2 calculation, we use the total energies of BOH(H3O)+ and BOH(H3O)+(H2O) for

Boron-Water and Aluminum-Water Cluster Ions

J. Phys. Chem., Vol. 100, No. 9, 1996 3385

TABLE 4: Basis Set Superposition Error (BSSE) Effect of the Hydration Energies of the Small Particles reaction

with BSSE

without BSSE

B + H2O f B+ + 2H2O f B+(H2O) + H2O f BOH + (H3O)+ f BOH(H3O)+ Al+ + H2O f Al+(H2O) Al+ + 2H2O f Al+(H2O)2 (4-2) Al+(H2O) + H2O f Al+(H2O)2 (4-2) Al+ + 2H2O f Al+(H2O)2 (6-2) Al+(H2O) + H2O f Al+(H2O)2 (6-2)

-235.04 -356.69 -136.13 -74.79 -125.09 -220.64 -98.95 -228.55 -105.52

-244.41 -390.63 -146.22 -73.29 -142.19 -257.71 -115.53 -248.82 -106.63

+

a

B+(H2O) B+(H2O)2 B+(H2O)2

4. Discussions

Units are given in kJ/mol.

EB+,1(2) and EB+,1(3), respectively. Thus, the hydration energies -∆EB+,1(2) and -∆EB+,1(3) refer to the following reactions:

B+(H2O) + H2O f BOH(H3O+)

and large, the BSSE correction is about 10% of the hydration energy, and therefore, it does not change the chemistry discussed above and below.

(5)

BOH(H3O+) + H2O f BOH(H3O+)(H2O) (structure 5-3b) (6) The isomer BOH(H3O+)(H2O) in eq 6 is the branch type structure 5-3b. We find a strong nonadditively in all series examined. The hydration energy ∆EM+,x(1) is largest, and it substantially decreases with the cluster size. Especially, the energy ∆EB+,x(1) is extremely large. As mentioned in subsection 3.2, the positive charge is localized on a boron atom in B+(H2O), but the charge of boron is substantially neutralized for n g 2. Because the electrostatic force is dominant in the binding of the cluster, through the other factors are not negligible, the hydration energy becomes small for n g 2. Whereas in Al+(H2O)n the positive charge is still localized on an aluminum atom, the reduction of ∆EAl+,2(n) is not as significant as ∆EB+,2(n). The incremental hydration energy, ∆EB+,2(n), is always larger than ∆EAl+,2(n). But the larger the cluster size n, the smaller the difference is. When B+(H2O)n and Al+(H2O)n have the outer water shell for n g 3, the similarity of the structure of the second hydration makes the difference of ∆EB+,2(n) and ∆EAl+,2(n) small. In the dimer-core [M+(H2O)2](H2O)n-2, the change of the incremental hydration energies between n ) 2 and 3 is small. This is because the incremental hydration energy for n ) 3 and n ) 4 mostly results from the ring formation in the outer shell. This is demonstrated in particular for the dimer-core structures of Al+(H2O)n (n ) 2 and 3, and n ) 4 and 5). The energy of the dimerization of water molecules is 30.61 kJ/mol with the MP2(frozen core)/6-31G* level of theory. The hydration energy -∆EM+,2(3) is much larger than twice the binding energy of the water dimer. The energy -∆EAl+,2(5) becomes close to twice the binding energy of the water dimer. As the hydration to the outer water shell proceeds, the interaction betwern water molecules becomes dominant in the hydration, and the hydration energies -∆EM+,2(n) converge to the binding energy of the water molecules. The incremental hydration energy of the monomer-core Al+(H2O)n, -∆EAl+,1(n), is somewhat smaller than that of the dimer-core Al+(H2O)n, -∆EAl+,2(n). This is because the monomer-core Al+(H2O)n is less stable than the dimer-core Al+(H2O)n. In contrast, -∆EB+,1(2) (the reaction energy of eq 5) is much larger than -∆EB+,2(2). The cluster is stabilized by the proton transfer. But structure 5-3b is not so stable and -∆EB+,1(3) becomes small again. We examined the basis set superposition error (BSSE) for several clusters, and they are summarized in Table 4. In the present case, because the electrostatic interaction is dominant

In this work, the reactions of the water clusters with a boron cation proved to be rich in various chemistries and are different from those of the other atomic ions. There are several factors in understanding the peculiar chemistry of the boron cationwater clusters and their intracluster reactions, which we discussed below by comparing them with those of the aluminum ion. The first factor is the difference of the ionic radii of boron (RB+-O ) 1.526 Å) and aluminum (RAl+-O ) 2.081 Å). The stabilities of dimer- and trimer-core B+(H2O)n can be understood with the small ionic radius of B+. The second factor is based on the fact that a boron atom tends to form sp hybridization. The sp and sp2 (and probably sp3) hybridization of boron atoms plays an important role in B-O bonds. The clusters [B+(H2O)](H2O)n-1 are isomerized without barrier to (HBOH)+(H2O)n-1 (sp), which is apparently the insertion reaction to the H-O bond of the water molecule. The isomerization reaction from (HBOH)+(H2O)n-1 (sp) to cis (HBOH)+(H2O)n-1 (sp2) requires activation energy (though not evaluated yet); the latter is much more stable than the former (see Table 2). The third factor is the electronegativity of boron in Pauling’s electronegativity (2.0) and aluminum (1.5). The larger electronegativity of boron explains the stronger reactivity for the proton transfer in the clusters. In the monomer-core [M+(H2O)](H2O)n-1, spontaneous proton transfer is seen for only M ) B. In the isomers (HMOH)+(H2O)n-1 (sp2), the proton transfer reaction takes place for both M ) B and Al for n g 4, but only M ) B for n ) 3. Structure 8-3, linear type (HAlOH)+(H2O)n-1 (sp), is an exception, but it is due to a weak Al-H bond, as is discussed in subsection 3.4. Because of the metallic character of aluminum, the positive charge in an HAlOH+ core is strongly localized as HAl2+OH-. Thus, it is expected that the hydration number of aluminum is larger than that of boron. In the bulk solution, the hydration numbers of aluminum and boron are 6 and 4, respectively. The molecular ions MgOH+ and CaOH+ are similar to AlOH+.16,23,27 The fourth factor is the Lewis basicity of the water dimer. The previous three factors are concerned with the difference between boron and aluminum. But this is the common factor in boron and aluminum. The binding energy of the water dimer, (H2O)2, is much larger than that of the water monomer:

H2O + H2O f (H2O)2

(7)

(H2O)2 + H2O f (H2O)3

(8)

The energy of the reaction 7 is 30.61 kJ/mol and that of reaction 8 is 68.34 kJ/mol with the MP2(frozen core)/6-31G* approximation. The increase of basicity of the dimer (and polymers) of water determines the structures and reactions of water clusters with the other atoms and molecules. Our previous studies revealed that the second hydration influences the structures and stabilities of the aluminum- and magnesiumwater clusters.6,16 We will discuss the similar effect for the structure and the infrared absorption spectra of the phenolwater cluster.28 The chemistry of the boron-water clusters is still much more complex due to the large Lewis basicity of (H2O)2.

3386 J. Phys. Chem., Vol. 100, No. 9, 1996

Watanabe and Iwata

If the collision experiment of the boron cation with water is carried out as for the other metallic ions,3,7,8,29-31 the most probable final products of the reaction are the clusters of (HBOH)+(H2O)n-1 (sp2). Note that we cannot differentiate these products with B+(H2O)n by mass spectroscopy. The reaction is expected to proceed for n g 3 in boron cation-water clusters. From the inorganic chemistry point of view, the proton transfer reactions we found, +

+

B (H2O)2 f BOH(H3O)

(9)

HBOH+(H2O)2 f HB(OH)2(H3O)+

(10)

HBOH+(H2O)3 f HB(OH)2(H5O2)+

(11)

HAlOH+(H2O)3 f HAl(OH)2(H5O2)+

(12)

can be regarded as the acid-base reaction: B+, HBOH+, and HAlOH+ dissolve in water and the solution is acidified. Usually the boron plays a role of a nonmetal (the oxide shows the acidity when it dissolves in the water), and the aluminum, a metal. The reaction like (9) does not proceed in the aluminum-water clusters because of aluminum’s metallic nature. Reaction 12 is, however, not inconsistent with inorganic chemical knowledge. An aluminum hydride Al(OH)3 shows the acidity in a strong alkaline solution. For n g 3, the cluster [BOH(H3O)+](H2O)n-2 has no stable structure. But cluster HB(OH)2‚H3O+(H2O)n-3 and HAl(OH)2‚ H3O+(H2O)n-3 may grow to larger size. Because the M-O bonds in HM(OH)2 have a covalent nature, the valence of M is saturated. For the reaction to proceed further, the substitution of H with OH has to take place. The difference in the natural charge of BOH(H3O)(H2O)n-2 and sp2 type HBOH+(H2O)n-1 suggests that HB(OH)2 is stronger than BOH in acidity. Generally, as the number of -OH groups bonding to the central atom directly increases, the acidity becomes stronger. The dissociation of boric acid in the bulk water is as follows:

H3BO3 + 2H2O f B(OH4)- + H3O+

(13)

A boron is bonded to four -OH groups in the bulk solution. It is chemically known in pure liquid water that a small fraction of molecules are dissociated to H3O+ and OH-. In cluster chemistry, the question is how many waters in the pure water cluster, (H2O)n, are needed for this dissociation reaction. How the number n changes with the effect of the metal ion in the water is also an important problem. Reaction 9 shows that only two water molecules are required for the spontaneous dissociation in the case of B+. Acknowledgment. The authors thank Prof. Hashimoto for his valuable discussion and Mr. Nakakmura for his help in the

early stage of the work. H.W. thanks Research Fellowships of the Japan Society for the promotion of Science for Young Scientists for the financial support. This work is partially supported by the Grants-in-Aid for Scientific Research (No. 04640458) and for the Priority Area (No. 04243102) by the Ministry of Education, Science, Sports and Culture, Japan. References and Notes (1) Mains, G. J. J. Phys. Chem. 1991, 95, 5089 and references therein. (2) Sakai, S. J. Phys. Chem. 1995, 99, 9080. (3) Fuke, K.; Misaizu, F.; Sanekata, M.; Tsukamoto, K.; Iwata, S. Z. Phys. D: At. Mol. Clusters 1993, 26S, 180. (4) Sodupe, M.; Bauschlicher, C. W., Jr. Chem. Phys. Lett. 1991, 181, 321. (5) Bauschlicher, C. W., Jr.; Partridge, H. J. Phys. Chem. 1991, 95, 9694. (6) Watanabe, H.; Aoki, M.; Iwata, S. Bull. Chem. Soc. Jpn. 1993, 66, 3245. (7) Misaizu, F.; Tsukamoto, K.; Sanekata, M.; Fuke, K. Chem. Phys. Lett. 1992, 188, 241. (8) Misaizu, F.; Tsukamoto, K.; Sanekata, M.; Fuke, K.; Iwata, S. Z. Phys. D: At. Mol. Clusters 1993, 26, 177. (9) Hrusˇa´k, J.; Sto¨ckigt, D.; Schwarz, H. Chem. Phys. Lett. 1994, 221, 518. (10) Hauge, R. H.; Kaufmann, J. W.; Margrave, J. L. J. Am. Chem. Soc. 1980, 102, 6005. (11) Kurtz, H. A.; Jordan, K. D. J. Am. Chem. Soc. 1980, 102, 1177. (12) McClean, R. E.; Nelson, H. H.; Campbell, M. L. J. Phys. Chem. 1993, 97, 9673. (13) Sakai, S. J. Phys. Chem. 1992, 96, 8369. (14) E-mail address: [email protected] (15) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision E.2; Gaussian, Inc.: Pittsburgh, PA, 1992. (16) Watanabe, H.; Iwata, S.; Hashimoto, K.; Fuke, K.; Misaizu, F. J. Am. Chem. Soc. 1995, 117, 755. (17) Hashimoto, K.; He, S.; Morokuma, K. Chem. Phys. Lett. 1993, 206, 297. (18) Hashimoto, K.; Morokuma, K. Chem. Phys. Lett. 1994, 223, 423. (19) Hahimoto, K.; Morokuma, K. J. Am. Chem. Soc. 1994, 116, 11436. (20) Bauschlicher, C. W., Jr.; Partridge, H. J. Phys. Chem. 1991, 95, 3946. (21) Bauschlicher, C. W., Jr.; Sodupe, M.; Partridge, H. J. Chem. Phys. 1992, 96, 4453. (22) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H. J. Chem. Phys. 1991, 95, 5142. (23) Watanabe, H; Iwata, S. In preparation. (24) Okumura, M.; Yeh, L. I.; Myers, J. D.; Lee, Y. T. J. Phys. Chem. 1990, 94, 3416. (25) Del Bene, J. E.; Frisch, M. J.; Pople, J. A. J. Phys. Chem. 1985, 89, 3669. (26) Yeh, L. I.; Okumura, M.; Myers, J. D.; Prince, J. M.; Lee, Y. T. J. Chem. Phys. 1989, 91, 7319. (27) Harms, A. C.; Khanna, S. N.; Chen, B.; Castleman, A. W., Jr. J. Chem. Phys. 1994, 100, 3540. (28) Watanabe, H.; Iwata, S. J. Chem. Phys., submitted. (29) Misaizu, F.; Sanekata, M.; Fuke, K.; Iwata, S. J. Chem. Phys. 1994, 100, 1161. (30) Sanekata, M.; Misaizu, F.; Fuke, K.; Iwata, S.; Hashimoto, K. J. Am. Chem. Soc., submitted. (31) Misaizu, F.; Sanekata, M.; Tsukamoto, K.; Fuke, K.; Iwata, S. J. Phys. Chem. 1992, 92, 8259.

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