J. Phys. Chem. 1989, 93, 2165-2169
2165
Ab Initio Self-Consistent-Field Molecular Orbital Study on the Hydration of Three Oxidation States of Beryllium in Aqueous Solution Kenro Hashimoto and Suehiro Iwata* Department of Chemistry, Faculty of Science and Technology, Keio University, Hiyoshi 3- 14- 1 , Kohoku. Yokohama 223, Japan (Received: June 10, 1988; In Final Form: September 19, 1988)
The analytical energy gradient technique for the closed-shell SCF wave function was applied to investigate the molecular structure of the hydrolysis products of Be2+ions in aqueous solution. The hydration energies of a [BeOH]' ion and a Be atom were calculated. The nonadditivity against the hydration number was analyzed in terms of electron population on a Be atom. A smooth and simple relationship between the hydration energy and the electron population on Be was found through three oxidation states, Be(O), Be(I), and Be(I1). A simple method to estimate the hydration energy was proposed and applied to some hydrolysis products.
I. Introduction The interaction of metal ions with water molecules is of interest from both chemical and biophysical points of view, because it is directly concerned with the behavior of electrolyte solutions. X-ray and neutron diffractions as well as vibrational and NMR spectroscopies have played an important role in determining the structure of hydrated ions in solution.I4 Both quantum chemical calculations and computer simulations have also provided useful information on interpreting various phenomena in aqueous ionic solutions, particularly when their results are combined.5,6 In spite of numerous experimental investigations, however, there are still many questions to be answered both experimentally and theoretically at a molecular level; for example, the chemical species in solution vary their form sensitively to pH, and their structures are difficult to determine. Hydrolysis products of hydrated Be2+ ion are among them. In a previous paper: we have determined the structure of hydrated Be2+ions with the ab initio MO method and found the nonadditivity of the hydration energy. It is known that the hydrated BeZ+ion exists only in the low (strong acid) pH range of aqueous solution. In the higher pH range, where hydrolysis of the ions takes place and the OH- ions contribute to forming the chemical species, only electrochemical experiments have been able to determine the constituents in solution; namely only the ratio of the Be2+ ions and OH- ions in the basic unit in solution is reported.' Because the identification of chemical species in such high pH range is difficult, only limited numbers of computer simulations have been reported. In addition, the tendency of the species to polymerize makes the system more complicated. In this report, we have carried out ab initio MO calculations on the hydrolysis products of hydrated Be2+ ions, which provide some information on their structures and hydration energies. 11. Method of Calculation
Basis sets used were the minimal STO-3GBand the standard split valence type 3-21G? In addition to the above two basis sets, (1) Ohtaki, H. Rev. Inorg. Chem. 1982, 4, 103. ( 2 ) Enderby, J. E.; Neilson, G. W. Rep. Prog. Phys. 1981,44, 593. ( 3 ) Conway, B. E. Ionic Hydration in Chemistry and Biophysics; Elsevier: New York, 1981;Vol. 12,Chapters 7, 9. (4) Verall, R. E.; Lilley, T.H. In Water; Franks, F., Ed.; Plenum: New York, 1973;Vol. 3, Chapters 5, 6. (5) Yamaguchi, T.;Ohtaki, H.; Spohr, E.; Palinkas, G.; Heinzinger, K.; Probst, M.M. Z . Naturforsch. 1987, 41A, 1175. (6) Hashimoto, K.; Yoda, N.; Iwata, S. Chem. Phys. 1987, 116, 193. (7) Brown, P. L.;Ellis, J. J . Chem. SOC.,Dalton Trans. 1983, 2001. (8) Hehre, W.J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2651. (9) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980,102, 939.
0022-3654/89/2093-2165$01.50/0
TABLE I: Incremental Hydration Energies ( - A E ( n ) ) of Be2+," [BeOH]', and Be Atom (in eV)
3-21G*
3-21G n
1 2 3
4
Be2+ 7.33 6.36 4.51 3.17
[BeOHI-
Be atom
4.7 1
0.56 0.48 0.64
2.88 2.00
Be2+ 6.99 5.93 4.09 3.17
Be atom 0.29 0.37 0.49
Reference 6. we used the 3-21G*I0which included d type polarization functions on Be and 0 atoms. By using the ab initio closed-shell S C F method with the energy gradient technique, we carried out our research from the following two standpoints. 1. The molecular structures of [Be2(0H)l3+and [Be3(0H)J3+, which were suggested experimentally' as the chemical species in the pH range from 4.0 to 6.0, were optimized by both the STO-3G and the 3-21G basis sets. We also calculated their second derivatives at the optimized structures to confirm all positive force constants. In addition to the above two species, the structure of the neutral [Be(OH),], which was also suggested experimentally for the same pH range, was optimized. For this species, the vibrational analysis was carried out only with the STO-3G basis set. The 3-21G basis set was used for refining the geometrical parameters by keeping the molecular symmetry determined with the STO-3G basis set. From our previous we have some knowledge on the basis set dependence of geometrical parameters in BeXz type compounds and the analogous HBeX type compounds. 2. In order to explore the relationship between the oxidation state of Be in the system and its hydration energy, we also optimized the geometries of the complexes [Be(H20),,l2+for n = 1-4 (hydrated Be2+ion), [Be(OH)(H20),]+ for n = 1-3 (hydrated [BeOH]+), and [Be(H20),] for n = 1-3 (hydrated Be atom) with the STO-3G basis set. We also carried out the vibrational analysis for each system. The structures optimized with the STO-3G basis set for the hydrated Be2+ ([Be(H2O),JZ+) ions have the same symmetry as those determined in our previous paper with the 3-21G basis set. Then, we carried out geometry optimizaton with the 3-21G and the 3-21G* basis sets for hydrated [BeOH]' and hydrated Be atom, by keeping the molecular symmetry unchanged from the one determined with the STO-3G basis set. (10)A value of 0.4 was used for the exponent of the Gaussian function of d type polarization function on Be and 0.8 for that on 0. (11) Hashimoto, K.;Osamura, Y . ;Iwata, S . Nippon Kagaku Kaishi 1986, 1377. (12) Hashimoto, K.; Osamura, Y.; Iwata, S . J . Mol. Struct. (THEOC H E W 1987, 152, 101.
0 1989 American Chemical Society
2166
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
Hashimoto and Iwata
TABLE 11: Gross Atomic PoDulstion on Be in the Hvdrated
3-2 1G
n 0 1 2 3 4
Be2+ 2.00 2.40 2.12 2.89 3.00 [Be,OH] 2.36
a Reference
3-21G*
[BeOH]+
Be atom
2.16 2.99 3.09 3.20
4.00 4.17 4.21 4.25
'+ [Be(OH)2] 3.16
[ Be,(OH),] 2.70
Be2+ Be atom 2.00 2.48 2.81 3.05 3.18
4.00 4.20 4.34 4.43
a
3t
6.
The incremental hydration energies were evaluated by the following formulas: for n = 1-3 (hydrated (BeOH]'): -AE(n) = E([Be(OH)(H,O),]+) E([Be(oH)W20),11+) - E(H20) (II-FI) for n = 1-3 (hydrated Be atom): - A w n ) = E([Be(H,O),I) - E([Be(H,O),-,I) - E(H2O) (11-F2)
(1.373)
b
i
They correspond to the incremental hydration energy of the Be2+ ion for n = 1-4: -AE(n) = E([Be(H20),l2+) - E( [Be(H20),,l2+) - E ( H 2 0 ) (11-F3) which we have reported in our previous paper.6 The AE(n) values for Be, [Be(OH)]+, and Be2+ are compared in Table I. The dependency on the basis set and the effect of electron correlation have been already discussed in our previous paper.6 We concluded that the split valence type basis set with at least two p type functions on Be is necessary to estimate the hydration energy and to describe the bonding nature of Be. In the calculation of the hydration energy of the Be2+ion, the SCF results with the 3-21G basis set and the third-order Merller-Plesset perturbation (MP3)I3 results with the 3-21G* basis set were almost the same. In addition, the hydration energies versus hydration number evaluated with and without electron correlation paralleled one another. In the present work, we used only the SCF method to estimate the nonadditive nature of the hydration energy. The Mulliken population analysisI4 was carried out for each optimized species and is given in Table 11. The program used was GAuSSIAN-~~,'~ and the computer used was a HITAC M-680H in the computer center of the Institute for Molecular Science. 111. Results and Discussion
The values in this section are calculated with the 3-21G basis set, unless mentioned otherwise. Those in parentheses are with the STO-3G basis set. A . Molecular Structure and Stability of [Bef(OH)q](2P-q)+. Brown and Ellis' reported the percentage distribution of the various [Bef(OH)q](2P-q)+type species in the Be(I1) aqueous solution, for a total concentration of 0.7 mmol/dm3 through the pH 4-6 range. The percentage of Be2+ ion (p = 1, q = 0) decreases drastically from about 95% to about 10% with the pH change. Three kinds of complexes, whose (p, q ) combinations are (2, l ) , (3, 3), and (1, 2), appear in turn. The optimized geometries of these complexes are shown in Figure 1. The molecular symmetry is C, for [Be2OHI3+(a), C, for [Be(OH)2] (b), and D3h for [Be3(0H)J3+ (c), as seen in (13) Pople, J. A.; Binkely, J. S.; Seeger, R. Int. J . Quantum Chem., Quantum Chem. Symp. 1976, 10, 1. (14) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833. (15) Binkley, J. S.; Frisch, M.; Raghavachari, K.; DeFrees, D.; Schlegel, H. B.; Whiteside, R. A.; Fluder, E.; Seeger, R.; Pople, J. A. GAUSSIAN 82, Carnegie-Mellon University, Pittsburgh, PA.
C Figure 1. Optimized geometries of (a) [Be20HI3+,(b) [Be(OH)2], and (c) [Be3(OH)3]3+with the 3-21G basis set. The values in parentheses are by the STO-3Gbasis set. The units are angstroms and degrees.
Figure 1. Both [BezOHl3+and [Be(OH)2] have two B e 4 bonds, and the stabilization energies by bond formation with a Be2+ion and an OH- ion are 2.6 and 15.3 eV, respectively; the difference can be. mainly due to the large Coulombic repulsion in [Bq0HI3+. From the viewpoint of chemical bonding, however, this difference of Be-0 bonds is analyzed in another way. W e have already shown that the electron transfer from oxygen to the vacant 2p orbitals of Be is very important for the strong Be-0 bond formatioa6 Mulliken population analysis in Table 11, which we will discuss in detail in a later section, reveals that a Be atom in [Be(OH)2] and [Be2(0H)l3+accepts 1.1 (1.6) and 0.5 (0.4) electrons, respectively, compared to a naked Be2+ ion. These values, of course, are dependent on the number of oxygen atoms with which a Be has bonding. The amount of the electron transfer reflects the strength of Be-0 bonding. It also results in much shorter B e 4 bond distance in [Be(OH)2] than in [Be2(0H)l3+. Comparing the structure of [Be(OH)2] with that of the analogous HBeOH studied in our recent works,11v*2 we notice that the angle of Be-O-H changes from linear in HBeOH to bent in [Be(OH)2]. In addition, the 0-Be-0 angle in [Be(OH)2] is slightly bent while H - B e 4 in HBeOH is linear. Concerning this bending, Sakai and Jordan16 have recently reported that Be-0-H in HBeOH is slightly bent, though it causes only little change in energy. We examined the potential energy surface for the dihedral angle of the H-OBeO coordinate in [Be(OH)*] and confirmed that it was very flat. In the previous work,I2 we showed that the HBeOH molecules tend to dimerize through the OH bridges as HBe(OH),BeH. Similarly, the [Be(OH)2] molecules are expected to form HOBe(OH)2BeOH, which is able to grow to HOBe[(OH)2Be],0H in the high pH condition. The polymer may eventually precipitate in real aqueous solution. (16) Sakai, S.; Jordan, K. D. Chem. Phys. Lett. 1986, 130, 103.
Hydration of Beryllium in Aqueous Solution
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 2167
The [Be3(OH)J3+ complex (Figure IC) can be regarded as a trimer of a simple [BeOH]+ ion. By trimerization, it is destabilized by 0.67 eV with the 3-21G basis set and stabilized by 0.29 eV with the STO-3G basis set. According to the above analysis of electron transfer, it is natural to expect that the trimer is not so substantially stabilized, because there is no oxygen atom which is the new source of the transferring electrons, compared to the [Be(OH)]+ ion. The Coulombic repulsion also contributes to the instability of the system. B. Hydration of [BeOH]+Ion and Be Atom. In real aqueous solution, the above hydrolysis products are strongly hydrated, and therefore, their relative stability depends on the hydration energy. In a previous paper,6 we have examined the hydration of a Be2+ ion. The method we used was straightforward to estimate the hydration energy; the structures of [Be(H20),,]” for n = 1-4 were optimized, and the increment of the stabilization energy on the hydration number n was evaluated. In principle, we can follow the similar procedure to estimate the hydration energy of the species in the previous section. However, it is not practical to apply the procedure for every chemical species we studied. In this subsection, we develop an alternative simpler method to estimate the hydration energy. In our previous paper on the hydrated Be2+ ion,6 we have found that the hydration energy depends on the hydration number in a nonadditive manner. This nonadditivity is the main reason for the failure of the computer simultion, which predicted incorrectly that the hydration number of Be2+ is six, while it is four both in the X-ray analysis and in our ab initio calculations. We have also shown that the nonadditivity is related to the character of the Be-0 bond, which is formed by the electron transfer from an oxygen atom to 2s and 2p orbitals of a beryllium ion. The bond is characterized by the dative structure Be+--OH2+ in Mulliken’s terminology.” The electron-accepting ability of a beryllium ion is very much dependent on the occupation number on the ion. The sum of the occupation numbers of the beryllium 2s and 2p orbitals in [Be(H20)4]2+is nearly one, and thus, the electron-accepting power becomes weaker. We can expect a similar relation for the hydration energy of the hydrolysis products; the number of electrons on the beryllium atom might be used as a measure of the hydration energy of the complexes. To examine this hypothesis, in the subsequent subsections we study the hydrated [BeOH]+ ion, [Be(OH)(H,O),]+, and the hydrated Be atom, Be(H20),. B.1. Hydrated [BeOH]’. Under strong acidic conditions, only the hydrated Be2+ion ([Be(H20)4]2+)can exist in solution. When the pH in solution increases, the hydrolysis reaction takes place. The reaction formula of the hydrolysis can be written as
-
[Be(H20)4]2+
+
[Be(H20)4-r(OH)r](2-r)+ rH+
+ nHzO
-
[Be(OH)(H,O),,]+
(111-2)
The optimized structures of [BeOH(H20),,]+ for n = 0-3 are shown in Figure 2. The molecular symmetry of [Be(OH)(H20),]+ was C,, ( n = 0 ) , C2, ( n = l ) , and C , (n = 2 , 3). The molecular symmetry for n = 2 and 3 is lowered by bending of the Be-(0-H) bond. We can easily find that the bond length of B e 4 between Be2+and OH- ion is much shorter than between Be and hydrating OH2. It means that the interaction of the ion-ion pair is stronger than that of ion-hydrating neutral water molecules. We can also notice that both Be-0 distances are lengthened with the increasing hydration number. One of the (17) Mulliken, R.S.; Person, W. B. Molecular Complex; Wiley: New York, 1969.
180.0 180.0)
0
Be 1.343 (1.276)
H
0.956 (0.970)
H 180.0 (180.0)
0 1.563 (1.518)
H
0.951 ( 0.964)
1.358 (1.2 85 1
H
n I
0.972 (0.978)
H H
0.988
I
(0.9791 I I
