Molecular orbital models of aqueous aluminum-acetate complexes

Geochimicaet CosmochimicaActa, Vol. 60, No. 24, PP. 4897-4911, 1996 Copyright 0 1996Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/96$15.00 + .OO

Pergamon

PI1 SOO16-7037(96)00285-2

Molecular orbital models of aqueous aluminum-acetate

complexes

J. D. KUBICKI, ’ G. A. BLAKE,* and S. E. APITZ ’ ‘Remediation Research Laboratory, Chemistry and Biochemistry Branch, Naval Command Control and Ocean Surveillance Center, RDT&E Division, Code 361, San Diego, CA 92152-6325, USA *Division of Geological and Planetary Sciences, California Institute of Technology, 170-25, Pasadena, CA 91125, USA (Received June 1, 1995; accepted in revised form August 19, 1996)

Abstract-Molecular orbital calculations with HF/3-21G* *, HF/6-311 +G* *, and MP2/6-311 +G* * basis sets (HF = Hartree-Fock approximation; MP2 = 2nd-order Moller-Plesset perturbation theory) have been performed on molecular clusters in the system acetate-aluminum-water. The results model the structures, energetics, and vibrational spectra of A13+ and A13+-acetate complexes in the aqueous phase. An octahedral to tetrahedral coordination change is predicted in the species A13+ (OH); - n(H20) [where m + n = 61 as m increases from two to three. Calculated reaction energetics for aqueous Al 3f -acetate complexation compare favorably with experimental enthalpies. In addition, the possible existence of more than one configuration for each A13*-acetate species was investigated. Theoretical vibrational spectra of the A13+-acetate complexes provide predictions for the identification of A13+acetate species

i;l aqueous

solutions.

1. INTRODUCTION

molecular kinetics. For instance, typically a species such as aqueous Al 3+-acetate is invoked without any regard as to whether the bonding is monodentate or bidentate (i.e., C-O-Al linkages through either one or two of the oxygens in the carboxylate group), although some authors have recognized the importance of such a distinction (e.g., Palmer and Bell, 1994). This work tested the feasibility of numerous possible structures for aqueous Al-acetate complexes via molecular orbital calculations. Although the effect of bulk liquid water on the complexes was neglected in these models, hydration of the Al and acetate were explicitly studied by the addition of water molecules to the model system. This approach has been used previously to study hydration of anions and cations (Kistenmacher et al., 1974; Mirabel and Ponch, 1991; Zhao et al., 1991; Keith and Frisch, 1994). Thermodynamic stabilities of each species can be calculated with regard to one another, and the theoretical reaction energies compared with experimental enthalpies of reaction. Predictions of vibrational spectra for each complex were made that can be used to interpret experimental infrared (e.g., Biber and Stumrn, 1994) or Raman (e.g., Dutta and Shieh, 1985; Marley et al., 1989) spectra of aqueous solutions. The purpose of this paper is to elucidate the large number of species that may exist in aluminum-acetate solutions. Further work including long-range solvent effects and derivation of nuclear magnetic resonance spectral properties (e.g., Sykes et al., 1995) will be necessary to more definitively answer the questions as to which species actually exist under a given set of thermodynamic conditions.

Complexation between Al and organic anions has been studied extensively because of the potential role organic acids,

such as acetic acid, can play in the transport of Al in geologic environments ( Fein, 1994, and references therein). Organic acids can also affect mineral dissolution rates and solubilities; hence, acetate-aluminum chemistry is important for understanding weathering and diagenetic reactions (Welch and Ullman, 1993; Huang and Keller, 1971). The stability of metal-organic complexes in solution is also related to the adsorption behavior of the organic ligand onto mineral surfaces (Schindler and Stumm, 1987). Soluble Al and other metals in natural waters also have environmental consequences (Parker et al., 1988; Parker and Bertsch, 1992). High trace metal concentrations degrade water quality and can be toxic. Bioavailability of metals can be affected by the aqueous-phase speciation (Sunda and Hanson, 1987; Sunda et al., 1990). Free ions, such as hexaaquo aluminum, Al 3+ * 6 ( H20) , may be incorporated into organisms much more readily than metals that are complexed with naturally-occurring organic matter (Kinraide and Parker, 1990; Hue et al., 1986). In addition, Al accumulation in the brain has been implicated in the generation of Alzheimer’s disease (Forbes et al., 1995). Consequently, understanding thermodynamics and kinetics of aqueous-phase organic metal complexes is important for determining potential biological effects (i.e., risk assessment) of trace metals in waters. Most work in the geochemical literature has focused on solubility and potentiometric measurements interpreted with thermodynamic models (e.g., Shock and Koretsky, 1993; Palmer and Bell, 1994; Benezeth et al., 1994). These approaches provide evidence on the relative speciation in solutions; however, they generally rely on assumptions as to the possible species that may exist. In addition, structural aspects of the complexes are commonly ignored because these bulk thermodynamic techniques provide only indirect information on molecular structures and their possible relationships with

2. METHODS These calculations were performed with the program Gaussian 92 (Frisch et al., 1992). HF/3-21G* * basis sets were used for structure optimizations and force constant analyses (HF symbolizes the Hartree-Fock approximation which neglects electron correlation. Each atomic orbital is described by three Gaussian functions with the valence orbitals split into sets of 2 and 1 Gaussians. The ** indicates that d-orbitals are included on the Al and Si atoms and 4897

J. D. Kubicki, G. A. Blake, and S. E. Apitz

4898

that p-orbitals are included on the H atoms to account for polarization effects.). Energy calculations were carried out with the HF/63ll+G** andMP2/6-31l+G * * basis sets [The + indicates a diffuse function that allows for electron density relatively far from the nucleus (Foresman and Frisch, 1993). This factor is especially important for anions with diffuse electron distributions. MP2 corrections help account for electron correlation effects (Mller and Plesset, 1934; Hehre et al., 1986)]. A larger number of Gaussian functions used to approximate the atomic orbital (i.e., 6 vs. 3) provides for a better description of the electron density distribution. Additional splitting of the sets of Gaussians used for the valence orbitals gives a more realistic representation of bonding. Diffuse functions and atomic orbitals with high angular momentum quantum numbers (e.g., d-orbitals on 0, Al, and Si and p-orbitals on H) also allows for greater accuracy. Unfortunately, computational time, memory, and disk space required in a calculation all increase rapidly with the size of the molecule and basis set. Thus, the choice of basis sets balances the need for accurate structural and energetic information with the practical limits of computing time and power. Molecules were optimized allowing all bond lengths, angles, and dihedral angles to vary independently. Dynamic stability was tested via diagonalization of the Hessian matrix (i.e., the second derivatives of the potential energy with respect to spatial coordinates) which provides harmonic frequencies for a given minimum energy structure. In a minimum of a molecular potential energy surface, all the eigenvalues of the Hessian matrix are positive; hence, all the harmonic vibrational frequencies are also positive. If the molecule is not at least in a local minimum, then at least one negative eigenvalue will result, leading to the prediction of an imaginary frequency. The eigenvalues are related to vibrational frequencies and eigenvectors to the vibrational modes. With the calculated electron densities of the stationary point and vibrational modes, changes in dipole moment and polarization can also be calculated to provide estimates of vibrational intensities. The missing factor is the bandwidth of the vibration, so we list vibrational frequencies as absorption lines rather than the bands that are observed in infrared and Raman spectra (see Lasaga and Gibbs, 1988, for a more thorough discussion of frequency analysis). Predicted reaction energies at the HF/3-21G * * level are generally of lower accuracy than calculated molecular structures and vibrational frequencies (Geisinger et al., 1985; Nicholas et al., 1992). Calculations with the HF/6-3 11 +G * * and MP2/6-3 11+G * * basis sets were carried out on the 3-2lG** optimized structures in order to improve upon predicted energies. These calculations, designated 6-31l+G**//3-2lG** and MP2/6-3ll+G**//3-2lG**, result in more accurate bonding energies because the diffuse function ( + ) allows for better description of electron densities in anions (Fore-

sman and Frisch, 1993), the larger number of Gaussian functions (6 vs. 3 per atomic orbital) improves the flexibility of the electron density within the molecules (Teunissen et al., 1993), and inclusion of configuration interaction in the MP2 calculations helps account for electron-electron correlation (Hehre et al., 1986). Re-optimizations of selected molecules were also performed at the MP2/631 l+G* * level to estimate errors in the 3-2lG** structures and the MP2/6-3ll+G**//3-2lG** energies. The potential energies with the ZPE-corrections computed for this study are the dominant terms of the internal energy of the molecules. Molecular translational and rotational energies as well as the relativistic rest-mass energy of the electrons are neglected, but these terms are minor compared to the potential and zero-point energies. Comparing results of the energies calculated for different complexes or molecular configurations provides an estimate for the gas-phase AE of reaction. These theoretical AEs are then either compared to the experimental AH or AG of reaction. Since the AEs calculated are generally so large ( 100’s of kJ/mol), the PAV term in the equation AH=AEi-PAV

can be ignored at low pressure and AH = AE. Comparisons of AE to AG then give an estimate of the TAS term necessary to balance the equation AG = AH - TAS.

3.1. Structures 3.1.1. Isolated molecules Table 1 compares calculated and observed structural parameters for isolated acetic acid. The results in Table 1 demonstrate that the calculated structure of the molecules is close to the observed value in matrix-isolated acetic acid. Although higher level calculations employing larger basis sets and electron correlation, such as MP2/6-311 +G* *, provide more accurate structures (Lasaga and Gibbs, 1988; Nicholas et al., 1992) than HF/3-21G** calculations, the differences in theoretical structures are marginal (Table 1) and do not justify the large increase in CPU required to model these molecules. Calculated structural parameters for isolated acetate are

acid and acetate

CH$GGH

cycoo-

Bond

Expt.

(2)

3. RESULTS AND DISCUSSION

Table1 - Expimemal (VANEUCKet d, 1981) andahdated structural parametersof acetic

Molecule

(1)

3-21G**

Ml’%-311+P*

(A)

(A)

(A)

C-H

1.090

1.079

1.091

C-C

1.494

1.501

1.504

c=o

1.209

1.201

1.210

c-o

1.357

1.362

1.356

G-H

0.970

0.944

0.968

C-H

1.083

1.095

c-c

1.578

1.559

c-o

1.249

1.260

Al complexation by acetate anions also listed in Table 1. C-H

bonds increase by only 0.004 A compared to acetic acid, but C-C bonds increase by 0.06-0.08 A depending on basis set. Of course, the C-O bonds are equivalent in acetate with values intermediate between the C=O and C-O bonds of acetic acid. Bond length differences between the HF/3-21G** and MP2/63 11 +G* * calculations are a maximum 0.02 A indicating that the HF/3-21G** structures are fairly robust, even for anionic species.

3.1.2. X* n(H,O)

4899 clusters

Minimum potential energy structures of various hydrated species calculated with the HP/3-21G* * basis set are found in Fig. 1. The optimized water dimer in Fig. la has a Ol02 distance of 2.83 A, shorter than the 2.91 A optimized with a MP2/6-31 l+G* * basis set, the 2.90-2.92 A value calculated by Kim et al. ( 1992), and the experimental gasphase value of 2.97-2.98 A (Odutola and Dyke, 1980).

-X49>

0)

FIG. 1. Optimized structures calculated with the HF/3-21G * * basis set of the model aqueous species (a) HZO-H20, (f) A13+(OH)-2*4(H20), (g) (b) Ac*2H20, (c) AC--2H20, (d) Al’+. 6(H,O), (e) AI”(.5(H20), 14]A13+(OH); .3(H,O), (h) t6]A13+(OH); *3(H,O), and (i) A13+(OH); *2(H,O). C is gray, H and Al are black, and 0 is white. Bond distances are in A, and bond angles in degrees are denoted with a “O.” Average values for equivalent bonds are denoted by “< >.” Thin black lines indicate hydrogen bonds. Where available, MP2/6311 +G* * optimized values are underlined and placed above HF/3-21G ** values. Molecules were drawn with the program Atoms (Dowty, 1993).

4900

J. D. Kubicki, G. A. Blake, and S. E. Apitz

However, the measured O-O distance in liquid water is 2.84 A (Narten and Levy, 1972), fortuitously close to the HF/3-21G* * value calculated for the dimer. The 01 -H02 angle is nearly linear (175”), in close agreement with the experimental value of 01-H-02 = 179 2 10” (Odutola and Dyke, 1980). The dipole moment of the water dimer with the 6-31 l+G**//3-21G** calculations is also fairly accurately predicted at 2.77 D compared to 2.60-2.64 D experimental (Odutola and Dyke, 1980; Odutola et al., 1988; Coudert et al 1987). The water dimer has been used as a test case of the accuracy of our method because higher level calculations (i.e., MP2/6-3 11 +G * * ) are readily performed on a small system such as H,O-H,O. We consider the 5% discrepancy of the 01-02 distance in the 3-21G* * structure compared to higher level theory to be an estimate of the structural error. Covalent bond lengths, such as the O-H bonds in the water dimer, are more accurate with an approximate 2% error in this case. For the purposes of this paper, however, we concentrate on relative changes in structures rather than absolute values because structural errors in the HF/3-2 1G * * calculations systematically underestimate bond lengths. Comparison of the isolated acetic acid and acetate structural parameters at the HF/3-21G* * level (Table 1) to the hydrated counterparts (Fig. lb,c) reveals structural changes with addition of HZ0 molecules. Explicit treatment of HzOmethyl group bonding was not calculated because H-bonding via C-H-O bonds is approximately an order of magnitude less energetic than via O-H-O bonds (Turi and Dannenburg, 1993). C-O and O-H bonds in Ac*2(H,O) lengthen by approximately 2% with a simultaneous decrease of 2% in the C-O bond compared to isolated acetic acid. The (OH) -OH1 bond is shorter than the two H-bonds to the C=O group ( 1.725 vs. 1.939 and 2.009 A). In AC - * 2(H20), the C-O bonds shift by less than 0.01 A with hydration. However, one C-O bond length decreases and one increases from the isolated acetate values. This predicted splitting is the result of asymmetry in the H-bonding as two O-H-O bond lengths of 1.681 and 1.867 A are formed. Asymmetric H-bonding between the water molecules and the acetate ion is probably generated by the formation of a H-bond between the two HZ0 molecules (Fig. lc). Although the calculated structural changes with hydration are on the order of 2% and comparable to the accuracy of the calculations, the relative structural changes predicted with a given basis set are significant compared to the precision of the optimization procedure. The structure of the AC - * 2( H20) complex was recalculated with a MP2/6-3 11 +G * * basis set to test the reliability of the HF/3-21G * * results. Structural parameters generally increase by 2% or less between the two levels of theory. One exception is the HzO-H20 H-bond distance which increases 9% (from 1.94-2.11 A). Since MP2 corrections for electron correlation tend to exaggerate bond length increases (Wiberg et al., 1992), the computational time saved by using the HF/3-21G** basis set is justified because HF/3-21G** calculations reproduce the bonding predicted by higher level theory fairly accurately. Figure Id illustrates the optimized structure of the hexaaquo Al 3+ ion, A13+ - 6( H20) . The complex is a regular octahedral configuration with Al- (OH*) bond distances of 1.9 12

A, comparable to an average Al-O of 1.93 A in solids (Shannon and Prewitt, 1969). O-H bond distances and HOH angles both increase in this complex compared to the H20-HZ0 dimer because the strong A13+ cation attracts electron density away from the O-H bond (Hermansson, 1991). Again, structural parameters change by -2% in the MP2/6-3 11+G* * optimized complex. Substitution of (OH) for HZ0 in the hexaaquo Al’+ complex results in the structures shown in Fig. le and If. Al- (OH*) bonds lengthen by eO.03 A for each (OH) substituted as the Al- (OH) bonds are much shorter at 1.66 and 1.74 A in Al’+(OH))*5(H,O) and Al’+bond lengths are also (OH) 2 *4 ( H20), respectively. O-H shorter in the hydroxo complexes compared to the hexaaquo A13+ complex. Shorter O-H bonds in addition to the decrease in charge in the hydroxo complexes will cause Hbonds formed to the complexes to be weaker than in [ A13+ * 6( H,O)] . These complexes were also structurally reoptimized with MP2/6-31 1 +G * * calculations, and the bond lengths increased by 3% or less. As protons are abstracted from the above complexes to form AI’+( .3(H20) and A13+(OH); *2(H20), the differential between the Al- (OH) and Al- (OH,) bonds becomes so large that a coordination change from octahedral to tetrahedral is induced (Fig. If,g). The complex pictured in Fig. lg has Al- (OH) bonds of 1.70 to 1.74 A with one Al- (OH,) bond at 1.87 A. The remaining two H20 molecules are over 3 A away from the A13+ ion. The Al’+ (OH); * 2(H20) complex (Fig. li) is in a more regular tetrahedral configuration with four Al- (OH) bonds all near 1.76 A. Both of these complexes were optimized from an initial configuration similar to the Al 3+(OH) r *4( HZO) octahedral complex; hence, the structures shown in Fig. 1g and i are not metastable states (i.e., local minima) formed by addition of HZ0 molecules to a tetrahedral Al’+ ion. In fact, a metastable state does exist with A13+(OH), * 3 ( H20) in octahedral coordination (Fig. lh). This complex has Al- (OH) bonds of 1.79 A and Al- (OH*) bonds of 2.03 A. However, the 6-311 +G* *//3-21G* * potential energy of the octahedral complex is =50 kJ/mol higher than the corresponding tetrahedral complex (Fig. lg ) . Entropy should also favor the tetrahedral complexes because two tightly bound HZ0 molecules are released into solution decreases from four to six. Conseas A13+ coordination quently, these calculations predict that speciation and coordination should be linked in aqueous aluminum species. Octahedral Al’+ is present in the acidic region where the species A13+*6(H,0) to A13’(OH), *4(H20) dominate, and tetrahedral Al’+ is common in neutral to basic solutions where [Al (OH),] is thought to dominate (Nordstrom and Munoz, 1985; Faust et al., 1995). The formation of tetrahedal [AI(O is also likely to be the first step toward formation of Al,, complexes (Parker and Bertsch, 1992; Thomas et al., 1993). 3.1.3. Aluminum-acetate

complexes

A hydrated, monodentate aluminum-acetate molecule, AC -A13+ * 5 (H,O) , is pictured in Fig. 2a. AC -A13’ * 5 (H,O) forms an Al-O bond to the acetate that is approximately the same length as the average tetrahedral Al-O bond in

Al complexation

2

by acetate

4901

anions


(a)

1.493

1.228

1.342 (f

1190

)

1.767V, 92y

+

c,

p92f3>

~~,:~955> Cd)

(b)

<1.913>

50>

b

<0.957>

(e)

c

4

‘“.“5%(go,>

4.937ai, (9)

(h)

(0

(b) AC- Al’+*4(H,O), (c) FIG. 2. Optimized structures of the Al-acetate species (a) AC-AI’+. 5(HZO), Ac~Al’+(OH))*4(H20), (d) AC-Al’+(OH); *3(H,O), (e) (Ac~)~AI”.~(H,O),,,, (f) (Ac-)~A~~+.~(H,O),,,., and (i) AC-AI:‘(,*6(H,O) calculated in this study (g) (Ac-)zAl’+.2(H,O),i,, (h) (Ac~)2Al’+.2(H,O),,,,,, with the 3-21G* * basis set. Atoms are colored according to the same scheme as in Fig. 1. Molecules drawn with the program Atoms (Dowty, 1993).

4902

J. D. Kubicki, G. A.

solids (1.77 A, Shannon and Prewitt, 1969). Formation of this Al-O-C linkage lengthened one C-O bond and shortened the other so that the acetate structure is closer to the protonated acetic acid molecule (Fig. 1b) than the acetate molecule (Fig. lc) . The remaining Al- (OH?,) bond lengths are increased by an average of 0.14 A compared to the A13’ - 6 ( H20) complex. These results suggest that the acetate-A13+ bond has a strong covalent component and may explain why anions of organic acids are more strongly complexed to Al 3+ than inorganic anions like Cl _ (Brimhall and Crerar, 1987; Fein, 1991; Palmer and Wesolowski, 1992). A bidentate aluminum-acetate complex, AC -Al 3+ 4( HzO), is shown in Fig. 2b. Compared to the monodentate complex (Fig. 2a), the Al-O bonds to the acetate are much longer, 1.873 vs. 1.767 A, and the Al-O bonds to the water molecules are shorter, 1.913 vs. 1.926 A. Thus, the bidentate aluminum acetate has Al - 0 bonds to water molecules similar to the Al”+ *6(HzO) complex (Fig. Id). The difference between the two C-O bond lengths disappears in the bidentate complex, but both C-O bonds are significantly longer, 1.301 A, than in the hydrated acetate (Fig. lc). In order to bond both oxygen atoms of the acetate to the A13+ cation, the OCO angle decreases from 119- 1 lo”. A large decrease to 1.478 A in the C-C bond is induced by the lengthening of the C-O bonds and decreasing the OCO angle. The existence of an acetate-aluminum hydroxide complex, AC -Al 3+(OH) ~, in moderately acidic solutions at high temperatures has been suggested by Benezeth et al. ( 1994). Figure 2c represents the structure of the AC -Al 3+( OH) _ * 4( HzO) complex. Compared to the AC -Al 3+ - 5 ( HzO) complex, the AI-O to the acetate anion is slightly longer, and the weaker bond to the acetate causes the difference between the C-O and C=O bonds to decrease. The Al-(OH) bond remains close to the value predicted for the Al”+ (OH); *4(H20) complex (Fig. If). Another possible species, AC -Al ‘+ (OH) ; * 3 ( H20) is shown in Fig. 2d. Addition of the second hydroxyl group to the molecule further lengthens the Al-O bond to the acetate anion up to 1.87 A. In contrast to the AC-A13+( OH) * 4( HzO) complex, the C-O and C=O bond length difference increases with the lengthening of the Al-O bond to the acetate anion, even when compared to AC -Al 3+ * 5 ( H20) (Fig. 2a). These differences between C -0 and C =0 bond lengths have implications for the splitting of C-O, and C-O, vibrational modes which will be discussed below (see section 3.3). We caution that the AC-AI”+( * 3(H20) configuration in Fig. 2d may be a metastable state. Al 3+(OH) ; * 3 ( HzO) also had a local minimum in the potential energy surface in an octahedral coordination state similar to that pictured in Fig. 2d. Hence, we are not certain that AC -Al 3+(OH ) 1 * 3 ( H20) does not have a lower energy tetrahedral structure. We did not investigate any tetrahedral configurations for this complex because AC -Al’+ (OH); * 3(Hz0) is likely to be a minor species (Benezeth et al., 1994) and does not justify the use of a larger amount of computer time. Complexes of Al 3+ with two acetate anions are thought to exist under a variety of conditions based on thermodynamic models (Shock and Koretsky, 1993; Palmer and Bell, 1994; Benezeth et al., 1994). Figure 2e and 2f show two possible

Blake, and S. E. Apitz structures of monodentate, aluminum-diacetate complexes, (AC-)*A13+ * 4(H20) (cis and trans). Bond lengths and angles are similar in both isomers with the largest difference between the Al-O bonds = 0.01 A. This bond length increases for the Al-O bonds to acetate and decreases for the Al-O bonds to water in the trans-isomer compared to the cis-isomer. The difference between the C-O and C=O bond lengths decreases in these monodentate, aluminumdiacetate species compared to the monoacetate species (Fig. 2a). Structural parameters in the bidentate, aluminum-diacetate species, (AC -)zAl 3+ - 2( H20) (cis and trans), in Fig. 2g and 2h generally are not significantly different from the bidentate, monoacetate species (Fig. 2b). The Al-O bonds increase by a maximum of 0.06 A in the cis-isomer as the Al-O bonds to the acetate split into values of 1.862 and 1.930 A. No such splitting is predicted for the trans-isomer. [AC -Al:+ (OH) -* * 6 ( HZ0 ) ] in Fig. 2i has been suggested as a dominant species of aluminum and monocarboxylic acids at pH’s near the pK, of acetic acid (Ohman, 1991). The Al-dimer structure is significant because it may play a role in depolymerization reactions of aluminum in solution that hinder precipitation (Masion et al., 1994). A di-aluminum complex can form because the acetate anion is able to bridge the two Al-octahedra without large distortions. The two hydroxyl groups act as bridges between the face-sharing octahedra. The acetate anion C-O bonds are stretched in this complex compared to the hydrated form (Fig. lc) by mO.03 A in order to link both octahedra. The Al-O bonds to acetate of 1.844 A and the Al- (OH) bonds bridging the two octahedra of 1.856 A are shorter than typical octahedrally-coordinated Al 3+, but the Al-O bonds to the water molecules are closer to those found for rh1Al in solids ( 1.93 A; Shannon and Prewitt, 1969). 3.2. Energetics 3.2.1. Isolated species Experimental proton affinities (PA) for gas-phase OHand HZ0 are reproduced fairly accurately by the 631 1 +G* *//3-21G* * calculations (Table 2). In addition, only relatively small changes in the calculated PA occur when energies are calculated with the MP2/6-3 11 +G * * basis set (e.g., AC- + H+ = -1471 and -1444 kJ/mol with and without MP2 corrections; Table 2). These results suggest that 6-311 +G* *//3-21G* * calculations on larger molecules, for which the MP2 electron correlation correction is not practical, can give reasonably accurate estimates of some reaction energies. 3.2.2. X. n(H,O)

clusters

Relative energetic stabilities of model hydrated species are compared in Table 2. Most of the reaction energies in Table 2 are from 6-311 +G* *//3-21G* * calculations, so it is important to remember that this level of theory performs reasonably well in predicting relative energetics even though absolute energies are not necessarily accurate. This point is illustrated by comparisons between 6-3 11 +G * *i/3-21G* * and MP2/6-311 +G* *l/3-21G* * reaction energies in Table

Al complexation

by acetate anions

Table 2 - Molecular (ZPE-corrected) and reaction energies calculated in this tidy. Molecule

4903

Experimental values are listed in parentheses

Reaction

&%3Y Harteesh0lecule

A&U& kJhO1

Isolated Species

OH’

-15.39636

H,O

-76.03045 (-76.46)*

--_-_ OH + H+e Hz0

-1665 (-1635)’

Hz0 + H+* H,O+

-694 (-697)’

-76.25110 -76.25304 YO’

-76.29483

+970

2(H20) o H,O+ + OH All+

-239.99385

ANOH),

-468.46448

WOH)J

-544.00520

KO%4toH~)11

-544.52135

[Ad’

-221.25468

_____

AI(

-379

+ OH-a [AyOH) ,j

[AI(OH)J’ + H+e

-1355

MOWOHz)l

AyOH), + Hz0 cs [(O~hAI(OHz)I

-69

AC + Hz0 Q AC‘+ H,O+

-776

[Acj+H+oAc

-1471

-227.94988 AC

-221.81481

-1444

-228.49974

-152.06265

-5 (-15)O

yO+yOoH,O-$0

-11

-152.50631 -152.51194

-&

HzO-OH‘

-151.46114

Hz0 + OH. e H&OH-

-9O(-111):

HzO-H,O+

-152.37425

Hz0 + HsO+CJ H,O-HsO+

AC-•2(H,O)

-379.35156

-129(-133):

4(HzO) 0 WO-OH’ + H&h&O+

+761

AC’+ 2&O)

-90

e Ac’*Z(I$O)

-106

-380.49658 Ac*2(H,O)

-379.88109

AC + 2(yO)

-10

CJ Ac*Z($O)

-25

-381.01549 -545.01441

At+.6($0)

-2360

A?+ + 4(HzO) cs Alw.4(HzO)

-545.98126

-2580

-546.01249

-2656

-691.24313

-2788

A?+ + 6(HzO) = Al%d(HzO)

-2797

-698.57738 -698.58325 -697.18091

N3+*6(YO)

*

,413+(OHj*wo)

+

l-I+

+m

-698.52591 Al’+(OH j*S(YO)

o Al”(OH)+4(YO)

+ H’

+546 +522

-698.31953

+5&

-698.32802’ -696.96108

+165 +155

-698.51829

-696.97293

-&Qz

Al’+(OHj*S(~O)

e Ai-(&(qO)

+ H+

+517

-698.30865

+.550

-698.32193

+m

-696.59705

A?+(OH)+4(YO)

c, A13+(OH)‘~.3(YO) + H’

+939

-697.96400’ -696.10034

+956 +930

-697.95452

Af+(OH)s~*3(Y0) e Al’+(OH)‘,*2(YO)

+ H’

+1304

-691.46032

+1298

-697.46765’

+m

J. D. Kubicki, G. A. Blake, and S. E. Apitz

4904

Table 2. (Continued) Al-Acetate Species Ac’Al’+(OH~~4(H~O)

-848.76338

Ac’*Z(YO) + A?+(OHj.S(~O)

e Ac-*(~O)A13+(O~.4(l$O)

+ (HzO-H20)

Ac’Al’+(OH~~*3(H~O)

-848.37525

Ac‘*Z(r$O) + Af+(OH).2.4($0)

e AC-.(~O)Af+(OH)-.4(yO)

+ HzO-(OH)’ +106

Ac.*2(%0)

e Ac-*(~O)Ai~(OH~,.3(yO)

+ (H@-HzO) -454

+ AJ’+(OH);d(I$O)

AC-*2&O) + Ai( -695.81012

Ac’Al(OH,,

+ 3/2(HzO-HzO) e Ac-.(~O)A13+(OH~~.3(yO)

AC’+ [AI(O

Ac’*ZHzO + [AI AC-•2HzO+ [AI -142.75280

-848.98270

AcAl’+*4(H~O)

-772.930 11

-239

jo

A~hl(0H)~

+140

+ (OH)-

J’ e Ac;Hzo-AI(

+203 +162

+ [Si(OH)J-Hz0 a Ac’*H@iiOH),

+ 1/2(HLLH~O) + HzO-(OH)’

Ac’*2HzO + Af+d(HzO) cs Ac’~(H~O)A?+.5(H~O) + HK%H20 0 Ac~*(~O@+O~(H~O)

Ac’*YHzO) + Ai3+d(H20) e Ac’Al”d(H,O)

Ac‘Al’+*5(HzO) o Acd+.4(H~O) -1000.57542 2[Ac.*2(HzO)] + Alf+(OH)-,.4&O) Ac’*2(HzO) + [Ac’*(~O)]~~(OH~.4(yO) Z[Ac’*2(HzO)] + Al’+d(~O) -1000.56960

(Ac-)&+*2(HzObi.

-848.47399

(Ac-)#+.2(H~OxN.

-848.46829

[A~ld+~4W~O~

o e

o

+ H#D-(OH)’

+406 - 1307 +108 - 1208

+ 2(H@-H20)

AC--2(HzO) + d3+(OH j*S(I$O) o AcAl*.4(H,O)

(Ac-)zAl’+*4(H~O)cii

+352

AC’+ [SiOH),] e Ac’SiOH), + (OH)-

Ace*2H20 + A40H)z’*5(~O)

(Ac~)&+*4(HzOX,

+99

+ &o-(OH)-

J-Hz0 c> Ac‘*(H~O~Ai(OH), + 1/2(I-I@H20) + H&(OH)-

Ac’*2(HzO) + [Si(OH)J e Ac~*(I-LO~SiiOH), + HD-(OH)Ac*2(BO) AcAl’+~5(H~O)

+ H&(OH)- +68

o ACRID

AC’+ [AI(

Ac’Si(OH),+

-896 -895

-850.58119

+ (H&HzO) + H@(OH)

+206 +56

+ 1/2(H@HzO)

FS [Ac..(~O)]&+.4(H~O),m_ + Z[H&(OH)-] +187 [AC~(yO)]zAhl(H~O)

[Ac’.($O)]zAl%(H~O~~

+ [H2o-(OH)~

+ 2(H&HaO)

+81 -2229 +15

[Ao%Al~*4(BO)ci,

2[Ac‘*2(HzO)] + Af+*6(HzO) e (Ac’)&+*2(%0)

+ s(H,O-H,O)

-2042

Ac’=2(HzO) + Ac-AlN*4(H,0) o (Ac’)&+d(H,O)

+ 2(H@HzO)

-834 +15

(Ac~)zA13+*2(H,0)ei, o (Ac’)&+.2(H,Oh_ [AcIA?+*4(%0)1,

c> (AC-)zAf+.z(H,Oh,

+ (HdM&O)

+117

Ac’Af+>(OH)-p!i(H~O) -1317.72443

2[Al’+*a(H,O)] + Ac’*2(&0)

+ 2[H3o-(OH)l

0 Ac’Al*z(OH)N(H~O) 2[AC@*5(&0)]

t 2w2O(OH)‘10

Ac’*2(HzO) + 2[Al*(OH)-•5($0)]

+ 5(H@I&O)

AhU)*l(OHy~*qH~O) + Ac’*2(HzO) + 2(Hso-H70) o Ac’Af+~OH)&5(H,O)

Ac’*2(HzO) + 2[Alw(OH)-~.4(I$O)] o Ac’A?+I(OH)X(H~O)

* - KM et al. (1992) +-LIASetrl.( 1988) *- MEOT-NORandSPELLER(1986) 8 - CURTISS et d. (1979)

+ 3(H2o_HzO) t 2fI-W(OH)-l + (H@H~O)

-3351 -823 -522 +1482

Values in italicsarcMP2/6-31 l+G**//3-21G** Values in i&&and &erlined are from MFW-3 1l+CP* optimiz.4stn~chues Y - Optimized to within 0.2 W/m01

2 where the MP2-corrected values are available. Generally, the agreement is good between these two levels of theory. For instance, the dimerization energy of Hz0 calculated with the 6-311+G**//3-21G** equals -5 kJ/mol (Table 2). Inclusion of the MP2 correction in the HF/3-21G** optimized structure yields a dimerization energy of - 11 kJ/mol. The dimerization energy of the HZ0 dimer calculated with the optimized MP2/6-31 l+G* * structure is -15 kJ/mol which agrees well with the experimental AH value reported by Curtiss et al. ( 1979). The hydration energy of acetate was predicted to be -90

kJ/mol; whereas, AEhydration for acetic acid was predicted to be - 10 kJ/mol (Table 2). The shorter H-bond distances between Hz0 and the acetate molecule, as well as the third H-bond between HZ0 molecules in this complex, add the 80 k.I/mol to the hydration energy. The AEhyhationof -25 kJ/ mol for acetic acid calculated with the MP2/6-3 11 +G * *// 3-21G** is fairly accurate, because the experimental AG~ration = -28 kJ/mol (Hine and Mookejee, 1975), and is dominated by the energy change of moving the AGhydration solute from the gas-phase to solution-phase (Carlson et al., 1993). However, both the acetic acid and acetate complexes

Al

are probably not fully hydrated by two water molecules. The total number of H-bonds to acetic acid should be approximately three: 1.5 to C=O, 0.6 to C-O, and 1.0 to H (Carlson et al., 1993). This under-representation of H-bonding may account for some of the discrepancy between theory and experiment in this case. Although A13+ * 6( HzO) has a large bonding energy (Table 2), deprotonation of this species to form A13C(OH)-~5(H20)andA131(OH);~4(H20)doesnotrequire a great deal of energy. The first two gas-phase PA’s of hexaaquo A13” are +165 kJ/mol (MP2/6-311+G** = +151 kJ/mol) and +546 kJ/mol (MP2/6-311+G** = +520 kJ/mol). Both of these values are lower than the PA of gas-phase Hz0 (Table 2). The relatively low PA of A13+ * 6(Hz0) is consistent with formation of this species at low pH (Nordstrom and Munoz, 1985). Calculated PA’s associated with the octahedral to tetrahedral coordination change of aqueous A13+ are +956 and +1304 kJ/mol (Table 2) for the formation of A13+(OH); *3(H20) and A13+ (OH); * 2( H20), respectively. These two values fall between the calculated PA’s of H30+ + Hz0 + H+ (+694 kJ/mol) and Hz0 -+ (OH)- + H’ (+1665 kJ/mol). Thus, the theoretical prediction is consistent witht the stabilization of these species near neutral pH in aqueous solutions (Nordstrom and Munoz, 1985 ) . 3.2.3. Aluminum-acetate

complexes

A13’ * 6( H20) was predicted to react with acetate in solution to form Al-acetate with AE = -1307 or -1208 kJ/mol, depending on whether AC-A13+* 5(Hz0) or AC-A13’ - 4( H20) was formed (Table 2). This large negative energy change is inconsistent with speciation studies that find AH = +17 + 6 kJ/mol (Palmer and Bell, 1994) or +73 kJ/mol (Benezeth et al., 1994) for the formation of AC -A13’ at 298 and 360 K, respectively. Even considering the differences between an internal energy at 0 K and enthalpy at 298 K, the discrepancy between experiment and theory here is too large. On the other hand, the exchange of acetate with an (OH) - group in the reactions (Table 2) AC- + [Al(OH

+ [AcAl]*+ + (OH)AE = +108,

AC- + [AI(OH

+ [AcAl(O

-+ [AcAl(O

-+ [AcAl(OH

(4)

+ (OH)AE = +68,

AC- + [Al(OH),]-

(3)

+ (OH)AE = +106,

AC- + [Al(OH),]

4905

complexation by acetate anions

(5)

+ (OH)AE = +140,

(6)

are much closer to the experimental AH values of Benezetb et al. (1994). Since the above reactions have positive AEs, it is curious that the acetate does not replace H20 and pair with A13* in solution because these reactions are predicted to have large negative AEs. This prediction makes sense because the acetate-Hz0 exchange replaces an ion-dipole interaction with a covalent bond. Longer-range ion-dipole and entropic effects

that are not accounted for in these MO calculations must dominate reaction energetics in solution and offset the calculated negative energy changes. We conclude that acetate(OH)- exchange reactions are the most formation pathways for Al-acetate complexes in aqueous solutions at a constant pH because the calculated energetics give the best agreement with experimental data. However, self-consistent reaction field calculations (Orozco et al., 1993; Keith and Frisch, 1994) or Monte Carlo simulations (Carlson et al., 1993) may be useful in more accurately predicting reaction energies between aqueous species. Experimental AH values for the formation of an aqueous Al-diacetate have been determined to be +30 ? 30 kJ/mol at 298 K (Palmer and Bell, 1994) and +82 kJ/mol at 360 K (Benezeth et al., 1994). As in the case of the Alacetate species discussed above, exchange of acetate with an Hz0 molecule in the aqueous aluminum species results in a large negative AE of reaction [ -2229 and -2042 kJ/mol for the trans-monodentate (Fig. 2f) and cis-bidentate (Fig. 2g) species, respectively; Table 21. If exchange between an acetate and an (OH)- group is considered, as in the reaction AC- + [AC-Al(OH)*+]

+ [(AC-),A13+]

+ (OH)-

AE = +81 kJ/mol,

(7)

then the calculated AE is more comparable to experiment. (This value for the tram-monodentate Al-diacetate species (Fig. 2f; Table 2) is perhaps fortuituously close to the Benezeth et al. (1994) value of +82 kJ/mol.) Calculated AE values between monodentate and bidentate configurations also fall within the range of AH values. For example, AE for the reaction of monodentate Al-acetate to the bidentate species was +58 kJ/mol (Table 2). Since formation of the bidentate species releases a water molecule, the entropy for this reaction is also positive. Shock and Koretsky ( 1993) have noted that the discrepancy in AS0 for the formation of Zn-acetate is approximately equal to So for H20 at 298 K (i.e., 70 J/mol-K). These authors suggested that this discrepancy was due to a coordination change of Zn *+ caused by formation of the acetate complex and subsequent release of a water molecule into solution. If this AS0 value is used here to approximate the entropy gain as a bidentate complex form from a monodentate AC -Al, the AG of the reaction AC-A13+*5(H20)

--t AC-A13+*4(H20)

+ Hz0

(8)

would be +37 kJ/mol at 298 K, which is equivalent to a log K m -6.5. The bidentate complex would not be thermodynamically favored below 825 K, and acetate in solution would not be stable at these temperatures (Palmer and Dmmmond, 1986). Although the +58 kJ/mol AE is lower than the AE of fotmation calculated for AC-A13+ +5(H20), the +58 kJ/mol for Bqn. 8 would be in addition to the calculated AE of formation. Thus, it is likely that only the monodentate species need be considered for most geochemical thermodynamic modeling. Our conclusion is consistent with the observation of Yang et al. (1989) that small metal ions induce too large a strain energy in the four-membered rings formed in bidentate acetate complexes to be stable. However, we caution that the AE = +58 kJ/mol may not be accurate because we have neglected long-range forces. The calculated AE should be tested by placing the

4906

J. D. Kubicki, G. A. Blake, and S. E. Apitz

model molecules within a dielectric continuum as in self-consistent reaction field calculations (Orozco et al., 1993; Keith and Frisch, 1994) to account for long-range forces of solvation. If the AE value is lower, then the bidentate species could become significant at high temperatures. Transformations between the cis- and trans-isomers of the monodentate Al-diacetate species may occur in geochemical solution because the AE is a relatively small +15 kJ/mol (Table 2). The trans-isomer is favored in the monodentate complex, but the low AE predicts that both isomers could be present in solution simultaneously. Bidentate Al-diacetate is + 117 kJ/mol higher in energy than the monodentate complex (Table 2). This higher energy would need to be offset by the entropy gain of releasing two water molecules from hydrating the A13+ cation if the bidentate species are to form in solution. As suggested above for the monodentate to bidentate transformation for the Al-acetate species, the calculated AE is too high to allow the formation of the bidentate species at reasonable temperatures. Two other factors that can affect the thermodynamic stability of each complex in solution are the ionic charge and dipole moment. Interactions between bulk water and these complexes has been ignored in our calculations. As mentioned above, the primary interaction may be the energetics of the ions with molecular water dipoles, and these forces are

Table 3 - 6-3 1l+G**//3-ZlCf*

Molecule

related to the charge on the complex. More highly-charged species will be favored by ion-dipole attraction, especially at lower temperatures. A secondary energy contribution will come from dipole-dipole interaction between water molecules and the aqueous complexes. Table 3 lists the calculated dipole moments for the hydrated and Al-acetate species. Configurations with larger dipole moments will have stronger interactions with bulk water (provided charges are equal between complexes). For example, the AC-A13+ * 5(H20) species has a dipole moment of 10.67 D compared to 7.17 D for AC-A13+.4(H20). Hence, the thermodynamic stability of the monodentate species will be enhanced in solution relative to the value calculated due to its lower potential energy (i.e., -56 kJ/mol). This effect can also work in the opposite direction. (Ac-)~A~~+ * 4 (ho hns is 15 kJlmo1 lower in potential energy than (AC-),A13+* 4(H20),i,, but the latter configuration has a much higher dipole moment that will tend to offset the potential energy difference. A comparison between aluminum-acetate and silicon-acetate reaction energies can be made at this point. With the same computational methodology, the reaction AC- + [Si(OH),]

-+ [AcSi(OH),]

AE = +203

dipole moments

Dipole Moment

Dipole Moment (Deb+

(Debve~ Hydmed

Isolated Species

Species 2.77

1.79

YO-YO

2.20

H&-OH.

2.70

Hs0+

0.0

H&H,O+

0.15

AYOH),

0.0

AC’-2($0)

3.83

IA1(OH),l

0.26

Ac*Z(YO)

1.32

I(oHhAI(oHz)l

2.13

Al%-6(H.,O)

0.0

IN’

4.29

Af+(OHj-S(YO)

3.42

AC

2.01

AI)*(OHhwJO)

2.86

“‘Al*(oH)3’.3(yo)

2.82

‘Y41~(OH)3’*3(YO)

1.47

Ar(oH),‘*2(yo)

0.84

OH’ YO

Al-Acetate Species Ac-Al(OH)*-l($O)

6.54

AcAl(OH)z+*3(~0)

3.54

ALu(OH&

3.70

Ac’SiiOH),’

1.84

AcA13+*5(H~0)

10.67

Ac-Al%(HzO)

7.17

(AC-hAf+-V&O~

2.79

(AC-)zAl-@zO)ti

6.75

(Ac’)&+.2(HzO)a

5.15

(Ac-)&+*2(H~O)c,

0.12

[Acl’AMOHh*6(HzO)

6.34

+ (OH)(9)

Al

complexation by acetate anions

results in a predicted energy greater than the equivalent Alacetate reaction. In addition, reactions of acetate with Al ( OHh and [ (OH),Al( OH*)] may actually have negative AEs (Table 2)) but these reaction pathways are not available to Si4+ because [Si(OH),]+ and [(OH),Si(OH,)]+ probably do not exist in aqueous solutions. Marley et al. (1989) suggested, based on Raman and FTIR spectroscopies, that Si-oxalate complexes exist in aqueous solutions. On the other hand, Fein and Hestrin ( 1994) concluded that silicon-oxalate complexes do not form because oxalate does not increase the solubility of quartz or amorphous silica. This argument was buttressed by the IR and NMR spectra of Tait et al. (1995) that show no evidence for Si-oxalate complexes. The higher energy required to form Si-acetate complexes calculated in this study is consistent with the conclusion that carboxylate will be more likely to form complexes with Al ‘+ than Si4+. 3.3. Theoretical Vibrational Spectra Figure 3 shows a comparison of measured and calculated vibrational frequencies for the acetic acid monomer. Agreement between the two sets of frequencies is generally good after the theoretical harmonic frequencies have been corrected for basis set and anharmonic effects (Pople et al., 1981). Discrepancies between experiment and theory are approximately lo-50 cm-’ for any given vibrational mode (Fig. 3) ; hence, we consider that calculated frequency shifts of greater than 50 cm-’ will be significant compared to our accuracy. One exception is the O-H stretch mode near 3600 cm-‘, for which a discrepancy of over 100 cm-’ exists between experimental and HF/3-21G* * calculated values. However, this error is only 3% of the vibrational frequency and much less than observed V(O-H) frequency shifts due to H-bonding (Rochester and Trebilco, 1979; Buckland et al., 1980). Although all experimental frequencies are not reproduced with great accuracy, the correlation between experimental and theoretical frequencies is excellent (Fig. 3; R* = 0.999, slope = 1.026 for HF/3-21G** and 1.015

4000 _ : s ‘&: 5 5 & n! LI. w 50

.z s

3500 o

3000

MP2/6-3 I l+G**

2500 2000 1500

1000 500 0 0

500

1000 1500 2000 2500 3000 3500 4000 Experimental

Frequencies (cm-‘)

of experimental (Bertie and Michaelian, vibrational frequencies for the isolated acetic acid molecule. Solid squares are from HP/3-21G * * calculations and scaled by 0.893 (Pople et al., 1981). Open circles are from MP2/ 6-3 11 +G * * calculations and scaled by the ratio v( OH),,,/v( OH)talc = 0.941. Solid lines represent linear regression analyses of the results. FIG. 3. Correlations

1982) and calculated

4907

for MP2/6-311 +G* *) . Interpretations of vibrational spectra can thus be made by correlating numerous peaks to calculated spectra, rather than by comparing isolated frequencies. Table 4 lists calculated vibrational frequencies of acetic acid and acetate in the hydrated and Al-acetate species. Frequencies above 1200 cm-’ are listed because these modes are readily distinguished in vibrational spectra of organoaluminum complexes (Biber and Stumm, 1994). The C-H stretch and CH3 deformation modes in Table 4 remain relatively constant with speciation compared to the bandwidth of vibrational spectra of aqueous species. The largest frequency shifts occur in the C-O., vibrational modes, as expected, since the linkage to A13’ occurs through the COO- group in these complexes. Compared to infrared spectra of acetate in solution (Marley et al., 1993), our calculations predict too large a split between the C-O, and C-O, modes (Table 4). Measured values are 1413 and 1552 cm-‘, but calculated values for C-O, and C-O,, in Ac-*2(H20) are 1308 and 1616 cm-‘. Examination of the C-O, vibrational mode shows that C-O motion is highly coupled with C-C stretching, and CCH, HCH, and OCO angle bending. However, substitution of D for H on the methyl group in AC * 2( H20) minimizes the calculated CCH and HCH contributions to the mode and the H-D isotopic frequency shift is only -6 cm-’ for the C-O, mode which is close to the experimentallyobserved value of -7 cm-’ (Ito and Bernstein, 1956). Optimized structures and force constant analyses with larger basis sets including configuration interaction may be necessary to accurately model hydrated molecular structures and vibrational spectra. In addition, increasing the number of water molecules included in the calculations may make the model more accurate and realistic (Carlson et al., 1993). The most diagnostic vibrational mode for the aluminumacetate complexes according to our calculated results is the C-O,, mode. Monodentate species C-O,, vibrations range from 1542-1663 cm-’ ; whereas, bidentate species C-O, vibrations range from 1404- 1468 cm-‘. Thus, there is an approximately 70 cm-’ gap between monodentate and bidentate species for the C-O, mode. Although the C-O, modes exhibit a wide range of frequencies from 1262- 1403 cm-’ depending on speciation (Table 4), the ranges for monodentate and bidentate configurations overlap. However, the monodentate complexes tend to be at the lower end of the range, so this mode may be used as a secondary identification feature. Our theoretical infrared intensities can change by up to a factor of two depending on the speciation (e.g., for C-O, from 5.8 X lo4 M-‘cm-’ in Ac-*2(H20) to 10.0 X IO4 M-’ cm-’ in Ac-A13+* 5(H20). See Kubicki et al. (1993) for a discussion of calculated vs. experimental integrated infrared intensities.). Marley et al. ( 1993) calculated integrated infrared absorptivities values of 1.21 x lo4 and 2.62 X lo4 M-‘cm-’ for the 1413 and 1552 cm-’ bands of aqueous acetate and discussed possible effects on atmospheric heat retention using these values. Since acetate in cloud droplets (Lawrence and Koutrakis, 1994) is likely to be bonded to ions in solution or the surfaces of dust particles that nucleate cloud formation (Siefert et al., 1994), organic-metal chemistry could have a significant effect on the contribution that species such as acetate make to the greenhouse effect.

4908

J. D. Kubicki, G. A. Blake, and S. E. Apitz Table 4 - Cehdated (with enhmonic comcth) acetic acid and acetate vibrationalf?equeecies above 1200 cm-’in aqueous and Al-acetate species.

Frequencies(cm-‘)

C&

c-o,

C-H

O-H

3342

Hyakated species Ac*2(HzO)

1260

Ac’*2(HzO)

<1452>

1675

<2976>

<138’P

1616

<2955>

Al-acetate species AC-Af’+.5(HzO)

1262

<1401>

1542

<2977>

AC-A13+.4(HzO)

1306

<1403>

1404

<2966>

AC-Al(OHfhQ$O)

1299

<1405>

1568

<2976>

Ac-Al(OH)l+*3(YO)

1277

<1407>

1663

<2970>

Ac.Al(Om

1306

<1405>

1655

<2964>

AC-[Si(Om]+

1245

<1407>

1708

<2978>

(Ac’)&+*WhO),u

<1314>

<1406>

<1555>

<2977>

<1405>

<1633>

<2977>

<1402>

<1465>

<2974>

(Ac-)&+*2(H~O)-

<1403>

<1447>

<2974>

(Ac%oHk*6(fi0)

<1388>

1468

<2972>

(Ac-)&+*4(H20)(Ad)&+*Z(HzO),

<1338>

Figure 4 is a plot of synthetic theoretical spectra of the complexesAl3+~6(H~O),Ac-A13+~5(H,O),and(Ac-),Al3+~ between 200 and 1200 cm-‘. (We term the spec4(HzO),,, tra synthetic because a constant arbitrary bandwidth was assigned to each peak.) These species were selected because they are probable candidates to be dominant A13’ species under certain conditions based on thermodynamic models (e.g., Palmer and Bell, 1994) and our calculations. Only the frequency region between 200 and 1200 cm-’ was plotted because the region 1200-3000 cm-’ is represented in Table 4, and the region above 3000 cm-’ is likely to be obscured by O-H stretching in aqueous solutions. The most intense infrared and Raman bands in these synthetic spectra may be used to interpret measured spectra of aqueous solutions of varying pH, temperature, and aluminum and acetate concentrations. There are numerous low-frequency peaks present in the region below 600 cm-’ (Fig. 4) that are similar in frequency to those observed in the spectra for other metal-acetate aqueous solutions (Yang et al., 1989; Bickley et al., 1990). However, these bands are not associated with stretching the Al-O bond to the acetate anion as they are in Pb- and Znacetate (Yang et al., 1989). Instead, the low-frequency bands are dominated by Al- ( OHI) librations and stretches (Fig. 5a). A peak near 300 cm-’ in the theoretical Raman spectrum of A13+ * 6(H20) is especially prominent in this lowfrequency region (Fig. 4b) ; complexation of Al 3+ to acetate diminishes the Raman intensity of this peak.

The vibrational mode with the purest component of Al-O stretching linked to the acetate anion occurs at 730 cm-’ (Fig. 5b). This peak is a weak Raman scatterer, but it does have a fairly strong infrared intensity (Fig. 4). The higher frequency of this vibrational mode compared to the 217 and 275 cm-’ frequencies of M-O modes in aqueous Pb- and Zn-acetate complexes (Yang et al., 1989) suggests that the Al-acetate ester has a stronger Al-O bond. Consequently, rates of Al-acetate dissociation would tend to be slower than for larger cations. A combination mode of C-C stretching and O-C-O angle bending occurs at 850 cm-’ (Fig. 5c) and has significant intensity in both the infrared and Raman spectra (Fig. 4). C-C stretching modes occur at 930-955 cm-’ in other metal acetate complexes (Yang et al., 1989; Bickley et al., 1990; Edwards and Lewis, 1993). In our calculations on acetic acid, the C-C stretch occurs at 795 cm-‘. Hence, the 100 cm-’ decrease in the Al-acetate C-C stretch is another indication of strong covalent bonding between the Al 3+ and acetate ions because the mode is closer in frequency to the acetic acid molecule than the acetate anion. 4. CONCLUSIONS Molecular orbital calculations of hydrated aluminum-acetate clusters provide reasonable approximations to the structures of aqueous-phase complexes. The relative stability of various species can be estimated, and the possible existence

Al complexation

of different

structural

configurations

can be tested.

Based

by acetate anions

4909

on

our present results, A13’ may undergo a coordination change from the octahedral hexaaquo complex to a tetrahedral [Al (OH),] complex as pH increases from acidic to basic. Monodentate aluminum-acetate complexes are likely to be predominant in aqueous solutions. However, the accuracy of these calculations is not great enough to rule out formation of bidentate complexes at high temperatures. Energy differences between isomers of the same species are small enough that both may exist in solution to some degree. Although discrepancies between the experimental and theoretical reaction energies exist, the acetate-hydroxide exchange reactions are generally the same sign and order of magnitude as the experimental values. On the other hand, calculated AE values for acetate-water exchanges in Alacetate complexes are generally much larger and opposite in sign to the experimental values. Based on the above results, we conclude that aluminum-acetate complexing reactions occur as exchanges between acetate and hydroxide ions rather than acetate and water molecules. This may be a reason why mixed acetate-hydroxo species are not as prevalent as might be expected (Benezeth et al., 1994). FIG. 5. Selected vibrational

modes of AC -Al’+

.5 (H,O) with sig-

nificant infrared or Raman intensity corresponding to the peaks IO00

,

.

I

.

,

(4 800 ?

d

-----

6oo[

1 --

AI-6(H,O)

marked with * in Fig. 4. Dominant motions within the vibrational mode are depicted by offset of atoms and with a “*.” Molecules were drawn with the program Atoms (Dowty, 1993).

AcAI-S(H,O)

A+-W,O) Theoretical vibrational frequencies of aluminum-acetatewater clusters provide predictions for the identification of aqueous-phase complexes. Future work on the Raman and infrared spectra of aluminum-acetate solutions would be useful for testing the results of our calculations.

0 200

400

Acknowledgments-Reviews by D. J. Wesolowski, J. B. Fein, C. D. Tait, and R. T. Cygan contributed significantly to this paper. Comments on an early version of the manuscript by C. M. Koretsky are also gratefully acknowledged. JDK acknowledges the National Research Council Research Associateship program. SEA and JDK acknowledge the financial support of ONT and ONR. GAB acknowledges NSF grant EAR-9316432. Computer resources were supplied by the Jet Propulsion Laboratory, Pasadena CA.

600 Frequency

(cm-‘)

(b)

--I Ediforial

handling:

D. J. Wesolowski

REFERENCES

Benezeth P., Castet S., Dandurand J.-L.. Gout R., and Schott J. ( 1994) Experimental study of aluminum-acetate complexing between 60 and 200°C. Geochim. Cosmochim Acta 58,4561-4571.

0 200

400

600 Frequency

800 (cm-‘)

FIG. 4. Synthetic (a) infrared and (b) Raman spectra of Al’+.6(H,O), AcmA13+.5(HZO), and (Ac-)~A~‘+.~(H,O) between 200 and 1200 cm-’ calculated with the HF/3-21G** basis set. Frequencies were scaled by 0.893. Peaks marked with a * have illustrations of the corresponding vibrational modes in Fig. 5.

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