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Author's personal copy Chemical Geology 357 (2013) 1–7

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Li+ speciation and the use of 7Li/6Li isotope ratios for ancient climate monitoring Stuart Bogatko a,⁎, Philippe Claeys a,b, Frank De Proft a, Paul Geerlings a a b

Eenheid Algemene Chemie, Vrije Universiteit Brussel (VUB), Faculteit Wetenschappen, Pleinlaan 2, 1050 Brussels, Belgium Earth System Science, Department of Geology, Vrije Universiteit Brussels, Pleinlaan 2, 1050 Brussels, Belgium

a r t i c l e

i n f o

Article history: Received 15 May 2013 Received in revised form 9 August 2013 Accepted 12 August 2013 Available online 19 August 2013 Editor: U. Brand Keywords: Aqueous lithium Isotope fractionation Ancient climate Density functional theory Carbonate formation

a b s t r a c t We have carried out a theoretical study of aqueous Li+ speciation including effects of ligand coordination, 7=6 Li , temperature and solution pH. We have calculated the isotope exchange equilibrium constant, K OH−H 2O associated with the Li acid/base equilibrium and can constrain it to positive values. The consequences of this species dependent isotope fractionation are then studied using a model for Li-Carbonate coordination. We define an effective isotope fractionation, eff Δ7=6 LiCO2− −H2 O , to model temperature and pH induced 3 changes in Li isotope fractionation associated with the formation of Li-Carbonate species. We predict that, 7=6 under normal oceanic conditions, eff Δ LiCO2− −H2 O is not sensitive to pH indeed but may be significantly 3 influenced (on the order of 12‰) by temperature. Since the isotope ratios found in Li containing calcium carbonate shells show no indications of variation in isotopic composition, we conclude that the mechanism by which Li is incorporated to this material is not dependent on aqueous Li speciation. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The Li+ ion has recently been recognized as a valuable tool in the area of ancient climate monitoring (Hoefs and Sywall, 1997; Hall et al., 2005; Hathorne and James, 2006; Misra and Froelich, 2012). This arises from the isotopic composition of Li in seawater being strongly influenced by continental weathering, one of the major sources of Li in seawater, and the incorporation of aqueous Li+ into calcium carbonate shells. Measured differences in Li isotope composition in ancient marine carbonates thus likely reflect fluctuations in continental weathering rates. By systematically analyzing the Li isotopic composition of lithium in ancient carbonates it is possible to reconstruct a record of Li isotope fractionation in seawater over the past 68 Ma. Due to the close association of Li isotope fractionation with ancient weathering, this record is able to provide critical information concerning the ancient earth climate. In spite of the immense potential of this method there is relatively little quantitative information concerning the identity and molecular structure of aqueous Li+ species. While there is evidence that Li ions incorporate into interstitial sites in calcite (Okumura and Kitano, 1986), it is not clear to what extent ligand coordination effects may play in the incorporation of Li+ into marine carbonates. Indeed, most if not all previous studies base their paleo-reconstructions on the close correspondence between modern values of Li isotope ratios ⁎ Corresponding author. Tel.: +32 2 629 3316; fax: +32 2 629 3317. E-mail address: [email protected] (S. Bogatko). 0009-2541/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chemgeo.2013.08.019

in calcium carbonates and seawater. Implicit is the assumption that Li isotope fractionation is not sensitive to environmental conditions such as temperature and pH. This assumption has been made following observations that Li fractionation during incorporation into calcium carbonate is not strongly influenced by temperature (Marriott et al., 2004a, 2004b) and, presumably, on the estimated high pKa value of Li+. Aqueous speciation of Li+ is poorly understood and experimental approaches to determine such fundamental properties as water coordination shell structure and acid/base properties are limited (Richens, 1997; Wulfsberg, 2000). While it is commonly assumed that Li+ exists as an aqueous ion, i.e. Li+ coordinated by water ligands, there remains some discussion concerning the total number of coordinating waters; hydration numbers ranging from 3 to 7 have been reported in a variety of experimental and theoretical studies on aqueous Li+ systems (Loeffler et al., 2003; Varma and Rempe, 2006; Bouazizi and Nasr, 2007; Ikeda et al., 2007; Jahn and Wunder, 2009; Harsányi et al., 2012). One interpretation of this result is that aqueous Li+ possesses a flexible hydration shell with a variable coordination number, as has been observed in other systems such as Ca2+ (Bogatko et al., 2013) and AlOH2+ (Bogatko et al., 2010). This is supported by the work of Jahn and Wunder (2009) which demonstrates that the coordination number of aqueous Li+ is sensitive to external pressure. Furthermore, geographic and paleo-historic variation of seawater pH is thought to be over the range of 6.5 to 8.5 pH units (Spivack et al., 1993; Lemarchand et al., 2002; Pagani et al., 2005; Hofmann et al., 2011; Gruber et al., 2012) suggesting that variations in the [Li]/[LiOH] ratio were also occurring. For such a

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S. Bogatko et al. / Chemical Geology 357 (2013) 1–7

potential variety of Li-bonding environments presented by distinct aqueous Li+ species, the large relative mass difference between the 7Li and 6Li isotopes is expected to lead to significant differences in the associated fractionation factors. Given that the presence of these species may be influenced by environmental factors, the assumption that Li isotope fractionation is not influenced by temperature and pH deserves further study. In this work we perform a density functional theory (DFT) investigation on aqueous Li+, LiOH, Li(CO3)1−, and Li(OH)(CO3)2− species. The chosen complexes provide an efficient means by which the isotopeexchange equilibrium constants between the aqueous non-carbonatecoordinating and carbonate-coordinating species may be computed while also including effects of solution pH via the Li+/LiOH acid base equilibria. The choice of carbonate as counterion permits us to bring a qualitative discussion on the relationship between carbonate and seawater Li isotope ratios and to gage the impact of temperature and pH on the above mentioned assumption of their equivalence. 2. Methods 2.1. Models The models used in this study are illustrated in Fig. 1. We used 8 models describing the aqueous equilibrium between Li and its 1st hydrolysis product. These models were differentiated by the amount and structure of coordinating ligands and surrounding water solvent. In Models 1 through 3 the coordination number of the Li and LiOH species increases from 3 to 5 for the aqua species. For the LiOH species of Model 3, however, during geometry optimization a water molecule moved from a Li-coordinating position to a water coordinating position in the 2nd hydration shell. Models 4 through 6 describe the gradual increase in the 2nd coordination shell increasing from 1 to 2 to 4 waters. In Model 7 the Li, 4 coordinating waters and 8 2nd shell waters were fully optimized. In Model 8 the Li and a single coordinating water of OH− ligand were optimized. An additional model, Model 9, was used to describe carbonate-coordinated Li+ and LiOH species. These models consisted of a Li+ (LiOH) coordinated by CO2− and two (one) water 3 molecules surrounded by 9 second shell waters. Geometry optimizations were performed using DFT (Hohenberg and Kohn, 1964); the Kohn–Sham equations of DFT (Kohn and Sham, 1965) were solved using the local density approximation (LDA) (Vosko et al., 1980) and the hybrid B3LYP exchange-correlation functional (Lee et al., 1988; Becke, 1993) with the Kohn–Sham orbitals expanded using the 6-311++G(d,p) basis set (Hehre et al., 1986). These approaches (basis set and functional) possess a good combination of efficiency and accuracy in describing fundamental metal–water interactions (Bogatko et al., 2010, 2011) and isotope exchange equilibrium constants (Rustad et al., 2010). These calculations were performed using the Gaussian 09 package (Frisch et al., 2010). Supplementary optimizations of the H2O, OH− and CO2− ligands were 3 also performed. In all cases, the system was ensured to be in a local minimum by verifying that all vibrational modes were positive. The XYZ coordinates of all optimized geometries are supplied in the supporting information. 2.2. Computing free energies The aqueous Li acid dissociation equilibrium and Li-CO2− complex 3 formation were investigated via the models provided in Eqs. (1a) and (1b) (where y = 0 or 1). þ

1þ

LiðH 2 OÞx þ H 2 O⇌LiðOH ÞðH2 OÞx−1 þ H 3 O ð1yÞþ

LiðOHÞy ðH 2 OÞx

2−

ð1aÞ 1y

þ CO3 ⇌LiðCO3 ÞðOHÞy ðH 2 OÞx2 þ 2ðH 2 OÞ:

ð1bÞ

Fig. 1. Illustrations of the models used in this study atom colors indicate type: white — H, red — O, cyan — C, ochre — Li. The dashed lines indicate hydrogen bonds. The model numbers correspond to those provided in Table 1.

The vibrational frequencies and standard state Gibbs free energy of formation for each of the reactants and products were computed at the same level of theory as outlined above. Once computed, the aqueous reaction Gibbs free energies were evaluated (Liptak and Shields, 2001; Kelly et al., 2006) and, using solvation corrections to the Gibbs free

Author's personal copy S. Bogatko et al. / Chemical Geology 357 (2013) 1–7

energy via the PCM model (Cancès et al., 1997; Tomasi et al., 1999) implemented in Gaussian 09, were used to compute the aqueous reaction Gibbs free energy, ΔG, the reaction equilibrium constant (Keq = e−ΔG/RT), and the acid dissociation constant (Ka = Keq ∗[H2O]) from which the pKa is computed (pKa = −log10Ka). The concentrations of these aqueous species were computed from the equilibrium constants of Eqs. (1a) and (1b) following the procedure outlined below. In Eqs. (2a) and (2b), the mole fractions [Li(H2O)1+ x ] and [Li(OH)(H2O)x − 1] are provided in terms of the equilibrium constant of Eq. (1a), using the molarity of water at 298.15 K, [H2O] = 55.5 (M), taking [H3O+] as a free parameter corresponding to the solution pH via [H3O] = 10−pH (M) and assuming that [Li+] + [LiOH] = 1. h

h

0þ LiðOH ÞðH 2 OÞx−1

1þ LiðH 2 OÞx

i

i

¼ K eq

h i LiðH 2 OÞ1þ ½H2 O x

ð2aÞ

½H 3 Oþ

ð2bÞ

1y LiðCO3 ÞðOHÞy ðH 2 OÞx−2

i

h ¼

7=6

y K eq

1y

LiðOHÞy ðH 2 OÞx

ih i 2− CO3

½H 2 O2

:

ð3Þ

Isotope fractionation between the Li and LiOH species is studied by computing the isotope exchange equilibrium constants for the reaction in Eq. (4) describing isotope exchange between the aqueous Li and LiOH species.

6

1þ

7

L iðH 2 OÞx þ L iðOH ÞðH2 OÞx−1 ⇌ L iðH 2 OÞx þ L iðOH ÞðH2 OÞx−1 :

ð4Þ

Li(OH)y(H2O)1x − y

Isotope fractionation between the aqueous −y and Li(OH)y(CO3)(H2O)−1 species is modeled by Eq. (5) for the Li x−2 (y = 0) and LiOH (y = 1) species. 7

1−y

L iðOH Þy ðH2 OÞx þ

7

6

−1−y

7

1−y

þ L iðOH Þy ðCO3 ÞðH2 OÞx−2 ⇌ L iðOHÞy ðH 2 OÞx

−1−y L iðOH Þy ðCO3 ÞðH 2 OÞx−2 :

ð5Þ

The isotope exchange equilibrium constant was computed following the method first laid out by Urey (1947) and by Bigeleisen and Mayer (1947). Initially, the vibrational frequencies of each of the species involved were computed in the harmonic approximation based on the ground state potential energy surface obtained from the DFT calculation. These harmonic frequencies (u7/6,i = hcω7/6,i/kT) were then used to compute the reduced partition function ratio (RPFR) for each of the species as in Eq. (6).

Li

ð8Þ

Similarly, the isotopic exchange equilibrium constants and isotopic fractionations are computed for the equilibrium described in Eq. (5). The equilibrium constants and isotope fractionations are indicated y

K

7=6 L i CO2− 3 −H 2 O

and

y

Δ7=6 LiCO2− −H2 O , respectively, where y = 0 or 3

y = 1. A key approach in this study is the calculation of an effective eff

Δ7=6 LiCO2− −H2 O , using a weighted combination of 3

the y = 0 and y = 1 isotope fractionations based on the equilibrium constants, Kyeq, and the relative abundances [Li(H2O)1+ x ] and [Li(OH)(H2O)x − 1]. This is accomplished using the straightforward approach provided in Eq. (9a), which simplifies to 9b. eff

7=6

Δ LiCO2− −H2 O 3 h i h i y¼0 7=6 y¼1 7=6 Δ LiCO2− −H2 O LiðCO3 ÞðH2 OÞ1− Δ LiCO2− −H2 O LiðCO3 ÞðOH ÞðH 2 OÞ2− x−2 þ x−2 3 3 ¼ 2− LiðCO3 ÞðH 2 OÞ1− x−2 þ LiðCO3 ÞðOH ÞðH 2 OÞx−2

ð9aÞ Δ

7=6

¼

LiCO2− −H2 O 3

y¼0

6

7=6

7=6 3 Li 7=6 10 ln K OH−H2 O ≈Δ LiOH−H2 O :

eff

1þ

Li

ð7Þ

2.3. Computing isotope fractionation parameters

7

7=6

Li

K OH−H2 O ¼ Z OH =Z H2 O

isotope fractionation,

For simplicity, we also assume that the sum [Li+] + [LiOH] = 1 is not significantly altered by the formation of the Li-Carbonate species. This allows for simple expressions for the [Li(CO3)(OH)y(H2O)-1-y x − 2] species to be evaluated in Eq. (3) (using two equilibrium constants corresponding to y = 0 and 1). h

7=6

Li equilibrium constant, K OH−H , which also provides important informa2O tion concerning the difference in isotopic composition (i.e. difference between isotopic rations in ‰) between the Li(OH)(H2O)x − 1 and Li(H2O)1+ species using Eq. (8). x

by

1 ¼ : ½H 2 O K 1þ ½H 3 Oþ eq

3

h i h i Δ7=6 LiCO2− −H2 O K y¼0 LiðH2 OÞ1þ LiðOH ÞðH 2 OÞ0þ þ y¼1 Δ7=6 LiCO2− −H2 O K y¼1 eq eq x x 3 3 : þ K y¼1 K y¼0 LiðH 2 OÞ1þ LiðOH ÞðH 2 OÞ0þ eq eq x x

ð9bÞ In this approach, the Li and LiOH species concentrations vary as a function of solution pH as described above (Eqs. (2a) and (2b)). 3. Results and discussion 3.1. Aqueous Li+ species dependent isotope fractionation 7=6

Li , The RPFRs and isotope exchange equilibrium constants, K OH−H 2O computed for the 8 models describing the aqueous Li/LiOH system speciation are provided in Table 1. For completeness, plots of the 7=6

7=6

Z H2 OLi and Z OHLi RPFRs for temperatures between 270 K and 400 K are also provided in Fig. 2A and B, respectively. Model 8, in which only the Li+ species is in interaction with a single water molecule or a single hydroxide species, is included as a means to judge the effect due to the presence of solvating waters. As is clear in Table 1 the values 7=6

Li of K OH−H display large variation and do not present a qualitatively 2O consistent picture (i.e. all N1) of isotope fractionation between the aqueous Li+ and LiOH species. Furthermore, the RPFRs in Fig. 2 show a wide variation depending on the chosen model. This demonstrates 7=6

7=6

Z

Li

¼∏ i

u7;i e−u7;i =2 1−e−u6;i : −u7;i u6;i 1−e e−u6;i =2

ð6Þ

The isotope exchange equilibrium constant is then computed as the 7=6

7=6

ratio (Eq. (7)) of the RPFRs. For example, Z OHLi and the Z H2 OLi RPFRs computed from the Li(OH)(H2O)x − 1 and Li(H2O)1+ species described in x Eq. (4) are combined in Eq. (7) to provide the isotope exchange

Li that the approach to computing K OH−H can itself be a significant 2O source of error. Therefore, in the analysis below we describe how we discriminated between these models and were able to reach our 7=6

Li conclusion that K OH−H is greater than 1. 2O The qualitative picture of the isotope exchange equilibrium dictates that there will be a higher concentration of the heavier isotope in the environment with a stronger bonding. It is generally accepted that, following hydrolysis of a charged metal species, the nearest neighbor coordination environment will adjust (Bogatko et al., 2010) such that



Table 1 List of models, their reduced partition function ratios, and isotope exchange equilibrium constants at 273.15 K and 298.15 K and the computed pKa. Model

1 2 3 4 5 6 7 8 9

7=6

Aqua species

Z H2 OLi

Formula

298.15 K

Li(H2O)+ 3 Li(H2O)+ 4 Li(H2O)+ 5 Li(H2O)+ 4 ·(H2O) Li(H2O)+ 4 ·(H2O)2 Li(H2O)+ 4 ·(H2O)4 Li(H2O)+ 4 ·(H2O)8 Li(H2O)+ 1 Li(CO3)(H2O)1− 2 ·(H2O)9

1.08243 1.08432 1.06829 1.08669 1.07880 1.07908 1.08920 1.03611 1.08449

7=6

7=6

Hydroxo species

Z H2 OLi

273.15 K

Formula

298.15 K

273.15 K

298.15 K

273.15 K

298.15 K

1.09700 1.09959 1.08060 1.10235 1.09290 1.09330 1.10525 1.04233 1.09974

Li(OH)(H2O)2 Li(OH)(H2O)3 Li(OH)(H2O)3·(H2O) Li(OH)(H2O)3·(H2O) Li(OH)(H2O)3·(H2O)2 Li(OH)(H2O)3·(H2O)4 Li(OH)(H2O)3·(H2O)8 LiOH Li(OH)(CO3)(H2O)2−·(H2O)9

1.08104 1.07671 1.07987 1.07987 1.08117 1.08215 1.08719 1.08219 1.07633

1.09523 1.09047 1.09402 1.09402 1.09568 1.09693 1.10288 1.09479 1.09000

0.99871 0.99298 1.01084 0.99372 1.00220 1.00284 0.99815 1.04448 0.99248

0.99839 0.99171 1.01241 0.99244 1.00254 1.00331 0.99786 1.05032 0.99114

35.81773 36.03340 28.53770 32.00906 22.55887 26.51510 29.07607 29.00027 29.55799

the metal–oxygen distance corresponding to the newly formed hydroxide species will contract due to a stronger interaction between the metal species and the anion. The contracted hydroxide species will more effectively shield the interaction between the charged metal and remaining water solvent resulting in an increase in their corresponding metal–oxygen distances. Based on these competing changes it is not a straightforward choice which species would provide a stronger bonding environment for the Li+ cation and hence would accumulate the heavier isotope. In order to quantify the relative changes in water bonding

Li K OH−H 2O

pKa

environment between the aqua- and hydroxo-Li+ species in a simple way we compute the change in the nearest neighbor water distance, Δw, between the two species following Eq. (10).

Δw ¼ min ðdLi−O Þ− min ðdLi−O Þ: aq:

ð10Þ

oh

7=6

Li The K OH−H values computed from our Models 1 through 7 are 2O plotted in Fig. 3 against the hydroxide Li-OH distances (dLi − OH) (left axis) and the Δw values (right axis). Both the Li-OH distances and Δw values display a high degree of scatter offering no clear 7=6

Li trend with K OH−H values. However, the negative Δw values clearly 2O indicate that the dLi − O distances for waters coordinating the Li-OH species tend to elongate relatively to their aqua counterparts, consistent with our expectation of a hydroxide induced labilization of these 7=6

Li waters. Furthermore, comparison with the rather large K OH−H value 2O of 1.04448 corresponding to an isotope exchange between Li-OH2 and Li-OH (Model 8 of Table 1), where we fully neglect the influence of coordinating waters, demonstrates that simply the presence of coordi7=6

Li by at least 0.03. nating waters has a very strong effect, reducing K OH−H 2O Based on this analysis we can conclude that a complicated Li coordination environment exists in which the Li-OH and Li-OH2 interactions 7=6

Li are both of similar importance in determining K OH−H . The effect of 2O solvent, estimated by the difference between Models 1–7 and Model 7=6 Li ≈0:03−0:05. Further8, is quite large and on the order of Δ K OH−H 2O 7=6

Li we more, because the water interaction is observed to reduce K OH−H 2O 7=6

Li can safely use K OH−H ¼ 1:04448 as an upper bound. Finally, for 2O

7=6 7=6 Fig. 2. Plots of (A) 103 ×ln Z H2 OLi and (B) 103 ×ln Z OHLi RPFRs versus 106 × T−2 for temperatures between 270 K and 400 K.

Fig. 3. The Li-OH distances (diamonds, values on left axes) and Δw (circles, right axes) plotted 7=6 Li against K OH−H for Models 1 to 7, each labeled by their model number from Table 1. 2O

Author's personal copy S. Bogatko et al. / Chemical Geology 357 (2013) 1–7

5 7=6

Li Based on these results, we are confident that K OH−H is greater than 2O one. Furthermore, taking a minimum value corresponding to Model 5 7=6

7=6

Li Fig. 4. Calculated K OH−H for aqueous Li+ speciation Models 1 to 7 compared with their 2O accompanying computed pKa values.

Li establishes a range of K OH−H from 1.00220 to 1.04448. This obser2O vation has some important consequences for aqueous processes that depend on speciation. A simple illustration of this is available by invoking the Eigen–Wilkins (EW) mechanism for ion pairing (Kleinberg, 1965; Richens, 1997, 2005). This mechanism describes the formation of an aqueous complex in which the two interacting species approach each other by a series of intermediate steps corresponding to the displacement of the waters of their hydration shells. The aqueous Li+ species possess a weakly bound 1st hydration shell. As the negative Δw values indicate in Fig. 4, the 1st hydrolysis product of Li+ has a significantly weakened Li+–water interaction. If one assumes that a preliminary step in the absorption of aqueous Li into a mineral will follow the EW mechanism and thus will involve the removal of coordinating ligands, it is clear then that the equilibrium constant for such 7=6

7=6 7=6 Li Li ≈ Models 1–7, K OH−H values are spread across a range of Δ K OH−H 2O 2O 0:02 showing a high sensitivity to the solvent model and thus to specific solvent representations. These observations are reminiscent of acid/base studies of aqueous metals which are well known to be computationally challenging (Liptak and Shields, 2001; Kelly et al., 2006; Bogatko et al., 2010, 2011; Wander et al., 2010). The estimate of an aqueous metal's acid strength (expressed as pKa) depends on the metal–ligand bonding of both the aqua and hydrolyzed species in a way very similar to the 7=6

Li estimate of K OH−H . A common source of error lies in the model used 2O to represent the solvent and it is generally regarded today that only with an accurate solvent model can one achieve quantitative agreement with experimental pKa measurements (Wander et al., 2010). Li+ is considered to be a very weakly acidic cation (pKa ~ 11–14) whose pKa has not been directly measured (Wulfsberg, 2000). Following the method outlined in Section 2.2 we have computed pKa values corresponding to Models 1–9. The values (also provided in Table 1) corresponding to 7=6

Li Models 1–7 are plotted against K OH−H in Fig. 4. This analysis provides 2O us the opportunity to discriminate between our solvent models on the basis of how well they approach the expected pKa range of aqueous Li+. Clearly, larger values of pKa correspond to smaller values of 7=6

Li K OH−H suggesting that these models are poorer representations of the 2O aqueous Li+ and LiOH bonding environments. The lower pKa estimates 7=6

Li (that is, closer to the 11–14 pKa range) tend towards K OH−H values 2O greater than one and, presumably, correspond more closely to a realistic behavior of aqueous Li+. Noticeably, Models 3, 5 and 6 all involve some degree of secondary hydration. This is also in agreement with observations that extended hydration provides a large degree of structural support to the metal's coordination shell and thus a strong influence in how well the metal–ligand interaction is described (Wander et al., 2010).

Li is greater a reaction will be distinct for Li+ and LiOH. Given that K OH−H 2O than 1, the absorption of these species will leave behind distinct contributions to the total 7Li/6Li isotopic ratio in the newly formed substance. This ratio thus depends not only on the absorption mechanism but also on environmental factors, which may influence the relative abundances of the Li+ and LiOH species, such as temperature and pH.

3.2. Isotope fractionation in the aqueous Li(I)/Li-CO3 system Using the model presented in Eq. (5) we have computed the isotope exchange equilibrium constants between the aqueous Li+ and LiOH species and the 2 structures (Table 1, Model 9) corresponding to −y Li(OH)y(CO3)(H2O)−1 (y = 0 and y = 1) representing possible x−2 carbonate coordination environments at 273.15 K and 298.15 K. The results are presented in Table 2 below along with the equilibrium constants for the carbonate coordination reaction described in Eq. (1b). Nearly all models of this study predict carbonate coordination equilibrium constants that are less than 1 whereas only one model (Model 7) predicts favorable carbonate coordination for both the [Li(OH)y(H2O)1x − y] species. Notably, this model contains an optimized, fully solvated 2nd coordination shell. In Fig. 5 these equilibrium constants are plotted as a function of water coordination and show a converging behavior towards this positive value for increasing number of solvating waters. One interpretation of this converging trend is based on earlier arguments that extended hydration, by providing structural support to the metal's coordination shell, provides a more reliable picture of the underlying chemistry of the system (Wander et al., 2010). In this regard, we put preference on the equilibrium constant generated by Model 7. In order to proceed cautiously, however, we also include an equilibrium constant generated by averaging those obtained with Models 3, 5 and 6 (that is, those aqueous Li-models which were judged 7=6

Li to perform well for K OH−H prediction). Finally, for comparison we also 2O include a model where we define Kyeq = 1 for both y = 0 and y = 1.

Table 2 List of models, carbonate coordination equilibrium constants, and isotope exchange equilibrium constants at 273.15 K and 298.15 K. [Li(OH)y(H2O)1x − y]

Kyeq

y

7=6

K COLi 2− −H 3

298.15 K

273.15 K

2O

298.15 K

273.15 K

Model

y=0

y=1

y=0

y=1

y=0

y=1

y=0

y=1

y=0

y=1

1 2 3 4 5 6 7 8

Li(H2O)+ 3 Li(H2O)+ 4 Li(H2O)+ 5 Li(H2O)+ 4 ·(H2O) Li(H2O)+ 4 ·(H2O)2 Li(H2O)+ 4 ·(H2O)4 Li(H2O)4+·(H2O)8 Li(H2O)+ 1

Li(OH)(H2O)2 Li(OH)(H2O)3 Li(OH)(H2O)3·(H2O) Li(OH)(H2O)3·(H2O) Li(OH)(H2O)3·(H2O)2 Li(OH)(H2O)3·(H2O)4 Li(OH)(H2O)3·(H2O)8 LiOH

1.15604E−26 6.29611E−26 1.81849E−18 6.14261E−22 2.01987E−11 1.27871E−08 8.21849E+06 5.05828E−19

2.10235E−20 1.88139E−19 1.73547E−19 1.73547E−19 2.02394E−18 1.15845E−11 2.70940E+06 1.40049E−19

3.51066E−30 2.99183E−29 5.57811E−21 9.06596E−25 3.66459E−13 7.51680E−10 3.52912E+07 4.28159E−22

2.38803E−23 3.49948E−22 4.29349E−22 4.29349E−22 8.40053E−21 3.58622E−13 1.05109E+07 1.05399E−22

1.00191 1.00016 1.01517 0.99797 1.00528 1.00501 0.99568 1.04670

0.99565 0.99966 0.99672 0.99672 0.99553 0.99463 0.99001 0.99458

1.00250 1.00014 1.01771 0.99763 1.00626 1.00589 0.99502 1.05508

0.99523 0.99958 0.99633 0.99633 0.99482 0.99369 0.98833 0.99563



for T = 298.15 K and 273.15 K, respectively; also indicated are the curves corresponding to the lower and upper bound of the pKa range (pKa = 11 and 14) chosen to represent aqueous Li+. The dashed lines, dotted lines and solid lines correspond to curves generated following the three approaches to compute Kyeq as discussed above, namely using Model 7 (dashed lines), averaging the Kyeq values obtained with Models 3, 5 and 6 (dotted lines), and by enforcing Kyeq = 1 (solid lines). The

Fig. 5. Calculated equilibrium constants, Kyeq, computed for the reaction described in Eq. (1b) using the 8 aqueous Li+ speciation models, plotted as a function of the number of coordination waters included in each model.

Using these equilibrium constants, the effective isotope fractionation, eff

Δ7=6 LiCO2− −H2 O, is evaluated by the weighted average in Eq. (9b) which 3

mixes the y Δ7=6 LiCO2− −H2 O isotope fractionations (y = 0 and y = 1). The 3

results are provided in Fig. 6 in which the variation of possible isotopic composition of the Li-CO3 system is estimated as a function of solution pH and temperature. Fig. 6A and B shows the curves computed

eff

Δ7=6 LiCO2− −H2 O clearly shifts by ~13‰ to lower values as 3

the solution pH increases, a similar shift is observed as temperature decreases from 298.15 to 273.15 K. Of primary importance to this study is the wide variation in the pH value at which this pH related shift occurs. This variation is due not only to the choices we have made of the metal pKa value but also are largely influenced by the model used to determine our carbonate coordination equilibrium constant. All of these models predict the strongest variations in isotope fractionation occurring at very high pH and no significant pH influence is observed at normally oceanic conditions. However, a significant temperature effect is observed and a systematic shift of −12‰ is observed between 298.15 K and 273.15 K. While these observations are based on a very simple model, we claim that the essential characteristics of this model, that is the substitution of coordinating waters with carbonates, may be regarded as a qualitative proxy for the mechanism for incorporation of aqueous Li into a carbonate matrix. We may thus discuss this mechanism insofar as it may be affected by this fundamental step in the otherwise largely unknown reaction mechanism. With this in mind, the implicit assumption commonly made of the equivalence between the Li isotope ratios in calcium carbonate and seawater does not reflect the coupling we observe between Li speciation and isotope fractionation. Notably, this assumption does not reflect possible speciation influences due to historic variations in oceanic pH and temperature. While the possible errors arising from neglecting effects due to pH induced Li speciation are limited by its very weak acidic character, the temperature dependence of the Li isotope fractionation parameters appears to be significant. 3.3. Li speciation and ancient climate monitoring The results of this study have allowed us to formulate an intriguing prediction. Namely, that aqueous speciation of Li+ results in significant Li isotope fractionation. While the fractionation due to Li+ and LiOH speciation is predicted to occur far outside the pH range normally associated with oceanic conditions, those due to changes in coordination (e.g. complex formation) are predicted to induce a significant temperature dependent isotope fractionation. This prediction is interesting when compared to measurements of Li isotopic composition in calcium carbonates (Hoefs and Sywall, 1997; Hall et al., 2005; Hathorne and James, 2006; Misra and Froelich, 2012). These measurements indicate a close correspondence between the Li isotopic compositions of calcium carbonates and seawater. If the mechanism by which aqueous Li+ was incorporated into calcium carbonate shells depended in some way on the identity of the aqueous Li+ species, the species dependent Li isotope fractionation that we predict would have an effect that would necessarily be observed on the Li isotope ratios found in calcium carbonates. Variation in Li speciation in response to changing oceanic conditions would then be apparent in ancient calcium carbonates. Because this is not the case, we can safely say that the mechanism of Li+ incorporation into calcium carbonates is insensitive of the aqueous Li+ species. 4. Conclusions

Fig. 6. Variation of eff Δ7=6 LiCO2− −H2 O as a function of system pH calculated using Eq. (9b) 3

where Kyeq was evaluated using Model 7 (dashed lines), an average of Models 3, 5 and 6 y (dotted lines) and by assuming Keq = 1 (solid lines) for y = 0 and y = 1. Curves corresponding to pKa values of 11 and 14 are indicated by arrows. Parts 6A and 6B correspond to 298.15 K and 273.15, respectively.

We have carried out a theoretical study of aqueous Li+ speciation including effects arising from water coordination number and geometry, ligand coordination effects and effects arising from temperature and solution pH. The choice of solvent model is observed to severely influence conclusions. It can however be stated that models which approach

Author's personal copy S. Bogatko et al. / Chemical Geology 357 (2013) 1–7 7=6

Li the expected pKa range of Li also predictK OH−H N1 suggesting that these 2O models are better suited to studying subtle differences between the Li+ 7=6

Li and LiOH species and thus are more capable of predictingK OH−H values. 2O Thus we conclude that the aqueous LiOH species preferentially accumulates the heavier Li isotope and we establish a tentative range of 1.00220 7=6

L i

to 1.04448 for K OH−H2 O . 7=6

Li The consequences of these K OH−H values are then studied using a 2O model for Li-Carbonate coordination from which the carbonate coordination equilibrium constants, Kyeq, and the isotope exchange equilibrium 7=6

constants, y K COLi2− −H O, are computed. We have shown that the computed 3

2

equilibrium constants, Kyeq, for Li+ (y = 0) and LiOH (y = 1) carbonate 7=6

Li coordination, as with K OH−H , also vary strongly with the solvent model 2O used. These Kyeq values appear to converge, however, for models, which are coordinated to a 2nd hydration shell. Proceeding cautiously, three estimates of Kyeq are implemented in a model which allows us to

predict the variation of isotope fractionation,

eff

Δ7=6 LiCO2− −H2 O , arising 3

from changes in oceanic conditions (temperature and pH). We observe that

eff

Δ7=6 LiCO2− −H2 O is not sensitive to pH (in the oceanic pH range) 3

but may undergo significant alterations (on the order of 12‰) as a function of temperature. Thus, the assumed equivalence between Li isotope ratios in calcium carbonate and seawater does not reflect possible speciation influences due to historic variations in oceanic conditions. An important constraint is thus placed on mechanism of Li+ incorporation into calcium carbonates, namely that this mechanism is insensitive of the aqueous Li+ species. Acknowledgments S.B. is grateful for a postdoctoral fellowship provided by the VUB Research Council. P.G., Ph. C. and F.D.P. thank the Fund for Scientific Research Flanders (FWO, project G.0091.13 for Ph. C) and the VUB for the continuous support. Appendix A. Supplementary data Supplementary information accompanying this article contains the XYZ coordinates of all optimized geometries Li species used in this study. Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.chemgeo.2013.08.019. References Becke, A.D., 1993. Density‐functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652. Bigeleisen, J., Mayer, M.G., 1947. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 15, 261–267. Bogatko, S., Moens, J., Geerlings, P., 2010. Cooperativity in Al3+ hydrolysis reactions from density functional theory calculations. J. Phys. Chem. A 114, 7791–7799. Bogatko, S., Cauët, E., Geerlings, P., 2011. Influence of F- coordination on Al3+ hydrolysis reactions from density functional theory calculations. J. Phys. Chem. C 115, 6910–6921. Bogatko, S., Cauët, E., Bylaska, E., Schenter, G., Fulton, J., Weare, J., 2013. The aqueous Ca2+ system, in comparison with Zn2+, Fe3+, and Al3+: an ab initio molecular dynamics study. Chem. Eur. J. 19, 3047–3060. Bouazizi, S., Nasr, S., 2007. Local order in aqueous lithium chloride solutions as studied by X-ray scattering and molecular dynamics simulations. J. Mol. Struct. 837, 206–213. Cancès, E., Mennucci, B., Tomasi, J., 1997. A new integral equation formalism for the polarizable continuum model: theoretical background and applications to isotropic and anisotropic dielectrics. J. Chem. Phys. 107, 3032–3041. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G.A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H.P., Izmaylov, A.F., Bloino, J., Zheng, G., Sonnenberg, J.L., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery Jr., J.A., Peralta, J.E., Ogliaro, F., Bearpark, M., Heyd, J.J., Brothers, E., Kudin, K.N., Staroverov, V.N., Keith, T., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A., Burant, J.C., Iyengar, S.S., Tomasi, J., Cossi, M., Rega, N., Millam, J.M., Klene, M., Knox, J.E., Cross, J.B., Bakken,

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