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The not-so-simple coordination chemistry of alkali-metal cations Li+, Na+ and K+ with one carbonate anion: A study using density functional and atoms in molecules theories
Accepted Manuscript Research paper The Not-so-Simple Coordination Chemistry of Alkali-Metal Cations Li+, Na+ and K+ with One Carbonate Anion: a Study Using Density Functional and Atoms in Molecules Theories Philip A.W Dean PII: DOI: Reference:
S0020-1693(17)30714-4 http://dx.doi.org/10.1016/j.ica.2017.09.015 ICA 17871
To appear in:
Inorganica Chimica Acta
Received Date: Revised Date: Accepted Date:
5 May 2017 2 September 2017 6 September 2017
Please cite this article as: P.A. Dean, The Not-so-Simple Coordination Chemistry of Alkali-Metal Cations Li+, Na and K+ with One Carbonate Anion: a Study Using Density Functional and Atoms in Molecules Theories, Inorganica Chimica Acta (2017), doi: http://dx.doi.org/10.1016/j.ica.2017.09.015 +
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The Not-so-Simple Coordination Chemistry of Alkali-Metal Cations Li+, Na+ and K+ with One Carbonate Anion: a Study Using Density Functional and Atoms in Molecules Theories.§
Philip A.W Dean* Department of Chemistry University of Western Ontario London, Ontario N6A 5B7 Canada
*E-mail: [email protected]; phone: 519-661-2111 Ext 86331 §
Dedicated to the memory of Professor Mehdi Rashidi, Shiraz University Chemistry
Department.
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Abstract A total of 23 new complexes in the series (CO3)Myy-2 (M = Li, Na or K; y = 1-5) have been optimized using DFT, adding to known planar complexes (CO3)Myy-2 (M = Li or Na; y = 1 or 2) and (CO3)Myy-2 (M = Na; y = 3). Planar structures are the most stable for: M = Li, y = 1-4; M = Na, y = 1-3; M = K, y = 1-3. For M = Na, three non-planar structures occur over a range in electronic energy of ca. 9 kJ/mol when y = 4, while for M = K only a single, non-planar structure occurs for y = 4. For M = Li, Na or K, two non-planar structures were the only ones found for y = 5. The CO3 moiety was found to be planar in all new species except for new isomers of (CO3)M- (M = Na or K) that have perpendicular (π-like) CO3:M bonding. No evidence was found for any stable species when y = 6. Atomic charges were calculated by the AIM method for most of the new species and confirm that the CO3 : M bonding is highly ionic. Stepwise complexation energies have been calculated for the addition of M+ to the most stable form of (CO3)My-1y-3 to give the most stable form of (CO3)Myy-2, for y = 1 - 5. The stepwise formation reactions are exothermic for all the metals when y = 1 - 3, but endothermic for all the metals when y = 4 or 5. However, addition of four or five M+ to one CO32- is exothermic overall for all three metals.
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Keywords
Lithium ion coordination by carbonate anion
Sodium ion coordination by carbonate anion
Potassium ion coordination by carbonate anion
Alkali-metal ion coordination by carbonate anion
DFT of alkali-metal ion-carbonate anion complexes
AIM charges of alkali-metal-carbonate anion complexes
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Graphical Abstract
(CO3)Na3+
Na+ ——► 1-4-1-Na
1-4-2-Na
1-4-3-Na
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Introduction
In 2001, Hao and March (1) used electrospray ionization tandem mass spectrometry to detect a very wide range of gaseous unsolvated aggregates of sodium ions and carbonate ions when using an aqueous solution of Na2CO3 as the analyte. Species of the form [(CO3)xNay]z were detected for x = 1–28, z = +1; x = 15–51, z = +2; x = 1-25, z = -1; x = 9-43, z = -2; x = 19-63, z = -3. To date, there has been no systematic study of possible structures for these intriguing aggregates, although the known polyfunctional ligand behaviour of CO32- (2) suggests that interesting, possibly new structural features may occur in the Na+:CO32- aggregates. The Na+ cation is relatively light, and CO32- is one of the lightest polyatomic ligands, so combinations of the two should be quite amenable to calculations of structure.
Two fundamental questions arise in considering possible structures of [(CO3)xNay]z: How many Na+ ions can bind to a single CO32- anion, and how do they bind? How might multiple CO32- anions be linked when x ≥ 2? In this paper I have attempted to answer the first question in a survey of aggregates that occur when x = 1, most relevantly for M = Na+, but also, following rather unusual structures found for (CO3)Na42+ (vide infra), for Li+ and K+. In so doing, I have completed the structural characterization of the series (CO3)Mxx-2 ((M = Li, Na or K; x = 1-5). For most of the complexes I have calculated charges on the non-metal and alkali metal atoms using the Atoms in Molecules (AIM) method (3).
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There have been previous calculational studies of planar (CO3)M- (M = Li or Na) (4), (CO3)M2 (M = Li or Na) (5) and (CO3)Na3+ (6), all containing exclusively bidentatelycoordinated M centres (c.f. structures of 1-1-1-M, 1-2-1-M and 1-3-1-M in the Results and Discussion below).
A second paper will provide results relevant to the second question presented above.
Experimental
DFT calculations were performed on a desktop computer using GAUSSIAN 03W, Version 6.1 (7). GAUSSVIEW 4.1 (8) was used as the user interface. As in a previous study (9), the functional was B3LYP (10-13), the basis set was 6-31G(d,p), and default convergence criteria were usually used. (The B3LYP: 6-31G(d,p) combination is known to provide acceptable structural data with efficient use of computational resources (14).) In cases where quadratically-convergent SCF was used, this is specifically mentioned; similarly, symmetry was applied only where specifically mentioned. The K+ cation, used in some comparison complexes, is just at the end of the range of atoms for which the 631G(d,p) basis set is appropriate (14), but this basis set was used throughout this work, for consistency. In our earlier study (9), the B3LYP:6-31G(d,p) combination was found to provide acceptable, consistent structural data for Na+-containing complexes of [Fe(CN)5(NO)]2- (NP2-) up to [(NP)2Na6]2+. The CO32- ion is much lighter than the NP2ion, 60.0 vs. 215 g/mol, so it can be anticipated that the B3LYP:6-31G(d,p) combination
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will allow structural calculations for [(CO3)xNay]z to be carried out to a larger value of x than the limit of x = 2 (for [(NP)2Na6]2+) in the previous work.
For each structure optimized in this work, the vibrational spectrum was calculated using GAUSSIAN, as a check on the authenticity of the structure and to provide the zero point vibrational energy (ZPE). Complexes with one negative frequency were re-optimized after the structure was moved along the negative vibrational coordinate, as usual. Complexes with more than one negative frequency were abandoned. Vibrational frequencies for all the complexes authenticated are given in Tables S1AC-S1CC of the Supplemental Material.
Using GAUSSIAN, the basis set superimposition error (BSSE) (15) was also calculated for each optimized structure, following the procedure given in Refs. 14 and 16. Thus, for example, the BSSE for the formation of a particular isomer of [(CO3)Na3]+ from CO32and 3 Na+, was treated as a 4-particle (1 CO32- and 3 Na+) problem, by setting the command Counterpoise=4 in GAUSSIAN. (Some manual insertion into the GAUSSIAN input file is required, c.f. Refs. 14 and 16).
Calculated optimized electronic energies for Na-containing species containing one CO32-, each with their associated ZPE, are given in Table S1A (Supplemental Material), together with relative energies of isomers based on electronic energy-plus-ZPE combinations. Also included in the Table is the value of the BSSE for each species (for formation of [(CO3)Nay]y-2 from CO32- and y Na+). The parallel data for species
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containing Li, and species containing K, are given in Tables S1B and Table S1C. Calculations of ZPE in GAUSSIAN are known to yield approximate results (via a specific warning in the output file), as are calculations of BSSE (by the Counterpoise Method for finite basis sets).
As a check on the relative electronic energies calculated for authenticated species using B3LYP:6-31G(d,p), two other functional:basis-set combinations were used to calculate single-point energies for structures that had been optimized using B3LYP:6-31G(d,p) (and authenticated): B3LYP:6-311G**, containing a better basis set (14), and B3PW91:6-31G(d,p), containing a better functional (17). The energies so calculated are given in Supplementary Material as Tables S1AB, S1BB and S1CB. For each of the three metals, the three sets of calculated relative electronic energies are generally in good agreement, with very few exceptions. It is especially re-assuring that with only two exceptions, all three calculations are in agreement over the structure with the minimum electronic energy for a particular stoichiometry, when several isomers occur. The exceptions, CO3Na53+ and CO3K53+, are cases where isomers are particularly close in energy.
Relative energies specifically included in the text are electronic energies, E, calculated using B3LYP:6-31G(d,p) with ZPE values added.to give corrected energies, ECorr,, i.e. data from column 4 of Tables S1A-C. Table 6 contains energy ranges calculated using (a) ECorr values from Tables S1AB-CB, together with the corresponding BSSE data from the Tables, and (b) corresponding values found by combining other electronic energies
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in Tables S1AB-S1CB with the appropriate ZPE and BSE values from Tables 1A-C. Then, for example, for the energy change occurring in the reaction CO3M2 + M+ → CO3M3+ ∆E = [ECorr +BSSE](for CO3M3+) – [{ECorr +BSSE}(for CO3M2) + E(for M+)].
The structures of the simple complexes CO3M- containing bidentate CO32- were difficult to optimize directly from a starting structure containing bidentate CO32-, (CO3-O,O’)2-. The structures for M = Li and Na were optimized from starting complexes with monodentate CO32-. The complex with M = K was optimized starting with the moiety (CO3-O,O’)K- left behind after one CO32- is removed from [(CO3-O,O’)2K]3- (P.A.W. Dean, unpublished work). To obtain a symmetrical (C2v) structure for (CO3-O,O’)K-, the symmetry had to be constrained, and quadratically-convergent SCF used.
Atomic charges were calculated using AIMAll Version 16.01.09, Standard or Version 17.01.25 Standard (18). Charges calculated by the AIM (Atoms in Molecules) method are derived from electron densities, which are experimentally observable, in principle (3). The input data for the AIMQB sub-program of AIMAll were formatted checkpoint (.fch) files. These were obtained via the checkpoint files (.chk) resulting from the GAUSSIAN calculations by use of the FormChk utility of GAUSSIAN. Durrant (19) has noted that AIM charges are relatively insensitive to the choice of quantum method used to obtain a structure. In this context it is worth noting that AIM charges are quite sensitive to the difference between the unsymmetrized and symmetrized structures of (CO3-O,O’)K-, though less so for its non-planar isomer (Table 1). The AIMQB
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calculation for Structure 1-5-2-Li (see below) failed, and this structure was approximated by the 1-5-2-M structure of (CO3)Li3Na23+ with the two Na atoms in positions 5 and 6, the positions that were the problem area for the fully lithiated structure. (For consistency, the same conditions were used for all the AIM calculations, and so no attempt was made to find alternative, satisfactory conditions for the calculation of charges, etc., for 1-5-2-Li.) The AIM charges on Na(5) and (6) in (CO3)Li3Na23+ are essentially identical to the corresponding charges in the fully sodiated analogue, so it seems reasonable to assume that the AIM charges on Li(7-9) are acceptable representations of the AIM charges on same metal centres in 1-5-2-Li also.
The versions of AIMAll that were used were range-limited by the software supplier, and (CO3)K42+, as well as (CO3)K53+, apparently fell outside the range for which calculations could be completed. The AIM charges for the lithiated and sodiated analogues have AIM charges ≥ 0.94, so it can be expected that AIM charges on K in (CO3)K42+ and (CO3)K53+ will also be very highly positive, approaching unity.
Particular structures are represented by the notation x-y-w-M, where x = number of CO32- (1 in this paper), y = number of M+, w = isomer number, and M is used generically, or replaced by the symbol for a particular alkali metal. Thus, for example, 1-5-2-M might refer to Isomer 2 of (CO3)M53+ with at least two different metals M, while Isomer 2 of (CO3)Li53+ would be 1-5-2-Li. Detailed sets of calculated structural data for stoichiometries CO3M2, (CO3)M3+, (CO3)M42+ and (CO3)M53+, are provided in Tables S2, S3, S4 and S5 of Supplemental Material, respectively.
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In the figures, the colours used are: C, grey; O, red; alkali metal, purple. Results and Discussion.
Structures with one M+. For this stoichiometry a total of two structures were found: 11-1-M and 1-1-2-M:
1-1-1-M
1-1-2-M
Calculated structural parameters, and AIM charges, are given in Table 1. Structure 1-11-M, of ideal C2v symmetry, was found for M = Li, Na or K. No symmetrization was necessary in this work to obtain C2v structures for 1-1-1-Li or 1-1-1-Na. However, the optimized structure found for 1-1-1-K in the absence of applied symmetry was of Cs rather than C2v symmetry. Constrainment was necessary to obtain the C2v structure, and it was found necessary to use quadratically-convergent SCF to optimize this symmetrized structure. The electronic energy for 1-1-1-K under the latter conditions was 7 kJ/mol less negative than the corresponding energy obtained by simple optimization, a barely significant difference. Previous results are available for 1-1-1-Li
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and 1-1-1-Na, albeit with different functionals and basis set (4). (Data for 1-1-1-Rb have also become available recently (17), and are included in Table 1 for comparison). Structural parameters calculated here for 1-1-1-Li and 1-1-1-Na agree with those of Ref. 4 to within 0.04 Å or better on bond lengths and within 1.3 ° or better on bond angles, as shown in Table 1. The Na-O bond distances in 1-1-1-Na and 1-1-2-Na (Table 1), 2.09 and 2.36 Å, may be compared with distances found in the crystal structure of Na2CO3.H2O (18), in which monodentate Na-O distances were found to range from 2.293(2) – 2.491(2) Å, and bidentate Na-O distances to range from 2.508(2) – 2.822(2) Å. However, in comparing Na-O distances in the hydrated salt with distances calculated for (gaseous unsolvated) 1-1-1-Na and 1-1-2-Na it is important to note that in the hydrated salt both crystallographically-distinct Na atoms exhibit 6-coordination, which is expected to lead to larger Na-O distances. (In addition, “lattice effects” may be important.)
Structure 1-1-2-M has not been reported previously for CO32- - containing species, although a C3v structure was considered for the related LiNO3 (4). In the current work, Structure 1-1-2-M was found for M = Na or K, but not for M = Li. A unique feature of the structures 1-1-2-Na and -K, not found in any other species discussed in this paper, is that in both complexes the CO32- anion is significantly non-planar, being concave on the side of the anion that faces M. For M = Na, 1-1-2-Na is less stable than 1-1-1-Na by over 60 kJ/mol, while for M = K, 1-1-2-K is less stable than 1-1-1-K by over 20 kJ/mol.
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The data in Table 1 show that bidentate coordination of CO32- to Li+-Rb+ in Structure 11-1-M lengthens the C-O bonds involving the O atoms involved in the coordination, while shortening the C-O bond involving the uncoordinated O atom. The effect is most pronounced in the length of the latter bond, although the variation of this bond distance with variation in M is slight, 1.24-1.26 Å. It is interesting that for all the structures 1-1-1M in Table 1, the weighted average C-O bond length is within 0.01 Å of the C-O value in free CO32-. The bite angle of the ligand in 1-1-1-M is smallest when M = Li, 114.1 °, but plateaus when M = Na-Rb, the range here being 117.1-117.9 ° at most. Other distances vary as expected with variation in M+.
The AIM charges calculated for 1-1-1-M and 1-1-2-M (Table 1) show that the bonding in all the species is largely ionic, as expected, the positive charge on M being ≥ 0.60. The relative order of the positive charges on the metal, Li > Na > K, is counterintuitive (since the smallest cation, Li+, is expected to be most polarizing, and the largest cation, K+, the least polarizing), and awaits explanation. The overall charge on the CO32- ions becomes less negative, consistent with the charges of less than unity found for the metal ions. Within the CO3 moieties, the changes in the positive AIM charges on the C atoms are relatively small, the overall reduction in negative charge of CO32- mainly occurring mainly through a reduction of weighted average negative charge on the O atoms. Changes (in a positive direction) in the negative charges on individual O atoms in the complexes are in the order O(2) > O(3,4), at least when M = Li or Na:. Thus, most negative charge is withdrawn from the uncoordinated O atom. This is consistent with the shortening found for the C(1)-O(2) bond lengths, compared with the
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corresponding C(1)-O(3) and -O(4) bond lengths. The significant difference in AIM charges on K in 1-1-1-K with and without imposed symmetry has already been commented on.
Structures with two M+. Two structures were found for this stoichiometry, 1-2-1-M and 1-2-2-M:
1-2-1-M
1-2-2-M
Selected calculated structural parameters and AIM charges for both structures are given in Table 2. Structure 1-2-1-M, of ideal C2v symmetry, has been described previously for M = Li and Na, albeit using a different functional and basis set (5), and present results agree closely with the earlier work. In the present study, no symmetrization was necessary to optimize the new K compound for this stoichiometry, unlike the case of CO3K- above.
It is interesting that although all three O atoms are involved in bonding in Structure 1-21-M, only the C(1)-O(2) bond, in which the O(2) atom is bonded to two M+ ions, is
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increased in length compared with the C-O distances of CO32- itself. The C(1)-O(3) and C(1)-O(4) bonds, in which the O atoms are linked to only one M+ ion, are shortened: As a generality, more highly coordinated O atoms are associated with longer C-O bonds. Overall, the weighted average C-O distances are again within 0.01 Å of the value in free CO32-. The AIM charges on the O(2) atoms in the three compounds 1-2-1-M are more negative than those on their O(3) and O(4) counterparts: the more highly coordinated O atom retains more negative charge. Overall, the AIM charges are consistent with very ionic M+ to CO32- bonding. The positive AIM charges on the metal centres in 1-2-1-M are again Li > Na > K, although the differences are smaller than those found for 1-1-1-M and 1-1-2-M. For all three complexes 1-2-1-M, however, the charges on M are more positive than for their counterparts in 1-1-1-M and 1-1-2-M, as expected for addition of more positive charge in going from 1-1-1-M and 1-1-2-M to 1-2-1-M.
Structure 1-2-2-M, found for M = Li or Na, but not for M = K, is new. For M = Li, this structure is less stable than 1-2-1-Li by ca.130 kJ/mol, and similarly, 1-2-2-Na lies ca. 100 kJ/mol above 1-2-1-Na. In Structure 1-2-2-M, both M atoms are bound in a bidentate manner to the same two O atoms of CO32-, both M atoms being out of the plane of the anion. As is the case for the C-O(2) of 1-2-1-M, in which O(2) is attached to two M atoms also, in 1-2-2-M the C-O bonds to O(3) and O(4) are lengthened compared with the C-O bonds of CO32-; O(2) in 1-2-2-M is uncoordinated and correspondingly the C-O(2) bond length is shortened compared with CO32-. The weighted average bond length in 1-2-2-M is 1.32 Å for both M = Li and M = Na, which can be compared with the 1.31 Å in CO32- itself. As in 1-2-1-M, the AIM charge on M in
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1-2-2-M is slightly more positive for M = Li than for M = Na. With regard to the AIM charges on the O atoms of 1-2-2-M, the charges are in the relative order O(2) less negative than O(3,4), as found for 1-2-1-M, above, a species that also has an uncoordinated O(2).
The relative instability of 1-2-2-M compared with 1-2-1-M, suggests that either out-ofplane bonding is less favorable than in-plane, or that bi-coordination of M at a single O is less favorable than mono-coordination, or both. The structure of 1-3-2-M, following, suggests the former. It is worth noting that for M = Li and Na, Structure 1-2-2-M pushes the metal ions into closer proximity than in 1-2-1-M: 2.56 vs. 3.61 Å for M = Li, and 3.33 vs. 4.29 Å for M = Na. The AIM charges on the metal centres for 1-2-2-M are ≥ 0.90 (Table 20), so positive:positive repulsions may also contribute to the relative instability of these isomers.
Structures with three M+. For all three metal ions, the most stable structure found, 13-1-M, without the need for any symmetrization, was close to the D3h structure found by Siu and co-workers for the case that M = Na with a different basis set (6). Selected calculated structural data, and AIM charges, are given in Table 3, and show the expected trends with change in the alkali-metal cation. In the case of 1-3-1-M, there is insignificant change in the AIM charges on M with change in the alkali metal (Table 3).
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1-3-1-M
1-3-2-M
1-3-3-Li
For M = Li , two isomers of 1-3-1-Li were found, 1-3-2-Li and 1-3-3-Li, while for M = Na, just one isomer of 1-3-1-Na was found, 1-3-2-Na. However, no isomers of 1-3-1-K were found. For M = Li, the two isomers were less stable than 1-3-1-Li, by ca. 130 kJ/mol, while for M = Na, 1-3-2-Na was less stable than 1-3-1-Na by ca. 120 kJ/mol.
Structure 1-3-2-M may be recognized as Structure 1-2-2-M to which a third M has been added at a vacant, in-plane, bidentate site. The Structure 1-3-2-M allows a comparison of bidentate O-M bonding distances in the plane of the CO32- with bidentate bonding distances out of the plane of the anion: r(O-Min-plane,ave) < r(O-Mout-of-plane) is found. However, the average value of r(O-Min-plane,ave), i.e. r(O-M(5)ave), is very close to the corresponding distance in 1-3-1-M. This latter observation suggests the tridentate bridging to M found for O(3) in 1-3-2-M, compared with the bidentate bridging (only) found at O in 1-3-1-M, is not strongly destabilizing. Thus, the out-of-planar bonding to M(6) and M(7), rather than the tridentate bridging by O, is the major factor destabilizing 1-3-2-M vs. 1-3-1-M.
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For 1-3-2-M, the shortness of the M(6)…M(7) distance compared with the M..M distance in the corresponding 1-3-1-M is noteworthy: for M = Li, 2.70 vs. 3.81 Å; for M = Na, 3.39 vs. 4.43 Å, and, as for 1-2-2-M (above), may contribute to the relative instability of 1-32-M.
Structures 1-3-1-Li and 1-3-3-Li (Table 3) allow a comparison of O-Li bond distances for bidentately- and monodentately-attached Li in species of the same overall charge. For this situation, r(O-Libidentate) > r(O-Limonodentate). However, in terms of C…Li distances, the order is 1-3-3-Li > 1-3-1-Li: bidentate bonding leads to more compact structures. Generalizing from the relative energies of 1-3-1-Li and 1-3-3-Li, it appears that bi-coordination of M is stabilizing compared with the mono-coordination of M.
With regard to the AIM charges in Table 4, it is interesting that the AIM charges on the O atoms of 1-3-2-M are O(2) > O(4) > O(3) consistent with the coordination numbers being one for O(2), two for O(4) and three for O(3). The overall range of AIM charges on O in 1-3-2-Li is -1.28 to -1.37, but smaller for 1-3-2-Na, -1.28 to -1.34.
A comparison of structural trends in the series 1-1-1-M - 1-2-1-M - 1-3-1-M is rewarding. Each of these complexes contains only bidentately-attached metal ions, with the metal ions exclusively in the plane of the CO32- anion. Observed trends along the series are that, for constant M: M-O distances increase with increasing number of metal ions, e.g. 2.09 – 2.21 Å for M = Na; C…M distances increase similarly, e.g. 2.44 – 2.55 Å
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for M = Na; O-M-O angles decrease along the series, e.g. 66.6 – 61.1 ° for M = Na (Tables 1-3). The results are consistent with overall expansion as an increasing number of 1+ ions is added to CO32-. As expected on the same basis, for constant M, the positive AIM charge on M increases along the series; this effect is strongest for M = K (0.60 – 0.92) and weakest for M = Li (0.89 – 0.92). Likewise, the positive AIM charge on C increases across the series, e.g. 2.18 – 2.26 for M = Li. Remarkably, the average AIM charge on the O atoms changes little across the series for constant M, e.g. -1.32 to -1.33 for M = Na, as does the average C-O distance, e.g. 1.30-1.31 Å for M = Na.
Structures with four M+. The most stable structures found for this stoichiometry are 14-1-M/1-4-2-M (M = Li or Na) and 1-4-1-K (the only structure of this stoichiometry for M = K). There is a negligible difference in energy between structures 1-4-1-M and 1-4-2-M for M = Li or Na. Structure 1-4-3-Na (not shown) is very similar to 1-4-1-K, and lies a bare 9 kJ/mol above 1-4-1-Na, a borderline difference. Selected structural parameters for the various M4 species are given in Table 4, together with AIM charges.
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1-4-1-Li
1-4-2-Li
1-4-1-Na (2 views)
1-4-2-Na
1-4-1-K
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Structure 1-4-1-Li is planar and of close-to-C2v symmetry; it contains two Li atoms that are bound bidentately and two that are bound monodentately. As now expected, the OLi bond distances have the relative values r(O-Li)bidentate, ave > r(O-Li)monodentate. For 1-41-Na, the planar equivalent of 1-4-1-Li does not represent a minimum in the potential energy surface. Rather, 1-4-1-Na has a structure of C2 symmetry in which both bidentately- and the monodentately-bound Na atoms are out of the plane of the CO32anion, most markedly the monodentately-bound Na atoms.
Structure 1-4-2-Li is planar and of C2v symmetry. It contains only one clearly bidentately-coordinate Li centre, a difference from the two of 1-4-1-Li. In contrast, structure 1-4-2-Na is non-planar and of Cs symmetry: a “humming-bird-like” (or “mosquito-like”) structure. It contains three bidentately-bound Na centres, of which one is in the plane of the anion and two are out-of-plane, and one monodentately-bound Na. The relative Na-O distances are r(Na-O)monodentate < r(Na-O)bidentate, in-plane < r(NaO)bidentate, out-of-plane, ave . The relative dispositions of Na(5), Na(6) and Na(8) in 1-4-2-Na are similar to those of Na(5), Na(6) and Na(9) in 1-5-1-Na (below).
The out-of-plane twisting of the two distinct pairs of metal atoms in Structure 1-4-2-Na reaches its extremity in the structures of 1-4-1-K/1-4-3-Na, which (when symmetrized, for M = K) have C2v symmetry. Here there are four bidentately bound M atoms, two inplane and two out of plane. This leads to a distorted tetrahedron of M atoms surrounding the planar CO32- ion. In both 1-4-1-K and 1-4-3-Na, r(O-M)in-plane, ave < r(OMout-of-plane, ave), as found in several instances above also. The structural variation from
22
1-4-1-Li via 1-4-1-Na to 1-4-1-K/1-4-3-Na, where the alkali-metal environment of the relatively-undistorted, planar CO32- ion changes with alkali metal, is reminiscent of the structural variation observed in anhydrous metal oxalates in which the shape of the anion responds to change of the alkali metal (19). The shortness of the M(7)…M(8) distances , compared with the other M…M distances is noteworthy in 1-4-1-K/1-4-3-Na (Table 4).
In all of the species containing four M atoms, the AIM charge on the metal centres is ≥0.94, just slightly more positive than values found in (CO3)M3+. (Software limitations prevented calculation of AIM changes for (CO3)K4, as well as (CO3)K5 (below).) The AIM charges on O atoms are all less negative than the corresponding AIM charge in CO32- itself. The influence of differing coordination number can be seen, e.g. O(2) (3coordinate) of 1-4-2-Na is more negative than O(3,4) (2-coordinate), but the differences are quite small. The AIM charges on M and O are such that the positive charge on the C atom is, in most cases, slightly more positive than in the free CO32- anion.
Structures with five M+. For this stoichiometry, two different structures, 1-5-1-M and 15-2-M, were found for all three alkali metals, Li, Na and K. Selected structural parameters, and AIM charges, for all the complexes are given in Table 5. The complexes with M = K show the most noticeable deviations from what would appear to be ideal Cs symmetry for Structure 1-5-1-M and ideal C2v symmetry for Structure 1-5-2:M.
For all three metals, structures 1-5-1-M and 1-5-2-M are close in energy, the
23
largest difference being only 10 kJ/mol for M = Li, where structure 1-5-1-Li is less stable than 1-5-2-Li. Structure 1-5-2-Li represents the first instance in which the most stable structure for a particular stoichiometry (CO3)Liyy-2 is not planar.
1-5-1-M
1-5-2-M
The similarity between the dispositions of Na(5), Na(6) and Na(9) in 1-5-1-Na and the dispositions of Na(5), Na(6) and Na(8) in 1-4-2-Na (above) has already been noted above. In all the complexes shown in Table 5, the average C-O bond distance is 1.30 Å, within experimental error the same value found in free CO32-.
The AIM charges on the metal centres found for Structures 1-5-1-M (M = Li or Na) and 1-5-2-Na are ≥ 0.95, while all the corresponding charges on O are again less negative than for CO32- itself, and the positive AIM charges on C are slightly higher than in free CO32-. The effect of differing coordination number of O on the AIM charges on O is slight but present, e.g. in 1-5-1-M, O(2), 3-coordinate, is more negative than O(3,4), 2coordinate.
24
Attempts to produce (CO3)M64+. No stable species of this stoichiometry were found for any of the three alkali metals, despite several efforts. The highly charged starting structures dissociated in all cases, e.g. a starting structure produced by adding an extra Na+ between the Na(7) and Na(8) positions of 1-5-1-Na, dissociated to 1-3-1-Na and three free Na+. Similarly, a starting structure derived by replacing Na(9) with two monodentately-bound Na+ added to O(3) and O(4) of 1-5-2-Na, dissociated to (CO3)Na42+ plus two free Na+.
Stepwise and Overall Complexation Energies. These energies are detailed in Table 6, where the ranges were calculated as described in the Experimental Section. As expected, the stepwise complexation energies become progressively less exothermic as the product species contain more M moieties, and indeed the products CO3M42+ and CO3M53+ are formed endothermically (from CO3M3+ and CO3M42+, respectively) for all three alkali metals. Overall the energy change for the addition of a total of 4, or 5, M+ to CO32- is negative for all the metals, i.e. the exothermicity of steps 1-3 outweighs the endothermicity of step 4, or 4 plus 5, in all cases.
Conclusions DFT has been used to investigate systematically the structures of [(CO3)My]y-2 (M = Li, Na or K; y = 1-5). (There have been earlier investigations of the most stable forms of [(CO3)M]- (M = Li or Na) (3), [(CO3)M2] (M = Li or Na) (4) and [(CO3)Na3]+ (5).) Results show (or, for the most stable isomers of [(CO3)M]- and [(CO3)M2] (M = Li or Na), as well as of [(CO3)Na3]+, confirm) that, except in isomers of [(CO3)M]- (M = Na or K; M ≠ Li)
25
that exhibit perpendicular bonding, the CO3 moiety remains planar in the aggregates, although angular distortions are common. Only one- and/or two-coordination of the alkali metal occurs in [(CO3)My]y-2 up to y = 5. In the two planar isomers of [(CO3)Li3]+, one with all bidentate bonding to Li, and one with all monodentate bonding to Li, Li-O distances may be compared directly and are Li-O1-coordinate Li < Li-O2-coordinate Li, although the corresponding C…Li distances are then 2-coordinate Li < 1-coordinate Li. The maximum number of M atoms coordinated to a single O atom in [(CO3)My]y-2 is three. Like the most stable forms of [(CO3)M2] (M = Li or Na), the K-containing analogue is planar and contains only bidentately-coordinated K. Likewise, as is the case for [(CO3)Na3]+, the most stable isomers of [(CO3)M3]+ (M = Li or K) are planar and contain only bidentately-coordinated Li or K. The planar form of [(CO3)M]- (M = Na or K) is more stable than its isomer containing perpendicularly-bonded M. For [(CO3)M2] and [(CO3)M3]+ (M = Li or Na; M ≠ K) less stable non-planar isomers exist (for M = Li, in addition to the less stable planar isomer [C(-O-Li)3]+ (see preceding)). Both isomers found for [(CO3)Li4]2+are planar, while the single form of [(CO3)K4]2+ and all three isomers of [(CO3)Na4]2+ are non-planar. However, the two isomers of [(CO3)M5]3+ are non-planar for all three metals. While no evidence was found for any [(CO3)M6]3+, the formation of all forms of [(CO3)M5]3+ (and of [CO3)M4]2+ from CO32- and M+ are exothermic overall. Charges calculated by the Atoms in Molecules (6) method show that the positive charge on M in the aggregates studied was 0.60 or higher: bonding in all these M+:CO32- aggregates has high ionic character. The AIM charges on O in the complexes are influenced by the extent to which the O atoms are coordinated.
26
Acknowledgments I am grateful to Dr. Gary D. Willett of UNSW for the loan of his GAUSSIAN and GAUSSVIEW software, Dr. Todd A. Keith for providing copies of AIMAll Standard, and Professors Charkin and McKee for providing copies of their papers in English translation. I thank the reviewers of this paper for several interesting and useful suggestions.
27
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D.A. Palmer and R. Van Eldik, Chem Rev. 83 (1983) 651.
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R.F.W. Bader, Monatsch. Chem.136. (2005) 819.
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O.P. Charkin and M.L McKee, Russ. J. Inorg. Chem. 43 (1998) 548.
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D.O Charkin, M.L. McKee and O.P. Charkin, Russ. J. Inorg. Chem. 43 (1998) 1572.
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T. Shi, J. Zhao, I. Shek, A.C. Hopkinson and K.W.M. Siu, Can. J. Chem, 83 (2005) 1941.
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M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J.Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W.
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Wong, C. Gonzalez, J.A. Pople, GAUSSIAN 03, Revision D.01, GAUSSIAN, Inc., Wallingford, CT, 2004. 8.
R. Dennington II, T. Keith, J. Millam, K. Eppinnett, W.L. Hovell, R. Gilliland, Semichem, Inc., Shawnee Mission, KS, 2003.
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Gaussian 03 Online Manual, http://www.lct.jussieu.fr/manuels/Gaussian03/g_ur/g03mantop.htm, accessed 2016_11_02.
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http://timn.ho.ua/ccs/bsse.htm, accessed 2017_01_16.
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18.
AIMAll (Version 16.01.09, Standard or 17.01.25 Standard), Todd A. Keith, TK Gristmill software, Overland Park KS, USA, 2013 (aim.tkgristmill.com).
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M.C. Durrant, Chem. Sci, 6 (2015) 6614.
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29
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M.J.S. Dewar and Y.-J. Zheng, J. Mol. Struct. (THEOCHEM), 209 (1990) 157; R.E.Dinnebier, S. Vensky, M. Panthöfer and M. Jansen, Inorg. Chem. 42 (2003) 1499; D.A. Reed and M.M. Olmstead, Acta Crystallogr., Sect. B 37 (1981) 938; B. Beagley and R.W.H. Small, Acta Crystallogr. 17 (1964) 783.
S30 Table 1. Calculated Bond Distances (Å), Bond angles (°) and AIM charges for CO32- and Some Structures 1-1-1-M and 1-1-2-M .a CO32- b
Structure 1-1-1-M c
Structure 1-1-2-Md
__________________________________________ M=
----
Lib
Nab
K
Ke
Rbf
Na
K
Kg
C(1)-O(2)
1.31(1.285)f
1.24(1.222)
1.25(1.232)
1.26
1.26
1.26
1.31
1.30
1.31
C(1)-O(3)
1.31(1.285)
1.35(1.315)
1.34(1.310)
1.33
1.33
1.33
1.31
1.30
1.31
C(1)-O(4)
1.31(1.285)
1.35(1.315)
1.34(1.310)
1.31
1.33
1.33
1.31
1.30
1.31
2.07(2.072)
2.44(2.443)
2.83
2.80
3.00
2.07
2.46
2.40
2.36
2.70
2.64
Bond lengths
C(1)…M(5) O(2)-M(5) O(3)-M(5)
1.75(1.746)
2.09(2.075)
2.43
2.39
2.57
2.36
2.70
2.64
O(4)-M(5)
1.75(1.746)
2.09
2.43
2.39
2.57
2.36
2.70
2.64
S31 Bond Angles O(2)-C(1)-O(3)
123.0
121.4
123.7 121.5 121.4
119.3 119.6 119.4
O(2)-C(1)-O(4)
123.0
121.4
118.4 121.5 121.4
119.3 119.6 119.4
O(3)-C(1)-O(4)
114.1(113.8) 117.2(116.3) 117.9 117.0 117.1
119.3 119.6 119.4
O(2)-M(5)-O(3)
57.2
49.0
50.6
O(2)-M(5)-O(4)
57.2
49.0
50.6
57.2
49.0
50.6
61.2
65.2
64.8
O(3)-M(5)-O(4)
80.5
66.6
55.5
56.9
52.5
C(1)-O(2)-M(5) C(1)-O(3)-M(5)
82.7(84.0)
88.1(89.4)
93.5
93.1
95.2
61.2
65.2
64.8
C(1)-O(4)-M(5)
82.7
88.2
93.0
93.1
95.2
61.2
65.2
64.8
S32 AIM Charges C(1)
2.21
2.18
2.18
2.24
O(2)
-1.40
-1.31
-1.30
-1.25 -1.31
-1.34 -1.27 -1.26
O(3)
-1.40
-1.38
-1.33
-1.24 -1.30
-1.34 -1.27 -1.26
O(4)
-1.40
-1.38
-1.33
-1.34 -1.30
-1.34 -1.27 -1.26
0.89
0.78
0.60
M(5)
2.19
0.73
2.15
0.88
0.88
2.23
0.58
2.18
0.62
a
This work unless otherwise specified.
b
Parenthesized data are from Ref. 4 in which optimized structures were calculated at the HF/6-31G* level, assuming D3h symmetry for CO32- and C2v symmetry for (OCO2)M-.
c
Without symmetrization except as noted.
d
With constrainment, initially, to C3v symmetry, and using quadratically-convergent SCF for 1-1-2-K.
e
With imposed C2v symmetry and using quadratically-convergent SCF.
f
Atomic coordinates and AIM charge from Ref. 17.
S33 g
With imposed C3v symmetry and using quadratically-convergent SCF.
S34 Table 2. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M2 (M = Li-K)a,b Structure 1-2-1-M
Structure 1-2-2-Mc
_____________________________________
_____________________
Li
Na
K
Li
Na
C(1)-O(2)
1.37(1.331)
1.36(1.325)
1.35
1.22
1.23
C(1)-O(3)
1.27(1.251)
1.28(1.257)
1.28
1.37
1.36
C(1)-O(4)
1.27
1.28
1.28
1.37
1.36
C(1)…M(5)
2.13(2.132)
2.49(2.495)
2.86
2.07
2.37
C(1)…M(6)
2.13
2.49
2.85
2.07
2.37
O(2)-M(5)
1.82(1.830)
2.14(2.154)
2.49
O(3)-M(5)
1.82(1.811)
2.13(2.121)
2.43
1.88
2.21
1.88
2.21
M= Bond lengths
O(4)-M(5)
S35 O(2)-M(6)
1.82(1.830)
2.14(2.154)
2.48
O(3)-M(6)
1.88
2.21
O(4)-M(6)
1.82(1.811)
2.13(2.121)
2.43
1.88
2.21
M(5)…M(6)
3.61
4.29
4.97
2.56
3.33
O(2)-C(1)-O(3)
116.3(116.4)
117.9(117.8)
118.5
126.4
124.1
O(2)-C(1)-O(4)
116.3
118.0
118.5
126.4
124.0
O(3)-C(1)-O(4)
127.5
124.1
123.1
107.2
111.9
O(2)-M(5)-O(3)
76.2
63.9
54.8 72.0
61.0
71.9
61.0
Bond Angles
O(3)-M(5)-O(4) O(2)-M(6)-O(4) O(3)-M(6)-O(4)
76.2
63.9
54.8
S36 AIM Charges C(1)
2.21
2.18
2.22
2.06
2.09
O(2)
-1.38
-1.35
-1.33
-1.23
-1.26
O(3)
-1.33
-1.32
-1.32
-1.34
-1.32
O(4)
-1.33
-1.32
-1.32
-1.34
-1.32
M(5)
0.92
0.90
0.88
0.92
0.90
M(6)
0.92
0.90
0.88
0.92
0.90
a
Parenthesized data are those of Ref. 5 for a C2v structure obtained using HF/6-31G*
b
For comparison, the calculated C-O distances and O-C-O angles of free CO32- in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
c
Not found for M = K.
S37 Table 3. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M3+ (M = Li-K)a,b Structure M=
1-3-1-M Li
Na
1-3-3-Mc
1-3-2-M K
Li
Na
Li
_____________________
_______________
_______________
C(1)-O(2)
1.29
1.30(1.290)
1.30
1.24
1.25
1.28
C(1)-O(3)
1.29
1.30
1.30
1.37
1.36
1.28
C(1)-O(4)
1.29
1.30
1.30
1.30
1.30
1.28
C(1)…M(5)
2.20
2.55
2.93
2.22
2.57
2.95
C(1)…M(6)
2.20
2.55
2.93
2.18
2.48
2.95
C(1)…M(7)
2.20
2.55
2.93
2.18
2.48
2.95
O(2)-M(5)
1.92
2.21(2.225)
2.54
1.88
2.18
1.67
O(3)-M(5)
1.92
2.21
2.54
1.97
2.27
Bond lengths
S38 O(3)-M(6)
2.03
2.37
1.67
O(2)-M(6)
1.92
2.21
2.54
O(4)-M(6)
1.92
2.21
2.54
1.94
2.24
O(3)-M(7)
1.92
2.21
2.54
2.03
2.37
O(4)-M(7)
1.92
2.21
2.54
1.94
2.24
1.67
M(5)…M(6)
3.81
4.42
5.08
3.65
4.23
5.11
M(5)…M(7)
3.81
4.43
5.07
3.65
4.23
5.11
M(6)…M(7)
3.81
4.43
5.07
2.70
3.39
5.11
Bond Angles O(2)-C(1)-O(3)
120.0 120.0
120.0
119.1
120.0
120.0
O(2)-C(1)-O(4)
120.0 120.0
120.0
130.0
125.9
120.0
O(3)-C(1)-O(4)
120.0 120.0
119.9
110.9
114.1
120.0
O(2)-M(5)-O(3)
71.6
52.7
71.7
61.1
61.1
S39 O(2)-M(6)-O(4)
71.6
61.1
52.7
O(3)-M(6)-O(4) 61.1
67.4
57.9
67.3
57.9
76.9
86.1
2.24
2.14
2.15
2.36
-1.33
-1.28,-1.37,
-1.28,-1.34,
-1.40
-1,33
-1.32
0.94
0.94,0.94,
O(3)-M(7)-O(4)
71.6
52.6
M(5)-O(2)-M(6)
168.4 178.9(179.7) 172.91
M(5)-O(3)-M(7)
168.4 178.8
172.5
M(6)-O(4)-M(7)
168.4 178.9
172.6
M(6)-C(1)-M(7) AIM Charges C(1)
2.26
O(2),O(3),O(4)
-1.36 -1.34
M(5),M(6),M(7)
0.92
2.24
0.93
0.92
0.95
0.94
S40
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Parenthesized data are those of Shi et al (6) calculated using B3LYP/6-311G** for the D3h structure.
c
Not found for M = Na or K.
S41 Table 4. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M42+ (M = Li-K)a M=
Li
Na
K
___________________
_______________________________
_______________________
Isomer
1-4-1-Li
1-4-2-Li
1-4-1-Na
1-4-2-Na
1-4-3-Na
1-4-1-K
1-4-1-Kb
C(1)-O(2)
1.30
1.26
1.29
1.32
1.28
1.28
1.28
C(1)-O(3)
1.29
1.31
1.30
1.29
1.31
1.31
1.31
C(1)-O(4)
1.29
1.31
1.30
1.29
1.31
1.31
C(1)-M(5)
2.35
2.86
2.65
2.72
2.67
3.05
C(1)-M(6)
2.35
2.87
2.65
2.74
2.67
3.05
C(1)-M(7)
3.00
2.28
3.21
2.64
2.61
2.93
C(1)-M(8)
3.00
3.02
3.21
3.16
2.61
2.93
O(2)-M(5)
1.85
3.22
2.19
2.62
2.28
2.61
2.61
O(3)-M(5)
2.17
1.81
2.41
2.18
2.38
2.73
2.73
3.05
2.93
S42 O(2)-M(6)
1.85
3.24
2.19
2.66
2.28
2.61
O(4)-M(6)
2.16
1.80
2.41
2.18
2.38
2.72
O(3)-M(7)
1.79
1.92
2.14
2.29
2.42
2.73
2.42
2.73
2.41
2.73
2.14
2.42
2.74
O(4)-M(7)
1.93
2.29
O(2)-M(8)
1.76
2.19
O(3)-M(8)
2.73
O(4)-M(8)
1.79
M(5)…M(6)
3.70
5.70
4.36
4.84
4.55
5.17
5.17
M(5)…M(7)
3.55
3.50
4.06
4.37
4.40
4.97
4.97
M(5)…M(8)
5.34
4.34
5.61
4.03
4.41
4.97
M(6)…M(7)
5.33
3.50
5.60
4.37
4.40
4.97
M(6)…M(8)
3.54
4.34
4.06
4.05
4.40
4.97
M(7)…M(8)
4.31
5.30
4.65
5.50
3.44
4.10
4.10
S43 Bond Angles O(2)-C(1)-O(3)
117.7
122.6
119.1
119.8
121.5
121.2
121.1
O(2)-C(1)-O(4)
117.7
122.7
119.1
119.9
121.5
119.1
O(3)-C(1)-O(4)
124.6
114.7
121.8
120.3
117.0
117.7
117.8
O(2)-M(5)-O(3)
66.3
42.7
57.9
55.2
57.9
50.0
50.0
O(2)-M(6)-O(4)
66.4
42.2
57.9
54.5
57.9
50.1
O(3)-M(7)-O(4)
69.8
58.4
55.1
48.5
48.5
O(2)-C(1)-M(7)
177.2
179.9
138.7
135.8
135.7
O(2)-C(1)-O(8)
138.8
135.6
O(3)-M(8)-O(4)
55.1
48.4
83.2
85.3
83.2
85.2
174.1
165.1
C(1)-O(3)-M(7)
152.0
87.8
136.1
90.6
C(1)-O(4)-M(8) M(5)-O(2)-M(6)
170.6
123.9
168.7
132.8
85.2
165.1
S44 M(5)-O(3)-M(7)
126.8
139.6
M(6)-O(4)-M(7)
126.4
139.0
156.5
133.2
131.2
155.0
133.4
131.2
133.5
131.2
M(5)-O(3)-M(8) M(6)-O(4)-M(8)
126.8
126.4
133.4
131.3
M(7)-C(1)-M(8)
91.9
93.0
82.5
88.6
131.2
88.7
Dihedral angles O(2)-C(1)-O(3)-M(5) -0.3
0.1
11.8
-24.1
O(2)-C(1)-O(3)-M(7) 179.2
-180.0
-129.4
176.8
O(2)-C(1)-O(4)-M(6) 0.3
0.1
11.9
25.4
179.9
167.0
-157.9
O(4)-C(1)-O(3)-M(5) 179.6
-179.9
-168.2
153.7
O(3)-C(1)-O(2)-M(6) 179.6
180.0
166.8
157.2
O(3)-C(1)-O(4)-M(6) 179.6
179.6
168.0
179.9
O(4)-C(1)-O(2)-M(5)
-179.5
-134.1
-131.3
-131.2
179.8
179.9
180.0
179.9
179.9
S45 M(7)-C(3)-C(4)-M(8) 0.5
72.2
AIM Charges C(1)
2.31
2.32
2.26
2.24
2.20
---
---
O(2)
-1.35
-1.37
-1.33
-1.37
-1.32
---
---
O(3),O(4)
-1.38
-1.38
-1.36
-1.33
-1.34
---
---
M(5),M(6)
0.95
0.96
0.94
0.94
0.95
---
---
M(7),M(8)
0.96
0.94,0.96
0.95
0.94,0.95
0.95
---
---
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- calculated in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Symmetrized to C2v
S46 Table 5. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M53+ (M = Li-K)a
Isomer
1-5-1-M
1-5-2-M
_______________
_____________________
M=
Li
Na
K
Li
Na
K
Kb
C(1)-O(2)
1.33
1.33
1.33
1.32
1.31
1.31
1.31
C(1)-O(3)
1.28
1.29
1.29
1.29
1.29
1.30
1.30
C(1)-O(4)
1.28
1.29
1.29
1.29
1.29
1.30
1.30
C(1)-M(5)
2.38
2.71
3.05
2.86
3.15
3.54
3.53
C(1)-M(6)
2.38
2.71
3.09
2.87
3.14
3.36
3.36
C(1)-M(7)
3.09
3.42
3.78
3.08
3.40
3.75
3.76
C(1)-M(8)
3.09
3.42
3.77
3.08
3.40
3.75
3.76
S47 C(1)-M(9)
3.06
3.31
3.58
2.36
2.70
3.09
3.09
O(2)-M(9)
1.98
2.33
2.71
3.68
4.02
4.40
4.40
O(2)-M(5)
2.13
2.41
2.75
1.94
2.27
2.63
2.63
O(3)-M(5)
2.02
2.37
2.74
3.61
3.85
4.21
4.22
O(2)-M(6)
2.12
2.40
2.73
1.94
2.27
2.64
2.64
O(4)-M(6)
2.02
2.37
2.72
3.61
3.84
4.24
3.99
O(3)-M(7)
1.92
2.25
2.60
1.90
2.23
2.59
2.59
O(4)-M(8)
1.92
2.25
2.60
1.89
2.23
2.59
2.59
O(3)-M(9)
2.02
2.33
2.69
2.69
O(4)-M(9)
2.02
2.33
2.69
2.69
M(5)…M(6)
3.86
4.24
4.71
3.30
3.93
4.65
4.65
M(5)…M(7)
3.47
4.00
4.56
4.57
4.95
5.35
5.37
M(5)…M(8)
5.36
5.98
6.55
4.57
4.95
5.38
S48 M(5)…M(9)
3.39
3.96
4.62
4.99
5.53
6.33
6.31
M(6)…M(7)
5.37
6.02
6.80
4.57
4.95
5.43
5.39
M(6)…M(8)
3.47
3.99
4.53
4.57
4.96
5.38
M(6)…M(9)
3.39
3.94
4.57
4.99
5.51
5.84
5.86
M(7)…M(8)
4.34
4.73
5.16
6.00
6.69
7.40
7.41
M(7)…M(9)
5.47
5.83
6.06
3.44
3.94
4.49
4.49
M(8)…M(9)
5.48
5.90
6.49
3.44
3.94
4.49
Bond Angles O(2)-C(1)-O(3)
117.1 118.0 118.6
121.3 120.4 120.1 120.1
O(2)-C(1)-O(4)
117.1 118.1 118.8
121.3 120.4 120.0 120.1
O(3)-C(1)-O(4)
125.6 123.8 122.5
117.5 119.1 119.9 119.9
O(2)-M(5)-O(3)
65.1
56.1
48.5
O(2)-M(6)-O(4)
65.1
56.2
48.8
S49 O(3)-M(9)-O(4)
66.2
57.2
49.5
49.5
C(1)-O(3)-M(9)
88.2
91.9
95.3
95.3
C(1)-O(4)-M(9)
88.2
91.8
95.3
95.3
M(5)-O(2)-M(6)
116.4 119.7 123.9 124.0
C(1)-O(2)-M(9)
133.7 127.0 121.4
M(5)-O(2)-M(9)
111.4 113.5 115.8
M(6)-O(2)-M(9)
111.4 113.1 114.4
M(5)-O(3)-M(7)
123.0 120.1 117.5
M(6)-O(4)-M(8)
122.9 119.8 116.8
AIM Charges C(1)
2.27
2.24
---
O(2)
-1.38 -1.35 ---
2.27c 2.25
---
---
-1.34c -1.36 ---
---
S50 O(3),O(4)
-1.35 -1.34 ---
-1.38c -1.35 ---
---
M(5),M(6)
0.96
0.95
---
0.97c,d 0.96
---
---
M(7),M(8)
0.97
0.97
---
0.96c 0.96
---
---
M(9)
0.97
0.97
----
0.95c 0.95
---
---
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Symmetry constrained to Cs; Symmetry could not be constrained to C2v.
c
In (CO3)Na2(5,6)Li3 3+.
d
Na+ ions
S51
Table 6. Stepwise and Overall Complexation Energies of (CO3)My-1y-3 (y = 1-5) by M+ (M = Li, Na or K).a ∆E (kJ/mol) M Reactant 1b
Reactant 2
Productb
Li
Na
K
CO32-
+
M+
→
CO3M-
-1271 to -1049
-1075 to - 865
-886 to -682
CO3M-
+
M+
→
CO3M2
-728 to -669
-655 to -600
-573 to -537
CO3M2
+
M+
→
CO3M3+
-295 to -279
-300 to -290
-280 to -268
CO3M3+
+
M+
→
CO3M42+
108 to160
154 to164
127 to 138
CO3M42+
+
M+
→
CO3M53+
459 to 465
412 to 420
374 to 402
-1682 to -1424
-1454 to -1189
-1214 to -975
(Σ ∆E (kJ/mol)) =
a
Derived from the three different electronic energies of Tables S1AB-S1CB combined with the appropriate corrections from Table S1A-C.
b
For the most stable form found for the reactants and products.
S52
Highlights
A total of 23 new complexes of formula (CO3)Myy-2 (M = Li, Na or K) have been optimized using DFT: the coordination chemistry of the carbonate ligand with the metals Li, Na and K is much more extensive than previously imagined. Up to 5 M+ (M = Li, Na or K) ions can be added to one CO32- ion, a process that is exothermic overall. Except in the rare case of π-type bonding, the anion remains planar, but when y = 5 some out-of-plane bonding of the metal ions occurs for each of the three metal ions. When M = Li, isomeric structures were found for y = 2-5. When M = Na, isomeric structures were found for y = 1-5. When M = K, isomeric structures were found for y = 1 and 5.
S53
Graphical Abstract
(CO3)Na3+
Na+ ——► 1-4-1-Na
1-4-2-Na
1-4-3-Na
S0020-1693(17)30714-4 http://dx.doi.org/10.1016/j.ica.2017.09.015 ICA 17871
To appear in:
Inorganica Chimica Acta
Received Date: Revised Date: Accepted Date:
5 May 2017 2 September 2017 6 September 2017
Please cite this article as: P.A. Dean, The Not-so-Simple Coordination Chemistry of Alkali-Metal Cations Li+, Na and K+ with One Carbonate Anion: a Study Using Density Functional and Atoms in Molecules Theories, Inorganica Chimica Acta (2017), doi: http://dx.doi.org/10.1016/j.ica.2017.09.015 +
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1
The Not-so-Simple Coordination Chemistry of Alkali-Metal Cations Li+, Na+ and K+ with One Carbonate Anion: a Study Using Density Functional and Atoms in Molecules Theories.§
Philip A.W Dean* Department of Chemistry University of Western Ontario London, Ontario N6A 5B7 Canada
*E-mail: [email protected]; phone: 519-661-2111 Ext 86331 §
Dedicated to the memory of Professor Mehdi Rashidi, Shiraz University Chemistry
Department.
2
Abstract A total of 23 new complexes in the series (CO3)Myy-2 (M = Li, Na or K; y = 1-5) have been optimized using DFT, adding to known planar complexes (CO3)Myy-2 (M = Li or Na; y = 1 or 2) and (CO3)Myy-2 (M = Na; y = 3). Planar structures are the most stable for: M = Li, y = 1-4; M = Na, y = 1-3; M = K, y = 1-3. For M = Na, three non-planar structures occur over a range in electronic energy of ca. 9 kJ/mol when y = 4, while for M = K only a single, non-planar structure occurs for y = 4. For M = Li, Na or K, two non-planar structures were the only ones found for y = 5. The CO3 moiety was found to be planar in all new species except for new isomers of (CO3)M- (M = Na or K) that have perpendicular (π-like) CO3:M bonding. No evidence was found for any stable species when y = 6. Atomic charges were calculated by the AIM method for most of the new species and confirm that the CO3 : M bonding is highly ionic. Stepwise complexation energies have been calculated for the addition of M+ to the most stable form of (CO3)My-1y-3 to give the most stable form of (CO3)Myy-2, for y = 1 - 5. The stepwise formation reactions are exothermic for all the metals when y = 1 - 3, but endothermic for all the metals when y = 4 or 5. However, addition of four or five M+ to one CO32- is exothermic overall for all three metals.
3
Keywords
Lithium ion coordination by carbonate anion
Sodium ion coordination by carbonate anion
Potassium ion coordination by carbonate anion
Alkali-metal ion coordination by carbonate anion
DFT of alkali-metal ion-carbonate anion complexes
AIM charges of alkali-metal-carbonate anion complexes
4
Graphical Abstract
(CO3)Na3+
Na+ ——► 1-4-1-Na
1-4-2-Na
1-4-3-Na
5
Introduction
In 2001, Hao and March (1) used electrospray ionization tandem mass spectrometry to detect a very wide range of gaseous unsolvated aggregates of sodium ions and carbonate ions when using an aqueous solution of Na2CO3 as the analyte. Species of the form [(CO3)xNay]z were detected for x = 1–28, z = +1; x = 15–51, z = +2; x = 1-25, z = -1; x = 9-43, z = -2; x = 19-63, z = -3. To date, there has been no systematic study of possible structures for these intriguing aggregates, although the known polyfunctional ligand behaviour of CO32- (2) suggests that interesting, possibly new structural features may occur in the Na+:CO32- aggregates. The Na+ cation is relatively light, and CO32- is one of the lightest polyatomic ligands, so combinations of the two should be quite amenable to calculations of structure.
Two fundamental questions arise in considering possible structures of [(CO3)xNay]z: How many Na+ ions can bind to a single CO32- anion, and how do they bind? How might multiple CO32- anions be linked when x ≥ 2? In this paper I have attempted to answer the first question in a survey of aggregates that occur when x = 1, most relevantly for M = Na+, but also, following rather unusual structures found for (CO3)Na42+ (vide infra), for Li+ and K+. In so doing, I have completed the structural characterization of the series (CO3)Mxx-2 ((M = Li, Na or K; x = 1-5). For most of the complexes I have calculated charges on the non-metal and alkali metal atoms using the Atoms in Molecules (AIM) method (3).
6
There have been previous calculational studies of planar (CO3)M- (M = Li or Na) (4), (CO3)M2 (M = Li or Na) (5) and (CO3)Na3+ (6), all containing exclusively bidentatelycoordinated M centres (c.f. structures of 1-1-1-M, 1-2-1-M and 1-3-1-M in the Results and Discussion below).
A second paper will provide results relevant to the second question presented above.
Experimental
DFT calculations were performed on a desktop computer using GAUSSIAN 03W, Version 6.1 (7). GAUSSVIEW 4.1 (8) was used as the user interface. As in a previous study (9), the functional was B3LYP (10-13), the basis set was 6-31G(d,p), and default convergence criteria were usually used. (The B3LYP: 6-31G(d,p) combination is known to provide acceptable structural data with efficient use of computational resources (14).) In cases where quadratically-convergent SCF was used, this is specifically mentioned; similarly, symmetry was applied only where specifically mentioned. The K+ cation, used in some comparison complexes, is just at the end of the range of atoms for which the 631G(d,p) basis set is appropriate (14), but this basis set was used throughout this work, for consistency. In our earlier study (9), the B3LYP:6-31G(d,p) combination was found to provide acceptable, consistent structural data for Na+-containing complexes of [Fe(CN)5(NO)]2- (NP2-) up to [(NP)2Na6]2+. The CO32- ion is much lighter than the NP2ion, 60.0 vs. 215 g/mol, so it can be anticipated that the B3LYP:6-31G(d,p) combination
7
will allow structural calculations for [(CO3)xNay]z to be carried out to a larger value of x than the limit of x = 2 (for [(NP)2Na6]2+) in the previous work.
For each structure optimized in this work, the vibrational spectrum was calculated using GAUSSIAN, as a check on the authenticity of the structure and to provide the zero point vibrational energy (ZPE). Complexes with one negative frequency were re-optimized after the structure was moved along the negative vibrational coordinate, as usual. Complexes with more than one negative frequency were abandoned. Vibrational frequencies for all the complexes authenticated are given in Tables S1AC-S1CC of the Supplemental Material.
Using GAUSSIAN, the basis set superimposition error (BSSE) (15) was also calculated for each optimized structure, following the procedure given in Refs. 14 and 16. Thus, for example, the BSSE for the formation of a particular isomer of [(CO3)Na3]+ from CO32and 3 Na+, was treated as a 4-particle (1 CO32- and 3 Na+) problem, by setting the command Counterpoise=4 in GAUSSIAN. (Some manual insertion into the GAUSSIAN input file is required, c.f. Refs. 14 and 16).
Calculated optimized electronic energies for Na-containing species containing one CO32-, each with their associated ZPE, are given in Table S1A (Supplemental Material), together with relative energies of isomers based on electronic energy-plus-ZPE combinations. Also included in the Table is the value of the BSSE for each species (for formation of [(CO3)Nay]y-2 from CO32- and y Na+). The parallel data for species
8
containing Li, and species containing K, are given in Tables S1B and Table S1C. Calculations of ZPE in GAUSSIAN are known to yield approximate results (via a specific warning in the output file), as are calculations of BSSE (by the Counterpoise Method for finite basis sets).
As a check on the relative electronic energies calculated for authenticated species using B3LYP:6-31G(d,p), two other functional:basis-set combinations were used to calculate single-point energies for structures that had been optimized using B3LYP:6-31G(d,p) (and authenticated): B3LYP:6-311G**, containing a better basis set (14), and B3PW91:6-31G(d,p), containing a better functional (17). The energies so calculated are given in Supplementary Material as Tables S1AB, S1BB and S1CB. For each of the three metals, the three sets of calculated relative electronic energies are generally in good agreement, with very few exceptions. It is especially re-assuring that with only two exceptions, all three calculations are in agreement over the structure with the minimum electronic energy for a particular stoichiometry, when several isomers occur. The exceptions, CO3Na53+ and CO3K53+, are cases where isomers are particularly close in energy.
Relative energies specifically included in the text are electronic energies, E, calculated using B3LYP:6-31G(d,p) with ZPE values added.to give corrected energies, ECorr,, i.e. data from column 4 of Tables S1A-C. Table 6 contains energy ranges calculated using (a) ECorr values from Tables S1AB-CB, together with the corresponding BSSE data from the Tables, and (b) corresponding values found by combining other electronic energies
9
in Tables S1AB-S1CB with the appropriate ZPE and BSE values from Tables 1A-C. Then, for example, for the energy change occurring in the reaction CO3M2 + M+ → CO3M3+ ∆E = [ECorr +BSSE](for CO3M3+) – [{ECorr +BSSE}(for CO3M2) + E(for M+)].
The structures of the simple complexes CO3M- containing bidentate CO32- were difficult to optimize directly from a starting structure containing bidentate CO32-, (CO3-O,O’)2-. The structures for M = Li and Na were optimized from starting complexes with monodentate CO32-. The complex with M = K was optimized starting with the moiety (CO3-O,O’)K- left behind after one CO32- is removed from [(CO3-O,O’)2K]3- (P.A.W. Dean, unpublished work). To obtain a symmetrical (C2v) structure for (CO3-O,O’)K-, the symmetry had to be constrained, and quadratically-convergent SCF used.
Atomic charges were calculated using AIMAll Version 16.01.09, Standard or Version 17.01.25 Standard (18). Charges calculated by the AIM (Atoms in Molecules) method are derived from electron densities, which are experimentally observable, in principle (3). The input data for the AIMQB sub-program of AIMAll were formatted checkpoint (.fch) files. These were obtained via the checkpoint files (.chk) resulting from the GAUSSIAN calculations by use of the FormChk utility of GAUSSIAN. Durrant (19) has noted that AIM charges are relatively insensitive to the choice of quantum method used to obtain a structure. In this context it is worth noting that AIM charges are quite sensitive to the difference between the unsymmetrized and symmetrized structures of (CO3-O,O’)K-, though less so for its non-planar isomer (Table 1). The AIMQB
10
calculation for Structure 1-5-2-Li (see below) failed, and this structure was approximated by the 1-5-2-M structure of (CO3)Li3Na23+ with the two Na atoms in positions 5 and 6, the positions that were the problem area for the fully lithiated structure. (For consistency, the same conditions were used for all the AIM calculations, and so no attempt was made to find alternative, satisfactory conditions for the calculation of charges, etc., for 1-5-2-Li.) The AIM charges on Na(5) and (6) in (CO3)Li3Na23+ are essentially identical to the corresponding charges in the fully sodiated analogue, so it seems reasonable to assume that the AIM charges on Li(7-9) are acceptable representations of the AIM charges on same metal centres in 1-5-2-Li also.
The versions of AIMAll that were used were range-limited by the software supplier, and (CO3)K42+, as well as (CO3)K53+, apparently fell outside the range for which calculations could be completed. The AIM charges for the lithiated and sodiated analogues have AIM charges ≥ 0.94, so it can be expected that AIM charges on K in (CO3)K42+ and (CO3)K53+ will also be very highly positive, approaching unity.
Particular structures are represented by the notation x-y-w-M, where x = number of CO32- (1 in this paper), y = number of M+, w = isomer number, and M is used generically, or replaced by the symbol for a particular alkali metal. Thus, for example, 1-5-2-M might refer to Isomer 2 of (CO3)M53+ with at least two different metals M, while Isomer 2 of (CO3)Li53+ would be 1-5-2-Li. Detailed sets of calculated structural data for stoichiometries CO3M2, (CO3)M3+, (CO3)M42+ and (CO3)M53+, are provided in Tables S2, S3, S4 and S5 of Supplemental Material, respectively.
11
In the figures, the colours used are: C, grey; O, red; alkali metal, purple. Results and Discussion.
Structures with one M+. For this stoichiometry a total of two structures were found: 11-1-M and 1-1-2-M:
1-1-1-M
1-1-2-M
Calculated structural parameters, and AIM charges, are given in Table 1. Structure 1-11-M, of ideal C2v symmetry, was found for M = Li, Na or K. No symmetrization was necessary in this work to obtain C2v structures for 1-1-1-Li or 1-1-1-Na. However, the optimized structure found for 1-1-1-K in the absence of applied symmetry was of Cs rather than C2v symmetry. Constrainment was necessary to obtain the C2v structure, and it was found necessary to use quadratically-convergent SCF to optimize this symmetrized structure. The electronic energy for 1-1-1-K under the latter conditions was 7 kJ/mol less negative than the corresponding energy obtained by simple optimization, a barely significant difference. Previous results are available for 1-1-1-Li
12
and 1-1-1-Na, albeit with different functionals and basis set (4). (Data for 1-1-1-Rb have also become available recently (17), and are included in Table 1 for comparison). Structural parameters calculated here for 1-1-1-Li and 1-1-1-Na agree with those of Ref. 4 to within 0.04 Å or better on bond lengths and within 1.3 ° or better on bond angles, as shown in Table 1. The Na-O bond distances in 1-1-1-Na and 1-1-2-Na (Table 1), 2.09 and 2.36 Å, may be compared with distances found in the crystal structure of Na2CO3.H2O (18), in which monodentate Na-O distances were found to range from 2.293(2) – 2.491(2) Å, and bidentate Na-O distances to range from 2.508(2) – 2.822(2) Å. However, in comparing Na-O distances in the hydrated salt with distances calculated for (gaseous unsolvated) 1-1-1-Na and 1-1-2-Na it is important to note that in the hydrated salt both crystallographically-distinct Na atoms exhibit 6-coordination, which is expected to lead to larger Na-O distances. (In addition, “lattice effects” may be important.)
Structure 1-1-2-M has not been reported previously for CO32- - containing species, although a C3v structure was considered for the related LiNO3 (4). In the current work, Structure 1-1-2-M was found for M = Na or K, but not for M = Li. A unique feature of the structures 1-1-2-Na and -K, not found in any other species discussed in this paper, is that in both complexes the CO32- anion is significantly non-planar, being concave on the side of the anion that faces M. For M = Na, 1-1-2-Na is less stable than 1-1-1-Na by over 60 kJ/mol, while for M = K, 1-1-2-K is less stable than 1-1-1-K by over 20 kJ/mol.
13
The data in Table 1 show that bidentate coordination of CO32- to Li+-Rb+ in Structure 11-1-M lengthens the C-O bonds involving the O atoms involved in the coordination, while shortening the C-O bond involving the uncoordinated O atom. The effect is most pronounced in the length of the latter bond, although the variation of this bond distance with variation in M is slight, 1.24-1.26 Å. It is interesting that for all the structures 1-1-1M in Table 1, the weighted average C-O bond length is within 0.01 Å of the C-O value in free CO32-. The bite angle of the ligand in 1-1-1-M is smallest when M = Li, 114.1 °, but plateaus when M = Na-Rb, the range here being 117.1-117.9 ° at most. Other distances vary as expected with variation in M+.
The AIM charges calculated for 1-1-1-M and 1-1-2-M (Table 1) show that the bonding in all the species is largely ionic, as expected, the positive charge on M being ≥ 0.60. The relative order of the positive charges on the metal, Li > Na > K, is counterintuitive (since the smallest cation, Li+, is expected to be most polarizing, and the largest cation, K+, the least polarizing), and awaits explanation. The overall charge on the CO32- ions becomes less negative, consistent with the charges of less than unity found for the metal ions. Within the CO3 moieties, the changes in the positive AIM charges on the C atoms are relatively small, the overall reduction in negative charge of CO32- mainly occurring mainly through a reduction of weighted average negative charge on the O atoms. Changes (in a positive direction) in the negative charges on individual O atoms in the complexes are in the order O(2) > O(3,4), at least when M = Li or Na:. Thus, most negative charge is withdrawn from the uncoordinated O atom. This is consistent with the shortening found for the C(1)-O(2) bond lengths, compared with the
14
corresponding C(1)-O(3) and -O(4) bond lengths. The significant difference in AIM charges on K in 1-1-1-K with and without imposed symmetry has already been commented on.
Structures with two M+. Two structures were found for this stoichiometry, 1-2-1-M and 1-2-2-M:
1-2-1-M
1-2-2-M
Selected calculated structural parameters and AIM charges for both structures are given in Table 2. Structure 1-2-1-M, of ideal C2v symmetry, has been described previously for M = Li and Na, albeit using a different functional and basis set (5), and present results agree closely with the earlier work. In the present study, no symmetrization was necessary to optimize the new K compound for this stoichiometry, unlike the case of CO3K- above.
It is interesting that although all three O atoms are involved in bonding in Structure 1-21-M, only the C(1)-O(2) bond, in which the O(2) atom is bonded to two M+ ions, is
15
increased in length compared with the C-O distances of CO32- itself. The C(1)-O(3) and C(1)-O(4) bonds, in which the O atoms are linked to only one M+ ion, are shortened: As a generality, more highly coordinated O atoms are associated with longer C-O bonds. Overall, the weighted average C-O distances are again within 0.01 Å of the value in free CO32-. The AIM charges on the O(2) atoms in the three compounds 1-2-1-M are more negative than those on their O(3) and O(4) counterparts: the more highly coordinated O atom retains more negative charge. Overall, the AIM charges are consistent with very ionic M+ to CO32- bonding. The positive AIM charges on the metal centres in 1-2-1-M are again Li > Na > K, although the differences are smaller than those found for 1-1-1-M and 1-1-2-M. For all three complexes 1-2-1-M, however, the charges on M are more positive than for their counterparts in 1-1-1-M and 1-1-2-M, as expected for addition of more positive charge in going from 1-1-1-M and 1-1-2-M to 1-2-1-M.
Structure 1-2-2-M, found for M = Li or Na, but not for M = K, is new. For M = Li, this structure is less stable than 1-2-1-Li by ca.130 kJ/mol, and similarly, 1-2-2-Na lies ca. 100 kJ/mol above 1-2-1-Na. In Structure 1-2-2-M, both M atoms are bound in a bidentate manner to the same two O atoms of CO32-, both M atoms being out of the plane of the anion. As is the case for the C-O(2) of 1-2-1-M, in which O(2) is attached to two M atoms also, in 1-2-2-M the C-O bonds to O(3) and O(4) are lengthened compared with the C-O bonds of CO32-; O(2) in 1-2-2-M is uncoordinated and correspondingly the C-O(2) bond length is shortened compared with CO32-. The weighted average bond length in 1-2-2-M is 1.32 Å for both M = Li and M = Na, which can be compared with the 1.31 Å in CO32- itself. As in 1-2-1-M, the AIM charge on M in
16
1-2-2-M is slightly more positive for M = Li than for M = Na. With regard to the AIM charges on the O atoms of 1-2-2-M, the charges are in the relative order O(2) less negative than O(3,4), as found for 1-2-1-M, above, a species that also has an uncoordinated O(2).
The relative instability of 1-2-2-M compared with 1-2-1-M, suggests that either out-ofplane bonding is less favorable than in-plane, or that bi-coordination of M at a single O is less favorable than mono-coordination, or both. The structure of 1-3-2-M, following, suggests the former. It is worth noting that for M = Li and Na, Structure 1-2-2-M pushes the metal ions into closer proximity than in 1-2-1-M: 2.56 vs. 3.61 Å for M = Li, and 3.33 vs. 4.29 Å for M = Na. The AIM charges on the metal centres for 1-2-2-M are ≥ 0.90 (Table 20), so positive:positive repulsions may also contribute to the relative instability of these isomers.
Structures with three M+. For all three metal ions, the most stable structure found, 13-1-M, without the need for any symmetrization, was close to the D3h structure found by Siu and co-workers for the case that M = Na with a different basis set (6). Selected calculated structural data, and AIM charges, are given in Table 3, and show the expected trends with change in the alkali-metal cation. In the case of 1-3-1-M, there is insignificant change in the AIM charges on M with change in the alkali metal (Table 3).
17
1-3-1-M
1-3-2-M
1-3-3-Li
For M = Li , two isomers of 1-3-1-Li were found, 1-3-2-Li and 1-3-3-Li, while for M = Na, just one isomer of 1-3-1-Na was found, 1-3-2-Na. However, no isomers of 1-3-1-K were found. For M = Li, the two isomers were less stable than 1-3-1-Li, by ca. 130 kJ/mol, while for M = Na, 1-3-2-Na was less stable than 1-3-1-Na by ca. 120 kJ/mol.
Structure 1-3-2-M may be recognized as Structure 1-2-2-M to which a third M has been added at a vacant, in-plane, bidentate site. The Structure 1-3-2-M allows a comparison of bidentate O-M bonding distances in the plane of the CO32- with bidentate bonding distances out of the plane of the anion: r(O-Min-plane,ave) < r(O-Mout-of-plane) is found. However, the average value of r(O-Min-plane,ave), i.e. r(O-M(5)ave), is very close to the corresponding distance in 1-3-1-M. This latter observation suggests the tridentate bridging to M found for O(3) in 1-3-2-M, compared with the bidentate bridging (only) found at O in 1-3-1-M, is not strongly destabilizing. Thus, the out-of-planar bonding to M(6) and M(7), rather than the tridentate bridging by O, is the major factor destabilizing 1-3-2-M vs. 1-3-1-M.
18
For 1-3-2-M, the shortness of the M(6)…M(7) distance compared with the M..M distance in the corresponding 1-3-1-M is noteworthy: for M = Li, 2.70 vs. 3.81 Å; for M = Na, 3.39 vs. 4.43 Å, and, as for 1-2-2-M (above), may contribute to the relative instability of 1-32-M.
Structures 1-3-1-Li and 1-3-3-Li (Table 3) allow a comparison of O-Li bond distances for bidentately- and monodentately-attached Li in species of the same overall charge. For this situation, r(O-Libidentate) > r(O-Limonodentate). However, in terms of C…Li distances, the order is 1-3-3-Li > 1-3-1-Li: bidentate bonding leads to more compact structures. Generalizing from the relative energies of 1-3-1-Li and 1-3-3-Li, it appears that bi-coordination of M is stabilizing compared with the mono-coordination of M.
With regard to the AIM charges in Table 4, it is interesting that the AIM charges on the O atoms of 1-3-2-M are O(2) > O(4) > O(3) consistent with the coordination numbers being one for O(2), two for O(4) and three for O(3). The overall range of AIM charges on O in 1-3-2-Li is -1.28 to -1.37, but smaller for 1-3-2-Na, -1.28 to -1.34.
A comparison of structural trends in the series 1-1-1-M - 1-2-1-M - 1-3-1-M is rewarding. Each of these complexes contains only bidentately-attached metal ions, with the metal ions exclusively in the plane of the CO32- anion. Observed trends along the series are that, for constant M: M-O distances increase with increasing number of metal ions, e.g. 2.09 – 2.21 Å for M = Na; C…M distances increase similarly, e.g. 2.44 – 2.55 Å
19
for M = Na; O-M-O angles decrease along the series, e.g. 66.6 – 61.1 ° for M = Na (Tables 1-3). The results are consistent with overall expansion as an increasing number of 1+ ions is added to CO32-. As expected on the same basis, for constant M, the positive AIM charge on M increases along the series; this effect is strongest for M = K (0.60 – 0.92) and weakest for M = Li (0.89 – 0.92). Likewise, the positive AIM charge on C increases across the series, e.g. 2.18 – 2.26 for M = Li. Remarkably, the average AIM charge on the O atoms changes little across the series for constant M, e.g. -1.32 to -1.33 for M = Na, as does the average C-O distance, e.g. 1.30-1.31 Å for M = Na.
Structures with four M+. The most stable structures found for this stoichiometry are 14-1-M/1-4-2-M (M = Li or Na) and 1-4-1-K (the only structure of this stoichiometry for M = K). There is a negligible difference in energy between structures 1-4-1-M and 1-4-2-M for M = Li or Na. Structure 1-4-3-Na (not shown) is very similar to 1-4-1-K, and lies a bare 9 kJ/mol above 1-4-1-Na, a borderline difference. Selected structural parameters for the various M4 species are given in Table 4, together with AIM charges.
20
1-4-1-Li
1-4-2-Li
1-4-1-Na (2 views)
1-4-2-Na
1-4-1-K
21
Structure 1-4-1-Li is planar and of close-to-C2v symmetry; it contains two Li atoms that are bound bidentately and two that are bound monodentately. As now expected, the OLi bond distances have the relative values r(O-Li)bidentate, ave > r(O-Li)monodentate. For 1-41-Na, the planar equivalent of 1-4-1-Li does not represent a minimum in the potential energy surface. Rather, 1-4-1-Na has a structure of C2 symmetry in which both bidentately- and the monodentately-bound Na atoms are out of the plane of the CO32anion, most markedly the monodentately-bound Na atoms.
Structure 1-4-2-Li is planar and of C2v symmetry. It contains only one clearly bidentately-coordinate Li centre, a difference from the two of 1-4-1-Li. In contrast, structure 1-4-2-Na is non-planar and of Cs symmetry: a “humming-bird-like” (or “mosquito-like”) structure. It contains three bidentately-bound Na centres, of which one is in the plane of the anion and two are out-of-plane, and one monodentately-bound Na. The relative Na-O distances are r(Na-O)monodentate < r(Na-O)bidentate, in-plane < r(NaO)bidentate, out-of-plane, ave . The relative dispositions of Na(5), Na(6) and Na(8) in 1-4-2-Na are similar to those of Na(5), Na(6) and Na(9) in 1-5-1-Na (below).
The out-of-plane twisting of the two distinct pairs of metal atoms in Structure 1-4-2-Na reaches its extremity in the structures of 1-4-1-K/1-4-3-Na, which (when symmetrized, for M = K) have C2v symmetry. Here there are four bidentately bound M atoms, two inplane and two out of plane. This leads to a distorted tetrahedron of M atoms surrounding the planar CO32- ion. In both 1-4-1-K and 1-4-3-Na, r(O-M)in-plane, ave < r(OMout-of-plane, ave), as found in several instances above also. The structural variation from
22
1-4-1-Li via 1-4-1-Na to 1-4-1-K/1-4-3-Na, where the alkali-metal environment of the relatively-undistorted, planar CO32- ion changes with alkali metal, is reminiscent of the structural variation observed in anhydrous metal oxalates in which the shape of the anion responds to change of the alkali metal (19). The shortness of the M(7)…M(8) distances , compared with the other M…M distances is noteworthy in 1-4-1-K/1-4-3-Na (Table 4).
In all of the species containing four M atoms, the AIM charge on the metal centres is ≥0.94, just slightly more positive than values found in (CO3)M3+. (Software limitations prevented calculation of AIM changes for (CO3)K4, as well as (CO3)K5 (below).) The AIM charges on O atoms are all less negative than the corresponding AIM charge in CO32- itself. The influence of differing coordination number can be seen, e.g. O(2) (3coordinate) of 1-4-2-Na is more negative than O(3,4) (2-coordinate), but the differences are quite small. The AIM charges on M and O are such that the positive charge on the C atom is, in most cases, slightly more positive than in the free CO32- anion.
Structures with five M+. For this stoichiometry, two different structures, 1-5-1-M and 15-2-M, were found for all three alkali metals, Li, Na and K. Selected structural parameters, and AIM charges, for all the complexes are given in Table 5. The complexes with M = K show the most noticeable deviations from what would appear to be ideal Cs symmetry for Structure 1-5-1-M and ideal C2v symmetry for Structure 1-5-2:M.
For all three metals, structures 1-5-1-M and 1-5-2-M are close in energy, the
23
largest difference being only 10 kJ/mol for M = Li, where structure 1-5-1-Li is less stable than 1-5-2-Li. Structure 1-5-2-Li represents the first instance in which the most stable structure for a particular stoichiometry (CO3)Liyy-2 is not planar.
1-5-1-M
1-5-2-M
The similarity between the dispositions of Na(5), Na(6) and Na(9) in 1-5-1-Na and the dispositions of Na(5), Na(6) and Na(8) in 1-4-2-Na (above) has already been noted above. In all the complexes shown in Table 5, the average C-O bond distance is 1.30 Å, within experimental error the same value found in free CO32-.
The AIM charges on the metal centres found for Structures 1-5-1-M (M = Li or Na) and 1-5-2-Na are ≥ 0.95, while all the corresponding charges on O are again less negative than for CO32- itself, and the positive AIM charges on C are slightly higher than in free CO32-. The effect of differing coordination number of O on the AIM charges on O is slight but present, e.g. in 1-5-1-M, O(2), 3-coordinate, is more negative than O(3,4), 2coordinate.
24
Attempts to produce (CO3)M64+. No stable species of this stoichiometry were found for any of the three alkali metals, despite several efforts. The highly charged starting structures dissociated in all cases, e.g. a starting structure produced by adding an extra Na+ between the Na(7) and Na(8) positions of 1-5-1-Na, dissociated to 1-3-1-Na and three free Na+. Similarly, a starting structure derived by replacing Na(9) with two monodentately-bound Na+ added to O(3) and O(4) of 1-5-2-Na, dissociated to (CO3)Na42+ plus two free Na+.
Stepwise and Overall Complexation Energies. These energies are detailed in Table 6, where the ranges were calculated as described in the Experimental Section. As expected, the stepwise complexation energies become progressively less exothermic as the product species contain more M moieties, and indeed the products CO3M42+ and CO3M53+ are formed endothermically (from CO3M3+ and CO3M42+, respectively) for all three alkali metals. Overall the energy change for the addition of a total of 4, or 5, M+ to CO32- is negative for all the metals, i.e. the exothermicity of steps 1-3 outweighs the endothermicity of step 4, or 4 plus 5, in all cases.
Conclusions DFT has been used to investigate systematically the structures of [(CO3)My]y-2 (M = Li, Na or K; y = 1-5). (There have been earlier investigations of the most stable forms of [(CO3)M]- (M = Li or Na) (3), [(CO3)M2] (M = Li or Na) (4) and [(CO3)Na3]+ (5).) Results show (or, for the most stable isomers of [(CO3)M]- and [(CO3)M2] (M = Li or Na), as well as of [(CO3)Na3]+, confirm) that, except in isomers of [(CO3)M]- (M = Na or K; M ≠ Li)
25
that exhibit perpendicular bonding, the CO3 moiety remains planar in the aggregates, although angular distortions are common. Only one- and/or two-coordination of the alkali metal occurs in [(CO3)My]y-2 up to y = 5. In the two planar isomers of [(CO3)Li3]+, one with all bidentate bonding to Li, and one with all monodentate bonding to Li, Li-O distances may be compared directly and are Li-O1-coordinate Li < Li-O2-coordinate Li, although the corresponding C…Li distances are then 2-coordinate Li < 1-coordinate Li. The maximum number of M atoms coordinated to a single O atom in [(CO3)My]y-2 is three. Like the most stable forms of [(CO3)M2] (M = Li or Na), the K-containing analogue is planar and contains only bidentately-coordinated K. Likewise, as is the case for [(CO3)Na3]+, the most stable isomers of [(CO3)M3]+ (M = Li or K) are planar and contain only bidentately-coordinated Li or K. The planar form of [(CO3)M]- (M = Na or K) is more stable than its isomer containing perpendicularly-bonded M. For [(CO3)M2] and [(CO3)M3]+ (M = Li or Na; M ≠ K) less stable non-planar isomers exist (for M = Li, in addition to the less stable planar isomer [C(-O-Li)3]+ (see preceding)). Both isomers found for [(CO3)Li4]2+are planar, while the single form of [(CO3)K4]2+ and all three isomers of [(CO3)Na4]2+ are non-planar. However, the two isomers of [(CO3)M5]3+ are non-planar for all three metals. While no evidence was found for any [(CO3)M6]3+, the formation of all forms of [(CO3)M5]3+ (and of [CO3)M4]2+ from CO32- and M+ are exothermic overall. Charges calculated by the Atoms in Molecules (6) method show that the positive charge on M in the aggregates studied was 0.60 or higher: bonding in all these M+:CO32- aggregates has high ionic character. The AIM charges on O in the complexes are influenced by the extent to which the O atoms are coordinated.
26
Acknowledgments I am grateful to Dr. Gary D. Willett of UNSW for the loan of his GAUSSIAN and GAUSSVIEW software, Dr. Todd A. Keith for providing copies of AIMAll Standard, and Professors Charkin and McKee for providing copies of their papers in English translation. I thank the reviewers of this paper for several interesting and useful suggestions.
27
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S30 Table 1. Calculated Bond Distances (Å), Bond angles (°) and AIM charges for CO32- and Some Structures 1-1-1-M and 1-1-2-M .a CO32- b
Structure 1-1-1-M c
Structure 1-1-2-Md
__________________________________________ M=
----
Lib
Nab
K
Ke
Rbf
Na
K
Kg
C(1)-O(2)
1.31(1.285)f
1.24(1.222)
1.25(1.232)
1.26
1.26
1.26
1.31
1.30
1.31
C(1)-O(3)
1.31(1.285)
1.35(1.315)
1.34(1.310)
1.33
1.33
1.33
1.31
1.30
1.31
C(1)-O(4)
1.31(1.285)
1.35(1.315)
1.34(1.310)
1.31
1.33
1.33
1.31
1.30
1.31
2.07(2.072)
2.44(2.443)
2.83
2.80
3.00
2.07
2.46
2.40
2.36
2.70
2.64
Bond lengths
C(1)…M(5) O(2)-M(5) O(3)-M(5)
1.75(1.746)
2.09(2.075)
2.43
2.39
2.57
2.36
2.70
2.64
O(4)-M(5)
1.75(1.746)
2.09
2.43
2.39
2.57
2.36
2.70
2.64
S31 Bond Angles O(2)-C(1)-O(3)
123.0
121.4
123.7 121.5 121.4
119.3 119.6 119.4
O(2)-C(1)-O(4)
123.0
121.4
118.4 121.5 121.4
119.3 119.6 119.4
O(3)-C(1)-O(4)
114.1(113.8) 117.2(116.3) 117.9 117.0 117.1
119.3 119.6 119.4
O(2)-M(5)-O(3)
57.2
49.0
50.6
O(2)-M(5)-O(4)
57.2
49.0
50.6
57.2
49.0
50.6
61.2
65.2
64.8
O(3)-M(5)-O(4)
80.5
66.6
55.5
56.9
52.5
C(1)-O(2)-M(5) C(1)-O(3)-M(5)
82.7(84.0)
88.1(89.4)
93.5
93.1
95.2
61.2
65.2
64.8
C(1)-O(4)-M(5)
82.7
88.2
93.0
93.1
95.2
61.2
65.2
64.8
S32 AIM Charges C(1)
2.21
2.18
2.18
2.24
O(2)
-1.40
-1.31
-1.30
-1.25 -1.31
-1.34 -1.27 -1.26
O(3)
-1.40
-1.38
-1.33
-1.24 -1.30
-1.34 -1.27 -1.26
O(4)
-1.40
-1.38
-1.33
-1.34 -1.30
-1.34 -1.27 -1.26
0.89
0.78
0.60
M(5)
2.19
0.73
2.15
0.88
0.88
2.23
0.58
2.18
0.62
a
This work unless otherwise specified.
b
Parenthesized data are from Ref. 4 in which optimized structures were calculated at the HF/6-31G* level, assuming D3h symmetry for CO32- and C2v symmetry for (OCO2)M-.
c
Without symmetrization except as noted.
d
With constrainment, initially, to C3v symmetry, and using quadratically-convergent SCF for 1-1-2-K.
e
With imposed C2v symmetry and using quadratically-convergent SCF.
f
Atomic coordinates and AIM charge from Ref. 17.
S33 g
With imposed C3v symmetry and using quadratically-convergent SCF.
S34 Table 2. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M2 (M = Li-K)a,b Structure 1-2-1-M
Structure 1-2-2-Mc
_____________________________________
_____________________
Li
Na
K
Li
Na
C(1)-O(2)
1.37(1.331)
1.36(1.325)
1.35
1.22
1.23
C(1)-O(3)
1.27(1.251)
1.28(1.257)
1.28
1.37
1.36
C(1)-O(4)
1.27
1.28
1.28
1.37
1.36
C(1)…M(5)
2.13(2.132)
2.49(2.495)
2.86
2.07
2.37
C(1)…M(6)
2.13
2.49
2.85
2.07
2.37
O(2)-M(5)
1.82(1.830)
2.14(2.154)
2.49
O(3)-M(5)
1.82(1.811)
2.13(2.121)
2.43
1.88
2.21
1.88
2.21
M= Bond lengths
O(4)-M(5)
S35 O(2)-M(6)
1.82(1.830)
2.14(2.154)
2.48
O(3)-M(6)
1.88
2.21
O(4)-M(6)
1.82(1.811)
2.13(2.121)
2.43
1.88
2.21
M(5)…M(6)
3.61
4.29
4.97
2.56
3.33
O(2)-C(1)-O(3)
116.3(116.4)
117.9(117.8)
118.5
126.4
124.1
O(2)-C(1)-O(4)
116.3
118.0
118.5
126.4
124.0
O(3)-C(1)-O(4)
127.5
124.1
123.1
107.2
111.9
O(2)-M(5)-O(3)
76.2
63.9
54.8 72.0
61.0
71.9
61.0
Bond Angles
O(3)-M(5)-O(4) O(2)-M(6)-O(4) O(3)-M(6)-O(4)
76.2
63.9
54.8
S36 AIM Charges C(1)
2.21
2.18
2.22
2.06
2.09
O(2)
-1.38
-1.35
-1.33
-1.23
-1.26
O(3)
-1.33
-1.32
-1.32
-1.34
-1.32
O(4)
-1.33
-1.32
-1.32
-1.34
-1.32
M(5)
0.92
0.90
0.88
0.92
0.90
M(6)
0.92
0.90
0.88
0.92
0.90
a
Parenthesized data are those of Ref. 5 for a C2v structure obtained using HF/6-31G*
b
For comparison, the calculated C-O distances and O-C-O angles of free CO32- in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
c
Not found for M = K.
S37 Table 3. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M3+ (M = Li-K)a,b Structure M=
1-3-1-M Li
Na
1-3-3-Mc
1-3-2-M K
Li
Na
Li
_____________________
_______________
_______________
C(1)-O(2)
1.29
1.30(1.290)
1.30
1.24
1.25
1.28
C(1)-O(3)
1.29
1.30
1.30
1.37
1.36
1.28
C(1)-O(4)
1.29
1.30
1.30
1.30
1.30
1.28
C(1)…M(5)
2.20
2.55
2.93
2.22
2.57
2.95
C(1)…M(6)
2.20
2.55
2.93
2.18
2.48
2.95
C(1)…M(7)
2.20
2.55
2.93
2.18
2.48
2.95
O(2)-M(5)
1.92
2.21(2.225)
2.54
1.88
2.18
1.67
O(3)-M(5)
1.92
2.21
2.54
1.97
2.27
Bond lengths
S38 O(3)-M(6)
2.03
2.37
1.67
O(2)-M(6)
1.92
2.21
2.54
O(4)-M(6)
1.92
2.21
2.54
1.94
2.24
O(3)-M(7)
1.92
2.21
2.54
2.03
2.37
O(4)-M(7)
1.92
2.21
2.54
1.94
2.24
1.67
M(5)…M(6)
3.81
4.42
5.08
3.65
4.23
5.11
M(5)…M(7)
3.81
4.43
5.07
3.65
4.23
5.11
M(6)…M(7)
3.81
4.43
5.07
2.70
3.39
5.11
Bond Angles O(2)-C(1)-O(3)
120.0 120.0
120.0
119.1
120.0
120.0
O(2)-C(1)-O(4)
120.0 120.0
120.0
130.0
125.9
120.0
O(3)-C(1)-O(4)
120.0 120.0
119.9
110.9
114.1
120.0
O(2)-M(5)-O(3)
71.6
52.7
71.7
61.1
61.1
S39 O(2)-M(6)-O(4)
71.6
61.1
52.7
O(3)-M(6)-O(4) 61.1
67.4
57.9
67.3
57.9
76.9
86.1
2.24
2.14
2.15
2.36
-1.33
-1.28,-1.37,
-1.28,-1.34,
-1.40
-1,33
-1.32
0.94
0.94,0.94,
O(3)-M(7)-O(4)
71.6
52.6
M(5)-O(2)-M(6)
168.4 178.9(179.7) 172.91
M(5)-O(3)-M(7)
168.4 178.8
172.5
M(6)-O(4)-M(7)
168.4 178.9
172.6
M(6)-C(1)-M(7) AIM Charges C(1)
2.26
O(2),O(3),O(4)
-1.36 -1.34
M(5),M(6),M(7)
0.92
2.24
0.93
0.92
0.95
0.94
S40
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Parenthesized data are those of Shi et al (6) calculated using B3LYP/6-311G** for the D3h structure.
c
Not found for M = Na or K.
S41 Table 4. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M42+ (M = Li-K)a M=
Li
Na
K
___________________
_______________________________
_______________________
Isomer
1-4-1-Li
1-4-2-Li
1-4-1-Na
1-4-2-Na
1-4-3-Na
1-4-1-K
1-4-1-Kb
C(1)-O(2)
1.30
1.26
1.29
1.32
1.28
1.28
1.28
C(1)-O(3)
1.29
1.31
1.30
1.29
1.31
1.31
1.31
C(1)-O(4)
1.29
1.31
1.30
1.29
1.31
1.31
C(1)-M(5)
2.35
2.86
2.65
2.72
2.67
3.05
C(1)-M(6)
2.35
2.87
2.65
2.74
2.67
3.05
C(1)-M(7)
3.00
2.28
3.21
2.64
2.61
2.93
C(1)-M(8)
3.00
3.02
3.21
3.16
2.61
2.93
O(2)-M(5)
1.85
3.22
2.19
2.62
2.28
2.61
2.61
O(3)-M(5)
2.17
1.81
2.41
2.18
2.38
2.73
2.73
3.05
2.93
S42 O(2)-M(6)
1.85
3.24
2.19
2.66
2.28
2.61
O(4)-M(6)
2.16
1.80
2.41
2.18
2.38
2.72
O(3)-M(7)
1.79
1.92
2.14
2.29
2.42
2.73
2.42
2.73
2.41
2.73
2.14
2.42
2.74
O(4)-M(7)
1.93
2.29
O(2)-M(8)
1.76
2.19
O(3)-M(8)
2.73
O(4)-M(8)
1.79
M(5)…M(6)
3.70
5.70
4.36
4.84
4.55
5.17
5.17
M(5)…M(7)
3.55
3.50
4.06
4.37
4.40
4.97
4.97
M(5)…M(8)
5.34
4.34
5.61
4.03
4.41
4.97
M(6)…M(7)
5.33
3.50
5.60
4.37
4.40
4.97
M(6)…M(8)
3.54
4.34
4.06
4.05
4.40
4.97
M(7)…M(8)
4.31
5.30
4.65
5.50
3.44
4.10
4.10
S43 Bond Angles O(2)-C(1)-O(3)
117.7
122.6
119.1
119.8
121.5
121.2
121.1
O(2)-C(1)-O(4)
117.7
122.7
119.1
119.9
121.5
119.1
O(3)-C(1)-O(4)
124.6
114.7
121.8
120.3
117.0
117.7
117.8
O(2)-M(5)-O(3)
66.3
42.7
57.9
55.2
57.9
50.0
50.0
O(2)-M(6)-O(4)
66.4
42.2
57.9
54.5
57.9
50.1
O(3)-M(7)-O(4)
69.8
58.4
55.1
48.5
48.5
O(2)-C(1)-M(7)
177.2
179.9
138.7
135.8
135.7
O(2)-C(1)-O(8)
138.8
135.6
O(3)-M(8)-O(4)
55.1
48.4
83.2
85.3
83.2
85.2
174.1
165.1
C(1)-O(3)-M(7)
152.0
87.8
136.1
90.6
C(1)-O(4)-M(8) M(5)-O(2)-M(6)
170.6
123.9
168.7
132.8
85.2
165.1
S44 M(5)-O(3)-M(7)
126.8
139.6
M(6)-O(4)-M(7)
126.4
139.0
156.5
133.2
131.2
155.0
133.4
131.2
133.5
131.2
M(5)-O(3)-M(8) M(6)-O(4)-M(8)
126.8
126.4
133.4
131.3
M(7)-C(1)-M(8)
91.9
93.0
82.5
88.6
131.2
88.7
Dihedral angles O(2)-C(1)-O(3)-M(5) -0.3
0.1
11.8
-24.1
O(2)-C(1)-O(3)-M(7) 179.2
-180.0
-129.4
176.8
O(2)-C(1)-O(4)-M(6) 0.3
0.1
11.9
25.4
179.9
167.0
-157.9
O(4)-C(1)-O(3)-M(5) 179.6
-179.9
-168.2
153.7
O(3)-C(1)-O(2)-M(6) 179.6
180.0
166.8
157.2
O(3)-C(1)-O(4)-M(6) 179.6
179.6
168.0
179.9
O(4)-C(1)-O(2)-M(5)
-179.5
-134.1
-131.3
-131.2
179.8
179.9
180.0
179.9
179.9
S45 M(7)-C(3)-C(4)-M(8) 0.5
72.2
AIM Charges C(1)
2.31
2.32
2.26
2.24
2.20
---
---
O(2)
-1.35
-1.37
-1.33
-1.37
-1.32
---
---
O(3),O(4)
-1.38
-1.38
-1.36
-1.33
-1.34
---
---
M(5),M(6)
0.95
0.96
0.94
0.94
0.95
---
---
M(7),M(8)
0.96
0.94,0.96
0.95
0.94,0.95
0.95
---
---
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- calculated in this work are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Symmetrized to C2v
S46 Table 5. Selected Calculated Bond Lengths (Å) and Bond Angles (°), and AIM charges, for CO3M53+ (M = Li-K)a
Isomer
1-5-1-M
1-5-2-M
_______________
_____________________
M=
Li
Na
K
Li
Na
K
Kb
C(1)-O(2)
1.33
1.33
1.33
1.32
1.31
1.31
1.31
C(1)-O(3)
1.28
1.29
1.29
1.29
1.29
1.30
1.30
C(1)-O(4)
1.28
1.29
1.29
1.29
1.29
1.30
1.30
C(1)-M(5)
2.38
2.71
3.05
2.86
3.15
3.54
3.53
C(1)-M(6)
2.38
2.71
3.09
2.87
3.14
3.36
3.36
C(1)-M(7)
3.09
3.42
3.78
3.08
3.40
3.75
3.76
C(1)-M(8)
3.09
3.42
3.77
3.08
3.40
3.75
3.76
S47 C(1)-M(9)
3.06
3.31
3.58
2.36
2.70
3.09
3.09
O(2)-M(9)
1.98
2.33
2.71
3.68
4.02
4.40
4.40
O(2)-M(5)
2.13
2.41
2.75
1.94
2.27
2.63
2.63
O(3)-M(5)
2.02
2.37
2.74
3.61
3.85
4.21
4.22
O(2)-M(6)
2.12
2.40
2.73
1.94
2.27
2.64
2.64
O(4)-M(6)
2.02
2.37
2.72
3.61
3.84
4.24
3.99
O(3)-M(7)
1.92
2.25
2.60
1.90
2.23
2.59
2.59
O(4)-M(8)
1.92
2.25
2.60
1.89
2.23
2.59
2.59
O(3)-M(9)
2.02
2.33
2.69
2.69
O(4)-M(9)
2.02
2.33
2.69
2.69
M(5)…M(6)
3.86
4.24
4.71
3.30
3.93
4.65
4.65
M(5)…M(7)
3.47
4.00
4.56
4.57
4.95
5.35
5.37
M(5)…M(8)
5.36
5.98
6.55
4.57
4.95
5.38
S48 M(5)…M(9)
3.39
3.96
4.62
4.99
5.53
6.33
6.31
M(6)…M(7)
5.37
6.02
6.80
4.57
4.95
5.43
5.39
M(6)…M(8)
3.47
3.99
4.53
4.57
4.96
5.38
M(6)…M(9)
3.39
3.94
4.57
4.99
5.51
5.84
5.86
M(7)…M(8)
4.34
4.73
5.16
6.00
6.69
7.40
7.41
M(7)…M(9)
5.47
5.83
6.06
3.44
3.94
4.49
4.49
M(8)…M(9)
5.48
5.90
6.49
3.44
3.94
4.49
Bond Angles O(2)-C(1)-O(3)
117.1 118.0 118.6
121.3 120.4 120.1 120.1
O(2)-C(1)-O(4)
117.1 118.1 118.8
121.3 120.4 120.0 120.1
O(3)-C(1)-O(4)
125.6 123.8 122.5
117.5 119.1 119.9 119.9
O(2)-M(5)-O(3)
65.1
56.1
48.5
O(2)-M(6)-O(4)
65.1
56.2
48.8
S49 O(3)-M(9)-O(4)
66.2
57.2
49.5
49.5
C(1)-O(3)-M(9)
88.2
91.9
95.3
95.3
C(1)-O(4)-M(9)
88.2
91.8
95.3
95.3
M(5)-O(2)-M(6)
116.4 119.7 123.9 124.0
C(1)-O(2)-M(9)
133.7 127.0 121.4
M(5)-O(2)-M(9)
111.4 113.5 115.8
M(6)-O(2)-M(9)
111.4 113.1 114.4
M(5)-O(3)-M(7)
123.0 120.1 117.5
M(6)-O(4)-M(8)
122.9 119.8 116.8
AIM Charges C(1)
2.27
2.24
---
O(2)
-1.38 -1.35 ---
2.27c 2.25
---
---
-1.34c -1.36 ---
---
S50 O(3),O(4)
-1.35 -1.34 ---
-1.38c -1.35 ---
---
M(5),M(6)
0.96
0.95
---
0.97c,d 0.96
---
---
M(7),M(8)
0.97
0.97
---
0.96c 0.96
---
---
M(9)
0.97
0.97
----
0.95c 0.95
---
---
a
For comparison, the calculated C-O distances and O-C-O angles of free CO32- are 1.31 Å and 120.0 °, while the calculated AIM charges on C and O are 2.21 and -1.40, respectively.
b
Symmetry constrained to Cs; Symmetry could not be constrained to C2v.
c
In (CO3)Na2(5,6)Li3 3+.
d
Na+ ions
S51
Table 6. Stepwise and Overall Complexation Energies of (CO3)My-1y-3 (y = 1-5) by M+ (M = Li, Na or K).a ∆E (kJ/mol) M Reactant 1b
Reactant 2
Productb
Li
Na
K
CO32-
+
M+
→
CO3M-
-1271 to -1049
-1075 to - 865
-886 to -682
CO3M-
+
M+
→
CO3M2
-728 to -669
-655 to -600
-573 to -537
CO3M2
+
M+
→
CO3M3+
-295 to -279
-300 to -290
-280 to -268
CO3M3+
+
M+
→
CO3M42+
108 to160
154 to164
127 to 138
CO3M42+
+
M+
→
CO3M53+
459 to 465
412 to 420
374 to 402
-1682 to -1424
-1454 to -1189
-1214 to -975
(Σ ∆E (kJ/mol)) =
a
Derived from the three different electronic energies of Tables S1AB-S1CB combined with the appropriate corrections from Table S1A-C.
b
For the most stable form found for the reactants and products.
S52
Highlights
A total of 23 new complexes of formula (CO3)Myy-2 (M = Li, Na or K) have been optimized using DFT: the coordination chemistry of the carbonate ligand with the metals Li, Na and K is much more extensive than previously imagined. Up to 5 M+ (M = Li, Na or K) ions can be added to one CO32- ion, a process that is exothermic overall. Except in the rare case of π-type bonding, the anion remains planar, but when y = 5 some out-of-plane bonding of the metal ions occurs for each of the three metal ions. When M = Li, isomeric structures were found for y = 2-5. When M = Na, isomeric structures were found for y = 1-5. When M = K, isomeric structures were found for y = 1 and 5.
S53
Graphical Abstract
(CO3)Na3+
Na+ ——► 1-4-1-Na
1-4-2-Na
1-4-3-Na