Computational Insights into Mg2+ Dehydration in the Presence of Carbonate

May combine two claims.

Formation of a contact MgCO3 ion pair either lowers the water-exchange energy barrier relative to free Mg2+ and/or substantially destabilizes the Mg-water contact state.

“Metadynamics simulations of the water exchange conducted with both models revealed that the formation of a contact magnesium carbonate ion pair either decreased the energy barrier for water exchange relative to the free magnesium ion in solution and/or significantly destabilized the magnesium-water contact state.”

May combine two claims.

The AMOEBA model overestimates the self-diffusion coefficient of Mg2+ by 13% compared with experiment, while the new and former rigid-ion force fields overestimate it by about 30% and 21%, respectively.

“The AMOEBA model was found to overestimate the self-diffusion coefficient by 13% compared to the experimental value but still gave better agreement than the new and former rigid-ion force fields for which the overestimation was about 30% and 21%, respectively.”

May combine two claims.

The current and former rigid-ion force fields predict shorter Mg-O distances in the first solvation shell, 1.94 Å for this work and 1.99 Å for Raiteri et al.

“both the current and former non-polarizable rigid-ion force fields predict slightly shorter Mg-O distances in the first solvation shell, with r M g-O = 1.94 Å (this work) and r M g-O = 1.99 Å. 20”

• cites [20] sourceNot checked yet

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May combine two claims.

The AMOEBA and new rigid-ion force fields reproduce the toroidal water oxygen density around carbonate, whereas the former rigid-ion parameters concentrate water oxygen density predominantly along each C-Oc direction.

“While the AMOEBA and new rigid-ion force fields are both able to reproduce this specific structure, this is not the case of the former rigid-ion parameters 20 which seem to concentrate the water oxygen density predominantly along each C-O c direction instead.”

• cites [20] sourceNot checked yet

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May combine two claims.

The former rigid-ion force field showed a significant free energy barrier of about 27 kJ/mol, lower than the current models, consistent with its less exergonic Mg2+ hydration free energy.

“this model also showed a significant free energy barrier (≈27”

• Also stated in: § Mg 2+ -CO 2 - 3 ion pairing free energy · plain

  “though it is lower than for the current models, which is consistent with the less exergonic Mg 2+ hydration free energy of that force field (Table 2).”

• cites [20] sourceNot checked yet

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May combine two claims.

The barrier for Mg-CO3 ion pair formation is about 39 kJ/mol for AMOEBA and about 51 kJ/mol for the new rigid-ion force field.

“leading to a high energy barrier of ≈39 kJ/mol and ≈ 51 kJ/mol for the AMOEBA and the new rigid-ion force fields, respectively.”

May combine two claims.

The reverse bidentate-to-monodentate process appears almost barrierless in one dimension (3.8 kJ/mol) but has a 17.5 kJ/mol barrier in the 2D free energy surface.

“While the reverse process appears almost barrierless in one-dimension (3.8 kJ/mol), there is in fact a higher 17.5 kJ/mol barrier to return to the monodentate configuration.”

May combine two claims.

Three free energy minima were obtained: a bidentate state, a five-fold coordinated monodentate state, and a six-fold coordinated monodentate state, listed in order of increasing stability.

“Three free energy minima were obtained, corresponding to the bidentate state, a monodentate state in which Mg is only five-fold coordinated, and the expected monodentate state with a six-fold coordinated cation, in order of increasing stability.”

May combine two claims.

The AMOEBA force field simulation did not show a minimum for the five-fold Mg2+ monodentate state and predicted a free energy barrier halfway between 20 and 40 kJ/mol.

“It is thus not surprising that the simulation carried out with the AMOEBA force field, which did not show a minimum for the five-fold Mg 2+ monodentate state (i.e.CNw=4, CNcarb=1), predicted a free energy barrier falling halfway between 20 and 40 kJ/mol.”

May combine two claims.

The transition from monodentate to bidentate involved overcoming two consecutive barriers of about 20 kJ/mol each: first a water molecule left the Mg2+ hydration shell, and then carbonate bound in a bidentate configuration.

“The transition from the monodentate to the bidentate state involved overcoming two consecutive ≈20 kJ/mol barriers for one water molecule to leave the Mg 2+ hydration shell first, and finally for the carbonate to bind in a bidentate configuration.”

May combine two claims.

Results with the new rigid-ion parameterization are more ambiguous, and the minimum free energy path suggests a one-step process with concerted movement of carbonate entering the magnesium inner shell while a water molecule leaves.

“Results obtained with the new parameterization of the rigid-ion force field are more ambiguous and the minimum free energy path seems to suggest a one step process with a concerted movement of the carbonate entering the magnesium inner shell while a water molecule simultaneously leaves.”

May combine two claims.

With both the AMOEBA and new rigid-ion force fields, the solvent-shared ion pair state at dMg-C ≈ 4.5 Å is the most stable state, more stable than the contact ion pair by 15 and 9 kJ/mol, respectively.

“the reverse was obtained here with both the polarizable AMOEBA and new rigid-ion force fields, which find the SSHIP state at d M g-C ≈ 4.5 Å to be the most stable state by 15 and 9 kJ/mol, respectively.”

May combine two claims.

From the intermediate state, an additional 11.5 kJ/mol is needed to form the monodentate ion pair, giving an overall free energy barrier of about 39 kJ/mol from SSHIP to CIP.

“From this intermediate state a further 11.5 kJ/mol is then needed to form the monodentate ion pair, which leads to an overall free energy barrier of ≈39 kJ/mol to be overcome to go from the SSHIP to the CIP.”

May combine two claims.

Reaching the five-fold coordinated Mg2+ configuration from the SSHIP state requires overcoming a barrier of 33.6 kJ/mol, and the state has stability of order 2kBT with a 5.5 kJ/mol barrier to return to SSHIP.

“Reaching this five-fold coordinated Mg 2+ configuration from the SSHIP state is an activated process that requires a high energy barrier (33.6 kJ/mol) to be overcome and its stability is of the order of 2k B T with only a 5.5 kJ/mol barrier to return to the SSHIP minimum.”

May combine two claims.

The monodentate state was more stable than the bidentate configuration by about 15 kJ/mol, in good agreement with the AMOEBA results.

“The monodentate state was found to be more stable than the bidentate configuration by about 15 kJ/mol which is in good agreement with the AMOEBA results.”

May combine two claims.

The Raiteri et al. rigid-ion force field overestimated the Mg-CO3 association free energy by more than 10 kJ/mol, largely because the contact ion pair state was excessively stable.

“this force field overestimated the Mg-CO 3 association free energy by more than 10 kJ/mol (Table 4), which was largely due to the excessive stability of the contact ion pair state.”

• cites [20] sourceNot checked yet

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May combine two claims.

The ion-pairing formation free energy is -15 kJ/mol for AMOEBA and -19 kJ/mol for the new rigid-ion model, compared with -30.4 kJ/mol for the old rigid-ion force field and -17.2 kJ/mol experimentally.

“significantly decrease the strength of the ion pairing formation free energy (-15 kJ/mol and -19 kJ/mol for AMOEBA and the new rigid-ion model, respectively) compared to the old rigid-ion force field (-30.4 kJ/mol) which brings the current values much closer to the experimental value (-17.2 kJ/mol)”

• cites De Visscher et al., 67Not checked yet

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May combine two claims.

The relative stabilities of the monodentate and bidentate states remain the same, with the monodentate ion pair more stable by about 12 kJ/mol.

“In both cases, the relative stabilities of the two states remain the same, with the monodentate ion pair more stable by about ≈12 kJ/mol.”

May combine two claims.

The new rigid-ion model predicts a free energy difference between monodentate and bidentate states of about 33 kJ/mol, more than double the ab initio (~15 kJ/mol) and AMOEBA (~12 kJ/mol) values.

“Here, poorer agreement is obtained with the new rigid-ion model, which predicts the free energy difference between monodentate and bidentate states, ≈33 kJ/mol, to be more than double the ab initio (≈15 kJ/mol) and AMOEBA (≈12 kJ/mol) values.”

May combine two claims.

The old rigid-ion force field did not display such an intermediate minimum, and its minimum energy path suggests that ion pair formation occurs with carbonate moving closer first and then pushing away a water molecule.

“This is at variance with the prediction from the old rigid-ion force field, which did not display such minimum in the 2D FES, and whose minimum energy path seems to suggest that the formation of the ion pair would occur with the carbonate group moving closer to Mg 2+ first and then pushing away one water molecule from the coordination shell.”

• cites [20] sourceNot checked yet

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May combine two claims.

In the case of Mg2+, two collective variables are required to describe the water exchange mechanism, in agreement with a previous study by Schwierz.

“We have demonstrated how in the case of Mg 2+ two collective variables are required to describe the water exchange mechanism, which is in agreement with a previous study by Schwierz 3 that suggests that this process requires the concerted motion of all the water molecules in the ion's hydration shell.”

• cites [3] sourceNot checked yet

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May combine two claims.

The magnesium carbonate ion pairing free energies are now in excellent agreement with experimental data, which is a significant improvement over former rigid-ion models.

“Importantly, the magnesium carbonate ion pairing free energies are now in excellent agreement with experimental data, which is a significant improvement over former rigid-ion models.20”

• cites [20] sourceNot checked yet

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Classified as probably not a substantial claim.

The prediction that water exchange is more labile around the Mg-CO3 complex is at variance with the computational results from Yang et al. and Hamm et al., who did not observe any significant increase in the water exchange rate when Mg2+ formed a complex with either HS- or aspartate.

“Our prediction that water exchange is more labile around the Mg-CO 3 complex is at variance with the computational results from Yang et al. 27 and Hamm et al., 28 who did not observe any significant increase in the water exchange rate when Mg 2+ formed a complex with either HS -or aspartate.”

• cites [27] sourceNot checked yet

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• cites [28] sourceNot checked yet

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Classified as probably not a substantial claim. May combine two claims.

Schwierz found that water exchange around Mg2+ requires concerted motion of two water molecules and collective rearrangement of all first-shell water molecules, implying a time scale of about 40 ms.

“Schwierz 3 found, using transition path sampling, that a concerted motion of two water molecules and a collective rearrangement of all the water molecules in the first solvation shell of Mg 2+ was required for water exchange to occur, leading to a much longer time scale than previously estimated, of ≈40 ms.”

• cites [3] sourceNot checked yet

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Classified as probably not a substantial claim.

Martinek et al. showed that a full ionic charge force field can overestimate the stability of the contact ion pair between divalent cations and negatively charged residues.

“Martinek et al. 23 showed that the use of a full ionic charge force field could lead to an overestimation of the stability of the contact ion pair between divalent cations and negatively charged residues.”

• cites [23] sourceNot checked yet

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Classified as probably not a substantial claim.

Water exchange between the first and second solvation shells of Mg2+ is the most fundamental step governing processes that occur in aqueous environments.

“water exchange between the first and second solvation shells of magnesium is the most fundamental step governing all stages of these processes occurring in aqueous environments.3”

• cites [3] sourceNot checked yet

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May combine two claims.

De Oliveira et al. reported Mg-acetate binding energies but did not investigate how complexation affects the water-exchange rate.

“De Oliveira et al. 29 used a scaled-charge force field to probe the interaction between divalent cations and carboxylate groups, and reported Mg-acetate binding energies but did not investigate the effect of complexation on the water exchange rate.”

• cites [29] sourceNot checked yet

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May combine two claims.

The lack of polarization in the SPC/Fw water model underestimates the water dipole moment next to Mg2+ and causes shorter water-cation distances in order to reproduce the experimental hydration free energy.

“This is due to the lack of polarization in the SPC/Fw water model that leads to the underestimation of the water dipole moment adjacent to magnesium and cause the water-cation distances to be shorter in order to reproduce the experimental hydration free energy.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Yang et al. found that HS- had little effect on lowering the water-exchange energy barrier around Mg2+.

“Yang et al. 27 conducted ab initio Reaction Path Ensemble (RPE) simulations to explore the possibility that HS -, a product of bacterial sulphate reduction, might promote Mg 2+ dehydration in aqueous solution, but found that it had little effect on lowering the water exchange energy barrier.”

• cites [27] sourceNot checked yet

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May combine two claims.

An accurate description of the Mg-carbonate ion pair in solution and quantitative data on the energy barrier for Mg2+ dehydration in the presence of carbonate are still lacking.

“An accurate description of the Mg-carbonate ion pair in solution and quantitative data on the energy barrier for the dehydration of Mg 2+ in the presence of carbonate remain lacking”

• cites [27] sourceNot checked yet

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• cites [28] sourceNot checked yet

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• cites [29] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

The authors previously introduced AMOEBA parameters for Ca-carbonate in solution that improved Ca-carbonate ion binding free energies relative to earlier non-polarizable models.

“We have recently introduced a new set of parameters based on the AMOEBA model for the interaction of calcium in solution with carbonate 26 that have improved the Ca-carbonate ion binding free energies compared to previous non-polarizable models.”

• cites [26] sourceNot checked yet

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Classified as probably not a substantial claim. May combine two claims.

Hamm et al. found that aspartate did not affect the magnesium solvation sphere and did not appear to lower the energetic cost of dehydration, although they used the non-polarizable CHARMM22 force field.

“Hamm et al. 28 found, using umbrella sampling, that the solvation sphere of magnesium was unaffected by the presence of aspartate, which did not seem to lower the energetic cost for dehydration, though they used the non-polarizable CHARMM22 force field for proteins.”

• cites [28] sourceNot checked yet

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May combine two claims.

Mg2+ strongly polarizes its environment, a feature that fixed-charge rigid-ion force fields do not treat explicitly.

“a second difficulty lies with the magnesium ion's tendency to strongly polarize its environment, 22 a feature that fixed charge rigid-ion force fields fail to consider explicitly.”

• cites [22] sourceNot checked yet

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May combine two claims.

The new rigid-ion force field was developed by targeting the experimental hydration free energy of the aqueous ions and using ab initio carbonate-water radial distribution functions to guide refitting of CO3-water interactions.

“Analogously to the AMOEBA potential, we targeted the experimental hydration free energy of the aqueous ions reported by Marcus, 38 and we used the ab initio carbonate water radial distribution functions 26 to guide the refitting of the CO 3 -water interactions.”

• cites [38] sourceNot checked yet

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• cites [26] sourceNot checked yet

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May combine two claims. The quote only partly states this claim.

The rigid-ion metadynamics simulations used 30 independent walkers and a bias factor of 20; repeating them with a bias factor of 30 produced no significant difference.

“Because of the lower computational cost, this allowed for the simulations to be run with 30 independent walkers”

• Also stated in: § Simulations with the rigid-ion force field · plain

  “for these simulations we used a bias factor of 20 to ensure that a correct description of the transition state was achieved.”

• Also stated in: § Simulations with the rigid-ion force field · plain

  “we also repeated the simulations with a bias factor of 30, and no significant difference was observed.”

Classified as probably not a substantial claim. May combine two claims.

The AMOEBA metadynamics simulations used 16 independent walkers, a bias factor of 15, and at least 300 ns aggregate time to ensure well-converged sampling.

“All the AMOEBA metadynamics simulations were run using 16 independent walkers with a bias factor of 15 for an aggregate simulation time of at least 300 ns to ensure well-converged sampling.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The AMOEBA model explicitly includes polarizability through static and self-consistent induced dipoles.

“polarizability can be explicitly considered via a model such as AMOEBA that includes both static and self-consistent induced dipoles.25”

• cites [25] sourceNot checked yet

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May combine two claims.

The absence of water exchange suggests a water residence time greater than 50 ns and a high energy barrier for water exchange at Mg2+.

“suggesting a water residence time greater than 50 ns and a high energy barrier for water exchange at Mg 2+ , in agreement with previous experimental 19 and theoretical 20,63 results.”

• cites [19]Not checked yet

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• cites [20] sourceNot checked yet

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• cites [63] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Limiting as much as possible the size of the space explored during the AIMD and using two walkers should slightly reduce the bias due to the choice of the starting configuration.

“Importantly, we have limited as much as possible the size of the space to be explored during the AIMD and have used two walkers, which should slightly reduce the bias due to the choice of the starting configuration.”

May combine two claims.

The well-tempered method does not flatten the free energy surface but reduces barrier heights by the magnitude of the chosen bias factor.

“In fact the well-tempered method does not flatten out the free energy surface, but it reduces the barrier heights by the magnitude of the bias factor chosen, e.g a bias factor of 20 would reduce a free energy barrier of 60 kJ/mol to 3 kJ/mol, which can be easily overcome by thermal fluctuations (Figures S13 and S14 in the SI).”

May combine two claims.

A bias factor that is too small does not allow an accurate estimate of the free energy barrier, while a value that is too large wastes computational resources by making the simulation very slow to converge.

“Hence, a bias factor that is too small does not allow for an accurate estimate of the free energy barrier, while using a value that is too large would waste computational resources by making the simulation very slow to converge.”

May combine two claims.

Starting each walker from different positions predetermines how the space will be explored; if the walkers cannot cross the free energy barriers, this limits the accuracy of barrier estimates and biases the relative stability of the free energy minima.

“In fact, by starting each walker from different positions within the region of interest, we effectively predetermine how the space will be explored and if the walkers are not able to cross the free energy barriers, this not only limits our accuracy as to the estimate of the free energy barriers but it also biases the relative stability of the free energy minima.”

May combine two claims.

Because of the computational cost of the polarizable AMOEBA force field, such an extensive set of validation calculations could not be performed, but given the agreement between the results shown here, a similar degree of accuracy is expected.

“Due to the computational cost of the polarizable AMOEBA force field we could not perform such an extensive set of validation calculations but given the agreement between the results shown here we would expect a similar degree of accuracy.”

May combine two claims.

The free energies reported here have an accuracy comparable to kBT, with the caveat that the free energy barriers are a lower bound to the exact barrier on the real reaction coordinate.

“Overall, we believe that the free energies reported here have an accuracy comparable to k B T , with the caveat that the free energy barriers are a lower bound to the exact barrier on the real reaction coordinate.”

Classified as probably not a substantial claim.

Without knowing a priori the largest free energy barrier in the system, the appropriateness of the chosen bias factor can only be assessed in post-processing by monitoring the multiple walkers and ensuring that all free energy barriers are regularly crossed, particularly toward the end of the simulations.

“Without knowing a priori what the largest free energy barrier in the system actually is, we can only assess whether the chosen bias factor is appropriate for the simulation in post-processing by monitoring the behaviour of the multiple walkers and making sure that all the free energy barriers are regularly crossed, particularly toward the end of the simulations.”

May combine two claims.

The minimum free energy path on the 2D FES suggests that bidentate CIP formation first involves a decrease in the water coordination number while the Mg-C distance remains unchanged, followed by shortening of the Mg-C distance, in agreement with ab initio results.

“the minimum free energy path on the 2D FES would suggest that, similarly to the SSHIP-to-monodentate transition, the formation of the bidentate CIP first involves a decrease of the water coordination number by Mg while the Mg-C distance remains unchanged, and then a shortening of the Mg-C distance, i.e. bidentate binding, in agreement”

May combine two claims.

The coordination number CV introduces a bias potential on the coordination shell that is orthogonal to the distance CV and allows a more accurate description of the water exchange barrier.

“Although the coordination number does not impose any symmetry on the structure of the hydration shell, it introduces a bias potential on the coordination shell that is orthogonal to the distance collective variable and allows for a more accurate description of the water exchange barrier.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Any statistical error in the AIMD calculations is expected to be much larger than for the rigid-ion simulations, and strategies were employed to minimize the influence of this factor.

“Although any statistical error is expected to be much larger than for the rigidion simulations, we have employed strategies to try minimize the influence of this factor.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Non-reproducible free energy surfaces indicate either that an important slow collective variable has been missed or that the well-tempered parameters were not appropriate for the system.

“Non-reproducible free energy surfaces are a clear indication that either an important (slow) collective variable has been missed or that the well-tempered parameters were not appropriate for the system at hand.”

Classified as probably not a substantial claim.

Water exchange around the Mg ion involves the concerted movement of all water molecules in the Mg2+ solvation shell to produce a symmetric transition state.

“This choice of CVs was inspired by the work of Schwierz 3 where the water exchange around the Mg ion was found to involve the concerted movement of all the water molecules in the Mg 2+ solvation shell to produce a symmetric transition state.”

• cites [3] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The accurate calculation of water exchange rates around aqueous ions is not a trivial task, even after determining the free energy barrier, because transition state theory may not provide a reliable estimate without correction for recrossing events.

“The accurate calculation of water exchange rates around aqueous ions is not a trivial task, even having determined the free energy barrier, since transition state theory may not provide a reliable estimate without correction for recrossing events.”

May combine two claims.

Although the polarizable AMOEBA force field appears superior to the rigid-ion one, the latter would still provide a qualitatively accurate description of the thermodynamics of the aqueous Mg-CO3 system.

“Although the polarizable AMOEBA force field appears to be superior to the rigid-ion one, the latter would still provide a qualitatively accurate description of the thermodynamics of the aqueous Mg-CO 3 system.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Lincoln suggested that each metal ion-ligand complex behaves differently; for example, he reported that CrO4^2- increases the water lability of the aqueous Ca2+ ion but has little effect on the water exchange around Mg2+.

“However, Lincoln 69 suggested that each metal ion-ligand complex behaves differently; for example he reported that CrO 2 - 4 increases the water lability of the aqueous Ca 2+ ion but has little effect on the water exchange around Mg 2+ , therefore more experimental work on the magnesium carbonate system is required to corroborate our results.”

• cites [69] sourceNot checked yet

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Classified as probably not a substantial claim.

Due to its lower computational cost, the rigid-ion force field could be more readily used to explore Mg/CaCO3 nucleation and growth processes where long simulations with large systems are needed.

“Due to its lower computational cost, this rigid-ion force field could therefore be more readily used to explore Mg/CaCO 3 nucleation and growth processes where long simulations with large systems need to be used.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

The presence of ion pairs could also play a significant role in a wide range of geochemical phenomena such as ion adsorption, nucleation and biomineralization, and could have significant implications in biochemistry.

“The presence of ion pairs could also play a significant role in a wide range of geochemical phenomena such as ion adsorption, nucleation and biomineralization, and this result could have significant implications in biochemistry where the transport of Mg 2+ ions across cell membranes and their catalytic activity help regulate many physiological processes in living organisms.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Similar behaviour has been reported for other metal ion-ligand complexes.

“Similar behaviour has been reported for other metal ion-ligand complexes, 69,70 but to the best of our knowledge no experimental values are available for water exchange around the Mg-CO 3 complex.”

• cites [69] sourceNot checked yet

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• cites [70] sourceNot checked yet

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