ORIGINAL PAPER

Force field parametrization of hydrogenoxalate and oxalateanions with scaled charges

Ondřej Kroutil1,2 & Milan Předota1 & Martin Kabeláč1

Received: 13 July 2017 /Accepted: 28 September 2017# Springer-Verlag GmbH Germany 2017

Abstract Models of the hydrogenoxalate (bioxalate, charge−1) and oxalate (charge −2) anions were developed for clas-sical molecular dynamics (CMD) simulations and parame-trized against ab initio molecular dynamics (AIMD) data fromour previous study (Kroutil et al. (2016) JMolModel 22:210).The interactions of the anions with water were described usingcharges scaled according to the electronic continuum correc-tion approach with rescaling of nonbonded parameters(ECCR), and those descriptions of anion interactions werefound to agree well with relevant AIMD and experimentalresults. The models with full RESP charges showed exces-sively strong electrostatic interactions between the solute andwater molecules, leading to an overstructured solvation shellaround the anions and thus to a diffusion coefficient that wasmuch too low. The effect of charge scaling was more evidentfor the oxalate dianion than for the hydrogenoxalate anion.Our work provides CMD models for ions of oxalic acid andextends previous studies that showed the importance of ECCRfor modeling divalent ions and ions of organic compounds.

Keywords Oxalic acid anions . Oxalate . Hydrogenoxalate .

Ab initio molecular dynamics . AIMD . Classical moleculardynamics . CMD . Electronic continuum correction . ECCR

Introduction

The structures and dynamic behavior of organic compoundsin water solutions is of particular interest in many branches ofchemistry; for example, environmental chemistry, catalyticchemistry, and biological chemistry [1]. Organic acids andespecially dicarboxylic acids represent an interesting combi-nation of a hydrophobic backbone and a hydrophilic carboxylgroup (or groups). Both of these properties (hydrophobicityand hydrophilicity) can influence solvation and solvent prop-erties significantly.

Oxalic acid (COOH)2 is the smallest dicarboxylic acid, andattracts a lot of research attention. It occurs in nature as calci-um oxalate minerals (including whewellite and weddellite), ispresent at trace levels in the atmosphere (it represents 37–69%of the total dicarboxylic acid in the air) [2], and its high solu-bility and moderate dissociation constants allow the formationof calcium-containing uroliths in the human body [3].

The neutral oxalic acid molecule (COOH)2 as well as theoxalate dianion (COO−)2 have been explored in many exper-imental and theoretical studies, whereas studies of thehydrogenoxalate anion (HOOC–COO−) are still sparse.Most theoretical studies of these three species have focusedon their structural properties [4, 5], microsolvation [6], orintramolecular proton transfer in the case of thehydrogenoxalate anion [7–9]. In our previous study [10], weexamined the structural properties and solvation shell of fullysolvated oxalic acid anions using ab initio molecular dynam-ics (AIMD) because there is no (or only an indirect) experi-mental description of the solvation shell of these anions [11,12]. We confirmed the presence of a staggered conformationof the oxalate dianion in the presence of a sufficient number(>32) of water molecules, and we highlighted that the struc-ture of the hydrogenoxalate anion in explicit water differedfrom that in implicit water. We also described in detail the

Electronic supplementary material The online version of this article(https://doi.org/10.1007/s00894-017-3490-x) contains supplementarymaterial, which is available to authorized users.

* Martin Kabeláčmkabelac@prf.jcu.cz

1 Faculty of Science, University of South Bohemia, Branišovská 1760,370 05 České Budějovice, Czech Republic

2 Faculty of Chemistry, Materials Research Centre, Brno University ofTechnology, Purkyňova 118, 612 00 Brno, Czech Republic

J Mol Model (2017) 23:327 https://doi.org/10.1007/s00894-017-3490-x

solvation shells of both anions using radial and spatial distri-bution functions (RDF and SDF), and we emphasized the roleof the explicit water and the H-bond network around thecharged systems.

Since the size of the system is limited in ab initio calcula-tions, we used the aforementioned AIMD results as the bench-mark for the parametrization of both anions for the AMBERforce field, because either standard AMBER parameters ortheir reparametrizations for other force fields were used inthe older papers. Darvas et al. [13–15] used the OPLS libraryto assign the Lennard-Jones parameters of the atoms of oxalicacid and partial charges based on the geometry obtained fromab initio calculations. The same force field was used byHalstead [16], who studied oxalic acid and its anions in super-critical water.

The RESP routine was used byMinofar et al. [17] to obtainpartial charges in conjunction with the standard Amber99SBforce field parameters to model the oxalate dianion. In anotherwork [18], the CHARMM27 force field with the MATCHroutine [19] was used to generate a model of the samecompound.

In all of the studies mentioned above, net charges corre-sponding to their normal charges were assigned to the modelsof both oxalic acid anions, i.e., −1 for the hydrogenoxalateanion and −2 for the oxalate dianion. However, our pilot clas-sical molecular dynamics (CMD) simulations with nominalRESP charges indicated an overstructured solvation shelland excessively strong interactions between the anion andwater in comparison with the AIMD results. This is thoughtto be a consequence of a general problem with the descriptionof interactions in solutions containing ions (especially multi-valent ones), where the strong polarization and charge-transfereffects that are missing from the standard MD force fieldscome into play.

Thus, we focused on the use of a computationally simpleand physically well-justified scheme for including electronicpolarization effects of ions in aqueous solutions, known aselectronic continuum correction (ECC) [20, 21], to overcomethis problem. The basic idea of this method is to include theelectronic polarization in a mean-field way by rescaling theionic charges by a factor of 1=

ffiffiffiffiffiεel

p, where ε

el= 1.78 is the

electronic part of the relative permittivity of water. This yieldsa scaling factor of ~0.75. Together with this scaling of thecharges, slight readjustments of the ionic radii are desirableto achieve perfect agreement with experiment [22]. This ap-proach has been denoted electronic continuum correction withrescaling (ECCR). For systems with monoatomic ions[22–24], guanidinium carbonate ions [25], and calmodulinand calcium ions [26], it was found that applying the ECCRapproach could lead to significant improvements to descrip-tions of electrolyte solutions, and could provide results that arein a good agreement with the neutron scattering data.

Here we present new models of the oxalate dianion and thehydrogenoxalate anion for CMD simulations with scaledcharges according to the ECCR approach. The neutral oxalicacid (pKa1 = 1.24) was omitted due to a very low concentra-tion of its nondissociated form except at very low pH. Bothstudied models were compared with AIMD and experimentaldata and to models with nominal RESP charges. In the case ofthe hydrogenoxalate anion, two possible scaling methodswithin the ECCR framework (denoted ECCR and ECCR-P)were employed. The geometric parameters of the anions werealso slightly modified to better reproduce the AIMDgeometries.

Computational methods

The oxalate dianion (net charge −2), hereafter abbreviated toBox-2,^ and the hydrogenoxalate anion (net charge −1), here-after abbreviated to Box-1^ (Fig. 1), were studied at variouslevels of theory, including via ab initio molecular dynamicsand classical molecular dynamics.

(a) Ab initio molecular dynamics (AIMD) in a periodic box

The ab initio molecular dynamics protocol used in thiswork has already been described in detail in [10]. Briefly,AIMD simulations with periodic boundary conditions werecarried out using a hybrid Gaussian plane-wave method(GPW) implemented in the CP2K [27] software. The BLYPfunctional [28] with an empirical dispersion term [29] for allelements was used in conjunction with double-ξ molecularlyoptimized basis functions augmented by a polarization func-tion (DZVP) [30] and the appropriate pseudopotential ofGoedecker, Teter, and Hutter (GTH) [31]. All hydrogens werereplaced with deuterium. Each simulation box consisted ofone ox-1/ox-2 molecule and 50 heavy water (D2O) molecules.The net charge of the system was neutralizing by adding theappropriate background charge. Time steps of 1 fs wereemployed. The 30-ps-long production runs carried out withinthe NVT ensemble using the Nosé–Hoover thermostat

Fig. 1 Structures of oxalate (ox-2) and hydrogenoxalate (ox-1) anions.Atom labels are depicted, along with atom (force field) types inparentheses. The atom labels Cx and Ox correspond to the same labelsused for those atoms in the ox-2 system

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(relaxation time 500 fs) in our previous work [10] were furtherextended to 60 ps in the present work to improve the samplingof the O–C–C–O dihedral angle. The trajectories wereinspected using the analytical tools of Gromacs [32], and theprogram VMD [33] was used to visualize them.

(b) Preparation of the model for classical moleculardynamics

We used the Amber99SB force field and routines found inthe Amber software package to prepare models of ox-1 andox-2. We aimed to make the models compatible with forcefields for inorganic surfaces such as ClayFF [34] or Interface[35], as well as with force fields for organic molecules. Theseforce fields for inorganic surfaces use bonding and nonbond-ing terms compatible with the Amber force field, which is wellestablished for simulations of organic molecules andbiomolecules.

Both starting models were prepared by combining theRESP routine for generating partial charges [36] with theAntechamber routine [37] for atom type assignment.

Partial charges RESP charges were prepared in the standardway—the anions were optimized in the gas phase at theB3LYP/6-31G* level and their electrostatic potentials werethen calculated at the HF/6-31G* level of theory. Finalcharges were generated from electrostatic potentials by theAntechamber routine.

For ox-2, the ECCR approach was adopted by scaling allRESP partial atom charges by a factor of 0.75 to get an overallcharge of −1.5e. This charge scaling of all atoms by the samefactor is justified by the small size of the molecule and thesymmetric roles of both COO− groups. Two approaches weretested for ox-1: all of the original RESP partial charges werescaled by a factor of 0.75 (this approach was denotedBECCR^); or the charge on a COOH group was derived fromthe atom charges developed in the standard way by the RESPprocedure for the neutral oxalic acid, whereas the ECCRcharge on a COO− group was derived from the atom chargesfor the oxalate dianion (this approach was denoted BECCR-P;^ see Table 1). Both approaches led to an overall charge of−0.75e for this compound. The former approach is expected towork better for small molecules, while the latter is an extremevariant of the ECCR modeling process for charged proteinsintroduced by Leontyev and Stuchebrukhov [38], and furtherdeveloped by Kohagen et al. [26], where only partial chargeson the relevant functional groups of the charged aminoacidsare scaled by a factor of 0.75. This approach should be supe-rior for larger molecules in which charging (deprotonation)has a relatively localized effect on partial charges. An im-promptu study demonstrated the success of the latter methodwhen it was applied to a hydrogenoxalate molecule. To pre-serve the charge neutrality of the studied systems and the

consistency of the ECC(R) approach, scaled charges for atom-ic ions such as Na+ [23], Ca2+ [22], and Cl− [22] need to beused.

Bonding parameters Standard Amber99SB force field pa-rameters [39] for bond stretching, angle bending, and torsionwere used as starting values. For the final models with RESP,ECCR, and ECCR-P charges, bond-stretching and angle-bending equilibrium distances/angles were varied iterativelyto achieve better agreement with AIMD values (see Tables S2and S3 of the BElectronic supplementary material,^ ESM),with the appropriate force constants kept at the defaultAmber99SB values. The dihedral angle O–C–C–O had to beparametrized because the parameters for the unusual directconnection of two COO− groups in the oxalate dianion arenot included in the standard Amber99SB force field. The di-hedral parameters were fitted against the ab initio derivedrotational profile following the standard Amber procedure[39].

Nonbonding parameters Atom types defining the nonbond-ing interactions of each atom were assigned by theAntechamber routine (Fig. 1), and the majority of those as-signments were left unchanged. The only exception was thedefault O2 atom type used for carbonyl oxygens in the COO−

and COOH groups; the sigma parameter was slightly in-creased in all of the ECCR models, so this atom type waschanged to the OX atom type (see BResults and discussion^).For heterogeneous Lennard-Jones interactions, the defaultLorentz–Berthelot combining rules were considered.

All models were converted fromAmber to Gromacs formatusing the Acpype software package [40].

(c) Classical molecular dynamics (CMD)

All molecular dynamics simulations were carried out inexplicit water using the Gromacs 5.0.2 software package[32]. The simulation box included one ox-1 or ox-2 and 512water molecules. To mimic the conditions used in AIMD sim-ulations, no ions were added. The net charge of the systemwas neutralized by applying a background charge. We usedthe SPC/E [41] water model by default, although we alsoemployed the TIP3P [42] water model in some simulationsto demonstrate the performance of this commonly used watermodel when used in conjunction with the new ox-1 and ox-2parameters. An initial equilibration protocol consisting of en-ergy minimization and a short NPT MD run (0.5 ns) at 1 barand 298 K resulted in a periodic cubic box with sides of length~24.9 Å. The equilibration phase was followed by a NVTMDproduction run with time steps of 1 fs. The particle meshEwald (PME) method was employed to treat long-range inter-actions, and the LINCS algorithm [43] was used for hydrogen

J Mol Model (2017) 23:327 Page 3 of 8 327

atoms. Each trajectory was 10 ns long, and structures weresaved every 1 ps.

We employed the approach ofWang and Hou [44] to obtainthe diffusion coefficients of the studied anions. This involvesperforming several shorter simulations to obtain the averagevalue of the diffusion coefficient. To this end, we generated 60trajectories for each ion and each charge model. Each trajec-tory was 6 ns long and started from the same initial configu-ration but with different, randomly generated, initial veloci-ties. The mean square displacement (MSD) curve for each ofthe 60 trajectories was calculated according to the followingequation:

MSD tð Þ ¼ r t0 þ tð Þ−r t0ð Þ½ �2D E

;

using all available time intervals.The diffusion coefficient was obtained from the linear fit

MSD tð Þ ¼ 6Dt þ C, where MSD tð Þ is the average MSDcurve derived from the 60 MSD curves obtained for each par-ticular ion and charge model, D is the diffusion coefficient of agiven species, and C is an offset constant. The fitting intervalwas 1–3 ns of simulation (Fig. S4 of the ESM). In this interval,the data were nicely fitted with straight lines, as the ballisticregime that occurs at small simulation times was avoided, aswere the data obtained at long simulation times, which featurelarge statistical uncertainties due to the limited number of sam-pled time intervals within the finite simulation length.

Results and discussion

Oxalate dianion

Not surprisingly, and in accordance with previous studies [22,45] of other charged compounds, the impact of the ECCR

approach on the behavior of the divalent oxalate dianion inwater was observed to be dramatic.

It is evident from Fig. 2a that the original RESP charges ledto excessively strong interactions between oxalate oxygens(Ox) and water oxygens/hydrogens (Ow/Hw) in comparisonwith the AIMD results. The heights of the Ox–Ow and Ox–Hw RDF peaks corresponding to the first hydration shell arerespectively 1.97 and 2.35 times higher than the AIMD re-sults, and they are also shifted by approximately 0.12 Å toshorter distances compared to the AIMD ones. A similartrend, though less prominent, can be seen for carbon–waterRDFs (Fig. 2b). In this case, the first Cx–Ow and Cx–HwRDF peaks are about 20% higher for the RESP model thanin the AIMD results, and the positions of the peaks are shiftedby 0.13 Å to shorter distances.

When the partial charges were rescaled according to theECCR method (i.e., the overall charge of the compound was−1.5e), and the Lennard-Jones σ parameter of the carbonyloxygens was altered slightly (see the next paragraph), thepositions and heights of all the peaks in the Ox–Ow and

Table 1 Partial charges of oxalic acid and its ions

Atomox-2 ox-1 ox-0

RESP ECCR RESP ECCR ECCR-P RESP

C1 0.71355 0.53516 0.65903 0.49427 0.70168 0.70168

O1 -0.85678 -0.64258 -0.61573 -0.46180 -0.64505 -0.64505

O2 -0.85678 -0.64258 -0.60677 -0.45508 -0.52824 -0.52824

H1 - - 0.34884 0.26163 0.47160 0.47160

C2 0.71355 0.53516 0.65701 0.49276 0.53516 0.70168

O3 -0.85678 -0.64258 -0.72119 -0.54089 -0.64258 -0.64505

O4 -0.85678 -0.64258 -0.72119 -0.54089 -0.64258 -0.52824

H2 - - - - - 0.47160

SUM -2.0 -1.5 -1.0 -0.75 -0.75 0

Color blocks indicate charges used to combine the ECCR-P model of the hydrogenoxalate ion

Fig. 2a–b Radial distribution functions between either a water oxygen(Ow, left column) or a water hydrogen (Hw, right column) and a anoxygen (Ox) or b a carbon (Cx) in the oxalate dianion

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Ox–Hw RDFs improved dramatically and agreed very wellwith the AIMD ones (Fig. 2a). The first peaks in both RDFswere only 1.15 and 1.24 times higher, respectively, than theAIMD ones, and the positions were on average only 0.02 Åoffset from the AIMD values. Similarly, all the other peaks inthe RDF curves were much better described. The first peaksfor carbon–water interactions (Fig. 2b) were underestimatedby only ~18%, with a better positional match than seen for theRESP model. As depicted in Fig. S1 of the ESM, the ECCRmodel works just as well when using TIP3P water.

As mentioned above, aside from the charge scaling, somenonbonding and bonding parameters of the system were alsoadjusted to achieve better fits to the bond lengths, angles, andthe solvent environment of oxalate from AIMD simulations.First, the original Lennard-Jones σ parameter for carbonyloxygens (atom type O2 with the Amber99SB force field,σ = 2.960 Å [39]) shifts the position of the first peak in theOx–Ow RDF 0.05 Å lower and slightly overstructures thewater distribution (Fig. S2 of the ESM). Replacing the σ pa-rameter for the O2 atom type with that from SPC water(σ = 3.165 Å) gives a good first peak height, but in contrastto the O2 atom type, the peak is shifted higher by 0.06 Åcompared to the AIMD data. The linear fit (σo = 3.046 Å)between the σ values of the O2 and Ow atom types, resultingin newly introduced BOX^ atom type (see Table S2 of theESM), gives the best agreement with the AIMD position, al-though the peak remains slightly high.

Second, all bond-stretching and selected angle-bending pa-rameters were modified (Table S2 of the ESM) to better re-produce the AIMD values (Table S1 of the ESM). In particu-lar, the equilibrium C–C bond length had to be lowered fromthe Amber99SB default value of 1.525 Å to 1.510 Å to matchthe AIMD results due to strong electrostatic repulsion betweenthe two COO− groups. Regarding the dihedral O–C–C–O an-gle, our previous study [10] showed that ox-2 prefers a stag-gered conformation in water. Prolonging the AIMD trajectoryfrom 30 to 60 ps (Fig. S3 of the ESM) confirmed this finding.The final values of the O–C–C–O dihedral at equilibrium andits force constant were found by fitting the data for the abinitio rotational profile.

Both the CMD and AIMD histograms of the O–C–C–Otorsion angle distribution presented very similar profiles(Fig. 3). The CMD histogram showed a slightly higher occur-rence of staggered configurations compared to the AIMDhistogram.

To further validate the ECCR model, we computed thediffusion coefficients and compared their values with ex-perimental data (Table 2 and Fig. S4 of the ESM).Whereas the diffusivity of the ECCR model matched theexperimental value to within 1%, the RESP modelunderestimated it by 40%. This can be attributed to theexcessively tightly packed solvation shell around the an-ion, which arises from the overly strong electrostatic

interactions. A similar trend was found for single-component ionic liquids [46].

Hydrogenoxalate anion

For the hydrogenoxalate anion, assigning the scaled ECCRcharges is less straightforward than for the oxalate dianion.Two different approaches were considered, as already men-tioned in the BMethods^ section: either all of the charges werescaled down equally by a factor of 0.75 (the ECCRmodel), orthe charges of the atoms in a COOH group were taken fromthe RESP ones for neutral oxalic acid, whereas the charges ofatoms in a COO− group were adopted from the ECCR oxalatedianion (Table 1) without further modification (ECCR-Pmodel).

The improvement achieved by applying the ECCR ap-proach rather than standard RESP charge fitting is not as sub-stantial for monovalent ions as that observed for divalent ions[23]. Our results for ox-1 confirm this trend, since each of theapproaches is better at reproducing some of the RDF proper-ties between hydrogenoxalate atoms and water, as shown inFig. 4a–e. Generally, the RESP model largely fails to accu-rately describe the hydrogenoxalate oxygen–water interac-tions, while both the ECCR models underestimate the oxalatecarbon–water interactions. The first peaks in the RDFs

Fig. 3 Histograms of the O–C–C–O dihedral angle distributions of ox-2(red lines) and ox-1 (black lines) obtained from AIMD simulations (fulllines) and CMD simulations (dashed lines) for the same timescale (60 ps).Note that the distribution profile obtained from the full-length (10-ns)CMD simulation is very similar (result not shown). The symmetrizedunfolded profiles (0–180°) are presented here to better illustrate theshapes of the distributions

Table 2 Diffusion coefficients D (in 10−9 m2 s−1)

Ox-2 Ox-1

RESP ECCR Exp.a RESP ECCR ECCR-P Exp.a

0.588 0.977 0.987 0.935 1.330 1.018 1.070

a Experimental data obtained from [47]

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between the O3 and O4 oxygens in the COO− group and wateroxygens and hydrogens (Fig. 4c) are overestimated by a factorof ~1.4/1.5 by RESP compared to AIMD. The ECCR modelunderestimates and the ECCR-P model overestimates theseinteractions to a similar degree, but the improvement achievedwith these models compared to the RESP model is still evi-dent. O2 oxygen–water interactions (Fig. 4b) are describedsimilarly well by both ECCR models (the ECCR-P methodbetter describes a small peak at around 4.6 Å in the O2–OwRDF), whereas the RESP model again has a tendency to over-estimate the first peak. Interactions between the O1 oxygenand water are the most sensitive to model selection (Fig. 4a).While the ECCR-P model is capable of localizing the firstpeak in the O1–Ow RDF at around ~2.6 Å, similar to theAIMD result, neither ECCR nor RESP capture this feature.The ECCR-P model has the most positive charge at the H1atom (Table 1), and the resulting increased electrostatic attrac-tion leads to greater solvent presence around this atom, givingrise to the first O1–Ow peak at the correct distance. In con-trast, the second peak of the O1–Ow RDF from AIMD, situ-ated between 2.8 and 4.2 Å, is quite well described by the

ECCR model, whereas the RESP and ECCR-P curvescompletely ignore it. Since the ECCR model gives theweakest negative charge on the O1 atom, the O1 atom is morehydrated by water molecules when using ECCR, due to theweaker O1–OWrepulsion. At the same time, water hydrogensare less attracted to O1, meaning that ECCR gives a lower firstpeak of O1–Hw RDF than AIMD or ECCR-P.

As mentioned earlier, the RESP model matches the car-bon–water interactions (Fig. 4d, e) more precisely, accuratelyaffording the heights and positions of the first peaks, especial-ly those for the C2 carbon–water interaction, whereas bothECCR models underestimate these pair interactions (especial-ly in the C2–Ow/HwRDFs) with respect to the AIMD curves.Out of the two ECCR models, ECCR-P performs better,underestimating the first peaks in the C2–Ow/Hw RDFs by~15%, as compared to the underestimates of ~30% given byECCR. Similarly, the shapes of the C1–Ow/Hw RDFs arebetter described by the ECCR-P model.

To ensure compatibility with ox-2, the O2 atom type that wassuggested for the O2, O3, and O4 atoms in the initial modelprovided by the Antechamber routine was replaced with theOX atom type. Especially for the O3 and O4 atoms, this changeincreased the agreement with the RDFs given by AIMD (resultsnot shown). As also done for ox-2, all of the bond-stretching andsome angle-bending equilibrium values were modified (Table S3of the ESM). The equilibrium C2–O3/O4 and C1–C2 bondlengths from ox-2 were adopted, as well as the equilibriumO3–C2–O4 angle. Others were adjusted to match the AIMDresults (Table S1 of the ESM). As pointed out in our previousstudy [10], the barrier height for the O–C–C–O torsion angledepends on the surroundings of the system, i.e., whether thesystem is in the gas phase or in implicit or explicit water.Whereas a planar geometry is the most stable for this system inthe gas phase and implicit water, the staggered geometry is themost populated one in explicit water. This preference for a stag-gered geometry was also supported by the results of ab initiooptimization and AIMD in a microsolvated system.

Again, as also done for ox-2, the previous 30-ps AIMDtrajectory was prolonged to 60 ps to further explore this phe-nomenon. The histograms and the time evolution of the O–C–C–O torsion angle depicted in Figs. 3 and Fig. S3 of the ESMconfirm that the staggered conformation is dominant inexplicit-water AIMD simulations. The distribution of this tor-sion angle is slightly different from that for ox-2. Due to thepossible formation of an intramolecular hydrogen bond be-tween a COOH hydrogen and one of the COO− oxygens andan intermolecular H-bond with a water molecule in the firstsolvation shell, planar structures are more common for ox-1than for ox-2 (Fig. 3), which leads to an average torsion anglethat is closer to 0° than seen for ox-2 (Table S1 of the ESM).However, this effect cannot be fully accounted for during thefitting procedure for the O–C–C–O torsion angle, since theempirical rotational profile is based on fitting ab initio data

Fig. 4a–e Radial distribution functions between a water oxygen (–) or awater hydrogen (right column) and various oxygen and carbon atoms inthe hydrogenoxalate ion: a O1 (protonated) oxygen, b O2 oxygen, cO3 and O4 oxygens, d C1 carbon, and e C2 carbon. For a guide to theatom labeling scheme used, see Fig. 1

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either in the gas phase or in implicit solvent (assuming wewant to be consistent with the philosophy applied to generatethe other Amber force-field parameters).

Therefore, we adopted the dihedral parameters from ox-2for the CMD model, with satisfactory results (Table S3 of theESM). In this case, the CMD torsion profile showed only aslightly higher preference for staggered geometries than seenin AIMD simulations (Fig. 3), but the broader dihedral distri-butions observed with AIMD were reproduced well.

The ECCR-P model gives a much better match to the ex-perimental value of the diffusion coefficient of ox-1 (Table 2and Fig. S4 of the ESM), whereas the RESP method slightlyunderestimates it. Interestingly, the ECCR model overesti-mates the experimental value of the diffusion coefficient by24%. Evidently, the reduction of all charges in the ECCRmodel leads to increased diffusivity compared to the morenegative COO− group in ECCR-P.

Conclusions

Models of hydrogenoxalate and oxalate ions for classical mo-lecular dynamics simulations were parametrized using theECCR approach, with partial charges reduced to 75% of theirnormal charges to compensate for the absence of electronicpolarizability in the CMD simulations. Selected bonding andnonbonding parameters of (hydrogen)oxalate ions were opti-mized. The resulting ECCR and ECCR-P models, togetherwith the standard RESP models, were evaluated by compari-son with AIMD and experimental data.

Compared to the RESP charges, the models with scaledECCR charges provided better agreement with the AIMDand experimental results. This was especially true for the di-valent oxalate dianion. Models with full RESP charges pre-sented solvation shells that were too compact, and the inter-actions between water and oxalate oxygens wereoverestimated. This led to reduced mobility and lower diffu-sivity of the oxalate ion in water compared to the experimentaldiffusion coefficient.

Our discussion of the results led us to conclude that for thedivalent oxalate ion, and highly probably similarly chargedpolyvalent organic ions in general, the ECCR model is signif-icantly superior to the standard RESP model and should beused—in conjunction with adequate ECCR models of otherions of course—to preserve the charge balance of the studiedsystems. We were not able to achieve satisfactory model per-formance by only modifying the geometric parameters of themodel; it was necessary to reduce the total charge of the oxa-late dianion from its normal value too.

For the monovalent hydrogenoxalate ion, the RESP,ECCR, and ECCR-P models (with the latter scaling only thecharges of the atoms in deprotonated COO−) did not showdifferences in performance that were as dramatic as those seen

for ox-2, but the ECCR-P model gave results that were in thebest agreement with AIMD and experimental data.

We can therefore conclude that the ECCR-P model givesthe most balanced results for all of the studied phenomena,and ensures consistency with the ECCR model for ox-2, forwhich the advantages of this approach are indisputable. Asalso seen for ox-2, the ECCR-P model performs equally wellwith the SPC/E and TIP3Pwater models (Fig. S5 of the ESM).Both of these common water models can therefore beemployed in CMD simulations of oxalic acid ions using ourmodels.

Acknowledgements The authors were supported by the Czech ScienceFoundation (project 17-10734S) and by the Ministry of Education, Youthand Sports of the Czech Republic (project LTAUSA17163).Computational resources were provided by the MetaCentrum under theprogram LM2010005 and the CERIT-SC under the program CentreCERIT Scientific Cloud, part of the Operational Program Research andDevelopment for Innovations, Reg. CZ.1.05/3.2.00/08.0144.

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