Article pubs.acs.org/JPCA
Theoretical Study on Stable Small Clusters of Oxalic Acid with Ammonia and Water Kevin H. Weber, Qian Liu, and Fu-Ming Tao* Department of Chemistry and Biochemistry, California State University, Fullerton, California 92834, United States S Supporting Information *
ABSTRACT: Thermodynamically stable small clusters of oxalic acid (CO2H)2, ammonia (NH3), and water (H2O) are studied through quantum chemical calculations. The (CO2H)2−NH3 core system with up to three waters of hydration was examined by B3LYP density functional theory and MP2 molecular orbital theory with the aug-cc-pVDZ basis set. The (CO2H)2−NH3 core complexes are observed to hydrogen bond strongly and should be found in appreciably significant concentrations in the atmosphere. Subsequent hydration of the (CO2H)2−NH3 core, however, is found to be somewhat prohibitive under ambient conditions. Relative populations of the examined clusters are predicted and the binding patterns detailed. Atmospheric implications related to new particle formations are discussed.
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INTRODUCTION Aerosols have a profound effect on humankind via their influence on weather/climate and health quality. As it stands, the initiation of new particle formation (NPF) events remains the least understood process related to aerosol production.1 At the same time, the initiation events are possibly the most important, as these initial formation steps are thought to be rate determining.2 The neutral seeds of newly formed particles (size range of ∼1−2 nm) have only recently begun to be directly characterized experimentally.3 A substantial pool of neutral thermodynamically stable clusters (TSCs) in the sub-2-nm cluster size range were observed to have a constant presence in the atmosphere, and although these clusters did not determine the occurrence of NPF events, they are believed to play an important role in the formation of the critical seed embryos that lead to further growth and NPF. Neutral TSCs dominated this cluster size range over previously identified charged clusters, being detected with concentrations on an order of magnitude greater than nucleation mode (3−12 nm range) aerosols. The key process is likely an activation of TSCs by stabilizing agents thus initiating nucleation. Eventually, the aerosols reach the size of ∼50 nm and beyond where they now affect cloud microphysics as cloud condensation nuclei (CCN) and effectively scatter light contributing to Earth’s albedo. Up to about 1.2 nm, the TSCs are working to overcome the Kelvin barrier in a constant state of evaporation and condensation with their resultant growth being quite slow. As the clusters reach a size of approximately 1.2−1.9 nm, acids, amines, and organics are believed to play the critical role in stabilization and growth of the TSCs to a critical embryo. At around this size the clusters overcome the Kelvin effect and rapidly grow resulting in NPF events. Experimental work has often produced conflicting results with regards to the role of © 2014 American Chemical Society
various chemical moieties in, and the composition of, critical clusters.4−8 The key role of sulfuric acid in these processes is well-known, and it is perhaps the most important nucleating species in the atmosphere. As a result, extensive theoretical and experimental investigation into the atmospheric chemistry of sulfuric acid has been conducted. Only more recently has the importance of amines and organic acids been contemplated and realized.9−11 Here, quantum chemical examinations of these initial TSCs can provide valuable insight into the gas to particle transition thus bridging the gap from aerosol precursor to initial TSCs and then to nascent particles. To better understand aerosol particle chemistry and its influence on the environment, it is important to study TSCs and examine the pathways that lead to the formation of the critical embryos capable of subsequent growth to aerosol particles (∼3−50 nm) and then to CCN. Atmospheric aerosols often contain a considerable amount of organic matter. Organic acids have been found to enhance nucleation and growth of nanoparticles involving sulfuric acid.12 However, the dimers and heterodimers of the biogenic organic acids investigated (e.g., cis-pinoic) alone were not found to be favorable in NPF due to the hydrophobic portion of those molecules. Dicarboxylic acids are common organic pollutants in the atmosphere produced by agricultural and industrial activities, automobile exhaust, and secondary pathways such as photo-oxidations of volatile organic precursors, heterogeneous reactions on particle surfaces, and aqueous in-cloud reaction mechanisms.13 These acids are now known to play an important role in ice nucleation,14−17 cloud condensation,18 Received: December 31, 2013 Revised: January 22, 2014 Published: January 28, 2014 1451
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and the production of fine particulate matter.19,20 For example, Satsumabayashi et al.21 report a study where dicarboxylic acids constitute 30−50% of the total organic particulate matter present in the sampled atmosphere. Oxalic acid is the most common dicarboxylic acid in Earth’s atmosphere22−25 and is quite soluble.23,26 Considering the high solubility in water, it is not surprising that dicarboxylic acids have also been found in rainwater, snow, ice, and fog.27 It is the major constituent of water-soluble organic matter in urban, rural, and remote background air28−30 correlating to concentrations 2−3 orders of magnitude greater than those of NH3, possibly the principle stabilizer of binary sulfuric acid−water clusters. Ammonia is the dominant base in the atmosphere, with a typical concentration between 0.1 and 10 ppb over the continental lower atmosphere, primarily a result of animal wastes, NH3-based fertilizers, and emissions.31 Ammonia plays an important role in aerosol growth by reducing the evaporation of nucleating acids and readily reacting with acidic constituents to form ammonium salts forming ion pairs that reduce the free energy of atmospheric particles.32 Both of these processes promote the growth of atmospheric aerosol particles. It is interesting to note that in field studies by Mensah et al.33 solid oxalic acid and its solutions commonly experienced significant contamination with ammonium when exposed to atmospheric air. The gas-phase reaction of (inorganic acid) H2SO4 and NH3 is responsible for the creation of sulfurcontaining particulates such as (NH4)HSO4 and (NH4)2SO4. Along with particulate H2SO4, these species represent the three major forms of sulfur-containing aerosols that play a central role in the formation of CCN.34 Previous work from this group clearly demonstrated that the stable form of H2SO4−NH3 in the gas phase is strongly hydrogen bonded, not an ion pair. However, the presence of as little as one single water molecule is sufficient to stabilize the NH4+·HSO4− ion pair.35 Subsequent work by Ianni and Bandy36 has shown that free energy of ion pair formation becomes favorable in clusters containing at least four water molecules. It has been shown that sulfuric acid and ammonia cannot explain the observed nucleation rates in the lower atmosphere. Organic acids, however, have been predicted to stabilize both neutral and positively charged prenucleation clusters and warrant further investigation.37 Here, we investigate the possibility for oxalic acid to behave in a manner similar to the ternary sulfuric acid system. Similar problems have been studied for the nitric acid−ammonia (HNO3−NH3) and the hydrogen chloride−ammonia (HCl-NH3) systems.38,39 For complete proton transfer to occur, two or more waters were required for those acids. Here we extend this technique to study the oxalic acid−ammonia system. Oxalic acid is somewhat surprisingly strong for a carboxylic acid, approximately ∼3000 times stronger than acetic acid. We can ask this question, how strong is the oxalic acid−ammonia complex interaction, and furthermore, how is that complex affected by the presence of explicit water molecules (i.e., at what point will ionization occur)? Of course, both neutral and ionic forms will be found dissolved in the aerosol; however, the ionized form is of particular interest as it may interact with polar dipoles of atmospheric precursor and promote nucleation in a more efficient manner than neutral species.40 To better understand the properties and effect for this particular compound it is advantageous to visit as many competitively stable cluster configurations and elucidate which lead on to proton transfer. Our previous work41 on the hydration of (CO2H)2−(H2O)n, with n = 0−6 water molecules demon-
strated the strong cooperative binding between water and oxalic acid, especially for two waters binding to a (Z) acid. As the clusters grow, dipole cancellations play a significant role in forming very stable neutral clusters. For n ≥ 5 ion pair, formation is predicted to be spontaneous and yet not favorable when entropic contributions are considered. For n = 5 and n = 6, an ion pair structure is found as a local minimum, but the global minimum is still a hydrogen bonded cluster. For all the clusters examined of the (CO2H)2−(H2O)n, n = (0−6) systems, neutral hydrogen bonded clusters are predicted to be more stable than the ion pair clusters. Eventually, one would expect the clusters containing ion pair to become global minima with respect to the other clusters when the nascent ions are properly solvated. For the case of similar carboxylic acids formic and acetic, neither theory nor experiment has yet identified any cluster size for which the lowest-energy form contains a microsolvated ion pair.42 The importance of homogeneous nucleation in NPF events has been demonstrated theoretically and experimentally.43,44 NPF have been directly linked to CCN production45 and exactly how these particles form and grow remains thus far elusive. The question remains as to what degree each mechanism governs the initial steps of particle formation and growth under different atmospheric conditions. Knowledge of the role of organic compounds in aerosols remains lacking, and theoretical work has only begun to glean insight to the role of organic acids in initial atmospheric nucleation events.46,47 A clear and insightful understanding of organic assisted nucleation is imperative to better understand and model aerosol formation. Aerosol embryos are not a true phase as they lack a sufficient number of molecules required to produce the behavior of the bulk phase.4 As a result they are difficult to model, as the shortcomings of classical nucleation theory have demonstrated. The importance of the quantum approach has been pointed out by Nadykto et al.40 Also, their extremely small size being at or often below the detection limit of the current instrumentation, have proved them difficult to observe and research experimentally. Here, quantum computational chemistry techniques have been quite useful for investigating these nanometer and subnanometer events. In this article, we detail the effect of water molecules on the structure and energies of clusters of the oxalic acid−ammonia system by calculation on the clusters (CO2H)2−NH3−(H2O)n (n = 0−3). We examine the feasibility of the gas phase accretion and also ion pair formations under atmospheric conditions. The ability of oxalic acid to stabilize cations and inorganic acid has been recently explored,2 but ionization events involving ammonia with oxalic acid remains, to our knowledge, unreported.
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THEORETICAL METHODS The equilibrium geometries of the monomers and clusters constructed in this work were optimized using the Becke threeparameter exchange density functional theory with the nonlocal correlation provided by Lee, Yang, and Parr (B3LYP). These computational methods have proved reliable for equilibrium parameters in these hydrogen bonded systems. However, the relative utility of B3LYP in comparison to simple correlated methods such as the Møller−Plesset second-order perturbation (MP2) level of theory has been debated without a clear conclusion. Therefore to further investigate the differences between the B3LYP and MP2 results, additional MP2/aug-ccpVDZ calculations were performed for the monomers and 1452
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oxalic−ammonia cores. The molecular clusters (CO2H)2− NH3−(H2O)n (n = 0−3) were assembled from the optimized monomers (CO2H)2, H2O, and NH3. These configurations were completely optimized implementing full analytical gradients. Configurations of competing stability are examined especially for the larger clusters where the most stable configurations are not necessarily obvious, and competing assemblages must be considered. The relatively small basis of 631+G* was used in conjunction with the computationally affordable B3LYP method to initially identify thermodynamically stable clusters. From that point the results were refined by making use of Dunning’s augmented correlation consistent polarized valence double-ζ basis, aug-cc-pVDZ, considered to be sufficiently large for reliable results. Although the accuracy of interaction energies produced by the B3LYP functional have been questioned, we have explored the single-point energies at the MP2 and QCISD levels of theory based on the B3LYP optimized structures for the oxalic acid−water system and found them to be reasonably comparable.41 All calculations were implemented using the Gaussian 09 program package.48 Although widely implemented in the theoretical study of these types of clusters, there have been questions raised about the accuracy of the interaction energies produced by the B3LYP functional method.49 Discrepancies have been observed in calculations due to differences in theory, basis set completeness, counterpoise (CP) correction for basis set supposition error, and the errors introduced by the harmonic oscillator approximation. Kurten et al.49 conclude that the anharmonic contribution to error is small compared to overcorrection by the CP method with B3LYP, that large augmented basis sets produce better values without CP correction, and that similar values are produced by both the B3LYP and MP2 level calculations. Thus, the B3LYP and MP2 values calculated in this work remain uncorrected for BSSE. Relative electronic energies are reported as the single-point energy of the cluster in a given conformation with respect to that of the cluster in the most stable conformation. Different cluster configurations with the same number of ammonia and water molecules (n) are arranged in order of increasing relative energy as determined by calculations. B3LYP/aug-cc-pVDZ frequency calculations were used to verify the existence of local minima and produce the interaction enthalpy and free energy changes, ΔH298K and ΔG298K, defined as the energy difference between the cluster and the corresponding infinitely separated monomers ((CO2H)2, NH3, and H2O) that compose the cluster. Relative free energies are also reported for monomers.
Figure 1. Optimized structures for the stable conformations of oxalic acid identified from B3LYP/aug-cc-pVDZ calculations. Symmetry is denoted in parentheses, and bond distances are in Angstrom. Also, in parentheses are the relative single-point (0 K) and Gibb’s free energies (298 K) in units of kcal mol−1. Dipoles are reported in units of Debye. Color coding of the elements are as follows: carbon (gray), hydrogen (white), oxygen (blue), and nitrogen (blue).
intramolecular interactions that are present. As a result, there has been considerable discussion and investigation into the nature of these interactions and indeed into the nature of hydrogen bonding in general. In the oxalic acid monomer, two very general types of intramolecular interactions are possible (1) the five-membered ring intramolecular hydrogen bonds (IHBs) created by a H−O−C−C−O circuit (of which there turns out to be two distinct forms, see below) and (2) the fourmembered ring dipole−dipole interaction (DDI) found in the (Z) carboxlic acid fragment. Hermida-Ramón and Mosquera56 conducted a quantum theory of atoms in molecules (QTAIM) analysis of the intramolecular interactions present in (Z) and (E) conformations of formic and acetic acid as well as those interactions found in the conformations of oxalic acid at the HF, B3LYP, and MP2 level of theory. They concluded that the preference for the (Z) conformation over the (E) is not due to an IHB nor increased hyperconjugation delocalizations of the E conformation. Rather, it was determined to be an effect related to the lone-pair/lone-pair repulsions (sterics) on the charge distribution. The work of Hirao57 on formic acid with HF/6311+G(d,p), B3LYP/cc-pVTZ, and CCSD(T)/cc-pVTZ calculations came to essentially the same conclusion with the (Z) preference explained by the secondary electrostatic interaction between carbonyl oxygen and proton. Hermida-Ramón and Mosquera’s analysis of oxalic acid found that according to the QTAIM bond critical point (BCP) criteria, an IHB is only consistently predicted to exist for the cCt isomer (although there is one predicted for the cTt conformer at the B3LYP level of theory). This conclusion seems to rather highlight the issue of whether the BCP criterion is appropriate or accurate in the demarcation of hydrogen bonds.58 Another example of the
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RESULTS AND DISCUSSION Oxalic Acid Monomers. Geometry and Energies. The structures of the oxalic acid monomers along with select interatomic distances, unscaled OH vibrational stretching frequencies, molecular dipoles, relative electronic, and free energies from B3LYP/aug-cc-pVDZ calculations are presented in Figure 1. The nomenclature is the system introduced by Nieminen et al.50 where the lower case letters refer to cis (c) or trans (t) dihedral angle of H−O−C-C where cis receives priority (is denoted first) over the trans configuration. The uppercase letter refers to cis (C) or trans (T) dihedral for O C−CO. The various monomer conformations have been studied extensively by this group41 and others.51−55 It turns out to be an interesting story. The relative stabilities of the various conformations of oxalic acid are largely determined by the 1453
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Figure 2. Optimized structures of (CO2H)2−NH3 cores from B3LYP/aug-cc-pVDZ calculations. Relative single-point energies, ΔEr, interaction enthalpies, ΔH298K in italics, and free energy changes, ΔG298K in red, are reported in parentheses. The values in brackets are the r(OH···N) hydrogen bond interaction distance, r(O−H) donor acid covalent O−H bond length (both in angstrom), and deviation from linearity (180°) of the formed hydrogen bond with ammonia (∠OH···N) reported in degrees. The local pKa1 values were calculated from the relationships developed in ref 62. The overall Boltzmann factor corrected pKa1 value for oxalic acid is 1.07.
to further examine the results of steric interactions. In the crystal structure of ammonium oxalate monohydrate62 the C− C bond is found to be particularly long, 1.569 Å, a feature that was not quite understood (along with an additional peculiarity of a twisting of the oxalate dicarbonyl dihedral to 26.6°). In the crystal structure of ammonium hydrogen oxalate hemihydrate, however, the C−C bond distance is typical, and the hydrogen oxalate backbone is planar.63 The IHB present in cTc has an interaction distance of 2.131 Å and the ν(OH) stretching frequencies are 3631 and 3634 cm−1 (these frequencies are considerably overestimated compared to experiment50,55). The O−H···O angle is 116°, characteristic of a highly strained hydrogen bond. The cTc conformation is the most stable and as such the electronic and free energies serve as the reference energies for the remaining conformations. The cTt conformation is found with Cs symmetry and a 3.14 D molecular dipole. The C−C bond distance is 1.545 Å, also typical of a C−C bond. The IHB distance is 2.081 Å, somewhat attenuated from that found in the cTc isomer with an O−H··· O angle of 117°. The carbonyl group participating in the IHB is also involved in the DDI of the (Z) carboxylic acid group. The DDI distance is 2.337 Å with an O−H···O angle of 74°, clearly not a hydrogen bond. The ν(OH) stretching frequency of the mode coupled to IHB is 3655 cm−1, slightly blue-shifted from the cTc modes indicating a slight dampening of the IHB (even though the IHB distance is slightly shorter, which is typically associated with an increase in hydrogen bond strength. The (Z) acid group ν(OH) frequency is calculated to be 3733 cm−1, significantly higher in energy than the IHB. Although the frequencies calculated are not believed to be quantitatively reliable, they are thought to be qualitatively correct. The relative single-point energy of cTt is 2.65 kcal mol−1, while the relative free energy is 1.93 kcal mol−1. The tTt conformation of oxalic acid was found with a C2h symmetry point group for this particular theory level and basis and thus no molecular dipole. The C−C bond distance is
convoluted nature of the situation are the results of Kurten et al.59 in which the presence of a BCP and the nature of the bond path in the binding of nucleation precursors H2SO4 and NH3 is dependent on the level of theory employed (in their study B3LYP, PW91, and MP2 with various basis). In our previous analysis41 the five-membered interactions were classified as strained hydrogen bonds and the four-membered interactions as strong dipole−dipole interactions (primarily electrostatic) based on the recent guidelines advanced by the IUPAC.60,61 However, the distinction appears to be subtle, at least in the case of the cCt conformer, where the five-membered ring interaction with a sp3 O acceptor as opposed to sp2 is found to be considerably deactivated with a predicted interaction energy comparable to the strong electrostatic dipole four-membered ring, (Z) carboxylic acid self-interaction. The existence (and conformation) of stable local minima varies considerably for calculations of different levels of theory and basis. For example, at the B3LYP/6-31+G* level of theory all stable minima are predicted to be planar.41 However, the inclusion of diffuse function causes the high energy cGc isomer found by others50−52 to lie on a repulsive potential energy surface. Another inconsistency encountered by the various methods is that with a 6-311++G(d,p) basis set both MP2 and B3LYP calculations predict a deviation from planarity for the monomers that are not locked into place by intramolecular hydrogen bonds, i.e., the tTt and tCt conformers with two (Z) acid groups.41,52,53 Further, with B3LYP/aug-cc-pVDZ calculations the tCt conformation is predicted to also lie on a repulsive surface,41 while with MP2/aug-cc-pVDZ calculations at an elevated temperature the tCt isomer is considered to be an excited state of tTt.53 In Figure 1 select parameters for the B3LYP/aug-cc-pVDZ identified stable minima are reported. The cTc conformation possesses C2h symmetry with no resultant molecular dipole. The C−C bond length is predicted to be 1.544 Å, which is typical for a C−C bond. The C−C bond lengths are monitored 1454
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mol−1. It is interesting to note that initially tTt-NH3 was predicted more stable than cCt-NH3 with a planar geometry for tTt, but upon frequency analysis (at least for the B3LYP/augcc-pVDZ calculations), it was discovered to not be a true bound complex, having a negative frequency. Further optimization to a predicted real bound tTt-NH3 conformation (see below) resulted in a switching in stability ordering. The interaction enthalpy and free energy changes for cCt-NH3 are the greatest predicted for the binding of an oxalic acid conformer to ammonia. However, the hydrogen bonding distance is longer, 1.647 Å, and the OH covalent bond similarly extended (approximately 0.05 Å) as in the cTc-NH3 cluster, 1.027 Å from 0.972 Å, compared to in the cTc cluster, yet the redshift of the ν(OH) stretching frequency is greater at 1066 cm−1. The IHB distance is slightly shorter than in the cCt monomer (1.998 Å from 2.042 Å), and the IHB angle is 118°, slightly relaxed from the monomeric value for cCt. The OH covalent bond participating in the IHB is slightly extended from 0.970 Å to 0.973 Å. The interaction distance resulting from the weaker hydrogen bond formed by a hydrogen of NH3 with the carbonyl oxygen of the (Z) acid that is hydrogen bonding is 2.627 Å, and the strained hydrogen bond angle is 111°. The binding of ammonia to the tTt conformer of oxalic acid induces a twisting of the OC−CO dihedral angle to 115.1°. The relative electronic energy of tTt-NH3 is similar to cCt-NH3 at 3.88 kcal mol−1 above the cTc-NH3 cluster. The interaction enthalpy, ΔH298K = −11.09 kcal mol−1, is very similar to the cTc-NH3 value; however, this appears to be serendipitous as the binding motif is to the otherwise unbound (Z) acid group as opposed to the (E) group in cTc. The free energy change of interaction is substantial at ΔG298K = −3.55 kcal mol−1. The O−H···N hydrogen bonding distance is 1.682 Å, while the ν(OH) redshift is 940 cm−1 and the O−H covalent bond is 1.020 Å, lengthened from 0.974 Å. The hydrogen bond angle is nearly linear, deviating by 7°. The secondary strained hydrogen bond distance is 2.665 Å with an angle of 111°. The DDI appears to remain unaffected as the distance is found to be 2.322 Å compared to 2.326 Å in monomer tTt and the DDI angle remains identical at 74°. The cTt monomer of oxalic acid has two locals for binding of the ammonia monomer: (1) the interior pocket created by the (E) acid and adjacent carbonyl of the (Z) acid or (2) the exterior pocket of the (Z) acid group. The cTt-(NH3)a cluster in which the ammonia is bound to the exterior is the most stable cTt-NH3 cluster with a single-point energy 3.94 kcal mol−1 above the cTc-NH3 reference. The cTt-(NH3)a cluster has NH3 bound to the exterior (Z) acid group of cTt with a hydrogen bonding distance of 1.666 Å, deviation from linearity of 4°, and extension of the OH covalent bond to 1.023 Å from 0.975 Å. The associated redshift of the bound OH group is 979 cm−1, slightly less than observed in binding of NH3 with (the more polar) cCt isomer. The calculated interaction enthalpy, ΔH298K = −12.06 kcal mol−1, is diminished in magnitude compared to the cCt-NH3 complex, consistent with the aforementioned structural parameters. The free energy change is also less favorable, ΔG298K = −3.83 kcal mol−1. Both the cCt and cTt conformers are binding to NH3 via a (Z) acid group however, in cCt the IHB is much weaker, as previously demonstrated. It is curious that the entire binding of NH3 appears to be somewhat deactivated compared to cCt. In addition to the previously described parameters, the secondary hydrogen bonding distance is also greater at 2.853 Å with an angle of 104°. This secondary interaction is similar to the
slightly shorter at 1.542 Å but still in the range of a typical value. Both the (Z) acid groups have a DDI distance of 2.325 Å calculated ν(OH) frequencies of 3743 and 3744 cm−1. The (Z) acid DDI angles are 74° as found for the DDI angle in cTt and the relative electronic and free energies are 4.15 and 2.94 kcal mol−1, respectively. The least stable minima located by B3LYP/aug-cc-pVDZ calculations, cCt, is perhaps also the most interesting of the conformers. In this conformation the cis-OC−CO dihedral introduces a oxygen to oxygen steric interaction ( O···O distance of 2.851 Å), which results in a lengthening of the C−C bond distance, now 1.550 Å, albeit modest to slight. This conformation has Cs symmetry and a relatively large molecular dipole of 4.85 D. Here, the basic scaffolding of the molecule based on the intramolecular interactions present is very similar to what would be predicted from the more stable conformations. The IHB and DDI angles are basically unchanged at 116° and 73°, respectively, while the IHB and DDI distances are 2.042 and 2.344 Å, remaining essentially unaltered. However, the ν(OH) stretching vibrational frequencies tell a different story as do the relative energies. In the cCt conformation the ν(OH) frequency for the OH involved in IHB is 3736 cm−1! This is much higher in energy than would be expected for an IHB and is comparable to the DDI interaction frequency of 3742 cm−1. Also, the relative electronic and free energies are higher than would be expected from combination of one IHB and one DDI at 6.00 and 4.75 kcal mol−1, again with respect. Both of these properties are evidence of a different type of IHB. Clusters with NH3 and H2O. (CO2H)2−NH3. The five stable clusters of oxalic with ammonia from B3LYP/aug-ccpVDZ calculations are presented in Figure 2. Relative electronic single-point energies, intermolecular enthalpy, and free energy changes corresponding to values at 1 atm and 298 K, ΔH298K and ΔG298K, for the (CO2H)2−NH3 complexes are presented. Also reported in the figure (in brackets) are the hydrogen bond acceptor (i.e., OH···N) distance, the O−H covalent bond length, and deviation from ideal hydrogen bond angle (180° − x, where x = ∠O−H···N) for analysis of bonding strengths. As found in the binding of acetic and formic acids with ammonia,46,47 two hydrogen bonds are predicted to form, one of moderate strength and one weak. The most stable cluster identified, cTc-NH3, produced an intermolecular enthalpy change ΔH298 = −11.07 kcal mol−1 and free energy change ΔG298 = −2.65 kcal mol−1. The stronger hydrogen bond, as evidenced by the shorter bond distance, nearly linear bond angle, and ν(OH) redshift of 1013 cm−1 is formed between one of the (E) acid groups of the cTc monomer and the nitrogen of ammonia with a distance of 1.631 Å, while the OH covalent bond extends to a length of 1.031 Å from 0.978 Å. A second, weaker, hydrogen bond is at the same time formed between a proton of ammonia and an adjacent carbonyl group of oxalic with a hydrogen bond distance of 2.280 Å creating a H···OC angle of 121°. In response to the opening of one side of the cTc conformation to accommodate the binding of ammonia, the strained IHB distance of cTc is constricted to a value of 1.955 Å from 2.131 Å. The OH covalent bond participating in IHB is nearly the same as in the monomer, extended 0.003 Å to 0.983 Å, meanwhile the IHB angle relaxes from 116° to 121°. The second most stable complex is predicted to be the cCtNH3 cluster, 3.83 kcal mol−1 above cTc in electronic energy and has ΔH298K = −12.87 kcal mol−1 and ΔG298K = −4.18 kcal 1455
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set in this study is slightly different than the 6-311+G(d) from the original work. It is interesting to look at the local pKa1 estimated for each conformer of oxalic acid. The most acidic conformation is the cCt conformation (pKa1 = 0.99). The cCt conformation is also the least stable conformation of oxalic acid and deprotonation results in formation of the resonance stabilized cTc− anion, which is estimated to be 12.45 kcal mol−1 more stable than the other potential conjugate base form, tTt−.64 Formation of the cCt-NH3 core cluster is predicted to be most exergonic, ΔH298K = −12.87 kcal mol−1, by both B3LYP methods. The second and third most acidic conformations are cTc (pKa1 = 1.03) and cTta (pKa1 = 1.92). Here, we note the stronger binding for the (Z) conformation of the carboxylic acid group (ΔH298K = −12.06 kcal mol−1 for cTt-(NH3)a and ΔH298K = 11.07 kcal mol−1 for cTc-NH3). Although the binding in cTt-(NH3)a is energetically more favorable, the geometric considerations indicate a more powerful interaction with cTc with greater redshifting of OH stretching mode (1013 vs 979 cm−1) and shorter hydrogen bond distances (1.631 vs 1.666 Å for the primary hydrogen bond and 2.280 vs 2.853 Å for the secondary hydrogen bond) with the cCt conformation; the more stable cTc− conjugate base results from deprotonation. The remaining conformations tTt and cTt-b have local pKa1 = 2.73 and pKa1 = 4.38, respectively. Both these acid conformations deprotonate to produce the tTt‑ conjugate base. Although the deprotonated conjugate bases are not actually yet formed in these complexes, i.e., they remain strongly hydrogen bound, the indications of the impending ionization can already be detected through the molecular parameters monitored in this analysis. Comparison to Formic and Acetic Acid Binding to Ammonia. The binding of the cTc conformer to ammonia was calculated by Xu et al.2 at the PW91PW91/6-311+ +(3df,3pd) level to be ΔH298 = 13.64 kcal mol−1 and ΔG298 = −4.42 kcal mol−1. For comparison, the ΔH298 and ΔG298 values from PW91PW91/6-311++(3df,3pd) calculations for the binding of formic acid with ammonia are ΔH298 = −11.63 kcal mol−1and ΔG298 = −2.82 kcal mol−1, and for acetic acid with ammonia, ΔH298 = −10.78 kcal mol−1 and ΔG298 = −2.35 kcal mol−1.46 This would indicate that oxalic acid binds more strongly to ammonia due to greater acidity, as expected from pKa. In comparison, our results with the aug-cc-pVDZ basis at B3LYP (ΔH298 = −11.07 kcal mol−1 and ΔG298 = −2.65 kcal mol−1) and MP2 levels of theory (ΔH298 = −12.24 kcal mol−1 and ΔG298 = −4.14 kcal mol−1) are consistent with the picture that has developed concerning the reliability of these methods. To be more specific, it has been revealed that the PW91PW91 functional tends to produce values that are overbinding and the B3LYP functional to be underbinding.59 The MP2 values (with a sufficiently large basis set) are believed to produce reasonable accurate depictions of the interaction energies, albeit at a greater computational cost. Unfortunately, in this instance there is still no experimental measurement of oxalic acid−ammonia complex for comparison. To further investigate the differences between these levels of theory in this work the oxalic acid− ammonia cores are also characterized by MP2/aug-cc-pVDZ calculations. The resultant structures along with select parameters are presented in Figure S1 (Supporting Information). Notably, the cTt-(NH3)a cluster is predicted to be much more stable by the MP2 method. Additionally, as noted previously, the tCt conformation of oxalic acid is predicted to be stable. The main concern regarding the implications for atmospheric processes is reliability of the resultant free energy
secondary interactions in the other previously discussed (Z) acid binders, cCt-NH3 and tTt-NH3. Although the cCt-NH3 interaction is not isolated in that the (E) acid group is participating in IHB with the (Z) acid OH group, for the cCtNH3 conformation the IHB to the oxygen of the (Z) OH group acts to further withdraw electron density from the acidic proton thus enhancing the hydrogen bond and the IHB as evidenced by the larger redshift and tighter hydrogen bond distances compared to tTt-NH3. In the cTt-(NH3)a cluster, the secondary interaction is formed with the carbonyl of the (ammonia binding) (Z) acid group that is a double acceptor, it also is directly involved in the IHB of the (E) configuration acid. This acts to slightly enhance the primary hydrogen bond between the (Z) acid group and ammonia (shorter distance, smaller deviation from linearity, and greater redshift compared to tTt-NH3). At the same time, the double coordination of the (Z) acid carbonyl group weakens the secondary interaction by competing for electron density. The IHB distance in the cTt(NH3)a cluster is 2.015 Å (compared to 1.955 Å in cTc-NH3) and the OH covalent bond distance is 0.978 Å (compared to 0.983 Å in cTc-NH3) both indicating that the IHB in cTt(NH3)a is also somewhat weakened. Binding of NH3 to the interior pocket of cTt oxalic is depicted in cTt-(NH3)b, which is 5.11 kcal mol−1 higher in relative energy. Formation of this cluster is the least favorable of the oxalic acid−ammonia cores. The change in enthalpy upon binding of NH3 is ΔH298K = −8.52 kcal mol−1 and the free energy change ΔG298K = −0.79 kcal mol−1. The weaker binding is also evidenced by the longer hydrogen bond distance of 1.707 Å, the less extended OH covalent bond length of 1.015 Å, greater deviation from ideal hydrogen bonding angle, 13°, and attenuated redshift of 751 cm−1. However, the secondary hydrogen bond formed between hydrogen of NH3 and oxygen of the adjacent carbonyl group is allowed to strengthen due to the weakening of the primary hydrogen bond. Here the NH··· O distance is 2.405 Å and angle, 114°. This distance is considerably greater than in the cTc-NH3 cluster in which there is also binding to the interior pocket but the DDI present (with distance of 2.302 Å, angle of 75°, and OH covalent bond length of 0.972 Å) acts to deactivate the binding for the interior pocket of cTt compared to cTc. This is consistent with previous results for the binding of oxalic acid with water.41 Estimation of pKa1. Calculating the DFT molecular parameters for the TSC of oxalic acid and ammonia heterodimers provided an opportunity to predict both local pKa1 values local minima and the global pKa1 for oxalic acid. Previous work64 has demonstrated effective prediction of pKa values for a large number of organic acids from established linear correlations to molecular parameters. These parameters are the covalent OH bond of the donor, r(O−H), the stretching frequency of the OH donor, ν(O−H), the intermolecular hydrogen bonding distance r(OH···N), and the electronic interaction energy, ΔEhb, taken to be the singlepoint energy difference between cluster and infinitely separated monomers. Tables S1−S3 (Supporting Information) detail the results of the analysis. As oxalic acid has many conformations each with differing reactivity, the relative contributions to pKa are corrected by a Boltzmann factor based on relative free energies of the monomer, and for the case of cTt-(NH3)a and cTt-(NH3)b, the monomer fraction is further corrected by the relative free energies of the complexes. The overall predicted pKa1 value for oxalic acid is 1.07 in good agreement with the experimental value of 1.25.65 It should be noted that the basis 1456
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Figure 3. Optimized monohydrated structures of (CO2H)2−NH3 cores from B3LYP/aug-cc-pVDZ calculations. Relative single-point energies, ΔEr, interaction enthalpies, ΔH298K in italics, and free energy changes, ΔG298K in red, are reported in parentheses. Select intermolecular distances are reported in Angstrom (Å). The values in brackets are the r(OH···N) hydrogen bond interaction distance, r(O−H) donor acid covalent bond length (both in angstrom), and deviation from linearity of the formed hydrogen bond with ammonia, reported in degrees. Redshifts from monomeric acidic OH stretching frequencies are reported in wavenumbers (cm−1).
OH···N) distance, the O−H covalent bond length, and deviation from ideal hydrogen bond angle (180° − x, where x = ∠O−H···N) for analysis of bonding strengths. All clusters examined here are found to be neutral in nature. The most stable cluster, cTt-NH3-Ia, has an interaction enthalpy of ΔH298K = −20.05 kcal mol−1 and free energy change of ΔG298K = 2.91 kcal mol−1. The acid to ammonia primary hydrogen bond is tight with a hydrogen bonding distance of 1.556 Å and
change values. The results from this work are further analyzed in the atmospheric relevance section presented subsequently. (CO2H)2−NH3−H2O. The stable clusters of oxalic acid with ammonia and one water from B3LYP/aug-cc-pVDZ calculations are presented in Figure 3. Relative electronic energies, intermolecular enthalpy, and free energy changes, ΔH298K and ΔG298K, for these clusters are reported. Additionally included in this figure (in brackets) are the hydrogen bond acceptor (i.e., 1457
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cTc-NH3-Ia cluster of 704 cm−1. This would seemingly be at odds with the previous prediction that cTt-a is less acidic than the cTc conformation, the pKa1 values being 1.92 and 1.03, respectively. Here we see that the specific local environment can have a profound effect on the chemistry in these molecular clusters compared to the bulk phase. The hydrogen bonds completing the circuit are 1.752 Å for water to ammonia and 2.194 Å for ammonia to carbonyl of oxalic acid. In the cTtNH3-Ib as in cTt-NH3-Ia, the IHB of cTt becomes part of the hydrogen bond network through a double accepting carbonyl of oxalic acid. Cluster cTc-NH3-Ic has a relative energy of 0.68 kcal mol−1 and interaction enthalpies and free energy changes of ΔH298K = −16.93 kcal mol−1 and ΔG298K = −0.60 kcal mol−1. The exergonicity is similar to the other cTc-NH3-H2O cluster formations, while the free energy change is the most favorable for this cluster type. The primary hydrogen bond to ammonia is noticeably shorter than the other cTc-NH3-H2O clusters, while the redshift is quite large at 1337 cm−1. The extension of the acid OH bond is considerable, to 1.053 Å, and although the hydrogen bonding angle deviates 16° to accommodate the bite of the cTc binding region (as found in the cTc-NH3-Ib cluster with 17° deviation), the binding in this cluster is positively cooperative. Note the IHB on the opposing side of cTc has an interaction distance of only 1.937 Å. This constriction is even more pronounced than in the cTc-NH3-Ib cluster (1.963 Å) indicating that the strength of these interactions is forcing the cTc conformer to deform in accommodation. For cCt-NH3-Ia, the relative energy is 1.77 kcal mol−1 and the interaction enthalpies and free energy changes are ΔH298K = −21.61 kcal mol−1 and ΔG298K = −4.14 kcal mol−1. The cCtNH3-Ia cluster has the most exergonic binding of any of the monohydrated oxalic acid−ammonia cores as well as the most favorable free energy change. Despite this, the relative electronic instability of the cCt conformation results in the nearly two kcal mol−1 relative energy. As expected, the primary hydrogen bond to ammonia is strong having a distance of 1.538 Å, extension of covalent OH length to 1.065 Å, redshift of 1642 cm−1, and a nearly linear hydrogen bonding angle. The water is accepting a hydrogen bond from the ammonia and secondarily bonding to the carbonyl of the (Z) acid group in cCt. The IHB coupled to the hydrogen bonded network displays a typical interaction distance of approximately two Angstroms (1.992 Å). The tTt-NH3-Ia and tTt-NH3-Ib clusters are found to have 1.97 and 2.02 kcal mol−1 relative energies. The enthalpy and free energy changes of tTt-NH3-Ia (ΔH298K = −19.15 kcal mol−1 and ΔG298K = −2.13 kcal mol−1) are similar to those for tTt-NH3-Ib (ΔH298K = −20.13 kcal mol−1 and ΔG298K = −2.17 kcal mol−1). This is interesting as the tTt-NH3-Ia cluster has a water or ammonia molecule bound to each of the (Z) acid groups. Because of the internal symmetry of the tTt conformer, additional stabilization is achieved through some cancellation of local dipoles. The tTt-NH3-Ib cluster, however, has both molecules bound to one (Z) acid group (with ammonia accepting the primary hydrogen bond), which affords cooperative binding. What is interesting here is the similarity of the thermodynamic parameters for these two clusters that have distinctively different binding modes. Upon inspection of the molecular parameters we can see a clear distinction. In tTtNH3-Ia, the redshifts are modest (927 cm−1 for NH3 binding and 457 cm−1 for H2O binding) as are the hydrogen bonding distances (1.686 and 1.757 Å) and covalent OH bond extensions (1.019 and 0.995 Å). For the tTt-NH3-Ib cluster,
the OH covalent bond significantly extended to 1.058 Å. The hydrogen bonding angle is nearly linear with only a 5° deviation. Note the hydrogen bond distance is much shorter and OH covalent bond longer than in the oxalic acid−ammonia core systems, an enhancement of binding. This is also reflected in the greater OH stretching redshift of 1529 cm−1. The bound ammonia also acts as a hydrogen bond donor to a water acceptor with a bonding distance of 1.956 Å. The water molecule simultaneously hydrogen bonds to the carbonyl oxygen of the binding (Z) acid group, which is also participating in an IHB with the adjacent (E) acid group. The resulting homodromic ring is typical of these stable hydrogen bonded networks. The cTc-NH3-Ia cluster is of competitive stability being only 0.11 kcal mol−1 less stable than cTt-NH3-Ia. The interaction enthalpy and free energy changes are ΔH298K = −17.42 kcal mol−1 and ΔG298K = −0.21 kcal mol−1. In this cluster, the binding is not as favorable and the greater stability of the cTc monomer no longer compensates. The ammonia and water bind to opposing sides of cTc forming a bicyclic homodromic system. The binding of ammonia appears to be strongest with a hydrogen bond distance of 1.655 Å and redshift of 932 cm−1 in comparison to the hydrogen bond distance with water of 1.711 Å and redshift of −390 cm−1. The overall binding, however, lacks the cooperativity of the cTt-NH3-Ia cluster as by the magnitude of the redshifts and the considerably less extended OH covalent bond lengths of 1.027 Å for the acid binding ammonia and 0.996 Å for the acid binding to water. The deviations from linearity for the hydrogen bonds are also greater with 12° deviation for ammonia and 7° for the water binding. The hydrogen bonds that complete the ring circuit are 2.291 Å for the secondary hydrogen bond between ammonia and carbonyl oxygen and 1.886 Å for the secondary hydrogen bond between water and (vicinal with respect to the aforementioned) carbonyl of oxalic acid. The cTc-NH3-Ib cluster is also similar in energy to cTt-NH3Ia, being 0.30 kcal mol−1 higher in electronic energy. The enthalpy and free energy changes for cTc-NH3-Ib are ΔH298K = −16.89 kcal mol−1 and ΔG298K = 0.25 kcal mol−1. The HB to water is fairly tight as evidenced by the 1.594 Å interaction distance. However, this hydrogen bonding network is somewhat awkward with a deviation angle of 17°. Nevertheless, cooperativity is present as the redshift of the bound acid OH is 704 cm−1 (compared to 390 cm−1 in cTc-NH3-Ia) and the OH covalent bond is extended to 1.014 Å, which is considerable when compared to the OH extension in cTc-NH3-Ia when bound to water is only 0.996 Å. The IHB on the opposing side of the hydrogen bonding network, in response to the accommodation of the bound water and ammonia, is now exhibiting an interaction distance noticeably shorter, similar to that found in the cTc-NH3 core cluster. The cTt-NH3-Ib cluster is similar in structure to cTt-NH3-Ia with the ammonia and water molecule positions in the cluster being exchanged. More specifically, water is the hydrogen bond acceptor to the donating (E) acid group and ammonia is bound by water and also, secondarily, to the neighboring carbonyl group. The result is a cluster that is 0.59 kcal mol−1 higher in energy with ΔH298K = −19.06 kcal mol−1 and ΔG298K = −1.02 kcal mol−1. The primary hydrogen bond distance is 1.580 Å, considerably shorter than hydrogen bonds to water itself, with a slight increase in the OH bond length and very nearly linear bonding angle, having a deviation of 3°. The redshift of the acid OH binding water is 880 cm−1, larger than that observed in the 1458
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Figure 4. Optimized dihydrated structures of (CO2H)2−NH3 cores from B3LYP/aug-cc-pVDZ calculations. Relative single-point energies, ΔEr, interaction enthalpies, ΔH298K in italics, and free energy changes, ΔG298K in red, are reported in parentheses. Select intermolecular distances are reported in Angstrom (Å).
the redshift is large at 1430 cm−1 and the primary hydrogen bond distance to ammonia is tight at 1.582 Å. The extension of the covalent OH bond is pronounced at 1.050 Å, and the hydrogen bond angles are nearly linear (deviation of 4° for the primary hydrogen bond). As observed in the binding of ammonia with tTt, the OC−CO dihedral of tTt twists significantly to 104.5° in tTt-NH3-Ia and 109.2° in tTt-NH3-Ib. The cCt-NH3-Ib cluster makes a primary hydrogen bond to water via the (Z) acid group with ammonia accepting HB from the water and donating a secondary HB to the (Z) acid
carbonyl group. The relative energy is approximately 0.5 kcal mol−1 above the cCt-NH3-Ia cluster for a total relative energy of 1.77 kcal mol−1. The interaction enthalpy, ΔH298K = −20.61 kcal mol−1, is almost one kcal mol−1 less exergonic than the binding in cCt-NH3-Ia. The free energy change, ΔG298K = −2.42 kcal mol−1, is approximately 40% less negative than for the cCt-NH3-Ia cluster. Although the primary hydrogen bond to water is strong with 1.565 Å interaction distance, redshift of 958 cm−1, and nearly linear hydrogen bond angle (2° 1459
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diminished with the resulting cluster more closely resembling a linear chain of hydrogen bonds than a tight cooperative circuit. (CO2H)2−NH3−(H2O)2. The most stable 12 (of the 14 identified in this work) TSC of oxalic acid−ammonia− dihydrates identified in this work are presented in Figure 4. The remaining two are greater than 3.5 kcal mol−1 in relative stability and are reported in Figure S2 (Supporting Information). Relative energies, interaction enthalpies, and Gibbs free energy changes at 298 K, ΔH298K and ΔG298K, are presented along with select bond distances, and torsion dihedrals of the dicarbonyl backbones (OC−CO) are reported if other than planar (0° or 180°). The hydrogen bond monitor system is again reported in brackets for those clusters that are completely neutral (i.e., not found as a hydrated CIP). The two most stable conformations of the (CO2H)2−NH3− (H2O)2 TSCs are the tTt-NH3-IIa and tCt-NH3-II clusters in which both of the carboxylic acid groups are in the (Z) configuration. Both clusters, as expected due to the binding of two (Z) acid groups, predict approximately the same interaction enthalpy change, ΔH298K = ∼29 kcal mol−1. These are the strongest binders with respect to enthalpy (with the exception to cTc-NH3-IIa, ΔH298K = −34.44 kcal mol−1, and cTc-NH3-IIb, ΔH298K = −30.21 kcal mol−1). These two most stable clusters, tTt-NH3-IIa and tCt-NH3-II, are the most favored entropically with free energy changes of ΔG298K = −2.49 kcal mol−1 and ΔG298K = −2.34 kcal mol−1. Note from the hydrogen bond monitor that the hydrogen bonds appear to be not as strong for these clusters that have two opposing binding regions. This apparent deactivation of the hydrogen bonds is coupled to lack of cooperativity. We have already seen that the binding of a water and ammonia in a ring is not as cooperative as the binding of two waters. The relative stability ordering for the TSC involving ammonia and two waters is a markedly different ordering of stability when compared to the corresponding pure hydrates, i.e., (CO2H)2−(H2O)3. In the pure trihydrate clusters calculated by a B3LYP/6-311++g(d,p) approach,41 the most stable clusters have the three waters arranged in a homodromic ring structure formed with one (Z), cTt-IIIa the most stable, or one (E) configuration, cTc-IIIa (0.26 kcal mol−1 higher in electronic energy as per B3LYP/6-311++G(d,p) calculations). However, the tTt-IIIa and tCt-IIIa clusters in which two waters are bound to one (Z) acid and one water to the opposing (Z) acid are the third and fourth most stable, being predicted to be slightly greater than one-half a kcal mol−1 in relative energy. The third most stable (CO2H)2−NH3−(H2O)2 TSC is predicted to be the cTc-NH3-IIa cluster. For this cluster, the enthalpy change is quite large, in fact it produces the greatest interaction enthalpy of any of the dihydrates studied here with a ΔH298K = −34.44 kcal mol−1. However, the resulting free energy change is the second largest positive free energy change of ΔG298K = 1.09 kcal mol−1 (the largest positive free energy change for the dihydrates is cTt-NH3-IIc with ΔG298K = 2.41 kcal mol−1). In this cluster, ammonia is bound to one of the interior regions created by the (E) acid conformation with a typical (for cTc-NH3) hydrogen bond distance of 1.653 Å and secondary hydrogen bond distance of 2.256 Å. The two waters are tightly bound in a cooperative manner to the opposing (E) acid with intermolecular distances similar to those observed in the binding of water dimer to (Z) acid, the two most stable (CO2H)2−NH3−(H2O)2 clusters, tTt-NH3-IIa and tCt-NH3II. The particular stability of the dihydrates of oxalic acid has been described previously.41
deviation) the extension of the OH covalent bond is rather small, to 1.021 Å. The binding in tTt-NH3-Ic is as in the tTt-NH3-Ib cluster, with one (Z) acid group of tTt binding the H2O−NH3 heterodimer, except the primary hydrogen bond is to water instead of ammonia. The relative energy is 2.54 kcal mol−1, and the enthalpy and free energy changes are ΔH298K = 18.69 kcal mol−1 and ΔG298K = −1.22 kcal mol−1. The overall exergonicity is less than for the other tTt-NH3-H2O clusters as the free energy change. As found for the cTc and cCt conformers binding of H2O−NH3 heterodimer, a noticeable effect on the resulting structure and molecular parameter is observed. The binding is cooperative, indicated by the pronounced redshift of 861 cm−1, rather large for a hydrogen bond to water, and the hydrogen bonding distance is 1.597 Å. The interatomic distance between water and ammonia is r(OH···N) = 1.751 Å, while the secondary hydrogen bond distance for ammonia with tTt is r(NH···O) = 2.131 Å. Compared to the tTt-NH3-I b cooperative binder the interaction distance between ammonia and water r(NH···O) = 1.953 Å and the secondary hydrogen bond distance for water and tTt r(OH···O) = 1.842 Å. The cTt-NH3-Ic cluster presents an unusual binding pattern with a primary hydrogen bond formed between cTt and NH3 through the (Z) configuration acid group. The ammonia secondarily hydrogen bonds to the water molecule, which then completes a tight homodromic ring by donating a hydrogen bond to oxygen of the (Z) acid hydroxyl group. The relative energy is 3.25 kcal mol−1, and enthalpy and free energy changes are ΔH298K = −16.74 kcal mol−1 and ΔG298K = −0.43 kcal mol−1. The hydrogen bond with NH3 is strong, as found for all the clusters in which oxalic acid is primarily bound to ammonia. The hydrogen bond distance of 1.598 Å is typical, with an extension of OH covalent bond to 1.042 Å and redshift in stretching frequency of 1277 cm−1. The remaining intermolecular distances around the homodromic ring are greater than two Angstroms, somewhat longer than typical for this type of system. This would presumably be due the accommodation of the hydrogen bonds by significant deviation from linearity; the deviation of the cTt-NH3 hydrogen bond is 17°, for example. In general, the bonding of one water to the oxalic acid− ammonia cores can either result in clusters with a cooperative binding motif that enhances hydrogen bonding or with pseudosymmetric binding that increases the cluster stability through dipole cancellations. These two scenarios are clearly evidenced by the hydrogen bonding analytical parameters reported in brackets and the redshifts of the acid OH stretching mode. For the (CO2H)2−NH3−H2O clusters the two effects produce competitive stabilizations. In contrast to the pure hydrates of oxalic acid,41 it appears that the dipole stabilizations are more important for the monohydrate of oxalic acid− ammonia cores. When the pseudosymmetric binding motif is possible (i.e., the cTc and tTt conformations) the most stable clusters are produced in this manner. Another observed trend is in the cooperative binding to the ammonia−water heterodimer; the formation of a primary bond between oxalic acid and ammonia is preferred thermodynamically. From the structural parameters that when the primary hydrogen bond is formed to the water molecule the resulting homodromic ring is deformed in comparison. That is to say that the secondary bond between ammonia and the carbonyl of oxalic acid is weak as evidenced by the rather long hydrogen bonding distance of greater than two Angstroms. As a result, the cooperativity of the system is 1460
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kcal mol−1 and the formation at elevated temperatures somewhat favorable with ΔG298K = −0.31 kcal mol−1. The cTt-NH3-IIc TSC binds ammonia to the (E) acid interior region with concomitant binding of water dimer to the exterior (Z) acid conformation. This cluster is 2.72 kcal mol−1 greater in relative stability, the resulting interaction enthalpy change, ΔH298K = −25.43 kcal mol−1, is the weakest overall binding in this cluster class, and the free energy change, ΔG298K = 2.41 kcal mol−1, is the most positive (unfavorable) free energy change observed for these one ammonia and two water clusters with oxalic acid. The last two clusters presented in Figure 6 have the (Z) acid conformation in cCt and tTt binding to water dimer and then ammonia through the carbonyl of the (Z) acid forming a homodromic, pentameric, and cyclic hydrogen bonding network. As might be anticipated the more polar cCt-NH3-IIb cluster has stronger binding than the tTt-NH3-IId (ΔH298K = −27.87 kcal mol−1 vs ΔH298K = −25.95 kcal mol−1). The interaction free energy changes are both favorable at 298 K with the ΔG298K values = −1.22 and 0.77 kcal mol−1, respectively. Interestingly, the tTt-NH3-IIe TSC (Figure S3, Supporting Information) is calculated to produce the exact same ΔH298K and ΔG298K values! The tTt-NH3-IIe cluster is similar to tTt-NH3-IId in that the tTt conformation of oxalic acid is bound to ammonia and two waters in a cyclic, pentameric, homodromic ring but in opposite ordering with respect to each other (i.e., the oxalic acid acts as HB donor to H2O−H2O−NH3 in tTt-NH3-IId and donor to NH3−H2O− H2O in tTt-NH3-IIe. The result is the tTt-NH3-IIe cluster is less stable than the tTt-NH3-IId structure by 0.17 kcal mol−1 with a portion of the destabilization due to the optimal conformation of the cluster. This result was somewhat unexpected as the tTt-NH3-IIe group is directly hydrogen bound to the NH3 and thus would presumably be the more strongly bound cluster. The hydrogen bond monitor values do detect differences between the clusters. Although both the primary hydrogen bonds are found to deviate from linearity by 10°, the corresponding bond distances are 1.544 Å for the acid directly bound to NH3 with the OH covalent bond of the acid being extended to 1.065 Å. This compares with the considerably longer primary bond distance between the acid and water in tTt-NH3-IId of 1.587 Å and less extended OH covalent bond length of 1.016 Å. These parameters clearly indicate that the ammonia is bound more tightly in the tTtNH3-IIe cluster. However, upon inspection of the remaining intermolecular interaction distances we notice that the water to water separation is much tighter at 1.681 Å in the tTt-NH3-IId cluster (the more stable one) compared to 1.759 Å in tTt-NH3IIe. Also, the separation of the ammonia and water is much shorter when ammonia is acting as hydrogen bond acceptor to H2O (1.760 Å) compared to HB donor to oxalic acid in tTtNH3-IIe (1.921 Å). The overall result is that the increased binding of ammonia to oxalic acid acts to disrupt bonding in the remainder of the network of tTt-NH3-IIe, whereas the water dimer bonding is seen to be enhanced when bound with oxalic acid. The final TSC considered here (Figure S2, Supporting Information) is cCt-NH3-IIc, which is 3.77 kcal mol−1 in relative electronic energy to reference and produces interaction enthalpies and free energy changes of ΔH298K = −26.85 kcal mol−1 and ΔG298K = −0.80 kcal mol−1. The (Z) acid group of cCt forms a cyclic hydrogen bonding network with (H2O)2. The (E) group of cCt binds NH3 to the interior with NH3 forming a secondary hydrogen bond to the oxygen of the (Z) acid OH group. The primary hydrogen bond has
The (CO2H)2−NH3−(H2O)2 clusters with the waters and ammonia all bound in one ring lead to ionization (i.e., formation of a CIP) when ammonia is primarily bound to the acid group, with the exception of tTt-NH3-IIe (presented in Figure S2 of the Supporting Information). These are the cTcNH3-IIb, cTt-NH3-IIa, cTt-NH3-IIb, and cCt-NH3-IIa TSCs (double ion). In these double ion TSCs a (Z) acid group binds the NH3 with the exception of the most stable, and we shall see, also the most important dihydrate oxalic acid−ammonia cluster, cTc-NH3-IIb. The cTc-NH3-IIb double ion TSC is within a kcal mol−1 relative stability (0.80 kcal mol−1) of the most stable tTt-NH3IIa cluster. The interaction enthalpy change for this cluster is also quite large with ΔH298K = −30.21 kcal mol−1, and the free energy change, even at 298 K, is favorable with ΔG298K = −1.88 kcal mol−1. Upon ionization, the cluster loses homodromicity, which is common for nascent ionic cluster formations. The back interaction distance is fairly strong with a CIP separation distance of 1.407 Å, while the remaining intermolecular interaction distances range from 1.743−1.812 Å. The cTt-NH3-IIa TSC is also a double ion cluster. It is predicted to be 1.12 kcal mol−1 less stable than the most stable tTt-NH3-IIa reference cluster. The enthalpy change is modest, ΔH298K = −26.99 kcal mol−1, one of the weaker overall binders in this cluster class. The free energy change is ΔG298K = 0.01 kcal mol−1. The ammonium formed in this cluster is found to be similarly, yet slightly more strongly, back interacting, as compared to the cTc-NH3-IIb TSC, as evidenced by the 1.392 Å CIP separation distance (compared to 1.407 Å). The remaining intermolecular interaction distances are fairly tight with values ranging from 1.710 Å to 1.807 Å. The tTt-NH3-IIb cluster has ammonia and then water bound to a (Z) acid group in a cyclic manner (opposed to the tTtNH3-IIa cluster in which two waters are bound to one of the (Z) acids). The remaining water molecule is bound to the opposing (Z) acid group. The interaction enthalpy suffers as a result being ΔH298K = 27.64 kcal mol−1 (more than one kcal mol−1 weaker), and the resulting free energy change, ΔG298K = −1.65 kcal mol−1 is also more than one kcal mol−1 less favorable than found in the tTt-NH3-IIa cluster. The cTt-NH3-IIb cluster is a double ion TSC with a ΔG298K = 0.97 kcal mol−1; so, although electronically favored, this cluster would not be expected to form spontaneously at elevated temperatures. In this cluster, the ammonium is backbound to the (Z) acid group and the two waters complete a circuit around to the carbonyl of the (Z) acid group. The cCtNH3-IIa TSC is also double ion in which the binding is notable stronger (ΔH298K = 28.28 kcal mol−1 compared to −26.30 kcal mol−1 for the cTt-NH3-IIb cluster). The relative stability of this cluster places it 2.50 kcal mol−1 higher in energy than the most stable oxalic−ammonia core dihydrate TSC, yet it is predicted to have a favorable free energy change with ΔG298K = −0.31 kcal mol−1. The tTt-NH3-IIc TSC is completely neutral and entropically favored (ΔG298K = −1.01 kcal mol−1) as are the other double (Z) acid conformer TSCs. For these clusters, cooperative binding and, in addition, dipole cancellations work together in concert to produce extremely stable neutral clusters. As a result, these clusters do not facilitate ion pair formation. The cCt conformation in the cCt-NH3-IIa TSC, however, does lead to a double ion cluster in which the CIP interaction distance is noticeably greater than the other CIP TSCs investigated in this study, being 1.502 Å. The strength of the total interaction if moderately favorable with ΔH298K = −28.18 1461
dx.doi.org/10.1021/jp4128226 | J. Phys. Chem. A 2014, 118, 1451−1468
The Journal of Physical Chemistry A
Article
Figure 5. Optimized trihydrated structures of (CO2H)2−NH3 cores from B3LYP/aug-cc-pVDZ calculations. Relative single-point energies, ΔEr, interaction enthalpies, ΔH298K in italics, and free energy changes, ΔG298K in red, are reported in parentheses. Select intermolecular distances are reported in Angstrom (Å).
separations of 1.470 and 1.514 Å, respectively. Both these TSC have similar cyclic and pentameric homodromic binding with an oxygen of the newly formed anion carboxlyate group being doubly coordinated in the network. These clusters are, in fact, essentially the same cluster with both possessing the same structural binding motif with one being left handed and the other being right handed. These clusters have different enough parameters that both are reported in this study. After the first two cTt-NH3 trihydrate double ion clusters the next most stable cluster, with respect to relative electronic energy, is tTt-NH3-III. In this cluster, both (Z) acid groups are binding two molecules in a cooperative manner. Here, the symmetrically opposed binding regions provide additional stability as observed previously.41 The resulting TSC exhibits rather strong enthalpy changes, ΔH298K = 37.42 kcal mol−1 and strongly favorable free energy change, ΔG298K = 2.43 kcal mol−1. Note that the OC−CO dihedral is strongly twisted in this cluster with a dihedral angle that is nearly perpendicular at 97.7°! This would presumably minimize steric repulsions from the two binding acid groups. The inclusion of water in the cyclic hydrogen bonding network enhances the binding of NH3 as found with the tTt-NH3-IIb cluster with similar hydrogen bond monitor parameters. For the tTt-NH3-III cluster the hydrogen bonding distance is 1.597 Å, an extension of the OH covalent bond to 1.046 Å, and a deviation from ideal angle of 4°. The cTt-NH3-IIIc TSC is found 0.83 kcal mol−1 above the cTt-NH3-IIa cluster, being 0.08 kcal mol−1 higher in energy than tTt-NH3-III. This TSC is double ion as found for the other cTt-NH3-(H2O)3 clusters with an interaction enthalpy of ΔH298K = −35.51 kcal mol−1 and ΔG298K = 1.89 kcal mol−1, also being found with a prohibitive free energy. As with the other trihydrated cTt-NH3 cores the nascent CIP appears to be somewhat stabilized by microsolvation having CIP separation of 1.500 Å. A TSC involving the tCt conformation of oxalic acid is found to be essentially isoenergetic with the cTt-NH3-
interaction distance of 1.635 Å, OH covalent bond length of 1.009 Å, and deviation of 4° from linearity, which all indicate that even though the geometry of this binding motif is conducive to binding, the binding is in fact not very strong. The hydrogen bond with ammonia is also exhibiting parameters that are indicative of weak binding. The interaction distance for the primary hydrogen bond to NH3 is 1.727 Å, the covalent bond length is 1.008 Å, and the deviation from ideality is 6°. The reason for the deactivation of the cCt conformation and relative instability of this TSC is likely due to the awkward conformation adopted to accommodate the hydrogen bonds present resulting in the considerable deformation of the cCt conformation by twisting the OC−CO dihedral from planarity to 61.4°! (CO2H)2−NH3−(H2O)3. The six stable trihydrate clusters of oxalic acid−ammonia cores examined in this work are presented in Figure 5. Relative energies as well as intermolecular enthalpies and free energies, ΔH298K and ΔG298K, of the (CO2H)2−NH3−(H2O)3 complexes are included. Note that these clusters are very close to each other in relative stability, all being well within 1.5 kcal mol−1 relative single-point energy. The cluster possessing the highest degree of stability is cTt-NH3-IIIa with ΔH298K = −35.98 kcal mol−1. This TSC is a double ion, and while it is the most stable electronically, it is noted that none of the double ion TSCs of the (CO2H)2−NH3−(H2O)3 cores are predicted to have favorable formation at appreciable temperatures (i.e., ΔG298 values are considerably positive). The second most stable (CO2H)2−NH3−(H2O)3 cluster, cTt-NH3-IIIb, is also double ion CIP with the cTt conformation of oxalic acid with a relative energy of 0.43 kcal mol−1 above the cTt-NH3-IIIa TSC. The interaction enthalpy is quite similar ΔH298K = −36.19 kcal mol−1, and the free energy change is positive, ΔG298K = 1.32 kcal mol−1. The NH4+ back interaction distances with the nascent hydrogen oxalate anion are both somewhat relaxed, compared to the dihydrated core clusters that have CIP 1462
dx.doi.org/10.1021/jp4128226 | J. Phys. Chem. A 2014, 118, 1451−1468
The Journal of Physical Chemistry A
Article
IIIc cluster with a relative energy of 0.84 kcal mol−1. The tCtNH3-III cluster has particularly strong interaction enthalpy as found in the tTt-NH3-III cluster, which seems quite reasonable as the have such similar binding. The enthalpy change for tCtNH3-III is ΔH298K = −37.31 kcal mol−1 (compared to ΔH298K = 37.42 kcal mol−1 with tTt-NH3-III) and the change in free energy is also significant, ΔG298K = −3.39 kcal mol−1. The (CO2H)2−NH3−(H2O)3 clusters have competitive stability, all located within
