Hydration of oxalic acid–ammonia complex: atmospheric implication and Rayleigh-scattering properties

Abstract

A previous study of the binary system (H₂C₂O₄)(NH₃)_n (n = 1–6) suggested that an oxalic acid–ammonia complex may participate in atmospheric aerosol formations. However, the mechanism of the hydration of these cores is poorly understood. In this study, the hydration of (H₂C₂O₄)(NH₃) and (H₂C₂O₄)(NH₃)₂ cores with up to three water molecules is investigated with respect to different routes of formation. The results may improve understanding of the nucleation of clusters containing oxalic acid in the atmosphere. Acid dissociation is found to occur during the hydration process, leading to a HC₂O₄⁻/NH₄⁺ ion pair. In contrast with the (H₂C₂O₄)(NH₃)₂ core, water molecules appear to be unfavorable with regard to the formation of hydrates with a (H₂C₂O₄)(NH₃) core; additionally, temperature is found to affect the formation of clusters and the distributions of different isomers with the same size, but the impact of relative humidity on the hydrates seems insignificant, implying that the formation of these clusters may be more favorable under cold ambient conditions. The monohydrates and dihydrates of the (H₂C₂O₄)(NH₃)₂ core may be relatively extensive in (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters and may contribute to the atmospheric nucleation. Furthermore, this study presents a first attempt at determining the Rayleigh scattering properties of oxalic acid–ammonia–water pre-nucleation clusters; the results show that adding a water molecule could effectively increase the Rayleigh scattering intensity, but a single ammonia molecule may be able to generate a larger increase in the Rayleigh light scattering intensity than a water molecule. This may also indicate that clusters containing oxalic acid and ammonia show high Rayleigh light scattering intensities, but the more ammonia molecules there are in clusters, the higher the Rayleigh light scattering intensity and the greater the contribution to the extinction properties.

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Introduction

Atmospheric aerosol particles formed via nucleation^1,2 play a crucial role in the global climate system by affecting precipitation and cloud properties^3,4 and are responsible for the adverse public health impacts of airborne ultrafine particles.^5–7 Aerosols are defined as suspensions of liquid or solid particles in the gas-phase or in ambient air. Formerly, the atmospheric nucleation process was described as nucleation of H₂SO₄–H₂O–X; namely, atmospheric nucleation involves sulfuric acid, the common atmospheric nucleation precursor, water, the dominant constituent of the mixture of condensable vapors in the Earth's atmosphere, and something else.^8–11 So far, several nucleation mechanisms have been proposed to explain atmospheric nucleation events in the continental troposphere, including binary H₂SO₄/H₂O nucleation (BHN), ternary H₂SO₄/H₂O/NH₃ nucleation (THN), ion-mediated nucleation (IMN) and nucleation enhanced by organic compounds.^11–14 However, the precise species involved in atmospheric nucleation remain unknown. The study of a ternary homogeneous H₂SO₄–H₂O–NH₃ model was found to grossly overestimate nucleation rates.¹⁵ Additionally, it has been pointed out that binary homogeneous nucleation of sulfuric acid and water cannot explain the rate of new particle formation observed by both field and lab measurements,^16–18 particularly in the lower regions of the troposphere, indicating that other ternary species as well as sulfuric acid may participate in the nucleation process.^12,19–25

A number of atmospheric observations have revealed that aerosols often contain abundant organic matter, which may participate in nucleation and grow to form nanoparticles.^23,26–33 The importance of organic species has been pointed out in the pioneering experiments of Zhang et al.,¹⁴ in which a considerable enhancement in nucleation rates due to organic species has been shown. Organic acids have been found to exist universally in nature and to play an important role in ice nucleation,^34–37 cloud condensation³⁸ and the production of fine particulate matter.^11,39 As the most common organic acid in the atmosphere,^40–43 oxalic acid has been observed at significant concentrations and is found to exist in the PM_2.5 atmospheric aerosols.^44–46 Furthermore, analysis of field measurements revealed a strong correlation between oxalate concentrations and cloud condensation nuclei (CCN), thus oxalate may participate in CCN activation.⁴⁷ Zhang et al. indicated that dicarboxylic acids (containing oxalic acid) can contribute to the aerosol nucleation process by binding to sulfuric acid and ammonia.⁴⁸ The theoretical investigation of Yu et al. predicted that oxalic acid could significantly enhance the stability of ionic clusters, catalyzing the production of positively charged pre-nucleation clusters.⁴⁹ Tao et al.⁵⁰ studied the binary nucleation of oxalic acid and water and suggested that the formation of neutral cores is the most important step in the initial formation of oxalic acid and water clusters; they then successively pointed out that thermodynamically stable H₂C₂O₄–NH₃ core clusters may participate in new particle formation (NPF) events and that their subsequent hydration is favorable compared to that of the monohydrates of oxalic acid.⁵¹ Our recent study⁵² indicated that oxalic acid and ammonia form relatively stable clusters and may participate in the aerosol nucleation process. Although a few computational quantum studies on the interaction of oxalic acids with atmospheric nucleation precursors have been performed,^48–53 a subsequent nucleation study of the stable neutral cores of (H₂C₂O₄)(NH₃)_n (n = 1–2) with other species is incomplete. Water is likely to be involved in many nucleation processes, as its concentration exceeds that of other condensable gases, often by 8–10 orders of magnitude.⁵⁴ It may be possible that (H₂C₂O₄)(NH₃) and (H₂C₂O₄)(NH₃)₂ cores form subsequent clusters by adding water molecules. Moreover, as a source of aerosol nucleation intermediates and catalytic agents in many reactions, hydrated complexes play an important role in the atmosphere.⁵⁵ Therefore, a clear and insightful understanding of the hydration phenomena is of particular importance in modeling atmospheric processes.

In this work, we studied the hydration of (H₂C₂O₄)(NH₃) and (H₂C₂O₄)(NH₃)₂ cores using the basin-hopping (BH) method^56–58 coupled with density functional theory (DFT) calculations at the molecular level. To understand the very first steps of particle formation, the initial molecular structures formed from the gas phase and the thermodynamic properties were calculated. To obtain information regarding which clusters are dominant in different atmospheric environments, we analyzed the distribution of the hydrates as well as the influence of temperature and humidity. Besides, it is known that aerosols can directly affect the global climate by scattering incident light from the sun; for molecular clusters, Rayleigh light-scattering is dominant.⁵⁹ The Rayleigh scattering properties of large aerosol particles have been relatively well studied; however, the scattering properties of molecular clusters have been neither studied, nor understood, especially for the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) system. The attenuation of atmospheric visibility is largely due to the extinction properties of atmospheric particles, Rayleigh scattering of particulate matter in urban areas often being the primary contributor to the extinction properties.^60–62 Thus, it is meaningful to investigate the Rayleigh light scattering properties, including the isotropic mean polarizabilities, anisotropic polarizabilities, depolarization ratios, and Rayleigh scattering intensities of these atmospheric pre-nucleation clusters.

Methods

The BH algorithm coupled with DFT was employed to search low-lying structures of the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) system. This method has turned out to be efficient for exploring atomic^63–68 and molecular^{52,53,69–75} systems. Generalized gradient approximation in the Perdew–Burke–Ernzerhof (PBE) functional and the double numerical plus d-functions (DND) basis set, implemented in DMol,^3,76 were chosen for the structural optimization of this system.

For this system, ten separate BH searches, consisting of 1000 sampling steps at 3000 K, starting with randomly generated molecular configurations, were performed. Then, the structures were first optimized at the PW91PW91/6-31+G* level of theory. The isomers located within 10 kcal mol⁻¹ of the global minimum were then selected and further optimized using the PW91PW91/6-311++G(3df,3pd) level of theory implemented in the Gaussian 09 software package.⁷⁷ The PW91PW91 functional was chosen because of its fine performance with respect to a large number of atmospheric clusters containing common organic acids, including predictions of structural characteristics, the thermodynamics of cluster formation and satisfactory similarity compared with experimental results.^48,49,78 In the benchmark work of a previous study,⁵² four other methods (ω B97x-D, M06-2X, CAM-B3LYP and B3LYP) were performed for the smallest clusters, including NH₃, C₂O₂H₄, (C₂O₂H₄)(NH₃) and (C₂O₂H₄)(NH₃)₂, to make sure that the results were consistent. Density functional theory was chosen instead of wave function theory methods (i.e. MP2) to compare with the previous work by Elm et al.⁷⁹ On one hand, the computational costs could be largely reduced. On the other hand, the accuracy of the DFT methods we selected could be maintained because recent benchmark articles^79,80 provide a pool of potential density functional methods. Frequency calculations were performed to confirm that no imaginary frequencies were present for each stationary point and that, consequently, the structure of interest stands for a local or a global minimum on the potential energy surface (details can be seen in the ESI†).

Finally, single-point energy calculations were performed at the DF-LMP2-F12/vdz-f12 level of theory based on the optimized geometries, implemented in Molpro 2010.1.^81,82 In the current work, a scale factor is used to propose a reasonably simple way to estimate the relative accuracies of the single-point energy calculations.⁸³ The single-point energy calculated for the small clusters (C₂O₄H₂, NH₃, H₂O, C₂O₄H₂·NH₃, C₂O₄H₂·2NH₃, and C₂O₄H₂·NH₃·H₂O) at the level of DF-LMP2-F12/VDZ-F12 and CCSD(T)-F12a/VDZ-F12 are displayed in Table 1, as well as the binding energies (ΔE₁, ΔE₂) without ZPE-correction, the scale factor being obtained by taking the average of the ratios of the CCSD(T)-F12a/VDZ-F12 binding energy to the DF-LMP2-F12/VDZ-F12 binding energy over these small clusters where binding energies calculated at both the CCSD(T)-F12a/VDZ-F12 and the DF-LMP2-F12/VDZ-F12 levels were available. The binding energies in the current manuscript have all been multiplied by a scale factor of 0.8 on the basis of previous energy values. The ZPE-corrected binding energies (ΔE₀) are obtained at a standard state of 0 K and 1 atm. Intermolecular enthalpies (ΔH) and Gibbs free energies (ΔG) were calculated at a temperature of 298.15 K and 1 atm.

Table 1 The single-point energies (in Hartree) of the studied small clusters calculated using DF-LMP2-F12/VDZ-F12 and CCSD(T)-F12a/VDZ-F12, the binding energies (ΔE₁, ΔE₂) without ZPE-correction, and the scale factor obtained by taking the average of the ratios of the CCSD(T)-F12a/VDZ-F12 binding energies to the DF-LMP2-F12/VDZ-F12 binding energies over these small clusters

Isomer	DF-LMP2-F12 (Hartree)	ΔE1 (kcal mol^−1)	CCSD(T)-F12a (Hartree)	ΔE2 (kcal mol^−1)	ΔE2/ΔE1	The scale factor
C2O4H2	−377.931		−377.893			0.8
NH3	−56.483		−56.489
H2O	−76.358		−76.356
C2O4H2·NH3	−434.438	−15.3	−434.404	−13.6	0.9
C2O4H2·2NH3	−490.933	−23.0	−490.901	−18.7	0.8
C2O4H2·NH3·H2O	−510.808	−23.1	−510.769	−19.4	0.8

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To evaluate the Rayleigh scattering intensities and polarization ratios of the oxalic acid–ammonia–water clusters, the most common dicarboxylic acid and the nucleation precursor in the atmosphere, the mean binding isotropic and anisotropic polarizabilities of all the clusters have been calculated at the CAM-B3LYP/aug-cc-pVDZ level of theory, and the corresponding geometries are also optimized using the CAM-B3LYP/aug-cc-pVDZ level of theory. In a previous article,⁵² in order to find a suitable methodology for calculating the optical properties of pre-nucleation clusters, a DFT functional with the aug-cc-pVDZ basis set analysis was performed for the smallest clusters, including NH₃, C₂O₂H₄, (C₂O₂H₄)(NH₃) and (C₂O₂H₄)(NH₃)₂. The performance of calculating the mean isotropic polarizability was tested using the ω B97x-D, M06-2X, MP2, CAM-B3LYP and PW91 functionals, together with the aug-cc-pVDZ basis set. On analysis of the benchmark, CAM-B3LYP/aug-cc-pVDZ was found to be a good compromise between accuracy and efficiency, yielding good agreement with MP2 values of the polarizability. Additionally, Elm et al. also performed a benchmark work on the smallest cluster subunits, H₂SO₄, NH₃ and H₂O,⁵⁹ in which the CAM-B3LYP/aug-cc-pVDZ level of theory was also found to be the most appropriate choice. The light-scattering intensities and the isotropic mean polarizabilities, [small alpha, Greek, macron], as well as the anisotropic polarizabilities, Δα, and the relevant computation methods have been expounded in our earlier studies.^52,53,71,74

Results and discussion

A. Structures and energetics

In this study, we use m × n − i notation to represent the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) conformations; “m” denotes the number of ammonia molecules, “n” denotes the number of water molecules, and “i” (i = a–r) was used to differentiate different isomers with the same value of m and n, ordered by the increasing relative single-point energy ΔE_rel. The ZPE-corrected binding energies (ΔE₀) of the clusters were calculated using three different reaction routes, as shown below. The interaction enthalpies (ΔH) and the free energy changes (ΔG) were performed in the same way with ΔE₀:

ΔE₀ = E_n − E_H2C2O4 − m × E_NH3 − n × E_H2O (1)

ΔE₀ = E_n − E_{(H2C2O4)(NH3)m(H2O)n−1} − E_H2O (2)

ΔE₀ = E_n − E_{(H2C2O4)(NH3)m} − n × E_H2O (3)

where m and n denote the numbers of ammonia and water molecules in the cluster, respectively. E_n is the total energy; E_NH3, E_H2C2O4, E_H2O, E_{(H2C2O4)(NH3)m(H2O)n−1} and E_{(H2C2O4)(NH3)m} are the total energies for ammonia, oxalic acid, water, hydrates and oxalic acid–ammonia complexes. The relative single-point energy ΔE_rel, the ZPE-corrected binding energies (ΔE₀), the intermolecular enthalpy (ΔH), the free energy changes (ΔG) and the Boltzmann averaged Gibbs free energy of (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3) (in kcal mol⁻¹), calculated using eqn (1) are listed in Tables S1 and S2 (ESI†). The binding energies of the global minima for the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 0–3) clusters are displayed in Tables 2 and 3.

Table 2 Energy changes calculated using three different methods for cluster (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) at a standard state of 1 atm and the given temperature in kcal mol⁻¹

Isomer	ΔE0 (0 K)	ΔH (298.15 K)	ΔG (298.15 K)
H2C2O4 + NH3 + nH2O → (H2C2O4)(NH3)(H2O)n
C2O4H2·NH3	−11.9	−12.4	−4.4
C2O4H2·NH3·H2O	−17.7	−18.6	−3.4
C2O4H2·NH3·2H2O	−25.9	−27.8	−3.4
C2O4H2·NH3·3H2O	−34.1	−36.5	−4.5
(H2C2O4)(NH3)(H2O)n−1 + H2O → (H2C2O4)(NH3)(H2O)n
C2O4H2·NH3	−11.9	−12.4	−4.4
C2O4H2·NH3·H2O	−5.8	−6.2	0.9
C2O4H2·NH3·2H2O	−8.2	−9.2	−0.1
C2O4H2·NH3·3H2O	−8.2	−8.7	−1.1
(H2C2O4)(NH3) + nH2O → (H2C2O4)(NH3)(H2O)n
C2O4H2·NH3	−11.9	−12.4	−4.4
C2O4H2·NH3·H2O	−5.8	−6.2	0.9
C2O4H2·NH3·2H2O	−13.9	−15.4	0.9
C2O4H2·NH3·3H2O	−22.2	−24.1	−0.2

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Table 3 Energy changes calculated using three different methods for cluster (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3) at a standard state of 1 atm and the given temperature in kcal mol⁻¹

Isomer	ΔE0 (0 K)	ΔH (298.15 K)	ΔG (298.15 K)
H2C2O4 + 2NH3 + nH2O → (H2C2O4)(NH3)2(H2O)n
C2O4H2·2NH3	−17.4	−18.3	−2.0
C2O4H2·2NH3·H2O	−25.7	−27.4	−2.9
C2O4H2·2NH3·2H2O	−34.4	−36.6	−4.3
C2O4H2·2NH3·3H2O	−41.7	−44.4	−4.5
(H2C2O4)(NH3)2(H2O)n−1 + H2O → (H2C2O4)(NH3)2(H2O)n
C2O4H2·2NH3	−17.4	−18.3	−2.0
C2O4H2·2NH3·H2O	−8.3	−9.0	−0.9
C2O4H2·2NH3·2H2O	−8.6	−9.2	−1.4
C2O4H2·2NH3·3H2O	−5.8	−7.9	−0.3
(H2C2O4)(NH3)2 + nH2O → (H2C2O4)(NH3)2(H2O)n
C2O4H2·2NH3	−17.4	−18.3	−2.0
C2O4H2·2NH3·H2O	−8.3	−9.0	−0.9
C2O4H2·2NH3·2H2O	−16.9	−18.2	−2.2
C2O4H2·2NH3·3H2O	−24.3	−26.1	−2.5

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The energy changes calculated using three different methods for cluster (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) are displayed in Table 2. According to the data, the free energy of the C₂O₄H₂·NH₃ cluster is −4.4 kcal mol⁻¹. The free energy of step-by-step hydration is 0.9 kcal mol⁻¹ for the C₂O₄H₂·NH₃·H₂O cluster, −0.1 kcal mol⁻¹ for the C₂O₄H₂·NH₃·2H₂O cluster and −1.1 kcal mol⁻¹ for the C₂O₄H₂·NH₃·3H₂O cluster. For the third method, which involves adding water molecules to the (H₂C₂O₄)(NH₃) core, the free energies of the monohydrate and the dihydrate are 0.9 kcal mol⁻¹, and for the trihydrate, the free energy is −0.2 kcal mol⁻¹. It may be deduced from Table 2 that the C₂O₄H₂·NH₃ cluster may not be favorable with water-forming hydrates by a stepwise route, while via the third route, C₂O₄H₂·NH₃·2H₂O may be favorable, with water forming the C₂O₄H₂·NH₃·3H₂O cluster.

According to Table 3, the free energies of step-by-step hydration and the third hydration route for the (H₂C₂O₄)(NH₃)₂ core are negative. For step-by-step hydration, the free energies of the monohydrate, the dihydrate and the trihydrate are −0.9 kcal mol⁻¹, −1.4 kcal mol⁻¹ and −0.3 kcal mol⁻¹, respectively. For the third route, via adding water molecules to the (H₂C₂O₄)(NH₃)₂ core, the free energies are −0.9 kcal mol⁻¹, −2.2 kcal mol⁻¹ and −2.5 kcal mol⁻¹ for the monohydrate, the dihydrate and the trihydrate. This may indicate that the (H₂C₂O₄)(NH₃)₂ cluster and the corresponding hydrates are favorable, with water forming subsequent hydrates via these two routes.

Considering that, here, we only take the thermodynamics into account and not dynamic properties such as collision and evaporation processes, ignoring the influence from molecules and clusters, we could only conclude that this is favorable without guaranteeing that these reactions would happen in practice.

As shown in Fig. 1, the length of the intramolecular O–H bond in one carbonyl of oxalic acid gradually increases with the number of water molecules, while that of the intermolecular N–H between acid and base decreases. Finally, one-proton transfer in (H₂C₂O₄)(NH₃)(H₂O)_n (n = 2,3) and (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 1–3) clusters, with oxalic acid as a donor and ammonia as a acceptor, results in acid dissociation and the formation of HC₂O₄⁻/NH₄⁺. According to Fig. S2 and S3,† in most clusters, oxalic acid binds with ammonia directly because of the acid–base reaction mechanism. Furthermore, the global minima are those in which ammonia or water molecules bind to one carbonyl of oxalic acid; those in which ammonia or water molecules bind to both carbonyls of oxalic acid are local minima. In the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 0–3) clusters, we may predict that the stability of complexes in which ammonia or water molecules bind to one carbonyl of oxalic acid is greater (Fig. 2 and 3).

Fig. 1 The lowest-energy structures and the Gibbs free energies (in kcal mol⁻¹) of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 0–3) clusters at the PW91PW91/6-311++G(3df,3pd) level of theory (red for oxygen, white for hydrogen, gray for carbon and blue for nitrogen).

Fig. 2 The optimized geometries of (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) at the PW91PW91/6-311++G(3df,3pd) level of theory (red for oxygen, white for hydrogen, gray for carbon and blue for nitrogen).

Fig. 3 The optimized geometries of (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3) at the PW91PW91/6-311++G(3df,3pd) level of theory (red for oxygen, white for hydrogen, gray for carbon and blue for nitrogen).

B. Temperature dependence of conformational populations

Previous findings^52,71,84,85 revealed that the thermodynamic properties of clusters may change at different temperatures and the stability order of isomers may change, affecting the population order of isomers. Thus, the temperature dependence of conformational populations should be important for understanding the specific nucleation mechanisms at various atmospheric temperatures. However, due to the increased wall losses of the clusters (H₂C₂O₄, NH₃ and H₂O) at low temperatures, it is hard to fulfill the relevant experiments as the temperature lowers. Here, quantum chemical calculations can provide such data.

In this work, the energies for the formation of H₂C₂O₄, NH₃ and H₂O complexes were calculated at temperatures of 100, 150, 200, 250, 298.15, 300, 350 and 400 K.

Considering the Boltzmann distribution of the low-lying energy isomers, here we used the Boltzmann averaged Gibbs free energy (Tables S1 and S2 in ESI†) to study the flatness of the potential energy surface of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3). The equations are listed as follows:

where

ΔG_m,nⁱ = G_m,nⁱ − G_C2O4H2 − mG_NH3 − nG_H2O (6)

ΔΔG_m,nⁱ = ΔG_m,nⁱ − min{ΔG_m,nⁱ} (7)

here i represents the isomer order in a cluster, and m and n stand for the number of NH₃ and H₂O molecules, respectively. The temperature dependence of the conformational population shown for clusters (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) is shown in Fig. S1 and S2.†

In Fig. S1,† the global minima of clusters (H₂C₂O₄)(NH₃)(H₂O)_n (n = 1–3) all carry the highest weight up to 400 K, but the weight has a declining trend from 100 K to 400 K. For clusters (H₂C₂O₄)(NH₃)(H₂O), the conformational population of the local minima increases with increasing temperature, but is still below the global minimum at 400 K. For clusters (H₂C₂O₄)(NH₃)(H₂O)₂, the global minimum of 1.2-a weighs more than other low-lying isomers below temperatures of 400 K, but around 400 K, the conformational population of isomer 1.2-d approximates that of 1.2-a. Below 300 K, the conformational population of 1.2-d weighs less than 1.2-c; however, the trend is reversed when the temperature exceeds 300 K. In addition, the free energy effect can be observed from the competing roles of 1.2-c and 1.2-d, because their free energies are quite close to the global minimum (energy differences of 0.706 kcal mol⁻¹ and 0.73 kcal mol⁻¹, respectively). The isomers 1.2-e, 1.2-f, 1.2-g, 1.2-h, 1.2-i, 1.2-j and 1.2-k follow a similar trend to 1.2-b. For clusters (H₂C₂O₄)(NH₃)(H₂O)₃, the conformational population of 1.3-a decreases with temperature and approximates that of 1.3-b; the conformational populations of other isomers follow the same trend.

In Fig. S2,† for (H₂C₂O₄)(NH₃)₂(H₂O) clusters, the competitive local minima (2.1-b, 2.1-d and 2.1-e) weigh more than other local minima when the temperature is above 300 K; the proportions of 2.1-d and 2.1-e increase with temperature and may exceed that of the global minimum above 400 K. Other isomers, 2.1-f, 2.1-g, 2.1-h and 2.1-i, follow the same trend from 100 K to 400 K. For (H₂C₂O₄)(NH₃)₂(H₂O)₂ clusters, when the temperature is above 350 K, the conformational population of isomer 2.2-f surpasses that of 2.2-a. Below 150 K, the conformational population of 2.2-b increases with temperature but then decreases above 150 K and weighs less than that of 2.2-f from 250 K. In addition, the free energy effect can be observed from the competing roles of 2.2-b, 2.2-c and 2.2-f because their free energies are quite close to each other. Finally, for (H₂C₂O₄)(NH₃)₂(H₂O)₃ clusters, the conformational population of 2.3-a gradually decreases from 100 K to 400 K, while that of 2.3-b rises slightly and then decreases from 250 K.

It is obvious that most of the global minima have the greatest weight over the range 100 K to 400 K, but in the system (H₂C₂O₄)(NH₃)_n, the conformational populations of the global minima always weigh higher than those of the local minima. As temperature increases, the weight of the global minimum decreases, and the approximate free energies of the local minima become competitive. But for all realistic atmospheric conditions (approximately 250–300 K), it is seen that the global minimum of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) dominates in all cases and the population ordering of the isomers does not change. The present work provides the information needed to understand the conformational population and temperature effects of clusters containing NH₃, H₂O and H₂C₂O₄ molecules.

C. Thermodynamics of cluster formation

Gibbs free energy changes are often used for evaluating the strength of intermolecular interactions and the spontaneity of cluster formation. As shown in Tables 2 and 3, the calculated thermodynamic parameters (ZPE-corrected binding energies at 0 K, enthalpies and Gibbs free energy changes at 298.15 K) for (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters are calculated using three different methods, which have been demonstrated in the method section.

From Tables 2 and 3, hydrates are formed via the stepwise route below:

(H₂C₂O₄)(NH₃)_m(H₂O)_n−1 + H₂O → (H₂C₂O₄)(NH₃)_m(H₂O)_n

The heterodimer of oxalic acid and ammonia is exothermic by 11.9 kcal mol⁻¹, and the trimer of one oxalic acid with two ammonia molecules is exothermic by 17.4 kcal mol⁻¹. The monohydrate of (H₂C₂O₄)(NH₃) is exothermic by 5.8 kcal mol⁻¹, the dihydrate of (H₂C₂O₄)(NH₃) is exothermic by 8.2 kcal mol⁻¹, and the trihydrate of (H₂C₂O₄)(NH₃) is exothermic by 8.2 kcal mol⁻¹. The monohydrate of (H₂C₂O₄)(NH₃)₂ is exothermic by 8.3 kcal mol⁻¹, the dihydrate of (H₂C₂O₄)(NH₃)₂ is exothermic by 8.6 kcal mol⁻¹, and the trihydrate of (H₂C₂O₄)(NH₃)₂ is exothermic by 5.8 kcal mol⁻¹. The calculation results of Gibbs free energies at room temperature are as follows: −4.4 kcal mol⁻¹ for the dimerization of one oxalic acid with one ammonia molecule, −2.0 kcal mol⁻¹ for the trimerization of one oxalic acid with two ammonia molecules, 0.9 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)(H₂O) cluster, −0.1 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)(H₂O)₂ cluster, −1.1 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)(H₂O)₃ cluster, −0.9 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)₂(H₂O) cluster, −1.4 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)₂(H₂O)₂ cluster, and −0.3 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)₂(H₂O)₃ cluster.

The process of adding water molecules to the (H₂C₂O₄)(NH₃)₂ core occurs according to the following route:

(H₂C₂O₄)(NH₃)_m + nH₂O → (H₂C₂O₄)(NH₃)_m(H₂O)_n

The energy changes of (H₂C₂O₄)(NH₃)_m (m = 1–2) are the same as for the stepwise route. The dihydrate of (H₂C₂O₄)(NH₃) is exothermic by 13.9 kcal mol⁻¹, and the trihydrate of (H₂C₂O₄)(NH₃) is exothermic by 22.2 kcal mol⁻¹. The dihydrate of (H₂C₂O₄)(NH₃)₂ is exothermic by 16.9 kcal mol⁻¹, and the trihydrate of (H₂C₂O₄)(NH₃)₂ is exothermic by 24.3 kcal mol⁻¹. The Gibbs free energies at room temperature are as follows: 0.9 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)(H₂O)₂ cluster, −0.2 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)(H₂O)₃ cluster, −2.2 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)₂(H₂O)₂ cluster, and −2.5 kcal mol⁻¹ for the (H₂C₂O₄)(NH₃)₂(H₂O)₃ cluster.

Thermodynamic analyses can provide insights into the realizability and possibility of cluster formation. Thermodynamics may favor the formation of the core (H₂C₂O₄)(NH₃)₂ with water molecules via both routes mentioned above. However, for the (H₂C₂O₄)(NH₃) core, hydration appears to be thermodynamically unfavorable via the step-by-step route of adding one water molecule; the formation of the (H₂C₂O₄)(NH₃)₂(H₂O)₃ cluster may be achieved by adding three water molecules to the (H₂C₂O₄)(NH₃)₂ core.

Additionally, in Fig. 4, ΔG of the global minima (obtained by the two routes demonstrated above in this section) for the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) cluster increases over the temperature range from 100 K to 400 K; this may indicate that the stability of the global minima becomes lower with increasing temperature. In other words, these clusters may be favored under low temperature conditions, having similar features to the (H₂C₂O₄)(NH₃)_n (n = 1–6) clusters.

Fig. 4 The Gibbs free energy changes (in kcal mol⁻¹) via two different routes^a,b from the global minimum for the (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters, depending on temperature, at the PW91PW91/6-311++G(3df,3pd) level of theory. ^a(H₂C₂O₄)(NH₃)_m(H₂O)_n−1 + H₂O → (H₂C₂O₄)(NH₃)_m(H₂O)_n. ^b(H₂C₂O₄)(NH₃)_m + nH₂O → (H₂C₂O₄)(NH₃)_m(H₂O)_n.

D. Atmospheric relevance

In a previous study,⁵² it was shown that oxalic acid may form stable clusters with ammonia and contribute to the aerosol nucleation process; thus, these small clusters could serve as cores and participate in the subsequent nucleation process. In addition, from the cluster formation path discussed above, we may know that clusters form more easily from a thermodynamics aspect but not know which clusters are dominant in the atmosphere. To obtain further results, the hydrate distributions of “cores” ((H₂C₂O₄)(NH₃) and (H₂C₂O₄)(NH₃)₂) were estimated at various relative humidities (RH) using the method demonstrated in our previous study.^53,74 The relative concentration of an n-hydrate in this study is defined by:where K_n are the equilibrium constants, related to the formation energy of an n-hydrate formed from one water molecule and (n − 1)-hydrate. Moreover, ρ represents the concentration of different species and S is the saturation ratio, which is defined as the ratio of the proper partial pressure of the water vapor to the saturation vapor pressure ρ^eq_W; thus, relative humidity is defined as RH = 100% × S, and the reference pressure (P) is 1 atm. The hydration level, n, can be any value between 0 and 3.

With the computational method used, the percentage of clusters in Fig. 5 represents the proportion of the hydrate in each system ((H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) and (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3)) at the same size and the same relative humidity at 298.15 K. As shown in Fig. 5(a), 99.8% of (H₂C₂O₄)(NH₃) is non-hydrated at 20% RH, then the percentage slightly decreases to 99.6% at 50% RH, 99.4% at 80% RH and 99.3% at 100% RH. At the same relative humidity, the percentages of the hydrates are almost negligible, except for monohydrates with a percentage of 0.5% at 80% RH. As shown in Fig. 5(b), the percentages of the non-hydrated (H₂C₂O₄)(NH₃)₂ at 20, 50, 80 and 100% RH are 96.9%, 92.1%, 87.1% and 83.6%, respectively. The percentages of the monohydrates range from 2.8–12.1%, the dihydrates from 0.2–4.0% and the trihydrates from 0–0.2%.

Fig. 5 Hydrate distributions of (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0∼3) clusters (label (a)) and (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0∼3) clusters (lable (b)) at four different relative humidities. In all cases, T = 298.15 K.

The change in hydrate distributions is slight as the RH increases. At the same relative humidity, the percentage of the hydrates may not only be influenced by the relative humidity but is also related to the stability of the clusters under atmospheric conditions. The minute proportion of the cluster (H₂C₂O₄)(NH₃) may be due to the binding of (H₂C₂O₄)(NH₃) with water via the stepwise route being unfavorable. However, for the cluster (H₂C₂O₄)(NH₃)₂, the monohydrates and the dihydrates of (H₂C₂O₄)(NH₃)₂ may be relatively extensive in (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters.

E. Optical properties

The extinction properties of atmospheric aerosols can directly reduce the atmospheric visibility, and Rayleigh scattering contributes largely to the extinction properties. However, the understanding of the impact of atmospheric pre-nucleation clusters on solar radiation is insufficient. Thus, it is imperative to investigate the Rayleigh-scattering properties of the clusters. For molecular clusters, Rayleigh scattering is the dominant mechanism.⁵⁹

This work is the first attempt to investigate the polarization and Rayleigh scattering properties for (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters; the optimized geometry and the relevant optical properties are calculated at the level of CAM-B3LYP/aug-cc-pVDZ. The variations of Rayleigh light scattering intensities, R_n, isotropic mean polarizabilities, [small alpha, Greek, macron], depolarization ratios, σ_n, and anisotropic polarizabilities, Δα, along with the number of water molecules, are displayed in Fig. 6. The depolarization ratios, σ_n, and anisotropic polarizabilities, Δα, are relatively size dependent, which is consistent with studies of the sulfuric acid hydration system⁵⁹ and the methylamine–sulfuric acid hydration system.⁷⁴ The influence of ammonia and water molecules on Rayleigh light scattering can be observed in Fig. 6(a); the Rayleigh light-scattering intensities increase by nearly 84 000–182 000 a.u. as a result of adding an ammonia molecule, in comparison to 59 000–78 000 a.u. in (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) clusters and 99 000–122000 a.u. in (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3) clusters as a result of adding a water molecule. In addition, as shown in Fig. 6(c), the isotropic mean polarizabilities increase by nearly 15–22 a.u. as a result of adding an ammonia molecule, in comparison to 9.4–10.5 a.u. in (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) clusters and 2.5–18.2 a.u. in (H₂C₂O₄)(NH₃)₂(H₂O)_n (n = 0–3) clusters as a result of adding a water molecule. These data may indicate that a single ammonia molecule is able to generate a larger increase in Rayleigh light scattering intensities and isotropic mean polarizabilities than a water molecule. Effective scattering is found to be associated not only with the size⁸⁶ and the concentration^87,88 of the atmospheric particles but also the composition.^89–91 According the results of our previous and current studies, (H₂C₂O₄)(NH₃)_n (n = 1–6) and (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters containing oxalic acid and ammonia may both participate in the atmospheric nucleation process and show relatively high Rayleigh scattering intensities in the atmosphere. This may also indicate that the more ammonia molecules in the clusters, the higher the Rayleigh scattering intensities and the greater the contribution to the extinction properties, resulting in a reduction in the visibility of the atmosphere.

Fig. 6 Rayleigh light-scattering and cluster-polarizability properties: (a) Rayleigh light-scattering intensities as a function of the number of water molecules; (b) depolarization ratio as a function of the number of water molecules; (c) isotropic mean polarizabilities as a function of the number of water molecules; (d) anisotropic polarizabilities as a function of the number of water molecules.

Comparatively, it is observed that the depolarization ratios, σ_n, and the anisotropic polarizabilities, Δα, show patterns quite different from those of Rayleigh light scattering intensities and isotropic mean polarizabilities. When n ≥ 1, with an increasing number of water molecules, the calculated depolarization ratio is observed to decay slightly from (H₂C₂O₄)(NH₃)(H₂O) to (H₂C₂O₄)(NH₃)(H₂O)₂, then the trend becomes steady, in contrast, decreasing more gently from (H₂C₂O₄)(NH₃)₂(H₂O) to (H₂C₂O₄)(NH₃)₂(H₂O)₃. The declining trend can be derived from the formula, due to the gradual increase in the mean isotropic polarizability with cluster size while the anisotropic polarizability remains within a smaller range. This is expected, as the cluster changes from a molecular cluster into a spherical isotropic particle.

Conclusion

In this study, the formation free energies have been calculated via three different routes to investigate the hydration of (H₂C₂O₄)(NH₃) and (H₂C₂O₄)(NH₃)₂ cores with up to three water molecules. The atmospheric relevance, temperature dependence and Rayleigh light scattering properties were also determined.

It is found that proton transfer exists in the clusters, (H₂C₂O₄)(NH₃)(H₂O)₂, (H₂C₂O₄)(NH₃)(H₂O)₃, (H₂C₂O₄)(NH₃)₂(H₂O), (H₂C₂O₄)(NH₃)₂(H₂O)₂ and (H₂C₂O₄)(NH₃)₂(H₂O)₃. In addition, compared with the (H₂C₂O₄)(NH₃)₂ core, the binding of the (H₂C₂O₄)(NH₃) core with a water molecule seems to be thermodynamically unfavorable, while the negative free energy changes of the hydrates of the (H₂C₂O₄)(NH₃)₂ core indicate that these hydrates are energetically favorable.

The thermodynamics indicates that water may form hydrates with oxalic acid and ammonia in the atmosphere. The Gibbs free energies of the global minima at different temperatures indicate that these clusters may form more favorably under low temperature conditions. Analyzing the contributions of the various isomers to the conformational populations, temperature is deemed to be an important factor with respect to the stability of the clusters, as well as affecting the population order variation of isomers. But for all realistic atmospheric conditions (approximately 250–300 K), it is seen that the global minima of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) dominate in all cases and the population ordering of the isomers does not change.

The general trend of hydration changes slightly as the relative humidity increases. The hydration of the (H₂C₂O₄)(NH₃) core is insignificant, and the monohydrates and the dihydrates of the (H₂C₂O₄)(NH₃)₂ core may be relatively extensive in (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) clusters.

Additionally, the Rayleigh scattering properties of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 0–3) clusters were also studied. It was found that the addition of both ammonia and water molecules results in increasing Rayleigh scattering intensities and isotropic mean polarizabilities, but a single ammonia molecule may be able to generate a larger increase in Rayleigh light scattering intensities than a water molecule. This may indicate that clusters containing oxalic acid and ammonia show high Rayleigh light-scattering intensities, but more ammonia in clusters results in higher Rayleigh light-scattering intensities and a greater contribution to the extinction properties.

Our work tentatively provides a reference for further research on cluster nucleation involving oxalic acid in the atmosphere; future experimental studies are required to investigate the contribution of oxalic acid to aerosol nucleation under atmospheric conditions.

Acknowledgements

The study was supported by grants from the National Natural Science Foundation of China (Grant No. 21403244, 21133008, 21573241, 41527808 and 41505114), the Director Foundation of AIOFM (AGHH201505, Y23H161131), the National High Technology Research and Development Program of China (863 Program) (Grant No. 2014AA06A501), and the program of Formation Mechanism and Control Strategies of Haze in China (Grant No. XDB05000000). We also appreciate the “Interdisciplinary and Cooperative Team” of CAS and the “Thousand Youth Talents”. The computation was performed in EMSL, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research, which is located at Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated for the DOE by Battelle. Part of the computation was performed at the Supercomputing Center of USTC.

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Footnote

† Electronic supplementary information (ESI) available: Details about the coordinates, harmonic frequencies (in cm⁻¹) and IR intensities for (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) isomers optimized by PW91PW91/6-311++G(3df,3pd) theory of level. The relative single-point energy ΔE_rel, the ZPE-corrected binding energies (ΔE₀), intermolecular enthalpy (ΔH), free energy changes (ΔG) and Boltzmann averaged Gibbs free energy of (H₂C₂O₄)(NH₃)(H₂O)_n (n = 0–3) (in kcal mol⁻¹) based on PW91PW91/6-311++G(3df,3pd) calculations (all the binding energies have multiplied a scale factor of 0.8). The conformational population changes in the low isomers of (H₂C₂O₄)(NH₃)_m(H₂O)_n (m = 1–2, n = 1–3) as a function of temperature. See DOI: 10.1039/c6ra03164a

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