Atmospheric implication of the hydrogen bonding interaction in hydrated clusters of HONO and dimethylamine in the nighttime

Abstract

In this study, the stability of clusters formed by the trans- and cis-isomers of nitrous acid (HONO) with dimethylamine (DMA) and water has been characterized by density functional theory. The large red shifts of the OH-stretching transitions of both HONO isomers in the clusters indicate the formation of strong hydrogen bonds. At standard temperature and pressure, H₂O (acceptor) binds to HONO (donor) with binding energies of −25.0 to −24.6 kJ mol⁻¹, less stable than those of DMA (acceptor) with HONO (donor) (−50.5 to −45.3 kJ mol⁻¹). Our findings indicate that hydration enhances proton transfer from HONO to DMA, and consequently increases the interaction strength (binding energies = −67.8 to −78.6 kJ mol⁻¹). The topological and generalized Kohn–Sham energy decomposition confirms strong hydrogen bond interactions. The clustering of HONO with DMA in the atmosphere is negligible as compared to the important H₂SO₄–DMA clusters.

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Environmental impact

HONO as an important atmospheric species starts to accumulate at nighttime. The chemistry of HONO has aroused research interest, but studies on clustering interactions from a molecular perspective are limited. In this paper, we provide an overview of the hydrogen bonding interactions between HONO and dimethylamine (DMA), and then demonstrate that hydration promotes proton transfer from HONO to DMA.

Introduction

Amines have been confirmed as potential stabilizers for atmospheric nucleation, enhancing new particle formation and growth.^1–4 About 150 amines have been identified in the atmosphere. The total emission of amines, including monomethylamine (MMA), dimethylamine (DMA) and trimethylamine (TMA), is estimated to be ∼300 Gg N a⁻¹ globally.⁵ Their atmospheric sources include anthropogenic sources (animal husbandry, industries and combustion, etc.) and natural sources (ocean organisms, biomass burning, vegetation, geologic sources, etc.).⁵ Amines can modify the acid/base nature of aerosols.⁶

Nitrous acid (HONO) is a source of the most important daytime radical, the OH radical, and its photolysis during the daytime may account for 30–60% of the OH production.^7,8 HONO could be formed by the heterogeneous conversion of NO₂ on wet surfaces:⁹

2NO₂ + H₂O → HONO + HNO₃ (1)

The heterogeneous conversion of NO₂ on adsorbed hydrocarbons (HC) is also of importance:^10,11

NO₂ + HC_red → HONO + HC_ox (2)

The following two heterogeneous reactions have been suggested to explain the observed nighttime reactions:¹²

NO + NO₂ (or N₂O₃) + H₂O → 2HONO (3)

HNO_3(ads) + NO_(g) → HONO + NO₂ (4)

In addition, the photo-induced heterogeneous reactions have been suggested to be potential sources of daytime HONO, for example, the photosensitized reduction of NO₂ on an organic surface.¹³ On the other hand, the homogeneous formation pathways of HONO could also play an important role. HONO is formed by the reaction of NO with OH radicals:^14,15

OH + NO (+M) → HONO (+M) (5)

The reaction of electronically excited NO₂ with H₂O vapor could also be an important homogeneous source of HONO:¹⁶

Furthermore, soil bacteria have been suggested as a significant source of the atmospheric HONO, which may account for up to 50% of the reactive nitrogen released from soil.¹⁷

Direct emissions are another source of HONO: combustion processes,¹⁸ diesel engines,¹⁹ gas space heaters and stoves,²⁰etc. The photolytic life time of HONO is only about 10 minutes at midday during summer time, due to the rapid production of OH and NO by absorbing sunlight at wavelengths shorter than 390 nm during the daytime.²¹ At nighttime, the photolytic loss mechanism stops. As a result, HONO starts to accumulate with concentrations of 0.1–10 ppbv and decreases rapidly after sunrise.^22–24 The concentration of HONO was observed to be 1.4 and 0.4–0.5 ppbv in the morning and in the afternoon, respectively, for the urban atmosphere of New York City.²⁵ In contrast, the concentrations of sulfuric acid (H₂SO₄) in the atmospheric boundary layers are about 0.04–1.2 pptv, which are much less than those of HONO.²⁶

HONO can form hydrogen bonded complexes with other compounds. The complexes formed between HONO and ethene,²⁷ diethyl ether,²⁸ and acetone²⁸ have been studied in argon matrices. The red shifts of the OH-stretching vibrational transitions were found to be 136, 376 and 413 cm⁻¹ for ethene,²⁷ diethyl ether²⁸ and acetone²⁸ with respect to the trans-HONO monomer, respectively. The investigation of the structural, energetic, and spectroscopic parameters of the hydrogen bonded complexes formed by HONO with many atmospheric species could help to understand its contribution to atmospheric clustering.

Hydrogen bonding interactions have been commonly suggested as the driving forces for the formation of atmospheric molecular complexes, and the corresponding hydrogen bonding strength reveals the thermodynamic stability of these complexes.^4,29–31 H₂SO₄ has been well accepted as one of the crucial nucleating species.^32–34 Besides H₂SO₄, other nucleating precursors, such as ammonia, amines, and organic compounds, have been suggested to be involved in the formation of the critical nucleus by serving as stabilizing components.⁴ For example, DMA can promote H₂SO₄–water nucleation in the atmosphere.^3,26 The experiments in the CLOUD (Cosmics Leaving OUtdoor Droplets) chamber at CERN show that amines can enhance particle formation rates more than 1000 times as compared with NH₃.²⁶ The lifetime of DMA against OH in the atmosphere is 4.3 h.³⁵ Since the concentration of OH decreases dramatically at nighttime and the lifetime of DMA becomes much longer, it is an interesting and essential topic to study the initial clustering steps involving amines.

In the present work, we report the hydrogen bonding interactions of HONO with atmospheric species (DMA, water) at nighttime. The most stable structures of the hydrogen bonded complexes and the changes in the structural and vibrational characteristics of the monomers upon complexation are predicted. Atoms in molecules (AIM) analysis was carried out to investigate the electronic densities and the inter-molecular hydrogen bonding interactions in the complexes.^36,37 Generalized Kohn–Sham energy decomposition analysis (GKS-EDA) was performed to study the contribution of different components to the total interaction energy.³⁸

Computational methods

All the structures were optimized using the B3LYP-D3 functional and the aug-cc-pVTZ basis set with the Gaussian 09 (Revision E.01) program.³⁹ There is no imaginary frequency for the optimized structures and the zero-point vibrational energy (ZPVE) was evaluated using thermodynamic corrections at the B3LYP-D3/aug-cc-pVTZ level of theory. The choice of the B3LYP-D3 computational method is based on its good performance on atmospheric relevant clusters, including the prediction of Gibbs free energies, infrared frequencies and structural characteristics.^40–44 In order to obtain explicit estimates of thermodynamic constants, two additional options, an extremely tight optimization convergence criteria (opt = verytight) and a very high accuracy grid integration (integral = ultrafine), were used in all DFT calculations.^45,46

Bader's theory of atoms in molecules (AIM) has been widely applied to understand and characterize both covalent and non-covalent molecular interactions.^36,37 The topological properties of electron density ρ(r) at the bond critical point (BCP) have been widely used to get deep insight into the nature of the hydrogen bonding.⁴⁷ The wavefunctions obtained at the B3LYP-D3/aug-cc-pVTZ level were used to evaluate the electron density ρ(r) and laplacian ∇²ρ(r) at the bond critical points and the atomic charge q(H) in the atomic basin of hydrogen. The topological analysis was carried out by utilizing the AIM2000 program (version 2) package for the monomers and complexes.

Hydrogen bonding interactions were investigated using a new energy decomposition analysis scheme (GKS-EDA) based on the generalized Kohn–Sham (GKS) and the localized molecular orbital energy decomposition analysis (LMO-EDA) scheme, which is implemented in the GAMESS (US) program.⁴⁸ The total interaction energy (E^INT) is divided into electrostatic energy (E^ES), exchange energy (E^EX), repulsion energy (E^REP), polarization energy (E^POL), Grimme's dispersion energy (E^DISP) and correlation energy (E^CORR).³⁸

Results and discussion

Structure and stability

The gas phase nitrous acid (HONO) molecule is one of the smallest molecules that can adopt both a cis- and a trans-form (Fig. 1), and exhibits a cis–trans conformational equilibrium. In an early study, the isotopic IR spectra of HONO were obtained in the vapor and solid phases. The energy difference between trans-HONO and cis-HONO was 1.6 ± 4.2 kJ mol⁻¹ with the trans-HONO being more stable, which was deducted from the temperature dependence of fundamentals of the two isomers and the isotopic frequencies of the torsion fundamentals.⁴⁹ However, the barrier of inter-conversion obtained was as much as 40 kJ mol⁻¹ through identifying all the observed fundamentals of both forms and fit into the barrier potential energy.⁴⁹ The energy difference between the trans- and cis-form was calculated to be 2.7 kJ mol⁻¹ (B3LYP-D3/aug-cc-pVTZ, with ZPVE correction), with the former being more stable. The structures of both forms were accurately determined on the basis of the inertial defects of microwave spectra.⁵⁰ The key parameters r_N=O, r_N–O, r_O–H, θ_ONO and θ_NOH for trans-HONO were found to be 1.170 Å, 1.432 Å, 0.958 Å, 110.7° and 102.1°, respectively. For cis-HONO, these parameters were determined to be 1.185 Å, 1.392 Å, 0.982 Å, 113.6° and 104.0°, respectively. Our calculated structures obtained at the B3LYP-D3/aug-cc-pVTZ level (Fig. 1) are consistent with these experimental values. The structural parameters of DMA have been experimentally determined based on the rotational constants in the microwave spectra,⁵¹ which are also in good agreement with our calculated values.

Fig. 1 The optimized HONO conformers at the B3LYP-D3/aug-cc-pVTZ level.

Quantum chemical calculations for the heterodimers (HONO–H₂O, HONO–DMA, H₂O–HONO, DMA–HONO) and the hydrated heterotrimer clusters (HONO–DMA–H₂O) were performed to search for stable structures. In these heterodimers and heterotrimers, HONO can be a hydrogen bond donor or an acceptor. The optimized structures of the most stable clusters at the B3LYP-D3/aug-cc-pVTZ level are shown in Fig. 2–4. For the HONO–DMA–H₂O heterotrimer, only cyclic ring structures were considered in this study.

Fig. 2 The stable structures of the heterodimer clusters consisting of one water and one HONO calculated at the B3LYP-D3/aug-cc-pVTZ level.

Fig. 3 The stable structures of the heterodimer clusters consisting of one DMA and one HONO calculated at the B3LYP-D3/aug-cc-pVTZ level.

Fig. 4 The stable structures of the heterotrimer clusters consisting of one water, one DMA and one HONO calculated at the B3LYP-D3/aug-cc-pVTZ level.

In the HONO–DMA (G–J) and HONO–H₂O (G–H) heterodimers, HONO acts as the hydrogen bond donor approaching DMA or H₂O. Upon complexation, the changes in the OH bond length of the HONO–H₂O (G–H) complexes vary from 0.0147 to 0.0167 Å, and the corresponding O–H⋯O hydrogen bond angles deviate within 10° from the ideal linear orientation. The changes in the OH bond length of the HONO–DMA (G–J) complexes are much larger (0.0448 to 0.0550 Å), and the corresponding O–H⋯N hydrogen bond angles (173.5–178.2°) are much closer to the linear orientation. The O–H⋯N hydrogen bonds between DMA and HONO are much stronger than the O–H⋯O hydrogen bonds between H₂O and HONO. This is similar with the results for the trans-HONO–NH₃ complex, where the hydrogen bond angle was calculated to be 175.8° (MP2/aug-cc-pVTZ).⁵² As compared with the HONO–acetone complex, the trans- and cis-HONO isomers deviate from a linear hydrogen bond of acetone: 170.3° for trans-HONO and 162.2° for cis-HONO (B3LYP/6-311++G**).⁵³ In the nitric acid (HONO₂)–H₂O complex, the hydrogen bond angle (HONO₂ as the hydrogen bond donor) was calculated to be 170.0° (B3LYP/6-31G**).⁵⁴ When proton transfer occurs in the formation of the heterodimer clusters, the DMA molecule obtains the proton from HONO to form an N–H bond. On the other hand, others such as water and acetone form weak hydrogen bonds. In the DMA–HONO (A–F) and H₂O–HONO (A–F) heterodimer clusters, HONO acts as the hydrogen bond acceptor. The changes in the OH bond length are small, 0.0021 to 0.0031 Å for H₂O–HONO (A–F). In contrast, the changes in the NH bond length are −0.0006 to 0.0004 Å for DMA–HONO (A–F). The elongated hydrogen bonded XH length is a typical feature of the traditional hydrogen bonding. However, there is another type of hydrogen bonds known as improper hydrogen bonds, which shows a decrease of the bonded XH length upon complex formation.^55,56

The HONO–DMA–H₂O heterotrimers form six- to eight-membered ring structures. In the HONO–DMA–H₂O (A, D, F) complexes, HONO binds with H₂O to form an O–H⋯O hydrogen bond. Similar to the HONO–H₂O (G–H) heterodimer complexes, the changes in the OH bond length of HONO are much larger in the HONO–DMA–H₂O (B, C, E, G) complexes. However, the changes of the OH bond length as HONO binds with DMA are much larger, ranging from 0.0667 to 0.5182 Å, in the HONO–DMA–H₂O (B, C, E, G) complexes than the HONO–DMA (G–J) complexes. We can clearly see the proton transfer from HONO to DMA. It may indicate that hydration enhances proton transfer (Table 1).

Table 1 Selected optimized geometric parameters for the hydrogen bonds in the HONO heterodimer and heterotrimer complexes at the B3LYP-D3/aug-cc-pVTZ level (angles in degrees; lengths/distances in Å)

Type		O–H⋯O/N (HONO)			N–H⋯O/N (DMA)			O–H⋯O/N (H2O)
		Δr^a	r	θ	Δr^a	r	θ	Δr^a	r	θ
a Δr = rdimer − rmonomer, is the change in the OH bond length upon complexation. b Inter-molecular hydrogen bond distance. c Inter-molecular hydrogen bond angle.
H2O–HONO	(A)	—	—	—	—	—	—	0.0021	2.1721	176.8
	(B)	—	—	—	—	—	—	0.0020	2.1713	177.0
	(C)	—	—	—	—	—	—	0.0026	2.2181	177.0
	(D)	—	—	—	—	—	—	0.0027	2.2212	178.7
	(E)	—	—	—	—	—	—	0.0021	2.1708	171.0
	(F)	—	—	—	—	—	—	0.0031	2.0853	156.2
HONO–H2O	(G)	0.0167	1.7846	170.9	—	—	—	0.0034	2.4363	113.5
	(H)	0.0147	1.8076	170.6	—	—	—	—	—	—
DMA–HONO	(A)	—	—	—	−0.0003	2.5000	122.7	—	—	—
	(B)	—	—	—	−0.0004	2.4272	127.1	—	—	—
	(C)	—	—	—	0.0003	2.5436	123.9	—	—	—
	(D)	—	—	—	−0.0002	2.6475	119.2	—	—	—
	(E)	—	—	—	−0.0006	2.4775	119.3	—	—	—
	(F)	—	—	—	−0.0003	2.4220	125.7	—	—	—
HONO–DMA	(G)	0.0448	1.7083	176.7	—	—	—	—	—	—
	(H)	0.0449	1.7079	173.5	—	—	—	—	—	—
	(I)	0.0537	1.6766	177.4	—	—	—	—	—	—
	(J)	0.0550	1.6740	178.2	—	—	—	—	—	—
HONO–DMA–H2O	(A)	0.0260	1.7014	171.9	0.0031	2.6303	121.2	0.0360	1.6033	172.4
	(B)	0.0667	1.7794	170.2	0.0037	2.8073	114.2	0.0056	1.5220	175.3
	(C)	0.0946	1.8573	168.6	0.0026	2.9844	107.2	0.0052	1.4407	178.2
	(D)	0.0322	1.6709	173.1	0.0037	2.4394	141.7	0.0411	1.7432	165.7
	(E)	0.0791	1.5885	179.7	0.0053	2.0562	144.0	0.0113	2.0072	158.2
	(F)	0.0339	1.6603	175.2	0.0018	2.4387	122.4	0.0418	1.7353	168.6
	(G)	0.5182	1.1067	175.9	0.0202	1.8162	146.6	0.0261	1.7408	168.0

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The calculated binding energy (BE), zero-point vibrational energy (ZPVE), enthalpy of formation (ΔH^θ_298K), and Gibbs free energy of formation (ΔG^θ_298K) at 298.15 K and 1 atm for the HONO heterodimer and heterotrimer complexes at the B3LYP-D3/aug-cc-pVTZ level are presented in Table 2. For the heterodimer complexes formed with the acid as the acceptor and DMA as the donor, the BEs show that the DMA–HONO (A–F) complexes are less stable (−8.7 to −6.0 kJ mol⁻¹) than their corresponding analogues (−50.5 to −45.3 kJ mol⁻¹) where the acid is the donor and DMA is the acceptor. The HONO–DMA complexes are slightly more stable than the trans-HONO–NH₃ and cis-HONO–NH₃ complexes (BEs = −40.1 and −36.4 kJ mol⁻¹ (MP2/6-311+G(2d,2p)), respectively).⁵⁷ For the HONO–H₂O complexes, the BEs are −9.0 to −4.7 kJ mol⁻¹ for the complexes with the acid as the acceptor and −25.0 to −24.6 kJ mol⁻¹ for the complexes with the acid as the donor. In a previous study, the BEs of the trans-HONO–(CH₃)₂CO and cis-HONO–(CH₃)₂CO complexes were calculated to be −29.6 and −27.6 kJ mol⁻¹ (MP2/6-311++G**), respectively.⁵³ This may imply that (CH₃)₂CO is similar to H₂O as a hydrogen bond acceptor. The BEs of the dimer clusters containing sulfuric acid and various amines (CH₃NH₂, (CH₃)₂NH, (CH₃)₃N, CH₃CH₂NH₂, (CH₃CH₂)₂NH, (CH₃CH₂)₃N, and CH₃CH₂NHCH₃) were calculated to be from −138.4 to −91.6 kJ mol⁻¹ (RI-MP2/aug-cc-pV(D+d)Z).³ This reveals that H₂SO₄ is a stronger hydrogen bond donor than HONO.

Table 2 Calculated binding energy (BE), zero-point vibrational energy (ZPVE), enthalpy of formation (ΔH^θ_298K) and Gibbs free energy of formation (ΔG^θ_298K) at 298.15 K and 1 atm of the HONO heterodimer and heterotrimer complexes at the B3LYP-D3/aug-cc-pVTZ level^a

Type		BE^b	ZPVE	ΔH^θ298K	ΔG^θ298K
a Energies are in kJ mol^−1. b BEs are corrected with ZPVE.
H2O–HONO	(A)	−4.7	4.6	−5.9	24.2
	(B)	−4.9	4.8	−3.8	19.2
	(C)	−4.8	5.1	−4.0	20.2
	(D)	−4.5	5.2	−3.6	20.2
	(E)	−5.1	5.0	−4.1	20.3
	(F)	−9.0	4.8	−8.3	15.1
HONO–H2O	(G)	−25.0	8.9	−27.0	9.9
	(H)	−24.6	7.8	−25.3	6.1
DMA–HONO	(A)	−6.9	3.6	−5.1	29.5
	(B)	−6.7	2.8	−4.2	25.0
	(C)	−8.3	2.9	−5.7	24.4
	(D)	−8.2	3.0	−5.8	26.2
	(E)	−8.7	3.6	−7.1	29.1
	(F)	−6.0	3.0	−3.7	26.2
HONO–DMA	(G)	−50.5	7.0	−49.8	−13.1
	(H)	−48.2	7.1	−48.0	−9.3
	(I)	−45.3	5.7	−45.3	−5.9
	(J)	−46.9	6.4	−47.4	−4.5
HONO–DMA–H2O	(A)	−67.8	15.5	−69.4	1.0
	(B)	−72.6	12.4	−72.8	−1.6
	(C)	−73.9	10.8	−74.5	0.5
	(D)	−74.5	16.5	−76.9	−0.2
	(E)	−79.3	14.2	−80.8	−4.8
	(F)	−74.0	15.7	−76.4	2.4
	(G)	−78.6	18.1	−81.8	1.8

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For the heterotrimer complexes, the BEs of −79.3 to −67.8 kJ mol⁻¹ indicate that these complexes are very stable. The heterotrimer complexes are more stable than the heterodimer complexes because these heterotrimer complexes are formed via three hydrogen bonds, and the heterodimer complexes contain only one hydrogen bond. Moreover, the seven- and eight-membered heterotrimer complexes are slightly more stable than the six-membered heterotrimer complexes.

Calculated NH- and OH-stretching transitions

The vibrational frequency shifts to lower wavenumbers and the infrared intensities of the stretching vibrational transitions of the monomer increase upon complexation. The red shift (Δ[small nu, Greek, tilde]) is the wavenumber difference between the free and hydrogen bonded NH-/OH-stretching vibrational transitions (Δ[small nu, Greek, tilde] = [small nu, Greek, tilde]_monomer − [small nu, Greek, tilde]_dimer). The calculated NH- and OH-stretching fundamental transition wavenumbers and the red shifts upon complexation of the HONO heterodimer and heterotrimer complexes at the B3LYP-D3/aug-cc-pVTZ level are summarized in Table 3.

Table 3 Calculated bonded NH- and OH-stretching wavenumbers and red shifts (in cm⁻¹) of the HONO complexes at the B3LYP-D3/aug-cc-pVTZ level^a

Type		O–H⋯O/N (HONO)			N–H⋯O/N (DMA)			O–H⋯O/N (H2O)
		[small nu, Greek, tilde]	Δ[small nu, Greek, tilde]^b	f D/fM^c	[small nu, Greek, tilde]	Δ[small nu, Greek, tilde]^b	f D/fM^c	[small nu, Greek, tilde]	Δ[small nu, Greek, tilde]^b	f D/fM^c
a The values in the parentheses are the parameters for the anti-symmetric OH-stretching transition of H2O. b Δ[small nu, Greek, tilde] = [small nu, Greek, tilde]monomer − [small nu, Greek, tilde]dimer. c f D/fM represents the increase of intensity upon complexation.
H2O–HONO	(A)	—	—	—	—	—	—	3773 (3883)	23 (16)	25.0 (2.4)
	(B)	—	—	—	—	—	—	3774 (3883)	22 (17)	24.6 (2.2)
	(C)	—	—	—	—	—	—	3762 (3878)	34 (21)	29.5 (2.1)
	(D)	—	—	—	—	—	—	3761 (3878)	35 (21)	29.7 (2.1)
	(E)	—	—	—	—	—	—	3773 (3883)	23 (16)	22.9 (2.4)
	(F)	—	—	—	—	—	—	3756 (3879)	40 (20)	31.2 (2.0)
HONO–H2O	(G)	3260	317	25.0	—	—	—	3763 (3875)	33 (24)	5.1 (1.6)
	(H)	3459	290	10.9	—	—	—	—	—	—
DMA–HONO	(A)	—	—	—	3531	−6	6.2	—	—	—
	(B)	—	—	—	3539	−13	5.6	—	—	—
	(C)	—	—	—	3526	0	5.2	—	—	—
	(D)	—	—	—	3539	−13	10.4	—	—	—
	(E)	—	—	—	3539	−13	8.9	—	—	—
	(F)	—	—	—	3534	−9	4.7	—	—	—
HONO–DMA	(G)	2868	880	30.2	—	—	—	—	—	—
	(H)	2865	883	27.6	—	—	—	—	—	—
	(I)	2582	995	82.4	—	—	—	—	—	—
	(J)	2564	1013	74.7	—	—	—	—	—	—
HONO–DMA–H2O	(A)	3267	482	15.2	3495	30	36.6	3107	792	11.4
	(B)	2507	1242	35.0	3492	34	80.3	3720	179	2.7
	(C)	2000	1576	79.3	3509	17	41.0	3728	171	2.3
	(D)	3163	585	17.3	3485	41	127.6	3009	890	12.1
	(E)	2310	1438	38.4	3462	64	219.4	3605	294	7.2
	(F)	2912	665	63.5	3517	9	30.4	3060	839	6.1
	(G)	2090	1487	82.8	3225	301	599.6	3347	552	15.5

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The OH-stretching transition of the trans-HONO monomer was calculated to be 3749 cm⁻¹ (B3LYP-D3/aug-cc-pVTZ). However, the OH-stretching transition of the cis-HONO monomer was computed to be red shifted by 172 cm⁻¹ and the intensity was reduced to 0.3 as compared with the value of the trans-HONO monomer. This may be due to the inter-molecular hydrogen bonding interaction. When HONO as a hydrogen bond donor approaches H₂O (HONO–H₂O (G–H)), the OH-stretching transitions in HONO were red shifted by 290–317 cm⁻¹. In contrast, the OH-stretching transitions were much red shifted by 880–1013 cm⁻¹ in the HONO–DMA (G–J) complexes. The OH-stretching transitions in the trans-HONO–NH₃ and cis-HONO–NH₃ complexes were calculated to be red shifted by 614–620 cm⁻¹ (MP2/6-31+G**) with respect to their corresponding monomer, and the experimental observations showed a red shift of 831 cm⁻¹ in an argon matrix.⁵⁷ In the same study, the observed 3323 cm⁻¹ band was assigned to the HONO–H₂O complex with a red shift of 249 cm⁻¹ in an argon matrix as compared to the trans-HONO monomer.⁵⁷ This is close to the calculated red shift of the OH-stretching transition (290 cm⁻¹) of the trans-HONO–H₂O (H) complex. The OH-stretching vibrational transitions of the bimolecular complexes formed between trans-HONO and acetone or diethyl ether were 413, 376 cm⁻¹ red shifted in an argon matrix with respect to the trans-HONO monomer, respectively.²⁸ Moreover, HONO could form stable 1 : 1 hydrogen bonded complexes with H₂C=CH₂ in an argon matrix, where the OH group of HONO interacts with the π-electron system of H₂C=CH₂. The corresponding red shifts of the OH-stretching transitions in the O–H⋯π complexes were much smaller (136 cm⁻¹ for the trans-complex and 103 cm⁻¹ for the cis-complex) as compared with the former red shifts in the O–H⋯O complexes.²⁷ For the DMA–HONO (A–F) complexes, the NH-stretching vibrational transitions of DMA were blue shifted by less than 13 cm⁻¹ with respect to the DMA monomer. For the H₂O–HONO (A–F) complexes where H₂O acts as the hydrogen bond donor, H₂O shows small red shifts of the symmetric (22–40 cm⁻¹) and anti-symmetric (16–21 cm⁻¹) OH-stretching vibrational transitions as compared with the H₂O monomer. As seen in Fig. 4, HONO binds with H₂O to form an O–H⋯O hydrogen bond in the HONO–DMA–H₂O (A, D, F) complexes. The OH-stretching transitions of HONO were calculated to be red shifted by 482–665 cm⁻¹ upon complexation. However, the same OH-stretching transitions in the HONO–H₂O (G–F) complexes were only red shifted by 290–317 cm⁻¹ with respect to the HONO monomer. Similarly, HONO binds with DMA to form O–H⋯N hydrogen bonds in the HONO–DMA–H₂O (B, C, E, G) complexes. The OH-stretching vibrational transitions of HONO were calculated to be red shifted by 1242–1576 cm⁻¹ upon complexation. Again, the same OH-stretching transitions in the HONO–DMA (G–J) have smaller red shifts (880–1013 cm⁻¹) with respect to the HONO monomer. These indicate that the O–H⋯O/N (HONO) hydrogen bonds in the heterotrimers are much stronger than the same type of bonds in the heterodimer complexes. It further proves that the heterotrimer complexes are much more stable than the heterodimer complexes.

Topological and GKS-EDA analysis

AIM analysis helps to understand the type of interactions using electron density and its topological information, and the analysis was performed using the wavefunctions computed at the B3LYP-D3/aug-cc-pVTZ level. The AIM plots of the HONO complexes with bond critical points (BCPs), ring critical points (RCPs) and electron density paths are shown in Fig. 5–7. The BCPs and RCPs are presented by the red and yellow balls, respectively. In addition, the C–H⋯O and C–H⋯N hydrogen bonds were obtained in the DMA–HONO (A–F) complexes as seen in Fig. 6. They are known as cooperative hydrogen bonding interactions, which play an important role in determining the structure and properties of materials.^58,59 Due to the weakness of these interactions, they are out of the scope of this study. The topological parameters, including electron density ρ(r) and laplacian ∇²ρ(r) at the BCPs and change in atomic charge Δq(H) at the H atom at the B3LYP-D3/aug-cc-pVTZ level, are listed in Table 4.

Fig. 5 The AIM plots of the heterodimer clusters consisting of one H₂O and one HONO obtained at the B3LYP-D3/aug-cc-pVTZ level. The bond critical points and ring critical points are represented by the red and yellow balls, respectively.

Fig. 6 The AIM plots of the heterodimer clusters consisting of one DMA and one HONO obtained at the B3LYP-D3/aug-cc-pVTZ level. The bond critical points and ring critical points are represented by the red and yellow balls, respectively.

Fig. 7 The AIM plots of the heterotrimer clusters obtained at the B3LYP-D3/aug-cc-pVTZ level. The bond critical points and ring critical points are represented by the red and yellow balls, respectively.

Table 4 AIM parameters of the complexes obtained at the B3LYP-D3/aug-cc-pVTZ level (a.u.)

Type		O–H⋯O/N (HONO)			N–H⋯O/N (DMA)			O–H⋯O/N (H2O)
		Δq(H)	ρ(BCP)	∇^2ρ(BCP)	Δq(H)	ρ(BCP)	∇^2ρ(BCP)	Δq(H)	ρ(BCP)	∇^2ρ(BCP)
H2O–HONO	(A)	—	—	—	—	—	—	0.033	0.0123	0.0635
	(B)	—	—	—	—	—	—	0.032	0.0123	0.0621
	(C)	—	—	—	—	—	—	0.034	0.0122	0.0654
	(D)	—	—	—	—	—	—	0.035	0.0122	0.0649
	(E)	—	—	—	—	—	—	0.030	0.0123	0.0623
	(F)	—	—	—	—	—	—	0.036	0.0153	0.0760
HONO–H2O	(G)	0.094	0.0264	0.1579	—	—	—	0.033	0.0097	0.0464
	(H)	0.094	0.0259	0.1434	—	—	—	—	—	—
DMA–HONO	(A)	—	—	—	−0.022	0.0079	0.0389	—	—	—
	(B)	—	—	—	−0.017	0.0076	0.0386	—	—	—
	(C)	—	—	—	−0.026	0.0078	0.0303	—	—	—
	(D)	—	—	—	−0.019	0.0068	0.0291	—	—	—
	(E)	—	—	—	−0.016	0.0082	0.0405	—	—	—
	(F)	—	—	—	−0.024	0.0081	0.0398	—	—	—
HONO–DMA	(G)	0.125	0.0346	0.2318	—	—	—	—	—	—
	(H)	0.127	0.0346	0.2323	—	—	—	—	—	—
	(I)	0.133	0.0360	0.2486	—	—	—	—	—	—
	(J)	0.139	0.0360	0.2484	—	—	—	—	—	—
HONO–DMA–H2O	(A)	0.115	0.0293	0.1915	0.026	0.0064	0.0285	0.127	0.0314	0.1846
	(B)	0.156	0.0394	0.2824	0.050	0.0119	0.0566	0.038	0.0150	0.0791
	(C)	0.184	0.0449	0.3271	0.044	0.0099	0.0445	0.040	0.0146	0.0791
	(D)	0.129	0.0319	0.2131	0.044	0.0087	0.0450	0.145	0.0330	0.2002
	(E)	0.171	0.0412	0.3040	0.078	0.0177	0.0943	0.067	0.0184	0.1133
	(F)	0.131	0.0320	0.2207	0.030	0.0080	0.0384	0.145	0.0332	0.2024
	(G)	0.048	0.0454	0.3700	0.153	0.0273	0.1764	0.106	0.0263	0.1872

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According to the criteria proposed by Popelier, the electron density at the BCPs ρ(BCP) is in the range of 0.002–0.040 a.u. for a hydrogen bond.^60,61 The electron densities at the BCPs are in the ranges of 0.0123–0.0332, 0.0068–0.0273 and 0.0259–0.0454 a.u. for the O–H⋯O/N (H₂O), O–H⋯O/N (DMA) and O–H⋯O/N (HONO) hydrogen bonds, respectively. Similarly, the laplacian of charge densities ∇²ρ(BCP) of the complexes are in the ranges of 0.0464–0.2024, 0.0285–0.1764 and 0.1434–0.3700 a.u. for the O–H⋯O/N (H₂O), O–H⋯O/N (DMA) and O–H⋯O/N (HONO) hydrogen bonds, respectively. These values are higher than the upper value of the laplacian criteria (0.014–0.139 a.u.) for a hydrogen bond.^60,61 In particular, the ∇²ρ(BCP) values of the O–H⋯O/N (HONO) hydrogen bond are much higher than the upper value of the laplacian criteria. This is due to the strong acid–base interactions between HONO and DMA, thus leading to proton transfer from HONO to DMA.

Upon complexation, charge transfer (CT) from the hydrogen bond acceptor to the donor is usually observed; thus the charge of the hydrogen atom involved in the hydrogen bond will decrease.⁶² AIM atomic charge difference on the H atoms (Δq(H)) upon complexation is summarized in Table 4. The atomic charges at the H atoms (Δq(H)) for the O–H⋯O/N (H₂O) hydrogen bonds are changed by 0.033–0.145 a.u., while 0.094–0.184 a.u. are obtained for the O–H⋯O/N (HONO) hydrogen bonds. For the O–H⋯O/N (DMA) hydrogen bond, the atomic charges at the H atoms are negative (−0.026 to −0.016 a.u.) in the DMA–HONO (A–F) complexes. For the remaining O–H⋯O/N (DMA) hydrogen bonds, the atomic charges at the H atoms are changed by 0.026–0.153 a.u. In general, the larger the Δq(H), the greater the red shifts of the NH-/OH-stretching transitions, which is a similar observation to that in our previous study on the hydrogen bonding in the carboxylic acid–sulfuric acid complexes.⁴³

The distance between a BCP and an RCP has been applied as an indicator to determine the structural stability of a hydrogen bond.⁶³ The distances between BCPs and RCPs are listed in Table 5. In the HONO : DMA : H₂O (1 : 1 : 1) heterotrimer complexes, the distances between the BCP of the O–H⋯O/N (H₂O) hydrogen bond and the RCP in the HONO–DMA–H₂O (A) complexes are much larger than the distances for the other two hydrogen bonds. The O–H⋯O/N (H₂O) hydrogen bonds in the HONO–DMA–H₂O (A) are relatively more stable than the other two hydrogen bonds. In the case of the HONO–DMA–H₂O (E) complex, the N–H⋯O/N (DMA) hydrogen bonds are the strongest hydrogen bonds. In the remaining HONO–DMA–H₂O complexes, the O–H⋯O/N (HONO) hydrogen bonds are the strongest.

Table 5 The distance (Å) between a BCP and an RCP in the HONO–DMA–H₂O complexes

Conformer	O–H⋯O/N (HONO)	N–H⋯O/N (DMA)	O–H⋯O/N (H2O)
(A)	2.2754	1.1251	2.3071
(B)	2.1451	1.8267	1.8313
(C)	2.1319	1.6718	1.8456
(D)	2.5685	1.8442	2.5510
(E)	2.4093	2.4265	2.1018
(F)	2.8998	1.8346	2.3551
(G)	2.6994	2.3176	2.0399

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The energy decomposition analysis (EDA) is a powerful tool for a quantitative interpretation of non-covalent interactions in terms of various components. In this study, we have utilized Su's generalized Kohn–Sham energy decomposition analysis (GKS-EDA) for energy decomposition analysis.⁶⁴ This method has been used to analyze the weak inter-molecular (phenylenediamine dimer clusters)⁶⁵ and intra-molecular (malonaldehyde, methallyl carbinol, etc.)⁶⁶ non-covalent interactions. The total interaction energy along with the individual components obtained at the B3LYP-D3/aug-cc-pVTZ level is listed in Table 6. The GKS-EDA shows that the E^ES and E^EX terms are the main driving forces for the formation of the complexes while the E^REP term is not favorable for the formation of complexes. The E^REP term is positive, which is about ∼75–87% of the total attractive energies. The terms E^ES and E^EX are the dominating contributors about ∼13–34% and ∼44–53% to the total attractive energies, respectively. For the HONO (acceptor) heterodimer complexes, the E^POL contribution is about −5% to 14% to the total attractive energies, and the E^CORR (∼6–22% to the total attractive energies) and E^DISP (∼4–22% to the total attractive energies) contributions are close to each other. However, for the remaining heterodimer and heterotrimer complexes, these three contributions are quite different from those of the HONO (acceptor) heterodimer complexes, where the E^POL contribution is about ∼15–21% to the total attractive energies, ∼3–4% for E^CORR and ∼3–5% for E^DISP.

Table 6 Results of generalized Kohn–Sham energy decomposition analysis (GKS-EDA) for the HONO complexes at the B3LYP-D3/aug-cc-pVTZ level (kJ mol⁻¹)^a

Type		ΔE^ES	ΔE^EX	ΔE^REP	ΔE^POL	ΔE^DISP	ΔE^CORR	ΔE^INT
a NP = the proton transfer from HONO to DMA is very large (0.5182 Å) in the HONO–DMA–H2O (G) complex; thus it was not possible to perform GKS-EDA analysis.
H2O–HONO	(A)	−11.7	−18.1	30.9	−4.2	−3.1	−3.1	−9.2
	(B)	−12.3	−18.2	31.1	−3.9	−3.1	−3.3	−9.7
	(C)	−13.8	−22.7	39.2	−2.9	−3.1	−6.4	−9.7
	(D)	−13.5	−22.5	38.9	−2.8	−3.1	−6.5	−9.5
	(E)	−12.4	−17.9	30.8	−4.5	−3.1	−2.9	−10.1
	(F)	−19.0	−26.2	45.5	−8.1	−3.7	−2.3	−13.8
HONO–H2O	(G)	−65.6	−96.0	171.8	−30.7	−5.9	−8.4	−35.0
	(H)	−52.7	−67.5	120.9	−22.7	−4.1	−7.6	−33.6
DMA–HONO	(A)	−9.3	−38.3	62.9	3.6	−13.0	−15.7	−9.8
	(B)	−7.6	−26.4	43.5	1.3	−10.7	−8.9	−8.9
	(C)	−13.6	−30.4	50.7	−3.7	−9.7	−3.8	−10.6
	(D)	−9.5	−28.5	46.0	−1.3	−12.5	−4.7	−10.5
	(E)	−11.1	−41.9	69.0	3.7	−14.2	−17.2	−11.8
	(F)	−6.8	−26.9	44.5	2.0	−10.8	−10.5	−8.4
HONO–DMA	(G)	−98.8	−145.7	267.0	−59.3	−10.0	−14.2	−61.0
	(H)	−99.2	−147.9	270.5	−60.5	−11.2	−14.8	−62.9
	(I)	−112.7	−183.4	335.1	−76.7	−12.0	−12.0	−61.7
	(J)	−114.2	−189.6	344.3	−78.1	−14.1	−13.0	−64.7
HONO–DMA–H2O	(A)	−148.0	−225.1	406.6	−81.8	−16.2	−24.3	−88.8
	(B)	−150.7	−232.2	423.5	−96.9	−18.5	−21.2	−95.9
	(C)	−177.1	−302.6	554.0	−137.3	−22.5	−18.0	−103.5
	(D)	−165.9	−256.8	464.9	−95.7	−16.5	−31.4	−101.3
	(E)	−179.2	−283.0	518.7	−118.1	−18.7	−33.6	−114.0
	(F)	−168.8	−272.8	492.2	−106.0	−18.9	−25.3	−99.1
	(G)	NP	NP	NP	NP	NP	NP	NP

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Atmospheric implications

The strong primary hydrogen bond in the HONO–DMA system is formed with the acid as the donor and the amine as the acceptor. The Gibbs free energies of formation were calculated in the range of −13.1 to −4.5 kJ mol⁻¹. The Gibbs free energies computed for the dimer containing sulfuric acid and various amine formation reactions at 298 K and 1 atm were much greater at −72.3 to −41.6 kJ mol⁻¹ (RI-CC2/aug-cc-pV(T+d)Z).³ The acidity of H₂SO₄ is much stronger than that of HONO. However, the hydration energies of the HONO–DMA complexes increased from −4.8 to 1.0 kJ mol⁻¹. The Gibbs free energy of H₂SO₄–DMA was −47.6 kJ mol⁻¹ (PW91PW91/6-311++G(3df)), and after hydration, it changed to −65.0 kJ mol⁻¹.⁶⁷ It shows that hydration is unlikely to promote (thermodynamically unfavorable reaction) clustering of the HONO–DMA clusters. The hydration of H₂SO₄ was computed to be thermodynamically stable (ΔG^θ_298K = −9.5 kJ mol⁻¹, PW91PW91/6-311++G(3df,3pd)).⁶⁸ However, the hydration free energies of HONO in the present study were much higher, 6 to 10 kJ mol⁻¹.

The atmospheric relevance of the calculated results has been assessed with the law of mass balance. The mixing ratio of the cluster, e.g. HONO–DMA, can be computed as following:

where [HONO–DMA], [HONO] and [DMA] are the atmospheric mixing ratios of HONO–DMA, HONO and DMA, respectively. R is the molar gas constant, T is the temperature in K, ΔG is the free energies of formation of the HONO–DMA complex. In the nighttime, the concentration of HONO is on the order of 0.1–10 ppbv.^22–24 The highest concentrations of C₂-amines (ethylamine (EA) and DMA) could reach 157 ± 20 pptv in boreal forests in Southern Finland.⁶⁹ The atmospheric amine concentrations were estimated to be 1–100 pptv by Kurtén et al.³ Water vapor strongly varies locally with concentrations of 10–50 000 ppmv.⁷⁰ Consequently, the upper limits of the concentrations for each species (10 ppbv for HONO, 100 pptv for DMA, 50 000 ppmv for H₂O) were used in the assessments. Using eqn (8) together with the calculated Gibbs free energies for complexation at 298 K and 1 atm (Table 2), we have computed the concentrations of the most stable conformers of the heterodimer clusters: HONO–H₂O (H) and HONO–DMA (G). The predicted cluster concentrations of HONO–H₂O (H) and HONO–DMA (G) are 1.0 × 10⁹ and 4.9 × 10³ molecule cm⁻³, respectively. In contrast, the Gibbs free energy of formation of H₂SO₄–DMA and H₂SO₄–H₂O was calculated to be −69.1 (298 K, RI-CC2/aug-cc-pV(T+d)Z//RI-MP2/aug-cc-pV(D+d)Z),³ and −9.5 kJ mol⁻¹ (298 K, PW91PW91/6-311++G(3df,3pd)),⁶⁸ respectively. The atmospheric concentration of H₂SO₄ is about 0.04–1.2 pptv.²⁶ Based on eqn (8), the concentrations of H₂SO₄–DMA and H₂SO₄–H₂O are estimated to be 1.3 × 10⁸–3.8 × 10⁹ and 2.3 × 10⁶–6.8 × 10⁷ molecule cm⁻³, respectively. Therefore, HONO could form more hydrated clusters in the atmosphere than H₂SO₄ due to the high concentration of HONO; however, the clustering of HONO with DMA is negligible as compared to the important H₂SO₄–DMA clusters. Consequently, the role of HONO in new particle formation in the atmosphere is very limited. In the troposphere, the temperature decreases about 6.49 K for every 1 km increase in height.^71,72 The temperature effects on the thermodynamic properties of clusters have been demonstrated to be important for understanding the atmospheric clustering mechanism.⁴³ However, it is not possible to obtain a reasonable estimate of the changes of DMA or HONO concentrations as a function of altitude due to the different sources and sinks of DMA and HONO. Thus, their corresponding atmospheric relevance as a function of altitude could not be obtained. Nevertheless, these calculations were only simplified models and the real situation in the atmosphere is very complicated.

Conclusions

Hydrated HONO and dimethylamine (DMA) clusters have been investigated to illustrate hydrogen bonding interactions with a theoretical approach. The presence of water enhances proton transfer from HONO to DMA, but reduces the Gibbs free energies of formation. The red shifts of the OH-stretching vibrational transition of HONO are very large upon complexation. Topological analysis confirms that the interactions between HONO (donor) and amine or H₂O exceed the upper range of hydrogen bond criteria. GKS-EDA demonstrates that the electrostatic and exchange interactions play a major role in stabilizing the heterodimer and heterotrimer complexes. HONO has higher concentration in the troposphere, and it is much less important in new particle formation than H₂SO₄ due to its relatively weaker bonding with the nucleation species.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21407095 and 21577080), Shandong Provincial Natural Science Foundation, China (ZR2014BQ013 and ZR2016BB36) and High Performance Computing Center of Shandong University. We thank Prof. Peifeng Su of Xiamen University for providing the generalized Kohn–Sham energy decomposition analysis (GKS-EDA) software package.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6em00598e

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