Article
pubs.acs.org/JPCA
Bidirectional Interaction of Alanine with Sulfuric Acid in the Presence
of Water and the Atmospheric Implication
Chun-Yu Wang,†,‡ Yan Ma,† Jiao Chen,†,‡ Shuai Jiang,† Yi-Rong Liu,† Hui Wen,† Ya-Juan Feng,†
Yu Hong,†,‡ Teng Huang,† and Wei Huang*,†,§,∥
†
Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, Hefei,
Anhui 230031, China
‡
University of Science and Technology of China, Hefei, Anhui 230026, China
§
School of Environmental Science & Optoelectronic Technology, University of Science and Technology of China, Hefei,
Anhui 230026, China
∥
Center for Excellence in Urban Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences,
1799 Jimei Road, Xiamen 361021, China
S Supporting Information
*
ABSTRACT: Amino acids are recognized as important components of atmospheric
aerosols, which impact on the Earth’s climate directly and indirectly. However, much
remains unknown about the initial events of nucleation. In this work, the interaction of
alanine [NH2CH(CH3)COOH or Ala], one of the most abundant amino acids in the
atmosphere, with sulfuric acid (SA) and water (W) has been investigated at the M06-2X/
6-311++G(3df, 3pd) level of theory. We have studied thermodynamics of the hydrated
(Ala)(SA) core system with up to four water molecules. We found that Ala, with one
amino group and one carboxyl group, can interact with H2SO4 and H2O in two directions
and that it has a high cluster stabilizing effect similar to that of ammonia, which is one of the
key nucleation precursor. The corresponding Gibbs free energies of the (Ala)(SA)(W)n
(n = 0−4) clusters formation at 298.15 K predicted that Ala can contribute to the
stabilization of small binary clusters. Our results showed that the hydrate distribution is
temperature-dependent and that a higher humidity and temperature can contribute to the
formation of hydrated clusters.
■
investigated. Zhang et al.21 have pointed out, and then Nadykto
et al.22 affirmed, the crucial role of organic compounds in
atmospheric aerosol formation. Organic compounds, such as
amines,23−31 organic acids,32−37 and aldehydes38 have been
focused on. Recently, amino acid interactions with common
atmospheric nucleation precursors also gained attention.39
Amino acids are ubiquitous compounds that make important contribution to compositions of atmospheric aerosols.40
They are an important component of water-soluble organic
nitrogen-containing compounds, which contributes approximately 18% to the total mass of fine aerosol particles.41 The most
interesting class and major portion of that accounts for most of
organic nitrogen are amino acids, which have been detected in
atmospheric aerosols, dew water, and fog droplets.42−47 In total,
32 different amino acids have been identified in the atmosphere,
especially in high humidity areas near the marine environment.48
It has been proposed that marine particles are derived from
bubbles bursting on open, which provide the material for both
nucleation and larger particle formation. Leck et al.49 has
INTRODUCTION
The frequent appearance of the haze weather in China receives
considerable interest. Recently studies1,2 showed that the particle
compositions in Beijing are consistent with the chemical
constituents dominated by secondary aerosol formation. New
particle formation (NPF) via nucleation is a significant source of
atmospheric aerosols,3 which plays an important role in the
Earth’s climate and atmospheric chemistry. A substantial pool of
neutral and thermodynamically stable clusters (TSCs) that are
<2 nm in size are believed to play an important role in the
formation of the critical seed embryos that lead to further growth
and NPF. TSCs are likely to be activated by stabilizing agents,
thereby initiating nucleation. Eventually, after new particle
formation and growth, the aerosols reach approximately 50 nm
or larger in size and can then affect the cloud microphysics as
cloud condensation nuclei (CCN) and effectively scatter light
contributing to Earth’s albedo.4
Sulfuric acid (SA) has been accepted as a key component in
atmospheric nucleation. Extensive theoretical5,6 and experimental7 investigations into the atmospheric chemistry of SA
have been conducted. The participation of an atmospheric
stabilizer such as ammonia,8−13 ionic species,14−20 and organic
compounds21−38 in the nucleation process has been previously
© 2016 American Chemical Society
Received: November 30, 2015
Revised: February 26, 2016
Published: March 21, 2016
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Table 1. Calculated Energies and Energy Changes (in kcal mol−1) Using Different DFT Functional and MP2 with
6-311++G(3df,3pd) Basis Set
method
B3LYP
CAM-B3LYP
PW91PW91
ωB97X-D
M06-2X
M06-2X/DF-MP2-F12
MP2
compound
E
G
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
Ala
SA
W
(Ala)(SA)
(Ala)(W)
−203168.82
−439502.60
−47968.87
−642687.30
−251142.92
−203080.17
−439446.92
−47951.17
−642545.19
−251037.71
−203097.64
−439445.58
−47951.58
−642562.04
−251055.80
−203101.33
−439433.06
−47952.21
−642553.60
−251060.31
−203080.48
−439412.87
−47945.13
−642513.32
−251032.98
−202824.48
−438974.60
−47902.38
−641818.59
−250732.82
−202736.82
−438858.63
−47880.69
−641616.15
−250624.32
−203188.40
−439520.33
−47980.35
−642714.49
−251165.58
−203099.71
−439464.61
−47962.65
−642572.38
−251059.92
−203117.46
−439463.39
−47963.08
−642589.01
−251077.94
−203120.65
−439450.74
−47963.68
−642581.01
−251082.03
−203099.89
−439430.50
−47956.61
−642539.80
−251054.84
−202843.90
−438992.22
−47913.46
−641845.07
−250754.68
−202756.30
−438876.30
−47892.17
−641643.00
−250646.38
ΔE
ΔG
−15.88
−5.23
−5.76
3.17
−18.10
−6.36
−8.06
2.44
−18.82
−6.58
−8.16
2.60
−19.21
−6.78
−9.61
2.31
−19.97
−7.37
−9.41
1.66
−19.51
−5.96
−8.95
2.69
−20.70
−6.80
−10.39
2.10
on the structure and thermodynamics of clusters with Ala and its
influence on new particle formation and growth.
In this study, we conducted a detailed geometrical analysis and
studied the thermodynamics, noncovalent interactions, temperature dependence of the conformational population and hydration
distribution at different temperatures, and humidities of
(Ala)(SA)(W)n (n = 0−4), which have not been reported
previously. We used these results to understand the nucleation of
Ala, SA, and water.
reported that nucleation occurs due to oxidation of the amino
acid, L-methionine. It also has been shown that interactions of
glycine with sulfuric acid indicate that amino acids could play an
important role in aerosol formation or in the stabilization of
existing clusters in the atmosphere.39 Despite their abundance,
the fate and properties of atmospheric amino acids are poorly
understood. In particular, the contribution of amino acids to
atmospheric nucleation remains unknown. Alanine (Ala) is one
of the most abundant amino acids, accounting for 10% of
total concentrations of atmospheric amino acids.50,51 This means
that studying of clusters of Ala with molecules of common
atmospheric nucleation precursors is important for gaining a new
and insightful understanding of molecular nature of atmospheric
nucleation phenomena.
Research has showed that dicarboxylic acids exhibited the
intriguing trend of enhancing nucleation in two directions in
geometrical space due to having two acid moieties.52 The
deprotonated glycine molecule is found to stabilize sulfuric
acid clusters through the interaction of both the amino- and
carboxylic-moieties.39 Similar bidirectional interaction could be
possible in Ala, which might enhance the interaction with aerosol
precursors through the formation of ionic species. This is the first
study of water-soluble nitrogen-containing organics that focuses
■
METHODS
The initial geometries were obtained using a basin-hopping
(BH) algorithm,53−55 a generalized gradient approximation in
the Perdue−Burke−Ernzerhof (PBE) functional and the double
numerical plus d-functions (DND) basis set, which was implemented in DMol3.56 This was employed in the density functional
theory (DFT) module coupled with BH, which includes two
procedures: (1) a new structure, which was generated via the
random displacement of molecules, was optimized to the local
minimum and (2) the local minimum was used as a criterion to
accept the initial structure spaces with the Boltzmann weight at a
finite temperature. This method has been validated to perform
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Table 2. Comparison of Changes in the Gibbs Free Energy (in kcal mol−1) Associated with Small Clusters Formation Calculated
Using M06-2X and M06-2X/DF-MP2-F12 at 6-311++G(3df,3pd) Level with Experimental Data
M06-2X/DF-MP2-F12
M06-2X
exptl
−1.15
−0.90
−10.82
−2.53
−2.21
−11.52
−3.6 ± 1.0a
−2.3 ± 0.3a
−8.5b
H2SO4 + H2O ⇔ (H2SO4)(H2O)
(H2SO4)(H2O) + H2O ⇔ (H2SO4)(H2O)2
H2SO4 + NH3 ⇔ (H2SO4)(NH3)
a
Ref 86. bRef 87.
program,71 which has been confirmed to be effective and
convenient for identifying NCI.
well in our previous studies when we have explored atomic and
molecular systems.53,57−61
Then, the results were optimized at the M06-2X/6-31+G*
level by DFT. The stable isomers within 9 kcal mol−1 of the stable
global minimum were reoptimized using the 6-311++G(3df,
3pd) basis set to determine the final configurations. Thus, much
less time is required to obtain the final structures than via direct
optimization using the M06-2X/6-311++G(3df, 3pd) method.
To ensure there were no imaginary frequencies, frequency
calculations were operated for each stationary point.
Recent benchmarks have shown M06-2X functional performs
adequately in calculating binding energies and Gibbs free
energies of formation for clusters of atmospheric relevance.62−65
To assess the performance of the chosen methodology, the
energies of Ala, SA, W, (Ala)(SA), and (Ala)(W) were investigated using another six methods that have shown promising
performance for investigating particle formation: B3LYP, CAMB3LYP, ωB97X-D, PW91PW91, M06-2X, M06-2X/DF-MP2-F12,
and MP2.66 M06-2X/DF-MP2-F12 represents the single-point
energies of the optimized geometries calculated using the DFMP2-F12 approximation, and the VDZ-F12 basis set in Molpro
2010.167 was combined to the M06-2X/6-311++G(3df, 3pd)
thermodynamic corrections. From the benchmark work displayed
in Table 1, the energies and Gibbs free energies calculated by
M06-2X were closer to the results of M06-2X/DF-MP2-F12,
PW91PW91, ωB97X-D, CAM-B3LYP, and MP2, rather than
B3LYP, which may be improved with counterpoise correction to
the energy.68 In cluster (Ala)(SA), free energy change (ΔG)
calculated by M06-2X was very close to that of PW91PW91
and MP2, the differences were 1.25 and 0.98 kcal mol−1,
respectively. In cluster (Ala)(W), the differences were only 0.94
and 0.44 kcal mol−1, respectively. In these two clusters, the
differences between M06-2X and the M06-2X/DF-MP2-F12
were 0.66 and 1.03 kcal mol−1, respectively.
Further, we do the comparison of the formation energies of
other three clusters to the experimental results like the work
by Xu et al.69 The comparison using M06-2X and M06-2X/
DF-MP2-F12 methods with experimental data summarized in
Table 2 shows that M06-2X predictions agree better with experiment results in the sulfuric acid hydration systems and worse
in the sulfuric acid ammonia binding system, which has been
stated by Nadykto et al.27,29 that the application of nonstandard
methods using single-point corrections to DFT will produce
uncertainties in the computed free energies. So, we select the
M06-2X/6-311++G(3df, 3pd) methodology due to its relatively
better performance even though more experimental data are
called for further confirmation. Details of all of the structures and
the single-point energies are provided in the benchmark works in
the Supporting Information (SI).
Additionally, to clarify the noncovalent interactions (NCI) of
the clusters of various sizes, we employed the reduced density
gradient (RDG) approach implemented in Multiwfn 3.070 and
visualized it with the visual molecular dynamics (VMD)
■
RESULTS AND DISCUSSION
A. Geometrical Analysis. The geometries of H2SO4, H2O,
Ala monomer, and the complexes of (Ala)(SA)(W)n (n = 0−4)
were optimized at the M06-2X level with the 6-311++G(3df,
3pd) basis set using the Gaussian 09 package. The optimized
complexes are depicted in Figures 1−5 and are ordered by
increasing ΔΔG. The ΔΔE and ΔΔG represent the relative
electronic energy and the relative free energy of cluster formation
to the global minimum at a standard state of 298.15 K and 1 atm.
The representations of these conformations were defined using
m−n notation. In this notation, “m” (m = I, II, III, IV, and V) and
“n” (n = a−p) were used to distinguish the clusters of different
sizes and isomers of the same size, respectively. In the notation of
Ala(N), Ala(O), and Ala(Di), the index “N” and “O” indicate
that the amino group or the carboxyl group in Ala interacts with
other molecules, respectively, and the index “Di” shows both the
amino group and carboxyl group in Ala bond with others at the
same time. All structures and energies in this work are shown in
Tables S1−S8 in the SI.
Proton Transfer. Considering the contribution of sulfuric acid
and water to aerosol formation, the proton transfer reaction in
hydrated sulfuric acids has been noticed by many researchers.72−74
The acid dissociation, one kind of proton transfer, may occur
in sulfuric acid−water−organic acid clusters, leading to cluster
stabilization.32,35
Because proton transfer is very interesting at the molecular level,
we pay attention to the dissociation of hydrated SA from Ala. The
top-five low-lying geometries for (Ala)(SA) are shown in Figure 1.
In the different isomers, Ala connects with SA differently.
Generally, both the amino group and the carboxyl group in Ala
can bond with SA, which may further stabilize small clusters. As
shown in Figure 2, “Ala-W-SA” indicts the water interacts with Ala
directly, whereas “Ala-SA-W” indicts the water only interacts with
SA. When the first water was added to the (Ala)(SA) cluster, the
cluster undergoes proton transfer. The proton in SA is transferred
to the N in Ala to form −NH3+ as an ionic structure, II-a, and this is
the global minima in terms of E(0 K) and G(298.15 K).
The top-seven low-lying geometries of the (Ala)(SA)(W)2
clusters are shown in Figure 3. When the second water molecule
was added, the resulting structures can be divided into three
groups based on the relative position of Ala, SA, and water:
Ala-SA-2W (III-b, III-f), Ala-2W-SA (III-a, III-c, III-d, III-e), and
the cage (III-g). All the structures undergo proton transfer except
for III-b, and the proton in SA is transferred to the water to form
H3O+ in III-g. According to earlier research on (H2SO4)(H2O)n
(n = 1−3), the ion pair formation starts with n = 3.72 Temelso
et al.75 concluded that the ionic (HSO4−)(H3O+)(H2O)n−1
cluster becomes the global minima in terms of E(0 K) and
G(298.15 K) when n ≥ 4 and n = 6, respectively. Our work shows
that less water molecules induce proton transfer in (Ala)(SA)(W)n than in (SA)(W)n. This could predict that the additional
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Figure 1. Optimized geometries of (Ala)(SA) at the M06-2X/6-311++G(3df, 3pd) level of theory, ordered by increasing ΔΔG (given in kcal mol−1).
Figure 2. Optimized geometries of (Ala)(SA)(W) at the M06-2X/6-311++G(3df, 3pd) level of theory, ordered by increasing ΔΔG (given in
kcal mol−1). The intramolecular and intermolecular interaction distances are given.
When a third water molecule was added, more isomers
were found, as shown in Figure 4. Based on the location of
water, which can be on the same side or on a different side
Ala can promote proton transfer of the binary clusters
of SA-W, and that fewer waters may be needed to cause the
proton transfer.
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Figure 3. Optimized geometries of (Ala)(SA)(W)2 at the M06-2X/6-311++G(3df, 3pd) level of theory, ordered by increasing ΔΔG (given in
kcal mol−1). The intramolecular and intermolecular interaction distances are given.
Thus, proton transfer occurs more easily when more water
molecules are added. We can predict that when the fifth water
molecule is added, almost all of the stable clusters undergo acid
dissociation. Proton transfer plays a crucial role in the stability of
clusters containing Ala, SA, and water.
Hydrogen Bonds. The electron-depleted H atom has a
particularly small size; thus, other electronegative atoms, such as
O and N, can get very close to these highly polar groups and
experience an unusually strong field. The resulting bond is
known as the hydrogen bond. Hydrogen bonds can be strongly
attractive and moderately directional, so they can orient
neighboring molecules. To study the stability of clusters, we
cannot neglect the contribution of the number and the type of
hydrogen bonds.
We observed that the OH···N bond acts a strong bond
that plays a leading role in stabilizing the (Ala)(SA) cluster.
As shown in Figure 1, for the global minimum isomer I-a,
two hydrogen bonds are formed: a stronger intermolecular
OH···N bond with the length of 1.4662 Å and a weaker
intramolecular H···O bond with the length of 2.2988 Å.
Although the following three isomers have three hydrogen
bonds, none of them is the most stable because of the lack of a
strong OH···N bond. All of the OH···N bonds are stronger with
a length of approximately 1.47 Å than the H···O bond in these
clusters.
of the chain formed by Ala and SA, isomers can be divided into
two types (on the same side, as shown using “3W” notation, and
on a different side of the chain, as shown using “3W(1 + 2)”
notation; this represents there are two water molecules on one
side and the other on the opposite side). Each isomer tends to
become spherical and is no longer the chain structure as
shown in Figures 1−3. Except for the IV-h and IV-l, proton
transfer occurs in all of the structures, as seen from
the hydrogen bond length in the relatively stable structures of
IV-a, IV-b, IV-c, IV-d, IV-e, and IV-g. The proton in SA is
transferred to the N in Ala to form −NH3+, while in higher
energy geometries of IV-f, IV-i, IV-j, and IV-k, the proton
in SA is transferred to the water to form a bisulfate and a
hydronium ion.
The optimized geometries of the 16 stable clusters of
(Ala)(SA) with four waters are presented in Figure 5. Similarly,
two types of geometries are formed, 4W and 4W(1 + 3),
respectively. Proton transfer occurs in all of the structures, except
for V-j. Typically, the proton in SA is transferred to the amino
group to form a HSO4− and an AlaH+ in the first four structures.
In the next 11 structures, the proton in SA is transferred to the
water to form a HSO4− and a hydronium ion. In particular,
V-i and V-n are both tetraionic isomers in which proton transfer
occurs in two groups of Ala to form a zwitterionic structure, a
HSO4−, and a hydronium ion.
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Figure 4. Optimized geometries of (Ala)(SA)(W)3 at the M06-2X/6-311++G(3df, 3pd) level of theory, ordered by increasing ΔΔG (given in
kcal mol−1). The intramolecular and intermolecular interaction distances are given.
(Ala)(SA)(W)2clusters, the amino group in the Ala always
directly binds to SA via hydrogen bonds. When the fourth water
molecule is added, ten internal hydrogen bonds are formed in
(Ala)(SA)(W)4.
In conclusion, for the (Ala)(SA)(W)2 clusters, all of the
isomers except III-b exist with the amino group in the Ala binds
to SA or W via hydrogen bonds. For the (Ala)(SA)(W)3 clusters,
the amino group in all of the isomers except IV-l, which is the
most unstable isomer, participates in hydrogen. For the
(Ala)(SA)(W)4 clusters, amino group in each isomer participates
in hydrogen. Thus, the amino group in Ala binds to SA or W via
hydrogen bonds more easily with increasing number of water
molecules.
Additionally, by comparing the most stable geometry
of different size (Ala)(SA)(W)n clusters (I-a, II-a, III-a, IV-a,
For the (Ala)(SA)(W) cluster, compared with the isomer
with four hydrogen bonds, the energy of the isomer containing five hydrogen bonds is lower. However, II-e is an
exception (higher in energy than that of II-d). Because of the
proton transfer, the N in Ala accepts a proton to form −NH3+,
and the three protons have a higher chance to form hydrogen
bonds. After a water molecule is added, isomers become more
stable, such as the II-a and III-a isomers of the (Ala)(SA)(W)2
cluster.
The number of hydrogen bonds increases as the size of the
cluster increases. When a third water molecule was added, more
hydrogen bonds formed. There are typically nine internal
hydrogen bonds in all of the geometries of the (Ala)(SA)(W)3
clusters, except for seven internal hydrogen bonds in
IV-b and eight in IV-l. Similarly to the (Ala)(SA)(W) and
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Figure 5. Optimized geometries of (Ala)(SA)(W)4 at the M06-2X/6-311++G(3df, 3pd) level of theory, ordered by increasing ΔΔG (given in
kcal mol−1). The intramolecular and intermolecular interaction distances are given.
and V-a), the amino group rather than the carboxyl group
in the Ala always directly binds with the SA to form
hydrogen bonds. When the number of water molecules is
greater than two, the carboxyl group in Ala can also directly form
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Figure 6. Noncovalent interactions (NCI) analysis among the global minimum at each size of the clusters.
B. Analysis of Noncovalent Interactions (NCI). In order
to determine whether the interaction in cluster is attractive or
nonbonding, we carried out the noncovalent interactions (NCI)
analysis. The NCI index is based on the correlation between the
a hydrogen bond with the nucleation precursor of water.
Specifically, amino acids could stabilize small clusters in two
directions in geometrical space due to having two characteristic
moieties.
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reduced density gradient and the electron density, as presented
by Yang and co-workers.76,77 The reduced density gradient
(RDG), s, in DFT
s=
|∇ρ|
1
2 1/3 4/3
2(3π ) ρ
Table 3. Stepwise Binding Energies (ΔE), Stepwise Binding
Enthalpies (ΔH), Temperature Multiplied by Stepwise
Binding Entropies (TΔS) (T = 298.15 K), and Stepwise
Binding Free Energies (ΔG) Associated with the Formation of
(Ala)(SA)(W)n (n = 0−4) (in kcal mol−1) Based on M06-2X/
6-311++G(3df, 3pd) Calculations
(1)
is used to describe the deviation from a homogeneous electron
distribution.78 The ∇ is the gradient operator, ρ is the electron
density, and |∇ρ| is electronic density gradient mode. The
location of the pairwise atoms that are connected along the bond
path can be identified, and the properties around bond critical
points (BCPs) can be visualized using the NCI. Therefore, the
NCI index is a useful tool to distinguish and visualize different
types of noncovalent interactions as regions of real space.
Figure 6 show plots of the RDG versus the electron density
multiplied by the sign of the second Hessian eigenvalue and
isosurfaces that were generated for the most stable geometry of
the (Ala)(SA)(W)n clusters, which were obtained using the
Multiwfn and VMD program.
In the left figure, one spike corresponds to one hydrogen bond
in the hydrogen bonds density region, which indicates that there
are two, five, seven, nine, and nine hydrogen bonds in the
structures of I-a, II-a, III-a, IV-a, and V-a, respectively. When the
x-coordinate value of the spike is smaller, there is a stronger
hydrogen bond, as indicated by the structures visualized by the
VMD program, in which the position, intensity, and type of the
weak interaction is clearly revealed. If the color coding of the
bonding isosurface is from green to blue, the noncovalent
interaction becomes stronger from a van der Waals force to a
strong attraction force, such as hydrogen bond.
In I-a, the smallest value of the electron density multiplied by
the sign of the second Hessian eigenvalue is approximately −0.1,
which corresponds to the strong OH···N bond with a length of
1.4662 Å. This bond is strong enough to be a covalent bond, as
shown in the isosurface figure. For both isomer II-a and IV-a, the
second Hessian eigenvalue of the NH···OS bond is approximately −0.07. For III-a, −0.06 corresponds to the NH···OS
bond, and for V-a, −0.095 corresponds to the H···O bond that
forms between the H atom in the carboxyl group and the O atom
in water. This bond has a length of 1.4252 Å. These results
indicate that Ala can directly form hydrogen bonds in two
directions with water and with SA to enhance nucleation.
C. Thermodynamics of the Cluster Formations. Different nucleation pathways are controlled by two key factors: the
thermodynamic stability of the prenucleation clusters and the
concentrations of the reacting species. To get reasonable cluster
growth pathways, we compared three different methods of
generating the (Ala)(SA)(W)n clusters based on the thermodynamic stability of the relevant compounds.
Stepwise Binding Path. The reactant is (Ala)(SA)(W)n‑1, and
the stepwise binding energies, enthalpies, and Gibbs free energies
(ΔE, ΔH, ΔG, respectively) for the (Ala)(SA)(W)n (n ≥ 1)
clusters were calculated as follows:
ΔE = En − En − 1 − EW
(2)
ΔH = Hn − Hn − 1 − HW
(3)
ΔG = Gn − Gn − 1 − GW
(4)
n
ΔE
ΔH
TΔS
ΔG
0
1
2
3
4
−19.97
−12.53
−11.28
−9.88
−9.65
−19.90
−13.24
−12.24
−10.59
−10.14
−10.49
−10.88
−10.74
−10.53
−9.89
−9.41
−2.36
−1.50
−0.06
−0.26
addition of a water molecule to an existing (Ala)(SA) complex is
−2.36 kcal mol−1. Clearly, thermodynamics favors the formation
of (Ala)(SA) cluster with up to four water molecules at room
temperature.
Total Binding Path. The total binding energy of the cluster
was calculated using
ΔE′ = En − n × EW − EAla − ESA
(5)
The corresponding change in the interaction enthalpies (ΔH′)
and free energies (ΔG′) were calculated in the same manner.
The ΔG″ is the Boltzmann-averaged Gibbs free energy change.
The energy changes for all of the isomers are shown in Table 4.
The formation of all the hydrous clusters are favorable because
of negative energies. For the formation of (Ala)(SA)(W)n
(n = 0−2), the lowest energy conformations are observed to
be the complex of SA or water with Ala at the amino group, while
the complex formation at the acid group is found to be higher in
energy (structure shown). Isomers I-c, II-e, and III-c with SA or
water residing at both functional groups are located negative in
Gibbs free energy. This indicates that Ala is able to enhance the
clusters formation in two directions even though these are not
the lowest identified minimum and thereby the population of
these clusters will be low to the “globally” identified minimum.
For the formation of (Ala)(SA)(W)n (n = 3,4), the lowest free
energy conformations correspond to SA or water residing at both
functional groups (structure shown).
The relationship between ΔG with ΔG′ can be expressed as
follows:
n
ΔGn′ =
∑ ΔGi
i=0
(6)
Similarly for the ΔE/ΔE′, ΔH/ΔH′, and ΔS/ΔS′. Figure 7
shows free energies change as a function of n in (Ala)(SA)(W)n
complexes. The overall trends of the ΔG′ (calculated between the global minimum, shown in boldface in Table 4) and
Boltzmann-averaged Gibbs free energy change, ΔG″, are
consistent with each other.
Synthetic Binding Path of SA to (Ala)(W)n. The synthetic
binding energies of the clusters were calculated using
ΔE″ = En − E(Ala)(W )n − ESA
(7)
The changes in the interaction enthalpies (ΔH″) and the free
energy (ΔG‴) were calculated in the same manner. All of the
changes in the energies are shown in Table 5. The addition
of a SA molecule to the (Ala)(W)n complex is seen to be very
favorable in all cases because every reaction has a very negative
ΔG value. This indicates that the potential difficulty associated
with the formation of the (Ala)(SA)(W)n cluster lies in the
difficulty in forming the (Ala)(W)n cluster.
As shown in Table 3, the Ala molecule has a strong interaction with SA because of the free energy of formation of
−9.41 kcal mol−1, which is close to the value for the formation of
the ammonia−sulfuric acid complex.79 The energy gain with the
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Table 4. Total Binding Energies (ΔE′), Total Binding
Enthalpies (ΔH′), Temperature Multiplied by Total Binding
Entropies (TΔS′) (T = 298.15 K), Total Binding Free
Energies (ΔG′), and Boltzmann Averaged Gibbs Free Energy
(ΔG″) Associated with the Formation of (Ala)(SA)(W)n
(n = 0−4) (in kcal mol−1) based on M06-2X/6-311++G(3df,
3pd) Calculations
n
isomer
ΔE′
ΔH′
TΔS′
ΔG′
0
I-a
I-b
I-c
I-d
I-e
II-a
II-b
II-c
II-d
II-e
II-f
II-g
III-a
III-b
III-c
III-d
III-e
III-f
III-g
IV-a
IV-b
IV-c
IV-d
IV-e
IV-f
IV-g
IV-h
IV-i
IV-j
IV-k
IV-l
V-a
V-b
V-c
V-d
V-e
V-f
V-g
V-h
V-i
V-j
V-k
V-l
V-m
V-n
V-o
V-p
−19.97
−19.91
−17.37
−15.01
−12.48
−32.50
−31.19
−30.72
−30.03
−28.90
−27.27
−28.77
−43.78
−42.15
−40.49
−39.74
−39.73
−40.20
−41.28
−53.66
−52.75
−50.54
−54.10
−53.37
−52.28
−53.11
−51.80
−52.03
−51.91
−49.94
−48.76
−63.31
−61.76
−61.94
−63.33
−63.35
−59.38
−61.50
−61.86
−60.89
−61.49
−58.85
−59.72
−57.87
−56.53
−57.13
−54.87
−19.90
−19.89
−17.47
−14.94
−12.24
−33.14
−31.93
−31.43
−30.77
−29.70
−27.92
−29.78
−45.37
−43.69
−41.85
−41.24
−41.56
−41.90
−43.90
−55.96
−54.90
−52.20
−57.32
−56.46
−54.74
−56.14
−54.42
−55.18
−54.75
−52.70
−52.04
−66.10
−65.00
−65.68
−67.05
−67.33
−62.06
−65.32
−65.66
−64.45
−65.65
−62.71
−63.74
−61.86
−60.50
−61.11
−58.20
−10.49
−10.99
−11.99
−11.27
−10.64
−21.37
−20.79
−20.48
−20.74
−21.21
−20.82
−22.80
−32.11
−30.62
−31.73
−32.02
−32.60
−33.12
−35.39
−42.64
−42.20
−40.34
−45.60
−44.85
−43.18
−44.78
−43.64
−45.10
−44.87
−43.17
−44.62
−52.53
−52.47
−53.38
−54.89
−55.45
−50.48
−54.37
−54.78
−54.28
−55.70
−53.52
−55.40
−55.45
−54.24
−54.93
−52.93
−9.41
−8.89
−5.48
−3.67
−1.60
−11.77
−11.14
−10.95
−10.03
−8.49
−7.10
−6.99
−13.27
−13.07
−10.12
−9.21
−8.96
−8.78
−8.51
−13.32
−12.70
−11.86
−11.72
−11.61
−11.56
−11.36
−10.78
−10.08
−9.88
−9.53
−7.42
−13.58
−12.54
−12.30
−12.16
−11.88
−11.58
−10.95
−10.87
−10.17
−9.95
−9.19
−8.34
−6.41
−6.25
−6.18
−5.27
1
2
3
4
Boltzmann
averaged ΔG″
−9.26
−12.24
Figure 7. Three kinds of free energies change at the M06-2X/
6-311++G(3df, 3pd) level as a function of n in the (Ala)(SA)(W)n
(n = 0−4) complexes.
Table 5. Synthetic Binding Energies (ΔE″), Synthetic Binding
Enthalpies (ΔH″), Temperature Multiplied by Synthetic
Binding Entropies (TΔS″)(T = 298.15 K) and Synthetic
Binding Free Energies (ΔG‴) Associated with the Formation
of (Ala)(SA)(W)n (n = 0−4) (in kcal mol−1) based on
M06-2X/6-311++G(3df, 3pd) Calculations through Synthetic
Binding Path of SA to (Ala)(W)n
−12.54
−10.365
n
ΔE″
ΔH″
TΔS″
ΔG‴
0
1
2
3
4
−19.97
−22.11
−25.07
−27.95
−27.41
−19.90
−22.18
−25.26
−28.19
−27.20
−10.49
−11.78
−12.65
−13.27
−12.74
−9.41
−10.40
−12.60
−14.92
−14.46
could contribute to the population order variation of the isomers.
Thus, the temperature dependence of the thermodynamic
properties is an important parameter that is required to
understand the roles of the specific cluster formation pathways
at various atmospherically relevant temperatures. In the
troposphere, the temperature ranges from 200 to 300 K. To
obtain a more accurate picture of the relative stabilities of the
isomers, we investigate the coupling effects of the lower-energy
isomer contributions and temperature effects.
The temperature dependence of the conformational population is shown in Figure 8. The global minimum has the greatest
weight in the group of energetically accessible conformers at
temperature changes between 200 and 300 K. As the temperature
increases, the roles of other local minima become competitive.
For the n = 1 (b), n = 2 (c), and n = 3 (d) clusters, the
percentage of the global minimum II-a, III-a, and IV-a carries the
highest weight, but this quickly decreases as the conformation
population of isomer b rises with an increase in temperature. For
n = 1, the II-a configuration contains two intramolecular
hydrogen bonds (OH···O and NH···O) and three intermolecular
hydrogen bonds, which form among each two molecules. This
makes II-a the most stable cluster. Based on all of the geometries
for (Ala)(SA)(W)2 we infer that III-a is the most stable. This is
because of the following: (1) the hydrogen atom in −NH3+ has
formed three hydrogen bonds as a hydrogen bond donor, the
oxygen atom in HSO4− also formed three hydrogen bonds as a
hydrogen bond acceptor, which is the largest number of hydrogen bonds in all of the isomers. (2) There are two intramolecular
hydrogen bonds within Ala+ and five other intramolecular
−9.72
In conclusion, the (Ala)(SA)(W)n cluster could form by
adding a single water molecule or a single SA molecule. It is very
difficult to confirm the first steps in the atmospheric electrically
neutral cluster formation and subsequent growth.
D. Temperature Dependence of the Conformational
Population. The lower-energy isomer and temperature effects
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Figure 8. Conformational population of different isomers with the same size as a function of the temperature variance.
In conclusion, as the temperature increases, the weight of the
global minima decreases, whereas those of other local minima
increase. Thus, the percentages of different isomers vary with the
height in the troposphere.
E. Hydrate Distributions and Influence of Humidity
and Temperature. Amino acids with lower hydrophobicity
have been found to be better kinetic hydrate inhibitors (KHIs)
that delay nucleation and retard growth,80 and the hydrophobicity value of Ala is 1.8.81 To further understand the
combined power of Ala with water on the microscopic aspect, we
analyzed their hydration properties. It is important to determine
the actual concentrations of the various hydrated clusters under
specific realistic atmospheric conditions. Mass spectrometry
(MS) is commonly used under ambient conditions to gain
comprehensive information on the chemical composition and
concentration. However, due to the insufficient size resolution
or selective sensitivity of instruments, the common reported
hydrogen bonds with a shorter length of approximately 1.75 Å.
For n = 3, The IV-a possesses nine hydrogen bonds, which is the
maximum number in the (Ala)(SA)(W)3 clusters to form
hydrogen bonds. The carboxyl and amino groups are involved in
bonding at the same time, and water is dispersed more evenly.
Further investigation is required to determine whether the
weight of isomer b would be more than the global minimum at
temperatures above 300 K.
For the n = 0 (a) clusters, the sum of the weight of I-a and I-b
almost reach 1, and each proportion hardly varies with
temperature. For the n = 4 (e) clusters, V-a weighs more than
other low-lying isomers with temperature changes, indicating that
this structure has an absolute advantage in the atmosphere. In the
most stable structure, V-a, there are nine hydrogen bonds, and the
carboxyl and amino group are involved in bonding simultaneously.
However, the weight of following V-b cannot be ignored, which
increases significantly with an increase of temperature.
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Figure 9. Hydrate distributions of (Ala)(SA)(W)n (n = 0−4) clusters at four different relative humidities when relative temperature varies.
clusters are sulfuric acid-amine containing clusters.82−84
According to the quantum chemistry method, the (Ala)(SA)(W)n concentration of each hydrate depends on the concentration of the (Ala)(SA)(W)n‑1 hydrate precursor, the concentration of water, and their thermodynamics.
According to Noppel et al.,85 we calculated the hydrate
distributions for the (Ala)(SA)(W)n clusters. Detailed information regarding the functions and explanations of the calculations
is provided in the SI. To assess the extent of hydration under
different circumstances, we calculated the hydrate distributions
for (Ala)(SA)(W)n at different temperatures (standard for
different altitudes) and relative humidities (RH), and the hydrate
distributions are presented in Figure 9. Four relative humidity
values (20%, 40%, 60%, and 80%) at three values of relative
temperatures (280, 298.15, and 300 K) were revealed.
The percentages of (Ala)(SA) are the highest at different
humidities and temperatures, as shown in Figure 9. There are few
clusters for n ≥ 3, which is consistent with earlier results that the
ΔG is close to zero. Moreover, (Ala)(SA)(W)n (n = 1,2) clusters
are favorable at higher relative humidities and at higher
temperatures, whereas the (Ala)(SA) cluster is favorable at
lower relative humidities and at lower temperatures.
temperature influences the distribution of clusters (isomers of
the same size and clusters of different sizes).
Due to the interesting connection between Ala and small
clusters, further analysis of more complex amino acids should be
investigated to determine whether the hydrophilic and hydrophobic nature of amino acids can influence the interaction with
common aerosol nucleation precursors and existing clusters.
■
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jpca.5b11678.
Details about all the optimized Cartesian coordinates by
M06-2X/6-311++G(3df,3pd), benchmarks of the methods, the method of calculating temperature dependence of
the conformational population, and the method for
hydrate distributions (PDF)
■
AUTHOR INFORMATION
Corresponding Author
■
*E-mail: [email protected].
Notes
CONCLUSIONS
In this study, the formation of (Ala)(SA)(W)n (n = 0−4) was
theoretically investigated using DFT calculations. Thermochemical data, including binding energies and Gibbs free energies, the
geometries and the abundance of (Ala)(SA)(W)n under ambient
conditions have also been presented. The following conclusions
were obtained from the present study:
Ala has two functional groups that can enhance the formation
of small clusters in two directions. The amino group in Ala always
directly binds with SA, whereas the carboxyl group binds with
water.
The favorable Gibbs free energies of the (Ala)(SA)(W)n
(n = 0−4) clusters formation indicate that Ala is capable of
acting as a stabilizer of small clusters that contain SA and/or no
water. In these clusters, (Ala)(SA) is the most abundant. As the
size increase, the reaction among clusters that are composed of
(Ala)(SA)(W)n‑1 and a water monomer becomes increasingly
difficult.
The hydrated (Ala)(SA) clusters are favorable under high
humidity conditions, but the small (Ala)(SA) cluster is more
favorable in low humidity environments. Additionally, the
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The study was supported by grants from the National Natural
Science Foundation of China (Grant No. 21403244, 21133008,
21573241, and 41527808), the National High Technology
Research and Development Program of China (863 Program)
(Grant No. 2014AA06A501), the program of Formation
Mechanism and Control Strategies of Haze in China (Grant
No. XDB05000000), and the Director Foundation of AIOFM
(AGHH201505, Y23H161131). We also appreciate the
“Interdisciplinary and Cooperative Team” of CAS and the
“Thousand Youth Talents Plan”. The computation was
performed at 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 multiprogram national
laboratory operated for the DOE by Battelle. Part of the
computation was performed at the Supercomputing Center of
USTC.
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■
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