August
物理化学学报(Wuli Huaxue Xuebao)
Acta Phys. -Chim. Sin. 2015, 31 (8), 1461–1467
[Article]
doi: 10.3866/PKU.WHXB201506013
1461
www.whxb.pku.edu.cn
铵根离子在水溶液中的跳跃转动机理
张
强1,*
程
程1
(1渤海大学化学系, 辽宁 锦州 121000;
张
霞1
赵东霞2
辽宁师范大学化学系, 辽宁 大连 116029)
2
摘要: 铵根离子的动力学行为与生命体内的生物和化学过程密切相关. 依据流体力学理论, 由于铵根离子与水
分子之间存在多个强氢键, 其转动应较慢, 但实验结果并非如此, 其转动的微观机理尚不清晰. 本文分子动力学
模拟研究表明, 水溶液中铵根离子主要以快速、大角度的跳跃方式进行转动, 像水分子一样遵从扩展分子跳跃
转动模型. 通过微观转动模式的分解和两种转动弛豫时间的比较发现, 相对其氢键骨架的扩散转动, 跳跃转动
对其转动速率贡献更大, 并随浓度增大不断强化. 与水分子氢键交换方式相比, 铵根离子更倾向于在非氢键相
连的水分子间发生交换.
关键词: 铵根离子; 跳跃转动; 氢键; 分子动力学模拟; 扩展跳跃模型
中图分类号: O641
Jump Rotational Mechanism of Ammonium Ion in
Aqueous Solutions
ZHANG Qiang1,*
CHENG Cheng1
ZHANG Xia1
ZHAO Dong-Xia2
1
( Department of Chemistry, Bohai University, Jinzhou 121000, Liaoning Province, P. R. China;
Department of Chemistry, Liaoning Normal University, Dalian 116029, Liaoning Province, P. R. China)
2
Abstract: The dynamic behavior of the ammonium ion is closely related to the biological and chemical
processes of life. A fast rotation of
in aqueous solution has been observed in previous experiments,
which is unexpected from hydrodynamic theories because of the multiple strong hydrogen bonds (HBs)
between ammonium ion and water. The mechanism behind this rotation is still not well understood. The
simulations in this work show that a sudden and large-magnitude angular jump rotation occurs during the
hydrogen bond exchange processes of the ammonium ion like water. The rotation of the ammonium ion
can be approximately described with the extended jump model, and can be decomposed into two
independent contributions: the jump rotation and the diffusive rotation of the HB frame. The rotational
mobility of the ammonium ion is determined by fast jump rotation compared with the slow diffusive rotation.
In addition, the contribution of the jump rotation increases with increasing
concentration. Compared
prefers to exchange its HB between two water molecules without forming a HB each other.
with water,
Key Words: Ammonium ion;
Jump rotation;
Hydrogen bond;
Molecular dynamics simulation;
Extended jump model
1 Introduction
Ions have significant impact on the structures and dynamics
of water in aqueous solution, which have been extensively explored by the experimental and theoretical methods.1–10 The rel-
Received: April 17, 2015; Revised: May 28, 2015; Published on Web: June 1, 2015.
*
Corresponding author. Email: [email protected].
The project was supported by the Scientific Research Foundation for Returned Scholars, Ministry of Education of China (No.46) and National
Natural Science Foundation of China (21473083).
教育部留学回国人员科研启动基金(46批)和国家自然科学基金(21473083)资助项目
© Editorial office of Acta Physico-Chimica Sinica
1462
Vol.31
Acta Phys. -Chim. Sin. 2015
evant phenomena are brought into sharp focus in recent years,
such as ion pairing5,6 and ion specific effect on the biological
systems.1,7–9 In recent years, the ion disturbance on the motion of
the water molecules has been extensively explored by the modern spectroscopy techniques 3 , 4 , 1 0 – 1 3 and the theoretical
methods.14,15 But the dynamic properties of ion itself in aqueous
solutions are not well addressed at the microscopic level, for
example ammonium ion.
The dynamics of ammonium ion and ammonium moieties
plays an important role in the chemical, environmental, and biological processes.16–18 Ammonium transport across the membranes is a crucial life-process for growth of plants, fungi, and
bacteria. The transport mechanism of ammonium ion and ammonia in the protein channels of the ubiquitous ammonium
transporter/methylamine permease/rhesus (Amt/MEP/Rh) family is far from understood.18 The previous measurements of the
nuclear magnetic resonance (NMR) suggested that the observed solvent dependence of the rotational mobility of ammonium ion showed a poor correlation with the hydrodynamic
Stokes-Einstein-Debye (SED) model. 19–23 There is stronger
short-range friction between ammonium ion and water due to
the multiple strong hydrogen bonds (HBs) than that between
+
ammonium ion and methanol. However, NH4 rotates rather fast
in aqueous solutions comparing to that in other solvents such as
methanol. This is unexpected for the hydrodynamic theories.
The further simulations with the classical, non-additive, and
electronic structure methods show that a discontinuous jump rotation possibly contributes to this unexpected fast rotation in
aqueous solution.23–31 However, the rotational mechanism of ammonium ion at the molecular level, is not well clarified intuitively and quantitatively until now.
The extended jump model (EJM) developed from Ivanov
jump model,32,33 shows that the rotation of water in aqueous
solutions is determined by a large-amplitude angular jump and
a less significant diffusive “frame diffusion”.14,15,32,33 It has been
applied to explore the rotational mechanism of water in the
electrolyte solutions and on the hydrophobic interfaces combined with infrared (IR) spectroscopy and molecular dynamics
simulations.32
+
In this work, the fast rotation of NH4 in previous experi-
ments was also observed in our simulations. The rotation of ammonium ion in NH4Cl aqueous solutions also follows the EJM
like water molecule. It is mainly due to the large-amplitude an+
gular jump during the HB switching processes of NH4 from
one acceptor to another in aqueous solutions. Two characteristic jump angles observed in our simulations are 50° and 65° for
water and ammonium ion, respectively. Water prefers the
former over the later, but conversely for ammonium ion.
2
Methods
2.1
Rotational correlation function
The rotational correlation function, C2(t), of water along OH
+
bond vector or NH4 along NH bond vector, u, can be expressed as:
C 2( ) = hP 2 [ (0) (t)]i
(1)
where P2 is the second-rank Legendre polynomial. C2(t) is usually employed to obtain the rotational relaxation time in simulations, which corresponds to the NMR and the ultrafast IR spectrum measurements.32 The rotational correlation functions can
be decomposed into two sub-processes (Fig.1), a short-time libration and a long-time rotational relaxation. The rotational relaxation times of two processes can be approximately obtained
by fitting the following function:
C 2(t) = [(1 ¡ A )exp(¡t=¿1) + A ]exp(¡t=¿2)
(2)
where A is a prefactor of the exponential functions. ¿1 is the librational time. ¿2 is the rotational relaxation time related to the
measurements of the ultrafast IR spectrum.4,12,13,32 The integration value of C2(t) within a long-time window is usually used
for the rotational relaxation time by NMR measurements. The
parameters in Eq.(2), ¿1 and ¿2 were determined from a fit of
equation (2) within 0–8 ps as previous works.4,12,13,32
2.2
Extended jump model
The jump rotation of water or ammonium is triggered by the
HB switching from initial HB acceptor to a new one (Fig.2).32
Before a HB exchange (t < 0 for the time window of the HB exchange process), O*H* or N*H* rotates diffusively with its HB
frame axis of O*···Oa or N*···Oa. The average direction is assumed to be the same as the frame axis, neglecting the libra-
Fig.1 Rotation correlation functions (C(t)), the HB correlation functions (1―CW-W(t)) and the rotation correlation functions of HB frame (Cf(t)) of the
¢
water and ammonium for the HB exchange between water molecules in NH4Cl solution at 0.5 mol L–1
No.8
1463
ZHANG Qiang et al.: Jump Rotational Mechanism of Ammonium Ion in Aqueous Solutions
Fig.2 Definitions of the geometric variables along the HB exchange path
µ is the angle between the (N*H*O*H*) vector and the bisector plane of OaN*Ob(OaO*Ob). Á i-j is defined as the jump angle (the angle between the vector O*Oa and
+
vector O*Ob at t=0) during the HB exchange from initial HB acceptor i to final HB acceptor j. Within the local HB frame of NH4 -water, the Z axis is defined as
the vector of N*H* direction. The X axis is defined as the perpendicular vector of Z axis in the plane of HN*H*.
tion of O*H* or N*H* in local HB frame axis. When a new HB
acceptor is available, a fast HB switching happens. H* jumps
from initial acceptor to a new one within the local frame of
OaO*Ob or OaN*Ob (Fig.2, Oa and Ob: the HB initial and final acceptors (oxygen atoms of water); H*: the HB donating hydrogen). When a new HB forms, the time window of the HB exchange process takes at t > 0. The middle time between the ending moment of old HB and the beginning time of new HB, is
taken as the time origin (t = 0) within the HB exchange process.
The jump angle Á is the angle between initial HB frame vector
and the new HB frame vector at t = 0 (Fig.2).
Based on the assumptions above, the rotational correlation
function of molecule along the vector u (O*H* and N*H* bond
vectors for water and ammonium ion, respectively), C2(t), can
be further decomposed into two sub-processes after an initial
fast libration decay (Fig.2):32 (1) a sudden large-amplitude angular jump rotation of uv (uv is the O*H* or N*H* bond vector
within the local HB frame uf, which is the O*···Oa or N*···Oa
vector of HB pair) and (2) a slow diffusive rotation of the frame
vector uf. The correlation functions of two sub-processes (a
jump rotational correlation function CJ(t) and a frame rotational correlation function Cf(t)) are both assumed to be exponential.
C 2(t) = hP 2[ (0) (t)]i
= hP 2[ v(0) v(t)]ihP 2[ f(0) f(t)]i
= C J (t)C f(t)
(3)
In NH4Cl aqueous solutions, the possible HB donors are the
+
hydrogen atoms of water and NH4 . The possible HB acceptors
are the water oxygen and chloride ion. Four HB exchange processes can be defined according to the types of initial and final
HB acceptors: from water to water (W-W), from water to Cl–
(W-Cl), from Cl– to water (Cl-W), and from Cl– to Cl– (Cl-Cl).
The HB exchange can be traced along the trajectories of simulations, if the HB criteria are defined. The HB criteria: RO O
(RO O ) < 0.350 nm, RH O (RH O ) < 0.245 nm and the HB angle
µ H O O < 30° for water-water HB as previous work, 32 R O O
*
*
b
*
*
b
a
*
*
a
*
a
b
(RO O ) < 0.345 nm, RH O (RH O ) < 0.235 nm and the angle
+
θH O O < 30° for the NH4 -water HB according to the radial distribution functions.34 Rij is the distance between two atoms i and
j of two HB connected molecules. θH O O is the angle between
the vectors O*H* and O*Ob.
For a HB exchange of O*H* or N*H* from initial acceptor i to
new acceptor j (Fig.2), the rotational relaxation time ¿i-j according to Eq.(3), can be written as
*
*
*
b
*
a
*
a
b
*
*
b
1
1
1
= J + f
¿i¡j
¿i¡j
¿i¡j
(4)
¿iJ¡j is the jump rotational time and ¿if¡j is the diffusive rotational time of HB frame. The rotational relaxation time (¿EJM) of
water or ammonium along the O*H* or N*H* bond is equal to the
weighted contributions from different types of HB exchanges
according to the EJM.
¿EJ M = A W ¡W ¿W ¡W + A W ¡Cl¿W ¡Cl+
A Cl¡W ¿Cl¡W + A Cl¡Cl¿Cl¡Cl
(5)
Ai-j and ¿i ¡j are the fraction and the rotational time of O*H* or
N*H* with an initial acceptor i and a final acceptor j.
According to the Ivanov model,33 the jump rotational relaxation time ¿iJ¡j is derived from
¿iJ¡j = ¿i0¡j f i ¡j (Ái ¡j )
f i ¡j (Ái ¡j ) =
½
1¡
(6)
¾¡1
(7)
f i ¡j (Ái ¡j )P(Ái ¡j )dÁ
(8)
1
sin[(n + 1=2)Ái ¡j ]
2n + 1
sin(Ái ¡j =2)
fi-j(Á i-j) is a function of jump angle Á i-j defined in Fig.2. Á i-j is
the average value of jump angle during the HB exchange from
initial HB acceptor i to final acceptor j. The jump angle has a
unsymmetrical distribution around the average value,32 so a numerical integration value Fi-j(Á ) over Á i-j from 0 to π, is adopted in this work instead of the average value in previous work,32
¿iJ¡j = ¿i0¡j F i ¡j (Ái ¡j ) = ¿i0¡j
0
P(Á i – j) is the possibility of the HB exchange from i to j with
jump angle Á .32
1464
The HB relaxation time, ¿i0¡j , can be derived from a HB exchange correlation function within the time range of 0–8 ps according to the stable state pictures.15,32 The strict HB criteria is
used for ¿i0¡j , so that the HB exchange events really happened
and excluded the transient breaking of hydrogen pair.32 Two
water molecules form HB, if RO O (RO O ) < 0.31 nm, RH O
(R H O ) < 0.20 nm and the HB angle θ H O O < 20°. The HB
+
between water and NH4 must satisfy the conditions, R N O
(RN O ) < 0.30 nm, RH O (RH O ) < 0.20 nm, and the HB angle
θH N O (θH N O ) < 20° (Fig.2) according to the pair radial distribution functions between ammonium nitrogen and water oxygen.34
f
The frame rotational time ¿i ¡j is determined from the rota*
*
*
b
*
b
*
Vol.31
Acta Phys. -Chim. Sin. 2015
*
b
*
*
a
a
*
*
a
*
a
*
a
*
a
b
b
b
tional correlation function of HB frame axis O*···Oa or N*···Oa
with equation (2) with the same time window as ¿i0¡j .
2.3 Simulation protocol
The cubic bulks were constructed for pure water and NH4Cl
aqueous solutions by inserting the water and ions into the
empty box randomly, then the simulations were performed.
+
2000 waters were filled into each sample box, then NH4 and
Cl– were inserted into the box until the concentration of solution is approximately equal to 0.5, 1, 2, and 5 mol L–1. The
SPC/E water model35 was used and ammonium force field was
taken from the previous publication by Jungwirth and his workfellows (Model I).34 In their work, the properties, such as the
solvation structures, ion clustering tendency in ammonium halide aqueous solutions, were well presented with the current
combined potentials in this work.34 Another force field of ammonium (Model II)26 was used to explore the effect of force
field in simulations on the rotation of ammonium ion. The jump
behaviors of ammonium ion and water are similar for two models (see Section 3.1). A little shorter HB relaxation time is observed for Model II than that for Model I. Additionally, previous work suggests that a classical force field is sufficient for the
jump rotation behavior of water.14 The jump rotation was also
found in ab initio simulations.28,29 The quantum effect on the rotation of ammonium ion should be further discussed, but the rotational mechanism of ammonium ion is expected to be not
changed.
+
The bond lengths and angles of water and NH4 were fixed at
the equilibrium values by the SHAKE algorithm.36 The LorentzBerthelot combination rules37 were used for the Lennard-Jones
interactions. For each sample, a 2 ns isothermal-isobaric ensemble (NPT) equilibration simulation was carried out to generate the proper size of the simulation box, followed by a 2 ns microcanonical ensemble (NVE) simulation to calculate the dynamic properties. For each NPT simulation, the bulk systems
were weakly coupled to a bath with the Nose-Hoover thermostats38,39 at the goal temperature with the relaxation time of 0.1
ps. The weak coupling Berendsen scheme was used to control
the system pressure at 1.01×105 Pa with the coupling time constant of 1 ps.40 The equations of motion were integrated using
¢
the velocity Verlet integration scheme37 and a time step of 2 fs.
The long-range Coulombic forces were calculated using the
particle-mesh Ewald method.41 The non-bonded van der Waals
interactions were truncated at 1.2 nm using the switching functions. Minimum image conditions were used.37 The simulation
configures were saved every 20 fs. All simulations were performed with the Tinker simulation code.42
3
Results and discussion
3.1 Jump rotation of
The rotational diffusion constant DR can be derived from the
mean square displacements (MSDs) of the labeled molecule or
ion in the solutions, according to the Einstein relation,43
Ã
!
1 1 X
2
DR = lim
j i (t) ¡ i (0)j
(9)
t!1 4t
N i
t
i (t) = 0
0
± i (t 0 )dt 0 , ± i (t ) is the rotational vector of NH bond
vector Pi(t) within the interval of [t 0 ; t 0 + ±t] with mode δµ . The
rotational diffusive constants of ammonium ion along Z, X, and
Y axes defined in Fig.2, are 0.088 × 1012, 0.085, and 0.092
rad2 s–1. The average value is 0.088 rad2 s–1, which is in reasonable agreement with the experimental value (0.075 × 10 12
rad2 s–1).19,20 This suggests that the force field used here is reasonable to describe the rotational dynamic behavior of water and
ammonium ion.
According to the ideal diffusive fluid model,44 the nth-rank
+
rotational time of NH4 (¿n ) along the NH vector would satisfy
the relationship with the rotational diffusion constant DR,
±
¿n = 1 n(n + 1)D R
(10)
¢
¢
¢
The ratios ¿1=¿2 and ¿1=¿3 should be equal to the constant values, 3 and 6. However they are only 1.97 and 2.71 at 0.50
mol∙L–1, which is much lower than the ideal constants. The similar case is also found for water with the values of 1.97 and
+
2.78. The rotation of NH4 apparently does not follow the diffusive Brownian motion picture.44,45
Does ammonium ion also follow the EJM like water?32,33 An
instantaneous and large-amplitude angular jump of water is motivated by the HB exchanges. The HB exchange can be considered as a chemical reaction from the reactant state O*H*···Oa
to the product state O*H*···Ob. This process passes through an
dangling or bifurcated HB state of O*H*, which is a transition
state with a very short lifetime, much shorter than the stable
single HB reactant and product states.32,33 Indeed in the NH4Cl
solution at 1 mol∙L–1, a very fast decay of the HB state correlation function to the value below 0.1 is observed within 0.1 ps
for ammonium ion hydrogen with the dangling, and bifurcated
HBs comparing to the single HB state (Fig.3). The lifetime of
+
NH4 hydrogen with dangling HB state and bifurcated HBs is
evidently shorter than those of water correspondingly. The facts
above suggest that a transition state passes during the HB exchanges of ammonium ion like water molecule.
For ammonium ion, we can construct a similar HB exchange
reaction system as water molecule. This exchange reaction system
No.8
Fig.3 HB state correlation functions of the hydrogen atom of
water and dangling state with HB number n=0, single HB state with HB number n=1,
and bifurcated HB state with HB number n=2
is made of three molecules (ammonium ion, its initial and final
HB acceptors). The configurations of remaining water molecules and ions in bulk solution are considered as the average
background effect. The reaction coordinates of the HB exchange (Fig.2), which are the distance between N * and O a
(RN O ), the distance between N* and Ob (RN O ) and the angle (µ )
between the N*H* bond and bisector plane of OaN*Ob, are analyzed from more than 250000 successful HB exchanging
events. Among the possible HB exchanges in NH4Cl solution at
0.5 mol L–1, the fraction of W-W HB exchange of N*H* (Fig.1)
has the highest value, 0.93 (the definitions of HB exchange type
*
1465
ZHANG Qiang et al.: Jump Rotational Mechanism of Ammonium Ion in Aqueous Solutions
a
*
a
¢
in method part).
An intuitive picture is presented in Fig.4 for the HB exchange reaction of ammonium. The departure of initial acceptor Oa and the arrival of new acceptor Ob take place cooperatively during the HB exchange process. A sudden and largeamplitude angular rotation of N*H* within the local HB frame of
OaN*Ob is observed at t = 0. It is reasonable to assume that the
local HB frame of OaN*Ob does not change during the transient
jump rotation of N*H*.32 This is suggested by the value of Á
(definition in Fig.2), which nearly does not change during the
W-W HB exchange (Fig.4). Jump angle populations of water
+
and NH4 are shown in Fig.5. For water, a main peak locates at
50° and a shoulder peak at 65º. However, only one peak is vis+
ible at 65° for the jump angle of NH4 . The jump angle distribu+
tion of NH4 is almost symmetrical around the average value.
+
The different features for the jump angles of water and NH4
suggest that the configurations at the transition state (t = 0) are
different. RN O and RN O are not sensitive to the configuration
of the transition state due to the strong HB interaction, so the
jump angle is mainly determined by the distance (RO O ) of HB
acceptors, Oa and Ob. The possibility of jump angle at about 500
is much lower for ammonium ion than that for water, if a hydrogen bond is formed between the initial HB acceptor water
and final HB acceptor water. The distances of N*···Oa, N*···Ob,
and Oa···Ob, are about 0.31, 0.31, and 0.28 nm for N*H* (Figs.2
and 4). The average jump angle at 65° is identified for both water
*
a
*
b
a
Fig.4 Reaction coordinates Rij, µ , and Á along the path of the W-W HB exchange of ammonium ion and water
Fig.5 Jump angle populations of W-W HB switching for water and ¢
–1
ion
P(θ) with Models I and II at 0.5 mol L ; the populations of jump angle for the HB exchange between two water molecules with
HB each other (P1(θ)) and without HB each other P2(θ)
b
1466
Acta Phys. -Chim. Sin. 2015
and ammonium ion for the HB exchange event without hydrogen bond between two HB acceptor water molecules at the
transition 46 state. The distances of N * ···O a , N * ···O b , and
Oa···Ob are about 0.31, 0.31, and 0.35 nm for anmonium ion,
about 0.33, 0.33, and 0.38 nm for the water. The possibility of
the HB exchange between two HB water molecules without
formation of HB each other, is higher for ammonium ion than
that for water. This is mainly due to less available new HB acceptor around N*H* than O*H*.
3.2 Contributions from the jump and frame rotations
The rotational relaxation times of water and ammonium directly from equations (1, 2) and from the EJM with equations
(3)–(5), are presented in Fig.6. The tendency of the rotational
relaxation times with concentration is well reproduced by the
EJM. The rotational relaxation times are a little underestimated
by the EJM relative to the direct measurements. The results
from EJM suggest that the water rotation along the OH vector
can be divided into two sub-processes. One is the large-amplitude and fast jump rotation. The other is the diffusive rotation
of HB frame O*Oa. In NH4Cl solution at the lowest concentration (0.5 mol L–1) of the samples in this work, the jump rotational times of water and ammonium ion are 3.81 and 4.57 ps,
respectively. Their frame rotational times are 5.96 and 9.30 ps,
respectively. The jump and diffusive rotational times rise to
7.30 and 18.59 ps at 5 mol L–1. The contribution from the jump
rotation to the rotational mobility of ammonium increases with
concentration. The rotation time of ammonium ion and water is
mainly determined by the jump rotation over the whole range of
concentration.
As for the underestimation of the EJM, this is mainly due to
the invalidation of its assumption and its intrinsic limitation.
For the jump rotation, the average direction used in the EJM is
assumed to be the same as the frame vector, neglecting the libration of O*H* or N*H* in local HB frame. The jump rotation
term in fact covers a part of fast libration contribution in its
long-time rotation contribution in equation (2). Additionally,
the EJM does not consider the rotations of ammonium and water in local basins suggested in reference.50 The fast HB exchange in local basin has bigger contribution on the fast decay
¢
¢
Vol.31
of the rotational correlation function than the long-time decay.47
A faster jump rotation is expected for the EJM, given its intrinsic limitations above.
4
Conclusions
The rotational mechanism of ammonium ion is explored by
MD simulations and the extended jump model. The fast rota+
tion of NH4 observed in previous experiments is due to the sud+
den jump rotation. The jump rotation of NH4 is motivated by
the HB exchanges. The rotational behavior can be approximately described with the EJM like water in aqueous solutions.
The rotational correlation function can be decomposed into a
jump rotation and a diffuse rotation of HB frame based on the
EJM. The contribution from the fast jump rotation is bigger
than the diffusive part. The jump rotation becomes more and
more important with concentration. Comparing to the HB exchange of water, the HB exchange of ammonium ion between
two water molecules forming HB each other has a lower possibility than water.
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