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Exploring preferential solvation, structure and dynamical properties or Rb+ in aqueous ammonia solution using ab initio Quantum Mechanical Charge Field (QMCF)
Journal Pre-proof Exploring preferential solvation, structure and dynamical properties or Rb+ in aqueous ammonia solution using ab initio Quantum Mechanical Charge Field (QMCF) Yuniawan Hidayat, Harno Dwi Pranowo, Wega Trisunaryanti PII:
S0167-7322(19)31662-9
DOI:
https://doi.org/10.1016/j.molliq.2019.112027
Reference:
MOLLIQ 112027
To appear in:
Journal of Molecular Liquids
Received Date: 22 March 2019 Revised Date:
23 September 2019
Accepted Date: 27 October 2019
Please cite this article as: Y. Hidayat, H.D. Pranowo, W. Trisunaryanti, Exploring preferential solvation, structure and dynamical properties or Rb+ in aqueous ammonia solution using ab initio Quantum Mechanical Charge Field (QMCF), Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/ j.molliq.2019.112027. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Exploring Preferential Solvation, Structure and Dynamical Properties or
2
Rb+ in Aqueous Ammonia Solution using Ab Initio Quantum Mechanical
3
Charge Field (QMCF)
4
Yuniawan Hidayat a,c, Harno Dwi Pranowo b,c, Wega Trisunaryantib
5 6 7 8 9 10 11 12 13 14
a
Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta 5712612, Indonesia b Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia c Austria-Indonesia Center for Computational Chemistry (AIC), Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia Corresponding author: [email protected]
15
Abstract
16
The QMCF simulation method has been performed to investigate the dynamics and
17
solvation structure of Rb+ in aqueous ammonia. The LANL2DZ-ECP basis set was
18
used for the ion and DZP (Dunning) for ligands, while the Hartree-Fock (HF) theory
19
was applied to calculate the interaction between molecules. The radial distribution
20
function (RDF) shows that there was only one solvation shell observed at a distance
21
of 2.6 Å to 4.16 Å, with an average coordination number of 7 and dominantly by
22
water ligand. Ion Rb+ prefers to be hydrated than solvated by ammonia. The MRT of
23
the first solvation shell of 1.5 ps confirms a rapid mobility of ligands. The NBO
24
analysis of ion-ligand affirms a weak electrostatic interaction and dominantly by the
25
charge donor from the LP orbital of ligands to the LP* orbital of the ion.
26 27
Keyword: simulation, QMCF, Rubidium ion, aqueous ammonia
28
Introduction
29
Water and liquid ammonia have similar properties in dissolving metals.
30
Experimental data always consistent in predicting that the ion-ligand average
31
distance of Rb+-H2O is shorter than Rb+-NH3 [1–5]. However, experiment cannot
32
observe the dynamics of solvation, such as the mechanism of ion exchange and 1
33
ligand residence time, especially below femtoseconds. The use of molecular
34
dynamics (MD) simulations becomes an alternative to study the dynamics of ion
35
solvation accurately [6]
36
Although the MD simulations have successfully determine the coordination
37
number of ion solvation but there are inconsistencies compared to the experimental
38
data. The coordination number of the first shell of Rb+ ion in the water system
39
spreads from 6 to 9 [1,4,5,7]. Meanwhile, Rb+ ion in liquid ammonia is solvated by 6
40
to 8 ammonia ligands [2,3,8–10]. The inconsistency in coordination number may
41
come from the different approximation of calculation in the MD simulation methods,
42
including the width of the QM region, the application of the QM and MM boundary
43
functions, and the difference in the interatomic pair potential forces.
44
The QMCF (Quantum Mechanical Charge Field) method is one of the most
45
recent modified MD methods based on QM/MM (Quantum Mechanical-Molecular
46
Mechanics), in which the QM region is enlarged twice than that of regular QM/MM to
47
provide a more accurate calculation of the first and second solvation shells. The
48
charges from the electron distribution of the solvent are incorporated into the force
49
field and dynamically adjusted, following the configuration of the solute-solvent
50
interaction. Therefore, the construction of interatomic pair potential no longer
51
necessary [11].
52
Our previous work on the QMCF molecular dynamics of K+ in liquid ammonia
53
and aqueous ammonia systems generated satisfactory results. The first solvation
54
shells in both systems were found to have the average coordination number of 6,
55
which met the data of experimental results. Thus, the method was proven reliable.
56
Data of dynamics shows that NH3 has a shorter residence time than H2O [12,13].
57
Besides, we also investigated Rb+ ions in the liquid ammonia system using QMCF.
58
The simulation predicts the coordination number 8 with the average distance of ion-
59
ligands that is consistent with experimental data. Moreover, the average residence
60
time of ligands that solvate Rb+ is shorter than that solvating K+. This difference in
61
residence time can be predicted accurately using the QMCF simulation method [8].
62
In aqueous ammonia, the preference of the solvation can be well-predicted
63
using the QMCF method. Soft metals tend to be easily solvated by ammonia instead
64
of water, with a high preferential factor [14–16], in contrast with alkali metals that 2
65
have the lower one [13,17]. The preference factor defines the amount of ammonia in
66
the solvation shells compared to its composition in solution, with the following
67
formulation, according to Harno [18]: i NH 3
FP
68
=
N iNH x N H 3
N
i H 2O
2
O
x N NH
3
i
69
N and N, respectively, represent the number of NH3 or H2O species and the total in
70
the solvation shell (i) and the system. If the solvation does not occur, Ni is equal to
71
the number of species in the system, so that the minimum preferential factor has a
72
value of 1.
73
The Natural Bond Orbital (NBO) analysis can be used to evaluate molecular
74
structures regarding the electronic donor-acceptor of ion-ligand and the bond
75
properties [19–25]. Combination of QMCF result with this analysis, the interaction of
76
ion-ligand of the first solvation shell was clarified. Ion-ligand interaction of K+ and Rb+
77
ions in the liquid ammonia dominantly contributed by the charge donor from the lone
78
pair orbital of ligands to unfilled occupancy covalent anti-bond of the ion. The
79
interaction was an electrostatic type, confirmed by less number of Wiberg bond
80
index. Higher in stabilization energy and the number of the Wiberg bond index stated
81
that ammonia solvation to K+ ion was stronger than Rb+ ion [8,12,13].
82
This paper presented the results of the investigation toward structural and
83
dynamical properties of Rb+ in aqueous ammonia of 18.4% using the QMCF method.
84
The results of the simulation are in the forms of radial distribution functions (RDF),
85
coordination number distribution (CND), and angular distribution function (ADF).
86
Dynamical data of ligands weew analyzed in term of mean residence times (MRT),
87
and distance evolution of ligands (DEL). he NBO analysis was used to confirm the
88
first solvation shell structure.
89
Method
90
The QMCF method has two substantial principles. First, the system is consisting of
91
three, namely the core, solvation layer, and classical regions. The core one is the
92
solute while the solvation layer region consists of the first and second solvation
93
shells. These two regions are treated quantum-mechanically while molecular
94
mechanics calculate the classical one. There is a transition region between the QM 3
95
and MM regions. A smoothing function equation is applicable in this region to
96
maintain the gap of potential force that resulted from the different calculation method.
97
The equation is also intended to ensure the atoms can be moved continuously
98
between the two regions. Secondly, the charge from electron distribution is included
99
in the force field calculation [6]. The equation of the QMCF below is following Hofer’s
100
concept [6,26].
{ ∑ {
N1 + N 2
101
F
core J
=F
QM J
+
qQM qJMM I
∑
I =1
N1 + N 2
102
F
layer J
=F
QM J
+
MM qQM I qJ
I=1
N1 + N2
M
103
F
MM J
=∑ F I= 1
MM IJ
+
r 2IJ
∑ I=1
r 2IJ
{
r
3
(1)
3 ϵ +1 r IJ · 1+ 2· · + F nC IJ 2ϵ − 1 r c
MM qQM I qJ 2 IJ
( )]}
[ [
ϵ+ 1 r IJ · 1+2· · 2ϵ − 1 r c
()
[
]}
( )]} ∑
ϵ +1 r IJ · 1+ 2· · 2ϵ − 1 r c
(2)
N2
3
+
F MM IJ
(3)
I= 1
104 105
Eq. 1 consists of two terms. The first one shows the force working on the
106
nucleus that is calculated using quantum mechanics. Meanwhile, the second is used
107
to calculate the Coulombic interaction between two particles (particles I and J) based
108
on their respective partial charges. The influence of the ambient medium is also
109
involved in the calculation through the inclusion of the dielectric constant (є).
110
Likewise, Eq. 2 consists of two terms, namely the force working on the solvation
111
region, which is calculated using quantum mechanics, and the non-Coulombic
112
interaction calculation between molecules in the solvation layer and those in the MM
113
region. Eq. 3 is used to calculate the molecular interaction force in the MM region.
114
The first term in this equation consists of the contribution of the Coulombic and the
115
non-Coulombic charges and the intra-molecular force field in the MM region. The
116
second one is the sum of the interaction of the force field with the particles in the QM
117
region, while the last term represents the sum of all interactions of its non-Coulombic
118
force. When species moves from QM to MM region, the charges of the species are
119
distributed and incorporated into the force field. It affects the configuration of the
120
solute-solvent interaction for both regions.
4
121
Water or ammonia are allowed to migrate, to enter, or leaving the quantum
122
region. It causes a potential gap in the calculation of QM and MM. However, the
123
smoothing region between the QM and MM was applied to minimize the potential
124
gap. A transition region stands to bridge the gap of the potential force interaction
125
between molecules in the QM and MM. Equation 4 describes the force in this region.
126
F Smooth = S(r )(F lJayer − F MM )+ F MM J J J ,
127
Smooth The F J is the force referring to the particles in the transition region, the l ayer
(4)
MM and F J are representing those calculated using QM and MM, respectively,
128
FJ
129
while the smoothing function of S(r) is applicable in a distance of 0.2 Å.
130 131 132
Dynamical properties such as mean residence time of the ligands is calculated using direct method by Eq. 5 [27]. τ 0,5=
t simulation· N AV
(5)
N0,5 ex
133
0,5 0,5 The terms τ , tsimulation, NAV, and N ex , respectively, refer to the average residence
134
time, total of simulation time, average coordination number, and number of ligand
135
exchange events, which persists about, at least, 0.5 ps. The sustainability of the
136
solvation layer is calculated by Eq. 6. 0.5
137
N Sex = ex N0ex
138
N ex reflects the total of all migrating ligands between the first and second
139
solvation shells. The sustainability inverse, namely Rex, corresponds to the number
140
of exchanges required for a successful exchange (at least 0.5 ps).
(6)
0
141 142
Procedure
143
One of Rb+ ion was positioned in the centre of the simulation box containing
144
814 water and 183 ammonia molecules. The length of the box was 31.7 Å with a
145
system density of 0.927 g/cm3 was considered to be equal to aqueous ammonia of
146
18.4% at 293.15 K. The ensemble of NVT was used by the implementation of the
147
Berendsen weak-coupling algorithm with relaxation time of 0.1 ps to keep the
148
temperature constant during the simulation. The QM radius was set at 6.8 Å with a
149
transition zone radius of 0.2 Å between QM and MM regions. The amount of 5
150
ammonia and water in the QM were 7 and 30, respectively. While in the MM region,
151
the amount of ammonia and water were 178 and 784. Both of the regions have a
152
balanced composition. To integrate the equation of motion with time step of 0.2 fs, a
153
second order Adams-Bashforth predictor-corrector algorithm was used. The system
154
was employed a flexible ammonia [28] and BJH-CF2 water model [29], while
155
interaction between water and ammonia in MM region used a pair potential that was
156
described by Schwenk and Rode [30]. The QM was calculated using the Hartree-
157
Fock theory with the LANL2DZ ECP basis set for Rb+ ion and DZP (Dunning) basis
158
set for ammonia and water. All partial charges of species in QM region were resulted
159
by Mulliken population analysis [31]. First, the system was equilibrated for 4 ps and
160
followed by performing simulation for 19 ps. The simulation was conducted using a
161
QMCF package (version 1.3.1) [19] , and calculated using Turbomole (version 5.9)
162
[32,33]. Based on the RDF and CND analysis, the solvation structure was captured
163
using VMD [34] and the coordinate of the first solvation shell generated. Then, a
164
single point optimization of the corresponding coordinate with the NBO analysis of
165
the structure was performed using Gaussian [35,36].
166
Results and discussions
167
The RDF curves of Rb-N and Rb-O appear in Figure 1.
Only one peak
168
appears in the Rb-O curve at the range of 2.60 Å to 4.16 Å with an average distance
169
of 3.08 Å. The peak that not touches the x-axis = 0 indicates a dynamic solvation
170
structure. The integral number of 7 indicates that the Rb+ ion experiences hydration
171
by seven ligands of water. The absence of the second solvation shell is caused by
172
the weak ionic attraction due to the blockade of ligands in the first solvation shell. No
173
peak appears in the RDF curve of Rb-N, signifying that the hydration interaction of
174
Rb+ ion is stronger than ammonia solvation. The absence of ammonia in the first
175
solvation shell indicates that Rb+ ions prefer to be solvated by water. Thus, the
176
ammonia preferential factor in the first solvation shell is zero. This conclusion
177
reinforces the results of other molecular dynamics simulations, which state that
178
alkaline ions such as Li+, Na+ and K+ prefer to be solvated by [10,13,37,38].
179
The first solvation shell is directly adjacent to the bulk region, where ammonia
180
and water molecules should have more high flexibility and mobility. The ion-ligand 6
181
interaction in the first solvation shell emerged through the orientation of the water
182
ligands with the oxygen position, leading to the Rb+ ion. It is confirmed by the peak of
183
Rb-H curve, which located at the right of that of Rb-O curve (Figure 2). The RDF
184
curve of the Rb-H ion has only one peak in the area of 2.6 Å to 4.8 Å with an
185
average distance of 3.7 Å further than Rb-O distance. Experimental data related to
186
the geometry shape and solvation structure of the Rb+ ion in the preferential system
187
of aqueous ammonia, so far, has not been found. However, the result can be
188
compared to the other simulations data, as presented in Table 1.
189
As shown in Table 1, the Rb-O distance at the range between 2.98 Å to 3.05
190
Å in the hydrous system has been successfully observed using LAXS, EXAFS, and
191
X-Ray [1,10,39]. Meanwhile, the QMCF-MD method is yielding a distance of 3.08,
192
which is close to the experimental data. The result is also almost the same as to
193
those of the other QM/MM methods. The QM calculation radius is up to 6 Å from the
194
ion centre in the QMCF method, indicating that the presence of ammonia does not
195
significantly affect the attraction of ions to water in the first solvation shell. Even, the
196
water solvation that prevents ionic potential forces to attract ammonia molecules or
197
other water molecules in a distance of more than 3.08 Å prevents the formation of a
198
second solvation shell.
199
The CND of the first solvation shell by water is ranging from 4 to 11, with an
200
average of 7 and the highest probability of 29.8% (Figure 3a). The numerous of CN
201
numbers indicate for a labile hydration structure. The experimental data confirming
202
the coordination number of the Rb+ ion in aqueous ammonia system has not been
203
found. However, the X-rays, LAX, and EXAFS analyses of Rb+ ion in aqueous
204
solution confirmed that the hydration number of Rb+ ions was 7 and 8 [1,40].
205
At a distance of 2.6 Å to 4.16 Å, if the coordination numbers are analysed for
206
both water and ammonia, the total CND of ligands (H2O+NH3) ranges from 5 to 11,
207
with an average coordination number of 7 with a probability of 30.6% (Figure 3b).
208
This number is equivalent to the coordination number in the first solvation shell. It
209
means that the Rb+ ion is consistent, meaning that it is always solvated only by
210
water. The distribution of coordination numbers of 9 and 10 in the total number of
211
CND of ligands increased respectively from 9% (H2O) to 20% (H2O+NH3) and from
212
2% (H2O) to 6% (H2O+NH3). It is possible because of the presence of ammonia 7
213
coming into the radius. If the activity of ammonia is observed at a distance from 2.60
214
Å to 4.16 Å, then its amount in that radius is shown in the histogram in Figure 4. The
215
graph shows that ammonia is observed with a probability of 45%, almost equivalent
216
to the absence of ammonia (42%). It indicates that there is ammonia coming in and
217
out of that radius. When Rb+ ions are solvated by a lot of water, the average distance
218
between the ion and the ligand becomes longer, and the potential force held by the
219
water is used to stabilise the interactions between bonds. Consequently, the
220
interaction of Rb+ and water ions becomes weak, so they have enough potential
221
force to attract ammonia. Significant increases were also seen in CNDs of 5 and 6
222
when ammonia was present. Under conditions of the amount of water that is slightly
223
solvating, Rb+ ion can attract ammonia thereby increasing the probability of ammonia
224
entering the area
225
In the bulk phase, the average distribution numbers of ammonia are 183, with
226
a probability of 47.6%. As shown in Figure 5a, the existence of 184 ammonia with
227
the probability of 35.5% strengthens the suspicion that there is one ammonia ligand
228
moves from the bulk phase to the first solvation shell. The distribution numbers of
229
waters in the bulk phase are more diverse than ammonia, ranging from 801 to 808,
230
with the average number of 805 and probability of 27% (Figure 5b). It indicates a
231
rapid water movement as well as a consequence of the ligand exchange between
232
the regions.
233
The absence of solvation by ammonia in the first shell indicates that the Rb+
234
ion is preferential to water and dominated by the complex species [Rb(H2O)7]+. In
235
other words, the ammonia preferential factor in the first solvation shell is zero. In the
236
bulk phase, the ratio the distribution of ammonia and water is 183:805, resulting in a
237
preferential factor of 1.04, which is close to the minimum value. It indicates that the
238
attraction force of the Rb+ ion against ammonia is weak. Moreover, the force working
239
on the bulk phase is dominated by the interaction style between the ligands
240
themselves [10].
241
As in Figure 6, the CNT curve of ammonia is alternating continuously between
242
one and zero (Figure 6a, black line), showing that single ammonia goes to and fro
243
the region of 2.60 Å to 4.16 Å. For water, the CNT curve is the rise and down from 4
244
to 11, dominantly at 7 and 8 (Figure 6a, red line). The sum of CNT water and 8
245
ammonia shows significant addition peak curve at the coordination number of 9
246
(Figure 6b), reinforcing that in being solvated by a lot of water, Rb+ ion can attract
247
ammonia into the solvation radius.
248
Orabi reported a similar finding [10]. In a system equivalent to aqueous
249
ammonia of 18.4%, the coordination number in the first solvation shell of Rb+ ion
250
consists of 0.2 molecules of NH3 and 6.9 molecules of H2O. Although Orabi varied
251
the NH3 mole fraction in the system, the total coordination number produced was
252
consistently 7. Moreover, experimental data taken from Rb + ion system in water
253
showed that the first solvation shell consisted of 7 to 8 ligands of H2O (Table 1).
254
The ADF of O-Rb-O of the solvation structure is ranging from 30° to 180° and
255
indicating for a flexible structure. Depicted in Figure 7a, the widening peak from 58o
256
to 93o corresponds to an asymmetric and distorted geometry. The widening peak of
257
the ADF curve is in contrast to the hydrous system that has a sharper peak at 80o.
258
Although ammonia does not solvate the Rb+ ion, its existence influences the
259
flexibility of the hydration structure. In the solvation shell, ligands do not only interact
260
with the Rb+ ion but also with other nearby molecules from the outside of the
261
solvation region. The interaction of H-O•••N and H-O•••O between ligands in the
262
solvation shell with those of other ammonia and water molecules in the bulk region
263
forms a stronger electrostatic bond.
264
solvation region. The roughness of the ADF curve of N-Rb-O refers to the
265
inconsistency of the ammonia’s presence in the first solvation shell as well as a rapid
266
exchange of a single ammonia existence (Figure 7b).
It affects the orientation of ligands in the
267
The first hydration shell with a coordination number of 7, averagely, has a
268
capped trigonal prismatic molecular structure, as shown in Figures 8a and 8b [41].
269
The ADF’s angle between 60o to 80o comes dominantly from the two adjacent
270
oxygen atoms. As seen in Figure 6, the adjacent oxygen atoms of O1–Rb–O2 and
271
O3–Rb–O4 have an ADF’s angle of 74,67o and 74,10o, respectively. Moreover, the
272
seven ligands coordination structure has a characteristic angle of 135o. This angle
273
appears to widen around 135o to 145o, corresponding to that of O1–Rb–O4. It
274
confirms that the hydration structure is labile and distorted from the original shape of
275
capped trigonal prismatic geometry. It is hard to predict the geometry structure of the
276
solvation shell with the presence of the ammonia molecule because of its continuous 9
277
movement. However, according to the sum of CND, ammonia is assumed to exist
278
mostly in the total coordination number of 9. The snapshot of the geometry structure
279
can be taken within the simulation time of 10 ps, as depicted in Figure 8c.
280
In the ligand evolution chart, each colour represents one ligand molecule. The
281
graph illustrates the dynamics of the distance between ligands and ions on a time
282
basis. The data illustrates the movement of a ligand that moves away from and
283
approaches the central ion. Ligands massively move in and out of the bulk phase
284
area into the first solvation shell. When ligands are separated, and only those of
285
water raised as shown in Figure 9b, it is clear that only a few ammonia molecules
286
move in and out into the first solvation shell. In other words, it is the water molecules
287
that massively move across the boundary between the bulk phase and the first
288
solvation shell. The graph in Figure 9b also indicates that there is only one ammonia
289
that stayed longer in the first solvation shell area of water in a span of 6 ps, while the
290
rest came in and out in a very short time. Even though ammonia enters the solvation
291
shell several times, its solvation is considered not to occur due to the shortened
292
average residence time. The graph also shows a build-up of curves at distances
293
above 6 Å, indicating that there is abundant ammonia at that distance.
294
Table 2 shows the details of dynamical data of the first solvation shell and the
295
bulk phase, compared to other simulations data. For Rb+ ion in aqueous ammonia
296
system, the mean residence time of H2O in the first solvation shell is 1.5 ps, less
297
than that of 2.0 ps in the aqueous system, calculated using QM/MM [42]. As a
298
consequence of the first shell adjacent directly to the bulk region, the hydration in the
299
aqueous ammonia system has more labile and flexible motion. While in the aqueous
300
system, the first hydration shell is surrounded by the second hydration shell, causing
301
more restrained flexibility. It is also supported by ligand migration events in term of
302
higher Sex and less Rex of 0.4 and 2.5 respectively, compared to those in the
303
aqueous system (0.25 and 4.0, respectively). It affirms the stronger interaction
304
between Rb+ ion and H2O.
305
In the bulk phase of aqueous ammonia system, the mean residence time of
306
316.8:180.2 ps, corresponding to ammonia:water, shows that NH3 stays longer than
307
water, which its mobility is higher than that of ammonia. It denotes that ammonia
308
experiences the “self-solvated” in the bulk phase. Salentinig et al. supported this 10
309
hypothesis [43]. The representative distribution diagram of ammonia in the
310
simulation of NaCl in the ammonia-water system indicates that ammonia is preferring
311
to be surrounded by other ammonia molecules, while the first solvation shell is
312
enriched by water.
313
The NBO analysis informs the formation of the solvation structure in term of
314
orbital interaction between ion and ligands. The most dominant species of
315
[Rb(H2O)7]+ in the solvation structure was observed. The results of the NBO analysis
316
are shown in Table 3. Three different types of orbital from ligand contribute to the
317
ion-ligand interaction, that the bonding orbital (BD) of O-H, the core orbital of N (CR)
318
and the lone-pair orbital (LP) of N. These orbitals donate the charge to the unfilled
319
valance non-bonding (LP*) Rb+ ion. However, the most dominant contributor to the
320
stabilization energy of the structure comes from the charge donation from the LP
321
orbital of H2O to the LP* orbital of Rb+ ion. These results are consistent with the
322
previews NBO analysis to other solvation systems [13,24,25]
323
The value of the Wiberg bond index and stabilization energy are affected by
324
the distance and geometry orientation of the ligands. The Wiberg bond indexes are
325
less than 0.05, confirming the less covalent character of ion-ligand interaction. It
326
denoted as a weak electrostatic type of interaction and met with Salentinging’s work
327
[43]. The Wiberg bond index of Rb-O is less than K-O in the solvation system of K+
328
ion in aqueous ammonia caused by the larger size of Rb+ ion that produces a weak
329
ligand attraction [13].
330
Conclusions
331
The QMCF method has successfully observed the dynamics and structure of
332
Rb+ ion solvation in aqueous ammonia. RDF data shows that there is only one area
333
of solvation formed by water, with an average coordination number of 7, and with
334
ion-ligand distances that corresponds to the experimental data. ADF data informs
335
that ions isolated by water have a distorted capped trigonal prismatic geometry. The
336
ligand distance evolution observed shows that ammonia is trying to continuously
337
migrate in and out from the bulk phase into the solvation shell area of 2.60 Å to
338
4.16Å. However, no ammonia solvation in the system was observed. The preferential
339
factor of ammonia that is zero strengthens the suspicion that Rb+ ion prefers to be 11
340
solvated by water. The presence of ammonia molecules is identified in the bulk
341
phase, at a distance over 6 Å from the ion. In this phase, the MRT value of ammonia
342
is higher than that of water, indicating the occurrence of the self-solvation of
343
ammonia and that water is more volatile than ammonia. The NBO analysis confirms
344
that the charge donor of the electron from LP orbital of water to LP* orbital of the ion
345
is dominant, constructing the electrostatic type of interaction.
346
Acknowledgements
347
Financial support by the Doctoral Scholarship from the Ministry of Research,
348
Technology and Higher Education of the Republic of Indonesia are gratefully
349
acknowledged.
350
References
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503
16
504
505 506 507
Pictures
Figure 1. The RDF shows only one peak that refers to a hydration shell. None solvation is formed by NH3. The black and red lines represent Rb-O and Rb-N, respectively.
508 509 510
Figur
511
e 2.
512
The
513
RDF
514
of
515
Rb-O
516
and
517
Rb-H.
518
17
519 520 521 522 523
Table 1. Comparison of the QMCF-MD of Rb+ ion in aqueous ammonia with experimental and other simulation results. The rM1 and CN1 denote the maximum distance of ion-ligand and Coordination Number of the first solvation shell, respectively. Meanwhile, at the second solvation shell denote the rM2 and CN2, respectively. The rM1 and rM2 are in Å unit. No
Methods rM1
524
NH3 CN1 rM2
CN2
rM1 2.99 2.83 3.05 2.95 2.98 3.05 3.03
H2O CN1 rM2
Reff. CN2
1 2
AIMD-DFTa Montecarloa
3 4 5 6
QM/Ma LAXS, EXAFSa X-RAYa QM/MMb
7
QMCF-MDb 3.08 7 This work a + b + Notes : Rb in hydrous system, Rb in aqueous ammonia system
-
-
-
-
2.88
0.2
6.2
4
6.6 7
4.85 -
21 -
[39] [44]
7.1 8 6.9 6.9
5.4 4.8
22 22.9
[42] [1] [40] [10]
525 526 527 528
Figure 3. The CND of the first solvation shell of (a) H2O (b) the sum of total CND of H2O +NH3
18
529 530
Figure 4. Probability of observed ammonia at the radius of 2.6Å to 4.16 Å
531
532 533 534
Figure 5. Distribution number of (a) ammonia and (b) water in the bulk phase
19
535 536 537 538 539
Figure 6. Number of ligand evolution during simulation time at the range of 2.6 Å to 4.16 Å. (a) black and red line are CN evolution of NH3 and H2O, respectively (b) blue line represent the sum of CN evolution of ammonia and water (NH3 + H2O)
540 541 542 543 544 545 546 547 548 549 550 551 552 553
Figure 7. The ADF of (a) O-Rb-O and (b) N-Rb-O.
20
554 555 556 557 558 559 560 561 562 563
(a)
(b)
(c)
564 565 566 567 568 569
Figure 8. Hydration structure with coordination number of 7. (a) The ADF’s angles of 74.57o, 74.10o, 145.55o are of O1–Rb–O2, O3–Rb–O4, and O1–Rb–O4, respectively (b) The structure of distorted capped trigonal prism follows the basic structure of the ideal capped trigonal prism, according to Clare and Kepert (c) The geometric structure of Rb+ ion solvation with coordination number of 9 and an ammonia included
570 571
Figure 9. Bond evolution of ligands to the Rb+ ion (a) water and (b) ammonia
572 573
21
574 575 576 577
Table 2. Mean residence time of ligand in the hydration shell and the bulk phase, compared to the dynamics of the first solvation shell in the aqueous system from another simulations. Hydration Shell Ligan
Rb–H2O
t=0 ps
t=0,5 ps
Nexa
Nexb
τ
171
68
1.5
Sex
0.4
Rb–NH3
578 579 580 581 582 583 584
Bulk phase Rex
2.5
t=0 ps
t=0,5 ps
Ref Sex
Rex
Nexa
Nexb
τ
231
85
180.2
0.4
2.5
87
11
316.8
0.1
10
This work
Rb–H2Oc 142 35 2.0 0.25 4.0 a b Nex and Nex correspond to the amount of ligand exchange events that are, at least, 0 ps (t=0 ps) and 0.5 ps (t=0.5 ps), τ is the mean ligand residence time in ps which is determined by a direct method, Sex is the sustainability coefficient of the migration process, Rex is sustainability reverse, showing an average number of processes needed for one successful ligand exchange. c In aqueous system (QM/MM method)
585 586 Species
Table 3. NBO analysis of the first solvation shell The Wiberg Donor-acceptor stabilization energy Donor Acceptor Bond Rb-O (kJ/mol)
Rb-H2O (1)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.28 0.55 12.44
Rb-H2O (2)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
1.39 0.51 12.35
Rb-H2O (3)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.70 0.93 13.49
Rb-H2O (4)
0.010
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
3.16 1.26 14.59
Rb-H2O (5)
0.010
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
3.12 1.10 14.00
Rb-H2O (6)
0.007
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
1.69 0.42 15.01
Rb-H2O (7)
0.011
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.91 1.48 16.11
22
587
23
•
Rb+ ion prefers to be solvated by water than ammonia in aqueous ammonia system.
•
Single observed ammonia was trying to enter or leave the first shell rapidly
•
Only one solvation shell was observed and dominated by [Rb(H2O)7]+ species.
•
The solvation shell has a labile and dynamics structure
•
The NBO analysis confirmed the electrostatic type of ion-ligand interaction
Competing Interests Statement Article/Work Title:
Exploring Preferential Solvation, Structure and Dynamical Properties or Rb+ in Aqueous Ammonia Solution using Ab Initio Quantum Mechanical Charge Field (QMCF) Declaration of interests ( √ ) I declare that I have no significant competing financial, professional, or might have influenced the performance or
presentation of the work described in this manuscript.
( ) I have described my potential competing financial, professional, and/or the space below: (Provide details; use additional space if necessary.
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personal interests that
personal interests in
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DOI:
https://doi.org/10.1016/j.molliq.2019.112027
Reference:
MOLLIQ 112027
To appear in:
Journal of Molecular Liquids
Received Date: 22 March 2019 Revised Date:
23 September 2019
Accepted Date: 27 October 2019
Please cite this article as: Y. Hidayat, H.D. Pranowo, W. Trisunaryanti, Exploring preferential solvation, structure and dynamical properties or Rb+ in aqueous ammonia solution using ab initio Quantum Mechanical Charge Field (QMCF), Journal of Molecular Liquids (2019), doi: https://doi.org/10.1016/ j.molliq.2019.112027. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Exploring Preferential Solvation, Structure and Dynamical Properties or
2
Rb+ in Aqueous Ammonia Solution using Ab Initio Quantum Mechanical
3
Charge Field (QMCF)
4
Yuniawan Hidayat a,c, Harno Dwi Pranowo b,c, Wega Trisunaryantib
5 6 7 8 9 10 11 12 13 14
a
Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta 5712612, Indonesia b Department of Chemistry, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia c Austria-Indonesia Center for Computational Chemistry (AIC), Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia Corresponding author: [email protected]
15
Abstract
16
The QMCF simulation method has been performed to investigate the dynamics and
17
solvation structure of Rb+ in aqueous ammonia. The LANL2DZ-ECP basis set was
18
used for the ion and DZP (Dunning) for ligands, while the Hartree-Fock (HF) theory
19
was applied to calculate the interaction between molecules. The radial distribution
20
function (RDF) shows that there was only one solvation shell observed at a distance
21
of 2.6 Å to 4.16 Å, with an average coordination number of 7 and dominantly by
22
water ligand. Ion Rb+ prefers to be hydrated than solvated by ammonia. The MRT of
23
the first solvation shell of 1.5 ps confirms a rapid mobility of ligands. The NBO
24
analysis of ion-ligand affirms a weak electrostatic interaction and dominantly by the
25
charge donor from the LP orbital of ligands to the LP* orbital of the ion.
26 27
Keyword: simulation, QMCF, Rubidium ion, aqueous ammonia
28
Introduction
29
Water and liquid ammonia have similar properties in dissolving metals.
30
Experimental data always consistent in predicting that the ion-ligand average
31
distance of Rb+-H2O is shorter than Rb+-NH3 [1–5]. However, experiment cannot
32
observe the dynamics of solvation, such as the mechanism of ion exchange and 1
33
ligand residence time, especially below femtoseconds. The use of molecular
34
dynamics (MD) simulations becomes an alternative to study the dynamics of ion
35
solvation accurately [6]
36
Although the MD simulations have successfully determine the coordination
37
number of ion solvation but there are inconsistencies compared to the experimental
38
data. The coordination number of the first shell of Rb+ ion in the water system
39
spreads from 6 to 9 [1,4,5,7]. Meanwhile, Rb+ ion in liquid ammonia is solvated by 6
40
to 8 ammonia ligands [2,3,8–10]. The inconsistency in coordination number may
41
come from the different approximation of calculation in the MD simulation methods,
42
including the width of the QM region, the application of the QM and MM boundary
43
functions, and the difference in the interatomic pair potential forces.
44
The QMCF (Quantum Mechanical Charge Field) method is one of the most
45
recent modified MD methods based on QM/MM (Quantum Mechanical-Molecular
46
Mechanics), in which the QM region is enlarged twice than that of regular QM/MM to
47
provide a more accurate calculation of the first and second solvation shells. The
48
charges from the electron distribution of the solvent are incorporated into the force
49
field and dynamically adjusted, following the configuration of the solute-solvent
50
interaction. Therefore, the construction of interatomic pair potential no longer
51
necessary [11].
52
Our previous work on the QMCF molecular dynamics of K+ in liquid ammonia
53
and aqueous ammonia systems generated satisfactory results. The first solvation
54
shells in both systems were found to have the average coordination number of 6,
55
which met the data of experimental results. Thus, the method was proven reliable.
56
Data of dynamics shows that NH3 has a shorter residence time than H2O [12,13].
57
Besides, we also investigated Rb+ ions in the liquid ammonia system using QMCF.
58
The simulation predicts the coordination number 8 with the average distance of ion-
59
ligands that is consistent with experimental data. Moreover, the average residence
60
time of ligands that solvate Rb+ is shorter than that solvating K+. This difference in
61
residence time can be predicted accurately using the QMCF simulation method [8].
62
In aqueous ammonia, the preference of the solvation can be well-predicted
63
using the QMCF method. Soft metals tend to be easily solvated by ammonia instead
64
of water, with a high preferential factor [14–16], in contrast with alkali metals that 2
65
have the lower one [13,17]. The preference factor defines the amount of ammonia in
66
the solvation shells compared to its composition in solution, with the following
67
formulation, according to Harno [18]: i NH 3
FP
68
=
N iNH x N H 3
N
i H 2O
2
O
x N NH
3
i
69
N and N, respectively, represent the number of NH3 or H2O species and the total in
70
the solvation shell (i) and the system. If the solvation does not occur, Ni is equal to
71
the number of species in the system, so that the minimum preferential factor has a
72
value of 1.
73
The Natural Bond Orbital (NBO) analysis can be used to evaluate molecular
74
structures regarding the electronic donor-acceptor of ion-ligand and the bond
75
properties [19–25]. Combination of QMCF result with this analysis, the interaction of
76
ion-ligand of the first solvation shell was clarified. Ion-ligand interaction of K+ and Rb+
77
ions in the liquid ammonia dominantly contributed by the charge donor from the lone
78
pair orbital of ligands to unfilled occupancy covalent anti-bond of the ion. The
79
interaction was an electrostatic type, confirmed by less number of Wiberg bond
80
index. Higher in stabilization energy and the number of the Wiberg bond index stated
81
that ammonia solvation to K+ ion was stronger than Rb+ ion [8,12,13].
82
This paper presented the results of the investigation toward structural and
83
dynamical properties of Rb+ in aqueous ammonia of 18.4% using the QMCF method.
84
The results of the simulation are in the forms of radial distribution functions (RDF),
85
coordination number distribution (CND), and angular distribution function (ADF).
86
Dynamical data of ligands weew analyzed in term of mean residence times (MRT),
87
and distance evolution of ligands (DEL). he NBO analysis was used to confirm the
88
first solvation shell structure.
89
Method
90
The QMCF method has two substantial principles. First, the system is consisting of
91
three, namely the core, solvation layer, and classical regions. The core one is the
92
solute while the solvation layer region consists of the first and second solvation
93
shells. These two regions are treated quantum-mechanically while molecular
94
mechanics calculate the classical one. There is a transition region between the QM 3
95
and MM regions. A smoothing function equation is applicable in this region to
96
maintain the gap of potential force that resulted from the different calculation method.
97
The equation is also intended to ensure the atoms can be moved continuously
98
between the two regions. Secondly, the charge from electron distribution is included
99
in the force field calculation [6]. The equation of the QMCF below is following Hofer’s
100
concept [6,26].
{ ∑ {
N1 + N 2
101
F
core J
=F
QM J
+
qQM qJMM I
∑
I =1
N1 + N 2
102
F
layer J
=F
QM J
+
MM qQM I qJ
I=1
N1 + N2
M
103
F
MM J
=∑ F I= 1
MM IJ
+
r 2IJ
∑ I=1
r 2IJ
{
r
3
(1)
3 ϵ +1 r IJ · 1+ 2· · + F nC IJ 2ϵ − 1 r c
MM qQM I qJ 2 IJ
( )]}
[ [
ϵ+ 1 r IJ · 1+2· · 2ϵ − 1 r c
()
[
]}
( )]} ∑
ϵ +1 r IJ · 1+ 2· · 2ϵ − 1 r c
(2)
N2
3
+
F MM IJ
(3)
I= 1
104 105
Eq. 1 consists of two terms. The first one shows the force working on the
106
nucleus that is calculated using quantum mechanics. Meanwhile, the second is used
107
to calculate the Coulombic interaction between two particles (particles I and J) based
108
on their respective partial charges. The influence of the ambient medium is also
109
involved in the calculation through the inclusion of the dielectric constant (є).
110
Likewise, Eq. 2 consists of two terms, namely the force working on the solvation
111
region, which is calculated using quantum mechanics, and the non-Coulombic
112
interaction calculation between molecules in the solvation layer and those in the MM
113
region. Eq. 3 is used to calculate the molecular interaction force in the MM region.
114
The first term in this equation consists of the contribution of the Coulombic and the
115
non-Coulombic charges and the intra-molecular force field in the MM region. The
116
second one is the sum of the interaction of the force field with the particles in the QM
117
region, while the last term represents the sum of all interactions of its non-Coulombic
118
force. When species moves from QM to MM region, the charges of the species are
119
distributed and incorporated into the force field. It affects the configuration of the
120
solute-solvent interaction for both regions.
4
121
Water or ammonia are allowed to migrate, to enter, or leaving the quantum
122
region. It causes a potential gap in the calculation of QM and MM. However, the
123
smoothing region between the QM and MM was applied to minimize the potential
124
gap. A transition region stands to bridge the gap of the potential force interaction
125
between molecules in the QM and MM. Equation 4 describes the force in this region.
126
F Smooth = S(r )(F lJayer − F MM )+ F MM J J J ,
127
Smooth The F J is the force referring to the particles in the transition region, the l ayer
(4)
MM and F J are representing those calculated using QM and MM, respectively,
128
FJ
129
while the smoothing function of S(r) is applicable in a distance of 0.2 Å.
130 131 132
Dynamical properties such as mean residence time of the ligands is calculated using direct method by Eq. 5 [27]. τ 0,5=
t simulation· N AV
(5)
N0,5 ex
133
0,5 0,5 The terms τ , tsimulation, NAV, and N ex , respectively, refer to the average residence
134
time, total of simulation time, average coordination number, and number of ligand
135
exchange events, which persists about, at least, 0.5 ps. The sustainability of the
136
solvation layer is calculated by Eq. 6. 0.5
137
N Sex = ex N0ex
138
N ex reflects the total of all migrating ligands between the first and second
139
solvation shells. The sustainability inverse, namely Rex, corresponds to the number
140
of exchanges required for a successful exchange (at least 0.5 ps).
(6)
0
141 142
Procedure
143
One of Rb+ ion was positioned in the centre of the simulation box containing
144
814 water and 183 ammonia molecules. The length of the box was 31.7 Å with a
145
system density of 0.927 g/cm3 was considered to be equal to aqueous ammonia of
146
18.4% at 293.15 K. The ensemble of NVT was used by the implementation of the
147
Berendsen weak-coupling algorithm with relaxation time of 0.1 ps to keep the
148
temperature constant during the simulation. The QM radius was set at 6.8 Å with a
149
transition zone radius of 0.2 Å between QM and MM regions. The amount of 5
150
ammonia and water in the QM were 7 and 30, respectively. While in the MM region,
151
the amount of ammonia and water were 178 and 784. Both of the regions have a
152
balanced composition. To integrate the equation of motion with time step of 0.2 fs, a
153
second order Adams-Bashforth predictor-corrector algorithm was used. The system
154
was employed a flexible ammonia [28] and BJH-CF2 water model [29], while
155
interaction between water and ammonia in MM region used a pair potential that was
156
described by Schwenk and Rode [30]. The QM was calculated using the Hartree-
157
Fock theory with the LANL2DZ ECP basis set for Rb+ ion and DZP (Dunning) basis
158
set for ammonia and water. All partial charges of species in QM region were resulted
159
by Mulliken population analysis [31]. First, the system was equilibrated for 4 ps and
160
followed by performing simulation for 19 ps. The simulation was conducted using a
161
QMCF package (version 1.3.1) [19] , and calculated using Turbomole (version 5.9)
162
[32,33]. Based on the RDF and CND analysis, the solvation structure was captured
163
using VMD [34] and the coordinate of the first solvation shell generated. Then, a
164
single point optimization of the corresponding coordinate with the NBO analysis of
165
the structure was performed using Gaussian [35,36].
166
Results and discussions
167
The RDF curves of Rb-N and Rb-O appear in Figure 1.
Only one peak
168
appears in the Rb-O curve at the range of 2.60 Å to 4.16 Å with an average distance
169
of 3.08 Å. The peak that not touches the x-axis = 0 indicates a dynamic solvation
170
structure. The integral number of 7 indicates that the Rb+ ion experiences hydration
171
by seven ligands of water. The absence of the second solvation shell is caused by
172
the weak ionic attraction due to the blockade of ligands in the first solvation shell. No
173
peak appears in the RDF curve of Rb-N, signifying that the hydration interaction of
174
Rb+ ion is stronger than ammonia solvation. The absence of ammonia in the first
175
solvation shell indicates that Rb+ ions prefer to be solvated by water. Thus, the
176
ammonia preferential factor in the first solvation shell is zero. This conclusion
177
reinforces the results of other molecular dynamics simulations, which state that
178
alkaline ions such as Li+, Na+ and K+ prefer to be solvated by [10,13,37,38].
179
The first solvation shell is directly adjacent to the bulk region, where ammonia
180
and water molecules should have more high flexibility and mobility. The ion-ligand 6
181
interaction in the first solvation shell emerged through the orientation of the water
182
ligands with the oxygen position, leading to the Rb+ ion. It is confirmed by the peak of
183
Rb-H curve, which located at the right of that of Rb-O curve (Figure 2). The RDF
184
curve of the Rb-H ion has only one peak in the area of 2.6 Å to 4.8 Å with an
185
average distance of 3.7 Å further than Rb-O distance. Experimental data related to
186
the geometry shape and solvation structure of the Rb+ ion in the preferential system
187
of aqueous ammonia, so far, has not been found. However, the result can be
188
compared to the other simulations data, as presented in Table 1.
189
As shown in Table 1, the Rb-O distance at the range between 2.98 Å to 3.05
190
Å in the hydrous system has been successfully observed using LAXS, EXAFS, and
191
X-Ray [1,10,39]. Meanwhile, the QMCF-MD method is yielding a distance of 3.08,
192
which is close to the experimental data. The result is also almost the same as to
193
those of the other QM/MM methods. The QM calculation radius is up to 6 Å from the
194
ion centre in the QMCF method, indicating that the presence of ammonia does not
195
significantly affect the attraction of ions to water in the first solvation shell. Even, the
196
water solvation that prevents ionic potential forces to attract ammonia molecules or
197
other water molecules in a distance of more than 3.08 Å prevents the formation of a
198
second solvation shell.
199
The CND of the first solvation shell by water is ranging from 4 to 11, with an
200
average of 7 and the highest probability of 29.8% (Figure 3a). The numerous of CN
201
numbers indicate for a labile hydration structure. The experimental data confirming
202
the coordination number of the Rb+ ion in aqueous ammonia system has not been
203
found. However, the X-rays, LAX, and EXAFS analyses of Rb+ ion in aqueous
204
solution confirmed that the hydration number of Rb+ ions was 7 and 8 [1,40].
205
At a distance of 2.6 Å to 4.16 Å, if the coordination numbers are analysed for
206
both water and ammonia, the total CND of ligands (H2O+NH3) ranges from 5 to 11,
207
with an average coordination number of 7 with a probability of 30.6% (Figure 3b).
208
This number is equivalent to the coordination number in the first solvation shell. It
209
means that the Rb+ ion is consistent, meaning that it is always solvated only by
210
water. The distribution of coordination numbers of 9 and 10 in the total number of
211
CND of ligands increased respectively from 9% (H2O) to 20% (H2O+NH3) and from
212
2% (H2O) to 6% (H2O+NH3). It is possible because of the presence of ammonia 7
213
coming into the radius. If the activity of ammonia is observed at a distance from 2.60
214
Å to 4.16 Å, then its amount in that radius is shown in the histogram in Figure 4. The
215
graph shows that ammonia is observed with a probability of 45%, almost equivalent
216
to the absence of ammonia (42%). It indicates that there is ammonia coming in and
217
out of that radius. When Rb+ ions are solvated by a lot of water, the average distance
218
between the ion and the ligand becomes longer, and the potential force held by the
219
water is used to stabilise the interactions between bonds. Consequently, the
220
interaction of Rb+ and water ions becomes weak, so they have enough potential
221
force to attract ammonia. Significant increases were also seen in CNDs of 5 and 6
222
when ammonia was present. Under conditions of the amount of water that is slightly
223
solvating, Rb+ ion can attract ammonia thereby increasing the probability of ammonia
224
entering the area
225
In the bulk phase, the average distribution numbers of ammonia are 183, with
226
a probability of 47.6%. As shown in Figure 5a, the existence of 184 ammonia with
227
the probability of 35.5% strengthens the suspicion that there is one ammonia ligand
228
moves from the bulk phase to the first solvation shell. The distribution numbers of
229
waters in the bulk phase are more diverse than ammonia, ranging from 801 to 808,
230
with the average number of 805 and probability of 27% (Figure 5b). It indicates a
231
rapid water movement as well as a consequence of the ligand exchange between
232
the regions.
233
The absence of solvation by ammonia in the first shell indicates that the Rb+
234
ion is preferential to water and dominated by the complex species [Rb(H2O)7]+. In
235
other words, the ammonia preferential factor in the first solvation shell is zero. In the
236
bulk phase, the ratio the distribution of ammonia and water is 183:805, resulting in a
237
preferential factor of 1.04, which is close to the minimum value. It indicates that the
238
attraction force of the Rb+ ion against ammonia is weak. Moreover, the force working
239
on the bulk phase is dominated by the interaction style between the ligands
240
themselves [10].
241
As in Figure 6, the CNT curve of ammonia is alternating continuously between
242
one and zero (Figure 6a, black line), showing that single ammonia goes to and fro
243
the region of 2.60 Å to 4.16 Å. For water, the CNT curve is the rise and down from 4
244
to 11, dominantly at 7 and 8 (Figure 6a, red line). The sum of CNT water and 8
245
ammonia shows significant addition peak curve at the coordination number of 9
246
(Figure 6b), reinforcing that in being solvated by a lot of water, Rb+ ion can attract
247
ammonia into the solvation radius.
248
Orabi reported a similar finding [10]. In a system equivalent to aqueous
249
ammonia of 18.4%, the coordination number in the first solvation shell of Rb+ ion
250
consists of 0.2 molecules of NH3 and 6.9 molecules of H2O. Although Orabi varied
251
the NH3 mole fraction in the system, the total coordination number produced was
252
consistently 7. Moreover, experimental data taken from Rb + ion system in water
253
showed that the first solvation shell consisted of 7 to 8 ligands of H2O (Table 1).
254
The ADF of O-Rb-O of the solvation structure is ranging from 30° to 180° and
255
indicating for a flexible structure. Depicted in Figure 7a, the widening peak from 58o
256
to 93o corresponds to an asymmetric and distorted geometry. The widening peak of
257
the ADF curve is in contrast to the hydrous system that has a sharper peak at 80o.
258
Although ammonia does not solvate the Rb+ ion, its existence influences the
259
flexibility of the hydration structure. In the solvation shell, ligands do not only interact
260
with the Rb+ ion but also with other nearby molecules from the outside of the
261
solvation region. The interaction of H-O•••N and H-O•••O between ligands in the
262
solvation shell with those of other ammonia and water molecules in the bulk region
263
forms a stronger electrostatic bond.
264
solvation region. The roughness of the ADF curve of N-Rb-O refers to the
265
inconsistency of the ammonia’s presence in the first solvation shell as well as a rapid
266
exchange of a single ammonia existence (Figure 7b).
It affects the orientation of ligands in the
267
The first hydration shell with a coordination number of 7, averagely, has a
268
capped trigonal prismatic molecular structure, as shown in Figures 8a and 8b [41].
269
The ADF’s angle between 60o to 80o comes dominantly from the two adjacent
270
oxygen atoms. As seen in Figure 6, the adjacent oxygen atoms of O1–Rb–O2 and
271
O3–Rb–O4 have an ADF’s angle of 74,67o and 74,10o, respectively. Moreover, the
272
seven ligands coordination structure has a characteristic angle of 135o. This angle
273
appears to widen around 135o to 145o, corresponding to that of O1–Rb–O4. It
274
confirms that the hydration structure is labile and distorted from the original shape of
275
capped trigonal prismatic geometry. It is hard to predict the geometry structure of the
276
solvation shell with the presence of the ammonia molecule because of its continuous 9
277
movement. However, according to the sum of CND, ammonia is assumed to exist
278
mostly in the total coordination number of 9. The snapshot of the geometry structure
279
can be taken within the simulation time of 10 ps, as depicted in Figure 8c.
280
In the ligand evolution chart, each colour represents one ligand molecule. The
281
graph illustrates the dynamics of the distance between ligands and ions on a time
282
basis. The data illustrates the movement of a ligand that moves away from and
283
approaches the central ion. Ligands massively move in and out of the bulk phase
284
area into the first solvation shell. When ligands are separated, and only those of
285
water raised as shown in Figure 9b, it is clear that only a few ammonia molecules
286
move in and out into the first solvation shell. In other words, it is the water molecules
287
that massively move across the boundary between the bulk phase and the first
288
solvation shell. The graph in Figure 9b also indicates that there is only one ammonia
289
that stayed longer in the first solvation shell area of water in a span of 6 ps, while the
290
rest came in and out in a very short time. Even though ammonia enters the solvation
291
shell several times, its solvation is considered not to occur due to the shortened
292
average residence time. The graph also shows a build-up of curves at distances
293
above 6 Å, indicating that there is abundant ammonia at that distance.
294
Table 2 shows the details of dynamical data of the first solvation shell and the
295
bulk phase, compared to other simulations data. For Rb+ ion in aqueous ammonia
296
system, the mean residence time of H2O in the first solvation shell is 1.5 ps, less
297
than that of 2.0 ps in the aqueous system, calculated using QM/MM [42]. As a
298
consequence of the first shell adjacent directly to the bulk region, the hydration in the
299
aqueous ammonia system has more labile and flexible motion. While in the aqueous
300
system, the first hydration shell is surrounded by the second hydration shell, causing
301
more restrained flexibility. It is also supported by ligand migration events in term of
302
higher Sex and less Rex of 0.4 and 2.5 respectively, compared to those in the
303
aqueous system (0.25 and 4.0, respectively). It affirms the stronger interaction
304
between Rb+ ion and H2O.
305
In the bulk phase of aqueous ammonia system, the mean residence time of
306
316.8:180.2 ps, corresponding to ammonia:water, shows that NH3 stays longer than
307
water, which its mobility is higher than that of ammonia. It denotes that ammonia
308
experiences the “self-solvated” in the bulk phase. Salentinig et al. supported this 10
309
hypothesis [43]. The representative distribution diagram of ammonia in the
310
simulation of NaCl in the ammonia-water system indicates that ammonia is preferring
311
to be surrounded by other ammonia molecules, while the first solvation shell is
312
enriched by water.
313
The NBO analysis informs the formation of the solvation structure in term of
314
orbital interaction between ion and ligands. The most dominant species of
315
[Rb(H2O)7]+ in the solvation structure was observed. The results of the NBO analysis
316
are shown in Table 3. Three different types of orbital from ligand contribute to the
317
ion-ligand interaction, that the bonding orbital (BD) of O-H, the core orbital of N (CR)
318
and the lone-pair orbital (LP) of N. These orbitals donate the charge to the unfilled
319
valance non-bonding (LP*) Rb+ ion. However, the most dominant contributor to the
320
stabilization energy of the structure comes from the charge donation from the LP
321
orbital of H2O to the LP* orbital of Rb+ ion. These results are consistent with the
322
previews NBO analysis to other solvation systems [13,24,25]
323
The value of the Wiberg bond index and stabilization energy are affected by
324
the distance and geometry orientation of the ligands. The Wiberg bond indexes are
325
less than 0.05, confirming the less covalent character of ion-ligand interaction. It
326
denoted as a weak electrostatic type of interaction and met with Salentinging’s work
327
[43]. The Wiberg bond index of Rb-O is less than K-O in the solvation system of K+
328
ion in aqueous ammonia caused by the larger size of Rb+ ion that produces a weak
329
ligand attraction [13].
330
Conclusions
331
The QMCF method has successfully observed the dynamics and structure of
332
Rb+ ion solvation in aqueous ammonia. RDF data shows that there is only one area
333
of solvation formed by water, with an average coordination number of 7, and with
334
ion-ligand distances that corresponds to the experimental data. ADF data informs
335
that ions isolated by water have a distorted capped trigonal prismatic geometry. The
336
ligand distance evolution observed shows that ammonia is trying to continuously
337
migrate in and out from the bulk phase into the solvation shell area of 2.60 Å to
338
4.16Å. However, no ammonia solvation in the system was observed. The preferential
339
factor of ammonia that is zero strengthens the suspicion that Rb+ ion prefers to be 11
340
solvated by water. The presence of ammonia molecules is identified in the bulk
341
phase, at a distance over 6 Å from the ion. In this phase, the MRT value of ammonia
342
is higher than that of water, indicating the occurrence of the self-solvation of
343
ammonia and that water is more volatile than ammonia. The NBO analysis confirms
344
that the charge donor of the electron from LP orbital of water to LP* orbital of the ion
345
is dominant, constructing the electrostatic type of interaction.
346
Acknowledgements
347
Financial support by the Doctoral Scholarship from the Ministry of Research,
348
Technology and Higher Education of the Republic of Indonesia are gratefully
349
acknowledged.
350
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503
16
504
505 506 507
Pictures
Figure 1. The RDF shows only one peak that refers to a hydration shell. None solvation is formed by NH3. The black and red lines represent Rb-O and Rb-N, respectively.
508 509 510
Figur
511
e 2.
512
The
513
RDF
514
of
515
Rb-O
516
and
517
Rb-H.
518
17
519 520 521 522 523
Table 1. Comparison of the QMCF-MD of Rb+ ion in aqueous ammonia with experimental and other simulation results. The rM1 and CN1 denote the maximum distance of ion-ligand and Coordination Number of the first solvation shell, respectively. Meanwhile, at the second solvation shell denote the rM2 and CN2, respectively. The rM1 and rM2 are in Å unit. No
Methods rM1
524
NH3 CN1 rM2
CN2
rM1 2.99 2.83 3.05 2.95 2.98 3.05 3.03
H2O CN1 rM2
Reff. CN2
1 2
AIMD-DFTa Montecarloa
3 4 5 6
QM/Ma LAXS, EXAFSa X-RAYa QM/MMb
7
QMCF-MDb 3.08 7 This work a + b + Notes : Rb in hydrous system, Rb in aqueous ammonia system
-
-
-
-
2.88
0.2
6.2
4
6.6 7
4.85 -
21 -
[39] [44]
7.1 8 6.9 6.9
5.4 4.8
22 22.9
[42] [1] [40] [10]
525 526 527 528
Figure 3. The CND of the first solvation shell of (a) H2O (b) the sum of total CND of H2O +NH3
18
529 530
Figure 4. Probability of observed ammonia at the radius of 2.6Å to 4.16 Å
531
532 533 534
Figure 5. Distribution number of (a) ammonia and (b) water in the bulk phase
19
535 536 537 538 539
Figure 6. Number of ligand evolution during simulation time at the range of 2.6 Å to 4.16 Å. (a) black and red line are CN evolution of NH3 and H2O, respectively (b) blue line represent the sum of CN evolution of ammonia and water (NH3 + H2O)
540 541 542 543 544 545 546 547 548 549 550 551 552 553
Figure 7. The ADF of (a) O-Rb-O and (b) N-Rb-O.
20
554 555 556 557 558 559 560 561 562 563
(a)
(b)
(c)
564 565 566 567 568 569
Figure 8. Hydration structure with coordination number of 7. (a) The ADF’s angles of 74.57o, 74.10o, 145.55o are of O1–Rb–O2, O3–Rb–O4, and O1–Rb–O4, respectively (b) The structure of distorted capped trigonal prism follows the basic structure of the ideal capped trigonal prism, according to Clare and Kepert (c) The geometric structure of Rb+ ion solvation with coordination number of 9 and an ammonia included
570 571
Figure 9. Bond evolution of ligands to the Rb+ ion (a) water and (b) ammonia
572 573
21
574 575 576 577
Table 2. Mean residence time of ligand in the hydration shell and the bulk phase, compared to the dynamics of the first solvation shell in the aqueous system from another simulations. Hydration Shell Ligan
Rb–H2O
t=0 ps
t=0,5 ps
Nexa
Nexb
τ
171
68
1.5
Sex
0.4
Rb–NH3
578 579 580 581 582 583 584
Bulk phase Rex
2.5
t=0 ps
t=0,5 ps
Ref Sex
Rex
Nexa
Nexb
τ
231
85
180.2
0.4
2.5
87
11
316.8
0.1
10
This work
Rb–H2Oc 142 35 2.0 0.25 4.0 a b Nex and Nex correspond to the amount of ligand exchange events that are, at least, 0 ps (t=0 ps) and 0.5 ps (t=0.5 ps), τ is the mean ligand residence time in ps which is determined by a direct method, Sex is the sustainability coefficient of the migration process, Rex is sustainability reverse, showing an average number of processes needed for one successful ligand exchange. c In aqueous system (QM/MM method)
585 586 Species
Table 3. NBO analysis of the first solvation shell The Wiberg Donor-acceptor stabilization energy Donor Acceptor Bond Rb-O (kJ/mol)
Rb-H2O (1)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.28 0.55 12.44
Rb-H2O (2)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
1.39 0.51 12.35
Rb-H2O (3)
0.009
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.70 0.93 13.49
Rb-H2O (4)
0.010
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
3.16 1.26 14.59
Rb-H2O (5)
0.010
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
3.12 1.10 14.00
Rb-H2O (6)
0.007
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
1.69 0.42 15.01
Rb-H2O (7)
0.011
BD(O-H) CR(O) LP(O)
LP*(Rb) LP*(Rb) LP*(Rb)
2.91 1.48 16.11
22
587
23
•
Rb+ ion prefers to be solvated by water than ammonia in aqueous ammonia system.
•
Single observed ammonia was trying to enter or leave the first shell rapidly
•
Only one solvation shell was observed and dominated by [Rb(H2O)7]+ species.
•
The solvation shell has a labile and dynamics structure
•
The NBO analysis confirmed the electrostatic type of ion-ligand interaction
Competing Interests Statement Article/Work Title:
Exploring Preferential Solvation, Structure and Dynamical Properties or Rb+ in Aqueous Ammonia Solution using Ab Initio Quantum Mechanical Charge Field (QMCF) Declaration of interests ( √ ) I declare that I have no significant competing financial, professional, or might have influenced the performance or
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