Supplemental Material
Insights into hydrogen bond dynamics at the interface of the
charged monolayer-protected Au nanoparticle from
molecular dynamics simulation
Yunzhi Li,a) Zhen Yang,a) Na Hu, Rongfei Zhou, and Xiangshu Chenb)
College of Chemistry and Chemical Engineering, Jiangxi Inorganic Membrane Materials
Engineering Research Center, Jiangxi Normal University, Nanchang 330022, People’s Republic
of China
a)Author
b)Author
contributed equally to this work.
to whom correspondence should be addressed. Electronic mail: cxs66cn@jxnu.edu.cn
1. The Lennard–Jones parameters and partial atomic charges
TABLE S1. Lennard–Jones parameters and partial atomic charges used in this work.

Groups

(kcal/mol)
(Å)
q (e)
Au
0.772
2.737
0.000
SH
0.397
4.450
0.000
0.118
3.905
0.000
CH2(–NH3
0.118
3.800
0.310
N(NH3
+)
0.170
3.250
–0.300
H(NH3
+)
CH2
+)
0.000
0.000
0.330
Cl–
0.118
4.417
–1.000
O(water)
0.152
3.151
–0.834
H(water)
0.000
0.000
0.417
1
2. The electronic properties of terminal NH3+ groups with different
surfactant chains
FIG. S1. Structure illustrations for the terminal NH3+ groups with different surfactant chains: (a)
SH(CH2)5–, (b) CH3CH2–, and (c) CH3–, which are denoted as types A, B, and C in the Table S2.
TABLE S2. The Mulliken and MK atomic charges for the terminal NH3+ groups of types A, B,
and C. The deviations are with respect to the corresponding atomic charges of type A.
Mulliken atomic charges
type A
N1
H2
H3
H4
NH3+
charge (e)
–0.315
0.330
0.330
0.345
0.691
type B
charge (e)
–0.325
0.334
0.334
0.341
0.684
deviation (%)
3.17
1.21
1.21
1.16
1.01
type C
charge (e)
–0.371
0.347
0.347
0.347
0.671
deviation (%)
17.78
5.15
5.15
0.58
2.89
MK atomic charges
type A
N1
H2
H3
H4
NH3+
charge (e)
–0.485
0.348
0.348
0.353
0.564
type B
charge (e)
–0.502
0.364
0.364
0.360
0.587
deviation (%)
3.51
4.59
4.59
1.98
4.08
type C
charge (e)
–0.304
0.330
0.330
0.331
0.688
deviation (%)
37.31
5.17
5.17
6.23
18.97
To test the validity of the NH3+–terminated ethane (CH3CH2NH3+) to represent the
2
NH3+–terminated pentanethiol (SH(CH2)5NH3+), we have compared the electronic
properties of terminal NH3+ groups with different surfactants, as shown in Fig. S1. All
geometry optimizations were performed at the B3LYP/6-311+G(d,p) level. Based on
the optimized geometries, the electronic properties of terminal NH3+ groups were
described by two different atomic charges: one is the Mulliken scheme and the other
is the Merz-Singh-Kollman (MK) scheme where the atomic charges are fitted to
reproduce the electrostatic potential at number of points. As shown in Table S2, we
find that both the Mulliken and MK atomic charges in CH3CH2NH3+ are well
consistent with those in SH(CH2)5NH3+ with the deviation less than 5%, while the
smaller CH3NH3+ fails to describe the electronic properties of NH3+ groups in
SH(CH2)5NH3+ with the largest deviation up to 37.31%. Therefore, the
SH(CH2)5NH3+ is replaced by the CH3CH2NH3+ to calculate the binding energies in
this work due to the computational economy.
3. MD Simulation for the bulk water
To better compare the structure and dynamics properties of water at the interface
of the charged MPAN, we provided the structure and dynamics properties of bulk
water molecules. The bulk water system contained 4000 water molecules. MD
simulation was carried out in NPT ensemble with the temperature of 298.0 K and the
pressure of 1.0 atm. In this simulation, Newton’s equations of motion were also
integrated using the velocity-Verlet algorithm. The cutoff distance of non-bonded
interactions was set to 12 Å and the long-range electrostatic interactions were
calculated by using the particle-mesh Ewald (PME) method. In this work, the bulk
simulation was totally run 3.5 ns with the time step of 1 fs. The first 1.5 ns of
trajectories were used for equilibration, and the rest of the time was used for data
analysis. After equilibration, the dimension of simulation box after equilibration is
about 49.6×49.6×49.6 Å3.
3
4. Solvation dynamics at the interface
The solvation time correlation function (TCF) can be related to the time
correlation function of energy fluctuation, which is defined as1
C S t  
E t E 0
E 0E 0
(1)
where Et  is the fluctuation in solvation energy from its equilibrium value at time t.
E(t) denotes the electrostatic contribution to the solvation energy of the Cl– counterion
at time t. To obtain the solvation dynamics in bulk water, we have also performed ten
independent NPT MD simulations of one Cl– ion and 4000 water molecules at 1 atm
and 298.0 K. As shown in the inset of Fig. S2, the solvation TCF for the Cl– ion in
bulk water decays within 1 ps, which is faster than the corresponding results of Br–
and Cs+ ions in bulk water proposed by Pal and co-workers.1 First, this is because the
Cl– ion is relatively lighter than both Br– and Cs+ ions. Second, Mark and Nilsson2
shown that the TIP3P water molecules used in this work move more rapidly than the
SPC/E water molecules, which is expected to result in the faster decay of solvation
TCF.
FIG. S2. Solvation time correlation functions for interfacial Cl– ions around the MPAN. For
comparison, the solvation time correlation function of a Cl– ion in bulk water at 298 K, is shown
as inset.
4
TABLE S3. The fitting parameters of a three-exponential function to the solvation time correlation
function of interfacial Cl– ions around the MPAN.
Time constant (ps)
Amplitude (%)
τa
0.02
26
τb
0.11
71
τc
3.30
3
<t> (ps)
0.18
As shown in the previous work,3,4 the solvation TCF at the interface can be fitted
by a three-exponential function, which is expressed as
C S t   A exp  t  a   B exp  t  b   C exp  t  c 
(2)
Then the fitting time constants and amplitudes are listed in the Table S3. We can see
from this table that the ultrafast component (sub-100 fs) observed in bulk water still
plays a dominant role at the MPAN interface and there is a minor slow component
(3.28 ps), which results in that the solvation dynamics at the interface are relatively
slower than that in bulk water. These results further support the slow translation and
rotation of interfacial water molecules and are favorable to make a connection of
simulation and experiment results.
1
S. Pal, B. Bagchi, and S. Balasubramanian, J. Phys. Chem. B 109, 12879 (2005).
2
P. Mark and L. Nilsson, J. Phys. Chem. A 105, 9954 (2001).
3
S. K. Sinha and S. Bandyopadhyay, J. Chem. Phys. 136, 185102 (2012)..
4
A. Jha, K. Ishii, J. B. Udgaonkar, T. Tahara, and G. Krishnamoorthy, Biochemistry,
50, 397 (2011).
5
5. The definition of all hydrogen bonds (HBs)
FIG. S3. Radial density distributions between (a) O (water) and O (water), (b) Cl– and O (water),
(c) N (NH3+) and O (water), as well as (d) N (NH3+) and Cl–.
FIG. S4. The definition of (a) H2O–H2O, (b) Cl––H2O, (c) NH3+–H2O, and (d) NH3+–Cl– HBs in
this work.
6
6. The sensitivity of the continuous time correlation function, SHB(t), to
the sampling time interval Δt
It should be emphasized that the time interval Δt that the trajectories are sampled,
has a great influence on the continuous time correlation function SHB(t) since its
relaxation time is relatively short (generally less than 1 ps). To better understand the
influence of the SHB(t) with the Δt, therefore, we have sampled the trajectories every 1,
5, 10, 50, and 100 fs to data analysis on the basis of the simulated phase space of bulk
water. The obtained time correlation functions SHB(t) and CHB(t) with different Δt are
displayed in Fig. S5. Accordingly, the average lifetime  SHB and the structural
relaxation time  CHB of the H2O–H2O HBs are listed in Table S4. As shown in Fig. S5,
we find that the Δt has a negligible effect on the CHB(t) functions. On the contrary,
different Δt values results in different SHB(t) functions. When the Δt values are up to
50 and 100 fs, the SHB(t) curves are very different from that of Δt = 1, 5, and 10 fs. As
shown in Table S4, furthermore, the obtained the HBs lifetime  SHB of Δt = 1 fs and
Δt = 5 fs is 0.29 ps, which is in excellent according with the previous work (S. K.
Sinha and S. Bandyopadhyay, J. Chem. Phys. 135, 135101, 2011). The  SHB of Δt =
100 fs is about 0.67 ps, which is about 2.3 times greater than that of the standard value.
On the other hand, the different time intervals show identical structural relaxation
time  CHB of 2.9 ps, suggesting that the CHB(t) and  CHB are insensitive to the Δt.
Hence, we sample the trajectories every 5 fs to calculate the SHB(t) functions and the
average lifetime  SHB since such Δt is short enough to obtain the accurate SHB(t) and
 SHB .
7
FIG. S5. Two time correlation functions (a) CHB(t) and (b) SHB(t) for the bulk H2O–H2O HBs with
different Δt.
HB
HB
TABLE S4. The corresponding  S and  C values for the bulk H2O–H2O HBs with different
Δt.
Δt (fs)
 SHB (ps)
 CHB (ps)
1
5
10
50
100
0.29
0.29
0.31
0.49
0.67
2.9
2.9
2.9
2.9
2.9
8
7. The residence time distribution of bulk water with different shell
thickness
To better understand the relaxation time of the hydration sublayers at the interface
of the charged MPAN, the residence time distributions of bulk water molecules in
different shells are given in Fig. S6. Similarly to the interface of MPAN, we have also
divided the bulk water into four shells with respect to the center of simulation box, i.e.,
the radial distance is 11.5–14.5 Å (shell 1), 14.5–17.5 Å (shell 2), 17.5–20.5 Å (shell
3), and 20.5–23.5 Å (shell 4), respectively. As shown in Fig. S6a, we find that the
residence time distributions of bulk water molecules in the shells 1–4 are identical and
the corresponding residence time is 1.97 ps (the shell thickness is 3 Å) although their
upper and lower limits of radial distances are different. For other shell thickness, the
same shell thickness also shows the same residence time for the water molecules (see
Fig. S6).
By comparison, however, we find that the residence time of water molecules in one
shell is related to the shell thickness even for the bulk water. When the shell thickness
increases up to 6, 9, and 12 Å, we can see from Table S5 that the corresponding
residence times also increase up to 6.41, 13.36, and 22.47 ps. It should be emphasized
that the relationship between the residence time and the shell thickness is not linear. It
is interesting to explore the dependence of the residence time of bulk water on the
shell thickness and the further investigation is still in progress. Hence, the residence
time of 1.97 ps for the bulk water obtained from the shell thickness of 3 Å (identical
with the thickness of each hydration sublayer defined in this work) is as the reference
for the residence times of water molecules in each sublayer.
9
FIG. S6. The residence time distributions of water molecules in one shell with different shell
thickness Δr : (a) 3 Å, (b) 6 Å, (c) 9 Å, (d) 12 Å.
TABLE S5. The fitting parameters and residence time τ of bulk water molecules in one shell with
different shell thickness d.
d (Å)
A
B
C
τa
τb
τc
τ (ps)
3
0.0464
0.0938
0.8598
0.8897
0.2276
2.2192
1.97
6
0.0965
0.849
0.0545
0.9461
7.4189
0.2539
6.41
9
0.1151
0.8374
0.0475
1.6031
15.7198
0.2989
13.36
12
0.1149
0.081
0.8041
3.9447
0.6432
27.6507
22.74
10
8. The distributions of the number of water molecules in different
sublayers
FIG. S7. The radial distributions of water molecule numbers in different hydration
sublayers.
11