Chemical Physics Letters 685 (2017) 322–327

Contents lists available at ScienceDirect

Chemical Physics Lettersjournal homepage: www.elsevier.com/locate/cplett

Research paper

Mechanism of translational jump of a hydrophobic solute in supercooled
water: Importance of presolvation
Sandipa Indra a, Snehasis Daschakraborty b,⇑ab

19 Nischintapur Lane, Santipur, Nadia, West Bengal 741404, India
Department of Chemistry, Indian Institute of Technology Patna, 801103 Bihar, Indiaa r t i c l e

i n f oArticle history:
Received 26 June 2017
In final form 31 July 2017
Available online 1 August 2017a b s t r a c t
Despite long study of translational jump of solute in supercooled water, a detailed mechanism of thisjump is still lacking. Through an analysis of several simulated cage-to-cage jumps of a dissolvedhydrophobic solute we find support for a pathway very similar to the proton transport in aqueous solution. Presolvation of water molecules occurs such that the final solvent cage, where the solute arrives
through jump, becomes structurally and energetically comparable to the initial cage where the solute
was trapped. This mechanism therefore clearly emphasizes the role of solvent for determining the jumpoccurrence time of a solute in supercooled water.
Ó 2017 Elsevier B.V. All rights reserved.

Supercooled liquids are often characterized by strong spatiotemporal heterogeneity. In such systems dynamics of a solute in
one region of the medium can be orders of magnitude faster thanthat in another region, separated by only a few nanometer distance. This dynamical heterogeneity of the medium has created acenter of attention for researchers for decades [1–5]. Solute’s
dynamics in supercooled liquids is remarkably intriguing. Breakdown of Stokes-Einstein (SE) relation for translational dynamics
is evidenced near glass transition temperature while the StokesEinstein-Debye (SED) relation involving rotational diffusion is stillvalid [1–17]. This signifies that even when the rotational motion ofsolute molecule is coupled to the viscosity of the medium, thetranslation of the same molecule is decoupled from viscosity.
Water, being a glass-former with the glass transition temperature136 K, is known to exhibit very similar behaviors including thedecoupling of translational dynamics from viscosity, which evenstarts from room temperature [11,12].
The above translation-rotation decoupling of solute and solventin supercooled liquids, supposedly, occurs due to the presence of
spatio-temporal heterogeneity in the medium [1–17]. However,this decoupling can also stem from non-diffusive translation ofmolecules. The rationale behind this hypothesis is the following.
The validity of the SE relation is based on the assumption that asolute molecule translates via Brownian motion with small amplitude displacements. Now, if the solute does not stringently follow
the Brownian motion then the SE relation will be violated naturally. This hypothesis—first proposed by Goldstein—states that
⇑ Corresponding author.
E-mail address: snehasis@iitp.ac.in (S. Daschakraborty).
http://dx.doi.org/10.1016/j.cplett.2017.07.0840009-2614/Ó 2017 Elsevier B.V. All rights reserved.

while molecules in low temperature liquid move via crossing a
potential energy barrier (activated transport or hopping), the liquid
molecules diffuse freely without hopping at high temperature as
the thermal energy is comparable to the barrier height [18]. Characteristics of this picture have been confirmed for more than one
model liquids by theory and computer simulation [19–23]. However, a detailed molecular mechanism for this solute’s jump fromone solvent cage to another is still elusive. In this context it’s worth
mentioning that a recent paper shows that translation-rotation
coupling can be a general mechanism of the breakdown of the SE
relation in the case of polyatomic ions [24].
Attempts were made to explain this behavior, modifying theidealized mode coupling theory after incorporating the hopping,which is considered to be arising from vibrational fluctuations in
the quasiarrested state where particles are trapped inside solvent
cage [25]. Regardless of the success of the theory for predicting
the long time dynamics of the density fluctuation correlation, theorigin of hopping from vibrational fluctuation of the solute in thesolvent cage is still questionable. Similar to the Grotthuss mechanism for proton transport in aqueous solution, the water solvents
must prearrange setting up the final cage before the solute actually
jumps from the initial to the final cage. Otherwise, the free energyof the system will eventually increase and the jump process will bethermodynamically infeasible [26–30]. Therefore, the reaction
coordinate for the solute’s jump must be the collective solvent
coordinate instead of the solute’s rattling motion inside the cage.
Interestingly, rotational jump of water molecules, at ambient condition, also shows similar behavior [31–33]. These motivate us to
explore the pathway for the cage-to-cage jump of the solute inmolecular detail.

S. Indra, S. Daschakraborty / Chemical Physics Letters 685 (2017) 322–327

In this letter we present results focusing pathway of ahydrophobic solute’s translational jump from one solvent cage toanother in supercooled water using classical molecular dynamics(MD) simulations. Hydrophobic hydration has been a fascinating
topic of debate for over decades (see eg., [34–39]). Both experimentand computer simulation studies evidenced that water solvent
molecules around the hydrophobic solute form strongly hydrogenbonded clathrate like structure (‘‘icebergs”) [34–39]. This clathrate
like structure of solvent water strongly encapsulates thehydrophobic solute. The escaping of the solute from the welldefined solvent cage, with the help of presolvation, is therefore
the key for the rattling-jump-rattling process in supercooled liquid.
The mechanism of this rattling-jump-rattling process is the central
focus of this letter.
We use GROMACS package [40] in order to obtain trajectory of
the molecules, placed in a cubic simulation box. The box contains
500 water molecules and 1 solute molecule. While the water molecules are modeled as rigid SPC/E, the solute is considered as a single Lennard-Jones (LJ) atom having LJ parameters similar to thoseof argon. (We have also checked the validity of our results using
TIP4P/2005 model [41] of water, presented in Supplementary
Material (SM).) The simulation is first run for 10 ns, during which
the temperature is kept constant at 250 K using Nosé-Hoover thermostat and the pressure at 1 atmosphere using Berendsen barostat
with a coupling constant of 0.5 ps. The above NPT simulation is run
in order to obtain appropriate density of the system at the given
temperature and pressure. The equations of motions are solved
by Leapfrog-Verlet algorithm with time step of 1 fs. Starting fromthe final configuration we initiate simulation using NVT ensemble
for another 40 ns using Nosé-Hoover thermostat with the same
coupling constant as before. Equations of motions are solved by L
eapfrog-Verlet algorithm again with time step of 1 fs. The trajectory is saved once in 50 fs. A cut-off of 1.2 nm (around the half ofthe box length) is applied for LJ and Coulomb interactions. Particle
Mesh Ewald summation technique and SHAKE algorithm are used
to handle long-range Coulomb interactions and constrain OAH
bonds of water molecule respectively. This 40 ns long trajectoryis used for analyses, which we discuss now.
The simulation results are organized as follows. First, we showthat the solute is momentarily trapped inside the solvent cage.
Next, we detail the spatial and orientational structure of the cagewater molecules in order to check whether it is hydrophobic
hydration structure or not. The escaping of the solute from one solvent cage and then trapping again in another cage are then examined by following over time the solute coordinate, which is actually
the position of the solute. Lastly, we focus on the solvent’s role infacilitating the jump process.
In order to get indication for caged dynamics of the solute wehave calculated here time dependent mean square displacement(MSD) of the solute. MSD is calculated using the equation,hjDrðtÞj2 i ¼ hjrðtÞ  rð0Þj2 i , where rðtÞ is the time dependent position vector of the solute. Fig. 1 exhibits MSD as a function of time.
Clearly, the plateau region of MSD with fractional time dependence(hjDrðtÞj2 i / t a ;a  0:2)—in between the short time ballistic(hjDrðtÞj2 i / t 2 )

and

the

long

time

diffusion

regime(hjDrðtÞj2 i / t)—implies rattling of the solute inside the solvent cage[3].
The present solute, being nonpolar in nature, is expected tohave hydrophobic hydration structure of solvent water molecules[34–39]. This hydrophobic hydration structure evidenced fromspatial and orientational structure of the solvent water moleculesaround the solute. We have presented in Fig. 2a, the radial distribution function (RDF) between the solute and the water oxygen atomand two-dimensional probability density distribution with theangle (between water OAH bond and the solute-water O atom vec-

323

Fig. 1. MSD of the solute as a function of time. The highlighted region signifies therattling motion of the solute in solvent water cage.

Fig. 2. Spatial and orientational structures of water molecules around thehydrophobic solute: (a) radial distribution function between solute and water O
atom (red solid line; values given by the right-hand ordinate axis) and twodimensional probability density distribution of the angle between water OAH bondand the solute-water O atom vectors in y-axis (values given by the left-handordinate axis) and the distance (between the solute and water O) in x-axis, (b)snapshot of the cage water molecules and the spherical solute at some time point
along trajectory. (For interpretation of the references to colour in this figure legend,
the reader is referred to the web version of this article.)tors) in y-axis and the distance (between the solute and water O
atoms) in x-axis. The positions of the first peak and the first minima at 3.6 Å and 5.35 Å respectively show that the first hydration shell is centered around 3.6 Å and extends up to 5.35 Åfrom the solute. The majority of OAH bonds in the first hydration
shell water molecules are either tangentially aligned around thesolute or towards the bulk water molecules. In the second hydration shell, on the other hand, majority of the OAH bonds are direc-

324

S. Indra, S. Daschakraborty / Chemical Physics Letters 685 (2017) 322–327

Z-axisted towards the hydrophobic solute. These water molecules basically donate H-bonds to the tangentially aligned first hydration
shell water molecules. The above picture is further visualized inFig. 2b, where the first hydration shell OAH bonds are mainly
either tangentially aligned or directed towards the bulk watermolecules. This picture is in close agreement with other simulation
studies, focused on hydrophobic hydration [34–39]. These tangential H-bonds are much stronger than bulk H-bonds and therefore
determine the lifetime of the solvent cage [34].
We now focus on the solute’s jump mechanism from one solvent cage to another. In Fig. S1 of SM we have shown a portionof the displacement of the solute where two jumps are clearly visible. Here, we divide the complete process into three steps: rattlingof the solute inside its initial cage, jump from one cage to another,and rattling of the solute again inside the final cage. The whole process is exhibited in Fig. 3a. Note that this rattling-jump-rattlingprocess of small solute is also seen in room temperature ionic liquids using MD simulation [23]. Here we examine 30 large amplitude jumps, the occurrence times of which are listed in Table S1of SM. The average amplitude of these 30 jumps is 3.25 Ǻ andis centered around 3.45 Ǻ (see Fig. S2 of SM). Analysis of all thesejump trajectories is useful to obtain the average picture, which isessential for predicting a precise mechanism. We follow all thejump processes over 20 ps duration with 10 ps each side of thejump occurrence time.
In order to follow the solute’s coordinate quantitatively we calculate jump coordinate QJ—normalized version of the solute coordinate—using the following equation:

(a)
III
II
I

X

-a

xi

s

Y-axisNh

21 (b)
20
19
18

QJ

1
0
-1
-10

-5

0

5

10

Fig. 3. (a) A portion of the solute’s trajectory in XYZ plane showing (I) the rattling
motion of the solute inside the initial cage, (II) the jump motion from the initial to
the final cage, and (III) the rattling motion of the solute inside the final cage; (b)Time evolution of the 30 trajectory-averaged jump coordinate QJ (black solid line)
and the coordination number Nh of the solute with t = 0 fixed at the jumpoccurrence time. While the vertical dashed line represents the jump occurrencetime (t = 0 ps), QJ = 0 is indicated by horizontal dashed line.

½rðtÞhr iþ½rðtÞhr i ;Q J ¼ ½rðtÞhri i rðtÞhrf i
½
i
f 

ð1Þ

where rðtÞ is the time dependent position of the solute. hr i i and hr f i
are the initial and final reference positions of the solute respectively. These are calculated by averaging over unnormalized solute’s
positions for 7 ps before and after the jump, as shown in Fig. 3a.
Therefore, hr i i and hr f i are the average positions during the solute’s
rattling motion inside the initial (state I in Fig. 3a) and the final
cages (state III in Fig. 3a) respectively. Evidently, QJ is an ‘orderparameter’ indicating the solute’s position. Note that QJ is 1 when
the solute is in its initial cage and is close to 1 when that is in the
final cage. This prompts our definition of the jump occurrence time
when QJ first crosses ‘‘0”, which is the midpoint between the initial
and the final cage positions. Note that the form of Eq. (1) is actually
motivated from the equation for normalized proton transfer coordinate, where the proton shifts its position from acid to base side [42].
30 trajectory-averaged QJ is displayed in Fig. 3b as a function oftime. The conspicuous fluctuations of QJ before and after the jump
are due to the rattling in the initial and the final cage respectively.
The swift transition of QJ value from 1 to 1 in 1 ps duration
characterizes the solute’s jump motion. Similar picture emerges
on using TIP4P/2005 model of water, as shown in Fig. S3a of SM.
However, the sudden jump of the solute from the initial cage tofinal one would cause higher energy unless solvent water molecules, which are in close proximity to the solute’s final cage position, do not rearrange to accommodate the arriving solute.
Because of the slower structural relaxation compared to ultrafast
solute-jump, the solvent water molecules must prearrange before
the jump occurs such that the final cage is almost built-up at thejump occurrence time. This is along the same line of Marcus theory[43] for electron transfer and Ando-Hynes theory [26,28] for proton transfer reaction in solution phase, where the thermallyinduced restructuring of the surrounding solvent molecules is the
key rate determining process. The role of water solvent for thejump of the solute is now discussed.
Fig. 3b also displays the coordination number, Nh, of the firsthydration shell (up to 5.35 Å distance from the solute) of the soluteas a function of time. Nh quickly decreases to 18.4 from the equilibrium value (Nh  20) at the jump occurrence time (t = 0 ps) andthen immediately regains its value. This subtle change of Nh value
occurs within 1 ps time, while the solute is on the fly between theinitial and the final cage. Note, this timescale is much smaller thanstructural relaxation timescale in supercooled water at 250 K[1,44–47]. Therefore the slight decrease of Nh value at t = 0 cannot
be due to the solvent water’s rearrangement. Instead, the above
decrease can be due to the fact that the first hydration shell of
the solute is slightly less crowded at the jump occurrence time
when the solute is halfway to the final cage. The similar picture
emerges for TIP4P/2005 model of water (see Fig. S3b of SM).
While the above discussion precludes the possibility of solvent
rearrangement during the ultrafast jump occurrence, we now show
the actual presolvation near the two reference positions of thesolute (hr i i and hr f i in Eq. (1)). We have plotted in Fig. 4 (Fig. S4
in SM for TIP4P/2005 model of water) the time dependent average
distance of the water molecules (hr SW i), present inside the distance
5.35 Å (first minima of solute-water RDF in Fig. 2a) distance fromthe two reference positions of the solute. Therefore, hrSW i provides
time dependent structural information of the solvent water forming the cage. This analysis is based on a simple anticipation thathr SW i has lower value when the solvent water molecules fill theentire spherical space in the absence of hydrophobic solute thanwhen they are organized to form solvent cage around thehydrophobic solute. Therefore, time dependent hrSW i will reveal
candidly the presolvation of water molecules, if any, near the initial

S. Indra, S. Daschakraborty / Chemical Physics Letters 685 (2017) 322–327

Fig. 4. Time evolution, centered on jump occurrence time, of average distance ofwater molecules hr SW i present inside the sphere of 5.35 Å radius from the two
reference positions. QJ is re-plotted (black solid line) for further elucidation. The
vertical dashed line represents the jump occurrence time (t = 0 ps).

and final cage positions of the solute. Fig. 4 clearly shows that hr SW ifrom initial (final) reference position of the solute decreases(increases) from a value of 4.22 Å (4.05 Å) to 4.05 Å(4.22 Å) after the jump occurrence. Interestingly, hrSW i values,
at initial and final reference positions, become equal at the jumpoccurrence time. In other words, the solute jumps from initial to
final solvent cage only when the hydration structures around thetwo reference positions of the solute are equivalent to each other.
A closer inspection of Fig. 4 further reveals that the increase of
hrSW i for final reference position starts increasing well before(3 ps) the solute actually jumps and almost levels off immediately after the jump. This provides absolutely clear picture thatwater solvents’ prearrangement starts when the solute stays in
the initial cage and continues till the final cage is almost built,
immediately after that the solute jumps to the final cage. This picture resembles to the presolvation of water molecules facilitating
proton transport in aqueous solution following the Grotthuss
mechanism [26–30].
Now we focus on the effect of the above prearrangement on thehydration structure around the two reference positions of thesolute. Fig. 5 displays the average number distribution of the solvent water molecules (NW) at various distances (up to 5.35 Å distance) from the reference positions at three different time slabs:

325

before (10 ps to 3 ps), during (0.5 to 0.5 ps), and after (3–10 ps) the jump occurrence time. The initial and the final reference
positions of the solute mimic H-bonded proton donor acid andacceptor base complex in acid-base PT reaction in aqueous solution[42]. Clearly, the two distinctly different distributions in Fig. 5a
before the jump indicate different hydration structures aroundthe two reference positions. While the one around the initial reference position corresponds to the hydrophobic hydration, the otheraround the final reference position corresponds to the neat liquidwater in a sphere. These two distributions become almost identicalat the jump occurrence time of the solute (see Fig. 5b). This indicates that the hydration structures around the initial and final reference positions of the solute become equivalent with each otherright at the jump occurrence time. This symmetrization of hydration structures at the jump occurrence time clearly stems fromthe presolvation of water molecules around the final reference
position, as shown in Fig. 4. Now, when the solute jump is overand the solute is trapped inside the final cage, the switching
between the hydration structures takes place, as evidenced from
Fig. 5c. This signifies stabilization of the solute in its final solvent
cage. We find similar results, presented in Fig. S5 of SM, from thesimulation considering TIP4P/2005 model of water.
In order to put this into perspective we have plotted in Fig. 6,
one-dimensional potential energy (PE) as a function of distanceof the solute from the initial reference position at three different
time points along 20 ps duration. These three time points are representative of before the jump (at 10 ps), at the jump (at 0 ps),and after the jump (at 10 ps) occurrences. PEs are evaluated by calculating the total interaction energy of the system (summation ofsolute-solvent and solvent-solvent interaction energy) at various
positions of the solute along the solute’s jump trajectory. Fig. 6
clearly reveals that while the solute is much more stable at the initial reference position before the jump occurrence, after the jumpoccurrence the solute becomes more stable in the final reference
position. This is evidenced by comparing the minima of the PE
wells. Before the jump occurrence the minimum of the PE wellshows up at r = 0 Å (center of the initial cage). After the jumpoccurrence, on the other hand, the minimum of the PE well is centered at r  6 Å (center of the final cage). Now, at the jump occurrence time the PE minima are almost the same for the solute at thetwo reference positions and in-between the barrier almost vanishes. The symmetrization of PE clearly occurs by the prearrangement of water molecules, as seen in Fig. 4. Interestingly, thesimilar symmetrization is also observed during rotational motionof water and some other dipolar liquids during H-bond partner
exchange [31–33,48–50], electron transfer reaction in aqueous
solution [43], acid-base proton transfer reaction in aqueous solution [42], and hopping of proton/hydroxide ion from one water
to another in liquid water following Grotthuss mechanism of proton transport [26–30].

Fig. 5. Water molecule number distribution, NW, as a function of distance from the initial (red line) and the final reference positions (blue) of the solute at three time points—(a) before jump, (b) during jump, and (c) after jump—along the trajectory of Fig. 3b. (For interpretation of the references to colour in this figure legend, the reader is referred to
the web version of this article.)326

S. Indra, S. Daschakraborty / Chemical Physics Letters 685 (2017) 322–327

jump amplitudes, and (iv) the results for TIP4P/2005 model ofwater. Supplementary data associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.cplett.
2017.07.084.

References

Fig. 6. Potential energies (solute-solvent plus solvent-solvent interaction potential)at several positions of the solute along the line joining the initial and final reference
positions of the solute at three reference time points: (a) 10 ps, (b) 0 ps, and (c)10 ps. See text for details. The potential energy minima around r = 0 in panel (c) is
too high to fit in the y-axis scale.

In conclusion, we have investigated the jump mechanism of asolute from one water solvent cage to another in supercooled
water using molecular dynamics simulation. We have found support for a pathway, very similar to the proton transport in aqueous
solution, where presolvation of solvent water molecules is the key
rate determining step. Presolvation of water molecules starts when
the solute is still in the initial cage. The jump occurs only when the
final cage becomes structurally and energetically comparable with
the initial cage. This mechanism, therefore, clearly emphasizes thatthe solvent coordinate is the reaction coordinate. We have also
checked the validity of the results using two different models ofwater, SPC/E and TIP4P/2005 model, and found that the results
are almost model independent.
Acknowledgement
SD acknowledges IIT Patna for financial and computational
support.
Appendix A. Supplementary material
Supplementary material contains (i) a small portion of thesolute’s displacement in order to show representative jumps, (ii)a table listing the jump occurrence times of the individual jumps,
examined for analysis, (iii) figure showing the distribution of 30[1] M.D. Ediger, Spatially heterogeneous dynamics in supercooled liquids, Annu.
Rev. Phys. Chem. 51 (2000) 99.
[2] R. Richert, Heterogeneous dynamics in liquids: fluctuations in space and time,
J. Phys.: Condens. Matter 14 (2002) R703.
[3] N. Giovambattista, M.G. Mazza, S.V. Buldyrev, F.W. Starr, H.E. Stanley, Dynamic
heterogeneities in supercooled water, J. Phys. Chem. B 108 (2004) 6655.
[4] E. Flenner, H. Staley, G. Szamel, Universal features of dynamic heterogeneity insupercooled liquids, Phys. Rev. Lett. 112 (2014) 097801.
[5] S.C. Glotzer, Spatially heterogeneous dynamics in liquids: insights fromsimulation, J. Non-Crys. Sol. 274 (2000) 342.
[6] G. Tarjus, D. Kivelson, Breakdown of the Stokes-Einstein relation insupercooled liquids, J. Chem. Phys. 103 (1995) 3071.
[7] I. Chang, H. Sillescu, Heterogeneity at the glass transition: translational androtational self-diffusion, J. Phys. Chem. B 101 (1997) 8794.
[8] S.F. Swallen, P.A. Bonvallet, R.J. McMahon, M.D. Ediger, Self-diffusion of trisnaphthylbenzene near the glass transition temperature, Phys. Rev. Lett. 90(2003) 015901.
[9] A. Dehaoui, B. Issenmann, F. Caupin, Viscosity of deeply supercooled water andits coupling to molecular diffusion, Proc. Natl. Acad. Sci. USA 112 (2015) 12020.
[10] S.R. Becker, P.H. Poole, F.W. Starr, Fractional Stokes-Einstein and DebyeStokes-Einstein relations in a network-forming liquid, Phys. Rev. Lett. 97(2006) 055901.
[11] M.G. Mazza, N. Giovambattista, H.E. Stanley, F.W. Starr, Connection oftranslational and rotational dynamical heterogeneities with the breakdownof the Stokes-Einstein and Stokes-Einstein-Debye relations in water, Phys. Rev.
E 76 (2007) 031203.
[12] S. Chen, F. Mallamace, C. Mou, M. Broccio, C. Corsaro, A. Faraone, L. Liu, Theviolation of the Stokes-Einstein relation in supercooled water, Proc. Natl. Acad.
Sci. USA 103 (2006) 12974.
[13] P. Henritzi, A. Bormuth, F. Klameth, M. Vogel, A molecular dynamics
simulations study on the relations between dynamical heterogeneity,
structural relaxation, and self-diffusion in viscous liquids, J. Chem. Phys. 143(2015) 164502.
[14] W. Kob, C. Donati, S.J. Plimpton, P.H. Poole, S.C. Glotzer, Dynamical
heterogeneities in a supercooled Lennard-Jones liquid, Phys. Rev. Lett. 79(1997) 2827.
[15] K.V. Edmond, M.T. Elsesser, G.L. Hunter, D.J. Pine, E.R. Weeks, Decoupling ofrotational and translational diffusion in supercooled colloidal fluids, Proc. Natl.
Acad. Sci. USA 109 (2012) 17891.
[16] B. Guchhait, S. Daschakraborty, R. Biswas, Medium decoupling of dynamics attemperatures 100 K above glass-transition temperature: a case study with(acetamide + lithium bromide/nitrate) melts, J. Chem. Phys. 136 (2012)
174503.
[17] L.E. Bove, S. Klotz, Th. Strässle, M. Koza, J. Teixeira, A.M. Saitta, Translationaland rotational diffusion in water in the gigapascal range, Phys. Rev. Lett. 111(2013) 185901.
[18] M. Goldstein, Viscous liquids and the glass transition: a potential energy
barrier picture, J. Chem. Phys. 51 (1969) 3728.
[19] S. Sastry, P.G. Debenedetti, F.H. Stillinger, Signatures of distinct dynamical
regimes in the energy landscape of a glass-forming liquid, Nature 393 (1998)554.
[20] A. Mukherjee, S. Bhattacharyya, B. Bagchi, Pressure and temperaturedependence of viscosity and diffusion coefficients of a glassy binary mixture,
J. Chem. Phys. 116 (2002) 4577.
[21] S. Bhattacharyya, B. Bagchi, Anisotropic local stress and particle hopping in a
deeply supercooled liquid, Phys. Rev. Lett. 89 (2002) 025504.
[22] M.T. Cicerone, Q. Zhong, M. Tyagi, Picosecond dynamic heterogeneity, hopping,and Johari-Goldstein relaxation in glass-forming liquids, Phys. Rev. Lett. 113(2014) 117801.
[23] J.C. Araque, S.K. Yadav, M. Shadeck, M. Maroncelli, C.J. Margulis, How isdiffusion of neutral and charged tracers related to the structure and dynamics
of a room-temperature ionic liquid? Large deviations from StokesEinsteinbehavior explained, J. Phys. Chem. B 119 (2015) 7015.
[24] P. Banerjee, S. Yashonath, B. Bagchi, Rotation driven translational diffusion ofpolyatomic ions in water: a novel mechanism for breakdown of StokesEinstein relation, J. Chem. Phys. 146 (2017) 164502.
[25] S.-H. Chong, Connections of activated hopping processes with the breakdownof the Stokes-Einstein relation and with aspects of dynamical heterogeneities,
Phys. Rev. E 78 (2008) 041501.
[26] K. Ando, J.T. Hynes, HCl acid ionization in water: a theoretical molecularmodeling, J. Mol. Liq. 64 (1995) 25.
[27] N. Agmon, The grotthuss mechanism, Chem. Phys. Lett. 224 (1995) 456.
[28] K. Ando, J.T. Hynes, Molecular mechanism of HCl acid ionization in water:
ab initio potential energy surfaces and Monte Carlo simulations, J. Phys. Chem.
B 101 (1997) 10464.

S. Indra, S. Daschakraborty / Chemical Physics Letters 685 (2017) 322–327[29] D. Marx, A. Chandra, M.E. Tuckerman, Aqueous basic solutions: hydroxidesolvation, structural diffusion, and comparison to the hydrated proton, Chem.
Rev. 110 (2010) 2174.
[30] R. Biswas, Y.-L.S. Tse, A. Tokmakoff, G.A. Voth, Role of presolvation andanharmonicity in aqueous phase hydrated proton solvation and transport, J.
Phys. Chem. B 120 (2016) 1793.
[31] D. Laage, J.T. Hynes, A molecular jump mechanism of water reorientation,
Science 311 (2006) 832.
[32] D. Laage, J.T. Hynes, On the molecular mechanism of water reorientation, J.
Phys. Chem. B 112 (2008) 14230.
[33] J.T. Titantah, M. Karttunen, Water dynamics: relation between hydrogen bondbifurcations, molecular jumps, local density & hydrophobicity, Scientific
Reports 3 (2013) 2991.
[34] D. Laage, G. Stirnemann, J.T. Hynes, Why water reorientation slows without
iceberg formation around hydrophobic solutes, J. Phys. Chem. B 113 (2009)2428.
[35] D. Chandler, Interfaces and the driving force of hydrophobic assembly, Nature
437 (2005) 640.
[36] N. Galamba, Water’s structure around hydrophobic solutes and the iceberg
model, J. Phys. Chem. B 117 (2013) 2153.
[37] D. Paschek, How the liquid-liquid transition affects hydrophobic hydration in
deeply supercooled water, Phys. Rev. Lett. 94 (2005) 217802.
[38] P. Ball, Water as an active constituent in cell biology, Chem. Rev. 108 (2008)74.
[39] J. Grdadolnik, F. Merzel, F. Avbelj, Origin of hydrophobicity and enhanced
water hydrogen bond strength near purely hydrophobic solutes, Proc. Natl.
Acad. Sci. USA 114 (2017) 323.
[40] D. van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E. Mark, H.J.C. Berendsen,
GROMACS: fast, flexible, and free, J. Comput. Chem. 26 (2005) 1701.

327[41] J.L.F. Abascal, C. Vega, A general purpose model for the condensed phases ofwater: TIP4P/2005, J. Chem. Phys. 123 (2005) 234505.
[42] S. Daschakraborty, P.M. Kiefer, Y. Miller, Y. Motro, D. Pines, E. Pines, J.T. Hynes,
Reaction mechanism for direct proton transfer from carbonic acid to a strong
base in aqueous solution I: acid and base coordinate and charge dynamics, J.
Phys. Chem. B 120 (2016) 2271.
[43] R.A. Marcus, Electron transfer reactions in chemistry. Theory and experiment,
Rev. Mod. Phys. 65 (1993) 599.
[44] F. Mallamace, C. Corsaro, H.E. Stanley, Possible relation of water structural
relaxation to water anomalies, Proc. Natl. Acad. Sci. USA 110 (2013) 4899.
[45] C. Masciovecchio, S.C. Santucci, A. Gessini, S. Di Fonzo, G. Ruocco, F. Sette,
Structural relaxation in liquid water by inelastic UV scattering, Phys. Rev. Lett.
92 (2004) 255507.
[46] B. Mukherjee, Microscopic origin of temporal heterogeneities in translational
dynamics of liquid water, J. Chem. Phys. 143 (2015) 054503.
[47] T. Yagasaki, S. Saito, Energy relaxation of intermolecular motions insupercooled water and ice: a molecular dynamics study, J. Chem. Phys. 135(2011) 244511.
[48] S. Das, R. Biswas, B. Mukherjee, Reorientational jump dynamics and its
connections to hydrogen bond relaxation in molten acetamide: an all-atom
molecular dynamics simulation study, J. Phys. Chem. B 119 (2015) 274.
[49] S. Das, R. Biswas, B. Mukherjee, Orientational jumps in (acetamide+ electrolyte) deep eutectics: anion dependence, J. Phys. Chem. B 119 (2015)
11157.
[50] S. Indra, R. Biswas, How heterogeneous are trehalose/glycerol cryoprotectant
mixtures? A combined time-resolved fluorescence and computer simulation
investigation, J. Phys. Chem. B 120 (2016) 11214.