Absolute Ion Hydration Free Energy Scale and the Surface Potential Of

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Downloaded by guest on September 28, 2021 www.pnas.org/cgi/doi/10.1073/pnas.2017214117 thermodynamics single-ion surface the near fields droplets. electric water of and interfaces, distributions hydrophobic ion chemistry, near acid–base concerning experiments water of of potential range surface the effective in an hydra- produces real free energy potential derived hydration free experimentally electrostatic bulk tion the the the with then in is Comparison energy. total orders contribution, computed odd The that removed. for all are data of anion terms and interfacial cumulant cation The long-range averaging the By shell. in resides term. energy inner free the the to contribution outside a potential produce interactions to all work the involves is that size nearby energy of with con- free cavity ion chemical packing the the or of 2) inner-shell interactions waters, direct the includes 1) that Na parts: tribution the three of the into for energy partitioned value free accurate an hydration obtain bulk to ion mechan- employed for quantum are scale initio simulations energy ab ical free 2020) and 13, absolute theory August an quasi-chemical review determining for hydration, (received of 2020 goal 26, a October approved With and NJ, Princeton, University, Princeton Car, Roberto by Edited a simulation quantum via Shi Yu water the of and potential scale surface energy free hydration ion Absolute eritrae,intase ecin,adeetoekinetics electrode distributions and proteins, on reactions, pair- or transfer ion in ion resins, binding interfaces, in specificity, near exchange its and ion understanding ing better interactions, a ion–solvent (25, gaining of energy include of energies free theories quantitative free or developing single-ion enthalpy for pair motivations can- ion Further term the 26). the potential composing to surface when single-ion linked interfaces cels The dissimilar turn measurable. chemically not elec- in across are the is shifts that potential states input trostatic that theoretical (22–24) for principle (18– input Gibbs–Guggenheim need theoretical The requires typically estimation 21). values measurable, single-ion the directly hydration of pair are single-ion ion While a quantities 17). establishing (16, thermodynamic hydration of for goal scale long-standing energy free the is effects ion (13–15). models classical not simple effects in transfer contained charge and simulation ener- polarization quantum free include and that partition (10–12), methods parts that physical theories distinct into molecular gies ions 9), specific (8, interrogate interfaces These that at behavior. probes spectroscopic observed include the to tools unravel leading to interactions begun fundamental have that tools theoretical/computational battery resur- and science proteins major relevance colloid (7). channel recognized materials fundamental biological a the to from to electrochemistry seen fields due and spanning has decades problems two effects the last to Hofmeister, the specific-ion in by these gence the precipitation of after protein shape, Well study size, on dramatically. different work vary with can pioneering but makeup that charge chemical solutions same of and/or the behaviors of physical ions The include (1–6). systems related I dynamics molecular quantum eateto hmsr,Uiest fCnint,Cnint,O 45221 OH Cincinnati, Cincinnati, of University Chemistry, of Department hs hscl hmcl ilgcl aeil,adenergy- and condensed- materials, diverse biological, to chemical, central physical, are phase phenomena solvation on idt h i fgiigfnaetlisgt nospecific into insights fundamental gaining of aim the to Tied and experimental of set a to due made been has Progress a n hmsL Beck L. Thomas and . to −0.4 λ nwtr n )teln-ag otiuinthat contribution long-range the 3) and water, in . .Tersl scnitn ihavariety a with consistent is result The V. −0.5 | yrto reenergy free hydration | ufc potential surface a,1 + o.Tefe nryis energy free The ion. | DFT | binitio ab 1 the under Published Submission.y Direct PNAS a is article This interest.y competing no paper.y declare the authors wrote The and research performed T.L.B. and Y.S. contributions: Author (38) form the of is ion an value. potential chemical the droplet the to in contribute regions long density is charge inhomogeneous potential any Coulomb ranged, are the waters Since and sampling. ion during the uncoupled indicates subscript zero the and molecules where (10) formula Widom other from involve (or water to of as sources). autoionization large near the so and from not in ions ion but extraneous the potential interface, near liquid–vapor electrostatic zones distant to average varying the enough rapidly the large between for a region is value the of droplet stable center the a the assume obtain near We located droplet. ion water large monovalent spherical single a water) into (pass- medium water hydrophobic 37). 36, a of (29, or potential phase approximately gas surface is the accumulating effective from at is the ing measurements evidence suggests spectroscopic Experimental (31–34), that (35). by chemistry surfaces probed acid–base directly droplet ion fields altered not electric nonuniform 30), are and include (8, shifts consequences profiles the density The though (29). even gradients measurable interface potential an solvent-induced through to consequences chemical fields force 28). accurate (27, more simulations molecular of in energy development employed free the hydration facilitates single-ion a scale establishing addition, In (16). owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To sclodsine lcrceity ipyis n energy and biophysics, electrochemistry, materials. storage science, specific colloid diverse interfacial as fields as of in kinetics studies and thermodynamics, for structure, ion footing quantitative provides firm work This energy. a free hydration of “real” the comparison experimental for with by values energy water free hydration of “bulk” computed potential the surface estimate ion effective accurate an sodium the free produce of the results the simulation of for The simulations water. zero in mechanical the- a quantum quasi-chemical paper, employing and this by ory determined single-ion In is century. scale for a energy nearly scale chem- condensed-phase for of energy istry goal elusive free an been has absolute hydration an Establishing Significance h rdtoa xrsinfrteecs hmclptnilof potential chemical excess the for expression traditional The ion the for potential chemical excess The of case the consider below, discussion the of sake the For and physical be may there that previously suggested have We ε X stettlitrcineeg fteinwt l solvent all with ion the of energy interaction total the is NSlicense.y PNAS µ X ex . ,i gemn iherirestimates earlier with agreement in V, −0.4 = −kT lnhexp[−ε X /kT NSLts Articles Latest PNAS ]i 0 X , sgvnb the by given is | f8 of 1 [1]

CHEMISTRY ex ex µX = µX ,che + qφ, [2] In the present paper, the target quantity is the bulk free energy ex + µX ,b for the Na ion (right side of Eq. 6). This bulk value ex where µX ,che is a “chemical” value deep in the liquid and φ is a has been shown (36) to correspond to the Marcus value (51) contribution from surface effects. It is clear by comparing Eqs. 1 that includes no interfacial potential contribution. Toward this and 2 that Eq. 2 involves some kind of partitioning of the electro- end we utilize quasi-chemical theory and quantum mechanical static potential. The questions addressed in this paper are, what simulation methodology to partition the free energy into spa- is the physical content of φ, and what is its numerical value? tially resolved and manageable parts. Employing the difference ex ex There are multiple choices for defining the generic interfacial (µX − µX ,b )/q = φnp via Eq. 6, we are able to estimate the effec- potential φ above. First, following refs. 18 and 39 we can com- tive surface potential of water (the net potential) in the absence pute the (planar) liquid–vapor surface potential by integrating of other interfering ions. In other words, we obtain the sol- the Poisson equation through the interface, vent contribution to the net potential. The computational results and experimental values are summarized in the last five lines Z ∞ of Table 1 (below). The resulting estimate of the effective sur- φsp = 4π zρ(z)dz, [3] −∞ face potential of water (−0.4 V) implies an electric field near the interface of magnitude 107 V/cm assuming an interfacial width where z is the coordinate perpendicular to the interface and of approximately 5 A.˚ ρ(z) is the charge density (due to electron and nuclear distri- This work builds upon previous efforts aimed at ab ini- butions). It is known that, for realistic charge distributions, this tio real ion hydration free energy calculations (14, 52–54), potential is large and positive (40, 41), with a value of about 4 V but differs by focusing on the bulk value. This avoids diffi- for the water liquid–vapor interface. The large magnitude arises culties related to the zero of the energy scale and finite-size from the internal molecular structure with electrons spatially effects for long-range electrostatics in periodic boundary simu- distributed around point-like nuclei (producing the quadrupo- lations. Once a value is established for one ion, free energies lar Bethe potential). The associated intrinsic chemical term for other ions can be obtained from thermodynamic measure- ex µX ,int (42) includes all local interactions of the ion with the ments. Our results resolve a recurrent debate concerning the solvent, including a large approximately canceling quadrupole surface electrostatic contribution to single-ion hydration free term. Thus, while the sum produces the “real” excess chemical energies. ex potential µX , We first outline the necessary theory for analysis of the ab ex ex µX = µX ,int + qφsp , [4] initio molecular dynamics (AIMD) simulations at the density the two contributing terms are of very large magnitude. Another functional theory (DFT) level. We then present the results with proposed partitioning of the surface potentials involves the dipo- relevant discussion and finish with our conclusions. The compu- lar surface potential for the liquid–vapor interface, as opposed tational methods are summarized following the conclusions. to the full φsp discussed above (43). This definition leads to an Theory alternative “intrinsic” chemical potential. We employ quasi-chemical theory (QCT) (6, 10, 11) to compute We have previously termed the potential contribution due to + a varying charge distribution near a molecular-sized cavity the the hydration free energy of the Na ion. QCT provides a means to partition the free energy spatially into three physical parts. The local potential φlp (29, 44, 45). The total electrostatic cavity potential from the two inhomogeneous water domains is then three components correspond to the processes of 1) forming a the net potential cavity somewhat larger than the ion in water (packing), 2) inserting the ion into the cavity (long-ranged or outer shell), and 3) φnp = φlp + φsp . [5] allowing the water solvent back into contact with the ion (inner The resulting excess chemical potential is shell). ex ex In the limit of a purely repulsive hard sphere cavity-forming µX = µX ,b + qφnp , [6] potential, the hydration free energy can then be expressed (in ex the order given above) as (11) where µX ,b is the bulk hydration free energy in the absence of the net interfacial potential (figure 1 of ref. 29). The net potential φnp should be defined in such a way that it is independent ex µX = −kT ln p0(λ) − kT lnhexp[−εX /kT ]iλ + kT ln x0(λ), of ion identity. It is thus associated with longer-ranged electro- [7] static effects outside the first solvation shell. Ref. 46 displays a stable net potential beyond a cavity size of about 4 A.˚ The quasi- where p0(λ) is the probability to observe no solvent molecules chemical theory discussed below provides a natural definition within the cavity of size λ (with the ion not included in the sam- based on length-scale partitioning of the free energy into near pling), the second term is the free energy for inserting the ion and far-field contributions (47). into the system while the cavity is present, and x0(λ) is the prob- ex The real hydration free energy µX on the left side of Eq. 6 ability to observe no solvent molecules within the cavity of size λ can be obtained indirectly from experiment using a combina- with the ion included. tion of conventional ion hydration free energies (referenced to The first and third terms of Eq. 7 can alternatively be viewed the proton) and cluster free energies of formation for an array as the reversible work to produce a cavity of size λ in pure water of ions (48–50) (the cluster-pair approximation). We previously and minus the work to create a cavity of size λ with the ion at obtained a revised estimate, shifted by +1.7 kcal/mol from the the center, respectively. Operationally, the growth process can value obtained in ref. 48, for the hydration free energy of the be enacted using a smooth yet strongly repulsive potential (47); proton (36, 37) after isolating and eliminating an extrathermo- the limit of a purely repulsive wall yields Eq. 7. Since in the mid- dynamic assumption. That assumption results from replacing a dle term of Eq. 7 the waters are constrained to locations some difference with a sum (equations 16–19 in ref. 36) in the basic distance from the central ion, useful approximations can be used free energy expressions. We note that ref. 37 utilizes a correla- for its estimation (see below). This “mechanical” picture of the tion method and standard thermodynamic expressions to extract hydration process yields physical insights into the driving forces the single-ion quantities without further extrathermodynamic through analysis of the separate terms. Note that the final result assumptions. Thus, the results do not depend appreciably on the is independent of the details of the potential used to create the ion–water cluster size used in the analysis. cavities.

2 of 8 | www.pnas.org/cgi/doi/10.1073/pnas.2017214117 Shi and Beck Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 where unu iuain Fg ) h lsia iuain utilized simulations classical and The classical 1). ion–water from (Fig. the obtained simulations through (rdfs) quantum structure functions solvation distribution the radial display first We Discussion and net Results the of Eq. estimate in mechanical energy quantum free fully hydration potential a bulk for the allows obtain This we (Na Thus, cation a tion. for (F energies anion free the an energy of Na average free the an the compute of to hydration contribution the QCT for each compute to ulations the of estimate accurate energy. an free as hydration term bulk inner-shell is the contribution and energy leaving energy free zero, free electrostatic formation long-ranged cavity the Born-like bulk of a sum the the scale, equals length monovalent term this 6 all roughly inner-shell (at for energy the free scale hydration which length at common ions a monatomic is ref. there from observation suggests empirical value an consistent 47 addition, a In at range. stabilizes size size, this a cavity for of of function a center as the plotted at potential 6- net to 4- the the potential as in interfacial cavity defined the be to usefully contribution can solvent the that Eq. of insight side the right-hand first the from on arises that term contribution from third potential contribution interfacial potential 6), any to surface Thus, 4 no shell. (typically or shell little first the is in there number hydration the with tent (55). kcal/mol) (−6.3 water in water of and water, into cluster ion/water number, coordination that water, of density phase), liquid condensed bulk the the in number hydration (where probable phase most gas the in cluster water h n Beck and Shi Eq. 11, ref. in derived energy numbers. 1. Fig. eew tlz otcvt eso fEq. of version soft-cavity a utilize we Here potential, cavity the that shown have (46) simulations Classical small for that, found we (36), work previous In hog nisgtu xc eomlto fteslainfree solvation the of reformulation exact insightful an Through µ X ex h Na The K = n (0) φ −kT np − steeulbimcntn o omn h ion/n the forming for constant equilibrium the is + See . oeiiaeteitrailptnilcontribu- potential interfacial the eliminate to ) Orda itiuinfntosadrsligcoordination resulting and functions distribution radial -O ln K aeil n Methods and Materials ierange. size A ˚ n (0) ρ W n + µ + XW ex kT 7 o.Frteln-ag em we term, long-range the For ion. stesm as same the is p n µ ln (n stefe nryt netthe insert to energy free the is W ex ncasclsmltos.At simulations). classical in A ˚ p ) (n stepoaiiyt observe to probability the is stehdainfe energy free hydration the is n + ) hsyed h physical the yields This 8. stpclycoe sthe as chosen typically is o ute details. further for µ XW ex 7 n n IDsim- AIMD and n − ausconsis- values n µ W ex + ρ and ) W [8] 6. is - oa ukhdain(E(or Sum potential net Computed (bulk) Experiment (real) Experiment (corr) (FE hydration bulk Total oa ukhdainFE hydration bulk Total Corrections akn aiygot 14.46 growth Cavity growth Cavity parts Long-range Packing shell Inner Contribution from energy free hydration simulations bulk mechanical the quantum to the Contributions 1. Table 1). (Table term quantum packing the The for kcal/mol simulations. 14.46 enacted and quantum process are and results growth mechanical classical the the from during computed work cumulative simulations classical previous our 47. in ref. using as in produced methodology are same cavities pack- the The (the water respectively. pure contribution), in ing radius and contribution) inner-shell of grow- the involve minus cavities terms energy. physical these free compute QCT ing to the processes to numerical contributions The packing and inner-shell simulations. reproduced quantum is (see the structure by accuracy solvation calculations sufficient the to chemical that conclude are quantum perturbatively We those sodium–water below). electron address for correlated we interactions thus with D3 and overestimated, the likely 2.53 Methods, at we and maximum interactions, rials water–water peak dispersion and a D3 ion–water the observed employing the simulation for single correction a (In results. tal cin ewe h o n ae rdcdafis maximum first inter- a produced dispersion water D3 2.56 and 2.43 included at ion to that the 2.40 between simulation range actions recent the A in 2.38 of results (57). estimate experimental experimental previous recent and a to close and (57) 2.42 at 5.8. occurs of lation value a produces simulation classical The 5.3 58). from (57, ranging 5.5 results experimental to the vs. 5.3 the is simulation to tum Up 3.2 consistent however. at relatively models, minimum first quantum are and ion classical the the from between hydra- distance integrated vs. The The numbers results. tion simulations. classical the quantum quantum to the the relative in simulation softened in clearly is included structure and hydration not ion inner-shell the was between waters interaction in dispersion the discussed the As Methods, field. and force als ion–water the (56) and al. model et water Horinek (SPC/E) charge–extended point simple the 3) 7) 6) 5) iprincorr Dispersion corr Quantum corr Finite-size )Ttlfluctuation Total 9) 8) 1) 2) 4) ueia eut r rsne nFg yehbtn the exhibiting by 2 Fig. in presented are results Numerical the computing to related results numerical present we Next, h rtmxmmlcto fterfi h unu simu- quantum the in rdf the of location maximum first The oa ogrnebl E(6) FE bulk long-range Total hi µ δ hi hi hi 1 2 1 2 /2 ¯ LR ex β β 0,cav 0,cav cav 0,m hδ hδ 5) hc swl usd h ag fexperimen- of range the outside well is which (58), A ˚ (Na 2 2 = i i (F (Na cav 0,cav − (1) + + ) ) + ) (3) /2 ,tecodnto ubrfo h quan- the from number coordination the A, ,cnitn ihohrAM simulations AIMD other with consistent A, ˚ ˚ 94 clmlfrteinrselterm inner-shell the for kcal/mol −49.40 enbn energy bind Mean enbn nry70.42 energy bind Mean enbn energy bind Mean CDT (5W) CCSD(T) AT (6W) SAPT2 λ lcuto 18.35 16.02 Fluctuation Fluctuation L nry(bulk) energy aclto au,kcal/mol Value, Calculation enbind Mean [(1)− (8) = (4) rudtein(producing ion the around Sum − 16.04 . sdsusdin discussed As A.) − + ˚ (7) 2]218.31 (2)]/2 (9) (5) NSLts Articles Latest PNAS 1.17 /2 A ˚ [−0.38, −129.75 0. 3,48) (37, −101.5 −11.36 −29.67 −49.40 −93.14 −92.8 −90.7 −28.5 ≈2.1 −0.8 15(51) −91.5 −29.36 ± ± ± .7 V −0.47] ± ± ± ± ± ± ± ± Materi- ± ± ± ± (58) A | ± ˚ 0.43 0.01 0.09 Mate- 0.27 0.65 0.57 0.26 0.33 0.64 0.65 0.56 0.24 0.36 0.18 0.36 f8 of 3 0.41 A ˚

CHEMISTRY removed (Materials and Methods), the interaction energy takes the form

ε = qφ + εind, [9]

where εind is the induction part of the interaction. The potential φ here is the cavity potential from the unperturbed molecular charge distributions. It is expected that the electric ﬁeld at the center of an approximately spherical cavity is very small. Thus, for the long-range term, the major contribution to the induction energy is likely to arise from induced polarization of the water molecules and not of the ion. It is also plausible that the polarization of the water molecules is symmetric in the ion charge. Below we test these hypotheses. To estimate the long-ranged contribution free of interfacial potential effects, we consider the (Gaussian) approximation

1 µex ≈ (< ε > + < ε > ) LR 2 0,cav cav 1 Fig. 2. The cavity formation free energies as a function of coupling param- + < δε2 > − < δε2 > , [10] eter γ. The open symbols are for the classical force field, and the solid 4kT cav 0,cav symbols are for the DFT calculations. The circles are for the packing (PK) contributions, indicating that the SPC/E model gives a lower cavity forma- where the sampling includes the cavity. For a purely Gaussian tion free energy, which agrees with the observations by Galib et al. (59). The process, the second term is zero. Hence, that term can serve as an squares are for the inner-shell (IS) contributions, indicating that the SPC/E indicator of the accuracy of the approximation. In classical simu- water model produces a larger cavity formation free energy around the ion. lations, it is apparent from figure 7 of ref. 47 that the long-range interactions are accurately Gaussian for cations with a cavity size of roughly 4 A.˚ The computed quantum free energy contribution We now turn to the long-ranged contribution that carries the from the second-order difference in Eq. 10 is of low magnitude interfacial potential portion of the free energy. In a study that (1 kcal/mol). Thus, the above approximation is of good accu- analyzed ion hydration in water droplets (60), the electrostatic racy, which is not surprising since the waters are restricted to be potential profile outside a central cavity shows that at least 1,000 ˚ water molecule systems are required to obtain a stable potential greater than 4 A from the ion. profile in the bulk-like region of the liquid. For the vast majority Since we have available the difference of the two means δε¯, the of AIMD quantum simulations of water, systems of much smaller first-order expression above can be rewritten as size are modeled. Thus, there may be an indeterminate potential ex shift within the periodic simulation box due to the lack of con- µLR ≈<ε> 0,cav − δε/¯ 2. [11] vergence of the potential to a constant value moving away from the cavity or ion. In addition, there is a second factor in the quantum model that produces a potential shift addressed previously in classical simulations (for which the shift is of much smaller magnitude than in the quantum simulations) (28). Namely, the Ewald potential integrates to zero over the simulation box. As mentioned above, previous work (41) has revealed an enormous potential jump across the water liquid–vapor interface due to the distribution of matter in quantum mechanical systems. When considering a 4-A˚ cavity at the center of a modest-sized box (here L = 16 A˚ for an N = 128 water system), the potential at the cavity center is roughly −4 V. Then a simple calculation shows that the average value outside the cavity must be of magnitude +0.3 V to cancel the cavity value. This implies a shift of −0.3 V that should be included in estimating a real single-ion hydration free energy, and it is of the same magnitude as the interfacial potential quantity that we seek. Thus, it cannot be neglected. Rather than pursuing the daunting computational challenge of modeling very large systems (at least 1,000 water molecules) over long times (multiple nanoseconds) to obtain accurate estimates of the required shifts, here we eliminate the interfacial potential contribution by estimating the bulk single-ion hydration free Fig. 3. Logarithms of the distributions of ion–water interaction energies energy. obtained during sampling with and without the ion present at the cavity Fig. 3 displays the log of the interaction energy distribu- center. The blue line is for the uncoupled sampling, where there is no ion– tions for the long-ranged term computed both for sampling water interaction, while the black line is for the coupled sampling case. The blue dashed and black dashed-dotted lines are the Gaussian fits to with the ion coupled to the water molecules (left distribution) the data. The average interaction energies for the uncoupled sampling are and then uncoupled (right distribution). We note that the two −93.14 kcal/mol with a standard derivation of 4.56 kcal/mol and a fluctu- distributions are accurately Gaussian with comparable widths. ation term in the free energy of 16.02 kcal/mol; for the coupled sampling, We focus on the two mean quantities < ε > 0,cav and < ε > cav. the results are −129.75 kcal/mol and σ = 4.88 kcal/mol, with a corresponding Since the dispersion part of the ion–water interactions has been fluctuation term of 18.35 kcal/mol.

4 of 8 | www.pnas.org/cgi/doi/10.1073/pnas.2017214117 Shi and Beck Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 h n Beck and Shi shifted is that (37) energy proton free hydration the real the of of estimate experimental revised a = 2.1 + −92.8 more to contribu- due kcal/mol. energy 2.9 free interaction is correction dispersion the total of a of remainder tion to of leads the a result waters assuming of a distant integration 1) interac- producing (via of level, the estimate value SAPT2 to An the kcal/mol. contribution simulation at −0.64 AIMD dispersion computed of coupled was The portion fully tion cavity). a this no from closest estimate drawn (with the were To of waters configurations (12). six correction, 2.1-kcal/mol accurate above quite the is small of imation be to a expected is vs. is there (61). DFT that magnitude addition, in correction In overpolarization dielectric The (64). known finite-size screening. calculations the no to quantum with due higher-level shell positive assumes first is it roughly the since shift overestimate of outside an interactions correction likely kcal/mol, is pair energy 4.2 This (63). be free kcal/mol to 2.1 approximate estimated an then The was producing interactions. correction the energy range, dominate The longer total effects average. to induction on out that kcal/mol integrating 1.9 by assuming estimated by overbind was molecules to correction water accurate found full the the was at to theory computed ion of level were the DFT waters The five level. with CCSD(T) ion the for gies correction. the of dispersion portion and dispersion induction the to 2) due and mainly chemi- (CCSD) quantum calculations high-level cal from obtained energy free hydration Na the is the corrections for is dispersion value energy Marcus free without corresponding hydration bulk The estimate level 62). (6, QCT (B3LYP) kcal/mol −93.3 previous DFT A the is a at interactions. produces size dispersion together the of system results ion–water energy the for free this of hydration approximation for all bulk Taking (61) the kcal/mol. correction −29.36 Thus, self-energy kcal/mol. is finite-size in 18.31 means term two is the long-range between 3 shift the Fig. half while kcal/mol, −11.36 the for result positive large above.) the two (Note the 1. for Table F energies in interaction listed average are the ions for results The (out- of Na ion. results waters the energy six for induction nearest kcal/mol obtained the −4.38 we with Indeed, cavity). ions the to the side contribution of energy induction binding the the computed we test To approximation, hypotheses. the above the satisfies contribution induction the expansion. cumulant energy free the in terms odd higher-order Eq. in term Na the for computed approximate results to is step final The au eotdi isnire l 4) hfigtevlefrthe for value the Shifting (48). al. Na et Tissandier in reported value ihorpeiu siae rsn rmatraiemethods alternative from arising range 37). estimates the 36, (29, in previous potential our interfacial with effective the of of estimate an Eq. of side contribution). left potential the for kcal/mol −101.5 − h eutn orce oa ukfe nryetmt is estimate energy free bulk total corrected resulting The approx- first-order a correction, the of part dispersion the For ener- interaction the correction, quantum the estimate To of energy free hydration bulk the of analysis our complete To is ions two the for energy binding average The that assumption the on relies approach this of accuracy The hstepeetqatmsmltosadaayi produce analysis and simulations quantum present the Thus + . to −8.7 o asdb h ag eaiecvt oeta discussed potential cavity negative large the by caused ion o yti mutpoue elhdainfe nryof energy free hydration real a produces amount this by ion + . clml hsipista h nuto ato the of part induction the that implies This kcal/mol. −0.8 o,w opt )qatmceia orcin othe to corrections chemical quantum 1) compute we ion, 9 08ka/o- or kcal/mol-e −10.8 acl uigteaeaigpoes ln ihall with along process, averaging the during cancels 07ka/o Tbe1.W rvosyobtained previously We 1). (Table kcal/mol −90.7 96 clml(al ) ial,the Finally, 1). (Table kcal/mol −29.67 + + o and ion 15ka/o (51). kcal/mol −91.5 and 28ka/o nteasneof absence the in kcal/mol −92.8 > ε < .8to −0.38 F +1.7 − .6ka/o o the for kcal/mol −4.36 os h rtelectrostatic first The ions. 0,cav clmlrltv othe to relative kcal/mol 6 ta nldstenet the includes (that steaeaeo the of average the as .7V consistent V, −0.47 g F (r − ) u rvosrsl o h rsigpiti hw sadse vertical dashed a as shown 5.60 is at point energy crossing free 6.17 the 6.15 bulk at the for at line exact result for energy the previous is free crosses Our simulation bulk line classi- quantum computed horizontal The computed from the (black) data. energy crosses solid classical free tribution The the the bulk kcal/mol). quantum (−92.8 and of the calculation the quantum kcal/mol), dependence is in (−98.3 line size shift include cally predicted horizontal the that The (blue) from simulations molecules. dashed obtained classical water is from 512 data results and ion line with one blue (black) simulations dashed squares open quantum solid shifted The the the and simulations. simulations for quantum classical are and the for classical are in (blue) squares energies free bulk puted i.4. Fig. iea hc h aiyfrainadln-agd(Born-type) cavity long-ranged the and for formation cavity calculation QM the scaling the which for simple at larger a is size size fact, cavity slope In vs. the energy simulations. of experi- free magnitude inner-shell both the tension. the Thus, than of surface models. tension classical liquid the models surface and the quantum higher ment the of significantly indicate root a (67) exhibit cube simulations initio the ab of Recent inverse the proportional be to should radius crossing-point expected the model, oehtls hnta bevdfrtecasclsimulations classical the for observed 5.6 that (6.15 roughly than at less energy somewhat free bulk puted 66). (20, limit ear- thermodynamic noted the corrections finite-size to as on convergence work size, and extensive system been has of There independent (61). lier largely total the is depen- so energy magnitudes), size similar free (and long-range signs and opposite have inner-shell inner-shell dences the the of dependence Interestingly, size determined term. the as of slope), by simulations of classical results change a by QM results with the classical (also of kcal/mol the ion shift 4.1 vs. roughly downward the size a of necessitates system QM waters) smaller consisting The (512 The system simulations. waters. a 128 CP2K on and our performed in were generated simulations data (QM) inner-shell ical the of 8- extrapolation to linear 6- the that to 47 out ref. figures term from from clear is 6 cho- it the and Nonetheless, at 65). over 5 ref. terms of regime 1 nonlinear (figure two nonlinear range quasi-linearity of sen the addition a that the (beyond suggested from func- we resulted a size Later, as scales). cavity length energy small increasing free inner-shell of the observed tion we of 47, behavior ref. near-linear in a discussed simulations free classical hydration In bulk energy. the of estimate approximate but independent i.4sosta h eutn Mcreitret h com- the intersects curve QM resulting the that shows 4 Fig. mechan- quantum the using analysis similar a performed We an with results computational the of discussion the close We ) hsrsl sntsrrsn ic,i ipecontinuum simple a in since, surprising not is result This A). ˚ ieretaoaino h ne-hl otiuin otecom- the to contributions inner-shell the of extrapolation Linear A. ˚ eghsaei appropriate. is scale length A ˚ N N = = 2 aes h downward- The waters. 128 NSLts Articles Latest PNAS 1 lsia ne-hl con- inner-shell classical 512 .Ti eghsaeis scale length This A. ˚ hl that while A ˚ | f8 of 5 A. ˚

CHEMISTRY free energies balance predicts a crossing point within 0.1 A˚ of the FIST module of the ab initio molecular dynamics package CP2K 2.6.1 (73). observed length scale. With the QuickStep module, we performed all of the DFT-based simulations This extrapolation procedure provides an independent esti- for systems consisting of 128 waters and 1 Na+ ion fixed at the center of 1 128 4π 3 3 mate of the bulk hydration free energy, very close to a cubic box. The box size was determined by L = ( ρ + 3 rc ) , where the −3 −92.8 kcal/mol, that does not include any interfacial potential water number density is ρ = 33.3285 (nm) , rc = 4.1 γ (A),˚ and γ was varied effects. It is not as accurate as the direct estimate above, but from 0 to 1 during the thermodynamic integration. provides further support to the prediction of an effective surface The initial configurations were generated by classical molecular dynam- potential of water close to −0.4 V. ics simulations using the GROMACS 4.5.5 package (74), in which waters were modeled with the SPC/E force field (75) and the Na+ ion was modeled with Conclusions Lennard-Jones parameters taken from ref. 56 (set one). With 1 fs as the time + step, all classical simulations were run for 2 ns in the canonical (NVT) ensem- A previous quasi-chemical estimate for the Na ion bulk hydra- ble after 1 ns of equilibration in the isothermal–isobaric (NPT) ensemble. We tion free energy (−93.3 kcal/mol, B3LYP-DFT) (6, 62), which used the same classical simulation protocols as in our earlier work (47). The omits interfacial potential effects and ion–water dispersion inter- temperature was set at 300 K for the classical simulations. actions, is very close to our corresponding quantum mechanical For quantum simulations, we employed dual basis sets of Gaussian- result (−92.8 kcal/mol). The quasi-chemical calculation in ref. 62 type orbitals of shorter-range double zeta bases (DZVP-MOLOPT-SR-GTH) employed density functional theory methods for the inner-shell and plane waves (with 400-Ry cutoff) (76). Atomic cores were modeled term and a dielectric model for the long-range term. Thus, our with the Goedecker–Teter–Hutter (GTH) pseudopotentials (77). The revised result provides confirmation of the accuracy of the QCT since Perdew–Burke–Ernzerhof (revPBE) (78, 79) functionals were used for all we employ a consistent quantum mechanical description for the atoms in the system, while the D3 dispersion corrections (80, 81) were used only for water–water interactions. The Ewald method was applied interactions at all length scales. for the electrostatic interactions under periodic boundary conditions and The computed effective surface potential of water, obtained the Nose–Hoover´ thermostat chain (82) of length 3 was coupled to each from Eq. 6, is close to −0.4 V. This is consistent with pre- molecule to maintain a temperature of 330 K for all of the NVT ensem- vious estimates that involved cluster simulations employing ble simulations. This higher temperature mimics the excess kinetic energy polarizable classical models (68). The value is also consistent of the protons in water due to quantum zero-point fluctuations. The the- with our previous modified cluster-pair approximation result oretical rationale for employing a higher temperature to model nuclear (37) and several standard models of single-ion hydration free quantum effects can be found in ref. 83, p. 104. Similar techniques have energies that are free of interfacial potential effects (29, 69). been used previously in simulations of water (84), and the full path integral Further related work consistent with the present results is simulations have been compared to higher-temperature classical models in ref. 85. Due to the requirement of many simulations along the ther- found in other calculations of surface-potential–free hydra- modynamic integration paths to grow in the nanoscale cavities, we were tion free energies (70, 71). Finally, the quantum mechani- not able to employ the path integral formalism for incorporating nuclear cal result obtained here fully justifies the association of the quantum effects. The time step was taken as 0.5 fs and the configura- Marcus experimental values (51) with the bulk hydration free tions were saved every 10 fs. For the long-range contributions, two 30-ps energies. simulations (coupled and uncoupled) were implemented with the first The potential limitations of the present results are 1) finite- 10 ps to equilibrate the system. For the 23-step integration performed size effects in the simulations, 2) the lack of a full quantum for the packing contribution and the 27-step integration for the inner- treatment for the nuclear motions, 3) the pairwise assump- shell contribution, we performed 15-ps simulations with the first 5 ps for tion employed to estimate the induction/dispersion correc- equilibration. During preliminary simulations for the long-ranged contribution at tion, 4) the accuracy of the underlying DFT functional, and 400 K (to speed up the equilibration), it was observed that the D3 dis- 5) convergence of the simulations. The near equality of the persion energy between Na+ and waters is more negative than that computed free energy result and the tabulated Marcus value between F− and waters, in contrast to the fact that the F− ion is sig- (neither of which contains an interfacial potential contri- nificantly more polarizable than the Na+ ion. In a dispersion calculation bution) suggests that the resulting errors are not of large for the optimized geometry of a system consisting of one ion and 128 magnitude. waters (without WCA cavity potentials), we obtained a Na+–water dis- − The results indicate a long-ranged electrostatic potential shift persion energy of −10.6 kcal/mol and a F –water dispersion energy of −4.5 kcal/mol. With inclusion of a WCA cavity potential with λ = 4.1, the acting on ions near the water liquid–vapor surface over and + − above the strong inner-shell interactions that can display non- Na –water dispersion energy is −11.2 kcal/mol and the F –water dispersion energy is −1.5 kcal/mol. In the simulations of the present work, we Gaussian behavior. Such uniform shifts (independent of the ion thus removed the ion–water dispersion interactions and used the D3 cor- size) were seen previously in classical simulations of ions in bulk rection only for the water–water interactions. As discussed in Results and water (47, 69). Experimental evidence related to ion distribu- Discussion, this leads to structural results that agree significantly better with tions near hydrophobic surfaces (8, 30) and acid–base shifts of experiment. several pKa units relative to bulk water (31, 32) provides sup- To calculate the induction and dispersion interaction energies between port to these conclusions. The observation in ref. 30 that the the ion and the closest six waters in the long-ranged contributions, we anion in the tetraphenyl-arsonium/tetraphenyl-borate (TATB) employed the SAPT2 (86) module with the basis set aug-cc-pvdz (87) in the PSI4 package (88). The calculations that compare the induction interactions hydrophobic ion pair prefers the interface while spectroscopy + − indicates the anion is more strongly hydrated in bulk water (72) with the closest six waters outside the cavity for the Na ion and the F ion included 101 configurations, while the calculations of the dispersion inter- gives a clear indication of an electrostatic driving force at work actions with six waters at close contact included 590 configurations. We also near the interface. It is also interesting to note that, in recent calculated the interaction energy between the Na+ ion and five waters (101 7 spectroscopic experiments (35), electric fields of magnitude 10 configurations) at the CCSD(T) (89) and DFT levels with the same basis set as V/cm were estimated from Stark shifts of fluorescent probes near above using the PSI4 package. droplet surfaces, very close to the effective field observed in the present simulations. Ref. 35 ascribed the field to a buildup of Data Availability. All study data are included in this article. anions near the surface, but the above results imply there is a significant contribution from water itself. ACKNOWLEDGMENTS. We thank Lawrence Pratt, Susan Rempe, Christopher Mundy, Timothy Duignan, Dilip Asthagiri, Travis Pollard, and Paolo Car- Materials and Methods loni for helpful discussions. This material is based upon work supported by the National Science Foundation under Grants CHE-1565632 and CHE- In the present work we set the cavity size at λ = 4.1 A.˚ All classical results 1955161. The computations were performed at the Ohio Supercomputer were obtained just as in ref. 47. For the cavity potential, the purely repulsive Center. Y.S. acknowledges the support of the College of Arts and Sciences at Weeks–Chandler–Andersen (WCA) potential was implemented within the the University of Cincinnati.

6 of 8 | www.pnas.org/cgi/doi/10.1073/pnas.2017214117 Shi and Beck Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 7 .Hrnk .I aaklv .R ez ainldsg finfrefilsbsdon based fields force ion of design Rational Netz, R. R. Mamatkulov, I. S. Horinek, D. 27. Pratt, R. L. Paulaitis, E. M. Beck, L. T. 10. 2 .Mishra H. 32. hydroxide specific Strong Djerdjev, M. A. Beattie, K. J. Graciaa, A. Lachaise, J. Creux, P. 31. H H. P. Kastenholz, A. M. 28. from interface water–vapor Horv the L. of potential 26. surface The Ichiye, T. Cendagorta, R. J. 25. Asthagiri D. 11. 5 .Xog .K e,R .Zr,W i,Srn lcrcfil bevda h interface the at observed field electric Strong Min, W. Zare, N. R. Lee, K. J. Xiong, and H. acetic 35. of acidity Enhanced Guzman, I. M. Colussi, J. A. Pillar, A. E. Eugene, J. A. 33. Bastos-Gonz D. 30. From phenomena: Hofmeister of theory quantitative a Toward Beck, L. T. Pollard, P. T. 29. immeasurable?. the Measuring potentials: Interfacial Lyklema, hydration” J. ion specific 24. of modeling and “Theory Pratt, R. L. Chaudhari, I. M. You, X. 23. com- chemical different of of solvation regions between the potentials on electrostatic Are boundaries Pethica, distant A. of B. influence 22. The Weeks, D. J. Remsing, C. R. 21. H P. 20. Fawcett, R. interfacial W. and equilibrium 19. Phase interfaces: solution of potentials Contact Pratt, bulk R. L. to clusters 18. from thermodynamics hydration Single-ion solution. Chialvo, in A. ions A. individual Vlcek, of properties L. of 17. use and evaluation The Conway, broken E. of role B. The Weeks, 16. D. J. Mundy, J. C. Schenter, K. G. Baer, D. calculations M. dynamics Remsing, molecular C. initio R. Ab Lilienfeld, 15. von A. potential O. Rempe, the B. S. Leung, of K. partitioning 14. energetic by Bucher energies D. free 13. Hydration Beck, L. T. 12. 4 .K Lee K. J. 34. h n Beck and Shi .W uz pcfi o fet nclodladbooia systems. biological and colloidal in effects ion Experimental Specific interface: Kunz, W. air–water the 4. at effects ion “Specific Henry, L. C. Craig, V. Nostro, Lo 3. P. Ninham, W. B. 2. Marcus, Y. 1. .A .Jb,W u,H .Aln niomna hmsr tvprwtrinterfaces: vapor/water at chemistry Environmental Allen, C. H. Hua, W. Jubb, M. A. 9. between interface electrochemical Hofmeister the with of affairs Examination Richmond, of L. state G. Conboy, present C. The J. Ninham, 8. W. Hydration B. Rempe, Nostro, B. Lo S. P. Muralidharan, Kunz, A. W. Pratt, R. 7. L. Vanegas, M. J. Chaudhari, I. M. 6. in electrolytes” of modeling “Molecular Borodin, O. 5. p 191–214. pp. in studies” 2010). UK, Cambridge, Press, University hroyai ovto properties. solvation thermodynamic (2013). Solutions Molecular of spectroscopy. generation frequency Chem. sum vibrational from Insights (1997). generation. 983–990 harmonic 101, second by solutions electrolyte immiscible two effects. channels. ion membrane York, by New mimicry (Springer, Eds. Ue, M. Borodin, O. 371–401. pp. Xu, 2014), K. NY, Jow, R. T. Batteries, Lithium-Ion Sci. Interface U.S.A. interfaces. air/water and oil/water (2009). pristine 14146–14150 the at binding ion hydrophobicity. and (2016). 19–28 hydration 23, of role central The energy free cation. hydration sodium The the II. simulations. of molecular from energies free solvation ionic solvation. ion on influence its and fluids polar (multi) simulations. classical (2017). channel. channels. ion fauosmicrodroplets. aqueous of microdroplets. water. of surface the on acids pyruvic (2016). thermodynamics. to effects quantum 434–442. pp. 2014), Australia, in and extended revisited. reconsidered, consequences principle its Gibbs–Guggenheim The measurable? position particles. charged Quantities 2011). Thermodynamics Elusive to Approaches Details Microscopic Modern 2004). to tions fields. electric modeling. molecular from (2016). insights Recent solutions: Chem. Solution models. water quantum and classical in Lett. cavity Chem. spherical Phys. a of solvation in symmetry energies. free hydration ion of theorem. distribution .Nna,P oNsr,Es Cno or ulsig Brisbane, Publishing, Court (Connor Eds. Nostro, Lo P. Ninham, B. Incognita, Aqua nnegr .Reif, M. unenberger, ¨ 87–88 (2012). 18679–18683 109, 0–3 (2012). 107–130 63, t,T e,M agi .Plei h ao-iuditraeptnilof potential interface vapor-liquid The Palmeri, J. Manghi, M. Beu, T. ath, ´ ur pn oli nefc Sci. Interface Colloid Opin. Curr. ipy.Chem. Biophys. pnaeu eeaino yrgnprxd rmaqueous from peroxide hydrogen of generation Spontaneous al., et ,Bøse aiiyo h i–ae interface. air–water the of basicity Brønsted al., et o Solvation Ion oaiainefcsadcag rnfri h cApotassium KcsA the in transfer charge and effects Polarization al., et .Kn,E.(ol cetfi,NwYr,N,2010), NY, York, New Scientific, (World Ed. Kunz, W. Effects, Ion Specific o eetvt rmlclcngrtoso iad nsltosand solutions in ligands of configurations local from selectivity Ion al., et 43 (2010). 34–39 15, hm hs Lett. Phys. Chem. .Py.Chem. Phys. J. iud,Sltos n nefcs rmCasclMcocpcDescrip- Macroscopic Classical From Interfaces: and Solutions, Liquids, rc al cd c.U.S.A. Sci. Acad. Natl. Proc. lz .P L. alez, ´ 2–7 (1978). 721–770 7, 7727 (2014). 2767–2774 5, .Sa.Phys. Stat. J. .Py.Ce.B Chem. Phys. J. .Ce.Phys. Chem. J. .Sa.Phys. Stat. J. CmrdeUiest rs,Cmrde K 2006). UK, Cambridge, Press, University (Cambridge Jh ie,NwYr,N,1985). NY, York, New Wiley, (John rzFets .Dumn,J aad,In tinterfaces: at Ions Faraudo, J. Drummond, C. erez-Fuentes, ´ 9–0 (2006). 292–301 124, nnegr optto fmethodology-independent of Computation unenberger, ¨ .Py.Ce.Lett. Chem. Phys. J. hs hm hm Phys. Chem. Chem. Phys. 53 (1992). 25–33 96, igeInSlain xeietladTheoretical and Experimental Solvation: Single-Ion 4–6 (2019). 743–763 175, .Ce.Phys. Chem. J. – (2010). 1–7 485, oeua ocsadSl Assembly Self and Forces Molecular 3–5 (2011). 335–354 145, 251(2006). 224501 124, nu e.Py.Chem. Phys. Rev. Annu. h oeta itiuinTermadModels and Theorem Distribution Potential The 1492 (2015). 9114–9122 119, .Ce.Phys. Chem. J. Langmuir ur pn oli nefc Sci. Interface Colloid Opin. Curr. –8(2004). 1–18 9, Ofr nvriyPes e ok NY, York, New Press, University (Oxford 99–99 (2019). 19294–19298 116, 057(2009). 204507 130, 4372 (2020). 7423–7428 11, 3791 (2018). 9307–9313 34, ur pn oli nefc Sci. Interface Colloid Opin. Curr. RCPbihn,Cmrde UK, Cambridge, Publishing, (RSC 2366 (2007). 6253–6262 9, 257(2009). 124507 130, lcrltsfrLtimand Lithium for Electrolytes li h Equil. Ph. Fluid .Ce.Phys. Chem. J. 6–8 (2020). 461–484 71, .Py.Ce.B Chem. Phys. J. rc al cd Sci. Acad. Natl. Proc. Substantia ur pn Colloid Opin. Curr. nu e.Phys. Rev. Annu. .Py.Ce.B Chem. Phys. J. 154702 138, 110–118 23, (Cambridge 58–75 407, 75–93 1, 113, J. J. 0 .A oad .R ilas nipoe lse arcreainmto o obtain- for method correlation pair cluster improved An Williams, R. E. Donald, A. W. 50. 2 .Vra .B ep,Srcua rniin nincodnto rvnb hne in changes Lee by M. driven H. coordination ion 63. in hydration. transitions ionic Structural Rempe, of B. energy S. Varma, Free S. Garcia, E. 62. A. Pratt, R. L. Hummer, for G. quadrupole molecular 61. water the of importance The Beck, L. T. Shi, Y. Doyle, C. C. 60. Galib M. 59. Galib M. 58. free solvation ion single Real Mundy, J. C. Schenter, K. G. Baer, D. M. Duignan, T. T. 52. Marcus, Y. 51. and ions of energies free solvation Aqueous Truhlar, G. D. Cramer, J. C. Kelly, P. C. 49. non-uniform and uniform in mobility and solvation Electrostatic Matyushov, water bulk V. in D. hydration ion 45. on potentials interfacial water of influence The Beck, L. T. 44. ener- free solvation Electrostatic Mundy, J. C. Schenter, K. liquid- G. a Baer, at D. difference M. Duignan, potential T. T. electrostatic surface the 43. of the origin Understanding the in On Schenter, Roux, orbital K. B. G. Harder, molecular Mundy, E. occupied J. C. 42. highest Kuo, the W. I. of Kathmann, position M. S. the 41. On Sprik, M. Hunt, P. 40. electro- the and hydration proton of thermodynamics The Beck, L. T. the for Pollard, approximation P. T. pair cluster 37. the of analysis Quasichemical Beck, L. T. Pollard, T. 36. 5 .P olr,T .Bc,R-xmnn h tetraphenyl-arsonium/tetraphenyl-borate the Re-examining Beck, L. T. density Pollard, exchange-corrected P. T. and 65. Dispersion- Rempe, B. S. Rogers, M. D. Soniat, M. 64. Na of structure Hydration Klein, L. M. Carnevale, V. Bankura, A. 57. Horinek D. ab using 56. modeled water of Thermodynamics Communication: Asthagiri, D. Weber, V. 55. H H. P. Prasetyo, N. 54. H H. P. Hofer, S. T. 53. hydration. ion Tissandier in potentials D. M. interfacial and 48. scales Length Beck, L. T. descriptions Shi, Y. continuum macroscopic 47. and molecular of Convergence Ashbaugh, S. H. 46. Lifshitz, E. Pitaevskii, L. Landau, D. L. 39. Schmickler, W. 38. 6 .J o,P .Gise,Itrailinslain bann h hroyai limit thermodynamic the Obtaining solvation: ion Interfacial Geissler, L. P. Cox, J. S. 66. 0 .Ataii .R rt,H sbuh bouehdainfe nriso os ion– ions, of energies free hydration Absolute Ashbaugh, H. Pratt, R. L. com- Asthagiri, consistent D. A 70. energies: free hydration ion Single Asthagiri, D. Ashbaugh, S. H. 69. R F. Houriez, C. 68. K D. T. Bonn, M. Ohto, T. Nagata, Y. 67. n h bouepoo yrto nryadetap vlae iha expanded an with evaluated enthalpy and set. energy data hydration proton absolute the ing cation-(water) water. liquid (2017). 084504 theory. functional (2014). density 1448–1456 modern on based dynamics molecular initio simulation. mechanical quantum with energies 2015). solvation aqueous absolute the for value proton. the accurate of an energy free on based clusters ion-water data. solvation (1998). cluster-ion from solvation of energy proteins. to ions simple From fields: electric interfaces. near and theory functional density with dynamics molecular interactions. using spheres hard charged of gies interface. vacuum water. of potential ions. simple of solutions aqueous 8. vol. 1984), UK, Oxford, 2, ed. Press, (Pergamon water. of potential surface chemical hydration. proton of thermodynamics TT)hptei o igeinslainfe energies. free solvation single-ion for hypothesis (TATB) hydration. (2015). ion sodium for theory functional solvation. hydrophobic simulations. initio single-electrode and simulations. energy dynamics free molecular Li hydration aqueous absolute of the potential of Calculation principles: principles: first hydration. from potassium electrode and hydrogen sodium of the Phys. simulations of free-energy potential MD redox QM/MM and water, of tial Phys. hydration. ion of 1996). rmmlclrsimulations. molecular from (2018). ae lses n usceia theory. quasichemical and clusters, water simulation. molecular (2008). classical 204501 and experiment between parison the and solution. approximation in pair energy cluster free The Gibbs drops: hydration nano proton water in potential surface water interface. water-air the optto o iadbinding. ligand for competition (1996). 1206–1215 100, interface. liquid-vapor the near ions Chem. on Phys. J. acting shifts potential interfacial estimating 284(2018). 222814 148, (2013). 044504 139, eiiigtehdainsrcueo qeu Na aqueous of structure hydration the Revisiting al., et .Py.Ce.B Chem. Phys. J. asdniyflcutosi unu n lsia ecitosof descriptions classical and quantum in fluctuations density Mass al., et tal. et pcfi o dopina h i/ae nefc:Terl of role The interface: air/water the at adsorption ion Specific al., et osi ouinadTerSolvation Their and Solution in Ions .Ce.Phys. Chem. J. .Ce.Phys. Chem. J. 1−6 3835 (2019). 3348–3358 123, a,V alt .Munr .Msla o yrto reeege and energies free hydration Ion Masella, M. Mautner, M. Vallet, V. eal, nihsit h tutrs nreis n irtoso monovalent of vibrations and energetics, structures, the into Insights , ´ nefca Electrochemistry Interfacial .Py.Ce.B Chem. Phys. J. h rtnsaslt qeu nhlyadGbsfree Gibbs and enthalpy aqueous absolute proton’s The al., et nnegr bouepoo yrto reeeg,sraepoten- surface energy, free hydration proton Absolute unenberger, ¨ .Ce.Phys. Chem. J. .Ce.Phys. Chem. J. clusters. .Py.Ce.B Chem. Phys. J. nnegr .S oe,Snl-o hroyaisfo first from thermodynamics Single-ion Hofer, S. T. unenberger, hm hs Lett. Phys. Chem. ¨ + hm hs Lett. Phys. Chem. .Ce.Phys. Chem. J. 38–30 (2010). 13189–13200 114, sn biii unu ehnclmlclrmechanical mechanical/molecular quantum initio ab using .Py.Ce.B Chem. Phys. J. .Py.Ce.A Chem. Phys. J. 676(2017). 161716 147, 451(2017). 244501 146, .Ce.Phys. Chem. J. .A.Ce.Soc. Chem. Am. J. .Ce.Ter Comput. Theory Chem. J. 411(2010). 141101 133, 263(2008). 12B613 129, hm hs Chem. Phys. Chem. 2573 (2000). 7235–7238 104, he ufc eso fa ntolqi ae at water liquid initio ab of tension Surface uhne, ¨ 3947 (2011). 4369–4377 115, .Ce.Phys. Chem. J. –3(2013). 1–13 561–562, 075(2016). 204705 144, .Ce.Phys. Chem. J. 7–8 (2009). 173–183 479, .Ce.Phys. Chem. J. 283(2018). 222823 148, 66–68 (2006). 16066–16081 110, lcrdnmc fCniuu Media Continuous of Electrodynamics Biomicrofluidics 9925 (2004). 2949–2958 108, .Ce.Ter Comput. Theor. Chem. J. Ofr nvriyPes xod UK, Oxford, Press, University (Oxford hm Sci. Chem. .Ce.Phys. Chem. J. 50–51 (2008). 15405–15419 130, 852(2014). 18C512 141, NSLts Articles Latest PNAS .Py.Ce.A Chem. Phys. J. 257(2014). 224507 140, 8510 (2005). 1805–1808 6, Jh ie,Hbkn NJ, Hoboken, Wiley, (John 7220 (2003). 2702–2708 119, .Ce.Phys. Chem. J. 1164 (2017). 6131–6140 8, 4365 (2018). 6443–6459 14, 616(2019). 064106 13, 754(2019). 174504 151, + + . .Ce.Phys. Chem. J. .Ce.Phys. Chem. J. n K and 7787–7794 102, o.Phys. Mol. .Py.Chem. Phys. J. 2958–2967 11, 222830 148, + | .Chem. J. .Chem. J. rmab from f8 of 7 146, 112, 129,

CHEMISTRY 71. J. R. Pliego, N. F. Carvalho Jr., Cluster-continuum quasichemical theory calculation 80. S. Grimme, Accurate description of van der Waals complexes by density functional of the lithium ion solvation in water, acetonitrile and dimethyl sulfoxide: An abso- theory including empirical corrections. J. Comput. Chem. 25, 1463–1473 (2004). lute single-ion solvation free energy scale. Phys. Chem. Chem. Phys. 17, 26745–26755 81. S. Grimme, J. Antony, S. Ehrlich, H. Krieg, A consistent and accurate ab ini- (2015). tio parametrization of density functional dispersion correction (DFT-D) for the 94 72. R. Scheu et al., Charge asymmetry at aqueous hydrophobic interfaces and hydration elements H-Pu. J. Chem. Phys. 132, 154104 (2010). shells. Angew. Chem. Int. Ed. 53, 9560–9563 (2014). 82. G. Martyna, M. Klein, M. Tuckerman, Nose-Hoover´ chains: The canonical ensemble via 73. J. Vandevondele, M. Sprik, A molecular dynamics study of the hydroxyl radical in continuous dynamics. J. Chem. Phys. 97, 2635–2643 (1992). solution applying self-interaction-corrected density functional methods. Phys. Chem. 83. L. D. Landau, E. M. Lifshitz, Statistical Physics (Pergamon, New York, NY, 1980). Chem. Phys. 7, 1363–1367 (2005). 84. M. Chen et al., Ab initio theory and modeling of water. Proc. Natl. Acad. Sci. U.S.A. 74. B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, Gromacs 4: Algorithms for highly 117, 10846–10851 (2017). efficient, load-balanced, and scalable molecular simulation. J. Chem. Theor. Comput. 85. R. Car, J. A. Morrone, Nuclear quantum effects in water. Phys. Rev. Lett. 101, 017801 4, 435–447 (2008). (2008). 75. H. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, The missing term in effective pair 86. E. G. Hohenstein, C. D. Sherrill, Density fitting of intramonomer correlation effects in potentials. J. Phys. Chem. 91, 6269–6271 (1987). symmetry-adapted perturbation theory. J. Chem. Phys. 133, 014101 (2010). 76. J. VandeVondele, J. Hutter, Gaussian basis sets for accurate calculations on molecular 87. T. H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I. The systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007). atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989). 77. S. Goedecker, M. Teter, J. Hutter, Separable dual-space Gaussian pseudopotentials. 88. R. M. Parrish et al., Psi4 1.1: An open-source electronic structure program emphasizing Phys. Rev. B 54, 1703–1710 (1996). automation, advanced libraries, and interoperability. J. Chem. Theor. Comput. 13, 78. J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made 3185–3197 (2017). simple. Phys. Rev. Lett. 77, 3865–3868 (1996). 89. K. Raghavachari, G. W. Trucks, J. A. Pople, M. Head-Gordon, A fifth-order pertur- 79. Y. Zhang, W. Yang, Comment on “generalized gradient approximation made simple”. bation comparison of electron correlation theories. Chem. Phys. Lett. 157, 479–483 Phys. Rev. Lett. 80, 890 (1998). (1989).

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