Free Energy Profile of NaCl in Water: First-Principles Molecular

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Free Energy Profile of NaCl in Water: First-Principles Molecular Dynamics with SCAN and #B97X-V Exchange-Correlation Functionals Yi Yao, and Yosuke Kanai J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b00846 • Publication Date (Web): 28 Dec 2017 Downloaded from http://pubs.acs.org on December 29, 2017

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Journal of Chemical Theory and Computation

Free Energy Profile of NaCl in Water: FirstPrinciples Molecular Dynamics with SCAN and ωB97X-V Exchange-Correlation Functionals

Yi Yao and Yosuke Kanai

Department of Chemistry University of North Carolina at Chapel Hill

Abstract

Properties of water and aqueous ionic solutions are of great scientific interest because they play a central role in the atmosphere, biological environments, and various industrial processes. Employing two advanced exchange-correlation (XC) approximations, ωB97X-V and SCAN, in first-principles molecular dynamics simulations, we calculate the potential of mean force of NaCl in water as a function of the ion separation distance. Compared to the commonly-used GGA-PBE functional, both of these XC functionals perform much better in simulating liquid water at room temperature for obtaining structural properties. The potential of mean force of

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NaCl in water exhibits two minima corresponding to two distinct types of ion pairing. The ωB97X-V predicts that the contact ion pair is energetically more stable than the solvent separated ion pair. The SCAN functional, however, predicts the opposite stability order, similarly to other XC functionals like the PBE. This is notable especially since classical molecular dynamics simulations with widely-used force field models predict greater stability for the contact ion pair. We also discuss how electronic structure of water molecules and ions depend on the XC approximations. The ωB97X-V and SCAN approximations noticeably improve the description of electron charge on Cl- ion in water while the charge on Na+ ion does not vary appreciably among the three XC functionals.

Introduction Properties of water and aqueous ionic solutions are of great scientific interest because they play a central role in the atmosphere, biological environments, and various industrial processes3-10. More than a century ago, the so-called Hofmeister series were introduced to correlate the ability of different salts to denature proteins. The concepts of structure-making and structure-breaking properties for different ions were put forward to explain the ordering of the Hofmeister series at a molecular level13. Different ions are thought to either strengthen or weaken the hydrogen-boding water network, and this classification on ions remains a largely debated concept even today14-15. At the same time, increasingly larger number of experimental observations suggest that the combined effects of cations and anions on the dynamics and hydrogen-bond network of waters are not additive16-17. Central to understanding such cooperative effects of cations and anions is ion pairing. The problem of ion pairing in electrolyte solutions in


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general has been of great scientific interest for many decades, and often the relative permittivity of the solvent is used to infer the presence of the ion pairs16, 18. Of particular interest are solutions of relatively simple salts consisting of alkali cations and halogen anions for developing conceptual understanding and also for many industrial and physiological applications19-27. In particular, NaCl solution is a prototypical case. There exist various experimental indications of ion pairing, through approaches such as conductometry, ultrasonic relaxation, dielectric relaxation spectroscopy, etc28-33. At the same time, direct experimental evidence from neutron diffraction or X-ray scattering is not straightforward because of their reliance on molecular dynamics simulations for interepreation34. Furthermore, molecular dynamics simulation itself is quite complicated for investigating NaCl ion pairs because there exist two distinct minima called the solvent-shared ion pair (SSIP) and the contact ion pair (CIP) in the free energy profile as a function of the Na-Cl separation distance11, 35-36. Classical molecular dynamics (MD) simulations with widely-used force field models such as CHARMM37, etc predict greater stability for the CIP than the SSIP, and the present-day firstprinciples MD simulations using density functional theory (DFT) with generalized gradient approximations (GGA) to the exchange-correlation (XC) functional show the opposite stability as discussed later. Relative stability of the CIP and SSIP in molecular dynamics simulations is quite sensitive to the underlying Hamiltonian, and accurate modeling of the aqueous NaCl solution has proven quite difficult in practice because a given inter-atomic potential needs to be able to describe various different types of interactions accurately (ion-ion, ion-water, water-water interactions, etc) to predict the correct energetics among SSIP, CIP, and the dissociation limit in the free energy profile2, 38-41. For example, the work by Ghosh, M. K. et al suggests the interionic hydration structure plays an important role in describing the Na-Cl pair in water42. We also


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remark here that a recent combined spectroscopy-theory study by Hou, et al. shows that the CIP and SSIP are nearly degenerate in energy for small clusters of NaCl(H2O)9-1243. Accurate modeling of the NaCl free energy profile would greatly advance our understanding of ion pairing at the molecular level. It will also benefit development of our fundamental understanding of reaction coordinate in solution chemistry. For example, Geissler and co-workers have shown that the reaction coordinate for ion pair formation must include both solvent and the solute degrees of freedom, using NaCl as an example44-45. Accurate description of the free energy profile for the NaCl separation would be an important step in obtaining the whole picture of the NaCl ion pair formation, both thermodynamic and kinetic aspects. In context of using classical molecular dynamics (MD) simulations to study aqueous solutioins, density functional theory (DFT)-based first-principles MD have been often used to assess accuracies of underlying the potential energy function11,

46-47

.

FPMD has been a

successful approach for investigating various physical and chemical properties in many different fields ranging from biology to chemistry to condensed matter physics48-54. At the same time, the accuracy of the FPMD simulation certainly depends on the underlying exchange-correlation approximation. In a recent 2015 perspective article by Jungwirth and co-workers46, this important point was cleverly summarized by asking “If DFT should serve as a “policeman” of the empirical force fields, then who checks the policeman?”. Establishing accurate predictive FPMD simulation results for water and aqueous solutions remain a great challenge even today despite recent great progresses55-56. An important challenge is to overcome limitations of the present-day generalized gradient approximations (GGA) to the exchange-correlation (XC) functional in these DFT-based FPMD simulations57-58. Although the GGA approximation represents a great compromise between the accuracy and computational efficiency, which is


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crucial for obtaining statistically meaningful results in MD simulations, most GGA XC functionals suffer from several shortcomings such as appreciable self-interaction error and the inadequate treatment of dispersion interaction56, 59. These aspects appear to be quite important in the description of liquid water60-61. Popular non-empirical GGA XC functionals such as the PBE approximation62, for example, lead to an over-structure of liquid water at the room temperature, and it is common to simulate the liquid water at an elevated temperature to mimic the room temperature water using the PBE approximation in FPMD simulations57. Indeed, modeling of NaCl in water using FPMD simulations also has largely relied on artificially elevating the temperature to mimic the room temperature behavior57-58. In the last several years, FPMD simulations have been improved beyond the over-structured PBE description of liquid water by using hybrid XC functionals (thanks to various novel computational techniques to achieve greater efficiency for evaluating the Hartree-Fock exchange term), which reduces the selfinteraction error, as well as through including of additional dispersion correction. As these recent results are encouraging, the extent to which the hybrid functionals such as PBE0 and adding a separate dispersion interaction correction improve over the PBE description call for further investigations, especially for aqueous solutions56. Also, FPMD simulations typically neglect quantum nature of hydrogen atoms, and Path-Integral simulations indeed show that part of the over-structuring of the liquid water within the PBE description is due to neglecting the nuclear quantum effects63-64. At the present time, combination of exact exchange (EXX) and randomphase approximation (RPA) correlation is perhaps the most accurate approximation to the XC functional for large extended systems65. Del Ben, et al. has reported the EXX-RPA results based on GGA-PBE Kohn-Sham wavefunctions1, 65-67. Their comparison between EXX-RPA and MP2 results show a good agreement between the two for structural properties such as the oxygen-


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oxygen pair correlation function in pure water. In regard to simulations of liquid water based on MP2 calculation instead of using DFT as typically done, we note that MP2 simulation results by Del Ben, et al.1 and by Willow, et al.68 appear to disagree, and further investigations are warranted69. For improving the XC approximation in the context of DFT-based FPMD simulations, two very promising XC functionals have emerged in the last few years, with distinctively different philosophies in their development. ωB97X-V functional was reported in 2014 by Mardirossian and Head-Gordon70-71, and it is a 10-parameter empirically-tuned functional of the range-separated hybrid GGA type with the non-local dispersion correction by Vydrov and van Voorhis72. The parameters were optimized against a very large test set of energetic properties of molecules and molecular reactions. Related work by the same authors also shows that the ωB97X-V functional is the best performing one by comparing a large number of candidate functionals at the range-separated hybrid GGA level with dispersion correction (4th rung of the Perdew’s “Jacob’s Ladder” of DFT”)73. This particular functional is especially appealing for the present study because it has shown to be quite accurate for relevant molecular interactions (e.g. H2O-H2O, H2O-Na+, and H2O-Cl- interactions) that are involved in describing aqueous NaCl solution71. In 2015, Sun, Ruzsinszky and Perdew reported a new non-empirical meta-GGA functional, called Strongly Constrained and Appropriately Normed (SCAN)74-75, following the non-empirical philosophy76 in XC functional development. This SCAN functional has an additional dependence on the reduced kinetic energy density beyond the density gradient, and the SCAN approximation is particularly interesting because it satisfied all known constrains at the semilocal functional level of meta-GGA. Interestingly, the SCAN functional appears to improve the description of water clusters substantially (even over PBE0), yielding the results that are


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Figure 1. (Left) : The oxygen-oxygen radial distribution functions goo(r) for pure liquid water simulation at 300K, with SCAN, ωB97X-V, and PBE XC functionals. The MP2 result from Ref.1 using Monte Carlo simulation at 295 K with the density of 1.02 g/cm3 is shown for comparison. The experimental result from X-ray diffraction data is taken from Ref.12. (Right) Distributions of molecular dipole moment magnitude for individual water molecules with the SCAN, ωB97X-V, and PBE XC functionals. Maximally-localized Wannier functions are used to obtained the dipole moments. a ref.1 b. ref. 12 comparable to CCSD(T) level of quantum chemical calculations75. For liquid water, SCAN functional has also shown improved structural properties77. In this paper, we report performance of these two advanced XC functionals, ωB97X-V and SCAN, in the context of FPMD simulations for calculating the potential mean force of NaCl in water.

Results and Discussion 1. Liquid Water at 300K We first examined how pure liquid water structure differs among the XC functionals. The over-structure is a well-known problem for the popular PBE GGA functional78-79. The SCAN functional has shown to be quite accurate for relative energies of several bulk ice structures75, and ωB97X-V functional also appears to provide great energetics for small water clusters80. Figure 1 (Left) shows the oxygen-oxygen radial distribution function from our 30-ps FPMD


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simulations. With the PBE functional, the oxygen-oxygen radial distribution function shows the peak positions and heights that are in agreement with the literature values79, showing the wellknown over-structured features. For comparison, we also show the result from MP2 calculation with Monte Carlo ensemble by Del Ben, et al1. The ωB97X-V and SCAN functionals clearly show much better agreement to the MP2 result than the PBE. The missing dispersion interaction in typical GGA functionals has been shown as being partly responsible for over-structured water in the literature

61

, and this could partially explain a better structure for SCAN and ωB97X-V.

The ωB97X-V approximation includes the VV10 dispersion term70, and SCAN can describe some dispersion interaction81-82. The coordination numbers of water molecules were calculated to be 4.1, 4.4, and 4.3 for the PBE, ωB97X-V, and SCAN functionals, respectively. Figure 1 (right) shows the distribution of dipole moment on individual water molecules using the maximally localized Wannier functions (MLWF) functions83. The average dipole moment was determined to be 3.25, 3.03, and 3.09 for PBE, ωB97X-V, and SCAN functionals, respectively. For the SCAN and ωB97X-V functionals, distributions of the dipole moment are somewhat narrower and their means are noticeably shifted to a lower value. The larger dipole moment for the PBE water is likely a result of the over-structure84.


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Figure 2. (Left) Potential energy curve of an isolated Na-Cl dimer in vacuum as a function of the separation distance according to several different XC approximations. The separation distance of 6 Å is used to align the curves for the comparison. The MP2 and ωB97X-V results are on top of each other at this scale. (Right) Deviations from the MP2 curve as a function of the separation distance. A horizontal purple line of E - E(MP2) = 0 is plotted to guide the comparison.

2. Potential Energy Curve of NaCl in Vacuum In order to put our results for Na-Cl in water using the SCAN and ωB97X-V functionals in perspective, we first discuss how different XC approximations perform for the potential energy curve for NaCl dissociation in vacuum85. MP2 calculation is used as the reference, and the same basis set is used for all calculations (see Supporting Informaiton for comparison between MP2 and CCSD(T) calculations). Figure 2 shows how the potential energy curves deviate from the MP2 result as a function of the Na-Cl separation distance for various DFT-XC functionals. The PBE GGA (as well as BLYP) results deviate quite substantially from the MP2 result, and the SCAN meta-GGA result is much closer to the PBE0 hybrid functional. The ωB97X-V functional is found to perform extraordinarily well especially in the physically important range of r(Na-Cl ) down to 2.5Å. Energy difference between the ωB97X-V and MP2 calculations is less than 0.25 kcal/mol. Recently, Mao and et. al71, have shown a similar test of


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the ωB97X-V for H2O-H2O, H2O-Na+, and H2O-Cl- interactions, and their work also showed that the ωB97X-V result is in an excellent agreement (< 0.20 kcal/mol) with the high-level reference based on CCSD(T) and MP2 calculations. We show equivalent comparisons for these interactions using the computational setup we used in this work in Supporting Information for convenience. Having observed these promising results for the SCAN and ωB97X-V XC approximations, we now proceed with computationally much more intensive FPMD simulations of aqueous NaCl solution for calculating the potential of mean force. 3. Potential of Mean Force for NaCl in Water Obtaining a converged pair correlation function between Na and Cl ions using a direct NVT simulation of aqueous NaCl solution is rather difficult. This is due to the fact that there exist two free energy minima that correspond to the contact ion pair (CIP) and the solvent separated ion pair (SSIP), and their relative stability and the energy barrier separating them depend significantly on the underlying Hamiltonian as will be shown in the following. Figure 3 shows the potential of mean force (PMF) as a function of the Na-Cl separation distance. In addition to our results using the ωB97X-V, SCAN, and PBE functionals, we also show available results from the literature using revPBE-D32 and BLYP11 functionals. Results from classical MD simulations are also shown for the fixed charge model of SPC/F w/ HMN86-88 and with a recent polarizable/charge-transfer model called FQ-DCT2. In general, all the calculated PMFs have a similar shape for a CIP minimum and another broader SSIP minimum. As can be seen, the relative energies and the energy barrier between the two minima vary quite substantially among them. Table 1 summarizes several key values from the calculated PMFs; Na-Cl distances for the CIP/SSIP minima, energy barrier from the CIP to the SSIP, and the energy difference between the CIP and the SSIP. Notable classical MD simulation results in the literature are also shown for


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comparison11. For the classical MD simulations with fixed charge potential models, the CIP is energetically more stable than the SSIP, with the energy difference ranging from 0.50 to 2.31 kcal/mol, depending on the particular model (SPC/F w/ HMN86-88, AMBER89, CHARMM37, GROMACS90, and Joung-and-Cheatham91). With the polarizable model by Smith and Dang36 and also with the recent polarizable/charge-transfer FQ-DCT model38,

40, 92

, the classical MD

simulations show that the CIP is more stable than the SSIP by 0.50 kcal/mol and 0.43 kcal/mol, respectively. However, except for the ωB97X-V functional, the FPMD simulations show the opposite trend, yielding the SSIP that is slightly more stable than the CIP by 0.02~0.41 kcal/mol. The only exception is with the ωB97X-V XC approximation, and the FPMD simulation based on it shows that the CIP is more stable than the SSIP by 0.69 kcal/mol. As discussed in Introduction, direct experimental measurements of the ion pairs are challenging and their interpretations need to rely on MD simulations34. Therefore, it is not possible to conclude whether the CIP should be indeed more stable than the SSIP at present time. At the same time, given the great performance of the empirical ωB97X-V functional for H2O-H2O, H2O-Na+, and H2O-Cl- interactions as shown above (and also in Supporting Information for the GPW implementation93 employed here), one might argue that the CIP is more stable than the SSIP based on the simulation result. In Supporting Information, we also include the analysis of the number of water molecules that are involved in bridging the Na and Cl ions as a function of the separation distance, as following the work by Ghost, et al.42 As expected, the analysis shows that the relative stability of the CIP and the SSIP is likely sensitive to the interplay between different types of interactions42.


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Table 1. Locations of free energy minima and transition states, as well as key energetic quantities (in kcal/mol) from the potential of mean force as a function of the Na-Cl separation distances in water, according to different potential energy descriptions. CIP: Na-Cl distance for the contact ion pair, TS: Na-Cl distance for the transition state, SSIP: Na-Cl distance for the solvent separated ion pair, Ub: Free energy barrier from CIP to SSIP, ∆UCIP-SSIP: Free energy difference between CIP and SSIP. CIP(Å)

TS(Å)

SSIP(Å)

Ub(kcal/mol)

∆UCIP-USSIP (kcal/mol)

2.82

ωB97X-V

SCAN

2.74

PBE

2.82

revPBE-D3

b

2.98

a.

BLYP

2.68

3.68

3.44

3.52

3.75

3.38

4.44

1.77

-0.69

(0.04)

(0.06)

4.60

1.22

0.11

(5.08)

(0.05)

(0.06)

4.76

0.75

0.26

(4.41)

(0.05)

(0.07)

4.68

0.75

0.41

(0.08)

(0.08)

1.40

0.02

4.74

(0.28) SPC/F w/ HMN a

AMBER

a

CHARMM

a

GROMACS

Smith and Dang Joung a Cheatham

a

and

b

FQ-DCT

2.58

3.60

4.99

4.35

-2.31

2.76

3.82

5.40

3.56

-2.03

2.62

3.58

5.10

3.49

-1.31

2.67

3.63

5.21

3.32

-1.24

2.81

3.67

5.27

2.70

-0.50

2.71

3.63

5.19

3.16

-1.20

2.65

3.41

4.94

1.18

-0.43

a. ref11. b. ref2


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Figure 3. Potential of mean force (PMF) as a function of the Na-Cl separation distances in water, according to different potential energy descriptions. The separation distance of 6 Å is used to align the PMF curves for the comparison. The shaded areas indicate the statistical error bars estimated for FPMD results. a ref.2; b ref.11

4. Charges on Na and Cl Ions To develop a simple conceptual understanding of aqueous salt solutions, classical description of non-integer charge transfer among constituent molecules is useful. Many classical MD simulations indeed employ a mean-field approach for treating the charge transfer between ions in water by reducing the charges on the ions from their integer values 39, 41, 46, 94 while more sophisticated treatments take the charge transfer explicitly into account as additional degrees of freedom2, 15, 38, 40, 92. Here, charge analysis using the Bader partitioning95 of the electron density is shown in Figure 4. All the presented charge values here are ensemble-averaged values from the FPMD simulations, and Figure 4 shows how the charges on Na/Cl ions vary as a function of


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the Na-Cl separation distance in water. Compared to the PBE approximation, the ωB97X-V and SCAN results show a larger charge on the ions. While the Na charge is only ~0.01q/0.005q larger for the ωB97X-V/SCAN approximations, the Cl charge is much larger by 0.060.08q/0.03-0.05q for these two, when compared to the PBE approximation. The ion charge of the Cl becomes noticeably closer to -1.0, going from the PBE, to the SCAN, to the ωB97X-V. The erroneous delocalization of electron density due to approximated XC functionals has been well documented in the literature for the solvated Cl ion96, and the self-interaction error is likely responsible for this observation at a fundamental level. The self-interaction error is well defined only for one-electron systems97 98, but its analogy to many-electron systems is widely discussed in the literature99-100. The self-interaction error results in the tendency of approximated XC functionals to spread out the electron density, and the widely-observed delocalization error can be also understood as a manifestation of the erroneous convex behavior of the electronic energy as a function of the fractional charge as observed for most XC approximations. The SCAN metaGGA construction is free of the self-interaction error for the correlation part74 while the ωB97XV is self-interaction free in the long-range for the exchange functional thanks to its rangeseparated hybrid form with the Hartree-Fock exchange.


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Figure 4. Averaged charge state of Na (Left) and Cl (Right) ions as a function of the Na-Cl separation distance in the FPMD simulations. The Bader paritioning of the electon density was used to quantify the charge on the ions, with 400 equally-sampled snapshots from the FPMD simulation trajectory for each XC functional. The shaded areas indicate the statistical error bars estimated for FPMD results.

5. Charge Transfer and Polarization of Water Molecules It is instructive to examine behavior of individual water molecules in the heterogeneous environment of ionic NaCl solution. In addition to using the Bader partitioning of the electron density, we also analyze the polarization of individual water molecules using maximally localized Wannier functions (MLWF). Recent success of the classical force field FQ-DCT2, 15, 38, 40, 92

, which includes explicit terms for water polarization and inter-molecular charge transfer, for

describing ionic solutions indicate that inclusion of both polarizabilty of water molecules and inter-molecular charge transfer is likely more important than previously expected in classical MD force fields2. Figure 5 (Left) shows the ensemble-averaged charge on individual water molecules near the NaCl dimer at three separation distances that approximately correspond to CIP, TS, and SSIP (see Table 1). On average, the Bader analysis shows that water molecules near the NaCl are slightly negatively charged irrespective of the Na-Cl separation distance. This finding is independent of a particular XC approximation used here. This qualitative behavior is


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in agreement with our previous findings from FPMD simulations with revPBE-D3 XC functional, and we previously found that the FQ-DCT classical force field can reproduce this charge transfer behavior as discussed in Ref.2. The area in which water molecules are negatively charged is noticeably larger near the Cl ion than near the Na ion in all cases. At the same time, the magnitudes of the charges on the water molecules decrease going from the PBE, to the SCAN, to the ωB97X-V XC functinals, as perhaps expected from the trend observed for the ion charge (Figure 4). For the water molecules that are shared in the first solvation shells of Na and Cl ions, the ωB97X-V and SCAN functionals show that the water molecules less negatively charged than the PBE functional as shown in Figure 5 (Right).


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Figure 5. (Left) Distribution plot of charges on individual water molecules around Na-Cl at three different Na-Cl separation distances. For example, green regions indicate where the water molecules are likely more negatively charged. Red and blue circles indicate where Na and Cl ions are located, respectively. The distribution is averaged in the circular direction around the Na-Cl axis. (Right) Averaged charge of individual water molecules that are shared in the first solvation shells of Na and Cl ions as a function of the Na-Cl separation distance. The Bader paritioning of the electon density was used to quantify the charge on water molecules, with 400 equally-sampled snapshots from the FPMD simulation trajectory for each XC functional.

Figure 6. (Left) Averaged dipole magnitude of individual water molecules as a function of the Na-Cl separation distance in the FPMD simulations. The dipole moment of individual water molecules was calculated using the maximally-localized Wannier functions. The ensemble average was obtained from 400 equally-sampled snapshots from the FPMD simulation trajectory for each XC functional. (Middle) Averaged dipole magnitude for only the water molecules that were shared in the first solvation shells of both Na and Cl ions. (Right) Snapshots of the water molecules from the FPMD simulation, with and without a nearby Na ion. Hydrogen bonds are indicated by blue dashed lines.

Figure 6 (Left) shows the averaged dipole moments of all water molecules as a function of the Na-Cl separation distance. MLWF centers on individual water molecules are used to


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calculate the molecular dipole moments for each water molecule. The ωB97X-V and SCAN XC approximations predict the average dipole magnitude that is noticeably smaller than the PBE prediction by approximately 0.1 Debye. For the water molecules that are shared in the first solvation shells of Na and Cl ions, the average dipole magnitudes are found to be somewhat lower as seen in Figure 6 (Middle). Intuitively, one might expect stronger dipole magnitudes for these water molecules because of their close proximity to the ions. However, it has been reported that when a water molecule is near an ion, presence of the ion excludes approximately two water molecules that otherwise form two hydrogen bonds as shown in Figure 6 (Right), leading to a smaller dipole magnitude for the nearby water molecules11.

Conclusion Employing two recent advanced XC approximations, ωB97X-V70 and SCAN74, in firstprinciples molecular dynamics (FPMD) simulations, we investigated a NaCl ion pair in water, calculating the potential of mean force as a function of the ion separation distance. The ωB97XV is an empirically-optimized range-separated hybrid functional with dispersion correction, and the SCAN is recent meta-GGA functional that was developed non-empirically by satisfying all 17 known exact conditions at the semi-local level. These two functionals were compared to the commonly used GGA-PBE functional in the FPMD simulations of NaCl in water. For pure water simulated at 300K, both XC functionals perform quite well for structural properties. For instance, these two functionals do not show the over-structure in the oxygen-oxygen pair correlation function that is observed when the PBE functional is used. Indeed, the agreement by these two XC functionals to a recent MP2 result by Del Ben, et al.1 is quite impressive. For the potential of mean force (PMF), the ωB97X-V predicts that the contact ion pair (CIP) is energetically more


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stable than the solvent separated ion pair (SSIP). The SCAN functional, however, predicts that the SSIP is slightly more stable than the CIP, similarly to other XC functionals like the PBE. This is notable especially since classical molecular dynamics simulations with widely-used force field models such as AMBER, CHARMM, etc. predict greater stability for the contact ion pair. To obtain physical insights at the molecular level, we used the Bader partitioning scheme and maximally-localized Wannier functions to quantify the charge transfer and dipole moments of individual water molecules, respectively. The qualitative behavior is the same among all three XC functionals. At the same time, there are some notable differences at the quantitative level. For example, the ωB97X-V and SCAN approximations noticeably improve the description of electron charge on Cl- ion in water while the charge on Na+ ion does not vary appreciably among the three XC functionals. In summary, both ωB97X-V and SCAN approximations noticeably improve structural properties of pure water, and the ωB97X-V result on the PMF for the NaCl ionic solution supports the experimentally-indicated stability of the CIP over the SSIP from neutron diffraction experiment34, which relies on molecular dynamics simulation for interpretation. Given the promising results presented here, further investigation of these two advanced XC functionals in the context of the FPMD for other condensed-phase matters and for dynamical properties such as the self-diffusivity is desired.

Computational Method Since the beginning of FPMD as marked by the development of Car-Parrinello extended Lagrangian approach, planewaves have been widely used to represent Kohn-Sham (KS) wavefuncttions and electron density as basis functions. In more recent years, the use of atomcentered localized functions such as Gaussians as basis functions have emerged for performing


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FPMD, partly due to their convenience in evaluating Hartree-Fock exchange integral in hybrid XC functionals. In a recent work, Miceli, et al101. compared the performance of the traditional planewaves (PW) basis set and a mixed Gaussian-PW (GPW) basis set scheme, in which Gaussians are used to expand KS wavefunctions while the electron density was represented using planewaves. Using the rVV10 XC functional, they found that a comparable accuracy can be achieved for the liquid water, specifically for thermodynamics properties like oxygen-oxygen pair correlation functions although the agreement appears to be less than perfect for dynamical properties like water self diffusivity. In the present work, we use the GPW scheme with the TZV2P basis set as implemented in the CP2K code93. The auxiliary plane-wave cutoff for the electron density was set to 1200 Ry, following the work by Miceli et al101, ensuring that the forces on atoms are well converged. Libxc102 library was linked to the code for the XC functionals of SCAN and ωB97X-V. For the ωB97X-V functional, the Hartree-Fock exchange energy was obtained using the auxiliary density matrix method (ADMM)103 method with pFIT3 auxiliary basis set for computational efficiency. The comparison of the potential energy with and without the ADMM method is shown in Supporting Information section for ensuring its accuracy. For core electrons, Goedecker-Teter-Hutter (GTH) pseudopotentials104 were used, using the PBE level of XC approximation for convenience. For Na+ ions, the 2p semi-core electrons were included explicitly as valence electrons in the simulations. We show comparison of the GPW scheme to the more conventional PW approach for simulating liquid water at 300K. The SCAN functional was implemented by modifying the CPMD code82, and the normconserving pseudopotentials were generated as discussed in Ref82. For structural properties such as oxygen–oxygen pair correlation functions, these PW and GPW schemes are in excellent agreement as shown recently by Miceli, et al. for using the rVV10 XC functional101 (See


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Supporting Information). Also, we show that using the PBE pseudopotentials for the SCAN functional in our FPMD simulations does not result in any noticeable error. We use orbital transformation method105 to optimize the wavefunctions at each time step such that the system propagates following the Born Oppenheimer potential energy surface. The NVT ensemble is generated by canonical sampling through velocity rescaling (CSVR)106 thermostat at the temperature of 300K. To analyze electronic structure, maximally-localized Wannier functions (MLWF)83 and Bader partitioning95 were employed for the analysis, and the electronic structure was analyzed every 50 steps in the FPMD simulations unless otherwise noted. In practice, direct FPMD simulation of NaCl in water is challenging when comparing different XC functionals. This is because there exist two free energy minima in the potential of mean force (free energy profile) along the Na-Cl separation distance, and the two minima correspond to the solvent-shared ion pair (SSIP) and the contact ion pair (CIP). Their relative stability is sensitive to a particular XC approximation as discussed in the main text. Therefore, we used the thermodynamics integration method to calculate the potential of mean force (PMF) along the Na-Cl separation distance. In the constrained dynamics, the Na-Cl separation distance is constrained by using the SHAKE algorithm107. The entropy correction due to performing the constrained dynamics is added by calculating the volume-entropy force formula108. The Na-Cl separation distances were sampled from 2.2Å to 6.0Å with a step of 0.2Å. At each distance, a 30 ps trajectory was collected. The trajectory was then separated into 5 evenly-spaced blocks for estimating the statistical error. Cubic simulation cells contain 64 water molecules and a single pair of Na+ and Cl- ions, which corresponds to the salt concentration of approximately 0.852 mol/L. The cell size is chosen such that the density matches the experimental value109, yielding the cubic simulation cell


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with 12.4934 Å. FPMD simulations were performed with a time step of 1.5 fs. In order to make sure that the time step of 1.5 fs is sufficiently small, we employed classical MD with SPC/F w/ HMN force field86-88 to examine the influence of the time step size on the potential of mean force as shown in Supporting Information.

Acknowledgements This work is supported by the National Science Foundation under Grant No. CHE-1565714. We thank the National Energy Research Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02- 05CH11231 for computational resources.

Supporting information Comparison between PW and GPW schemes in FPMD for the SCAN meta-GGA functional (Figure S1); Influence of using ADMM method for the ωB97X-V XC functional (Figure S2); Comparison between MP2 and CCSD(T) calculations for NaCl potential energy curve (Figure S3); Comparison of Potential Energy Curves for Na+-H2O and Cl--H2O interactions with respect to MP2 calculations (Figure S4); Convergence of Potential of Mean Force with respect to the step size in MDs (Figure S5); Convergence of Potential of Mean Force with respect to the system size in MDs (Figure S6); Inter-ion hydration structures between Na and Cl ions (Figure S7). This information is available free of charge via the Internet at http://pubs.acs.org

References


22

Page 23 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.

Del Ben, M.; Schönherr, M.; Hutter, J.; VandeVondele, J., Bulk Liquid Water at Ambient

Temperature and Pressure from MP2 Theory. J. Phys. Chem. Lett. 2013, 4 (21), 3753-3759. 2.

Yao, Y.; Berkowitz, M. L.; Kanai, Y., Communication: Modeling of concentration

dependent water diffusivity in ionic solutions: Role of intermolecular charge transfer. J. Chem. Phys. 2015, 143 (24), 241101. 3.

Cheng, J.; Sprik, M., Aligning electronic energy levels at the TiO2/H2O interface. Phys.

Rev. B 2010, 82 (8), 081406. 4.

Esposito, D. V.; Baxter, J. B.; John, J.; Lewis, N. S.; Moffat, T. P.; Ogitsu, T.; O'Neil, G.

D.; Pham, T. A.; Talin, A. A.; Velazquez, J. M.; Wood, B. C., Methods of photoelectrode characterization with high spatial and temporal resolution. Energy Environ. Sci. 2015, 8 (10), 2863-2885. 5.

Ikeshoji, T.; Otani, M.; Hamada, I.; Okamoto, Y., Reversible redox reaction and water

configuration on a positively charged platinum surface: first principles molecular dynamics simulation. Phys. Chem. Chem. Phys. 2011, 13 (45), 20223-20227. 6.

Pham, T. A.; Lee, D.; Schwegler, E.; Galli, G., Interfacial Effects on the Band Edges of

Functionalized Si Surfaces in Liquid Water. JACS 2014, 136 (49), 17071-17077. 7.

Reeves, K. G.; Kanai, Y., Electronic Excitation Dynamics in Liquid Water under Proton

Irradiation. Sci. Rep. 2017, 7, 40379. 8.

Reeves, K. G.; Yao, Y.; Kanai, Y., Electronic stopping power in liquid water for protons

and α particles from first principles. Phys. Rev. B 2016, 94 (4), 041108.


23


9.

Page 24 of 36

Wood, B. C.; Schwegler, E.; Choi, W. I.; Ogitsu, T., Hydrogen-Bond Dynamics of Water

at the Interface with InP/GaP(001) and the Implications for Photoelectrochemistry. JACS 2013, 135 (42), 15774-15783. 10. Wood, B. C.; Schwegler, E.; Choi, W. I.; Ogitsu, T., Surface Chemistry of GaP(001) and InP(001) in Contact with Water. J. Phys. Chem. C 2014, 118 (2), 1062-1070. 11. Timko, J.; Bucher, D.; Kuyucak, S., Dissociation of NaCl in water from ab initio molecular dynamics simulations. J. Chem. Phys. 2010, 132 (11), 114510. 12. Skinner, L. B.; Huang, C.; Schlesinger, D.; Pettersson, L. G. M.; Nilsson, A.; Benmore, C. J., Benchmark oxygen-oxygen pair-distribution function of ambient water from x-ray diffraction measurements with a wide Q-range. J. Chem. Phys. 2013, 138 (7), 074506. 13. Zhang, Y.; Cremer, P. S., Interactions between macromolecules and ions: the Hofmeister series. Curr. Opin. Chem. Biol. 2006, 10 (6), 658-663. 14. Marcus, Y., Effect of Ions on the Structure of Water: Structure Making and Breaking. Chem. Rev. 2009, 109 (3), 1346-1370. 15. Yao, Y.; Kanai, Y.; Berkowitz, M. L., Role of Charge Transfer in Water Diffusivity in Aqueous Ionic Solutions. J. Phys. Chem. Lett. 2014, 5 (15), 2711-2716. 16. van der Vegt, N. F. A.; Haldrup, K.; Roke, S.; Zheng, J.; Lund, M.; Bakker, H. J., WaterMediated Ion Pairing: Occurrence and Relevance. Chem. Rev. 2016, 116 (13), 7626-7641. 17. Stirnemann, G.; Wernersson, E.; Jungwirth, P.; Laage, D., Mechanisms of Acceleration and Retardation of Water Dynamics by Ions. JACS 2013, 135 (32), 11824-11831.


24

Page 25 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


18. Marcus, Y.; Hefter, G., Ion Pairing. Chem. Rev. 2006, 106 (11), 4585-4621. 19. Cohen-Tanugi, D.; Grossman, J. C., Water Desalination across Nanoporous Graphene. Nano Lett. 2012, 12 (7), 3602-3608. 20. Cohen-Tanugi, D.; Grossman, J. C., Water permeability of nanoporous graphene at realistic pressures for reverse osmosis desalination. J. Chem. Phys. 2014, 141 (7), 074704. 21. Cohen-Tanugi, D.; Lin, L.-C.; Grossman, J. C., Multilayer Nanoporous Graphene Membranes for Water Desalination. Nano Lett. 2016, 16 (2), 1027-1033. 22. Cohen-Tanugi, D.; McGovern, R. K.; Dave, S. H.; Lienhard, J. H.; Grossman, J. C., Quantifying the potential of ultra-permeable membranes for water desalination. Energy Environ. Sci. 2014, 7 (3), 1134-1141. 23. Wang, E. N.; Karnik, R., Water desalination: Graphene cleans up water. Nat Nano 2012, 7 (9), 552-554. 24. Im, W.; Roux, B. t., Ions and Counterions in a Biological Channel: A Molecular Dynamics Simulation of OmpF Porin from Escherichia coli in an Explicit Membrane with 1M KCl Aqueous Salt Solution. J. Mol. Biol. 2002, 319 (5), 1177-1197. 25. Lefebvre, O.; Moletta, R., Treatment of organic pollution in industrial saline wastewater: A literature review. Water Res. 2006, 40 (20), 3671-3682. 26. Munns, R., Comparative physiology of salt and water stress. Plant, Cell Environ. 2002, 25 (2), 239-250.


25


Page 26 of 36

27. Shrivastava, I. H.; Sansom, M. S. P., Simulations of Ion Permeation Through a Potassium Channel: Molecular Dynamics of KcsA in a Phospholipid Bilayer. Biophys. J. 2000, 78 (2), 557570. 28. Aziz, E. F.; Zimina, A.; Freiwald, M.; Eisebitt, S.; Eberhardt, W., Molecular and electronic structure in NaCl electrolytes of varying concentration: Identification of spectral fingerprints. J. Chem. Phys. 2006, 124 (11), 114502. 29. Fuoss, R. M., Conductimetric determination of thermodynamic pairing constants for symmetrical electrolytes. Proc. Natl. Acad. Sci. 1980, 77 (1), 34-38. 30. Kaatze, U.; Hushcha, T. O.; Eggers, F., Ultrasonic Broadband Spectrometry of Liquids A Research Tool in Pure and Applied Chemistry and Chemical Physics. J. Solution Chem. 2000, 29 (4), 299-368. 31. Sebe, F.; Nishikawa, K.; Koga, Y., Spectrum of excess partial molar absorptivity. Part II: a near infrared spectroscopic study of aqueous Na-halides. Phys. Chem. Chem. Phys. 2012, 14 (13), 4433-4439. 32. Wachter, W.; Fernandez, Š.; Buchner, R.; Hefter, G., Ion Association and Hydration in Aqueous Solutions of LiCl and Li2SO4 by Dielectric Spectroscopy. J. Phys. Chem. B 2007, 111 (30), 9010-9017. 33. Chan, C. B.; Tioh, N. H.; Hefter, G. T., Fluoride complexes of the alkali metal ions. Polyhedron 1984, 3 (7), 845-851.


26

Page 27 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


34. Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K., Hydration of Sodium, Potassium, and Chloride Ions in Solution and the Concept of Structure Maker/Breaker. J. Phys. Chem. B 2007, 111 (48), 13570-13577. 35. Guàrdia, E.; Rey, R.; Padró, J. A., Potential of mean force by constrained molecular dynamics: A sodium chloride ion-pair in water. Chem. Phys. 1991, 155 (2), 187-195. 36. Smith, D. E.; Dang, L. X., Computer simulations of NaCl association in polarizable water. J. Chem. Phys. 1994, 100 (5), 3757-3766. 37. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M., CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 1983, 4 (2), 187-217. 38. Soniat, M.; Rick, S. W., The effects of charge transfer on the aqueous solvation of ions. J. Chem. Phys. 2012, 137 (4), 044511. 39. Li, J.; Wang, F., Pairwise-additive force fields for selected aqueous monovalent ions from adaptive force matching. J. Chem. Phys. 2015, 143 (19), 194505. 40. Soniat, M.; Pool, G.; Franklin, L.; Rick, S. W., Ion association in aqueous solution. Fluid Phase Equilib. 2016, 407, 31-38. 41. Li, J.; Wang, F., Accurate Prediction of the Hydration Free Energies of 20 Salts through Adaptive Force Matching and the Proper Comparison with Experimental References. J. Phys. Chem. B 2017, 121 (27), 6637-6645.


27


Page 28 of 36

42. Ghosh, M. K.; Re, S.; Feig, M.; Sugita, Y.; Choi, C. H., Interionic Hydration Structures of NaCl in Aqueous Solution: A Combined Study of Quantum Mechanical Cluster Calculations and QM/EFP-MD Simulations. J. Phys. Chem. B 2013, 117 (1), 289-295. 43. Hou, G.-L.; Liu, C.-W.; Li, R.-Z.; Xu, H.-G.; Gao, Y. Q.; Zheng, W.-J., Emergence of Solvent-Separated Na+–Cl– Ion Pair in Salt Water: Photoelectron Spectroscopy and Theoretical Calculations. J. Phys. Chem. Lett. 2017, 8 (1), 13-20. 44. Geissler, P. L.; Dellago, C.; Chandler, D., Kinetic Pathways of Ion Pair Dissociation in Water. J. Phys. Chem. B 1999, 103 (18), 3706-3710. 45. Bolhuis, P. G.; Chandler, D.; Dellago, C.; Geissler, P. L., Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 2002, 53 (1), 291-318. 46. Pluhařová, E.; Marsalek, O.; Schmidt, B.; Jungwirth, P., Ab Initio Molecular Dynamics Approach to a Quantitative Description of Ion Pairing in Water. J. Phys. Chem. Lett. 2013, 4 (23), 4177-4181. 47. Luo, Y.; Jiang, W.; Yu, H.; MacKerell, A. D.; Roux, B., Simulation study of ion pairing in concentrated aqueous salt solutions with a polarizable force field. Faraday Discuss. 2013, 160 (0), 135-149. 48. Car, R.; Parrinello, M., Unified Approach for Molecular Dynamics and DensityFunctional Theory. Phys. Rev. Lett. 1985, 55 (22), 2471-2474. 49. Laasonen, K.; Sprik, M.; Parrinello, M.; Car, R., ‘‘Ab initio’’ liquid water. J. Chem. Phys. 1993, 99 (11), 9080-9089.


28

Page 29 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50. Tuckerman, M.; Laasonen, K.; Sprik, M.; Parrinello, M., Ab initio molecular dynamics simulation of the solvation and transport of hydronium and hydroxyl ions in water. J. Chem. Phys. 1995, 103 (1), 150-161. 51. Dal Peraro, M.; Ruggerone, P.; Raugei, S.; Gervasio, F. L.; Carloni, P., Investigating biological systems using first principles Car–Parrinello molecular dynamics simulations. Curr. Opin. Struct. Biol. 2007, 17 (2), 149-156. 52. Marx, D.; Hutter, J., Ab initio molecular dynamics: basic theory and advanced methods. Cambridge University Press: 2009. 53. Tocci, G.; Joly, L.; Michaelides, A., Friction of Water on Graphene and Hexagonal Boron Nitride from Ab Initio Methods: Very Different Slippage Despite Very Similar Interface Structures. Nano Lett. 2014, 14 (12), 6872-6877. 54. Li, L.; Kanai, Y., Excited Electron Dynamics at Semiconductor–Molecule Type-II Heterojunction Interface: First-Principles Dynamics Simulation. J. Phys. Chem. Lett. 2016, 7 (8), 1495-1500. 55. Jr., R. A. D.; Santra, B.; Li, Z.; Wu, X.; Car, R., The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water. J. Chem. Phys. 2014, 141 (8), 084502. 56. Gaiduk, A. P.; Zhang, C.; Gygi, F.; Galli, G., Structural and electronic properties of aqueous NaCl solutions from ab initio molecular dynamics simulations with hybrid density functionals. Chem. Phys. Lett. 2014, 604, 89-96.


29


Page 30 of 36

57. Pham, T. A.; Ogitsu, T.; Lau, E. Y.; Schwegler, E., Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations. J. Chem. Phys. 2016, 145 (15), 154501. 58. Gaiduk, A. P.; Galli, G., Local and Global Effects of Dissolved Sodium Chloride on the Structure of Water. J. Phys. Chem. Lett. 2017, 8 (7), 1496-1502. 59. DiStasio, R. A.; Santra, B.; Li, Z.; Wu, X.; Car, R., The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water. J. Chem. Phys. 2014, 141 (8), 084502. 60. Lin, I. C.; Seitsonen, A. P.; Coutinho-Neto, M. D.; Tavernelli, I.; Rothlisberger, U., Importance of van der Waals Interactions in Liquid Water. J. Phys. Chem. B 2009, 113 (4), 1127-1131. 61. Lin, I. C.; Seitsonen, A. P.; Tavernelli, I.; Rothlisberger, U., Structure and Dynamics of Liquid Water from ab Initio Molecular Dynamics—Comparison of BLYP, PBE, and revPBE Density Functionals with and without van der Waals Corrections. J. Chem. Theory Comput. 2012, 8 (10), 3902-3910. 62. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865-3868. 63. Morrone, J. A.; Car, R., Nuclear Quantum Effects in Water. Phys. Rev. Lett. 2008, 101 (1), 017801.


30

Page 31 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


64. Ceriotti, M.; Fang, W.; Kusalik, P. G.; McKenzie, R. H.; Michaelides, A.; Morales, M. A.; Markland, T. E., Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. Chem. Rev. 2016, 116 (13), 7529-7550. 65. Del Ben, M.; Schütt, O.; Wentz, T.; Messmer, P.; Hutter, J.; VandeVondele, J., Enabling simulation at the fifth rung of DFT: Large scale RPA calculations with excellent time to solution. Comput. Phys. Commun. 2015, 187, 120-129. 66. Del Ben, M.; Hutter, J.; VandeVondele, J., Forces and stress in second order MøllerPlesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach. J. Chem. Phys. 2015, 143 (10), 102803. 67. Del Ben, M.; Hutter, J.; VandeVondele, J., Probing the structural and dynamical properties of liquid water with models including non-local electron correlation. J. Chem. Phys. 2015, 143 (5), 054506. 68. Willow, S. Y.; Salim, M. A.; Kim, K. S.; Hirata, S., Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction. Sci. Rep. 2015, 5, 14358. 69. Willow, S. Y.; Zeng, X. C.; Xantheas, S. S.; Kim, K. S.; Hirata, S., Why Is MP2-Water “Cooler” and “Denser” than DFT-Water? J. Phys. Chem. Lett. 2016, 7 (4), 680-684. 70. Mardirossian, N.; Head-Gordon, M., [small omega]B97X-V: A 10-parameter, rangeseparated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy. Phys. Chem. Chem. Phys. 2014, 16 (21), 9904-9924.


31


Page 32 of 36

71. Mao, Y.; Demerdash, O.; Head-Gordon, M.; Head-Gordon, T., Assessing Ion–Water Interactions in the AMOEBA Force Field Using Energy Decomposition Analysis of Electronic Structure Calculations. J. Chem. Theory Comput. 2016, 12 (11), 5422-5437. 72. Vydrov, O. A.; Van Voorhis, T., Nonlocal van der Waals density functional: The simpler the better. J. Chem. Phys. 2010, 133 (24), 244103. 73. Mardirossian, N.; Head-Gordon, M., Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and rangeseparated hybrid functionals with and without dispersion corrections. J. Chem. Phys. 2014, 140 (18), 18A527. 74. Sun, J.; Ruzsinszky, A.; Perdew, J. P., Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett. 2015, 115 (3), 036402. 75. Sun, J.; Remsing, R. C.; Zhang, Y.; Sun, Z.; Ruzsinszky, A.; Peng, H.; Yang, Z.; Paul, A.; Waghmare, U.; Wu, X.; Klein, M. L.; Perdew, J. P., Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional. Nat Chem 2016, 8 (9), 831-836. 76. Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I., Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits. J. Chem. Phys. 2005, 123 (6), 062201. 77. Chen, M.; Ko, H.-Y.; Remsing, R. C.; Calegari Andrade, M. F.; Santra, B.; Sun, Z.; Selloni, A.; Car, R.; Klein, M. L.; Perdew, J. P.; Wu, X., Ab initio theory and modeling of water. Proc. Natl. Acad. Sci. 2017, 114 (41), 10846-10851.


32

Page 33 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


78. Grossman, J. C.; Schwegler, E.; Draeger, E. W.; Gygi, F.; Galli, G., Towards an assessment of the accuracy of density functional theory for first principles simulations of water. J. Chem. Phys. 2003, 120 (1), 300-311. 79. Schwegler, E.; Grossman, J. C.; Gygi, F.; Galli, G., Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II. J. Chem. Phys. 2004, 121 (11), 5400-5409. 80. Manna, D.; Kesharwani, M. K.; Sylvetsky, N.; Martin, J. M. L., Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets. J. Chem. Theory Comput. 2017, 13 (7), 3136-3152. 81. Peng, H.; Yang, Z.-H.; Perdew, J. P.; Sun, J., Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation. Phys. Rev. X 2016, 6 (4), 041005. 82. Yao, Y.; Kanai, Y., Plane-wave pseudopotential implementation and performance of SCAN meta-GGA exchange-correlation functional for extended systems. J. Chem. Phys. 2017, 146 (22), 224105. 83. Marzari, N.; Mostofi, A. A.; Yates, J. R.; Souza, I.; Vanderbilt, D., Maximally localized Wannier functions: Theory and applications. Rev. Mod. Phys. 2012, 84 (4), 1419-1475. 84. Sharma, M.; Resta, R.; Car, R., Dipolar Correlations and the Dielectric Permittivity of Water. Phys. Rev. Lett. 2007, 98 (24), 247401. 85. Yao, Y.; Kanai, Y., Reptation Quantum Monte Carlo calculation of charge transfer: The Na–Cl dimer. Chem. Phys. Lett. 2015, 618, 236-240.


33


Page 34 of 36

86. Paesani, F.; Zhang, W.; Case, D. A.; Cheatham, T. E.; Voth, G. A., An accurate and simple quantum model for liquid water. J. Chem. Phys. 2006, 125 (18), 184507. 87. Horinek, D.; Mamatkulov, S. I.; Netz, R. R., Rational design of ion force fields based on thermodynamic solvation properties. J. Chem. Phys. 2009, 130 (12), 124507. 88. Wu, Y.; Tepper, H. L.; Voth, G. A., Flexible simple point-charge water model with improved liquid-state properties. J. Chem. Phys. 2006, 124 (2), 024503. 89. Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A., Development and testing of a general amber force field. J. Comput. Chem. 2004, 25 (9), 1157-1174. 90. Oostenbrink, C.; Villa, A.; Mark, A. E.; Van Gunsteren, W. F., A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force-field parameter sets 53A5 and 53A6. J. Comput. Chem. 2004, 25 (13), 1656-1676. 91. Joung, I. S.; Cheatham, T. E., Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations. J. Phys. Chem. B 2008, 112 (30), 9020-9041. 92. Lee, A. J.; Rick, S. W., The effects of charge transfer on the properties of liquid water. J. Chem. Phys. 2011, 134 (18), 184507. 93. Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J., CP2K: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4 (1), 15-25. 94. Wu, B.; Yamashita, Y.; Endo, T.; Takahashi, K.; Castner, E. W., Structure and dynamics of ionic liquids: Trimethylsilylpropyl-substituted cations and bis(sulfonyl)amide anions. J. Chem. Phys. 2016, 145 (24), 244506.


34

Page 35 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


95. Tang, W.; Sanville, E.; Henkelman, G., A grid-based Bader analysis algorithm without lattice bias. J. Phys.: Condens. Matter 2009, 21 (8), 084204. 96. Cohen, A. J.; Mori-Sánchez, P.; Yang, W., Insights into Current Limitations of Density Functional Theory. Science 2008, 321 (5890), 792-794. 97. Perdew,

J.

P.;

Zunger,

A.,

Self-interaction

correction

to

density-functional

approximations for many-electron systems. Phys. Rev. B 1981, 23 (10), 5048-5079. 98. Zhang, Y.; Yang, W., A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons. J. Chem. Phys. 1998, 109 (7), 2604-2608. 99. Ruzsinszky, A.; Perdew, J. P.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E., Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+. J. Chem. Phys. 2007, 126 (10), 104102. 100. Mori-Sánchez, P.; Cohen, A. J.; Yang, W., Many-electron self-interaction error in approximate density functionals. J. Chem. Phys. 2006, 125 (20), -. 101. Miceli, G.; Hutter, J.; Pasquarello, A., Liquid Water through Density-Functional Molecular Dynamics: Plane-Wave vs Atomic-Orbital Basis Sets. J. Chem. Theory Comput. 2016, 12 (8), 3456-3462. 102. Marques, M. A. L.; Oliveira, M. J. T.; Burnus, T., Libxc: A library of exchange and correlation functionals for density functional theory. Comput. Phys. Commun. 2012, 183 (10), 2272-2281. 103. Guidon, M.; Hutter, J.; VandeVondele, J., Auxiliary Density Matrix Methods for Hartree−Fock Exchange Calculations. J. Chem. Theory Comput. 2010, 6 (8), 2348-2364.


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104. Goedecker, S.; Teter, M.; Hutter, J., Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54 (3), 1703-1710. 105. VandeVondele, J.; Hutter, J., An efficient orbital transformation method for electronic structure calculations. J. Chem. Phys. 2003, 118 (10), 4365-4369. 106. Bussi, G.; Donadio, D.; Parrinello, M., Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126 (1), 014101. 107. Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. C., Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comput. Phys. 1977, 23 (3), 327-341. 108. Li, J.-L.; Car, R.; Tang, C.; Wingreen, N. S., Hydrophobic interaction and hydrogen-bond network for a methane pair in liquid water. Proc. Natl. Acad. Sci. 2007, 104 (8), 2626-2630. 109. Novotny, P.; Sohnel, O., Densities of binary aqueous solutions of 306 inorganic substances. J. Chem. Eng. Data 1988, 33 (1), 49-55. TOC


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Free Energy Profile of NaCl in Water: First-Principles Molecular

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