Simulated Solvation of Organic Ions: Protonated Methylamines in Water Nanodroplets. .... [10] The water O-H bonds and ZH - O - H angles were both restrained ...
Supporting Information Simulated Solvation of Organic Ions: Protonated Methylamines in Water Nanodroplets. Convergence Toward Bulk Properties, and the Absolute Proton Solvation Enthalpy C´eline Houriez,1 Michael Meot-Ner (Mautner),2 and Michel Masella3 1
MINES ParisTech, Centre Thermodynamique des Proc´ed´es (CTP), 60 bd Saint-Michel, 75006 Paris, France. 2
Department of Chemistry, Virginia Commonwealth University, Richmond, VA 23284-2006, and Department of Chemistry, University of Canterbury, Christchurch, New Zealand 8001.
3
Laboratoire de Chimie du Vivant, Service d’ing´enierie mol´eculaire des prot´eines, Institut de biologie et de technologies de Saclay, CEA Saclay, F-91191 Gif sur Yvette Cedex, France
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I.
THE ION AND ION/WATER MODEL PARAMETERS
Carbon, nitrogen and potassium polarizabilities correspond to quantum estimates at the ˚3 ). All the repulsive, MP2/aug-cc-pVQZ level of theory (namely, 2.10, 1.35 and 0.83 A dispersion, U pol damping parameters and the NH+ 4 electrostatic charge set are assigned to reproduce quantum gas phase data concerning K+ /(water)n=1−4 and NH+ 4 /(water)n=1−4 small clusters and the methane/water dimer. Concerning the NH+ 4 /water parameters, they were also assigned to reproduce the NH+ 4 /water dimer energy profile corresponding to the intermolecular angle ∠N − H · · · O (see Figure 1), as well as the comparable weight of the polarization and dispersion energies in the NH+ 4 /water binding energy, as predicted by the quantum decomposition energy approach SAPT. [1] Note that this SAPT study showed the dispersion interaction energy in the K+ /water dimer to be about four to five times smaller in + magnitude than in the NH+ 4 /water dimer. Our K /water parameters were assigned also to
reproduce these results, which lead to dispersion effects affecting marginally the K+ solvation process.
All the NH+ 4 parameters are used to model microscopic interactions involving the NH moiety of alkylammonium ions, with the exception of the atomic electrostatic charge set. Quantum Natural Bond Order (NBO) analysis performed on alkylammonium monomers showed methyl carbon and hydrogen electrostatic charges to be very similar in all the ions (see Table V). We assigned the alkylammonium ion charges accordingly, i.e. the methyl hydrogen and carbon charges are set to the same values for all the ions. On the other hand, the charges of the NH moiety atoms depend on the ion nature. They are assigned to reproduce the quantum binding energies of small ion/water clusters. Lastly, the standard stretching, bending and torsional energy components (and their parameters) used to handle alkylammonium ion intramolecular degrees of freedom are taken from the CHARMM v. 27 force field. [2], which were checked to reproduce accurately the gas phase geometry of the ions (note also that there is a weak coupling between the inter molecular and the intra molecular degrees of freedom, as our simulations are performed by restraining the X − H bond lengths and the covalent H − X − H angles). 2
II.
QUANTUM COMPUTATIONS AT THE CBS LIMIT
All quantum calculations have been performed using the GAUSSIAN09 package of programs. [3] To compute accurate interaction energies of (CH3 )(4−n) NH+ n /(water)m complexes, we first optimized the complex geometries at the MP2/aug-cc-pVTZ level of theory. We computed then the complex total energies by performing single point energy calculations at the MP2/aug-cc-pVXZ//MP2/aug-cc-pVTZ level, with X = D, T and Q. The corresponding Hartree-Fock EHF and correlation Ecorr energy components were used to extrapolate the complex total energies to their complete basis set (CBS) limit using a three-point exponential formula for EHF [4, 5] CBS EHF (p) = EHF + A exp (−Bp),
(1)
and a two-point extrapolation for Ecorr [6] CBS Ecorr (p) = Ecorr + C(p + 1)−3 ,
(2)
p is the cardinal number of aug-cc-pVpZ basis set (p = 2 − 4). Here, A, B and C are two adjustable parameters.
III.
MOLECULAR DYNAMICS, FREE ENERGY COMPUTATIONS, ION/WATER
POTENTIAL OF MEAN FORCE AND ION LOCATION PROBABILITY
MD simulations in condensed phase were performed by considering periodic boundary conditions and the Smooth Particle Mesh Ewald (SPME) summation technique. [7] The direct energy term cutoff distance was set to 12 ˚ A, the expansion of the B-spline functions was set to 8, and the interpolation grid size was set 1 ˚ A. No surface term was considered. The Newtonian equations of motion were solved using the multiple time steps r-RESPAp algorithm, [8] with two time steps: 1 fs for short range inter-molecular interactions (including U rep , U dips and U hb ), and 5 fs for the remaining long-range electrostatic interactions. For large clusters (Nw > 300), we used the same MD propagator, whereas for small clusters, we used a standard Verlet propagator, the time step being set to 2 fs. For NVT simulations, we used the generalized Gaussian moment thermostat, [9] and for NPT ones, the Nos´e-Hoover barostat. [10] The water O-H bonds and ∠H − O − H angles were both restrained to their equilibrium values using the iterative RATTLE procedure, 3
regardless of the thermodynamic ensemble considered (the convergence criterion was set to 10−6 ˚ A). To compute the potential of mean force (PMF) corresponding to the interaction of an ion with the droplet center of mass (COM), we applied the umbrella sampling technique at droplet simulations where the ion position is restrained by a harmonic potential U res = kc (r − rc )2 , with the harmonic constant kc set to 5 kcal mol−1 . For all systems, we performed 40 simulations, corresponding to reference ion/COM distances rc ranging from 0 to 19.5 ˚ A, and regularly spaced of 0.5 ˚ A. For ions interacting at the air/liquid water interface, the PMFs are computed from simulations where the ion is restrained by the same potential U res . However, we consider now the distance r between the ion and the simulation cell center (SCC). The total energy conservation along these simulations is maintained according to the protocol proposed in Ref. 11. The sampling protocol is the same as for droplets, except for rc , whose value is included within 15 and 34.5 ˚ A. The PMFs are estimated from the ion/COM and ion/SCC distance distribution functions computed along the simulations and post-processed according to the Umbrella Integration method. [12]
IV.
K+ AND METHANE ABSOLUTE SOLVATION FREE ENERGY IN BULK
WATER
We estimated the absolute solvation free energy of K+ from our model, by performing a TI computation corresponding to the mutation of the ion into a ghost atom, and by adding to the computed value, the standard corrections for a charged solute, to remove the artefacts arising from the simulation cell dimension and from the absence of an explicit air/liquid water interface, i.e. the so-called Wigner, vapor/liquid interface potential and solute size corrections (see, among others, Ref. 13). To estimate the vapor/liquid interface potential correction, we used the standard point charge approximation, which is inferred to overestimate the latter correction for ions like K+ by several kcal mol−1 (see Ref. 14 and the references mentioned therein, for instance). Note that the water model TCPE/2013 predicts the water surface potential to be -390 mV, slightly smaller in magnitude than the estimates computed from different force field approaches (about -500 ± 30 mV [13]), but clearly non zero as indicated by a recent quantum DFT simulation, [15] and far from the +3100 mV value reported in a quantum ab initio simulation. [16] For the solvation free energy of K+ , 4
we get 88.8 kcal mol−1 as a result, in good agreement with the experimental value of about 86 kcal mol−1 . [17, 18] Note that both the latter values are larger by about 10 % than the target ones commonly used to assign model parameters (see Ref. 19, for instance). For methane by considering the parameters summarized in Table I, our TI computations lead to an absolute solvation free energy of 2.0 kcal mol−1 , also in good agreement with experiment.
V.
ION/WATER DROPLET RESULT SENSITIVITY TO MODEL PARAME-
TERS
To check the sensitivity of our results to the model parameters, we have also investigated the solvation of the ion CH3 NH+ 3 in a water droplet of size Nw = 300 by using different parameter sets, in particular: 1. the parameter sets denoted by S(+) and S(−) : the repulsive and dispersion parameters for methane/water interactions lead respectively to a stronger and to a weaker methane/water gas phase binding energy (by 0.1 kcal mol−1 ) than that corresponding to our reference parameter set, denoted byS0 and detailed in Table I. Note that the carbon/oxygen distance is 3.33 ± 0.03 ˚ A, regardless of the parameter set. H H 2. the parameter sets qhigh and qlow : they correspond to S0 , with the exception of the
methyl hydrogen charge, which is respectively increased and decreased by 0.02 e, compared to the values mentioned in Table I. The methyl carbon charge is thus also decreased or increased accordingly by 0.06 e. That leads thus to consider a stronger H H (qhigh ) or weaker (qlow ) CH bond dipole during our simulations.
3. the set Sα : it corresponds to S0 , with the exception of the methyl carbon polarizability, which is smaller by 25%. The mean ion/water energies U¯ iw (¯ r), and their components, as well as the mean water interaction energies U¯ ww (¯ r) computed from the above parameter sets are plotted as a function of the mean ion/droplet COM distance r¯ in Figure 7. The ion location probabilities Pd (¯ r) and the ion/water PMFs are plotted as a function of r¯ in Figure 8. All the latter quantities are insensitive to the methyl charge set, whereas they are much more sensitive to 5
the methyl/water dispersion energy. However, in the latter case, the difference in the mean ion/droplet energy U¯ iw between the parameter sets S(+) and S(−) is 1.2 kcal mol−1 , which means that our conclusions concerning the extrapolated absolute ion solvation enthalpies discussed in the main manuscript are not affected by the choice of the parameter sets. Note also that the solvation free energy in bulk solution of methane is 1.5, 2.0 and 2.4 kcal mol−1 for the parameter sets S(+) , S0 and S(−) , respectively. Hence, the best agreement with experiment is reached by using the parameter set S0 . Lastly, the parameter set Sα H H provide results included within those of the parameter sets qhigh and qlow .
VI.
ENTROPY EFFECTS AFFECTING ION SOLVATION IN DROPLETS
We computed the PMF entropic components TS(¯ r), by calculating the difference between the mean total potential energy U¯ (¯ r) = U¯ iw (¯ r) + U¯ ww (¯ r) and the PMF(¯ r) along our simulations, once U¯ (¯ r) shifted to be zero at the droplet COM. Note that TS does not include the component TSgeom . We plot the TS(¯ r) profiles for Nw = 1000 as a function of r¯ in Figure 6. These profiles are similar for the various ions. They are flat at the vicinity of the droplet core, and they decrease then as r¯ increases. Because of the large uncertainties affecting the mean total water/water interaction energies U¯ ww (¯ r), about 5 kcal mol−1 , it is not obvious to comment on the difference among the TS(¯ r) profiles of the ions. Note that, as our ions are far from being fully desolvated outside the droplets (they still interact then with a number of water molecules close to the ion CN in bulk solution), our PMFs measure therefore the free energy cost for solvating within a droplet, an ion already interacting in gas phase with its almost complete first hydration shell. Hence, TS(¯ r) corresponds to entropic effects tied to interactions between ion/water clusters and the second ion hydration shell, as well as to water exchange reactions between the first and the second hydration shells of an ion. Hence, TS(¯ r) does not correspond to the total entropy cost when solvating a free ion in a water system, which should be significantly negative.
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[1] Lee, H. M.; Tarakeshwar, P.; Park, J.; Kolaski, M. R.; Yoon, Y. J.; Yi, H.-B.; Kim, W. Y.; Kim, K. S. Insights into the Structures, Energetics, and Vibrations of Monovalent Cation/(Water)1-6 Clusters. J. Phys. Chem. A 2004, 108, 2949–2958. [2] Brooks, B.; Brooks III, C.; Mackerell, A.; Nilsson, L.; Petrella, R.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S. et al. J. Comput. Chem. 2009, 30, 1545–1615. [3] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09 Revision D.01. Gaussian Inc. Wallingford CT 2009. [4] Feller, D. Application of Systematic Sequences of Wave Functions to Water Dimer. J. Chem. Phys. 1992, 96, 6104–6114. [5] Feller, D. The Use of Systematic Sequences of Wave Functions for Estimating the Complete Basis Set, Full Configuration Interaction Limit in Water. J. Chem. Phys. 1993, 98, 7059–7071. [6] Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. Basis-Set Convergence of Correlated Calculations on Water. J. Chem. Phys. 1997, 106, 9639–9646. [7] Toukmaji, A.; Sagui, C.; Borad, J.; Darden, T. Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions. J. Chem. Phys. 2000, 113, 10913–10927. [8] Masella, M. The Multiple Time Step r-RESPA Procedure and Polarizable Potentials Based on Induced Dipole Moments. Mol. Phys. 2006, 104, 415–428. [9] Liu, Y.; Tuckerman, M. Generalized Gaussian Moment Thermostatting: A New Continuous Dynamical Approach to the Canonical Ensemble. J. Chem. Phys. 2000, 112, 1685–1700. [10] Martyna, G. J.; Tuckerman, M. E.; Tobias, D. J.; Klein, M. L. Explicit Reversible Integrators for Extended Systems Dynamics. Mol. Phys. 1996, 87, 1117–1157. [11] Tepper, H. L.; Voth, G. A. J. Phys. Chem. B 2006, 110, 21327–21337. [12] Kastner, J.; Thiel, W. J. Chem. Phys. 2005, 123, 144104. [13] Warren, G. L.; Patel, S. Hydration Free Energies of Monovalent Ions in Transferable Intermolecular Potential Four Point Fluctuating Charge Water: An Assessment of Simulation Methodology and Force Field Performance and Transferability. J. Chem. Phys. 2007, 127, 064509. [14] Horv´arth, L.; Beu, T.; Manghi, M.; Palmeri, J. The Vapor-Liquid Interface Potential of
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(Multi)Polar Fluids and its Influence on Ion Solvation. J. Chem. Phys. 2013, 138, 154702. [15] Baer, M. D.; Mundy, C. J. Toward an Understanding of the Specific Ion Effect Using Density Functional Theory. J. Phys. Chem. Lett. 2011, 2, 1088–1093. [16] Kathmann, S. M.; Kuo, I.-F. W.; Mundy, C. J. Electronic Effects on the Surface Potential at the Vapor/Liquid Interface of Water. J. Am. Chem. Soc. 2009, 131, 1752217522. [17] Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Aqueous Solvation Free Energies of Ions and Ion: Water Clusters Based on an Accurate Value for the Absolute Aqueous Solvation Free Energy of the Proton. J. Phys. Chem. B 2006, 110, 16066–16081. [18] Ben-Naim, A.; Marcus, Y. J. Chem. Phys. 1984, 81, 2016. [19] Lamoureux, G.; Roux, B. J. Phys. Chem. B 2006, 110, 3308–3322. [20] R´eal, F.; Vallet, V.; Flament, J.-P.; Masella, M. Revisiting a Many-Body Model for Water Based on a Single Polarizable Site. From Gas Phase Clusters to Liquid and Air/Liquid Water Systems. J. Chem. Phys. 2013, 139, 114502.
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FIGURES
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FIG. 1. Binding energy of the NH+ 4 /water heterodimer as a function of the intermolecular angle ∠N − H · · · O. The complex energies estimated at the MP2/aug-cc-pVTZ level of theory are shown in black line, whereas the energy profile corresponding to the model (reference parameter set S0 ) is shown in dashed line.
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¯ ww interaction energies computed along pure water droplet trajectories FIG. 2. Mean water/water U as a function of the droplet molecular size Ns (up: droplet of total size Nw =100 molecules; down: 600 molecules), i.e., the mean number of water molecules interacting at short range from each ¯ ww other along the simulations. The linear regression fit allows one to extrapolate the values U for Ns = Nw and to estimate their corresponding uncertainties (here, 1 kcal mol−1 for the 100molecules droplet, and 3 kcal mol−1 for the largest droplet). Note that the regression coefficient is equal to 0.99 for Nw = 100 and to 0.80 for Nw = 600.
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FIG. 3. Ion/water radial distribution functions (up) and methane/water one (down) in bulk solu+ + + tion. Dashed line: K+ ; black: NH+ 4 ; blue: CH3 NH3 ; green: (CH3 )2 NH2 ; and orange: (CH3 )3 NH .
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¯ iw (¯ ¯ iw (¯ ¯ iw r) + U FIG. 4. Sum of the components U rep r ) + Upol (¯ dips r ) plotted as a function of the mean ion/droplet COM distance r¯. The droplet size is here Nw = 300. Same notation as in Figure 3.
13
FIG. 5. Mean molecular water dipole in pure water droplets plotted as a function of the droplet size Nw . Its bulk limit is 2.51 Debye at ambient conditions, according to the water model TCPE/2013. [20]
14
FIG. 6. Entropic component TS of the PMF as a function of the ion/droplet COM distance, for + + + Nw = 1000. Black: NH+ 4 ; blue: CH3 NH3 ; green: (CH3 )2 NH2 ; orange: (CH3 )3 NH ; dashed grey
line: K+ .
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FIG. 7. Energy sensitivity to the model parameters. S0, S(-) and S(+) correspond to the model parameter sets S0 , S(−) and S(+) , and the subscript corresponds to the simulation duration. H H . The data correspond to the S0 qHhigh and S0 qHlow correspond to the force fields qhigh and qlow
CH3 NH+ 3 /(water)300 system.
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FIG. 8. Ion location probability (dashed lines) and ion/water PMF (plain lines) sensitivity to the model parameters. Up: data corresponding to the parameter sets S0 , S(−) and S(+) ; down: data H (see Figure 7). H and qlow corresponding to qhigh
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FIG. 9. Root mean square deviation of the total water/water interaction energy as a function of −1/2
the droplet size Nw . In dashed line: fitting of these data with the function Nw
18
.
FIG. 10. Water energy components for ions solvated in a Nw = 300 droplet. Same notation as in Figure 6 of the manuscript.
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FIG. 11. Water stepwise energies, for ion/water and neat water droplets, as computed from equations 14, for Nw ranging from 2 to 50.
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TABLES
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TABLE I. The reference set S0 of the ion/water model parameters. “all” refers to parameters that are used regardless of the alkylammonium ion. Energy term U qq
0
U pol
U rep
U disp
cation
Unit
Parameter Value Parameter
Value
all
e
qC
0.19
qH
0.07
NH+ 4
e
qN
-0.60
qHN
0.40
CH3 NH+ 3
e
qN
-0.40
qHN
0.36
(CH3)2 NH+ 2
e
qN
-0.50
qHN
0.35
(CH3)3 NH+
e
qN
-0.58
qHN
0.38
K+
e
qK
1.00
all
˚ A3
αN
1.35
αC
2.10
all
˚ A−3
cN
0.300
cHN
0.350
all
˚ A−3
cC
0.300
cHC
0.500
K+
˚ A−3
cK
0.080
all
kcal mol
−1
aN,O
19 750
aC,O
2 000 000
all
kcal mol
−1
aN,HO
75 000
aC,HO
75 000
all
kcal mol
−1
aHN,O
70 000
aHC,O
60 000
all
kcal mol
−1
aHN,HO
75 000
aHC,HO
60 000
K+
kcal mol
−1
aK,O
860 000
aK,HO
75 000
all
˚ A−1
bN,O
2.825
bC,O
4.80
all
˚ A−1
bN,HO
6.00
bC,HO
6.00
all
˚ A−1
bHN,O
7.00
bHC,O
6.00
all
˚ A−1
bHN,HO
6.00
bHC,HO
6.00
K+
˚ A−1
bK,O
4.75
bK,HO
7.00
all
˚ A kcal mol−6
∗ rN,O
3.5193
∗ rC,O
2.9780
K+
˚ A kcal mol−6
∗ rK,O
2.4183
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TABLE II. Specific parameters for the force field sets S(+) , S(−) and Sα . If not mentioned here, the parameters correspond to the S0 ones. Energy term cation
Unit
Parameter
Value
˚ A3
αC
1.60
aC,O
1 000 000
Sα U pol
all
S(+) U rep
all
kcal mol
−1
all
˚ A−1
bC,O
4.550
all
˚ Akcal mol−6
∗ rC,O
3.1072
all
kcal mol
−1
aC,O
1 000 000
S(−) U rep
all
˚ A−1
bC,O
4.675
all
˚ Akcal mol−6
∗ rC,O
2.8173
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m
1
2
3
4
5
6
K+
17.4 [17.1]
32.9 [32.9]
47.1 [46.4]
58.9 [57.9]
68.8 [66.5]
82.0 [79.9]
NH+ 4
20.6 [20.3]
37.8 [37.5]
52.4 [52.3]
64.9 [64.9]
CH3 NH+ 3
18.5 [18.4]
34.3 [34.1]
48.1 [47.8]
(CH3 )2 NH+ 2
17.1 [16.9]
32.0 [31.1]
(CH3 )3 NH+
16.2 [16.2]
TABLE III. Binding energies of alkylammonium/(water)m=1−4 clusters and of K+ /(water)m=1−6 clusters, from quantum MP2 computations at the CBS limit and from the model (in brackets). All data are in kcal mol−1 .
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K+
NH+ 4
Eint [U ]
17.6 [17.3] 21.04 [20.3]
Eexch [U rep ]
-7.1 [-3.1] -15.3 [-11.6]
Ees [U
qq 0
]
Eind [U pol ]
18.8 [17.0] 24.2 [20.8] 4.3 [3.1]
8.2 [6.3]
Edisp (Etc ) [U disp ] 1.7 [0.6]
4.0 [5.3]
TABLE IV. Decomposition of the K+ /water and of the NH+ 4 /water heterodimer binding energies, from the quantum SAPT scheme [1] and from our model (in brackets). In the first column, an equivalence between the SAPT energy components (denoted by E) and the model ones (denoted by U ) is proposed. All data are in kcal mol−1 .
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+ + + CH Atom types NH+ 4 4 CH3 NH3 (CH3 )2 NH2 (CH3 )3 NH
N
-0.820
-0.680
-0.524
-0.413
-
HN
0.455
0.440
0.423
0.413
-
C
-
-0.303
-0.288
- 0.283
-0.707
HC
-
0.217
0.210
0.205
0.177
TABLE V. Electrostatic charges in alkylammonium ion monomers, as computed from the quantum NBO analysis at the MP2/aug-cc-pVTZ. All data are in e.
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