Supplementary Material Comparative assessment of the ELBA coarse-grained model for water

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1 Supplementary Material Comparative assessment of the oarse-grained model for water Mario Orsi Shool of Engineering & Materials Siene, Queen Mary University of London Mile End Road, London E 4NS, United Kingdom m.orsi@qmul.a.uk Shifted-fore interations The total potential energy U ij of an interating pair of water sites i,j is: U ij = U LJ ij +U dip ij, with U LJ ij the Lennard-Jones term and U dip ij the point dipole term. Shifted-fore Lennard-Jones interation The shifted-fore form of the Lennard-Jones potential is []: { [(σ 2 ( σ ) ] [ ( ) 6 2 ( ) ] 6 ( ) 2 ( ) 2 ( ) } 6 σ σ r σ σ Uij LJ = 4ǫ , r) r where r is the interpartile distane, is the utoff radius, and σ and ǫ have the standard meaning [2]. The orresponding fore is given by: { [ ( σ ) 2 ( σ ) ] [ ( ) 6 2 ( ) ] } 6 σ σ f ij = 48ǫ 24ǫ r r r 2 48ǫ 24ǫ r where r is the pair distane vetor, r = r i r j. Shifted-fore point dipole interation Considering two point dipoles µ i and µ j, the shifted-fore pair potential energy is: [ ( ) 3 ( ) ] 4 [ U dip r r ij = 4 +3 r 3(µ i µ j ) 3 ] r 5(µ i r)(µ j r) where r and r are the pair distane vetor and its magnitude, respetively, and is the utoff distane. The standard fator (4πε 0 ) is assumed, and omitted folarity here and in the following formulae. Note that we use the onvention r = r i r j. Fores and torques were derived following the approah in Appendix C.3 of Allen and Tildesley [2]. In partiular, the pair fores are: f ij = f ji = 3 ( ) ] 4 [ r {[ r 5 (µ i µ j ) 3 ] r 2(µ i r)(µ j r) r + The pair torque τ ij is: τ ij = ( r [ 4 r 3 [ ( ) 3 ( r r 4 +3 The pair torque τ ji is: τ ji = ( r [ 4 r 3 ) 4 ] [ (µ j r)µ i +(µ i r)µ j 2 r 2(µ i r)(µ j r)r ) 3 ( ) [ 4 r +3 ](µ r i µ j )+ 3r ( ) 3 ( ) ] 4 r r (µ r j r)(µ i r) ) 3 ( ) [ 4 r +3 ](µ r j µ i )+ 3r ( ) 3 ( ) ] 4 r r (µ r i r)(µ j r) The expressions above, for both the Lenard-Jones and the point dipole potential, have been implemented in the pair lj sf dipole sf.pp module of the program LAMMPS [3]. r 2 ] }

2 Integration timestep and energy onservation Compared to previous publiations [4, 5], in this work we have redued the inertial features of the water model. In partiular, we have here set a realisti mass of 8gmol, and a prinipal moment of inertia of 30gÅ 2 mol. In the original model [4], values of respetively 40gmol and 00gÅ 2 mol were hosen to permit a stable integration of the equations of motion with a 5fs timestep; this hoie was made to maximise the effiieny of serial simulations, as at the time the in-house software used did not allow parallel alulations. Sine the model is now available in the parallel program LAMMPS [3], maximising the timestep is less ritial, and we have deided to redue the timestep size to permit the setting of a realisti (lower) mass. The timestep hoie was validated by running NVE simulations and monitoring the total energy. In partiular, Figure S reports the time evolution of the total energy for a range of timesteps from 5 to 5fs. Total energy / (kal mol - ) t = 5fs t = 2.5fs t = 0fs t = 7.5fs t = 5fs Simulation time / ps Figure S: Total energy onservation for different integration timesteps. Folarity, the different data sets were shifted up or down to avoid overlaps. It an be seen that the total energy is onserved aurately up to t = 0fs. A larger timestep of 2.5fs ould still be aeptable; over 30 ps, while the energy osillates slightly (within 0.%), there is no net drift. For t = 5fs, the total energy is learly not onserved. The flutuations in potential, kineti, and total energy as a funtion of the t are displayed in Figure S2. 00 Potential energy flutuation Kineti energy flutuation Total energy flutuation Energy flutuation E / (kal mol - ) Integration timestep t / fs Figure S2: Average energy flutuation E = (E E ) 2. For timesteps up to 2.5fs, the average flutuation in the total energy is at least 0times smaller than the average flutuations in both the potential and kineti energy, satisfying reommended riteria [6]. 2

3 Overall, ouhoie of t = 0 fs for prodution simulations should guarantee aurate and robust integration of the equations of motion. Computational timings Simulations of a liquid-vapour interfae omprising 8000 water moleules were run for the single-site oarse-grained model, a representative 3-site model (), and a representative 4-site model (). For eah model, the same parameters reported in the main body of the paper were used; in partiular, the timestep was 0fs for and 2fs for the atomisti models, and the utoff radii were.2,.0 and.3 nm for respetively, and. The alulations were run on a GNU/Linux luster of 2.66 GHz Intel Westmere proessors based on 2 sokets and 2 proessors per node, with QLogi TrueSale interonnet. Figure S3 reports a omparison in terms of sampling speed, defined as number of ns sampled / day, where day is intended in terms of alulation (wall-lok) time. 000 Sampling speed [ns/day] Number of proessors Figure S3: Comparison of sampling speed between representative water models. Simulations were run on 2, 24, 48 and 96 proessors. Note the logarithmi sale used to represent the sampling speed. It an be seen that the speed up fators in the simulations are respetively 40 and 00 ompared to and. It is also lear that suh fators are rather insensitive to the number of proessors employed. Mean square displaement and time-dependent diffusion urves The mean square displaement (M SD) was obtained with: MSD = N N [r i (t) r i (0)] 2 () i= with N the number of water moleules, t the time, and r i the 3-dimensional vetor defining the position of partile i. Figure S4 shows the MSD from the liquid bulk simulations of eah model. The self-diffusion oeffiient D was obtained from the bulk systems using the standard expression [7]: D = MSD 6t where MSD is defined in Eq. and t is the simulation time; see Fig. S5. (2) 3

4 5 0 /E MSD / nm Time / ns Figure S4: Mean square displaement as a funtion of simulation time. 4.5 D / (0-9 m 2 /s) /E Time / ns Figure S5: Self-diffusion oeffiient as a funtion of simulation time. 4

5 Radial distribution funtion: main peaks g OO (r ) r /Å g OO (r 2 ) r 2 /Å /E Experiment [8] Table S: Properties of the radial distribution funtion for bulk water at 298K and atm. Height of first peak: g OO (r ). Loation of first peak: r. Height of seond peak: g OO (r 2 ). Loation of seond peak: r 2. Relative unertainties are < 0.%. Mass density profiles ρ / g m /E Figure S6: Mass density profiles. It an be notied that the TIP4P-like models feature small yet nonnegligible density peaks at the liquid-vapour interfaes. In previous work, suh peaks were observed to disappear with inreasing system size [9]. 5

6 ρ / g m /E e-05 e Figure S7: Mass density profiles. To failitate interpretation in the vapour regions, the density is displayed using a logarithmi sale. For the liquid region, see Figure S6. Eletrostati potential and eletri field profiles φ / V /E Figure S8: Eletrostati potential profiles. Foonveniene, a representative mass density profile is also shown with a dotted line (ordinate values not on sale). 6

7 2.5 E z / 0 9 V m /E Figure S9: Eletri field profiles. Foonveniene, a representative mass density profile is also shown with a dotted line (ordinate values not on sale). Referenes [] S.D. Stoddard and J. Ford, Phys. Rev. A 8, 504 (973). [2] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, st ed. (Oxford Siene Publiations, Oxford, 987). [3] S. Plimpton, J. Comp. Phys. 7, (995), [4] M. Orsi and J.W. Essex, PLoS ONE 6, e28637 (20). [5] M. Orsi and J.W. Essex, Faraday Disuss. 6, 249 (203). [6] S. Riniker and W.F. van Gunsteren, J. Chem. Phys. 34, 0840 (20). [7] D.C. Rapaport, The Art of Moleular Dynamis Simulation, 2nd ed. (Cambridge University Press, Cambridge, 2004). [8] A. Soper, Chem. Phys. 258, 2 (2000), [9] J. Alejandre and G.A. Chapela, J. Chem. Phys. 32, 0470 (200). 7