Supporting Information for "Many-Body Contributions in Water Nano-Clusters"

Supporting Information for "Many-Body Contributions in Water Nano-Clusters" David Abella,†,‡ Giancarlo Franzese,∗,‡,¶ and Javier Hernández-Rojas∗,§ †Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain. ‡Secció de Física Estadística i Interdisciplinària - Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain. ¶Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, 08028 Barcelona, Spain. §Departamento de Física e IUdEA, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain. E-mail: [email protected]; [email protected] 1 Results for the DC model Figure 1: DC potential: As in Fig. 2 of the main text, but for water clusters of 6 (a), 10 (b), 16 (c), and 20 (d) molecules. 2 Figure 2: DC potential: Energy deviation from the reference DC value as a function of the cut-off radius r(left) and as a function of the average number of interacting molecules hNii(right) for clusters of 6 (blue circles), 8 (orange squares), 10 (green pluses), 16 (red triangles), and 20 (purple crosses) DC water molecules. The deviations are within 5% when the cut-off radius coincides with the first coordination shell (r∼3Å). We take the absolute value of the energy deviations for the artificial minimum-energy configurations–at rbetween two consecutive coordination shells. Minimum-energy configurations with the cut-off at the first coordination shell for the DC model In Fig.3, we show that, when we include many-body effects until the first coordination shell, the minimum energy configurations are more similar to the results in the DC limit rather than the TIP4P-like limit. Figure 3: DC potential: The lowest-energy configuration for a cluster with 6 (a), 8 (b), 10 (c), 16 (d), and 20 (e) water molecules calculated for our model with the cut-off corresponding to the 1rst coordination shell (r∼3Å). 3 Results for the MB-pol potential Figure 4: MB-pol potential: Average number of interacting molecules hNiias a function of the cut-off radius r(left) and energy deviation from the reference DC value as a function of hNii(right) for clusters of 6 (blue circles), 8 (orange squares), 10 (green pluses), 16 (red triangles), and 20 (purple crosses) MB-pol water molecules. The deviations are within 5% when the cut-off radius coincides with the first coordination shell (r∼3Å). We take the absolute value of the energy deviations for the artificial minimum-energy configurations–at rbetween two consecutive coordination shells. Among the available many-body models, MB-pol1–3 has been shown to correctly perform the many-body analyses of small clusters.4,5 Here we use the MBX calculator6to produce the results in Fig. 4. Due to the expensive computational cost, we adopt the minimum-energy configurations for the DC potential as a starting point for the MB-pol analysis. Results for the KJ potential The many-body KJ potential7is a rigid and four-site model similar to the DC potential. In both models, the polarizable site M is located on the bisector of the H-O-H bond angle. The most crucial difference between the two models is the sites associated with the dispersion force: the oxygen atom for the DC model and the M site for the KJ potential. Due to the expensive computational cost, we computed only two cluster sizes for the KJ potential: 8 and 20 molecules (Fig. 5). 4 Figure 5: KJ potential: As in Fig. 4 but for the KJ water model for clusters of 8 (orange squares) and 20 (purple crosses). References (1) Babin, V.; Leforestier, C.; Paesani, F. Development of a “first principles” water potential with flexible monomers: Dimer potential energy surface, VRT spectrum, and second virial coefficient. Journal of chemical theory and computation 2013,9, 5395–5403. (2) Medders, G. R.; Babin, V.; Paesani, F. Development of a “first-principles” water potential with flexible monomers. III. Liquid phase properties. Journal of chemical theory and computation 2014,10, 2906–2910. (3) Babin, V.; Medders, G. R.; Paesani, F. Development of a “first principles” water potential with flexible monomers. II: Trimer potential energy surface, third virial coefficient, and small clusters. Journal of chemical theory and computation 2014,10, 1599–1607. (4) Medders, G. R.; Paesani, F. Infrared and Raman spectroscopy of liquid water through “first-principles” many-body molecular dynamics. Journal of Chemical Theory and Computation 2015,11, 1145–1154. (5) Reddy, S. K.; Straight, S. C.; Bajaj, P.; Huy Pham, C.; Riera, M.; Moberg, D. R.; Morales, M. A.; Knight, C.; Götz, A. W.; Paesani, F. On the accuracy of the MB5 pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice. The Journal of chemical physics 2016,145, 194504. (6) MBX v0.7. https://github.com/paesanilab/MBX. (7) Kozack, R. E.; Jordan, P. C. Polarizability effects in a four-charge model for water. The Journal of Chemical Physics 1992,96, 3120–3130. 6