Supplementary Information for Electronic signature of the instantaneous asymmetry in the first coordination shell in liquid water

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1 Supplementary Information for Electronic signature of the instantaneous asymmetry in the first coordination shell in liquid water Thomas D. Kühne 1, 2 and Rustam Z. Khaliullin 1, 1 Institute of Physical Chemistry, Johannes Gutenberg University Mainz, Staudingerweg 7, Mainz, Germany 2 Center for Computational Sciences, Johannes Gutenberg University Mainz, Mainz, Germany (Dated: December 2, 212) rustam@khaliullin.com 1

2 SUPPLEMENTARY FIGURES a g(r OO ) ND, Soper 2 XD, Parise 212 NVT AIMD PBE NVT RPMD TPSS-D3-FF NPT RPMD TPSS-D3-FF c ND, Soper 2 XD, Hura 2 ND, Soper 27 ND + XD(set1), Soper 27 ND + XD(set2), Soper 27 ND + XD(set3), Soper 27 XD, Brennan 29 XD, Parise 212 NVT AIMD PBE NVT RPMD TPSS-D3-FF R OO (Angstrom) g(r OO ) 2 b ND, Soper 2 NVT AIMD PBE NVT RPMD TPSS-D3-FF NPT RPMD TPSS-D3-FF g(r OH ) R OH (Angstrom) R OO (Angstrom) Supplementary Figure S1. Experimental (solid lines) and calculated (dashed lines) radial distribution functions for liquid water. Experimental data is derived from neutron diffraction (ND) and X-ray diffraction (XD) measurements. The following references have been used: Soper 2 [4], Hura 2 [61], Soper 27 [62], Brennan 29 [63], Parise 212 [64]. Lines denoted ND+XD(setN) are obtained from the structure refinement based on both x-ray and neutron diffraction data with the XD data from the following references: set1 [6], set2 [65], set3 [66]. 2

3 a 1 MD: PBE NVT ALMO EDA: BLYP b 1 MD: TPSS-D3-FF NVT ALMO EDA: BLYP % of E C E D A (kj/mol) % of E C E D A (kj/mol) E N C E C N. E N C E C N. c 1 MD: TPSS-D3-FF NPT ALMO EDA: BLYP d 1 MD: PBE NVT ALMO EDA: HSE % of E C E D A (kj/mol) % of E C E D A (kj/mol) ḥhdt E N C E C N. E N C E C N. Supplementary Figure S2. Five strongest interactions. Average contributions of the strongest acceptor E N C and donor E C N interactions calculated with various methods, which are described briefly in the titles. The color legend is in Figure 1 of the main text. 3

4 a E C N (kj/mol) b R(O C O N ) (Angstrom) c β(o C O N H) (Degree) Supplementary Figure S3. Results of ALMO EDA based on the BLYP XC functional for snapshots taken from NVT TPSS-D3-FF RPMD simulations. Distribution of the (a) strength, (b) intermolecular distance R and (c) hydrogen bond angle β for the first (red) and second (blue) strongest donor interactions C N. 4

5 a b E C N (t) (kj/mol) R(t) (Angstrom) c β(t) (Degree) Time (fs) Supplementary Figure S4. Results of ALMO EDA based on the BLYP XC functional for snapshots taken from NVT TPSS-D3-FF RPMD simulations. Time dependence of the average (a) strength, (b) intermolecular distance R and (c) hydrogen bond angle β for the first (red) and second (blue) strongest donor interactions C N. Solid lines show the instantaneous values while the dashed lines correspond to the time-average values. 5

6 Density (kg/m 3 ) Supplementary Figure S5. Density distribution in the constant pressure TPSS-D3-FF simulation. 6

7 a E C N (kj/mol) b R(O C O N ) (Angstrom) c β(o C O N H) (Degree) Supplementary Figure S6. Results of ALMO EDA based on the BLYP XC functional for snapshots taken from NPT TPSS-D3-FF RPMD simulations. Distribution of the (a) strength, (b) intermolecular distance R and (c) hydrogen bond angle β for the first (red) and second (blue) strongest donor interactions C N. 7

8 a E C N (kj/mol) b R(O C O N ) (Angstrom) c β(o C O N H) (Degree) Supplementary Figure S7. Results of ALMO EDA based on the HSE6 functional for snapshots taken from NVT PBE AIMD simulations. Distribution of the (a) strength, (b) intermolecular distance R and (c) hydrogen bond angle β for the first (red) and second (blue) strongest donor interactions C N. 8

9 SUPPLEMENTARY TABLE Supplementary Table S1. Hydrogen bond statistics. PBE AIMD TPSS-D3-FF RPMD Double donor of hydrogen 82.8% 69.5% Single donor of hydrogen 16.6% 27.5% No donor of hydrogen.7% 3.% Number of bonds formed by a molecule SUPPLEMENTARY METHODS Assessment of the realibility of molecular dynamics simulations. Energy decomposition analysis (ALMO EDA) described in this work was performed for a set of molecular configurations taken from ab initio molecular dynamics (AIMD) simulations with classical nuclei and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation (XC) functional [67]. Our previous work [15] has shown that PBE provides a realistic description of many important structural and dynamical characteristics of liquid water including radial distribution functions, self-diffusion coefficient, viscosity, vibrational spectrum and hydrogen-bond lifetime. However, the PBE water is somewhat overstructured (Supplementary Figure S1) suggesting that the degree of network distortion, fraction of broken bonds and, thus, the asymmetry in PBE simulations can be underestimated. In this section, we performed ALMO EDA for another set of snapshots generated with molecular dynamics with quantum nuclei and based on a water model, which was constructed to rectify the main shortcomings of the PBE functional. The new water potential was created using the functional form of the flexible q-tip4p/f model [68]. The potential was parameterized by matching its forces to DFT forces calculated for a set of 15 reference configurations. The reference configurations each containing 125 water molecules were extracted from ring polymer molecular dynamics (RPMD) simulations [69] of liquid water in the temperature range of K. These simulations used the q-tip4p/f potential parametrized by Habershon and Manolopoulos [68]. The reference forces were calculated with the CP2K package using a TZV2P basis and a density cutoff 9

10 of 32 Ry in conjunction with the TPSS meta-gga XC functional [7] and the DFT-D3 dispersion correction [71]. We will refer to the newly created potential as TPSS-D3-FF [72]. TPSS-D3-FF was used to perform RPMD simulations with quantum nuclei represented by 32 ring-polymer beads, which correctly account for the quantum behaviour. The simulation cell contained 125 water molecules, the density was fixed at the experimental value of.9966 g/cm 3 and the temperature was set to 3 K as in the main PBE simulation. Supplementary Figures S1a and S1b show that the overstructuring of the first coordination shell is significantly reduced in the new simulation bringing the radial distribution functions closer to the experimental reference (note the large spread in the experimentally derived position and intensity of the first-shell peak in Supplementary Figure S1c). The fraction of intact hydrogen bonds calculated with a commonly used geometric criterion [16] is also smaller than that obtained in PBE simulations (Supplementary Table S1). ALMO EDA was performed for 11 decorrelated snapshots collected from the new trajectory every 1 fs (i.e. 125,125 molecular configurations). The same settings (i.e. basis set, plane-wave cutoff, XC functional) were used for the decomposition analysis as those described in the main text. Supplementary Figure S2b shows that more distorted bonds in the new set of configurations results in a reduction of the average delocalization energy per molecule to 32 kj/mol ( E C 4 kj/mol for the PBE trajectory). However, comparison of the relative contributions of the first two strongest interactions (Supplementary Figures S2a and S2b) shows that their 2.2:1 ratio remains close to that calculated for the PBE trajectory (2.1:1). Furthermore, the distribution of strengths of the donor-acceptor contacts (Supplementary Figure S3) and temporal characteristics of the asymmetry relaxation (Supplementary Figure S4) are very close to those presented in the main text. Such an insignificant difference in the asymmetry for the PBE and TPSS-D3-FF trajectories suggests that the main contribution to the electronic asymmetry (i.e. calculated with ALMO EDA) comes from the distorted hydrogen bonds that are considered intact according to the geometric criteria. To understand the influence of density fluctuations on the asymmetry we performed RPMD simulations with TPSS-D3-FF at constant temperature (3 K) and pressure (1 atm). The histogram in Supplementary Figure S5 demonstrates that despite the relatively small size of the simulation cell (125 molecules) density fluctuations are not significant and the average density of water predicted with the new potential (15 ± 21 kg/m 3 ) is in 1

11 excellent agreement with the experimental value (997 kg/m 3 ). The radial distribution functions (Supplementary Figure S1), decomposition of E C (Supplementary Figure S2c), distribution of strengths of the first two strongest donor-acceptor contacts (Supplementary Figure S6) and characteristics of the time-relaxation process obtained with the NPT simulation are almost indistinguishable from those extracted from the NVT trajectory. In summary, the results of this section show that the main characteristics of the asymmetry obtained for a set of molecular configurations taken from the PBE trajectory are accurate. These characteristics do not change appreciably if more realistic models are used to generate snapshots. Assessment of the realibility of ALMO EDA performed with the BLYP XC functional. The decomposition analysis in this work was performed with the BLYP semilocal XC functional [73, 74]. As many semilocal functionals, BLYP has several important shortcomings. For instance, it systematically underestimates the band gaps with respect to experiment and, thus, overestimate electron delocalization effects. Recent studies have shown that hybrid XC functionals, which include a portion of Hartree-Fock exchange, partially solve these problems. Therefore, to assess the accuracy of the results obtained with the BLYP functional we performed ALMO EDA calculations using the HSE6 screened hybrid XC functional [75]. Since HF exchange drastically increases the computational demand for calculations in periodic systems, we performed ALMO EDA for only 281 snapshots taken from the PBE trajectory and separated by 25 fs. The quality of the Gaussian basis set was reduced to DVZP. Supplementary Figure S2d shows that the HSE6 functional indeed predicts a slightly lower delocalization energy per molecule E C 34 kj/mol than BLYP. However, the ratio between the first two strongest interactions remains 2:1 to 1 in agreement with that presented in the main text. The distribution of the strength of the donor-acceptor contacts (Supplementary Figure S7) is noisy because of the small number of configurations but nevertheless is very close to that shown in Figure 3 in the main text. 11

12 SUPPLEMENTARY REFERENCES [61] G. Hura, J. M. Sorenson, R. M. Glaeser, and T. Head-Gordon, A high-quality X-ray scattering experiment on liquid water at ambient conditions, J. Chem. Phys., 113, (2). [62] A. K. Soper, Joint structure refinement of X-ray and neutron diffraction data on disordered materials: application to liquid water, J. Phys.: Condens. Matter, 19, (27). [63] L. Fu, A. Bienenstock, and S. Brennan, X-ray study of the structure of liquid water, J. Chem. Phys., 131, (29). [64] L. B. Skinner, C. J. Benmore, and J. B. Parise, Comment on Molecular arrangement in water: random but not quite, J. Phys.: Condens. Matter, 24, 3381 (212). [65] A. H. Narten and H. A. Levy, Liquid water - molecular correlation functions from X-ray diffraction, J. Chem. Phys., 55, 2263 (1971). [66] R. T. Hart, C. J. Benmore, J. Neuefeind, S. Kohara, B. Tomberli, and P. A. Egelstaff, Temperature dependence of isotopic quantum effects in water, Phys. Rev. Lett., 94, 4781 (25). [67] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 77, (1996). [68] S. Habershon, T. E. Markland, and D. E. Manolopoulos, Competing quantum effects in the dynamics of a flexible water model, J. Chem. Phys., 131, 2451 (29). [69] I. R. Craig and D. E. Manolopoulos, Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics, J. Chem. Phys., 121, (24). [7] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Climbing the density functional ladder: Nonempirical metageneralized gradient approximation designed for molecules and solids, Phys. Rev. Lett., 91, (23). [71] S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H- Pu, J. Chem. Phys., 132, (21). 12

13 [72] T. Spura, C. John, S. Habershon, D. M. Manolopoulos, and T. D. Kühne, in preparation. [73] A. D. Becke, Density-functional exchange-energy approximation with correct asymptoticbehavior, Phys. Rev. A, 38, (1988). [74] C. T. Lee, W. T. Yang, and R. G. Parr, Development of the colle-salvetti correlation-energy formula into a functional of the electron-density, Phys. Rev. B, 37, (1988). [75] A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys., 125, (26). 13