Supporting Information. How Different are the Characteristics of Aqueous Solutions of tert-

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1 Supporting Information How Different are the Characteristics of Aqueous Solutions of tert- Butyl Alcohol and Trimethylamine--oxide? A Molecular Dynamics Simulation Study Dibyendu Bandyopadhyay, 1 Yash Kamble, 2,$ iharendu Choudhury 2,#,* 1 Heavy Water Division, 2 Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 4 85, India # Homi Bhabha ational Institute, Anushaktinagar, Mumbai 494, India $ Present address: Department of Chemical Engineering, Institute of Chemical Technology, Mumbai 419 *Corresponding author: nihcho@barc.gov.in, niharc22@yahoo.com, niharc27@gmail.com S1

2 Methods Order parameters to gauge water structure: Perfect ice structure is ideally tetrahedral with an almost perfect three-dimensional hydrogenbonded (H-bonded) network. Therefore, in ice there are 4 nearest neighbors around a central water molecule. In bulk water, due to thermal fluctuations, the H-bonded network is partially broken and therefore, perfect tetrahedral local order is not maintained. The presence of solutes or ions in water can also disrupt the perfect H-bonded structure and hence the tetrahedral order parameter. Here, we use two order parameters to assess the local structure of water, namely (1) average tetrahedral order parameter (<q>) and distribution of the tetrahedral angle made by any two nearest neighbors to the central water molecule and (2) distribution of hydrogen bonding angle of the first five neighbors of a water molecule. (1). Tetrahedral Order Parameter. The tetrahedral order parameter for the i th water molecule with its four nearest neighbors, q i is defined as qi 1 cos 8 jik (1) j k j where θ jik is the angle formed by the neighbors j and k with the central molecule i. The angle jik 2 is the tetrahedral angle referred in the main text as Td. The average value of the tetrahedral order parameter is then defined by averaging over all the water molecules in the system, viz., 1 q q i, (2) i1 S2

3 where the angular brackets denote time average. However, in case of broken H-bonded structure there will be two- and three-h-bonded water molecules. Therefore, the 3/8 pre-factor in the 2 nd term in Eq. (1) should be changed for two- and three-h-bonded water molecules as the numbers of angles formed are now one and three respectively. So, the pre-factor with the 2 nd term in the equation (1) will be 9/4 and ¾ for two- and three-h-bonded central water molecules respectively so that the molecular tetrahedral order parameter q i varies between and 1. For detailed discussion about the normalization refer to Refs. 1 and 2. (2). Hydrogen-bonded angle of the nearest neighbors. In a solution at high concentration of solutes, the possibility of replacing some of the water neighbors of a central water molecule by the sites of solute molecule is finite. And therefore, to calculate the distribution of hydrogen bonded angle HB of the different neighbors of a central water molecule, correct choice of neighbors is necessary. Once correct neighbors are chosen, we can easily calculate O O - H angle and its distribution. Splitting of g(r) into two hemispheres: In general g(r) can be defined as a ratio of local number density to bulk number density, viz., g ( r) ( r) / V ( r) r), ( where (r) is the number of species/molecules in a spherical shell of inner and outer radii r and r+dr around a central species/molecule. S3

4 ow total number (r) of particles can be split into (r) upper hemisphere + (r) lower hemisphere. For the definition of upper and lower hemispheres see Figure 6 of the main text. ow g (r) can be written as g ( r) ( g Upper hemisphere Upper hemisphere Upper hemisphere ( r) g Lower hemisphere / V ( r) ) / V ( r) Lower hemisphere Lower hemisphere / V ( r) It is apparent that the normalization at large distances for these two quantities will be.5 instead of 1 as in case of normal RDF. ( r) Local mole fraction of TBA/TMAO around a reference TBA/TMAO molecule is calculated by calculating the average numbers of TBA or TMAO and water molecules in a specified spherical region around the reference molecule and calculating the local mole fraction from the above as X 1 st shell solute solute water rcut and the ration X 1st shell /X bulk is finally calculated with the bulk mole fraction of the solute. Here we have chosen a spherical shell of radius 7.8Å around the solute for calculating the above ratio. Dipole moment of TBA and TMAO molecules Dipole moment (DM) of a molecule with atoms are calculated from the following relation: DM q i i1 r i S4

5 where q i is the partial charge on atom i and r i is the position vector of the i th atom with respect to molecular centre. Using the charge distribution and coordinates of the atoms corresponding to the force-field 3 used here, the calculated dipole moments for TBA and TMAO are 2.19 and 5.52 Debye respectively. The DM of only the polar part of the molecule is also calculated by considering C-OH group in case of TBA and =O group in case of TMAO using the same coordinate frame as the whole molecule. The calculated values for polar parts of TBA and TMAO are 2.12 and 4.83 Debye respectively. Results Density of the solution Densities of the aqueous solutions of TBA and TMAO molecules are calculated and the density values are plotted as a function of mole fraction for TBA and TMAO in Figure S1. The available S5

6 experimental densities are also shown in the same figure. The calculated values from the (g/cm 3 ) TBA-water MD Experiment TMAO-water MD Experiment X TBA/TMAO Figure S1: Density of the solution as a function of mole fraction of the solute (TBA or TMAO) present simulation are in very good agreement with the corresponding experimental results. [Refs. 4-6] Thus, the model used here in the present simulation correctly reproduces the volume expansion (density decrease) in case of TBA and volume contraction (density increase) in case of TMAO as a function of the solute mole fraction. 4 It justifies the validity of the model used here. Peak heights of the RDFs The height of the first peak of the RDF presented in Figure 1 of the main text varies with the mole fraction of TBA or TMAO. For TBA-TBA RDF, there are two peaks, one small and the other large peaks within 7.8 Å. Here in Figure S2(a) we show how the heights of these two peaks S6

7 varies with the concentration of TBA. The blue line (see scale on the right axis) is for the small peak at 4.6 Å, which forms probably due to TBA-TBA hydrogen bond formation. The almost Peak height Peak height TBA-TBA Height of the peak at 5.9 A o Height of the peak at 4.6 A TMAO-TMAO Height of the 1st peak Mole fraction of the solute Figure S2: Peak heights of (a) g CC (r) for TBA solution and (b) g (r) for TMAO solution. o linear increase of it with the TBA mole fraction demonstrates that in a concentrated solution, more and more TBA molecules are close to each other with their OH groups aligned towards each other. The change in the peak height of the major RDF peak (the red line) shows nonmonotonic changes with increasing concentration of the TBA. Beyond the TBA mole fraction of.8, the peak height decreases rapidly with concentration. Average number of hydrogen bonds S7

8 <n > <n > HB HB TBA-Wat HB TMAO-Wat HB TBA-TBA HB (a) water-water HB TBA Soln. TMAO Soln (b) X TBA/TMAO Figure S3: Average number of hydrogen bonds formed between two species as a function of concentration of the solute (TBA or TMAO). The extent of hydrogen bond formation between any pair of species in the solution can be quantified by calculating average number of hydrogen bonds formed per molecule of the different species. In Figure S3 (a) we show TBA-TBA and TBA-water hydrogen bonds and in Figure S3(b) the same between TMAO and water is shown as a function of mole fraction of the solute (TBA or TMAO). The TBA-TBA H-bond although small in number (see green line and right axis for the scale) increases monotonically with the concentration of TBA. The average number of TBA-water (red line) and TMAO-water (blue line) hydrogen bonds in aqueous S8

9 solutions of TBA and TMAO respectively however decreases with concentration of the solute ( TBA or TMAO). References (1) Errington, J. R.; Debenedetti, P. G. Relationship between Structural Order and the Anomalies of Liquid Water. ature 21, 49, (2) Bandyopadhyay, D.; Mohan, S.; Ghosh, S. K.; Choudhury,. Correlation of Structural Order, Anomalous Density, and Hydrogen Bonding etwork of Liquid Water. J. Phys. Chem. B 213, 117, (3) Fornili, A.; Civera, M.; Sironi, M.; Fornili, S. L. Molecular Dynamics Simulation of Aqueous Solutions of Trimethylamine--Oxide And tert-butyl Alcohol. Phys. Chem. Chem. Phys. 23, 5, (4) Anikeenko, A.V. ; Kadtsyn, E.D. ; Medvedev,.. Statistical geometry characterization of global structure of TMAO and TBA aqueous solutions. J. Mol. Liq. 217, 245, (5) G. I. Egorov; D. M. Makarov. Densities and volume properties of (water + tert-butanol) over the temperature range of ( to ) K at pressure of.1 MPa, J. Chem. Thermodyn. 211, 43, (6) G. I. Egorov; D. M. Makarov; A. M. Kolker. Density and Volumetric Properties of Aqueous Solutions of Trimethylamine Oxide in the Temperature Range from ( to ) K and at Pressures up to 1 MPa. J. Chem. Eng. Data. 215, 6, S9

Structure of the First and Second Neighbor Shells of Water: Quantitative Relation with Translational and Orientational Order.

Structure of the First and Second Neighbor Shells of Water: Quantitative Relation with Translational and Orientational Order Zhenyu Yan, Sergey V. Buldyrev,, Pradeep Kumar, Nicolas Giovambattista 3, Pablo