SUPPLEMENTARY MATERIAL

Dynamics of Linear Molecules in Water: Translation-Rotation Coupling in Jump Motion Driven Diffusion

Anjali S Nair, Puja Banerjee, Sarmistha Sarkar and Biman Bagchi*

Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India – 560012

*Corresponding author’s E-mail: profbiman@gmail.com; bbagchi@iisc.ac.in

S1. Reproducibility of our system with the experimental range for dissolution of CO and NO

The solubility value of CO in water at 298K is 0.028 g/L [G.W.C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longman, London, 1986)], which corresponds to 0.9 x 10-3 M concentration of CO in water. In order to achieve this concentration, for 1 CO molecule, we have to consider 61000 water molecules. Also, NO has a solubility value of (1.94 ± 0.03) x 10-6 mol cm-3 atm-1 at 298 K [I. G. Zacharia and W. M. Deen, Ann. Biomed. Eng 33, 214 (2005)], which corresponds to 1.9 x 10-3 M concentration of NO in water. To achieve this concentration, for 1 NO molecule, we have to consider 29000 water molecules. We have reproduced our results for CO and NO at a concentration of 0.9 x 10-3 M and 1.9 x 10-3 M respectively.

For the simulation of CO in water at 300K, we have considered 1 CO in 61000 water molecules in a cubic simulation cell of length 123 Å (which is equivalent to 0.9 x 10-3 M concentration). Also, for the simulation of NO in water at 300K, we have taken 1 NO in 29000 water molecules in a cubic simulation cell of length 96 Å ( which is equivalent to 1.9 x 10-3 M concentration). For CO in water (at 300K), the new diffusion coefficient that we obtain is (2.64 ± 0.05) x 10-5 cm2 sec-1 , which is comparable to the diffusion value that we have reported in our manuscript (i.e., (2.68±0.07) x 10-5 cm2 sec-1. Similarly, for NO in water (at 300K), the new diffusion coefficient that we obtain is (3.42 ± 0.09) x 10-5 cm2 sec-1, which is comparable to the diffusion value that we have reported in our manuscript (i.e., (3.48±0.10) x 10-5 cm2 sec-1 Furthermore, we have also studied the rotational dynamics by analysing the orientational time correlation function of the new system. For CO in water (at 300K), the decay constants τ1 and τ2 that we obtain are 0.21 ps and 0.16 ps respectively ( τ1 and τ2 values reported in our manuscript are 0.21ps and 0.15 ps respectively). Similarly, for the new system of NO in water (at 300K), the decay constants τ1 and τ2 that we obtain are 0.24 ps and 0.18 ps respectively ( τ1 and τ2 values reported in our manuscript are 0.25 ps and 0.17 ps respectively). Thus, the study of the structural and diffusive properties of the new system do not show significant variation from the system that we have considered in the manuscript (i.e., at 0.1 M concentration). We show the comparison of diffusion coefficients and decay constants in the Table 1 and Table 2 respectively.

Table 1: Comparison of diffusion coefficient from our work and new simulation

Molecule

Temperature(K)

Diffusion coefficient

(1 x 10-5 cm2 s-1)

In manuscript

New simulation

CO

300

2.68±0.07

2.64 ± 0.05

NO

300

3.48±0.10

3.42 ± 0.09

Table 2. Comparison of decay constants τ1 and τ2 of the molecules CO and NO in water at T=300K from our work and new simulation.

Molecule

Temperature(K)

In manuscript

New simulation

CO

300

τ1

(ps)

0.21

0.21

τ2

(ps)

0.15

0.16

NO

300

τ1

(ps)

0.25

0.24

τ2

(ps)

0.17

0.18

Below we also provide the plots of mean square displacement and orientational time correlation function for the new system.

FIG SI. 1. We show the mean square displacement plot of CO and NO in water at temperature T=300 K (from the new simulations)

FIG SI. 2. (a) First order orientational time correlation function of CO and NO molecules in water at 300K (from the new simulation) (b) Second order orientational time correlation function of CO and NO molecules in water at 300K. (from the new simulations).

S2. Pearson Correlation Coefficient

In order to find quantitative, viable support of our claim of correlated jump motion, we have also calculated the Pearson correlation coefficient of translational displacement of CO, NO and CN- with its nearest neighboring water molecules. We have calculated and presented the Pearson correlation coefficients of all eight molecules of CO, NO and CN- separately in tabular forms. Interestingly, all the values of the Pearson coefficient obtained signify positive correlation for the correlated jump motion of each solute molecule with its neighboring water molecules.

The Pearson correlation coefficient ( ) is calculated as follows:

where

cov is the covariance

RS is the translational displacement of CO/NO/CN-

RW is the translational displacement of nearest neighboring water molecule

is the standard deviation of RS

is the standard deviation of RW

Additionally, in order to get a clear visualization of the Pearson correlation, we have provided a few scatter plots (for various Pearson correlation coefficient) of translational displacements of CO, NO and CN- with the translational displacements of nearest neighboring water molecules separately. From the direction of all the scatter plots, it is to be noted that the scatter plots signify the positive correlation for the correlated jump motion. A positive linear trend (i.e., points closely resemble a straight line) in the scatter plots represent strong positive correlation. When the points in the scatter plot are far away from each other or more scattered, the correlation becomes weak.

Table I: Pearson correlation coefficient of translational displacement of all the eight CO molecules with that of its neighboring water molecules.

Pearson correlation coefficient

CO

Neighboring water molecules

WaterNGH1

WaterNGH2

WaterNGH3

CO-1

0.74

0.61

0.77

CO-2

0.67

0.92

0.56

CO-3

0.73

0.55

0.63

CO-4

0.74

0.89

0.66

CO-5

0.60

0.44

0.87

CO-6

0.61

0.92

0.98

CO-7

0.67

0.87

0.75

CO-8

0.60

0.88

0.94

FIG SI. 3. Pearson correlation of CO and neighboring water visualized as scatter plot. It is to be noted that the scatter plots show the positive correlation for the correlated jump motion of CO and neighboring water.

Table II: Pearson correlation coefficient of translational displacement of all the eight NO molecules with that of its neighboring water molecules.

Pearson correlation coefficient

NO

Neighboring water molecules

WaterNGH1

WaterNGH2

WaterNGH3

NO-1

0.76

0.63

0.64

NO-2

0.60

0.55

0.53

NO-3

0.53

0.55

0.64

NO-4

0.74

0.71

0.52

NO-5

0.96

0.66

0.59

NO-6

0.81

0.48

0.56

NO-7

0.74

0.88

0.55

NO-8

0.63

0.73

0.85

FIG SI. 4. Pearson correlation of NO and neighboring water visualized as scatter plot. Scatter plots show the positive correlation for the correlated jump motion of NO and neighboring water.

Table III: Pearson correlation coefficient of translational displacement of all the eight CN- molecules with that of its neighboring water molecules.

Pearson correlation coefficient

CN-

Neighboring water molecules

WaterNGH1

WaterNGH2

WaterNGH3

CN- -1

0.72

0.77

0.79

CN- -2

0.73

0.83

0.56

CN- -3

0.76

0.78

0.75

CN- -4

0.80

0.91

0.89

CN- -5

0.73

0.67

0.50

CN- -6

0.36

0.48

0.59

CN- -7

0.82

0.80

0.90

CN- -8

0.79

0.73

0.75

FIG SI. 5. Pearson correlation of CN- and neighboring water visualized as scatter plot. It is to be noted that the scatter plots show the positive correlation for the correlated jump motion of CN- and neighboring water.

References

1. G.W.C. Kaye and T.H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longman, London, 1986).

2. I.G. Zacharia and W.M. Deen, Ann. Biomed. Eng. 33, 214 (2005).

2