Supplemental Material
Molecular Simulation of Structures and Solvation Free Energies of
Passivated Gold Nanoparticles in Supercritical CO2
Zhen Yang, Xiaoning Yang,a) Zhijun Xu, Nannan Yang, Yanruo Yu
State Key Laboratory of Materials-Oriented Chemical Engineering,
College of Chemistry and Chemical Engineering,
Nanjing University of Technology,
Nanjing 210009, China
a)
Author to whom correspondence should be addressed. Electronic mail: Yangxia@njut.edu.cn
1. Distributions of the total solute-solvent interaction energies
FIG. S1. Distributions of the total solute-solvent interaction energies for the 100 windows at
stage 4 in the FC10 passivated gold nanoparticle at the scCO2 density of 1.0 c. This figure
manifests that there is no substantial overlap between adjacent  values near the end points.
Hence, smaller  = 0.005 or 0.0025 was used in the  range from 0.9 to 1.0 at the stage 4,
-1-
since the perturbation approach will be accurate only when states 0 and 1 differ by only a
small amount.
2. Comparison of AC between two simulation runs with different time
scales
FIG. S2. Calculated AC as a function of  for the FC10 passivated gold nanoparticle at the
scCO2 density of 1.0 c. As shown in this figure, the two distribution curves obtained from the
simulation steps of 1  105 and 2  105 are rather identical at each windows. Meanwhile, the
statistical error of AC is estimated by the standard (A ' ) from the block averaging
procedure defined as1
(A ' )  (A   / 2 )  (A ' '  / 2 )
(9)
where
 2 (A    / 2 ) 
nb
1
2
 (A    / 2,b A    / 2 )
nb (nb  1) b 1
(10)
and
 2 (A ' '  / 2 ) 
nb
1
2
 (A ' '  / 2,b A ' '  / 2 )
nb (nb  1) b 1
-2-
(11)
where nb is the total number of blocks. A   / 2 is the block averaged quantity for the
block b at  window. The total error can be obtained from the sum of all windows.
For the case of 1  105 steps, the final AC is – 16.0 ± 1.6 kcal mol–1, whereas the computed
AC is – 16.6 ± 1.1 kcal mol–1 in the case of 2  105 steps. In fact, the illustrated example is
the worse case for the FB-FEP calculation compared to other three stages (AI, AM, and
AS). In terms of above discussions, one can concluded that the simulation length of 1  105 is
enough to sampling the different states at each windows in the FB-FEP calculation.
References
(1) W. L. Jorgensen, and L. L. Thomas, J. Chem. Theory Comput. 4, 869 (2008).
3. Final snapshots of passivated nanoparticles in vacuum or in scCO2 and
the corresponding angle distributions of SAMs
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FIG. S3. Final snapshots of the FC6 passivated gold nanoparticle in scCO2 solvent as well as
in vacuum. For clarity, the CO2 molecules have been removed. Left column: along the Z-axis
direction; Right column: along the Y-axis direction.
FIG. S4. Same as FIG. S3 but for the FC10 passivated gold nanoparticle.
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FIG. S5. Same as FIG. S3 but for the FC16 passivated gold nanoparticle.
FIG. S6. Same as FIG. S3 but for the FC20 passivated gold nanoparticle.
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FIG. S7. Normalized angle distributions between passivating chains for the passivated
nanoparticles. (a) FC6, (b) FC10, (c) FC16, and (d) FC20.
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