Supporting Information on:
“Growth mechanisms of metal nanoparticles by first principles” by Giannis
Mpourmpakis and Dionisios G. Vlachos
Truncated decahedron
Truncated
decahedral
Icosahedral
Icosahedron
Ih
D5h
Cuboctahedron
Cuboctahedral
Oh
Q=0.2
Q=0.2
Q=0.3
Total Charge of inner silver atoms:
Q=-2.6
Q=-3.3
Q=-3.0
Q=+8.3
Q=+8.0
Total Surface Charge:
Q=+7.6
Figure S1: Schematic representation of charge distribution on Ag55+5 Nanoparticles
(NPs) of Truncated decahedral (Tdec), Icosahedral (Ico), and Cuboctahedral (Cubo)
symmetries. The silver atoms in red are the ones that hold the most positive charge. The
Ico NP distributes the positive charge equally to all its surface atoms (red shading).
Charge distribution details for the Ag55+5 NPs
A natural bond orbital (NBO) analysis of the charge distribution on the NPs revealed that
the inner silver metal had stored almost 3 electrons and the outer-surface silver atoms
“lack” a total of 8 electrons, so that the total charge remains +5. Despite those structures
being slightly distorted from the symmetric ones (Icosahedral-Ih, Cuboctahedral-Oh, Tdecahedral-D5h), the charge distribution on the surface followed the symmetry operations.
This means that the less symmetric structure (Tdec) showed a preferential localization of
the positive charge on its edges, whereas the most symmetric (Ico) diffused the positive
charge equally to all the surface atoms.
1
2 bonds
2.5 bonds
3 bonds
Binding energy (kcal/mole)
- 54
7.5
5.55.5
- 52
6.5
7
6
6
- 50
- 48
7.5
7
7.5
7
7
7.25 8
8
7
7
7.5
6.5
6.5
- 46
6
7
- 44
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
Sum of possitive charge on silver atoms
Figure S2: Binding energy of the acetate when bound on silver atoms of the Ag55+5 NPs
possessing different charge distribution. Black squares denote the formation of two bonds
between the acetate and the NP, whereas the red triangles three. The point (circle), which
has 2.5 bonds, is an intermediate state between the other two (with two and three bonds).
The numbers shown near the symbols are the mean coordination number of the silver
atoms interacting with the acetate. In narrow charge regions, linear correlations can be
retrieved between the acetate’s binding energy and the coordination number of the silver
atoms. The binding energy increases by decreasing the coordination number of the silver
atoms in the two-bond region. Contrary, the binding energy increases by increasing the
coordination number of the silver atoms in the three-bond region.
2 bonds
- 54
- 53
Binding energy (kcal/mole)
5.5
5.5
6.5
- 52
7
6
6
6
- 51
7
- 50
7.5
8
- 49
- 48
7.5
6.5
- 47
0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48
Sum of possitive charge on silver atoms
Figure S3: Focus on the two-bond region of the results shown in Figure S2.
2
Figure S4: Initial (left) and final, after optimization (right), structural configurations of
the Ag55 NP interacting with the citrate. Even though in the initial structure the citrate
was interacting with the NP with its three carboxyl groups, it ended up interacting with
the two of them having the third free in solution, responsible for colloidal stabilization.
3
Electron affinity calculations
Calculation of the acetate’s binding energy difference (ΔBE) upon reduction. This
difference can be expressed via the electron affinity (EA) values of the neutral NP and
the NP-acetate complex. BE1 is the unreduced case, where a neutral NP interacts with the
acetate molecule, and BE2 is the reduced case. E stands for the total energy of the system.
   2  1
BE1  E ( Ag 55CH 3COO )   E ( Ag 55 ) 0  E (CH 3COO) 
BE 2  E ( Ag 55CH 3COO )
2

 E ( Ag 55 )  E (CH 3COO )
(1)
(2)

(3)
EA( Ag 55CH 3COO )   E ( Ag 55CH 3COO ) 2  E ( Ag 55CH 3 COO ) 
(4)
EA( Ag 55 ) 0  E ( Ag 55 )   E ( Ag 55 ) 0
(5)
Substitution of the term E(Ag55CH3COO)-2 in Eq. 3 from Eq. 4, substitution of the term
E(Ag55)0 in Eq. 2 from Eq. 5, and substitution of terms BE1 and BE2 of Eq. 1 from Eqs. 2
and 3 gives:
(1)(2)(3)(4)(5)   EA( Ag 55CH 3COO )   EA( Ag 55 ) 0
Detailed explanation of symmetry breaking
We have shown that the capping agent’s binding energy depends on the coordination
number of the silver surface atoms (geometrical characteristics) and on the NP’s EA
value, consequently on the NP’s symmetry (electronic characteristics). The decrease of
the capping agent’s binding energy upon reduction of the NP is different for each NP
studied. The binding energy appears to decrease less on the Tdec NP than on the Ico and
Cubo ones. Considering reduction and growth of these NPs of different symmetry, the
citrate will bind stronger the (100) planes of the Tdec symmetry than the ones of the
Cubo. Moreover, the citrate will bind weaker the (111) planes of the Ico and Cubo NPs
than the (111) plane of the Tdec. Thus, the Ico structure will more easily release citrate (it
only consists of (111) planes), then the Cubo one from its (111) planes and last the Tdec
from its (111) planes. Structures that release citrate will coalesce and reform NPs of
different symmetries, whereas the ones that still bind the citrate will keep their initial
symmetry during NP growth.
Potential Energy Surface calculations
The PES results for each curve are charge consistent, meaning that the deprotonated NP
colloid is always charged -2, the Ag4 system is neutral, and the citrate Ag4 complex is
charged -1.
4
Simulation of solvent by explicit water molecule inclusion
A water molecule interacts with the citrate’s free COOH groups on Ag NP. A hydrogen
bond network forms that further shields the NP surface in the van-der Waals stabilization
mechanism, responsible for the formation of nanowires (as demonstrated in Figures 3 and
4 of the present manuscript). This hetero-hydrogen bond network has actually been
inferred experimentally (water molecules1 and water clusters [see ref 28 of the
manuscript] interacting via hydrogen bonding with COOH groups, in the interstice of the
NPs).
Ag40Citrate2-H2O
Figure S5: Hydrogen bonding when simulating the solvent with explicit water molecule.
1
P.D. Jadzinsky, G. Calero, C.J. Ackerson, D.A. Bushnell, and R.D. Kornberg, Structure of a thiol
monolayer-protected gold nanoparticle at 1.1 angstrom resolution. Science 318(5849), 430-433 (2007).
5
(a)
(C6H5O7)-2
(b)
(c)
(C7H7O7)-2
(C8H9O7)-2
Figure S6 Hydrogen bonding with increasing R-chain of the capping agent. Ag13 NP
interacting with (a) five (C6H5O7)-2 molecules (citrate-2), (b) five (C7H7O7)-2 molecules
(citrate-2 with one more -CH2- group added to the CH2COOH tail), and (c) five (C8H9O7)-
6