Journal of Colloid and Interface Science xxx (2015) xxx–xxx
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Solvent effects on geometrical structures and electronic properties of metal Au, Ag, and Cu nanoparticles of different sizes Mingqiang Hou ⇑, Qingqing Mei, Buxing Han ⇑ CAS Key Laboratory of Colloid, Interface and Chemical Thermodynamics, Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
g r a p h i c a l a b s t r a c t
The properties of the solvents influence the geometrical structure and electronic nature of the metallic nanoparticles of different sizes.
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Article history: Received 1 December 2014 Accepted 31 December 2014 Available online xxxx Keywords: Solvent effect Metal nanoparticles Electronic property
a b s t r a c t Study of the geometrical structures and electronic properties of metal nanoparticles is a very interesting topic. In this work we studied the effects of cyclohexane, benzene, ethanol, and water on bond lengths, Mulliken charge distributions, binding energy (BE), energy gap between highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (DHL), ionization potential (IP) and electron affinity (EA) of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 nanoparticles by using density functional theory (DFT). The results indicated that the properties of the solvents influence the geometrical structures and electronic properties of the metallic nanoparticles considerably, and the solvent effect depends on the properties of the solvents, the size of the metal particles, and the category of the metals. Generally, the properties of smaller particles are more sensitive to the change of the solvents, and the polar solvents have larger effect on the properties. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction Nano-materials have been widely used in many fields, such as catalysis, nano-electronics, and nano-medicine due to their unique properties. For example, nanoparticles have excellent catalytic properties in chemical reactions comparing with bulk catalysts in ⇑ Corresponding authors. Fax: +86 10 62559373. E-mail addresses: [email protected] (M. Hou), [email protected] (B. Han).
many cases. Their performances vary with sizes, shapes, structures, and solvents [1–10]. Study of the variation of the geometry, structure, and electronic property with different factors is of great importance from both academic and practical points of view, and this has attracted much attention in recent years. For example, Li et al. investigated the decomposition of HCOOH on a Pd7 cluster in vacuum and water, and found that water affects the reaction pathway, activation energy, and reaction energy obviously [11]. The interactions between solvent and metal atoms on the surface
http://dx.doi.org/10.1016/j.jcis.2014.12.096 0021-9797/Ó 2015 Elsevier Inc. All rights reserved.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
of nanoparticles change the electronic properties and geometric structures of nanoparticles, and indirectly affect their catalytic properties. Remacle et al. calculated the electronic properties of different geometric structures of Au11 and Au55 clusters in vacuum and water [12–14]. It was demonstrated that water has considerable influence on the structure and electronic properties. Li and Liu carried out a comprehensive study on electronic and geometrical properties and the photocatalytic activity of TiO2 anatase nanoparticles in aqueous solution [15]. Study of the dependence of the properties of metallic nanoparticles on the size of metals, nature of metals, and properties of solvents is a very interesting topic. However, our literature survey indicates that there is a lack of systematic investigation on this. In this paper, we studied the effects of different solvents on the structures and electronic properties of gold, silver, and copper nanoparticles of different sizes. It was demonstrated that the properties of the solvents influence the properties of the metallic nanoparticles considerably, and the solvent effects depend on the properties of the solvents, the size of the metal particles, and the category of metals. 2. Method All the calculations were carried out by employing Amsterdam Density Functional (ADF2014) program package. In order to account for the relativistic effect which is quite significant for Au, Ag, and Cu atom, we performed the calculations using the scalar relativistic method based on zeroth-order regular approximation (ZORA) [16,17]. All the structures were optimized using the Perdew–Wang 1991 (PW91) exchange–correlation (XC) potential [18] within a generalized gradient approximation (GGA). For all atoms, we used the triple-n Slater type orbital (STO) basis set added with two polarization functions (TZ2P in ADF basis library) at the frozen core approximation level. The frozen cores considered for various atoms are 1s–4f for Au, 1s–4p for Ag, and 1s–3p for Cu. The geometries were optimized using the quasi-Newton method and the Hessian is updated in the optimization process using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [19–22] until the convergence criteria of 104 au for the Cartesian gradient and
106 au for energy were met. We also carried out vibrational analysis on the optimized structures of substituted clusters in order to check the stability of these clusters, and all of them turned out to be stable with no imaginary vibrational frequency. The conductor-like screening model (COSMO) was implemented to study the solvent effect on material properties in solution. 3. Results and discussion 3.1. Effect of solvents on the bond lengths In this work, we used the Au20 [23], Ag20 [24], Cu20 [25] with Td symmetry and Au38 [26], Ag38 [27], Cu38 [28] with Oh symmetry as the research objects, which are shown in Fig. 1. We studied the effects of solvents cyclohexane, benzene, ethanol, and water on the bond lengths of the nanoparticles, and the results are listed in Table 1. For the metal particles, the bond lengths in vacuum calculated in this work agree well with that reported by other researchers [23,29]. Our results in this work indicate that, in general, the bond lengths of the M20 (M = Au, Ag, Cu) changes notably as the solvent changes, and the polar solvents, ethanol and water, have larger effect on the bond lengths than the non-polar solvents, cyclohexane and benzene. For the M38 (M = Au, Ag, Cu), the effect of the solvents on the bond lengths is not obvious. Therefore, we can conclude that the geometric structures of smaller nanoparticles are more sensitive to the change of their environment, and the polar solvents have larger effect. 3.2. Effect of the solvents on the Mulliken charge distributions Table 2 and Fig. 2 present the Mulliken charge distributions on atoms of the nanoparticles in vacuum and different solvents. In vacuum, the charge of the vertex and surface atoms in Au20 is negative, and the charge of edge atoms is positive. With the increase of polarity of the solvents, the positive charge of the surface atoms gradually become less, and the absolute value the negative charge on the edge atoms become more, but the vertex atoms change from negatively charged into positively charged. The results show that the polarity of the solvents influences the Mulliken charge
Au20
Ag20
Cu20
Au38
Ag38
Cu38
Fig. 1. Structures of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 nanoparticles.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx Table 1 Bond lengths of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents. The unit is in Å. Vacuum
Cyclohexane
Benzene
Ethanol
Table 2 Mulliken charge distributions of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents.
Water
Au20 dV–E d1E–E dE–S d2E–E dS–S
2.710 2.937 2.814 2.679 3.129
2.709 2.937 2.815 2.680 3.134
2.709 2.936 2.814 2.680 3.139
2.707 2.935 2.815 2.681 3.140
2.707 2.935 2.815 2.681 3.140
Ag20 dV–E d1E–E dE–S d2E–E dS–S
2.803 2.970 2.876 2.775 3.099
2.803 2.970 2.876 2.775 3.099
2.803 2.970 2.876 2.775 3.099
2.799 2.964 2.878 2.787 3.094
2.799 2.964 2.878 2.787 3.094
Cu20 dV–E d1E–E dE–S d2E–E dS–S
2.454 2.577 2.522 2.464 2.676
2.454 2.570 2.520 2.466 2.676
2.454 2.569 2.520 2.467 2.676
2.453 2.565 2.520 2.471 2.677
2.453 2.565 2.520 2.471 2.677
Au38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.837 2.803 2.835 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
Ag38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
Cu38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.544 2.525 2.537 2.529 2.555 2.638
2.544 2.524 2.537 2.529 2.555 2.638
2.544 2.524 2.537 2.529 2.555 2.638
2.544 2.525 2.538 2.529 2.555 2.638
2.544 2.525 2.538 2.529 2.555 2.638
Note: In this table dX–Y is distance between two atoms located at X and Y positions, where X, Y stand for V (vertex), E (edge), S (surface), and I (inner) positions (Fig. 1). d1E–E and d2E–E denote the distances between two atoms which lie on the different edges and on the same edge, respectively. The d1V–V and d2V–V are the distances between two atoms which lie on the edge between a square and a hexagon and between two neighbor hexagons, respectively.
distribution considerably, and with the increase of polarity, electrons flow from the vertex atoms to edge and surface atoms. For Ag20, the vertex and surface atoms are negatively charged, and the charge of edge atoms is positive in vacuum. With the increase of solvent polarity, the positive charge of edge atoms gradually become less, and the negative charge on the surface atoms gradually become more, and negative charge on the vertex atoms decreases gradually. So with the increase of solvent polarity, electrons flow from the vertex atoms to edge and surface atoms. In vacuum, the charges of vertex and edge atoms of Cu20 are positive, and that of the surface atoms is negative. With the increase of polarity of the solvents, the vertex atoms become more positively charged, and the surface atoms is more negatively charged. The positive charge on the edge atoms gradually reduces with increasing the polarity of the solvents, and changes into negative in the polar solvents ethanol and water. The results indicate that with the increase of polarity of the solvents, electrons flow from the vertex atoms to edge and surface atoms. For Au38, in vacuum the charges of the vertex and surface atoms are negative, and the charges of inter atoms are positive. With the increase of polarity of the solvents, the negative charge of the ver-
Vacuum
Cyclohexane
Benzene
Ethanol
Water
Au20 V E S
0.0640 0.0109 0.0967
0.0354 0.0169 0.0861
0.0300 0.0182 0.0847
0.0112 0.0265 0.0684
0.0142 0.0271 0.0672
Ag20 V E S
0.0801 0.0113 0.1139
0.0585 0.0153 0.1045
0.0545 0.0161 0.1028
0.0198 0.0212 0.0834
0.0174 0.0216 0.0823
Cu20 V E S
0.0221 0.0208 0.0402
0.0554 0.0270 0.0257
0.0613 0.0281 0.0228
0.1111 0.0362 0.0026
0.1147 0.0368 0.0044
Au38 V S I
0.0541 0.0054 0.2236
0.0499 0.0133 0.2173
0.0493 0.0145 0.2165
0.0447 0.0240 0.2107
0.0452 0.0238 0.2124
Ag38 V S I
0.0947 0.0100 0.3920
0.0893 0.0229 0.3877
0.0884 0.0250 0.3871
0.0824 0.0404 0.3835
0.0818 0.0422 0.3836
Cu38 V S I
0.0032 0.0460 0.0483
0.0044 0.0304 0.0581
0.0055 0.0279 0.0593
0.0137 0.0093 0.0672
0.0139 0.0077 0.0659
tex atoms becomes smaller, and the negative charge on the surface atoms gradually becomes larger, and positive charge on inner atoms decreases slightly. So with the increase of polarity of the solvents, electrons flow from the vertex atoms to surface and inner atoms. For Ag38, the charges of the vertex and surface atoms are negative, and the charge of inner atoms is positive in vacuum. With the increase of polarity of the solvents, the negative charge of vertex atoms becomes less and negative charge on the surface atoms becomes more, and the positive charge on inner atoms decreases. The results indicate that with the increase of polarity of the solvents, electrons flow from the vertex atoms to surface and inner atoms. For Cu38, in vacuum the charges of vertex and inner atoms are negative, and that of surface atoms is positive. For the vertex atoms, the charge changes from negative in vacuum into positive in all the solvents, and the positive charge becomes larger with the increase of polarity of the solvents. Moreover, with increasing the polarity of the solvents the positive charge on the surface atoms gradually become less, and negative charge on inner atoms increases. So with the increase of polarity, electrons flow from the vertex atoms to surface and inner atoms. In general, it can be known from the results above that the polarity of the solvents affects the charge distributions of the nanoparticles considerably. The charge distribution of the smaller particles is more sensitive to their environments than the larger ones. The solvent effect of the charge distributions increases with increasing polarity of the polar solvents. The main reason is that the interaction between the solvent and the nanoparticles becomes stronger with the increase of the polarity of the solvents.
3.3. Other properties The bond energy (BE), energy gap between HOMO and LUMO (DHL), ionization potential (IP), and electron affinity (EA) were also calculated in this work, and the results are listed in Table 3. The
Please cite this article in press as: M. Hou et al., J. Colloid Interface Sci. (2015), http://dx.doi.org/10.1016/j.jcis.2014.12.096
-0.1
Vac
C
B
E
W
Solvent
0.2 0.1
Au38
0.0 -0.1
Vac
C
B
Solvent
E
W
Ag20 0.0
-0.1
Vac
C
B
E
W
Solvent
0.4 0.2
Ag38
0.0 -0.2
Vac
C
B
E
W
Solvent
Mulliken charge distributions
0.0
0.1
Mulliken charge distributions
Au20
Mulliken charge distributions
Mulliken charge distributions
0.1
Mulliken charge distributions
M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
Mulliken charge distributions
4
0.1
Cu20 0.0
-0.1
Vac
C
B
E
W
Solvent
0.1
Cu38 0.0
-0.1
Vac
C
B
E
W
Solvent
Fig. 2. Mulliken charge distributions of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water; N, vertex atom in M20; d, edge atom in M20; j, surface atom in M20; 4, vertex atom in M38; h, surface atom in M38; s, inner atom in M38).
Table 3 Binding energy (BE), energy gap between HOMO and LUMO (DHL), ionization potential (IP) and electron affinity (EA) of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents. The units of all are properties are in eV.
DHL
IP
EA
Au20
Vacuum Cyclohexane Benzene Ethanol Water
BE 50.98 51.01 51.02 51.08 51.08
1.785 1.831 1.837 1.899 1.903
7.179 6.444 6.350 5.801 5.755
2.603 3.120 3.208 3.643 3.672
Ag20
Vacuum Cyclohexane Benzene Ethanol Water
37.26 37.30 37.31 37.36 37.36
1.801 1.839 1.845 1.891 1.897
6.237 5.450 5.347 4.746 4.694
1.828 2.272 2.330 2.695 2.716
Cu20
None Cyclohexane Benzene Ethanol Water
49.58 49.69 49.71 49.86 49.86
1.527 1.567 1.574 1.638 1.644
6.443 5.596 5.487 4.859 4.805
1.984 2.480 2.546 2.968 2.993
Au38
Vacuum Cyclohexane Benzene Ethanol Water
100.15 100.13 100.13 100.11 100.09
0.0757 0.0764 0.0766 0.0789 0.0794
5.806 5.107 5.014 4.457 4.403
3.423 3.862 3.920 4.274 4.309
Ag38
Vacuum Cyclohexane Benzene Ethanol Water
74.30 74.33 74.33 74.35 74.35
0.3718 0.3731 0.3736 0.3760 0.3760
5.071 4.321 4.221 3.622 3.551
2.786 3.129 3.172 3.457 3.488
Cu38
Vacuum Cyclohexane Benzene Ethanol Water
100.95 101.01 101.02 101.08 101.06
0.4926 0.4922 0.4927 0.4949 0.4958
5.513 4.695 4.587 4.013 3.880
2.966 3.369 3.421 3.755 3.766
results are also illustrated in Figs. 3–6 in order to show the variation of the properties more clearly. It can be known from the data in Fig. 3 that, as expected, the binding energy is negative for all the metal particles. The effect of solvents on the binding energy is not considerable for these nanoparticles. Fig. 4 shows that in vacuum, the DHL values of the M20 (M = Au, Ag, and Cu) are much larger than that of the
M38, indicating that the M20 particles are more stable than the M38 particles. The solvents influence the energy gap DHL of Au20, Ag20, and Cu20 considerably, and the DHL becomes larger with the increase of polarity of the solvents, demonstrating that the M20 particles is more stable in the polar solvents. The solvents have less effect on the DHL of the M38 particles than that of the M20 particles.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
Au20 -51.0
Vac
C
B
E
W
Ag20 -37.3
-37.4
Vac
C
-100.0
Au38 -100.1
-100.2
Vac
C
B
E
-49.5
W
Cu20
-49.6 -49.7 -49.8 -49.9
Vac
C
E
W
-74.2
Ag 38 -74.3
-74.4
Vac
C
Solvent
B
B
E
W
Solvent
Solvent Binding Energy /ev
Binding Energy /ev
Solvent
B
E
W
Binding Energy /ev
-51.1
-37.2
Binding Energy /ev
Binding Energy /ev
Binding Energy /ev
-50.9
-100.9
Cu38 -101.0
-101.1
Vac
C
Solvent
B
E
W
Solvent
2.0
1.8
C
B
E
W
1.9 1.8 1.7
Vac
C
0.09
Au38
0.08
0.07
Vac
C
B
E
E
W
Cu20 1.7 1.6 1.5
Vac
C
W
0.38
Ag38
0.37
0.36
Vac
Solvent
C
B
E
B
E
W
Solvent
Solvent Energy gap /eV
Energy gap /eV
Solvent
B
Energy gap /eV
Vac
Ag20
Energy gap /eV
1.9
1.7
1.8
2.0
Au20
Energy gap /eV
Energy gap /eV
Fig. 3. The bond energy of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
0.50
0.48
W
Cu38
0.49
Vac
C
B
E
W
Solvent
Solvent
Fig. 4. The energy gap between HOMO and LUMO of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
Au20 Au38
Ag20 Ag38
Cu20 Cu38
7 6 5 4 3
C
B
E
W
Solvent Fig. 5. The ionization potential of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
The results in Fig. 5 show that the ionization potentials of the metal particles in the solvents are smaller than those in vacuum, and decrease with the increase of the polarity of the solvents. In
Ag20 Ag38
Cu20 Cu38
-2.0 -2.5 -3.0 -3.5 -4.0 -4.5
Vac
Au20 Au38
-1.5
Electron Affinity / eV
Ionization Potential / eV
8
Vac
C
B
E
W
Solvent Fig. 6. The electron affinity of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
other words, it is easier for a neutral particle to lose electron in the solvents, and losing electron in the polar solvents is easier than in the non-polar solvents. It can be known from Fig. 6 that for all of
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
the metal particles, the electron affinity, which is a measure of how tightly the cluster can bind an electron, is negative in vacuum and the solvents. The absolute value in the solvents is larger than that in vacuum, and increases with increasing the polarity of the solvents. Therefore, it is easier for a neutral particle to get an electron in solvent than in vacuum, and is easier in a polar solvent than in a non-polar solvent. 4. Conclusion The geometrical structures and electronic properties of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in vacuum, cyclohexane, benzene, ethanol, and water have been investigated by DFT method in order to explore the effects of solvents and particles size on these properties. The solvents affect the properties of the nanoparticles considerably. The charge distribution of the smaller particles is more sensitive to the change of the solvents, and the solvent effect increases with increasing polarity of the polar solvents. The solvents have considerable influence on the DHL of Au20, Ag20, and Cu20, and the DHL becomes larger with the increase of polarity of the solvents, demonstrating that the M20 particles is more stable in the polar solvents. The solvents have less effect on the DHL of the M38 than that of the M20. The ionization potentials of the metal particles in the solvents are smaller than those in vacuum, and decrease with the increase of the polarity of the solvents. For all the metal particles, the electron affinity is negative in vacuum and in the solvents, and the absolute value in the solvents is larger than that in vacuum, and increases with the increase of the polarity of the solvents. Acknowledgments The authors acknowledge the National Natural Science Foundation of China (21133009, U1232203, 21021003) and Chinese Academy of Sciences (KJCX2.YW.H16).
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Solvent effects on geometrical structures and electronic properties of metal Au, Ag, and Cu nanoparticles of different sizes Mingqiang Hou ⇑, Qingqing Mei, Buxing Han ⇑ CAS Key Laboratory of Colloid, Interface and Chemical Thermodynamics, Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
g r a p h i c a l a b s t r a c t
The properties of the solvents influence the geometrical structure and electronic nature of the metallic nanoparticles of different sizes.
a r t i c l e
i n f o
Article history: Received 1 December 2014 Accepted 31 December 2014 Available online xxxx Keywords: Solvent effect Metal nanoparticles Electronic property
a b s t r a c t Study of the geometrical structures and electronic properties of metal nanoparticles is a very interesting topic. In this work we studied the effects of cyclohexane, benzene, ethanol, and water on bond lengths, Mulliken charge distributions, binding energy (BE), energy gap between highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (DHL), ionization potential (IP) and electron affinity (EA) of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 nanoparticles by using density functional theory (DFT). The results indicated that the properties of the solvents influence the geometrical structures and electronic properties of the metallic nanoparticles considerably, and the solvent effect depends on the properties of the solvents, the size of the metal particles, and the category of the metals. Generally, the properties of smaller particles are more sensitive to the change of the solvents, and the polar solvents have larger effect on the properties. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction Nano-materials have been widely used in many fields, such as catalysis, nano-electronics, and nano-medicine due to their unique properties. For example, nanoparticles have excellent catalytic properties in chemical reactions comparing with bulk catalysts in ⇑ Corresponding authors. Fax: +86 10 62559373. E-mail addresses: [email protected] (M. Hou), [email protected] (B. Han).
many cases. Their performances vary with sizes, shapes, structures, and solvents [1–10]. Study of the variation of the geometry, structure, and electronic property with different factors is of great importance from both academic and practical points of view, and this has attracted much attention in recent years. For example, Li et al. investigated the decomposition of HCOOH on a Pd7 cluster in vacuum and water, and found that water affects the reaction pathway, activation energy, and reaction energy obviously [11]. The interactions between solvent and metal atoms on the surface
http://dx.doi.org/10.1016/j.jcis.2014.12.096 0021-9797/Ó 2015 Elsevier Inc. All rights reserved.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
of nanoparticles change the electronic properties and geometric structures of nanoparticles, and indirectly affect their catalytic properties. Remacle et al. calculated the electronic properties of different geometric structures of Au11 and Au55 clusters in vacuum and water [12–14]. It was demonstrated that water has considerable influence on the structure and electronic properties. Li and Liu carried out a comprehensive study on electronic and geometrical properties and the photocatalytic activity of TiO2 anatase nanoparticles in aqueous solution [15]. Study of the dependence of the properties of metallic nanoparticles on the size of metals, nature of metals, and properties of solvents is a very interesting topic. However, our literature survey indicates that there is a lack of systematic investigation on this. In this paper, we studied the effects of different solvents on the structures and electronic properties of gold, silver, and copper nanoparticles of different sizes. It was demonstrated that the properties of the solvents influence the properties of the metallic nanoparticles considerably, and the solvent effects depend on the properties of the solvents, the size of the metal particles, and the category of metals. 2. Method All the calculations were carried out by employing Amsterdam Density Functional (ADF2014) program package. In order to account for the relativistic effect which is quite significant for Au, Ag, and Cu atom, we performed the calculations using the scalar relativistic method based on zeroth-order regular approximation (ZORA) [16,17]. All the structures were optimized using the Perdew–Wang 1991 (PW91) exchange–correlation (XC) potential [18] within a generalized gradient approximation (GGA). For all atoms, we used the triple-n Slater type orbital (STO) basis set added with two polarization functions (TZ2P in ADF basis library) at the frozen core approximation level. The frozen cores considered for various atoms are 1s–4f for Au, 1s–4p for Ag, and 1s–3p for Cu. The geometries were optimized using the quasi-Newton method and the Hessian is updated in the optimization process using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [19–22] until the convergence criteria of 104 au for the Cartesian gradient and
106 au for energy were met. We also carried out vibrational analysis on the optimized structures of substituted clusters in order to check the stability of these clusters, and all of them turned out to be stable with no imaginary vibrational frequency. The conductor-like screening model (COSMO) was implemented to study the solvent effect on material properties in solution. 3. Results and discussion 3.1. Effect of solvents on the bond lengths In this work, we used the Au20 [23], Ag20 [24], Cu20 [25] with Td symmetry and Au38 [26], Ag38 [27], Cu38 [28] with Oh symmetry as the research objects, which are shown in Fig. 1. We studied the effects of solvents cyclohexane, benzene, ethanol, and water on the bond lengths of the nanoparticles, and the results are listed in Table 1. For the metal particles, the bond lengths in vacuum calculated in this work agree well with that reported by other researchers [23,29]. Our results in this work indicate that, in general, the bond lengths of the M20 (M = Au, Ag, Cu) changes notably as the solvent changes, and the polar solvents, ethanol and water, have larger effect on the bond lengths than the non-polar solvents, cyclohexane and benzene. For the M38 (M = Au, Ag, Cu), the effect of the solvents on the bond lengths is not obvious. Therefore, we can conclude that the geometric structures of smaller nanoparticles are more sensitive to the change of their environment, and the polar solvents have larger effect. 3.2. Effect of the solvents on the Mulliken charge distributions Table 2 and Fig. 2 present the Mulliken charge distributions on atoms of the nanoparticles in vacuum and different solvents. In vacuum, the charge of the vertex and surface atoms in Au20 is negative, and the charge of edge atoms is positive. With the increase of polarity of the solvents, the positive charge of the surface atoms gradually become less, and the absolute value the negative charge on the edge atoms become more, but the vertex atoms change from negatively charged into positively charged. The results show that the polarity of the solvents influences the Mulliken charge
Au20
Ag20
Cu20
Au38
Ag38
Cu38
Fig. 1. Structures of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 nanoparticles.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx Table 1 Bond lengths of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents. The unit is in Å. Vacuum
Cyclohexane
Benzene
Ethanol
Table 2 Mulliken charge distributions of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents.
Water
Au20 dV–E d1E–E dE–S d2E–E dS–S
2.710 2.937 2.814 2.679 3.129
2.709 2.937 2.815 2.680 3.134
2.709 2.936 2.814 2.680 3.139
2.707 2.935 2.815 2.681 3.140
2.707 2.935 2.815 2.681 3.140
Ag20 dV–E d1E–E dE–S d2E–E dS–S
2.803 2.970 2.876 2.775 3.099
2.803 2.970 2.876 2.775 3.099
2.803 2.970 2.876 2.775 3.099
2.799 2.964 2.878 2.787 3.094
2.799 2.964 2.878 2.787 3.094
Cu20 dV–E d1E–E dE–S d2E–E dS–S
2.454 2.577 2.522 2.464 2.676
2.454 2.570 2.520 2.466 2.676
2.454 2.569 2.520 2.467 2.676
2.453 2.565 2.520 2.471 2.677
2.453 2.565 2.520 2.471 2.677
Au38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.837 2.803 2.835 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
2.837 2.803 2.836 2.835 2.807 3.073
Ag38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
2.903 2.885 2.898 2.898 2.896 3.018
Cu38 d1V–V d2V–V dV–S dV–I dI–I dI–S
2.544 2.525 2.537 2.529 2.555 2.638
2.544 2.524 2.537 2.529 2.555 2.638
2.544 2.524 2.537 2.529 2.555 2.638
2.544 2.525 2.538 2.529 2.555 2.638
2.544 2.525 2.538 2.529 2.555 2.638
Note: In this table dX–Y is distance between two atoms located at X and Y positions, where X, Y stand for V (vertex), E (edge), S (surface), and I (inner) positions (Fig. 1). d1E–E and d2E–E denote the distances between two atoms which lie on the different edges and on the same edge, respectively. The d1V–V and d2V–V are the distances between two atoms which lie on the edge between a square and a hexagon and between two neighbor hexagons, respectively.
distribution considerably, and with the increase of polarity, electrons flow from the vertex atoms to edge and surface atoms. For Ag20, the vertex and surface atoms are negatively charged, and the charge of edge atoms is positive in vacuum. With the increase of solvent polarity, the positive charge of edge atoms gradually become less, and the negative charge on the surface atoms gradually become more, and negative charge on the vertex atoms decreases gradually. So with the increase of solvent polarity, electrons flow from the vertex atoms to edge and surface atoms. In vacuum, the charges of vertex and edge atoms of Cu20 are positive, and that of the surface atoms is negative. With the increase of polarity of the solvents, the vertex atoms become more positively charged, and the surface atoms is more negatively charged. The positive charge on the edge atoms gradually reduces with increasing the polarity of the solvents, and changes into negative in the polar solvents ethanol and water. The results indicate that with the increase of polarity of the solvents, electrons flow from the vertex atoms to edge and surface atoms. For Au38, in vacuum the charges of the vertex and surface atoms are negative, and the charges of inter atoms are positive. With the increase of polarity of the solvents, the negative charge of the ver-
Vacuum
Cyclohexane
Benzene
Ethanol
Water
Au20 V E S
0.0640 0.0109 0.0967
0.0354 0.0169 0.0861
0.0300 0.0182 0.0847
0.0112 0.0265 0.0684
0.0142 0.0271 0.0672
Ag20 V E S
0.0801 0.0113 0.1139
0.0585 0.0153 0.1045
0.0545 0.0161 0.1028
0.0198 0.0212 0.0834
0.0174 0.0216 0.0823
Cu20 V E S
0.0221 0.0208 0.0402
0.0554 0.0270 0.0257
0.0613 0.0281 0.0228
0.1111 0.0362 0.0026
0.1147 0.0368 0.0044
Au38 V S I
0.0541 0.0054 0.2236
0.0499 0.0133 0.2173
0.0493 0.0145 0.2165
0.0447 0.0240 0.2107
0.0452 0.0238 0.2124
Ag38 V S I
0.0947 0.0100 0.3920
0.0893 0.0229 0.3877
0.0884 0.0250 0.3871
0.0824 0.0404 0.3835
0.0818 0.0422 0.3836
Cu38 V S I
0.0032 0.0460 0.0483
0.0044 0.0304 0.0581
0.0055 0.0279 0.0593
0.0137 0.0093 0.0672
0.0139 0.0077 0.0659
tex atoms becomes smaller, and the negative charge on the surface atoms gradually becomes larger, and positive charge on inner atoms decreases slightly. So with the increase of polarity of the solvents, electrons flow from the vertex atoms to surface and inner atoms. For Ag38, the charges of the vertex and surface atoms are negative, and the charge of inner atoms is positive in vacuum. With the increase of polarity of the solvents, the negative charge of vertex atoms becomes less and negative charge on the surface atoms becomes more, and the positive charge on inner atoms decreases. The results indicate that with the increase of polarity of the solvents, electrons flow from the vertex atoms to surface and inner atoms. For Cu38, in vacuum the charges of vertex and inner atoms are negative, and that of surface atoms is positive. For the vertex atoms, the charge changes from negative in vacuum into positive in all the solvents, and the positive charge becomes larger with the increase of polarity of the solvents. Moreover, with increasing the polarity of the solvents the positive charge on the surface atoms gradually become less, and negative charge on inner atoms increases. So with the increase of polarity, electrons flow from the vertex atoms to surface and inner atoms. In general, it can be known from the results above that the polarity of the solvents affects the charge distributions of the nanoparticles considerably. The charge distribution of the smaller particles is more sensitive to their environments than the larger ones. The solvent effect of the charge distributions increases with increasing polarity of the polar solvents. The main reason is that the interaction between the solvent and the nanoparticles becomes stronger with the increase of the polarity of the solvents.
3.3. Other properties The bond energy (BE), energy gap between HOMO and LUMO (DHL), ionization potential (IP), and electron affinity (EA) were also calculated in this work, and the results are listed in Table 3. The
Please cite this article in press as: M. Hou et al., J. Colloid Interface Sci. (2015), http://dx.doi.org/10.1016/j.jcis.2014.12.096
-0.1
Vac
C
B
E
W
Solvent
0.2 0.1
Au38
0.0 -0.1
Vac
C
B
Solvent
E
W
Ag20 0.0
-0.1
Vac
C
B
E
W
Solvent
0.4 0.2
Ag38
0.0 -0.2
Vac
C
B
E
W
Solvent
Mulliken charge distributions
0.0
0.1
Mulliken charge distributions
Au20
Mulliken charge distributions
Mulliken charge distributions
0.1
Mulliken charge distributions
M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
Mulliken charge distributions
4
0.1
Cu20 0.0
-0.1
Vac
C
B
E
W
Solvent
0.1
Cu38 0.0
-0.1
Vac
C
B
E
W
Solvent
Fig. 2. Mulliken charge distributions of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water; N, vertex atom in M20; d, edge atom in M20; j, surface atom in M20; 4, vertex atom in M38; h, surface atom in M38; s, inner atom in M38).
Table 3 Binding energy (BE), energy gap between HOMO and LUMO (DHL), ionization potential (IP) and electron affinity (EA) of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents. The units of all are properties are in eV.
DHL
IP
EA
Au20
Vacuum Cyclohexane Benzene Ethanol Water
BE 50.98 51.01 51.02 51.08 51.08
1.785 1.831 1.837 1.899 1.903
7.179 6.444 6.350 5.801 5.755
2.603 3.120 3.208 3.643 3.672
Ag20
Vacuum Cyclohexane Benzene Ethanol Water
37.26 37.30 37.31 37.36 37.36
1.801 1.839 1.845 1.891 1.897
6.237 5.450 5.347 4.746 4.694
1.828 2.272 2.330 2.695 2.716
Cu20
None Cyclohexane Benzene Ethanol Water
49.58 49.69 49.71 49.86 49.86
1.527 1.567 1.574 1.638 1.644
6.443 5.596 5.487 4.859 4.805
1.984 2.480 2.546 2.968 2.993
Au38
Vacuum Cyclohexane Benzene Ethanol Water
100.15 100.13 100.13 100.11 100.09
0.0757 0.0764 0.0766 0.0789 0.0794
5.806 5.107 5.014 4.457 4.403
3.423 3.862 3.920 4.274 4.309
Ag38
Vacuum Cyclohexane Benzene Ethanol Water
74.30 74.33 74.33 74.35 74.35
0.3718 0.3731 0.3736 0.3760 0.3760
5.071 4.321 4.221 3.622 3.551
2.786 3.129 3.172 3.457 3.488
Cu38
Vacuum Cyclohexane Benzene Ethanol Water
100.95 101.01 101.02 101.08 101.06
0.4926 0.4922 0.4927 0.4949 0.4958
5.513 4.695 4.587 4.013 3.880
2.966 3.369 3.421 3.755 3.766
results are also illustrated in Figs. 3–6 in order to show the variation of the properties more clearly. It can be known from the data in Fig. 3 that, as expected, the binding energy is negative for all the metal particles. The effect of solvents on the binding energy is not considerable for these nanoparticles. Fig. 4 shows that in vacuum, the DHL values of the M20 (M = Au, Ag, and Cu) are much larger than that of the
M38, indicating that the M20 particles are more stable than the M38 particles. The solvents influence the energy gap DHL of Au20, Ag20, and Cu20 considerably, and the DHL becomes larger with the increase of polarity of the solvents, demonstrating that the M20 particles is more stable in the polar solvents. The solvents have less effect on the DHL of the M38 particles than that of the M20 particles.
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
Au20 -51.0
Vac
C
B
E
W
Ag20 -37.3
-37.4
Vac
C
-100.0
Au38 -100.1
-100.2
Vac
C
B
E
-49.5
W
Cu20
-49.6 -49.7 -49.8 -49.9
Vac
C
E
W
-74.2
Ag 38 -74.3
-74.4
Vac
C
Solvent
B
B
E
W
Solvent
Solvent Binding Energy /ev
Binding Energy /ev
Solvent
B
E
W
Binding Energy /ev
-51.1
-37.2
Binding Energy /ev
Binding Energy /ev
Binding Energy /ev
-50.9
-100.9
Cu38 -101.0
-101.1
Vac
C
Solvent
B
E
W
Solvent
2.0
1.8
C
B
E
W
1.9 1.8 1.7
Vac
C
0.09
Au38
0.08
0.07
Vac
C
B
E
E
W
Cu20 1.7 1.6 1.5
Vac
C
W
0.38
Ag38
0.37
0.36
Vac
Solvent
C
B
E
B
E
W
Solvent
Solvent Energy gap /eV
Energy gap /eV
Solvent
B
Energy gap /eV
Vac
Ag20
Energy gap /eV
1.9
1.7
1.8
2.0
Au20
Energy gap /eV
Energy gap /eV
Fig. 3. The bond energy of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
0.50
0.48
W
Cu38
0.49
Vac
C
B
E
W
Solvent
Solvent
Fig. 4. The energy gap between HOMO and LUMO of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
Au20 Au38
Ag20 Ag38
Cu20 Cu38
7 6 5 4 3
C
B
E
W
Solvent Fig. 5. The ionization potential of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
The results in Fig. 5 show that the ionization potentials of the metal particles in the solvents are smaller than those in vacuum, and decrease with the increase of the polarity of the solvents. In
Ag20 Ag38
Cu20 Cu38
-2.0 -2.5 -3.0 -3.5 -4.0 -4.5
Vac
Au20 Au38
-1.5
Electron Affinity / eV
Ionization Potential / eV
8
Vac
C
B
E
W
Solvent Fig. 6. The electron affinity of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in different solvents (Vac, vacuum; C, cyclohexane; B, benzene; E, ethanol; W, water).
other words, it is easier for a neutral particle to lose electron in the solvents, and losing electron in the polar solvents is easier than in the non-polar solvents. It can be known from Fig. 6 that for all of
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M. Hou et al. / Journal of Colloid and Interface Science xxx (2015) xxx–xxx
the metal particles, the electron affinity, which is a measure of how tightly the cluster can bind an electron, is negative in vacuum and the solvents. The absolute value in the solvents is larger than that in vacuum, and increases with increasing the polarity of the solvents. Therefore, it is easier for a neutral particle to get an electron in solvent than in vacuum, and is easier in a polar solvent than in a non-polar solvent. 4. Conclusion The geometrical structures and electronic properties of Au20, Ag20, Cu20, Au38, Ag38, and Cu38 in vacuum, cyclohexane, benzene, ethanol, and water have been investigated by DFT method in order to explore the effects of solvents and particles size on these properties. The solvents affect the properties of the nanoparticles considerably. The charge distribution of the smaller particles is more sensitive to the change of the solvents, and the solvent effect increases with increasing polarity of the polar solvents. The solvents have considerable influence on the DHL of Au20, Ag20, and Cu20, and the DHL becomes larger with the increase of polarity of the solvents, demonstrating that the M20 particles is more stable in the polar solvents. The solvents have less effect on the DHL of the M38 than that of the M20. The ionization potentials of the metal particles in the solvents are smaller than those in vacuum, and decrease with the increase of the polarity of the solvents. For all the metal particles, the electron affinity is negative in vacuum and in the solvents, and the absolute value in the solvents is larger than that in vacuum, and increases with the increase of the polarity of the solvents. Acknowledgments The authors acknowledge the National Natural Science Foundation of China (21133009, U1232203, 21021003) and Chinese Academy of Sciences (KJCX2.YW.H16).
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