DFT and TD-DFT Assessment of the Structural and Optoelectronic

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Article

DFT and TD-DFT Assessment of the Structural and Optoelectronic Properties of Organic-Ag Nanocluster 14

Francesco Muniz-Miranda, Maria Cristina Menziani, and Alfonso Pedone J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp507679f • Publication Date (Web): 23 Sep 2014 Downloaded from http://pubs.acs.org on September 29, 2014

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The Journal of Physical Chemistry

DFT and TD-DFT Assessment of the Structural and Optoelectronic Properties of Organic-Ag14 Nanocluster Francesco Muniz-Miranda, Maria Cristina Menziani,∗ and Alfonso Pedone University of Modena and Reggio Emilia (UniMoRE), Department of Chemical and Geological Sciences (DSCG), Via G. Campi 183, I-41125, Modena, Italy E-mail: [email protected]

∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment


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Abstract An extensive benchmark of exchange-correlation functionals on the structure of the X-ray resolved phosphine and thiolate-protected Ag14 -based nanocluster, named XMC1, is reported. Calculations were performed both on simplified model systems, with the complexity of the ligands greatly reduced, and on the complete XMC1 particle. Most of the density functionals that yielded good relaxed structures on analogous calculations on gold nanoclusters (viz. those employing the generalized gradient approximation) significantly deform the structure of XMC1. On the contrary, some of the exchange-correlation functionals including part of the exact Hartree-Fock exchange (hybrid functionals) reproduce the experimental geometry with minimal errors. In particular, the widely adopted B3LYP yields fairly accurate structures for XMC1, while it is outperformed by many other functionals (both hybrids and generalized gradient corrected) in similar calculations on analogous gold-based systems. Time-dependent density functional calculations have been employed to recover the experimental UV-Vis spectrum. The present investigation shows that to correctly reproduce the optical feature of XMC1 the ligands cannot be omitted, since they interact with the metal core at energies much closer to the optical gap than in the case of gold-based nanoclusters of similar size. Due to this fact, a functional that accurately describes charge-transfer electronic transitions (such as the long-range corrected CAM-B3LYP) has to be adopted.

Keywords TD-DFT, Ag, Nanoparticle, UV-Vis, Benchmark

Introduction Nanoparticles with cores made up of noble metals atoms do not show metallic properties when the size of the particles approach the single-digit nm, displaying finite and appreciable band gaps (or, more correctly, HOMO-LUMO gaps). 1 In particular, this is found in gold and 2 ACS Paragon Plus Environment

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silver-based nanoparticles, whose HOMO-LUMO gaps increase with the reduction in size, reaching values between about 1 and 2 eV at the sub-nanometer scale. 2 Computational approaches can be used to elucidate the relationship between sizes, shapes, and optoelectronic properties. Calculations based on density functional theory (DFT) are nowadays one of the preferred approaches to achieve this understanding, because they often represent by far the best compromise between accuracy and feasibility of the computations. 3–6 Furthermore, the time-dependent (TD) extension 7 of DFT also allows the investigation of the electronic excited states (Sn , n ≥1), thus enabling the prediction and elucidation of optical spectra of the target systems. 6,8–11 While many studies probed nanosized gold particles by DFT means (e.g. Ref. 2,8,12), only very recently systematic investigations of the various exchange-correlation functionals and pseudopotentials on real nanogold experimental structures started appearing in the literature. 11,13 Yet, such studies still lack for nanosized silver, also because only recently Ag-based clusters were resolved by means of X-ray diffraction, 14,15 and most calculations are limited to model systems. 16–20 In this work, we investigate the Ag-based nanocluster of molecular formula Ag14 (SC6 H3 F2 )6 (SC6 H2 F3 )6 (PPh3 )8 , denoted as “XMC1” in Ref. 14. This nanocluster, protected by both aromatic thiols and phosphines, is of interest due to at least three peculiar features. First, its crystallographic structure determined through X-ray diffraction shows the lack of so-called “sulfur-staples”, i.e. motifs M −S−M (M being a noble metal atom), which are quite common in Au-based nanoclusters (NCs) capped by thiols. 21–24 In fact, differently to gold NCs, in this Ag14 -based particle sulfur atoms are bound not to two, but to three metal atoms, as shown in Figure 1. At the same time, Ag atoms bordering the ligands (eight metal atoms, colored in blue in Fig.1, left) are each bound to four non-metal atoms (three S and one P). The octahedral Ag6 inner core of XMC1 (colored in red in Fig.1, left) is another structural feature that has also been observed 15 or theoretically expected 25 on other silver-based particles, but not in gold-based NCs of similar size, as for example the Au38 -based particle whose



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Figure 1: (Left) structure of the core of XMC1; (right) structure of the core of an Au38 -based nanocluster. 23 Metal atoms (either Ag or Au) are colored in red or blue depending on whether they belong to the inner or outer region of the core, respectively. S and P atoms are colored in yellow and orange, respectively. Agcore −S bonds are colored in violet. There are no Aucore −S bonds. Bonds between central metal atoms and outer metal atoms are not pictured for better clarity.

core is shown in Figure 1 (right). 23 Moreover, its optical properties are characterized by a clearly structured optical absorption and emission profile, the latter giving rise to yellow luminescence. In order to check the reliability of current functionals to reproduce the structural features of XMC1, ground-state DFT calculations have been carried out. Furthermore, more limited TD-DFT calculations have been employed to recover and elucidate the optical features of XMC1, in particular the origins of its complex UV-Vis spectrum. The paper is organized as in the following. Details regarding the DFT calculations performed on the simplified and complete model systems of XMC1 are reported in Methods and Computational Details. Findings are presented and commented on in Results and Discussion, with particular regard to the similarities and differences between XMC1 and previous calculations on gold nanoclusters, while the Concluding Remarks section contains final comments and observations.

Methods and Computational Details To choose the optimal quantum-chemistry approach to simulate XMC1, we tested several exchange-correlation (XC) functionals, pseudopotentials (PPs), and basis set (BSs) on a 4 ACS Paragon Plus Environment

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model system (XMC1core) composed by the metal Ag14 -core and the simplified molecular groups directly bonded to them (i.e. PH3 and SH groups in place of aromatic phosphines and thiols, respectively). Then, more limited calculations were performed to simulate the complete XMC1 structure. TD-DFT spectra were computed on XMC1core and a model including part of the ligands (XMC1core+Ls). Models XMC1core and XMC1core+Ls are pictured in the upper-central and upper-right corners of Fig. 2, respectively, along with the complete XMC1 and the PPh3 and thiophenol ligands.

Figure 2: Three-dimensional structure of XMC1, the core of XMC1 with ligands (XMC1core+Ls), the core of XMC1 (XMC1core), fluorurated-thiophenol (SAr), and triphenylphosphine (PPh3 ). Standard CPK color scheme is adopted: H atoms are white, Ag atoms are light gray, C atoms are dark gray, S atoms are yellow, P atoms are orange, F atoms are green.

All DFT calculations presented here have been carried out using the Gaussian09 suite of programs, 26 and consist of structural optimizations, single-point calculations, and timedependent calculations to obtain excitation energies. The ground-state (GS) calculations have been performed adopting “tight” convergence criteria for the optimization of geometries (corresponding to forces and atomic displacements below the 10−5 Hartree/Bohr and 4·10−5 Bohr thresholds, respectively). The experimental X-ray crystal structure of XMC1 14 has been used as starting configuration for the geometry optimizations. The accuracy of the



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structural relaxations has been monitored by calculating the atom-averaged absolute value of the difference between Ag-Ag distances of the initial (experimental) and final (relaxed) ij ij − Ropt |i, where Rij represents the distance between i and geometries, defined as hδi = h|Rexp

j silver atoms. We have benchmarked many combination of basis-sets and pseudopotentials (BS/PPs) to correctly reproduce the core-valence interaction of silver electrons. We imported in the calculations “families” of BS/PPs (LANL2, def2, SDDECP (as defined in Ref. 27), and others that are available for silver through the Basis Set Exchange 28 website. The benchmarks consist of structural optimizations on a simple model made of two bonded Ag atoms, in analogy to previous analysis. 29 Table 1 lists the computed equilibrium distances (req ) of Ag2 and their deviation (∆) from the experimental value. 29,30 While the def2-TZVP combination Table 1:

Ag−Ag bond length computed with various combined BS/PPs. All calculations were performed adopting the B3LYP 40,41 XC functional. ∆ is the deviation with respect to experimental data reported in Ref. 29. req / ˚ A 2.715 2.611 2.607 2.610 2.608 2.597 2.934 2.695 2.596 2.589 2.582 2.585 2.530

LANL1-DZ 31 LANL2-DZ 32 LANL2-DZ+p 32,33 LANL2-TZ 34 LANL2-TZ+f 34,35 mWB60 36 CRENBS 37 DGDZVP 38 def2-TZVP 36,39 def2-TZVPPD 36,39 def2-QZVPPD 36,39 aug-cc-pV5Z-PP 29 exp 29,30

∆/˚ A 0.185 0.081 0.077 0.080 0.078 0.067 0.404 0.165 0.066 0.059 0.052 0.055 −

does not yield the absolute best bond lengths (def2-QZVPPD does), it represents the best compromise between accuracy and computational burden. In fact, def2-QZVPPD and augcc-pV5Z-PP are much more computational expensive. Thus, the def2 PP and the TZVP BS have been employed in all the calculations reported in this paper to take into account core and valence electrons of Ag atoms, respectively. The environment given by the CH2 Cl2 solvent has been accounted in all calculations by 6 ACS Paragon Plus Environment

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linear response polarizable continuum model. 42,43 The UV-Vis experimental spectra were recorded in CH2 Cl2 and the latter also co-crystallized along XMC1. 14 Calculations on the Bare Metal Cluster The selection of the best computational scheme to reproduce the relevant geometric features of the NC has been based on calculations carried out on a reduced model particle (XMC1core) in order to make the computations feasible and save computer time. Similar simplifying choices have already been successfully employed on noble-metal NCs. 2,8,12,13,24 DFT geometry optimizations and single point calculations have been performed adopting a number of XC functionals, which could be sorted in at least three large families: simple GGA or meta-GGA functionals with 0% Hartree-Fock exchange, such as BLYP, 41,44 PBE, 45 TPSS, 46 rev-TPSS, 47,48 TPSS-LYP, 41,46 PBE-LYP, 41,45 B-PBE, 44,45 B-PW91, 44,49 B-P86, 44,50 VSXC, 51 HCTH, 52 τ HCTH, 53 B97D, 54 MN12L; 55 so called “global” hybrids with a fixed amount of Hartree -Fock exchange, like B3LYP, 40,41 X3LYP, 41,56 O3LYP 41,57 B3P86, 40,50 B3PW91, 40,49 B1LYP, 58 BHandH-LYP (as defined in Ref. 27), PBE0, 59 M05, 60 M06, 61 M06HF, 62 mPW1-PW91, 63 TPSSh, 64 τ HCTHhyb, 65 SOGGA11x; 66 range-separated/long-range-corrected hybrids with an Hartree-Fock exchange contribution that changes with the interelectronic distance, namely HSE06, 67 CAM-B3LYP, 68 LCBLYP, 41,44,69 LC-PBE, 45,69 LC-TPSS, 46,69 M11, 70 N12sx, 71 MN12sx. 71 This selection of XC functionals can be considered representative of most families and types of currently adopted functionals. This is a much more extended ensemble of that employed for the benchmarks reported in Ref. 13. All the non-metal atoms of XMC1core have been simulated adopting a Gaussian 6311G basis set, with the exception of the S and P atoms which, being hypervalent, have



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been treated with the larger 6-311G(d,p) basis set. No geometrical constraint has been imposed on atoms during these geometry relaxations.

Calculations on the Complete Cluster Both constrained and non-constrained optimizations have been performed on the full XMC1 particle. When constrains have been applied, we fixed the atomic positions of C, H, and F atoms, i.e. the atoms belonging to the outer ligands; all P and S atoms were always let free to relax, as well as the metal atoms. Due to the fact that XMC1 has more than 430 atoms, the level of theory had to be adjusted to make the computations viable. A full-electron 6-311G(d,p) BS has been employed to describe non-metal atoms directly bonded to the metal core (sulfur and phosphorous atoms), while the other non-metal elements have been treated with simpler STO-3G or 6-31G BSs. As shown in Ref. 13, the DFT-optimized structure of isolated triphenyl-phosphine shows that with 6-31G(H,C atoms)/6-311G(d,p)(P atom) and STO-3G(H,C atoms)/6-311G(d,p)(P atom) BSs the bond-distance error with respect to optimizations carried out with 6-311++ G(d,p) basis set is at max. of order to ∼10−2 ˚ A; also bond angles change of maximum 1◦ and dihedral angles of at most 2◦ . Four exchange-correlation functionals (BPBE, 44,45 B3LYP, 40,41 M06HF, 62 and CAMB3LYP 68 ) belonging to different families have been tested to simulate complete XMC1, each one with a different contribution of exact Hartree-Fock exchange (from 0% of BPBE to 100% of M06HF).

Electronic Spectra The electronic spectra have been investigated computing the first 200 S0 7→Sn optical transition (n ≤200) at the TD-BLYP, TD-B3LYP, and TD-CAM-B3LYP levels of theory. These three XC functionals share the same correlation expression 41 and part of the same exchange


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functional, 44 thus they can be viewed as belonging to the same “family” but at very different level of complexity and sophistication. CAM-B3LYP is known to perform particularly well in reproducing charge-transfer optical transitions, as those that can occur between the silver core and its aromatic ligands. 6,68,72 It was also the reference choice to study the electronic spectra of undecagold-based NCs. 73 Due to the size of XMC1, TD-DFT calculations on excited states have been performed on two simplified models: one corresponding to the bare metal cluster (XMC1core) described before, and the other one being the bare metal cluster model capped with one complete PPH3 and three SAr ligands (with Ar=C6 H3 F2 and C6 H2 F3 ) labeled XMC1core+Ls in Fig. 2, in order to reproduce the interaction between the silver core and the aromatic molecules surrounding it, as well as the interactions between ligands. These models and the structure of the complete XMC1 particle, the PPh3 ligands, and a fluorurated-thiophenol ligand are displayed in Fig. 2. Computed UV-Vis spectra obtained with XMC1core, XMC1core+Ls, PPh3 and SAr are compared and discussed. The calculated wavelengths (λ) of the TD-DFT computed spectra have been multiplied by a linear scaling factor of 1.5 (i.e. λscaled = λ·1.5). This scaling corresponds to a product for a multiplying linear scaling factor of 1/1.5 ' 0.667 in the energy (E) domain:

E scaled = E · const. ,

const. ' 0.667 .

(1)

This means that scaling wavelengths changes the energetics of the system, including the band separation. Anyway, this change also occurs with the simple translation of the spectrum in the wavelength domain, which is a widely adopted procedure for computed optical spectra (see for example Ref. 5,9,73–75). In fact, when wavelengths are translated (of a factor ∆λ ) we have that λtrans. = λ + ∆λ

,


(2)


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which can be written in terms of corresponding energies (E) as 1 E trans.

=

1 1 + E ∆E

,

(3)

due to the fact that λ ∝ 1/E and ∆λ ∝ 1/∆E , with E trans. being the energy corresponding to λtrans. . The latter equation can be rearranged so to obtain

E trans. =

E · ∆E E + ∆E

.

(4)

Therefore, scaling the wavelengths expressed by Eqn. 1 actually results in a much simpler transformation in energy domain than the translation of the spectrum in the wavelength domain expressed by Eqn. 4. The scaling of frequencies is also routinely applied in ab initio and molecular dynamics calculations to obtain vibrational energies. 76–81 The procedure (scaling of wavelengths and energies) and the scaling factors (1.5 in wavelength domain, 0.667 in energy domain) adopted here has been chosen mainly to achieve an optimal superimposition between computed and experimental spectra of XMC1, 14 so to ease and make straightforward their comparison. In fact, for XMC1, a shift in wavelength or energy domain would not have reproduced correctly the shape and position of the optical bands along all the investigated scale. The wavelengths and energies discussed in the following text and figures are all multiplied by a factor of 1.5 and 0.667, respectively, unless explicitly stated otherwise (i.e. Table 5).

Results and Discussion Structural properties on the bare cluster The mean unsigned errors (defined in the previous section as hδi) yielded by the geometry optimizations on XMC1core have been used to check the structural accuracy with respect to the X-ray data. Figure 3 reports the hδi values as a function of the XC functional employed. 10 ACS Paragon Plus Environment

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All optimizations carried out with GGA functionals (green histograms) yield very distorted

Figure 3: Histograms showing changes in the average Ag−Ag distance (the function hδi as defined in Computational Details) by varying DFT functionals (on the x-axis). GGA, hybrids, and functionals are represented by green bars, hybrid functionals are represented by red bars, and range-separated/long-rangecorrected hybrids are represented by blue bars. The Hartree-Fock optimization has a black bar. Errors greater than 0.45 ˚ A are not shown in this scale. Structures with hδi ≥ 0.25 ˚ A are very distorted.

geometries, with large mean unsigned errors (hδi ≥0.30 ˚ A). BPBE, BP86, and BPW91 give somewhat better results than other GGA and meta-GGA XC functionals, nevertheless a mean unsigned error of about 0.30−0.35 ˚ A denotes a severe distortion of the crystallographic geometry. Hybrids functionals provide better results, although with many ups and downs. Some hybrid functionals (red histograms) such as B1LYP, B3LYP, X3LYP, BHandHLYP, M06HF, and SOGGA11x give accurate geometries, with hδi values under 0.1˚ A. Also O3LYP, B98, and τ -HCTHhyb yield fairly accurate structures, with mean unsigned errors below the 0.15 ˚ A threshold. All other hybrids tested here yielded more distorted geometries, particularly M05, M06, and TPSSh. The only range-separated hybrids (blue histograms) tested here that gives accurate optimized structures is CAM-B3LYP (with a hδi value of about 0.1˚ A), although LC-BLYP and M11 also provide acceptable geometries (hδi '0.17 ˚ A), and all the others yielding deformed structures. Overall, the “general” hybrids tested here have the better structural performances, closely followed by the long-range corrected hybrids, and then lastly the GGAs. 11 ACS Paragon Plus Environment


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This behavior of the various XC functionals is in striking contrast with what was observed on gold nanoclusters 13 composed of 11 and 24 metal atoms and similar ligands (thiophenols and triphenylphosphines). In fact, in the case of Au-based NCs, GGA functionals yielded the best structures, particularly when a PBE-like correlation was employed. Not surprisingly, most DFT studies on Au-based particles employed GGAs, and PBE-like functionals (e.g. PBE itself, P86, PW91) in particular (e.g. 2,11). The benefits of the PBE-like correlations extended also to the hybrids functionals when employed to simulate gold-based clusters, with PBE0, B3P86, and B3PW91 outperforming B3LYP, and to the range-separated hybrids, with HSE06 (which includes the PBE exchange) outperforming CAM-B3LYP. In the case of the Ag-based XMC1 the opposite occurs, and the LYP correlation seems to improve the structural accuracy of the calculations, at least for hybrid functionals. This is particularly evident in case of the BHandHLYP, which outperforms the pure BHandH for XMC1core. For Au-based clusters instead, BHandHLYP provided deformed relaxed structures. 13 Overall, M06HF and CAM-B3LYP seem to be the best XC functionals to reproduce the structure of both gold and silver-based core NCs, while M05 and M06 are inadequate for both of them. While these observations can be qualitatively understood by considering that Au atoms, having more electrons, have a more metallic character than silver (with Au performing better with the simpler GGA functionals), probably the binding geometry of the ligands plays its part as well. In fact, most of the distortions occur at the eight outer Ag atoms that are each bound to four non-metal atoms (three S and one P atoms). To the best of our knowledge, this type of binding geometry did not occur in known X-Ray determined Au NCs, and seems a peculiar feature of silver-based NCs, 15 or at least with significant Ag presence. 14 Moreover, the Au particles investigated in Ref. 13 had the gold atoms at the surface bonded with only one non-metal element (either S, P, Br, or Cl), whereas in XMC1 every surface Ag atom is bonded to two different non-metal elements (S and P) at the same time. The accurate description of these many non-metallic interactions in XMC1core requires a higher contribution of exact Hartree-Fock exchanges than for similar gold-based clusters. In fact,


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even the pure Hartree-Fock calculation (black bar in Fig. 3, hδi '0.27˚ A) outperform all the GGAs tested here on XMC1core, while for the undecagold-based particles it was the post Hartree-Fock MP2 to be outperformed 13 by many GGA-based relaxations.

Structural and electronic properties on XMC1 The complete structure of XMC1 has been investigated with a more limited set of XC functionals, namely BPBE, B3LYP, CAM-B3LYP and M06HF (see Table 2). These functionals, belonging to different families and levels of sophistication, were already employed in analogous calculation on complete Au particles. 13 After relaxation of the constrained geometry, Table 2: Errors in Ag−Ag distances (the hδi function defined in the Computational Details), of XMC1 adopting BPBE, B3LYP, M06HF, and CAM-B3LYP functionals. Some values are missing because either structural optimizations did not converge or required too long computation time. Data are reported as depending on the adopted functionals (BPBE, B3LYP, CAM-B3LYP, and M06HF) and basis sets employed for outer atoms (STO-3G or 6-31G), as well as on the presence of constraints. Results of the structural optimizations performed on XMC1core are also reported as a reference.

Complete XMC1

BPBE B3LYP CAM−B3LYP M06HF STO-3G 6-31G STO-3G 6-31G STO-3G 6-31G STO-3G 6-31G ˚ 0.05 constrained hδi / A 0.01 0.08 0.03 0.06 0.00 0.10 0.04 unconstrained hδi / ˚ A — 0.25 — 0.31 — 0.20 — 0.12 XMC1core hδi / ˚ A

BPBE 0.35

B3LYP 0.08

CAM−B3LYP 0.10

M06HF 0.09

accurate structures are obtained with all these functionals. Using 6-31G BS to describe the aromatic ligands results in an even increased accuracy (particularly for M06HF), even if atoms of the ligands are fixed to their experimental positions. On the other hand, the unconstrained relaxations yield overall unsatisfactory results. Only optimizations performed with M06HF provide fair accuracy, and only when 6-31G BS for the organic ligands (C, H, and F atoms, while S and P are described by 6-31++G(d,p) BS) is adopted in place of the simpler STO-3G. The other three functionals distorted the experimental geometry significantly, in particular B3LYP that is one of the top performers on



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the XMC1core model. This, and the fact that M06HF (the best performer on full XMC1) is known to well mimic Van der Waals interactions, 27,62 suggests that ligands interactions are not well described by BPBE and B3LYP, which yield mean unsigned errors for the Ag atoms distances ≥0.20 ˚ A. Table 3 shows the M06HF-optimized bond-lengths deviations from experimental values. Contrary to what observed on Au−based clusters, 13 when all the NC is simulated we observe Table 3: Mean interatomic distances in ˚ A for the experimental and M06HF/6-31G (unconstrained) optimized structure. Agext refers to the 8 external silver atoms, Agcore refers to the six silver atoms of the innermost core, ∆ is the unsigned difference between experimental and optimized mean distances. ˚ distances / A 14 exp. M06HF opt. ∆

Agext −P 2.480 2.560 ∼0.08

Agext −S 2.646 2.695 ∼0.05

Agcore −S 2.539 2.615 ∼0.08

Agcore −Agext 3.581 3.629 ∼0.05

Agcore −Agcore 2.839 2.983 ∼0.14

that the distortions occurring on the central Agcore atoms (belonging to the Ag6 inner cage) are of similar magnitude than the distortions involving outer Ag atoms (Agext atoms). On the other hand, the errors on Ag−P and Ag−S distances are similar to those on Au−P and Au−S, 13 respectively, when the M06HF functional is adopted. Physical insights can also be obtained by investigating with population analysis how electrons distribute on XMC1. Hirshfeld partial charges 82 for Ag atoms and the atoms directly bound to them, are listed in Table 4 and sorted by the XC functional employed. The hybrid Table 4: Averaged Hirsfeld partial charges on XMC1. The charges are in units of unsigned electrons (|e|). The 6-31G BS has been adopted for C, H, and F atoms (not reported in the Table). Hirshfeld charges / |e| Agcore Agext S P

BPBE -0.005 -0.038 -0.036 +0.236

B3LYP +0.007 -0.032 -0.050 +0.253

CAM−B3LYP +0.013 -0.028 -0.063 +0.255

M06HF +0.014 -0.029 -0.056 +0.245

functionals (both “global” and long-range corrected) split the Ag population into a core of six positively-charged atoms and further eight negatively-charged atoms (bonded to S and 14 ACS Paragon Plus Environment

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P atoms). The charge difference between these two populations is about 0.03−0.04|e|/atom. A positive Ag6 core was also expected experimentally, 14 although with much larger average charges (0.667|e| per atom, resulting into a net charge of +4|e| on the Ag6 core). BPBE, on the contrary, predict a core of almost neutral silver atoms. All XC functional predict S and P atoms negatively and positively charged, respectively. These results presents some significant qualitative and quantitative divergences with respect to those obtained for undecagold clusters by the same means. 13 In fact, while Au11 -based NCs indeed have a central atom with structural properties different from the other ten metal atoms, its partial charge is negative as that of the others, hence hindering the identification of a “core” region by population analysis only. More importantly, the M −P bonds (M being a metal, either Ag or Au) have a much more ionic character for gold NCs than for XMC1. For example, in undecagold particles with CAM-B3LYP and M06HF the average charge difference along the M −P bond exceeds ∼0.48 and ∼0.50|e|, respectively. 13 For silver-based XMC1 the corresponding differences are only ∼0.28 and ∼0.27|e|. Analogous differences can be obtained with B3LYP functional calculations. This means that the Ag−P bond is significantly more covalent than Au−P, and provides some explanation of hybrid functionals outperforming GGAs for XMC1, contrary to what was observed on gold-based particles. Also the electronic density of states (DoS) can be helpful to characterize the XMC1 particle, particularly if it is partitioned per atomic species so to sort out contributions due to the core or to the ligands. Figure 4 summarizes this analysis, performed with the Multiwfn software. 83 As can be seen, the relative contribution to the occupied orbital density of the metal atoms (blue line) and the atoms directly bound to them (S and P atoms, yellow and red lines, respectively) are of comparable magnitude, particularly in the range of energies closer to the HOMO-LUMO gap (indicatively, the [−6, 0] eV interval). This is in contrast with what was observed in undecagold nanoclusters, 73 where the contribution due to gold was largely predominant, and suggests an increased coupling between the energy levels of silver atoms and the S and P atoms around them.



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Figure 4: DoS decomposed per atomic species. Calculation has been performed on the XMC1core+Ls model at the cam-B3LYP level of theory. The energies are shifted so to have the center of the HOMO-LUMO gap at 0 eV.

Optical properties Gold-based NCs showed that often the aromatic ligands surrounding the metal cores gave little contribution to the resulting visible spectrum. 13,84 In fact, the gross shape of their optical spectrum could be recovered also if the organic ligands were completely omitted (except for the atoms directly bound to gold, such as P and S), up to the point that Au11 (PPh3 )7 (SPh)3 and Au11 (PH3 )7 (SH)3 yielded basically the same excitation profile when computed with TD-DFT. 73 A further observation of the orbitals involved into the transitions of such undecagold particles also showed that Au→Au excitations were by far the most abundant, while Au→ligands transitions were rare and outside the Vis region, and ligand→ligand even rarer and blue-shifted at energies of ∼5 eV (corresponding to wavelengths of about ∼250 nm). 73 This does not occur here with the silver-based XMC1. In fact, as shown in Figure 5, the TD-DFT computed spectra on the XMC1core (left panels) and on the model including one PPh3 and three SAr molecules (XMC1core+Ls model, right panels) are significantly different. The distributions of excited states (red sticks) are altered by the presence of triph-


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Figure 5: Calculated electronic spectra on XMC1core (left panel) and XMC1core+Ls (right panel) models at the TD-BLYP, TD-B3LYP, and TD-CAM-B3LYP levels of theory. Blue lines represent the UV-Vis spectra of the different models obtained from the convolution of 200 S0 →Sn transitions (red sticks) with Gaussians of half-width at half-height of 0.25 eV. The x-axis bins correspond to 25 nm. The computed TD-DFT wavelengths have been multiplied by a 1.5 scaling factor (i.e. a ∼ 0.667 scaling factor in frequency space) for a better comparison with the experimental data.

enylphosphine and of the substituted thiophenols, up to the point that the resulting spectral shapes (blue lines) differ considerably. As was noted for gold, 13,73 the BLYP XC functional, being a GGA, yields lower frequencies, 10,13,73,85 while a long-range corrected functional such as CAM-B3LYP gives a blue-shifted spectrum. Apart from these shifts, the BLYP spectra appear unstructured (both for XMC1core and XMC1core+Ls), while those obtained employing B3LYP and CAM-B3LYP are more similar to each other. Since the spectra reported in Fig. 5 are limited to the first 200 S0 →Sn transitions, the higher frequency maximum (λ '310 nm) in the spectrum of XMC1core+Ls model obtained with CAM-B3LYP (represented with a blue line in the lower-right panel of Fig. 5)



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is an artifact due to this truncation. To elucidate this latter feature, we repeated the TDCAM-B3LYP calculation computing the first 600 S0 →Sn transitions, thus reaching higher frequencies that exceed even those investigated by UV absorption experiments, as shown in Figure 6, Part A.

Figure 6: A) Calculated electronic spectrum on XMC1core+Ls model considering 600 excited states (upper panel), and the experimental 14 UV-Vis spectrum (lower panel). B) Calculated electronic spectrum on the first 200 excited states of PPh3 (left) and SC6 H3 F3 (right). The computed spectra were obtained at the TD-CAM-B3LYP level of theory. Wavelengths have been multiplied by a 1.5 scaling factor (i.e. a ∼ 0.667 scaling factor in frequency space) for a better comparison with the experimental data. Blue lines represent the UV-Vis spectra obtained from the convolution of the S0 →Sn transitions (red sticks) with Gaussians of half-width at half-height of 0.25 eV. The x-axis bins correspond to 25 nm.

Including more states into the calculation, the experimental profile at higher energy (the rising of absorbance for λ ≤ 350 nm) can be correctly recovered with the CAM-B3LYP XC functional. Thus, this XC functional can correctly describe the shape of the optical


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bands, which simpler functionals of the same “family” such as B3LYP and BLYP cannot do. This is probably due to the fact that CAM-B3LYP is proved to better reproduce chargetransfer transitions, 6,68 and these latter contribute to the rising of absorbance for λ ≤350 nm. In fact, in this range of wavelengths the absorption of triphenylphosphine and fluorurated thiophenols occurs (see Figure 6, Part B). Thus, excitations due to the silver core and the ligands overlap significantly for XMC1, contrary to what happens in undecagold NCs, and this overlapping prevents recovering a reliable optical spectrum with calculations performed only on the metal part. This is related to another issue that hinders TD-DFT calculations on the simplified XMC1core model: while the occupied orbitals of XMC1core have a shape similar to the occupied orbitals of XMC1core+Ls, the virtual orbitals of XMC1core (up to LUMO+20, at least) are abnormally localized on the PH3 groups, in particular on the P atoms. The clearly unphysical shape of the virtual orbitals seems proper of the XMC1core model, since it was not observed on the gold cores discussed in Ref.s [ 13,73 ], nor in the XMC1core+Ls model discussed here. We also performed calculations with a more complex simplification scheme, putting CH3 groups in place of the H atoms of the XMC1core model, but the shape of the virtual orbitals still appear unrealistic and very localized on the phosphorous atoms. On the contrary, the occupied orbitals of the XMC1core model resemble the occupied orbitals of the XMC1core+Ls model. Thus, the ground state properties (including the structural optimizations) are not particularly affected at the orbital level by omitting or simplifying the ligands, which anyway is a common procedure to investigate noble metal NCs. 2,8,12,13,24 The orbitals of the XMC1core+Ls model that give the main contribution to the most intense transitions (oscillator strength ≥0.07) are reported in Figure 7 as contour plots, while in Table 5 these latter transitions are described in detail. Most transitions are of the type metal→metal, as in the case of the undecagold NCs. However, transitions n=30 (HOMO→LUMO+10) and n=43 (HOMO→LUMO+6) show a clear metal→ligand character. In particular, it has to be noticed that in the case of the Au11 (PPh3 )7 Cl3 particle, the



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Figure 7: Isosurfaces of some selected occupied and virtual orbitals of the XMC1core+Ls model computed with the CAM-B3LYP XC functional. Blue denotes the positive lobes, while red the negative lobes. These orbitals are involved into the transitions described in Table 5.


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Table 5: Some selected (osc.str. ≥700) optical S0 →Sn transitions of XMC1core+Ls model and their orbital contributions. The table lists the transition number (n), the occupied (occ.orb.) and virtual (virt.orb.) orbitals involved into the transitions, their relative contribution (CI coeff.), oscillator strengths (osc.str.), energies (energy), and corresponding wavelengths (λ). Calculations are performed at the TD-CAM-B3LYP level of theory. The computed TD-DFT energies and wavelengths have not been multiplied by a scaling factor in this table. n 1 2 3 7 10 30‡ 31 34 36 37 43‡

orb.occ. HOMO HOMO HOMO HOMO-1 HOMO-1 HOMO HOMO-9 HOMO-10 HOMO-11 HOMO-11 HOMO

→ → → → → → → → → → → →

orb.virt. LUMO LUMO+1 LUMO+2 LUMO LUMO+2 LUMO+10 LUMO LUMO LUMO+2 LUMO+1 LUMO+6

CI coeff. 0.52 0.54 0.65 0.36 0.24 0.30 0.22 0.20 0.26 0.21 0.24

osc.str. (·104 ) 2659 1901 2045 1042 1023 731 980 1511 1731 1234 832

energy/eV 3.62 3.64 3.70 4.40 4.49 4.84 4.87 4.91 4.94 4.95 5.04

λ/nm 342 340 335 281 276 255 255 252 251 250 246

‡

Transitions with a significant Ag→PPh3 character. All other transitions reported here have a predominant Ag→Ag character.

first metal→triphenylphosphine transition was the n=68, occurring at 4.83 eV (un-scaled value), 73 while in the present case of XMC1 the first metal→triphenylphosphine transition occurs at about the same energy (4.84 eV, un-scaled value) but much earlier in terms of number states (n=30). This finding helps to explain why the spectrum of XMC1 is so affected by ligands, while those of Au11 -based particles were not: in the case of Au11 (PPh3 )7 Cl3 , the first metal→PPh3 transition occurred at (un-scaled) energies εgap +1.9 eV (εgap being the optical gap energy, i.e. the n=1 optical excitation 10 ), whereas in the case of XMC1 the first metal→PPh3 transition occurs at the (un-scaled) energy of εgap +1.2 eV, ∼0.7 eV closer to the lower energy boundary of the XMC1 spectrum.

Concluding Remarks Ground-state and time-dependent density functional calculations have been performed to evaluate the most reliable approaches to reproduce the structure and electronic spectrum of



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the hybrid organic-silver nanocluster named XMC1. We have found that many exchange-correlation functionals that proved to be effective for hybrid organic-gold nanoclusters actually perform badly for XMC1. This is probably due to the more “metallic” character of the undecagold clusters, which favors functionals belonging to the GGA family. On the contrary, XMC1 shows a much more intricate network of metal−nonmetal bonds, which are better described by functionals that include the exact Hartree-Fock exchange. In fact, the electronic populations analysis shows that the Ag−P bonds are much less ionic than the corresponding Au−P bonds, thus requiring the use of functionals better suited to describe covalent chemical bonds. The M06HF functional (with 100% of Hartree-Fock exchange) yields good optimized geometries for both the metal core and the full nanocluster, while CAM-B3LYP (with 65% of Hartree-Fock exchange at long distances) provides an optical spectrum in good agreement with the experimental one. The virtual orbitals of the metal core model are very different from those obtained from calculations in which at least one triphenylphosphine and three substituted thiophenols are retained. This is probably due to the fact that the Ag−P bond is significantly more covalent than Au−P, thus facilitating the occurrence of metal→ligand charge transfer transitions. As a consequence, we have found that time-dependent density functional calculations on the metal core yield electronic spectra significantly different from the experimental one regardless of the functional adopted, thus suggesting that omitting the ligands is not a viable choice to investigate the excited state of silver clusters. Charge transfer transitions of the type Ag→ligands occur closer to the optical gap than in undecagold nanoclusters, thus affecting a larger portion of the electronic spectrum. In conclusion, some of the main computational schemes to simulate noble metal nanoclusters, such for example the simplification of the protecting organic ligands, cannot be carelessly adopted for silver-based XMC1. On the contrary, it requires the specific approaches described here, in particular to recover its optoelectronic properties.


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Acknowledgements This work was supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca” (MIUR) through the ‘‘Futuro in Ricerca” (FIRB) Grant RBFR1248UI 002 entitled “Novel Multiscale Theorethical/Computational Strategies for the Design of Photo and Thermo responsive Hybrid Organic-Inorganic Components for Nanoelectronic Circuits”, and the “Programma di ricerca di rilevante interesse nazionale” (PRIN) Grant 2010C4R8M8 entitled “Nanoscale functional Organization of (bio)Molecules and Hybrids for targeted Application in Sensing, Medicine and Biotechnology” is also acknowledged. Computation time was granted through the CINECA project AUNANMR-HP10CJ027S.

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Graphical TOC Entry

Schematic description of the UV-Vis spectrum of Ag14 (SC6 H3 F2 )6 (SC6 H2 F3 )6 (PPh3 )8 (XMC1) nanocluster. Silver→Silver transitions are ubiquitous, but Silver→Ligand transitions occur just 1.2 eV above the optical gap.


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DFT and TD-DFT Assessment of the Structural and Optoelectronic

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