published on J. Phys. Chem. A, Just Accepted Manuscript, DOI: 10.1021/jp507679fPublication Date (Web): September 23, 2014Copyright 2014 American Chemical Society

1

DRAFT OF: “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: menziani@unimore.it

∗To whom correspondence should be addressed

2

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 parti-

cle. Most of the density functionals that yielded good relaxed structures on analogous

calculations on gold nanoclusters (viz. those employing the generalized gradient ap-

proximation) 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 par-

ticular, 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 fea-

ture 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 elec-

tronic 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

3

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 of-

ten represent by far the best compromise between accuracy and feasibility of the computa-

tions.3–6 Furthermore, the time-dependent (TD) extension7 of DFT also allows the investiga-

tion of the electronic excited states (Sn , n ≥1), thus enabling the prediction and elucidation

of optical spectra of the target systems.6,8–12

While many studies probed nanosized gold particles by DFT means (e.g. Ref. 2,9,13–15),

only very recently systematic investigations of the various exchange-correlation functionals

and pseudopotentials on real nanogold experimental structures started appearing in the

literature.12,16 Yet, such studies still lack for nanosized silver, also because only recently

Ag-based clusters were resolved by means of X-ray diffraction.17,18

In this work, we investigate the Ag-based nanocluster of molecular formula Ag14(SC6H3F2)6

(SC6H2F3)6 (PPh3)8, denoted as “XMC1” in Ref. 17. 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 com-

mon in Au-based nanoclusters (NCs) capped by thiols.19–23 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 observed18 or theoretically expected24 on other silver-based parti-

cles, but not in gold-based NCs of similar size, as for example the Au38-based particle whose

core is shown in Figure 1 (right).22 Moreover, its optical properties are characterized by a

4

Figure 1: (Left) structure of the core of XMC1; (right) structure of the core of an Au38-based nanocluster.22

Metal atoms (either Ag or Au) are colored in red or blue depending on whether they belong to the inner orouter region of the core, respectively. S and P atoms are colored in yellow and orange, respectively. Agcore−Sbonds are colored in violet. There are no Aucore−S bonds. Bonds between central metal atoms and outermetal atoms are not pictured for better clarity.

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 per-

formed 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 calcu-

lations 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

model system (XMC1core) composed by the metal Ag14-core and the simplified molecular

5

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), thecore of XMC1 (XMC1core), fluorurated-thiophenol (SAr), and triphenylphosphine (PPh3). StandardCPK color scheme is adopted: H atoms are white, Ag atoms are light gray, C atoms are dark gray, S atomsare yellow, P atoms are orange, F atoms are green.

All DFT calculations presented here have been carried out using the Gaussian09 suite

of programs,25 and consist of structural optimizations, single-point calculations, and time-

dependent 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 XMC117 has

been used as starting configuration for the geometry optimizations. The accuracy of the

structural relaxations has been monitored by calculating the atom-averaged absolute value

6

of the difference between Ag-Ag distances of the initial (experimental) and final (relaxed)

geometries, defined as 〈δ〉 = 〈|Rijexp−R

ijopt|〉, where Rij represents the distance between i and

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. 26), and others

that are available for silver through the Basis Set Exchange27 website. The benchmarks

consist of structural optimizations on a simple model made of two bonded Ag atoms, in

analogy to previous analysis.28 Table 1 lists the computed equilibrium distances (req) of Ag2

and their deviation (∆) from the experimental value.28,29 While the def2-TZVP combination

Table 1: Ag−Ag bond length computed with various combined BS/PPs. All calculationswere performed adopting the B3LYP40,41 XC functional. ∆ is the deviation with respect toexperimental data reported in Ref. 28.

req / A ∆ / ALANL1-DZ30 2.715 0.185LANL2-DZ31 2.611 0.081

LANL2-DZ+p31,32 2.607 0.077LANL2-TZ33 2.610 0.080

LANL2-TZ+f 33,34 2.608 0.078mWB6035 2.597 0.067

CRENBS36 2.934 0.404DGDZVP37 2.695 0.165

def2-TZVP38,39 2.596 0.066def2-TZVPPD38,39 2.589 0.059def2-QZVPPD38,39 2.582 0.052aug-cc-pV5Z-PP28 2.585 0.055

exp28,29 2.530 −

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 aug-

cc-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 CH2Cl2 solvent has been accounted in all calculations by

linear response polarizable continuum model.42,43 The UV-Vis experimental spectra were

7

recorded in CH2Cl2 and the latter also co-crystallized along XMC1.17

Calculations on the Bare Metal Cluster

The selection of the best computational scheme to reproduce the relevant geometric fea-

tures 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.2,9,14,16,21,23,44

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,41,45

PBE,46 TPSS,47 rev-TPSS,48,49 TPSS-LYP,41,47 PBE-LYP,41,46 B-PBE,45,46 B-PW91,45,50

B-P86,45,51 VSXC,52 HCTH,53 τHCTH,54 B97D,55 MN12L;56

so called “global” hybrids with a fixed amount of Hartree -Fock exchange, like B3LYP,40,41

X3LYP,41,57 O3LYP41,58 B3P86,40,51 B3PW91,40,50 B1LYP,59 BHandH-LYP (as de-

fined in Ref. 26), PBE0,60 M05,61 M06,62 M06HF,63 mPW1-PW91,64 TPSSh,65 τHCTH-

hyb,66 SOGGA11x;67

range-separated/long-range-corrected hybrids with an Hartree-Fock exchange contribution

that changes with the interelectronic distance, namely HSE06,68 CAM-B3LYP,69 LC-

BLYP,41,45,70 LC-PBE,46,70 LC-TPSS,47,70 M11,71 N12sx,72 MN12sx.72

All the non-metal atoms of XMC1core have been simulated adopting a Gaussian 6-

311G basis set, with the exception of the S and P atoms which, being hypervalent, have

been treated with the larger 6-311G(d,p) basis set. No geometrical constraint has been

imposed on atoms during these geometry relaxations.

8

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. 16, 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 ∼10−2A; also bond angles change of maximum 1◦ and

dihedral angles of at most 2◦.

Four exchange-correlation functionals (BPBE,45,46 B3LYP,40,41 M06HF,63 and CAM-

B3LYP69) 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 tran-

sition (n ≤200) at the TD-BLYP, TD-B3LYP, and TD-CAM-B3LYP levels of theory. These

three XC functionals share the same correlation expression41 and part of the same exchange

functional,45 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

9

core and its aromatic ligands.6,69,73 It was also the reference choice to study the electronic

spectra of undecagold-based NCs.74

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 cupped with one complete PPH3

and three SAr ligands (with Ar=C6H3F2 and C6H2F3) 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) to achieve a better superposition with

the experimental spectrum of XMC1.17 This scaling results into 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)

Obviously, scaling frequencies changes the energetics of the system, including the band sep-

aration. 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. 5,8,74–77). In fact, when wavelengths are translated (of a factor ∆λ) we

have that

λtrans. = λ+ ∆λ , (2)

10

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

1

E trans.=

1

E+

1

∆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.78–80

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 〈δ〉) 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 〈δ〉 values as a function of the XC functional employed.

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

geometries, with large mean unsigned errors (〈δ〉 ≥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,

11

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

M06HF, and SOGGA11x give accurate geometries, with 〈δ〉 values under 0.1A. 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 〈δ〉 value of

about 0.1A), although LC-BLYP and M11 also provide acceptable geometries (〈δ〉 '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.

This behavior of the various XC functionals is in striking contrast with what was observed

on gold nanoclusters16 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.2,12,13,81 The benefits of the PBE-like correlations ex-

12

tended 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.16 Over-

all, 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,18 or at least with significant Ag presence.17

Moreover, the Au particles investigated in Ref. 16 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,

even the pure Hartree-Fock calculation (black bar in Fig. 3, 〈δ〉 '0.27A) outperform all the

GGAs tested here on XMC1core, while for the undecagold-based particles it was the post

Hartree-Fock MP2 to be outperformed16 by many GGA-based relaxations.

13

Structural and electronic properties on XMC1

The complete structure of XMC1 has been investigated with a more limited set of XC func-

tionals, namely BPBE, B3LYP, CAM-B3LYP and M06HF (see Table 2). These functionals,

belonging to different families and levels of sophistication, were already employed in analo-

gous calculation on complete Au particles.16 After relaxation of the constrained geometry,

Table 2: Errors in Ag−Ag distances (the 〈δ〉 function defined in the Computational Details),of XMC1 adopting BPBE, B3LYP, M06HF, and CAM-B3LYP functionals. Some values aremissing because either structural optimizations did not converge or required too long com-putation 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), aswell as on the presence of constraints. Results of the structural optimizations performed onXMC1core are also reported as a reference.

Complete XMC1 BPBE B3LYP CAM−B3LYP M06HFSTO-3G 6-31G STO-3G 6-31G STO-3G 6-31G STO-3G 6-31G

constrained 〈δ〉 / A 0.05 0.01 0.08 0.03 0.06 0.00 0.10 0.04unconstrained 〈δ〉 / A — 0.25 — 0.31 — 0.20 — 0.12

XMC1core BPBE B3LYP CAM−B3LYP M06HF〈δ〉 / A 0.35 0.08 0.10 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

the XMC1core model. This, and the fact that M06HF (the best performer on full XMC1)

is known to well mimic Van der Waals interactions,26 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.

14

Table 3 shows the M06HF-optimized bond-lengths deviations from experimental values.

Contrary to what observed on Au−based clusters,16 when all the NC is simulated we observe

Table 3: Mean interatomic distances in A for the experimental and M06HF/6-31G (uncon-strained) optimized structure. Agext refers to the 8 external silver atoms, Agcore refers to thesix silver atoms of the innermost core, ∆ is the unsigned difference between experimental andoptimized mean distances.

distances / A Agext−P Agext−S Agcore−S Agcore−Agext Agcore−Agcore

exp.17 2.480 2.646 2.539 3.581 2.839M06HF opt. 2.560 2.695 2.615 3.629 2.983∆ ∼0.08 ∼0.05 ∼0.08 ∼0.05 ∼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,16 respectively, when the M06HF functional is adopted.

Physical insights can also be obtained by investigating with population analysis how elec-

trons distribute on XMC1. Hirshfeld partial charges82 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 unsignedelectrons (|e|). The 6-31G BS has been adopted for C, H, and F atoms (not reported in theTable).

Hirshfeld charges / |e| BPBE B3LYP CAM−B3LYP M06HFAgcore -0.005 +0.007 +0.013 +0.014Agext -0.038 -0.032 -0.028 -0.029S -0.036 -0.050 -0.063 -0.056P +0.236 +0.253 +0.255 +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

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,17 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

15

and P atoms negatively and positively charged, respectively. These results presents some

significant qualitative and quantitative divergences with respect to those obtained for un-

decagold clusters by the same means.16 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.16 For silver-based XMC1 the corre-

sponding 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,74 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.

Optical properties

Gold-based NCs showed that often the aromatic ligands surrounding the metal cores gave lit-

tle contribution to the resulting visible spectrum.16,84 In fact, the gross shape of their optical

16

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

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.74 A further observation of the orbitals involved into the transitions of such un-

decagold 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).74

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-

enylphosphine and of the substituted thiophenols, up to the point that the resulting spectral

shapes (blue lines) differ considerably. As was noted for gold,16,74 the BLYP XC functional,

being a GGA, yields lower frequencies,11,16,74,85 while a long-range corrected functional such

as CAM-B3LYP gives a blue-shifted spectrum. Apart from these shifts, the BLYP spec-

17

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-Visspectra of the different models obtained from the convolution of 200 S0 →Sn transitions (red sticks) withGaussians 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 scalingfactor in frequency space) for a better comparison with the experimental data.

tra 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)

is an artifact due to this truncation. To elucidate this latter feature, we repeated the TD-

CAM-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.

18

Figure 6: A) Calculated electronic spectrum on XMC1core+Ls model considering 600 excited states(upper panel), and the experimental17 UV-Vis spectrum (lower panel). B) Calculated electronic spectrumon the first 200 excited states of PPh3 (left) and SC6H3F3 (right).The computed spectra were obtained at the TD-CAM-B3LYP level of theory. Wavelengths have beenmultiplied by a 1.5 scaling factor (i.e. a ∼ 0.667 scaling factor in frequency space) for a better comparisonwith the experimental data. Blue lines represent the UV-Vis spectra obtained from the convolution of theS0 →Sn transitions (red sticks) with Gaussians of half-width at half-height of 0.25 eV. The x-axis binscorrespond 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

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 charge-

transfer transitions,6,69 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

19

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 [ 16,74 ], 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.2,9,14,16,21,23,44

The orbitals of the XMC1core+Ls model that give the main contribution to the most

intense transitions (oscillator strength ≥700) 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 charac-

ter. In particular, it has to be noticed that in the case of the Au11(PPh3)7Cl3 particle, the

first metal→triphenylphosphine transition was the n=68, occurring at 4.83 eV (un-scaled

value),74 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 num-

ber states (n=30). This finding helps to explain why the spectrum of XMC1 is so affected

20

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

21

Table 5: Some selected (osc.str. ≥700) optical S0 →Sn transitions of XMC1core+Ls modeland 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 contri-bution (CI coeff.), oscillator strengths (osc.str.), energies (energy), and corresponding wave-lengths (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 factorin this table.

n orb.occ. → orb.virt. CI coeff. osc.str. (·104) energy/eV λ/nm1 HOMO → LUMO 0.52 2659 3.62 3422 HOMO → LUMO+1 0.54 1901 3.64 3403 HOMO → LUMO+2 0.65 2045 3.70 3357 HOMO-1 → LUMO 0.36 1042 4.40 28110 HOMO-1 → LUMO+2 0.24 1023 4.49 27630‡ HOMO → LUMO+10 0.30 731 4.84 25531 HOMO-9 → LUMO 0.22 980 4.87 25534 HOMO-10 → LUMO 0.20 1511 4.91 25236 HOMO-11 → LUMO+2 0.26 1731 4.94 25137 HOMO-11 → LUMO+1 0.21 1234 4.95 25043‡ HOMO → LUMO+6 0.24 832 5.04 246

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

by ligands, while those of Au11-based particles were not: in the case of Au11(PPh3)7Cl3, 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 excitation11), 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

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

22

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 nan-

oclusters, 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.

Acknowledgements

This work was supported by the Italian “Ministero dell’Istruzione, dell’Universita e della

Ricerca” (MIUR) through the ‘‘Futuro in Ricerca” (FIRB) Grant RBFR1248UI 002 enti-

23

tled “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 en-

titled “Nanoscale functional Organization of (bio)Molecules and Hybrids for targeted Ap-

plication 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 ofAg14(SC6H3F2)6(SC6H2F3)6(PPh3)8 (XMC1) nanocluster.

Silver→Silver transitions are ubiquitous, but Silver→Ligand transitionsoccur just 1.2 eV above the optical gap.

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