Anthony Ventresque

Sylvie Cazalens

Philippe Lamarre

Patrick Valduriez
email: patrick.valduriez@inria.fr

Query expansion and interpretation to go beyond semantic P2P interoperability

In P2P data management systems, semantic interoperability between any two peers that do not share the same ontology relyes on ontology matching. The established correspondences, i.e. the "shared" parts of the ontologies are indeed essential to exchange information. But to what extent the "unshared" part can contribute to information exchange. In this paper, we address this question. We focus on a P2P document management system, where documents and queries are represented by semantic vectors. We propose a specific query expansion step at the query initiator's side and a query interpretation step at the document provider's. Through these steps, unshared concepts contribute to evaluate the relevance of documents wrt a given query. The experiments show that the proposed method enables to correctly evaluate the relevance of a document even if concepts of a query are not shared. In some cases, we are able to find up to 90% of the documents that would be selected when all the concepts are shared.

Introduction

In peer-to-peer (P2P) data systems, semantic interoperability means that any two peers are able to exchange information of which meaning is correctly interpreted by both of them. Several solution in P2P data management use local mappings to ensure the systems global interoperability [START_REF] Ives | Piazza: mediation and integration infrastructure for semantic web data[END_REF][START_REF] Rousset | Somewhere: a scalable p2p infrastructure for querying distributed ontologies[END_REF]. Most of the solutions focus on what (i.e. the concepts and relations) the peers share, which is important. However, no matter how the shared part is obtained (through consensus or mapping), there might be concepts (and relations) that are not consensual, and thus not shared but still useful for information exchange. Thus the question is to know whether the unshared parts are useful for information exchange.

In this paper, we restrict this question to the case of a P2P document management system, with unstructured or semi-structured documents. More precisely, we focus on semantic interoperability and information exchange between two peers, a query initiator p 1 and a document provider p 2 , which use different ontologies but share some common concepts. Each of them represents its queries and documents, according to its own ontology. The, the problem we address is to find documents which are relevant to a given query although the documents and the query may be both represented with concepts that are not all shared.

We represent documents and queries by semantic vectors [START_REF] Woods | Conceptual indexing: A better way to organize knowledge[END_REF] which are a common way to represent unstructured documents. The principle is simple: each concept of the ontology is weighted according to its representiveness of the document. The same is done for the query. The resulting vector represents the document (respectively, the query) in the n-dimensional space formed by the n concepts of the ontology. Then the relevance of a document with respect to a query corresponds to the proximity of the vectors in the space.

In order to improve information exchange beyond the "shared part" of the ontology, we promote both query expansion (at the query initiator's side) and query interpretation (at the document provider's side). Query expansion may contribute to weight linked shared concepts, thus improving the document provider's understanding of the query. Similarly, by interpreting an expanded query with respect to its own ontology (i.e. by weighting additional concepts of its own ontology), the document provider may find additional related documents that would not be found by only using the matching concepts in the query and the documents. To our knowledge, the best of the problem of improving information exchange by using the unshared concepts of different ontology has not been addressed before. Our proposal is a first, encouraging solution.

This paper is organised as follows. Section 2 gives preliminary definitions. In Section 3, we present query expansion in the case of a shared ontology. Its main property is to keep separate the results of the propagation from each central concept of the query. Section 4 considers the case where two peers use different ontologies, and describes query interpretation. Section 5 gives preliminary experiments. Finally, we conclude in Section 6.

Preliminary Definitions

We use a semantic vector space, i.e. a multi-dimensional linear space with the concepts of an ontology as dimensions. The content of each document (respectively query) is abstracted to a semantic vector by characterizing it according to each concept. The more a given document is related to a given concept, the higher is the value of the concept in the semantic vector of the document.

We simply define an ontology as a set of concepts together with a set of relations between those concepts [START_REF] Gómez-Pérez | Ontological Engineering[END_REF]. In our experiments we consider an ontology with only the is-a relation (specialization link). This does not restrict the generality of our relevance calculus.

Definition 1 (Semantic Vector). A semantic vector -→

v Ω , or -→ v when there is no ambiguity, is an application defined on the set of concepts C Ω of an ontology Ω:

∀c ∈ C Ω , -→ v Ω : c → [0, 1]
Expansion is based on weight propagation, which consists in weighting initially unweighted concepts which seem linked to weighted concepts. We propose to propagate weight from a given concept c i , according to the similarity [START_REF] Resnik | Using information content to evaluate semantic similarity in a taxonomy[END_REF] of the other concepts with c i . Thus, we introduce a similarity function sim ci which denotes the similarity to a central concept c i .

Definition 2 (Similarity function). Let c be a concept of C Ω . Function sim c :

C Ω → [0, 1], is a similarity function iff sim c (c) = 1 and 0 ≤ sim c (c j ) < 1 for all c j = c in C Ω .
The concepts of C Ω can then be ordered according to their similarity value. A propagation function Pf c is a decreasing function which assigns a weight to each similarity value, c being assigned the highest weight. Figure 1 is an example of a propagation function, inspired by membership functions used in fuzzy logic. For the sake of simplicity, we assume in this section that the query initiator and the document provider use the same ontology but they can still differ on the similarity measures and the propagation functions. Most propagation methods propagate the weight of each concept in the same vector. We call this kind of method "rough" propagation. Although the results are not bad, this method has some drawbacks, in particular, a possible unbalance of the relative importance of the initial concepts [START_REF] Nie | Integrating logical operators in query expansion invector space model[END_REF]. This is why we choose to keep separate the results of the propagation from different concepts in semantic enriched dimensions (SEDs).

First, let us denote by C-→ q the set of the central concepts of query -→ q , i.e. those weighted concepts which best represent the query. Each central concept of C-→ q is semantically enriched by propagation, in a separate vector (see figure 2). Definition 3 (Query expansion). Let -→ q be a query vector; let c be a concept in C-→ q and let Pf c be a propagation function.

The semantically enriched dimension of c, noted -→ sed c , is the semantic vector defined by: ∀c

′ ∈ C Ω , -→ sed c [c ′ ] = Pf c (c ′ ) The expansion of -→ q , noted E-→ q is defined as: E-→ q = { -→ sed c : c ∈ C-→ q } Fig. 2.
A query expansion composed of 2 semantically enriched dimensions.

The relevance of a given document is computed using the cosine of its image wrt the query and the query itself. This image is obtained using the expansion of the query (i.e. the set of SEDs).

Relevance in the Context of Unshared Concepts

We now assume that the query initiator, p 1 , and the document provider, p 2 , use different ontologies, respectively noted Ω 1 and Ω 2 . Each peer also has its own similarity and propagation functions. We also assume that the peers share some common concepts: each of them regularly (although may be not often) computes an ontology matching algorithm which provides a non-empty set of correspondences (equivalences) between those concepts [START_REF] Euzenat | Ontology matching[END_REF]. For the sake of simplicity of notations, when there is an equivalence, we make no difference between the name of the given concept at p 1 's, its name at p 2 's, and the identifier of the correspondence, which all refer to the same concept.

Overview of the Relevance Calculus

The query initiator and the document provider do not use the same vector spaces. An additional step is needed in order to be able to evaluate relevance in a same and single space. We call it interpretation of the query. Thus, the different steps involved in the relevance calculus of some document -→ d of p 2 wrt a given query -→ q initiated by p 1 are the following.

Query expansion. It remains unchanged. Peer p 1 computes an expansion of its query, which results in a set of SEDs. Each SED is expressed on the set C Ω1 , no matter the ontology used by p 2 . Then, the expanded query is sent to p 2 , together with the initial query. Query interpretation. Query interpretation by p 2 provides a set of interpreted SEDs on the set C Ω2 and an interpreted query. Each SED of the expanded query is interpreted separately. Interpretation is composed of two problems:

-The first problem is to find a concept that corresponds to the central concept of the SED. This is difficult when the central concept is not shared. It might even lead p 2 to introduce "new" concepts. Because of space limitations, we do not detail this part. In the following, we assume that the corresponding concept belongs to C Ω2 , even if the initial concept is not shared, and that it keeps the weight of this latter. -The second problem is to attribute weights to unshared concepts of C Ω2 which are linked to the SED. This is detailed below.

Image of the document and cosine calculus. They remain unchanged. Provider p 2 computes the image of its document with respect to the interpreted SEDs and then, its cosine based relevance with respect to the interpreted query, no matter the ontology used by p 1 . This is possible because the previous interpretation step makes both the image of the document and the interpreted query belong to space C Ω2 .

Interpretation of a SED

In this section, we describe the interpretation process for a given SED (expressed on C Ω1 ), of which central concept is noted c. The concept corresponding to c in C Ω2 is noted i E -→ q (c) and is assigned the weight of c. Peer p2 ranks its own concepts in function of sim iE -→ q (c) . Among these concepts, some are shared and their initial SED has a given weight, which we preserve in the interpretation. The problem is how to weight the unshared concepts, given that some of them might be more similar to i E -→ q (c) than shared concepts. Figure 4 illustrates our general solution. Let us call f i a piecewise affine function which defines a weight for each similarity value in [0, 1]. To guide the definition of f i , we use the weights given by -→ sed c to the shared concepts (c1, c2, c3 in figure 4). However, there might be several shared concepts that have the same similarity value with respect to i E -→ q (c), but have a different weight according to -→ sed c . We only require function f i to assign one of (or a function of) these values to the given similarity value.

For instance, it can be the minimum value. Given a function f i that satisfyes this condition, the unshared concepts (c4, c5, c6 in the figure) are assigned the weight they obtain by function f i . This is illustrated for c 5 by a dotted arrow.

Preliminary Experiments

The ontology we use is lightweight, i.e. an ontology composed of a taxonomy of concepts and a taxonomy of relations : WordNet. We use the Cranfield corpus, a testing corpus consisting of 1400 documents and 225 queries in natural language, all related to aeronautical engineering1 . For each query, each document is scored by humans as relevant or not relevant (boolean relevance). Although it is similar in size to other classical testing corpora like CACM, CISI, Medline, etc. it is small compared to recent TREC corpus. As we are not experts in textual IR nor in natural language processing, we do not focus on a large corpus for our experiments. However, this is one direction of our future work. Semantic indexing is the process which extracts concepts within documents or queries in natural language [START_REF] Sanderson | Retrieving with good sense[END_REF]. The aim is to find the most representative concepts for documents and queries. We use a program made in our lab : RIIO [START_REF] Desmontils | The Emerging Semantic Web, chapter Indexing a web site with a terminology oriented ontology[END_REF], which is based on the selection of synsets from WordNet. Thus, there is no human intervention in the process. We use a similarity function based on [START_REF] Bidault | Repairing queries in a mediator approach[END_REF], because it has good properties and results. The propagation functions used are of the form f 1,l2,v (see figure 1) We compare our image based method with two others that are classicaly used in the context of a shared ontology. In the cosine based method, relevance is defined by the cosine between the query and the document vectors. In the rough expansion method, the effects of propagating weights from different concepts are mixed in a single vector. Relevance is obtained using the cosine. This method avoids some silence, but often generates too much noise, without any highly accurate sense disambiguation [START_REF] Voorhees | Query expansion using lexical-semantic relations[END_REF]. In the context of a shared ontology, our method shows i) better results than rough expansion and ii) results that are comparable with the cosine ones (a 2% increase of recall and precison). In the context of two different ontologies, the cosine based method is applied by the document provider p 2 in space C Ω2 : in the query, only the shared concepts are considered. Rough expansion is done at the query intiator p 1 's and the cosine is calculted at p 2 's.

Because the manipulation of two different ontologies is a heavy process, we decided to simulate that use. Wordnet is used by both p 1 (to express its queries) and p 2 (to index its documents). However, in the result of the ontology mapping, we randomdly remove a given percentage of the shared concepts (from 10% to 90%). This amounts to simulate two peers that use the same ontology but are not aware of it. Of course, this eases interpretation. In particular, taking the lowest common ancestor of the shared concepts of -→ sed c to find the corresponding concept of central concept c gives good results most of the time.

Figure 5 shows the results obtained in average for the first twelve queries of the testing corpus. The reference method is the cosine one when no concept is removed, which gives a given reference precision and recall. Then, for each method and each percentage of removed concepts, we compute the ratio of the precision obtained (respectively recall) by the reference precision. When the percentage of randomly removed concepts increases, precision (figure 5 The main contribution of this paper is a solution which improves information exchange between two peers that use different ontologies. Our solution uses semantic vectors to represent documents and queries. It only requires the peers to share some concepts and uses the unshared concepts to find additional relevant documents. To the best of our knowledge, the problem has never been addressed before and our approach is a first, encouraging solution.

When performing query expansion, the query initiator makes more precise the concepts of the query by associating an expansion to each of them (SED). The expansion depends on the initiator's characteristics: ontology, similarity, propagation function. Interpretation by the document provider is not easy because the peers do not share the vector space. Given its own ontology and similarity function, it first finds out a corresponding concept for the central concept of each SED, and then interprets the whole SED. The interpreted SEDs are used to compute an image of the documents and their relevance. This is only possible because the central concepts are expanded separately. The results of our preliminary experiments show that our approach significantly improves information exchange, finding up to 90% of the documents that would be found if all the concepts were shared.

As future work, we plan to conduct additional testing in different contexts to verify the robustness of our approach. Another aspect that we want to consider carefully is complexity to improve efficiency. Finally, we plan a theoretical study of the impact of interpretation when several peers are involved

Fig. 1 .

 1 Fig. 1. Example of a f0.7,0.4,1 function with central concept c2

  Given a SED -→ sed c , we consider the product of the respective values of each concept in -→ sed c and -→ d . The image of -→ d keeps track of the best value assigned to one of the linked concepts if it is better than -→ d [ c ], which is the initial value of c . All the central concepts of the initial query vector are then weighted in the image of the document as far as the document is related to them.

Fig. 3 .

 3 Fig. 3. Obtaining the image of a document.

Fig. 4 .

 4 Fig. 4. SED interpretation: assigning weights to unshared non-central concepts

  (a)) and recall (Figure 5 (b)) decrease i.e. the results are less and less relevant. However, our image and interpretation based solution shows much better results. When the percentage of removed concepts is under 70%, we still get 80% or more of the answers obtained in the reference case.

Fig. 5 .

 5 Fig. 5. Evolution of (a) precision and (b) recall in function of the percentage of concepts randomly removed from the set of shared concepts.

It was collected between 1957 and 1968 by Cyril W. Cleverdon. The documents are abstracts of research papers.


Louis Ledoux

Marc Casas

An Open-Source Framework for Efficient Numerically-Tailored Computations

Scientific HPC: The Mathematical Aspect

• Many scientific problems are reduced to Matrix-Matrix Multiplications (MMM)

• Arouse the interest in GEMM kernels present in the BLAS libraries

Contrasting Numerical Requirements

• Ill-conditioned linear systems require high-precision arithmetic to ensure correct and reproducible results [START_REF] Bailey | High-Precision Computation and Mathematical Physics[END_REF].

• Emerging workloads such as DNNs, which can have millions up to billions of parameters, have shown resilience to arithmetic tinkering [START_REF] Johnson | Rethinking floating point for deep learning[END_REF] and precision lowering [START_REF] Courbariaux | Binarized Neural Networks: Training Deep Neural Networks with Weights and Activations Constrained to +1 or -1[END_REF].

Current Limitations

• General purpose arithmetic units and computer formats such as the IEEE754 standard naturally underperform in this vast land of scenarios • We propose the generation of numerically tailored circuits where the necessary and sufficient internal precision is generated to improve numerical quality while reducing the energy cost

3.A. Evaluation: Sea Surface Height Computation

Workload presentation

Results

• Our 91-bit ⟨ovf : 30, msb : 30, lsb : 30⟩ FDP always maintains reproducibility unlike IEEE754-64 and -128 FMAs.

• Our proposed FDP consistently exhibits 52 correct bits, which is at least 5× and 27.7× more than quad-precision and double-precision

• On VU3P-2 FPGA at 200M Hz, the units draw 0.266, 0.549, and 0.491 Watts for the IEEE754-64, -128 FMAs, and the 91-bit FDP, respectively

• For all evaluated sizes, the 91-bit FDP yields at least 5.6× and 15.1× more correct bits for the same wattage as 128-bit and 64-bit FMAs, respectively.

References Biography

Open Source SW/HW Co-designed Framework

• Our framework [START_REF] Ledoux | A Generator of Numerically-Tailored and High-Throughput Accelerators for Batched GEMMs[END_REF] can be used with any software language. Below is depicted how its two phases work

Runtime Execution Flow

• 1 malloc(): Allocates space for matrices to be multiplied

Conclusions

• Our work highlights the importance of numerically tailored accumulators for reproducibility

• Our results provide valuable insights into the trade-offs between power consumption and accuracy, and we believe that our results have the potential to inform the design of scientific computing systems

• In light of this, we encourage other researchers to explore the possibilities of custom precision accumulators using our open-source framework

• 2

 2 gemm(): BLAS kernels calls, either directly, or via higher-level code such as pytorch • 3 cast(): Convert computer formats and pad matrices if required • 4 DMA(): performs virtual addresses translations; runs at 20GB/s; uses shared memory A priori Hardware Generation Flow • A make image: With a set of functional and performance specifications calls all following steps • B flopoco[5]: Automated Pipelined datapath of custom arithmetic operators for any (frequency,target) couples; Design of custom Fused-Dot-Product (FDP) unit • C Systolic Array: Local and Distributed control; HSSD (Half Speed Sink Down) mechanism to allow overlaps of in-and out-going matrices to saturate OpenCAPI link • D AXI-Stream: Wrapping with well known buses/protocols to communicate with HOST DMA transfer @ ~20GB/s I/O control; pointer passing; start dma; register pooling A priori Hardware generation flow Runtime execution flow

3.B. Evaluation: Artificial Intelligence

	Experimental Setup	Results
	• Pytorch code without required changes • Models: ResNet18, ResNet34, DenseNet121, DenseNet161, DenseNet169, and ResNet50, VGG11_BN	• Notable example: On the following fig-ure we see that if 84% Top1 accuracy is satisfying for Imagenet with Resnet50, the less power-consuming arithmetic/ac-cumulator combination is IEEE-754 32-
	• Datasets: CIFAR-10 and ImageNet

bit/⟨ovf : 9, msb : 6, lsb : -20⟩

Acknowledgements

• Marc Casas is supported by Grant RYC-2017-23269 funded by MCIN/AEI/ 10.13039/501100011033 and by "ESF Investing in your future".


Yu-Rong Ni

Michael N Pillay

Tzu-Hao Chiu

Ying-Yann Wu

Dr Samia Kahlal

Jean-Yves Saillard
email: jeanyves.saillard@univ-rennes1.fr

C W Liu

Dr Y. -R Ni

Dr T. -H Chiu

Prof. Dr Y. -Y Wu

Prof. Dr J. -Y Saillard

Controlled Shell and Kernel Modifications of Atomically Precise Pd/Ag Superatomic Nanoclusters

Keywords: Superatom, Palladium hydride, atomically precise nanoclusters, dithiophosphate

The first 8-electron Pd/Ag superatomic alloys with an interstitial hydride [PdHAg19(dtp)12] (dtp = S2P(O i Pr)2 -) 1 and [PdHAg20(dtp)12] + 2 are reported. The targeted addition of a single Ag atom to 1 is achieved by the reaction of one equivalent of trifluoroacetic acid, resulting in the formation of 2 in 55 % yield. Further modification of the shell results in the formation of [PdAg21(dtp)12] + 3 via an internal redox reaction, with the system retaining an 8-electron superatomic configuration. The interstitial hydride in 1 and 2, contributes its 1s 1 electron to the superatomic electron count, and occupies a PdAg3 tetrahedron. The distributions of isomers corresponding to different dispositions of the outer capping Ag atoms are investigated by multinuclear VT-NMR spectroscopy. The emissive state of 3 has a lifetime of 200 μs (λex =448; λem =842), while 1 and 2 are non-emissive. The catalytic reduction of 4-nitrophenol is demonstrated with 1-3 at room temperature.

Introduction

Palladium hydride chemistry has a rich history, dating back to 1869 when T. Graham was perhaps the first one to identify the hydrogen-palladium combination as an alloy and the ability of palladium to restrain the volatility of hydrogen. [START_REF] Graham | Proc. R. Soc[END_REF] The hydride atom plays a crucial role in the era of atomic precise nanoclusters (NC) and in particular superatomic cluster formation. The evolution in the understanding of the superatomic concept began with exploiting the stability of NC electronic closed shells, yielding a new class of compounds with unique properties, different from that of bulk metal. [START_REF] Khanna | [END_REF] In this field, the chemistry of superatomic gold NCs has been particularly prolific in providing valuable data on the superatomic concept, both from theoretical and experimental approaches. [3,[START_REF] Walter | Proc. Natl. Acad. Sci[END_REF] Structural determination by X-ray crystallography and charge determination by mass spectrometry provide crucial evidence for the identification of superatomic species. [START_REF] Jadzinsky | [END_REF] Ligand-protected silver superatomic constructs are often based on a centered icosahedral kernel encapsulated in larger structures. [6,7] The contribution of the Pd atom to the superatomic electron count in silver-doped species has been demonstrated to be zero. [8][9][10][11] The role of hydrides in superatomic kernels in forming silver superatomic NCs is dual in nature. They provide the necessary reduction of metal centers in the formation of superatomic frameworks, as well as an H atom which contributes its valuable 1s [START_REF] Graham | Proc. R. Soc[END_REF] electron to the kernel in both homo-and hetero-metallic systems. [12][13][14][15][16][17][18][19] Although discrete palladium hydride motifs have been established in traditional coordination chemistry, few examples of a PdH unit encapsulated within a metallic framework have been realized. [20] NCs encaging the PdH motif are a relatively recent development, and few examples have been reported for coinage metals. In terms of bimetallic clusters composed of palladium and coinage metals, silver remains the outlier, with copper and gold both represented in literature. [20,21] Tsukuda and coworkers reported gold-rich frameworks of the type HPd@Au10 and trimetallic systems HPd@M2Au8 (M = Ag, Cu). [22] With respect to silver-doped frameworks, Lee and coworkers reported the superatomic rhodium NC [RhH@Ag24(SPhMe2)18] 2-, which contains a RhH unit. [23] Recently our group reported PtH-containing 8-electron superatoms of the type [PtHAg19{E2P(O n Pr)2}12](E = S, Se). [18] After our seminal work on the inclusion of Pd into an Ag12 icosahedron in 8-electron clusters of the types [PdAg20(dtp)12] (dtp = dithiophosphate), [24] and [PdAg20(dsep)12] (dsep = diselenophosphate), [25] we now turn our attention to PdH-doped silver superatoms.

Three new NCs are reported, [PdHAg19(dtp

)12] 1, [PdHAg20(dtp)12](TFA) ([2](TFA)); TFA = trifluoroacetate) and [PdAg21(dtp)12](BF4) ([3](BF4)).
The composition and structural properties are determined by singlecrystal X-ray diffraction, X-ray photoelectron spectroscopy (XPS), ESI-TOF-MS, UV-vis, and multinuclear NMR spectroscopy. The screening of effective reagents for the facile conversion of the Ag shell are explored and monitored by in-situ NMR studies. The effect of the solvation sphere on the dynamics of the isomerization in solution is also investigated by VT-NMR. The screening of silver precursors and organic acids for silver framework modifications indicates the intricate role counter ions can play in NC modification, beyond the role of spectators. ]. [25] Notably, in the preparation of 1, we found no evidence for the presence of 2 in the same pot. To confirm the presence of the hydride in the clusters, NaBH4 was substituted by NaBD4 with the same synthetic protocol to obtain the deuteride analogues [Pd(D)Ag19(dtp)12] 1D and [Pd(D)Ag20(dtp)12]TFA 2D. Adding a single Ag atom to the shell occurs under acidic conditions, but is only induced by the addition of selected anions. The addition of HTFA or HBF4 results in the formation of 2, with the largest selectivity/yield achieved with TFA. Importantly the addition of any acid does not necessarily accommodate this transition. Notably, HOAc leaves 1 intact. In contrast to the addition of the acetic acid, the addition of silver acetate results in a modification of the passivating outer shell after hydride loss, yielding [PdAg20{S2P(O i Pr)2}12]. Furthermore, adding silver salts, [Ag(TFA)] and [Ag(BF4)], to 1 also yields 2 but with poorer selectivity, resulting in the formation of several by-products and no improvement in the isolated yield. We propose that the transfer occurs via an inter-cluster reaction between two molecules of 1, with the donor cluster scavenged during the formation of 2. The transfer occurs in solution due to the lability of the ligand shell at room temperature, evident from the VT NMR behavior (Figure S2). The identical ligand framework supports the harvesting of a capping atom from the donor cluster. Thus, the steric and electronic transition is more efficient than adding a virgin silver atom from a precursor salt. A similar screening process was undertaken for the controlled transformation of [PdAg20(dtp)12] to 3. NaBF4 was found to be the optimal reagent for the modification of [PdAg20(dtp)12] to 3. This provides further evidence for the ability of counter-anions to play a role in the customization of NCs. [26] In all cases, the transitions prefer the retention of the 8-electron superatomic core.

Results and Discussion

The second type of inter-cluster reaction results in the conversion of the shell without the need for an additional reducing agent but with loss of the central hydride, indicating self-reduction. [27] In comparison to the homometallic [Ag20(dtp)12] (Ag@Ag19), which is prepared from the addition of NaBH4 to [Ag21(dtp)12] + (Ag@Ag20), [13] [PdHAg19(dtp)12] 1 and [PdHAg20(dtp)12] + 2 undergo an internal redox process in solution to form [PdAg20(dtp)12] and [PdAg21(dtp)12] 3, respectively. [28] The process can be accelerated by heat and monitored by 31 P-NMR, the conversion of 1 to [PdAg20(dtp)12] is given in Figure S14, and shows the transition occurring over a period of 48 hours at 60 °C. The time-dependent 1 H NMR indicates the formation of hydrogen gas and a corresponding loss of the hydride resonance, Figure S15. A similar trend is observed for the conversion of 2 to 3 in the 31 P NMR, Figure S16. However the evolution of hydrogen gas is not observed, due to anion present in 2. The transition at ambient conditions takes 2 weeks, and can be monitored by UV/vis spectroscopy (Figure S17). The two-week transition further indicates the stability of the hydridedoped core, at ambient conditions. The compositions of clusters 1-3 were confirmed by ESI-TOF-MS spectrometry, and a comparison of experimental and simulated spectra is presented in Figure 1. The experimental and simulated isotopic patterns show agreement. The mass spectrum of 1 shows a prominent m/z peak at 4823.4185 m/z assigned to the silver adduct [1 + Ag] + (calc. 4823.2163). Due to the ambiguous nature of a silver adduct in the current system, cesium iodide was added to the sample prior to analysis to obtain a cesium adduct [1+Cs] + observed 4847.4653 m/z (calc. m/z 4847.2204) (Figure 1a). The spectrum of 2 contains a molecular ion peak [2] + at m/z 4823.4185 (calc. m/z 4823.2163) (Figure 1b). The deuterated analogues, 1D and 2D, also showed similar fragmentation patterns with peaks [1D+Ag] + at 4824.2202 m/z (calc. m/z 4824.2227) and [2D] + at m/z 4824.5447 (calc. m/z 4824.2227), Figure S1. Similarly, the fragmentation peak observed in 3 corresponds to [3] + with m/z 4930.5205 (calc. m/z 4931.1133) (Figure 1c). The composition of the clusters was further confirmed by X-ray photoelectron spectroscopy (XPS); the percentage compositions and spectra are shown in Figure S13. The spectra explicitly indicate the presence of both Pd and Ag in ratios similar to the expected molecular composition. Furthermore, the spectra indicate the oxidation state of Pd to be zero and the Ag approaching Ag(Ⅰ) for 1-3, Figure S13. [29] The hydride provides a unique probe for configuration changes in the metallic framework due to the coupling with its surrounding silver atoms. The integration ratios of the 1 H NMR spectra for 1 and 2 indicate 12 dtp ligands to one hydride. At ambient temperature (293 K) in CD2Cl2, the encapsulated hydride moves inside its Ag12 icosahedral prison, with a multiplet resonance observed at -8.56 ppm (1) and -8.39 ppm (2) (Figure S7a andS7c). The broad shape of the peak indicates that the hydride indiscriminately couples to all 12 atoms. The corresponding deuterated resonance in the 2 H NMR spectra of 1D and 2D confirms the position and magnetic state of the hydride with relatively similar resonances observed at δ = -8.41 ppm and δ = -8.33 ppm for 1D and 2D, respectively (Figure S7b andS7d). The dynamics of the nanoclusters in solution have been investigated with multinuclear VT-NMR (Figures S2-S5). Reduction in temperature to 173 K decreases the hydride mobility, resulting in a well-defined quartet observed at -8.97 ppm ( 1 J1H-107Ag = 55.6 Hz, 1 J1H-109Ag = 63.9 Hz) and -8.38 ppm ( 1 J1H-107Ag = 52.7 Hz, 1 J1H-109Ag = 60.6 Hz) for 1 and 2, respectively (Figure 2). The quartet resonance corresponds to the hydride position found in the solid state, wherein the hydride couples with three equivalent Ag atoms while occupying a tetrahedral position (Figure 3a). A similar observation to the related Pt centered NC was previously reported. [18] 1 H NMR splitting patterns obtained from simulation are in good agreement with the experimental results and are shown in Figure S6. A comparison of the hydride behavior in 1 and 2 indicates similar environments, with the hydride seemingly unperturbed by the external cluster rearrangements in CD2Cl2. The hydride behavior is also in stark contrast to those observed in [RhH@Ag24(SPhMe2)18] 2-wherein the hydride position, inferred from NMR and DFT calculations, indicate preferential bonding to the central Rh atom, with minimal interaction with the Ag framework. [23] The external configuration of the cluster can be monitored by 31 P NMR. At ambient conditions in CD2Cl2, a single peak is observed at 101.38, 98.72, and 97.43 ppm for 1, 2 and 3, respectively. The reduction in temperature and the concurrent decrease in lability of the ligand shell results in the singlet peak in 1 spreading over a range of 105 -96 ppm, giving rise to 12 well-resolved peaks at 173 K in CD2Cl2 (Figure 2a). Each peak corresponds to a unique phosphorus environment (nonsymmetric) for each of the twelve dtp ligands, corresponding to the C1 symmetry of 1 (vide Infra.). In 2, a similar trend is observed in CD2Cl2. However, four dominant peaks are observed, attributed to the C3 isomer found in the solid state (Figure 2b). The various changes in symmetry caused by the movement of the outermost shell are more apparent in (CD3)2CO. At ambient conditions, the hydride resonance follows suit with the CD2Cl2 experiments, with peaks at -8.66 ppm (1) and -8.59 ppm (2). However, in (CD3)2CO, a decrease in temperature results in the formation of two distinct broad peaks at 173K without the resolution of the quartet recorded in CD2Cl2. In (CD3)2CO, there are magnetically distinct environments for the hydride in both 1 and 2, with a pair of resonances observed (Figure S4b-5b). The 31 P NMR is more complex in (CD3)2CO, with several peaks observed for 1 and 2 suggesting the presence of several isomers resulting from the lability of the peripheral silver layer, Figure S4a-5a. This lability is directly related to the interaction with the solvation sphere and is evident by the differential isomeric distributions in CD2Cl2 and (CD3)2CO. The presence of the counter anion TFA⁻ in 2 was confirmed by 19 F NMR, with singlet resonance observed at -76 ppm, Figure S8. Similarly, the BF4⁻ anion in 3 is observed as a singlet at -154.9 ppm and -155 ppm, for isotopes 10 B and 11 B respectively, Figure S11. Single-crystal X-ray diffraction data collected for 1, 2 and 3 were of ample quality that electron density consistent with the hydride dopant in 1 and 2 could be assigned from the difference density map and their positions were subsequently confirmed by density functional theory (DFT) calculations (vide infra). Molecular representations are illustrated in Figure 3, with selected bond lengths and angles given in Table 1. [30] Refinements and crystallographic data are provided in Table S1. structures contain a 12-atom silver icosahedron centered by a PdH unit in 1 and 2 and a Pd atom in 3 (Figure 3d-f). The encapsulated Pd-H motif causes a significant distortion of the Ag12 icosahedron, highlighted by the continuous symmetry measure (CSM) values of 0.22 and 0.14 for 1 and 2, respectively (Figure 3b). In contrast, the Pd-centered Ag icosahedron of 3 approaches an idealized geometry with a CSM value of 0.04 (Figure 3c). The icosahedron distortion in 1 and 2 is also evident in examining the bond distances, as illustrated by a plot of the bond distance as a function of occurrence (Figure S12). Furthermore, the bond distances in 1 and 2 (Table 1) are significantly longer in average than in 3, in order to accommodate the hydride. Importantly, the core is geometrically similar to the Pt derivative previously reported, in which neutron diffraction confirmed the position of the hydride. [18] The tetrahedron encapsulation of the hydride is substantially different from that in the Tsukuda's HPd@Au10 frameworks, which contain incomplete icosahedra providing a missing vertex for the hydride to occupy. [21,22] Furthermore, the similarity in the core dimensions of 1-3, indicate the hydride occupies an interstitial tetrahedral site. Due to hydrogen atom being sufficiently small, the overall metal framework is retained. The stability of the interstitial alloy is demonstrated in solution at ambient conditions and in the catalytic application in aqueous medium, described in this report. In the solid state, the outer layer of silver atoms in 1-3 can be divided into two groups, Agcap (blue) and Agcap ' (green), as depicted in Figure 3d-f. Six Agcap atoms occupy similar triangular faces of the Ag12 icosahedron in all clusters. They are grouped by pairs, occupying adjacent faces of the icosahedron, in such a 3-fold fashion that the resulting (A)@Ag12@(Agcap)6 (A = PdH,1 and 2; A = Pd, 3) framework have an ideal C3v symmetry. (Figure 3d-f). Adding now the unique green Agcap' in 1 results in a complete loss of symmetry (Figure 3d). The same situation occurs when adding the two Agcap' in 3 (Figure 3f). In contrast, the two Agcap' in 2 occupy positions along the Pd-H motif, resulting in the preservation of C3 axis, (Figure 3e). The M22 (M1Ag21) configuration in 3 is the first report of such stabilized by dichalcogenolato ligands and is exceedingly rare in literature. Only few examples of bimetallic system are present, in particular those with M13 centered-icosahedral kernels: monometallic Ag22 protected by nitrogen donor ligands [31] and M1Ag21 (M = Au/Ag) stabilized by 1,1'-bis-(diphenylphosphino)ferrocene ligands. [32] To our knowledge no reports on group 10 doped M22 frameworks can be found in literature. The stabilizing ligand shell accommodates the silver framework in such a way each capping Ag is approximately planar-tricoordinated. The twelve dtp ligands in cluster 1 of C1 symmetry can be classified by connectivity with one η 2 (μ1, μ1), three η 4 (μ2, μ2) and eight η 3 (μ2, μ1). In cluster 2 of C3 symmetry, two coordination environments can be found, with three η 3 (μ2, μ2) and nine η 3 (μ2, μ1). In cluster 3 of C1 symmetry, one ligand is η 2 (μ1, μ1), three are η 3 (μ2, μ1) and eight are η 4 (μ2, μ2).

Whereas the NMR analysis indicates the presence of isomers in solution, only one isomer is found for each cluster in the solid state. It is possible to elaborate a geometrical prediction of the most probable isomers, by analogy with the known dicalcogenolate-protected 8-electron clusters having Ag20 and MAg20 kernels. Furthermore, these predictions are supported by DFT calculations discussed below. As mentioned above, both frameworks of 1 and 2 contain the same (PdH)@Ag12@(Agcap)6 sub-unit of ideal C3v symmetry (PdHAg18 in Figure 4). Assuming that this very recurrent motif [12,14,33] is preserved in all the clusters discussed here, the nature of the possible isomers depends on the distribution of the supplementary Agcap' (green) atoms on the available triangular faces of the Ag12 icosahedron.

Adding one atom to the PdHAg18 C3v framework in Figure 4 allows to generate four different topologies. When added on the C3 axis, the C3a isomer of 1 is generated, the metal arrangement of which being that of [Ag20{S2P(dtp}12]. [13] Three additional structures, all of C1 symmetry, can be generated by capping each one of the three symmetry-independent faces of PdH@Ag18 that do not intersect the C3 axis. One of them is the solid-state structure of 1, also reported for the Pt derivative. [18] We propose discarding the two other C1 structures, since no report of these topologies exist so far in this chemistry. On the other hand, we suggest another C3 structure (C3b), derived from the T structure of [PdAg20(dsep)12] + [34] by the removal of one capping Ag. Alternatively, C3b can be derived from C3a by a concerted rotational displacement of three Agcap atoms, making them of the Agcap' type, as illustrated in Figure 4. Adding now two Agcap' atoms along the C3 axis of the PdH@Ag19 framework generates the X-ray C3 structure of 2. Actually, there are several additional possibilities to distribute the two Agcap' on the available positions of PdHAg18 in such a way that at least one Agcap' is not on the C3 axis. We propose to retain three structures of C1 symmetry in which none of the Agcap' atom is on the C3 axis, but which have been reported for [MAg20{S2P(O n Pr)2}12 (M = Pd, Pt), [24,17] [PdAg20{E2P(O i Pr)2}12 (E = S, Se), [25] and [AuAg20{S2P(O i Pr)2}12], [16] respectively (C1a, C1b and C1c in Figure 4). Owing to the complexity of the ligand topology in 3 and the uniqueness of this M@Ag21 structure, no reasonable isomer of 3 could be proposed. The relative energies of the isomers of clusters 1 and 2 depicted in Figure 4 were computed through DFT calculations at the BP86/Def2-TZVP level of calculations (see Computational Details in the SI). For the sake of computational limits, the dtp ligands were replaced by S2PH2, a simplification which has been proved to be reasonable in many past investigations. [7, 12-18, 20,24, 25, 27, 33] The optimized geometries of the three structures found in the solid state match with their experimental counterpart, in particular with respect to the hydride location in 1 and 2. Selected computed data are provided in Table 2. The experimental structures of 1 and 2 correspond to the most stable computed isomers, both in total (E) and free (G) energies. However, the energy differences between isomers remain small, as usually found in this family of compounds. [13,33] Owing to the considered level of theory and modelling, the computed relative energies are consistent with the existence of several isomers in solution. Those considered in our calculations constitute good candidates, although other 8electron isomers, also differing from the spatial configuration of their outer shell, (including in the case of 3) are possible. In fact, all the computed data of the 1-3 systems reported in Table 2 are very similar. Their atomic charges computed from natural atomic orbital (NAO) analysis and their Wiberg bond indices (WBIs) are consistent with the view of the outer capping atoms being in the formal +I oxidation state and only weakly bonded to the Agico triangle they are capping. [12,15,33] Neglecting this capping interaction, they can be viewed as stable 16-electron trigonal planar AgS3 metal centers, leaving the centered icosahedral kernel with an 8-electron superatomic count. Since the computed isomers of 1 and 2 display very similar features, we comment below only the most stable structures, i.e. that characterized in the solid state. Their Kohn-Sham orbital diagrams (Figure S23), illustrate their 1S 2 1P 6 1D 0 superatomic configuration, with the 1P and 1D levels (plotted in Figure S24) being the frontier orbitals. The electronic structure of 1 is very similar to that of its [PtHAg19(dtp)12] relative. [18] The H-Pd and H-Ag WBI values (Table 2) indicate that the hydrogen atom interacts preferentially with Pd, although the H-Ag interaction is not as weak as in [PtHAg19(dtp)12]. [18] The Pd-H interaction, which is sketched for an isolated Pd-H unit in Figure 5, involves primarily a 4dz 2 (Pd) orbital. Owing to the strong destabilization of the *(Pd-H) orbital, the unpaired electron prefers occupying the orbital of large 5s(Pd) character, i.e. that which mainly contributes to the building of the superatomic orbitals. Thus, the contribution of PdH to the superatomic electron count is 1, similarly to Ag (4d 10 5s 1 ). [(PdH)@Ag19(dtp)12] (1) and [(Ag)@Ag19(dtp)12] [13] are strongly related 8-electron superatoms, the former being however somewhat axially distorted. Thus, though the hydride participation to the superatomic orbitals is low, its electron should be included in the superatomic count. The electronic structure of 2 is essentially the same as that of 1, with a similar 8-electron [(PdH)@Ag12] 5+ icosahedral core. That of 3 is strongly related to those of [PdAg20{S2P(O n Pr)2}12] [24] and [PdAg20{S2P(O i Pr)2}12], [25] which have one less Ag(I) capping atom. The optical properties of the NCs were investigated by UV-vis and PL spectroscopy. The UV-vis spectra of 1 and 2 are relatively similar, with a common peak observed at 405 nm and with marginally different shoulder peaks at 455 and 462 nm for 1 and 2, respectively (Figure 6). Furthermore, the emission in 3 is red-shifted in comparison to [PdAg20{S2P(O i Pr)2}12], with a broad emission profile centered at 842 nm in comparison to 741 nm in the latter (Figure S18). The emission lifetime recorded for 3 is 200 μs (Figure S19), which is relatively close to the 235 μs recorded for [PdAg20{S2P(O i Pr)2}12]. The additional silver capping atom has a dramatic influence on the emission profile.

Compared to the monometallic 8-electron superatomic species, the luminescent profile in these systems seems more sensitive to shell configuration than the central metal species, [12,13] demonstrating the tunability afforded by atomically precise single-atom tailoring. The TD-DFT UV-Vis spectra simulated at the CAM-B3LYP/Def2-TZVP level (see Computational Details in the SI) of clusters 1-3 considered in their respective C1, C3 and C1 solid state configurations are shown in Figure 6b. There is a good agreement with the experimental spectra (Figure 6a), It is noteworthy that the simulated spectra of 1, 2 and [PtHAg19(dtp)12] [18] exhibit similar double band shape in the 300-500 nm region. These peaks are of 1P→1D as well as unique band shown by 3 in the same range. The reduction of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP) has been chosen as a model reaction to determine the catalytic activity of 1-3. The reaction has been established as a reliable model for the quantitative assessment of nanoparticle catalytic activity. [START_REF] Pradhan | Colloids Surfaces A Physicochem[END_REF]36] The mechanism has been extensively studied for silver nanoclusters. [37] More recently, it has been applied to NCs, due to the ability to analyze the reaction by routine UV-vis spectrometry quantitatively. [38,39] The hydrolysis of NaBH4 in aqueous media results in the deprotonation of 4-NP to yield 4nitrophenolate (4NP⁻). The 4NP⁻ has a strong absorption band at 400 nm allowing for facile quantitative analysis of the 4NP reduction. In the current context, the precision afforded by ligand-protected NC's enables the development of uniform catalysts tailored atom by atom. It is therefore, appropriate to determine the comparative influence of kernel and shell modifications on the catalytic efficacy. The UVvis absorption spectra for the catalytic reduction of 4-NP, with 1-3, are given in Figure 7. The reduction is done at room temperature, with a catalytic loading of 10 mol % found to be optimum. The addition of NaBH4 is capped at 20 mol eqv. Excessive amounts of NaBH4 decrease the catalytic activity and result in the catalyst's decomposition. The complete conversion of the 4-NP is achieved within 25, 30, and 60 min for 1-3, respectively. All clusters perform the reduction with the hydridedoped clusters 1 and 2, superior to 3, solely based on the rate of decay, Figure S21. The calculated apparent rate constant, k for 1, 2, and 3 are 0.1195 min⁻ 1 , 0.0901 min⁻ 1 and 0.0509 min⁻ 1 , respectively. Fundamentally, the steric factors involved in the approach of the reactants to the catalytic site (Ag atom) in 1-3, appear to be similar, as seen in the space-filling representations in Figure S22. The Ag atoms are accessible in all instances, however with the complexity of the dynamic behavior of the cluster at ambient conditions, it is difficult to confirm the reaction mechanism directly, although the linear correlation of the ln(C/C0) vs. time corresponds to the Langmuir-Hinshelwood model for the reduction. We tentatively propose that the reduction follows first-order kinetics. The catalyst has reasonable stability in an aqueous environment and the differential solubility allows for facile separation and reuse. The catalyst remains active for at least 4 catalytic runs with an increase time required for complete conversion. A flaw of bare Ag nanoparticles is the oxidation of the surface silver atoms during the catalytic cycles and the formation of AgO layer over the catalytic surface. In the current report, the dtp ligands, act as protecting layer. Importantly the absence of support implies that the cluster is solely responsible for the catalytic activity, both the electronic and steric factors governing the reduction.

Conclusion

This report demonstrates the ability to control cluster composition at the kernel and shell levels. This allows for the atomic-level manipulation of the electronic and physical properties of the NC. Judicious choice of 'non-innocent' spectator anions, and the form in which they are introduced, play a crucial role in dictating the nature of the isolated product. The formation of these new NCs and the transitions between them have been confirmed by multinuclear NMR, mass spectroscopy and crystallography.

Modifications of the parent cluster [Pd(H)Ag19{S2P(O i Pr)2}12] 1 result in a practical solubility change with the addition of a single Ag atom to yield [Pd(H)Ag20{S2P(O i Pr)2}12]TFA 2. In both 1 and 2, the interstitial hydrogen provides to the central Pd atom with the electron it misses to complete the superatomic 8-electron count with the other metals (in other words, PdH is isoelectronic with Ag). The removal of the interstitial hydrogen from the cluster together with the addition of a supplementary outer (capping) Ag atom form a luminescent species 3, a new silver-rich M22 species. The catalytic activity of 1-3 indicates that the hydride-doped catalysts are superior. The reported physical characteristics will prove to be helpful in inevitable future applications.

1 .

 1 Scheme 1. Synthetic protocol for the controlled modification 1 to yield 2 and 3 while retaining superatomic character. The parent cluster 1 is isolated from the co-reduction of [Ag(CH3CN)4](BF4) and [Pd(OAc)2] by NaBH4 in the presence of [NH4][S2P(O i Pr)2] in a 19:1:12 molar ratio (Scheme 1). After purification by column chromatography, 1 is isolated in ~17 % yield. The one-pot reaction yields a mixture of products along with the target compound and the non-hydride Pd-centered NC [PdAg20{S2P(O i Pr)2}12].[25] Notably, in the preparation of 1, we found no evidence for the presence of 2 in the same pot. To confirm the presence of the hydride in the clusters, NaBH4 was substituted by NaBD4 with the same synthetic protocol to obtain the deuteride analogues [Pd(D)Ag19(dtp)12] 1D and [Pd(D)Ag20(dtp)12]TFA 2D. Adding a single Ag atom to the shell occurs under acidic conditions, but is only induced by the addition of selected anions. The addition of HTFA or HBF4 results in the formation of 2, with the largest selectivity/yield achieved with TFA. Importantly the addition of any acid does not necessarily accommodate this transition. Notably, HOAc leaves 1 intact. In contrast to the addition of the acetic acid, the addition of silver acetate results in a modification of the passivating outer shell after hydride loss, yielding [PdAg20{S2P(O i Pr)2}12]. Furthermore, adding silver salts, [Ag(TFA)] and [Ag(BF4)], to 1 also yields 2 but with poorer selectivity, resulting in the formation of several by-products and no improvement in the isolated yield. We propose that the transfer occurs via an inter-cluster reaction between two molecules of 1, with the donor cluster scavenged during the formation of 2. The transfer occurs in solution due to the lability of the ligand shell at room temperature, evident from the VT NMR behavior (FigureS2). The identical ligand framework supports the harvesting of a capping atom from the donor cluster. Thus, the steric and electronic transition is more efficient than adding a virgin silver atom from a precursor salt. A similar screening process was undertaken for the controlled transformation of [PdAg20(dtp)12] to 3. NaBF4 was found to be the optimal reagent for the modification of [PdAg20(dtp)12] to 3. This provides further evidence for the ability of counter-anions to play a role in the customization of NCs.[26] In all cases, the transitions prefer the retention of the 8-electron superatomic core.

Figure 1 .

 1 Figure 1. Experimental (black) and simulated (brown) ESI-TOF-MS spectrums for 1(a), 2(b), and 3(c).

Figure 2 .

 2 Figure 2. 31 P{ 1 H} NMR (CD2Cl2) (left) indicating the lability of the ligand environment at 293 K, and the isomeric distribution observed at 173 K for 1 (a) and 2 (b). 1 H NMR (CD2Cl2, δ) (right) illustrating the formation of a quartet resonance peak at 173 K for both 1 (a) and 2 (b).

Figure 3 .

 3 Figure 3. (a) Molecular representation of HPdAg3 kernel present in 1 and 2. (b) Distorted Ag12 icosahedron present in 1 and 2. (c) Pd@Ag12 core present in 3. The thermal ellipsoid plot of 1-3 (d-f) illustrates the symmetry induced by the capping atoms, with the primary Ag cap occupying symmetrically favorable positions on the triangular facets of the icosahedron. The remaining capping atoms, Ag cap' and ligand stabilization result in the following symmetry for the metallic framework C1 for 1 (d), C3 for 2 (e) and C1 for 3 (f). (Color code. Pd: dark green; H: pink; Ag: grey; Agcap: blue; Agcap′: light green; S: yellow; P: purple)

Figure 4 .Figure 5 .

 45 Figure 4. Inferred isomeric distribution in 1, and 2 with crystallographic confirmed isomers with red labels. (Color code. Pd: dark green; H: pink; Ag: grey; Agcap: blue; Agcap′: light green)

Figure 6 .

 6 Figure 6. a) UV-vis absorption spectra for 1-3, and emission spectrum of 3 (λex = 448 nm) recorded in CH2Cl2. b) TD-DFT-simulated UV-vis spectra for 3 in their respective C1, C3 and C1 solid state configurations.

Figure 7 .

 7 Figure 7. Uv-vis spectra showing reduction of 4-nitrophenol catalyzed by 1, 2 and 3, in the presence of NaBH4.

Table 1 .

 1 Selected metal bond lengths and geometry parameters.

		1	2	3
	CSM	0.22	0.14	0.04
	Pdcen-Agico	2.7129(7)-2.9793(12)	2.756(2)-2.829(2)	2.721(2)-2.778(2) Å,
	(Å)	avg. 2.7926	avg. 2.793(2)	avg. 2.752(2)
	Agico-Agico	2.8124(8)-3.2135(11)	2.808(2)-3.227(2)	2.854(2)-2.995(2) Å,
	(Å)	avg. 2.9204(8)	avg. 2.936(2)	avg. 2.702(2)
	Agico-Agcap	2.8911(8)-3.1254(7)	2.921(2)-3.231(2)	2.660(2)-3.120(4)
	(Å)	avg. 2.9915(8)	avg. 3.003(2)	avg.2.702 (3)
	Agico-Agcap′	2.8952(8)-3.0191(8)	2.975(2)-3.012(2),	2.857(3)-3.085(3) Å,
	(Å)	avg. 2.9624(8)	avg. 2.990(2)	avg. 2.945(2)

Table 2 .

 2 Selected DFT-computed data for 1, 2 and 3. Distances are in Å and their corresponding Wiberg bond indices into brackets.

	Isomer		1 C1	1 C3a	1 C3b	2 C3	2 C1a	2 C1b	2 C1c	3 C1
	E (kcal/mol)	0.0	1.9	0.9	0.0	6.6	6.2	4.6
	G (kcal/mol)	0.0	1.7	1.8	0.0	4.1	3.1	1.7
	EHOMO-LUMO (eV)	1.67	1.85	1.96	1.86	1.56	1.66	1.51	1.37
		H	-0.46	-0.43	-0.46	-0.46	-0.44	-0.44	-0.44
	NAO	Pd	-1.01	-0.99	-0.96	-1.04	-1.00	-0.98	-1.00	-1.18
	charges
	(avg.)	Agico	+0.36	+0.35	+0.35	+0.35	+0.34	+0.34	+0.34	+0.27

Acknowledgements

This work was supported by the National Science and Technology Council in Taiwan (111-2123-M-259-002). and the GENCI French National Computer Resource Center (grant A0030807367).


Yu-Ming Tseng

Jian-Hong Liao

Tzu-Hao Chiu

Hao Liang

Samia Kahlal

Jean-Yves Saillard

C W Liu

Superatom Pruning by Diphosphine Ligands as a Chemical Scissor

A two-electron silver superatom, [Ag6{S2P(O i Pr)2}4(dppm)2] (1), was synthesized by adding dppm (bis(diphenylphosphino)methane) into [Ag20{S2P(O i Pr)2}12] (8e). It was characterized by singlecrystal crystallography, multinuclear NMR spectroscopy, ESI-MS, DFT and TD-DFT calculations. The added dppm ligands, which carry out the nanocluster-to-nanocluster transformation, act as a chemical scissor to prune the nanocluster geometrically from an icosahedron-based Ag20 NC to an octahedral Ag6 NC and electronically from eight-electron to two-electron. Eventually dppm was involved in the protective shell to form a new heteroleptic NC. The temperature-dependent NMR spectroscopy confirms its fluxional behavior, showing the fast atomic movement at ambient temperature. Compound 1 exhibits a bright yellow emission under

INTRODUCTION

The chemistry of ligand-protected atom-precise metal nanoclusters (NCs) is currently flourishing, boosted by the intense interest in their unique properties that are substantially different from their corresponding bulk materials, with various fields of potential applications. [START_REF] Du | Atomically Precise Metal Nanoclusters for Catalysis[END_REF][START_REF] Maity | An overview on the current understanding of the photophysical properties of metal nanoclusters and their potential applications[END_REF][START_REF] Tang | Ultrasmall Au and Ag Nanoclusters for Biomedical Applications: A Review[END_REF] In this context, altering the composition, shape, and electronic configuration of NCs at the atomic level will sensitively induce significant changes for fine-tuning optical properties. [START_REF] Yang | Tailoring silver nanoclusters via doping: advances and opportunities[END_REF] Strategies such as galvanic replacement, [START_REF] Wang | Customizing the Structure, Composition, and Properties of Alloy Nanoclusters by Metal Exchange[END_REF][START_REF] Sharma | Structurally Precise Dichalcogenolate-Protected Copper and Silver Superatomic Nanoclusters and Their Alloys[END_REF] ligand exchange, [START_REF] Wang | Ligand exchange reactions on thiolate-protected gold nanoclusters[END_REF][START_REF] Chang | Eight-Electron Silver and Mixed Gold/Silver Nanoclusters Stabilized by Selenium Donor Ligands[END_REF] and thermally-induced structural change [START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reaction of a Silver(I) Hydride[END_REF][START_REF] Ren | Cluster-to-cluster transformation among Au6, Au8 and Au11 nanoclusters[END_REF] are commonly used to control cluster-to-cluster transformations. Such atomic-level molecular surgery on a specific site is currently an extremely challenging project, [START_REF] Li | Molecular "surgery" on a 23-gold-atom nanoparticle[END_REF] and developing new methodologies in molecular engineering is an urgent need. Our previous report on atomically precise Ag20 NCs revealed a centered icosahedron as [Ag13] 5+ kernel surrounded by seven Ag atoms and twelve dithiophosphate (dtp) ligands. [START_REF] Dhayal | Ag20{S2P(OR)2}12]: A Superatom Complex with a Chiral Metallic Core and High Potential for Isomerism[END_REF] It has been further confirmed that the electronic property of those homoleptic M20L12 (L = dtp or dsep; dsep = diselenophosphate) NCs can be tuned by doping heterometal such as Pd, Pt, Cu, and Au. [START_REF] Chang | Eight-Electron Silver and Mixed Gold/Silver Nanoclusters Stabilized by Selenium Donor Ligands[END_REF][START_REF] Barik | Mono-and hexa-palladium doped silver nanoclusters stabilized by dithiolates[END_REF][START_REF] Chiu | Homoleptic platinum/silver superatoms protected by dithiolates: Linear assemblies of two and three centered icosahedra isolobal to Ne2 and I3[END_REF][START_REF] Zhong | Doping effect on the structure and properties of eight-electron silver nanoclusters[END_REF][START_REF] Yen | Homoleptic Silver-Rich Trimetallic M20 Nanocluster[END_REF][START_REF] Lin | Synthesis, structural characterization and transformation of an eight-electron superatomic alloy, [Au@Ag19{S2P(OPr)2}12[END_REF] However, these NCs maintain the same nuclearity and number of ligands. Thus, it is expected that reacting our easy-to-synthesize and neutral Ag20 NCs with heteroligands would affect their structure and properties. In this work, we report a facile way to reach NC pruning from an 8-electron heptacapped centered icosahedral Ag20 NC to a 2-electron octahedral Ag6 NC. It is noteworthy that most of the known Ag6 octahedral clusters are composed of solely Ag(I), i.e. are 0-electron species. [START_REF] Yue | A Polynuclear d 10 -d 10 Metal Complex with Unusual Near-Infrared Luminescence and High Thermal Stability[END_REF][START_REF] Wei | Octahedral hexanuclear silver(I) and copper(I) ferrocenylacetylide complexes[END_REF] Although 2-electron [Ag6] 4+ cores have also been reported, they constitute kernels embedded in larger metal cages. [START_REF] Yang | Crystal structure of a luminescent thiolated Ag nanocluster with an octahedral Ag6 4+ core[END_REF][START_REF] Kikukawa | A discrete octahedrally shaped [Ag6] 4+ cluster encapsulated within silicotungstate ligands[END_REF][START_REF] Wang | Atomically Precise Site-Specific Tailoring and Directional Assembly of Superatomic Silver Nanoclusters[END_REF][START_REF] Wang | Trapping an octahedral Ag6 kernel in a seven-fold symmetric Ag56 nanowheel[END_REF][START_REF] Deng | Alkynyl-Protected Ag12Cu4 Cluster with Aggregation-Induced Emission Enhancement[END_REF] To our knowledge, there is only one exception of a 2-electron octahedral hexanuclear silver species that was recently reported by Liu et al., which is protected by trithiane and alkynyl ligands. [START_REF] Cheng | Compact accumulation of superatomic silver nanoclusters with an octahedral Ag6 core ligated by trithiane[END_REF] In any case, reports on small superatomic silver clusters remain scarce. [START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reaction of a Silver(I) Hydride[END_REF] The synthesis, characterization, and structural analysis of a new heteroleptic 2-electron Ag6 NC is discussed below.

RESULTS AND DISCUSSION

The reaction was carried out by adding 13 equiv. of dppm (dppm = 1, 1bis(diphenylphosphino)methane) to [Ag20{S2P(O i Pr)2}12] (abbrev. as Ag20) in THF, and the reaction was kept stirring in the dark at 40 ℃ overnight. The reaction was terminated when the solution color changed from dark reddish brown to yellowish brown. The resulting product was further purified with methanol to yield [Ag6{S2P(O i Pr)2}4(dppm)2] (1) as a yellow precipitate. It is of note that a large excess of dppm is necessary for obtaining 1 in good yield, indicating that the extra dppm ligands act to cut the Ag20 NC into fragments. Thus, the destabilization under mild conditions of [Ag20{S2P(O i Pr)2}12] in the presence of dppm ligands leads to cluster pruning from a capped icosahedral structure to an octahedron. Interestingly, the superatomic electron count is also modified from 8 (1S 2 1P 6 configuration) in Ag20 to 2 (1S 2 configuration) in 1, maintaining a closed-shell configuration from [Ag13] 5+ to [Ag6] 4+ (vide infra.). The dppm ligand not only plays the role of a chemical scissor but also eventually participates in the protective layer. Generally, heteroleptic Ag NCs co-protected by diphosphines are prepared through a one-pot process or mixing all the precursors in a specific sequence. [START_REF] Huang | Spontaneous Resolution of Chiral Multi-Thiolate-Protected Ag30 Nanoclusters[END_REF][START_REF] Zou | Multi-ligand-directed synthesis of chiral silver nanocluster[END_REF][START_REF] Yuan | Alkynylprotected silver nanoclusters featuring an anticuboctahedral kernel[END_REF] Thus, the synthesis reported herein is a twostep process: (i) preparation of an 8-e Ag NC; (ii) adding dppm ligands under mild reaction conditions (Scheme 1), the driving force of the reaction originating from the dppm excess. Scheme 1. Schematic representation of a two-step process in the synthesis of 1.

Compound 1 crystallizes in the P1 ̅ space group, with two half-molecules in the asymmetric unit. Thus, the crystal structure contains two symmetry-independent molecules (I and II), each one being of Ci symmetry (Figure 1). Both comprises an Ag6 octahedron, two dppm ligands bridging opposite edges, and four dtp ligands bridging four among the eight triangular faces of the Ag6 octahedron. The two molecules differ slightly in the connectivity of their dtp ligands. In each molecule, the four dithiophosphates can be separated into two LA and two LB ligands with respect to their coordination patterns. In molecule I (Figure 1a), LA exhibit a trimetallic tetraconnectivity ( 3 : 2, 2) and LB a trimetallic triconnectivity ( 3 : 1, 2). In molecule II (Figure 1b), LA is shifted to one side, leading to the non-bonding S5…Ag4 separation (3.728(2) Å), which can be compared with the corresponding S2-Ag3 bonding distance (2.841(2) Å) in molecule I. Thus, the coordination mode of LA shifts from trimetallic tetraconnectivity in I to bimetallic triconnectivity ( 3 : 1, 2) in II. There are indications that in I the position of S1 of LA is in close non-bonding contact (2.935 Å) with one adjacent proton on the phenyl group (Figure 1c). By comparison, in II, the S6 counterpart has more intramolecular contacts with three adjacent protons in the 2.957-2.979 Å range (Figure 1d), which could be one of the reasons to account for the LA shift in II. In addition, both molecules I and II show similar intermolecular S…H interactions (2.925 Å in I and 2.806 Å in II) along the crystallographic b axis (Figure S1). However, such weak interactions are easily destroyed in solution, due to the NMR-evidenced easy molecular mobility (vide infra). It is worth noting that the Ag…Ag distances (avg. 2.8490(9) Å and avg. 2.8239 (10) Å in I and II, respectively) are comparable to that in the related octahedral 2-electron NC [Ag6(3S)4(OTf)4] (3S = 1,3,5-trithiane, OTf = trifluoromethanesulfonate), [START_REF] Cheng | Compact accumulation of superatomic silver nanoclusters with an octahedral Ag6 core ligated by trithiane[END_REF] (avg. 2.8006 Å). On the other hand, they are significantly shorter than that in the 0-electron silver(I) octahedral clusters such as Ag6(bmt)6 (avg.

3.1939 Å, bmt = 2-benzimidazolethiolate), [START_REF] Yue | A Polynuclear d 10 -d 10 Metal Complex with Unusual Near-Infrared Luminescence and High Thermal Stability[END_REF] [Ag6(dppm)2(C≡CFc)4(CH3OH)2] 2+ (avg. 3.028 Å), [START_REF] Wei | Octahedral hexanuclear silver(I) and copper(I) ferrocenylacetylide complexes[END_REF] and [Ag6(3S)4(C≡C t Bu)4] 2+ (avg. 2.9000 Å). [START_REF] Wei | Octahedral hexanuclear silver(I) and copper(I) ferrocenylacetylide complexes[END_REF] . Selected bond lengths and angles are summarized in Table 1. of dppm and 107 Ag/ 109 Ag nuclei (Figure 2b). This resonance becomes a broad peak at 233K and splits into a doublet at 213 K. However, scalar couplings of 1 J( 31 P-107 Ag) and 1 J( 31 P-109 Ag) remain un-resolved upon decreasing the temperature to 183K. It can be attributed to the fluxional nature of 1. As a result, a broad doublet (FWHM = 115 Hz) is observed at 183K instead of a pseudo doublet of doublets for a heteronuclear AX spin system. The splitting pattern is correlated to each dppm phosphorus atom connecting to one silver (Figure 2d). The low-temperature spectra are wellmatching with the solid-state structure. Interestingly, a septet pattern observed at 0.61 ppm with an average coupling constant ( 1 J( 31 P-107,109 Ag) of 72 Hz (Figure 2c) suggests that each phosphorus nucleus is coupled with six magnetically equivalent silver nuclei. The phenomenon can be attributed to a fast molecular motion at room temperature. The molecular mobility can also be observed in the VT 1 H spectrum (Figure S6). The chemical shift of the dtp methine protons is at 4.48 ppm at room temperature and splits at 183K into two sets at 3.66 and 4.85 ppm with equal intensity, corresponding to the two LA and LB coordination environments. Both temperature-dependent NMR spectra confirm its fluxional behavior, which is directly visible, especially through the close proximity between P(dppm) and Ag. In contrast, a two-bond coupling between P(dtp) and Ag is not observed in the 31 P{ 1 H} spectrum and therefore no additional information can be gained. [START_REF] Liao | A Twelve-Coordinated Iodide in a Cuboctahedral Silver(I) Skeleton[END_REF] We previously demonstrated that cluster mobility can be observed via one-bond proton-silver J-couplings in hydrido silver clusters. [START_REF] Liao | Ag7(H){S2CC(CN)2}6] 6-: An Anionic Heptanuclear Silver Hydride Cluster Compound Stabilized by Dithiolate Ligands[END_REF][START_REF] Liao | A Copper(I) Homocubane Collapses to a Tetracapped Tetrahedron Upon Hydride Insertion[END_REF][START_REF] Liao | Anion templating from a silver(i) dithiophosphate 1D polymer forming discrete cationic and neutral octa-and decanuclear silver(i) clusters[END_REF][START_REF] Liu | Stable Silver(I) Hydride Complexes Supported by Diselenophosphate Ligands[END_REF][START_REF] Liu | Anion-templated syntheses of octanuclear silver clusters from a silver dithiophosphate chain[END_REF] For example, [Ag7(H)(S2CC(CN)2)6] 6- showed an octet of octets resonance in the [START_REF] Du | Atomically Precise Metal Nanoclusters for Catalysis[END_REF] H NMR spectrum at room temperature, which was assigned to the central hydride coupled to the seven magnetically equivalent silver nuclei. [START_REF] Liao | Ag7(H){S2CC(CN)2}6] 6-: An Anionic Heptanuclear Silver Hydride Cluster Compound Stabilized by Dithiolate Ligands[END_REF] These spectroscopic evidences can be tentatively explained by rapid Ag intracluster exchange on the octahedron in solution, for example through a mechanism of triangular rotations. [START_REF] Zheng | Real Time Monitoring of the Dynamic Intracluster Diffusion of Single Gold Atoms into Silver Nanoclusters[END_REF] Another possibility is rapid ligand exchange. We note that in 1, the average Ag-P bond dissociation energy is computed to be 0.86 eV (see DFT calculations below), a value significantly lower than its Ag-S counterpart (1.25 eV). On the other hand, a dtp ligand coordinated to an Ag3 triangle can move nearly freely on it by exchanging various  3 and/or  4 coordination modes (see below). We therefore suggest a ligand exchange process initiated by (partial) dppm decoordination coupled with soft dtp coordination changes. This scenario is also supported by the fact that we could not identify by exploratory DFT calculations any transition state associated with exchange of Ag positions on the octahedron. reported. [START_REF] Liu | The influence of alkane spacer of bis(diphenylphosphino)alkanes on the nuclearity of silver(I): Syntheses and structures of P, P'-bridged clusters and coordination polymers involving dithiophosphates[END_REF][START_REF] Liu | Syntheses and structures of silver(I) clusters uniquely exhibiting three distinct binding modes, two of which are novel, for a dithiophosphate ligand[END_REF] The fragmentation occurring in the gas phase can be related to the cluster instability in solution. When compound 1 is dissolved in solutions such as chloroform, dichloromethane, or THF, the color gradually changes from yellow to dark purple. It indicates that a further reaction occurs, which can be monitored by time-dependent 31 P{ 1 H} NMR spectroscopy (Figure S7). The The UV-vis absorption spectrum (Figure 4a) of 1 in CH2Cl2 shows two prominent bands at 378 nm ( = 15,700 M -1 cm -1 ) and 270 nm ( = 66,300 M -1 cm -1 ). Cluster 1 in solid state emits bright yellow light at ambient temperature with a maximum emission wavelength of 598 nm (Figure 4b) and is slightly red-shifted to 629 nm at 77K. The excitation maximum of 1 around 366 nm (r.t.) matches with its absorption band at 378 nm. A second excitation maximum at 401 nm appears at 77K. Time-resolved photoluminescence (PL) spectra of 1 at 298K (Figure S10) and 77K (Figure S11) exhibit single-exponential decay with lifetimes at nanosecond scale (2.04 ns at 298K; 7.07 ns at 77K), indicating the fluorescence nature of the emission. The PL quantum yield at 298K is approximately 16.3% (Figure S11), associated with slightly faster non-radiative decay (knr = 4.10 × 10 8 s -1 ) than radiative decay (kr = 7.99 × 10 7 s -1 , see Table 2).

It is of note that other two-electron species, [Ag6(3S)4(tfa)4] (tfa = trifluoroacetate), [START_REF] Cheng | Compact accumulation of superatomic silver nanoclusters with an octahedral Ag6 core ligated by trithiane[END_REF] [Ag8(pfga)6] species, exhibits also a yellow emission at 535 nm. [START_REF] Cheng | Compact accumulation of superatomic silver nanoclusters with an octahedral Ag6 core ligated by trithiane[END_REF] Unlike the red-shift solid state emission spectra observed in 1 upon lowering the temperature, [Ag10{S2P(O i Pr)2}8] shows a blue shift from 762 nm (r.t.) to 693 nm (77K, Figure S9). [START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reaction of a Silver(I) Hydride[END_REF] Presumably the thermochromism, which is commonly observed on the emission wavelength difference in the ultrasmall NCs, [START_REF] Zhou | Optical Properties and Excited-State Dynamics of Atomically Precise Gold Nanoclusters[END_REF] is very sensitive to their size, nuclearity and shape. The PL properties of 1 in solution are not reported due to its instability in common organic solvents. This is consistent with its ligand fluxional behavior in solution, as demonstrated by time-dependent 31 P{ 1 H} NMR spectroscopy (vide supra). In order to shed some light on the electronic structure of 1, density functional theory (DFT) calculations at the PBE0/Def2-TZVP level were performed on this compound (see Computational Details). We first addressed the question of molecular configuration by running geometry optimizations with the starting geometries of molecules I and II taken from the crystal X-ray structure of 1 (vide supra). Both optimizations converged to structures of type I; i.e., LA adopting trimetallic tetraconnectivity ( 3 : 2, 2). These two optimized structures, both characterized as true energy minima by vibrational frequency calculations, are almost isoenergetic (E = 0.05 eV; G = 0.04 eV) and exhibit quite similar metrics. Their non-perfect structural identities reflect the (relative) flatness of the potential energy hypersurface around its minimum and is consistent with the molecular ligand fluxionality evidenced by the RT NMR behavior of 1. It is of note that the simplified model [Ag6{S2PH2}4(dppm)2] provided similar results, with even less differences between the two optimized structures, as expected from the dtp simplification. Therefore, in the following, we discuss only the results obtained through the optimization of the molecular structure

State

Absorbance λabs (nm), ε (M -1 cm -

a kr: radiative decay. b knr: nonradiative decay. 1. There is a good match with the X-ray structure of molecule I, with an overestimation by around 2 % of the Ag-Ag contacts, as expected at the level of theory. Its Kohn-Sham orbital diagram (Figure 5) exhibits a substantial HOMO-LUMO gap of 3.85 eV. The HOMO, which lies 0.56 eV above the HOMO-1, can be considered as the 1S superatomic orbital. The LUMO+1, LUMO+2 and LUMO+15 can be identified as the 1P superatomic orbitals, but with significant ligand admixture. Their splitting in energy is in a large part related to the cluster anisotropy induced by its heteroleptic nature. The averaged metal natural atomic orbital (NAO) charges of the Ag atoms is 0.46, a value consistent with the superatomic 2electron count. [START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reaction of a Silver(I) Hydride[END_REF] The Ag-Ag Wiberg bond indices (avged. 0.1080) are consistent with the existence of some covalent bonding associated with the 1S bonding electron pair. Temperature-dependent 31 P{ 1 H} and 1 H NMR spectra of 1 confirm the fast atomic movement at ambient temperature and its slowing down at 183K, the latter spectrum matching well with the solid-state structure. Compound 1 is highly luminescent, the emission being likely of 1P→1S X-ray Crystallography. Single crystals suitable for X-ray diffraction analysis of 1 were obtained by slow diffusion of n-hexane into dichloromethane solution of the compound at 4℃ within a week. Single crystals were mounted on the tip of a glass fiber with epoxy resin. Data were collected on a Bruker APEX II CCD diffractometer using graphite monochromated Mo Kα radiation (λ = 0.71073 Å) at 296K. Absorption corrections for area detector were performed with SADABS [START_REF] Sadabs | version[END_REF] and the integration of raw data frame was performed with SAINT. [START_REF] Saint | V8.30A, Software for the CCD Detector System[END_REF] The structures were solved by direct methods and refined by least-squares against F 2 using the SHELXL-2018/3 package, [START_REF] Sheldrick | A short history of SHELX[END_REF] incorporated in SHELXTL/PC V6.14. [START_REF]Version 6.14[END_REF] All non-hydrogen atoms were refined anisotropically.

I. Its major metric data are given in Table

CCDC no. 2202272 contains the supplementary crystallographic data for compound 1 in this article. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www. ccdc.cam.ac.uk/data_request/cif.

Computational details. DFT calculations were carried out with the use of the Gaussian 16

program. [START_REF] Gaussian ; Frisch | [END_REF] The valence triple-zeta polarization functions (def2-TZVP) [START_REF] Schaefer | Fully optimized contracted Gaussian basis sets for atoms Li to Kr[END_REF][START_REF] Schaefer | Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr[END_REF] basis set was used, together with the Perdew-Burke-Ernzerhof (PBE0) [START_REF] Perdew | Rationale for Mixing Exact Exchange with Density Functional Approximations[END_REF][START_REF] Adamo | Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model[END_REF] correlation functional. All the optimized structures were confirmed as true minima on their potential energy surface by analytical vibration frequency calculations. The compositions of the molecular orbitals were calculated using the AOMix program. [START_REF] Gorelsky | AOMix program[END_REF] Natural atomic orbital (NAO) populations and Wiberg bond indices were computed with the natural bond orbital NBO 6.0 program [START_REF] Reed | Natural Bond Orbital Analysis of Near-Hartree-Fock Water Dimer[END_REF][START_REF] Carpenter | Analysis of the Geometry of the Hydroxymethyl Radical by the Different Hybrids for Different Spins Natural Bond Orbital Procedure[END_REF][START_REF] Reed | Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint[END_REF] implemented in the Gaussian 16

package. The UV-visible transitions were calculated by means of TD-DFT calculations at the same level of theory. The UV-visible spectrum weas simulated from the computed TD-DFT transitions and their oscillator strengths by using the SWizard program, [START_REF] Gorelsky | SWizard program[END_REF] each transition being associated with a Gaussian function of half-height width equal to 3000 cm -1 .

Figure 1 .

 1 Figure 1. (a) The ORTEP drawing (30% probability) of molecule I and (b) molecule II in [Ag6{S2P(O i Pr)2}4(dppm)2], isopropoxy and phenyl groups were omitted for clarity. (c) The

Figure 2 .

 2 Figure 2. (a) VT 31 P{ 1 H} NMR spectrum of 1 in CD2Cl2. (b) P-Ag coupling in the 31 P{ 1 H} NMR

resonances of 1

 1 at 103.2 and 0.65 ppm decrease in intensity over time, indicating a gradual decomposition of compound 1. A two-electron species, [Ag10{S2P(O i Pr)2}8],[START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reaction of a Silver(I) Hydride[END_REF] which depicts distinct[START_REF] Liao | A Copper(I) Homocubane Collapses to a Tetracapped Tetrahedron Upon Hydride Insertion[END_REF] P resonances at 104.3 and 105.8 ppm, is formed upon dissolution within 30 minutes. The formation of unidentified species is observed after 60 minutes at 105.1, 105.7 (broad), and -3.3 ppm (doublet, JPAg = 446 Hz), respectively, accompanied by dppmO2 at 24.7 ppm. The resonance of dppm changes from 0.65 (in 1) to -3.3 ppm, as well as the splitting pattern from a septet to a doublet. The latter suggests that dppm could be in a bridging mode with each P atom connecting to one Ag atom. The mixture can be separated on a TLC plate using a mixed solvent of Et2O and hexane (v/v =1:9, FigureS8). The purple band was collected then re-crystallized to obtain crystals of the previously published [Ag10{S2P(O i Pr)2}8]. Unfortunately, single crystals of another species displaying orange emission under UV light could not be obtained. This result shows that 1 is an intermediate nanocluster proceeding another superatom-to-superatom transformation. In contrast, 1 is much stable in the solid state than in solution.

Figure 3 .

 3 Figure 3. The positive-mode ESI-MS of 1.

Figure 4 .

 4 Figure 4. (a) Experimental (red) and simulated (blue) absorption spectra (CH2Cl2, r.t.) of 1. The

Figure 5 .

 5 Figure 5. Kohn-Sham orbital diagram of 1. The MO localizations (in %) are given in the following

Table 1 .

 1 Selected bond distances (Å) and angles (deg.) of 1.

		X-ray	DFT
		Molecule I	Molecule II
	Ag…Ag	2.7530(9) -3.0478(9), avg. 2.8490(9)	2.7665(10) -2.8783(9), avg. 2.8239(10)	2.810-3.000 avg. 2.880
	S-Ag	2.519(2) -2.968(2), avg. 2.739(2)	2.581(2) -2.945(2), avg. 2.706(2)	2.547-2.907 avg 2.747
	P-Ag	2.4679(19) -2.5077(19), avg. 2.4878(19)	2.474(2) -2.499(2), avg. 2.487(2)	2.486-2.517 avg. 2.501
	P…P bite	3.112(3)	3.094(3)	3.109

Table 2 .

 2 The photophysical data of 1.

  nature, with a QY of 16.3% in the solid state which prevents fluxionality and minimizes nonradiative vibrational decay. Furthermore, another two-electron species, [Ag10{S2P(O i Pr)2}8], can be formed upon dissolving 1 in solution. Therefore, 1 is an intermediate nanocluster of moderate stability in a cluster growth process, in agreement with the differences in the computed ligand-to-The product was washed by MeOH, and the precipitate was collected and dried to yield a yellow powder as [Ag6{S2P(O i Pr)2}4(dppm)2]. Yield: 0.0481 g (22.3%, based on Ag).[START_REF] Liao | A Copper(I) Homocubane Collapses to a Tetracapped Tetrahedron Upon Hydride Insertion[END_REF] P{ 1 H} NMR (161.98 MHz, CD2Cl2, , ppm, 293K): 103.2 (S2P), 0.65 (sept, 1 JPAg = 72 Hz,

	dppm). 31 P{ 1 H} NMR (161.98 MHz, CD2Cl2, , ppm, 183K): 102.1 (s, S2P), 105.0 (s, S2P), 0.36
	(d, 1 JPAg = 325 Hz, dppm). 1 H NMR (300.13 MHz, CDCl3, , ppm, 293K): 0.98 (d, 3 JHH = 7 Hz,
	cluster bonding averaged energies (dithiophosphate: 4.36 eV; diphosphine: 1.72 eV). This work 48H, CH3), 2.99 (br, 4H, CH2), 4.48 (m, 8H, OCH), 7.24 (m, 25H, meta-and para-protons on
	provides new insight into the ligand-induced structural transformation between nanoclusters. phenyl rings), 7.73 (br, 15H, ortho-protons on phenyl rings). UV-Vis [ in nm ( in M -1 cm -1 )]:
	EXPERIMENTAL SECTION 270 (66,300), 378 (15,700).
	All chemicals used as received were purchased from commercial sources. Solvents were purified
	following standard protocols. Synthesis of [Ag6{S2P(O i Pr)2}4(dppm)2] (1). [Ag20{S2P(O i Pr)2}12] was prepared by a previously
	reported	method. 12	[Ag20{S2P(O i Pr)2}12]	(0.1343	g,	0.028	mmol)	and
	Bis(diphenylphosphino)methane (0.1423 g, 0.370 mmol) were dissolved in THF (30 mL), kept
	stirring at 40 ℃ in dark for 24h. The yellowish brown solution was dried under vacuum. The

[START_REF] Perrin | Purification of laboratory chemicals, 3rd Edition[END_REF]

All reactions were performed in oven-dried Schlenk glassware using standard inert atmosphere techniques. All reactions were carried out under N2 atmosphere by using standard Schlenk techniques. The 1 H and 31 P{ 1 H} NMR spectra were recorded on a Bruker Avance II 400 MHz NMR spectrometer, operating at 400.13 MHz for 1 H, and 161.98 MHz for

[START_REF] Liao | A Copper(I) Homocubane Collapses to a Tetracapped Tetrahedron Upon Hydride Insertion[END_REF]

P. The chemical shifts (δ) and coupling constants (J) are reported in ppm and Hz, respectively. X-ray diffraction data were collected on a Bruker APEX II CCD diffractometer. UV-visible absorption spectra were measured on a Perkin Elmer Lambda 750 spectrophotometer using quartz cells with path length of 1 cm. The emission, lifetime, and quantum yield spectra were recorded on an Edinburgh FLS920 fluorescence spectrometer. product was washed with DI-H2O (10 mL x 3) and then extracted by CH2Cl2 (30 mL). The solution was filtered and dried.

ASSOCIATED CONTENT

Supporting Information.

The Supporting Information is available of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.xxxxxxx.

Multinuclear NMR spectra, photophysical data, and computational results (PDF)

AUTHOR INFORMATION