Christina Lioma
email: c.lioma@di.ku.dk

Fabien Tarissan

Jakob Grue Simonsen
email: simonsen@di.ku.dk

Casper Petersen

Birger Larsen
email: birger@hum.aau.dk

Exploiting the Bipartite Structure of Entity Grids for Document Coherence and Retrieval

Keywords:

.

The state of the art in unsupervised coherence modelling represents documents as bipartite graphs of sentences and discourse entities, and then projects these bipartite graphs into one-mode undirected graphs. However, one-mode projections may incur significant loss of the information present in the original bipartite structure. To address this we present three novel graph metrics that compute document coherence on the original bipartite graph of sentences and entities. Evaluation on standard settings shows that: (i) one of our coherence metrics beats the state of the art in terms of coherence accuracy; and (ii) all three of our coherence metrics improve retrieval effectiveness because, as closer analysis reveals, they capture aspects of document quality that go undetected by both keyword-based standard ranking and by spam filtering. This work contributes document coherence metrics that are theoretically principled, parameter-free, and useful to IR.

INTRODUCTION

Document coherence is the logical organisation and development of thematic content in a document. The more coherent a document is, the more understandable it tends to be. Automatically measuring document coherence is useful for several tasks, such as text summarisation [START_REF] Hakkani-Tür | Discovery of topically coherent sentences for extractive summarization[END_REF][START_REF] Parveen | Integrating importance, non-redundancy and coherence in graph-based extractive summarization[END_REF][START_REF] Zhang | Sentence ordering driven by local and global coherence for summary generation[END_REF], ma-Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. chine translation [START_REF] Lin | Combining coherence models and machine translation evaluation metrics for summarization evaluation[END_REF][START_REF] Xiong | Lexical chain based cohesion models for document-level statistical machine translation[END_REF][START_REF] Xiong | Topic-based coherence modeling for statistical machine translation[END_REF], and information retrieval (IR) [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF][START_REF] Tan | To each his own: personalized content selection based on text comprehensibility[END_REF]. For IR in particular, document coherence is typically treated as a feature of document quality (similarly to e.g. readability [START_REF] Bendersky | Quality-biased ranking of web documents[END_REF], information-to-noise ratio [START_REF] Zhou | Document quality models for web adhoc retrieval[END_REF], or comprehensibility [START_REF] Tan | To each his own: personalized content selection based on text comprehensibility[END_REF]). Such document quality features have been found to improve retrieval performance when used to boost the ranking of documents which are more relevant and of better quality. We present three new ways of measuring document coherence, and we practically show their usefulness to IR.

The starting point of our work is the linguistic definition [START_REF] De Beaugrande | Introduction to Text Linguistics[END_REF] of document coherence as the thematic unity that stems from the links among the underlying ideas of a document and from the logical organisation and development of its content. It is this logical continuity of senses that characterises coherent documents and makes them overall understandable. This continuity of senses is traditionally modelled as the transition of topics throughout sentences. Typically this topic transition is approximated by extracting salient discourse entities from a document (for instance, the subject and object of each sentence) and measuring their occurrence (and distance) through sentences in an entity grid [START_REF] Barzilay | Modeling local coherence: An entity-based approach[END_REF] (see example in Table 1). Recently the elements of such an entity grid (i.e., the discourse entities and the sentences in which they occur) have been represented as a graph, the topology of which has been used to approximate document coherence, for instance as the average out-degree [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF], pagerank, clustering coefficient, or betweenness [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF] computed over the whole graph (each graph representing a single document). This type of graph-based coherence modelling, despite being completely unsupervised, performs comparably to equivalent supervised approaches, thus showing great promise. We posit that these existing graph-based computations of document coherence are suboptimal in capturing the transition of entities across sentences, and we present a principled solution for improving this. We explain this next.

Existing graph-based computations of text coherence [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF][START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF] represent each document as a bipartite graph of sentences and their discourse entities. A bipartite graph is a particular class of graph also known as two-mode graph. In the case of coherence, one type of vertices denotes discourse entities, and the other type denotes the sentences in which these entities appear. The edges in a bipartite graph in typical coherence modelling connect only vertices of unlike types, i.e. only entities and sentences. Current graph-based coherence approaches project this bipartite graph of entities and their sentences onto a one-mode graph of only sentences that are connected if they contain at least one common entity. This projection is motivated by convenience: it is easier to work with direct connections between vertices of just one type. All current graph-based metrics of document coherence are computed solely on such one-mode projections of bipartite graphs.

Even though one-mode projections of two-mode graphs are widely employed, they are a less powerful representation of the data because they discard part of the information present in the structure of the original bipartite graph. This point is graphically illustrated in Figure 1, which shows a bipartite graph (middle) and its two one-mode projections (top and bottom). For entity bipartite graphs, the analogy would be that the sentences of a document are denoted by A-D and its entities are denoted by 1-7. As Figure 1 shows, part of the information captured by the bipartite graph about the entity transition throughout the document is lost or compressed with one-mode projections. We reason that this information loss is propagated to any coherence metric that is then computed on an one-mode projection of such a graph, resulting in potentially suboptimal approximations of document coherence.

We present three coherence metrics that are applied directly on the original bipartite graph, not on its one-mode projection (Section 3). Our metrics are new, constituting a contribution not only to coherence modelling but also to graph metrics. In addition, our bipartite metrics incur no additional efficiency cost over existing one-mode graph metrics. One of our metrics is shown to be a much more accurate approximation of document coherence than the state of the art computed from one-mode projections [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF][START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF] (Section 4). All three coherence metrics are shown to be useful to retrieval effectiveness (Section 5). To our knowledge, such two-mode graph-based coherence metrics have not been investigated before.

RELATED WORK

Several metrics using the entity grid (or extensions thereof) have been proposed for approximating the coherence of a document (see [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF][START_REF] Xiong | Topic-based coherence modeling for statistical machine translation[END_REF][START_REF] Zhang | Encoding world knowledge in the evaluation of local coherence[END_REF] for recent overviews). Broadly these methods compute probabilities of entity transitions on the grid, and use these probabilities to learn coherence in a supervised way. The particular line of research extending the entity grid that is relevant to our work transforms the entity grid into a bipartite graph of sentences and entities [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF]. Coherence is then approximated in an unsupervised way as the average out-degree [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF], pagerank, clustering coefficient, betweeness centrality, entity distance, or adjacent and non-adjacent topic flow [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF] on one-mode projections on the sentence vertices of that graph (equivalent to the top projection in Figure 1). This process of reducing a two-mode "entity-and-sentence" graph into an one-mode "sentence-only" graph loses all information about how many and which entities two sentences share, as well as the exact entities occurring in a given sentence. Part of this information can be captured in one-mode projections by making the projection weighted. This has been done [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF], by weighting each edge in the projection by the number of entities its two connecting vertices share. This type of weighted projection retains information about how many entities two sentences share, but still fails to capture the identity and the transition of those entities across sentences, thus removing the option of drawing entity-oriented insights from the graph. Another interesting weighted one-mode projection of such bipartite graphs has also been presented [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF], which weights edges according to the grammatical roles of the entity vertices they share. This has been done by assigning arbitrary scores of 3, 2, 1 for the grammatical roles of subject, object or other, respectively, and then summing these scores over all shared entity vertices between two sentence vertices. This projection, despite being weighted, does not compensate for any information loss incurred by compressing a bipartite graph into an one-mode projection, but rather it attempts to enrich the graph with grammatical information. To our knowledge, our work is the first to propose coherence metrics computed directly on the bipartite graph and not on its one mode projections.

The document coherence metrics we present can be seen as estimating an aspect of document quality. A wide variety of document quality aspects have been used in IR, ranging from heuristics on document format (e.g., the fraction of anchor text on a hyperlinked document [START_REF] Ntoulas | Detecting spam web pages through content analysis[END_REF]), to hyperlinked-derived estimations of popularity (e.g., PageRank, HITS [START_REF] Ntoulas | Detecting spam web pages through content analysis[END_REF]). Another common type of document quality approximations are content-based. These are numerous and diverse, including for instance, ratios of information-to-noise, of stopwords per document, or of document words per stopword list [START_REF] Bendersky | Quality-biased ranking of web documents[END_REF][START_REF] Zhou | Document quality models for web adhoc retrieval[END_REF][START_REF] Zhu | Incorporating quality metrics in centralized/distributed information retrieval on the world wide web[END_REF]; average term length per document [START_REF] Kanungo | Predicting the readability of short web summaries[END_REF]; term part-ofspeech [START_REF] Lioma | Extending weighting models with a term quality measure[END_REF][START_REF] Lioma | Part of speech n-grams and information retrieval[END_REF]; ratio of technical terminology per (scientific) document [START_REF] Larsen | Preliminary study of technical terminology for the retrieval of scientific book metadata records[END_REF]; ratio of non-compositional phrases per document [START_REF] Michelbacher | A cascaded classification approach to semantic head recognition[END_REF]; syllable, term and/or sentence statistics [START_REF] Tan | To each his own: personalized content selection based on text comprehensibility[END_REF] as per standard readability indices [START_REF] Coleman | A computer readability formula designed for machine scoring[END_REF][START_REF] Gunning | The technique of clear writing[END_REF][START_REF] Kincaid | Derivation of new readability formulas for navy enlisted personnel[END_REF][START_REF] Mcclure | Readability formulas: Useful or useless[END_REF][START_REF] Mclaughlin | Smog grading -a new readability formula[END_REF]; discourse structure [START_REF] Lioma | Rhetorical relations for information retrieval[END_REF]; document entropy computed from terms [START_REF] Bendersky | Quality-biased ranking of web documents[END_REF] or discourse entities [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF]. The lexical or syntactic features used in the above content-based document quality approximations are assumed to indicate syntactic or semantic difficulty. They are thus used to compute scores of document quality aspects such as readability, cohesiveness, comprehensibility or coherence, which are generally found to improve retrieval effectiveness when integrated into ranking, in particular with respect to precision at ranks 1-20 [START_REF] Bendersky | Quality-biased ranking of web documents[END_REF][START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF][START_REF] Tan | To each his own: personalized content selection based on text comprehensibility[END_REF].

In addition to using document coherence for improving IR, the reverse has also been reported, namely using IR to improve coherence modelling [START_REF] Zhang | Encoding world knowledge in the evaluation of local coherence[END_REF]. The idea here is to link entities that have different lexical form but are semantically related (e.g. Gates and Microsoft), by retrieving mentions of those entities from multiple web sources and mining their relations. This approach gives good performance. Interestingly, when mining such relations between entities from web data, the task of characterising the type of these relations has also been addressed using graph representations and has been modelled as an IR, and specifically learning to rank, problem [START_REF] Voskarides | Learning to explain entity relationships in knowledge graphs[END_REF].

To our knowledge, the current state of the art in coherence modelling in terms of accuracy is the deep learning approach of [START_REF] Li | A model of coherence based on distributed sentence representation[END_REF], where a recursive neural network learns sentential compositionality and is then used to model document coherence. This approach is supervised and computationally much heavier than graph-based coherence modelling.

BIPARTITE GRAPH METRICS OF DOCUMENT COHERENCE WITHOUT PROJECTION

Our work builds on the early assumption [START_REF] Grosz | Centering: A framework for modeling the local coherence of discourse[END_REF] that a document is more coherent if its adjacent or near-adjacent sentences refer to the same entities. This transition of entities across sentences is typically represented as an entity grid [START_REF] Barzilay | Modeling local coherence: An entity-based approach[END_REF]. The entity grid of a document is defined as a table whose rows represent (consecutive) sentences in that document, and whose columns represent discourse entities that occur in that document. Each cell (i, j) is either empty or contains infor- mation about the syntactic, discourse, or other grammatical role of entity j in sentence i. Table 1 displays an example of an entity grid borrowed from [START_REF] Barzilay | Modeling local coherence: An entity-based approach[END_REF].

S1 S2 S3 S4 S5 e3 e2 e1 e4 e5 e6 e7
Following [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF], we represent the entity grid as a bipartite graph B = (V , V ⊥ , E B ), where V is the set of sentences in the document, V ⊥ is the set of entities in the document, and E B ⊂ × ⊥ is the set of edges relating entities to the sentences in which the entities appear, each edge labelled with the value in cell (i, j). An example of such a bipartite graph B is given in Figure 2, where vertices (sentences) are depicted by squares (V = {S1, S2, S3, S4, S5}) and ⊥ vertices (entities) are depicted by circles (V ⊥ = {e1, e2, e3, e4, e5, e6, e7}). Every such bipartite graph can be one-mode projected, resulting for instance in a graph G = (V, E) where V = V and 1). This projection allows to re-use all metrics defined for one-mode graphs, but we claim that valuable information is discarded in the process.

E = {(u, v) ∈ V 2 | ∃w ∈ V ⊥ , (u, w) ∈ E B and (v, w) ∈ E B } 1 (see example in Figure
In this paper, we extract information about coherence from the bipartite structure itself, without projecting the structure over entities nor sentences. We reason that principles from existing research on using (projected) graphs for coherence can be retained, and that bespoke metrics for bipartite graphs can be combined with these principles. We identify two primary such principles:

Length of paths: short paths between vertices representing

entities generally imply rapid cognitive information processing [START_REF] Blanco | Graph-based term weighting for information retrieval[END_REF], hence are good indicators of coherence.

Local density: locally dense documents tend to involve successive sentences that share similar concepts and entities, hence are good indicators of coherence.

In the remainder of this section, we propose coherence metrics that align with the above principles and are thus able to capture such short path or local density properties in the bipartite structure. It is worth noting that even though the notion of local density is well known for one-mode graphs, there exist no standard definitions for it for bipartite graphs. Indeed, the local density (usually captured by the clustering coefficient and the transitive ratio) consists in computing the number of triangles (three vertices, all connected) present in the graphs but, by definition, no such pattern can exist in a bipartite graph.

However, several extensions of the clustering coefficient have been proposed [START_REF] Borgatti | Network analysis of 2-mode data[END_REF][START_REF] Latapy | Basic notions for the analysis of large two-mode networks[END_REF][START_REF] Opsahl | Triadic closure in two-mode networks: Redefining the global and local clustering coefficients[END_REF][START_REF] Snijders | The statistical evaluation of social network dynamics[END_REF][START_REF] Zhang | Clustering coefficient and community structure of bipartite networks[END_REF] to serve as proxy for this notion in bipartite graphs. These proxies have proven to be useful in many contexts, ranging from improving the modelling of the large-scale link structure of the Internet [START_REF] Tarissan | Towards a bipartite graph modeling of the internet topology[END_REF], to analysing online social networks [START_REF] Tackx | Revealing intricate properties of communities in the bipartite structure of online social networks[END_REF], or detecting landmark decisions in judicial decision networks [START_REF] Tarissan | Analysing the first case of the international criminal court from a network-science perspective[END_REF].

Next, we show how to adapt those definitions to account for the specific context of local coherence estimation. We do so, reasoning on a bipartite graph, where u ∈ V , and where we define N (u) = {v ∈ ⊥ | (u, v) ∈ E B } as the subset consisting of the vertices in V ⊥ that are linked to u.

Bipartite distance-based clustering coefficient (bipDCC)

We call our first coherence metric bipartite distance-based clustering coefficient (bipDCC). The clustering coefficient in standard graphs quantifies, roughly, how dense the graph is around its vertices. In our case, we are interested in estimating the extent to which successive sentences share similar or identical2 entities (suggesting coherence). To do so, we propose the following adaptation of the bipartite clustering coefficient [START_REF] Latapy | Basic notions for the analysis of large two-mode networks[END_REF]. Given two sentences si and sj that have at least one entity in common:

1. Compute the fraction of shared entities with respect to the number of total entities occurring in si and sj (classic notion of bipartite clustering coefficient based on the Jaccard index [START_REF] Latapy | Basic notions for the analysis of large two-mode networks[END_REF]), and 2. Account for the relative position of the involved sentences by dividing the former quantity by the distance between si and sj.

Formally, assuming that i and j denote the position of sentences si and sj in the document:

bipDCC (si, sj) = 1 |j -i| • |N (si) ∩ N (sj)| |N (si) ∪ N (sj)| (1)
For instance, in Figure 2, bipDCC (si, sj) would attain its highest values for vertices S2 and S3 (bipDCC(S2, S3) = 0.75).

Then, we define bipDCC (si) as the average value of bipDCC (si, sj) for all sj that share at least one entity with si. We compute the bipartite distance-based clustering coefficient, bipDCC (B), of the entire bipartite graph of the document as the average value of bipDCC (si) for all sentences si.

The intuition is that a coherent document will involve successive (or almost successive) sentences sharing similar or identical entities, thus increasing the value of the bipartite distance-based clustering coefficient.

Regarding the complexity of Equation 1, we note that by properly implementing the set operations (e.g., as bitwise operations on boolean strings) the worst-case complexity of computing the right-hand side of the formula is linear in the total number of bottom nodes.

Bipartite asymmetric clustering coefficient (bipACC)

The bipartite distance-based clustering coefficient proposed above gives a similar role to si and sj. In particular, it does not account for the number of entities related to each of the sentences. This raises some issues for small (in terms of number of entities) sentences. In Figure 2 for instance, the reader might notice that bipDCC (s5) = 0.4, although the only two entities involved in s5 are both shared with another sentence, which turns out to be the closest in the document. As such, the coefficient should be the highest value (1.0).

In order to account for this, we propose the following asymmetric variant of bipDCC. Given two sentences si and sj that share at least one common entity:

1. Compute the fraction of shared entities with respect to the number of entities that si could have shared with sj, and 2. Use this fraction to discount the distance between si and sj, as previously for the bipartite distance-based clustering coefficient.

Formally, we define the bipartite asymmetric clustering coefficient of si and sj as:

bipACC (si, sj) = 1 |j -i| • |N (si) ∩ N (sj)| |N (si)| (2)
Then, the bipartite asymmetric clustering coefficients of vertex si (bipACC (si)) and of the whole document (bipACC (B)) are respectively derived as averages, in the same way as for the distance-based clustering coefficient presented above. Note that while bipDCC (si, sj) = bipDCC (sj, si), we have in general bipACC (si, sj) = bipACC (sj, si) now.

By using this asymmetric variant of the bipartite distancebased clustering coefficient, we expect to highlight in particular short sentences that are well connected to each other. This might be particularly useful in domains where this type of writing is predominant (although we do not evaluate this potential domain adaptivity of this coherence metric in this work).

Bipartite Linkage Coefficient (bipLC)

The two coefficients proposed so far are straight-forward variants of the original bipartite clustering coefficient that attempt to capture local density in bipartite graphs. However, it has been shown in [START_REF] Latapy | Basic notions for the analysis of large two-mode networks[END_REF] that such coefficients might miss some important properties of the overlapping between vertices (in our case sentence vertices) in the bipartite structures. This is why [START_REF] Latapy | Basic notions for the analysis of large two-mode networks[END_REF] suggested to use the redundancy coefficient rd (v) of a vertex. The redundancy coefficient focuses on the impact of removing v in regards to the ⊥-projection.

To illustrate this impact on the example of Figure 2, consider sentences S1 and S5. Although they are both related to two entities, they have a very different way to relate to the rest of the sentences. One way to measure this consists in projecting the bipartite graph over the entities and comparing the resulting structure to the same projection if we remove S1 or S5. Removing vertex S1 results in the loss of one edge (between e1 and e2). In contrast, if we look at the impact of removing vertex S5, the projection is exactly the same with or without the vertex because the two entities it relates (e6 and e7) are also related by sentence S4. In this respect, S5 is said to be redundant. The above are two extreme cases; in practice a wide range of situations usually depict different levels of redundancy.

Following this principle of graph redundancy, and letting v ∈ V , we define Dv as the set

Dv = |{{u, w} ∈ N (v) 2 |∃v = v, (v , u) ∈ E B and (v , w) ∈ E B }| .
That is, Dv is the set of pairs of entities in sentence v such that there is (at least) another sentence containing both of them. The redundancy of a node s ∈ V is then formally defined as:

rd (v) = D |N (v)|(|N (v)|-1) 2 (3)
Intuitively, a high value of the rd (v) indicates that two entities that v relates are likely to be related by another sentence. In the example above, rd (v) assumes its highest values for sentences S3 and S5. This is expected because all entities in these sentences occur in (perhaps several) other sentences.

As we wish to model coherence, and there is a natural order on sentences, we define a new variation of the redundancy that also captures closeness, which we call bipartite linkage coefficient (bipLC) as follows. Given a sentence si:

1. For each pair of entities (e k , e l ) in si, compute the distance between si and the closest sentence that contains also e k and e l (∞ if there is no such other sentence), and 2. Compute the average of the inverse of the distances computed in step 1.

Formally, ∀si and ∀e k , e l ∈ N (si), let

d ikl = min{|j - i| | sj ∈ N ⊥ (e k ) ∩ N ⊥ (e l ) -{si}}.
We define:

ds i (e k , e l ) = ∞ if N ⊥ (e k ) ∩ N ⊥ (e l ) = {s} d ikl otherwise
Then, the bipartite linkage coefficient of a sentence si is:

bipLC (si) = e k ,e l ∈N (s i ) 1 ds i (e k ,e l ) |N (s i )|(|N (s i )|-1) 2 (4)
We then compute the linkage coefficient of the entire document bipLC (B) as the average value of bipLC (si) for all sentences si.

This coefficient is interesting because it explicitly relates the property of the bipartite structure to the one of the ⊥projection, i.e. to the projection of entities, which are central in modelling coherence.

COHERENCE EVALUATION

Before evaluating the effectiveness of our coherence metrics for IR, we perform a pre-study to assess how accurately our coherence metrics approximate actual coherence.

Experimental Setup

We use the standard dataset for coherence evaluation, Earthquakes and Accidents 3 , which contains 200 newswire articles (henceforth documents) concerning earthquakes and accidents from the North American News Corpus and the National Transportation Safety Board. These documents are short (240 terms on average); we expect them to be coherent because they have been produced by human professionals aiming to inform the public. We parse these documents with the Stanford parser and consider as entities those words tagged by the parser as the subject(s) or object(s) of a sentence. We do not treat as entities words of other grammatical roles (marked x in Table 1) because we wish to consider only the most salient 3 http://people.csail.mit.edu/regina/coherence/ entities (i.e. the closest approximation to topics) of a document, and not modifiers of those topics by e.g. prepositional or other peripheral phrases (such as with evidence, through collusion, into markets in Table 1). We use the extracted entities to build entity grids, represent them as bipartite graphs, and compute our three coherence metrics as described in Section 3. All three of our coherence metrics are unsupervised -they contain no parameters, hence no training is involved.

We compare our coherence metrics to four coherence modelling baselines:

1. Barzilay [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF]).

Note that baselines (1) and ( 2) are not graph-based, and that baselines (3) and ( 4) use undirected one-mode projections; on the contrary, our bipDCC, bipACC, and bipLC coherence metrics are defined (and computed) directly on the bipartite graph of a document's entity grid, rather than on its one-mode projection.

We use the standard practice of evaluating coherence, which consists of re-ordering progressively larger numbers of sentences in actual, coherent documents. This has the effect of simulating grades of incoherence; hence, good coherence metrics would have high coherence scores for the original documents, but progressively lower coherence scores as more and more sentences are re-ordered.

For each document, we pick n ∈ [1 .

. 20] pairs of sentences at random and switch them (e.g., for n = 20, a total of 40 sentences switch places). We then compute our coherence metrics on both the original and each of the re-ordered documents. If the coherence score of the original document is not lower than the coherence score of the re-ordered document, then we reason that the coherence metric accurately predicts the re-ordered document to be less coherent that the original. The total number of accurate predictions is then averaged over all documents.

Coherence Accuracy Findings

Table 2 shows the accuracy of each coherence metric averaged over all re-ordered documents. We see that our bipLC metric is the most accurate, both on the individual subsets of the data, and on their overall average. Our two other metrics (bipDCC, bipACC) are less accurate than bipLC but also than the two graph-based baselines computed on one-mode projections (out-degree and entity distance) and the original entity grid, on average. A possible explanation is that bipDCC and bipACC focus primarily on local clusters of entities, whereas the other metrics focus more on entity linkages across sentences (in different ways for each metric). This emphasis on entity linkage as opposed to entity clustering is possibly better suited to approximating coherence, as all currently best performing graph-based models of coherence [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF][START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF] -which we use as baselines ( 3) and ( 4) -prioritise the (graph-based) distance between entities in a document. In particular, the best performing bipLC metric emphasises the likelihood that two entities that are linked by a sentence will be linked by another sentence too. This property is related to the theory of lexical chains [START_REF] Halliday | Cohesion in English[END_REF], an early foundation in coherence modelling. To the best of our knowledge, of all existing coherence metrics, our bipLC metric models this idea of taking into account the trajectory of an entity across sentences the closest. Figure 3 shows the average accuracy of the n th re-ordered document relative to the original document for each of the coherence metrics, separately for the Accidents and Earthquakes subsets. A perfect coherence metric would be a straight line with an accuracy of 1 as the coherence score of the original document would always be larger than a re-ordered version. Instead, we see fluctuations that diverge more (for bipDCC and bipACC) or less (bipLC) from that ideal straight line. Consistently with Table 2, bipLC has the most accurate and most robust performance. Of interest are the extreme peaks and drops as n increases: whereas for Accidents accuracy plummets for bipDCC and bipACC , for Earthquakes accuracy shoots up for bipDCC and bipACC but drops for bipLC. Closer inspection reveals that these more or less dramatic fluctuations are likely due to data sparsity: many documents are shorter than 40 sentences; thus, for high n values, there are fewer documents where it is possible to do n permutations, and consequently only a few documents determine the accuracy, making the overall findings less generalisable.

RETRIEVAL EVALUATION

We now test the usefulness of our coherence metrics to retrieval.

Integration of Coherence to Ranking

Our assumption is that more coherent documents are likely to be more relevant. To test this we rerank the top 1000 4documents retrieved by a baseline model according to their coherence scores. In doing so, we treat document coherence as a type of query independent aspect of document quality that we combine with a query dependent baseline. The main idea is: (i) attach a static weight to each document based on its coherence; and (ii) combine this weight with the query dependent baseline score, to give a new score and ranking. For step (ii) we choose to use three types of linear combination which make it intuitively easy to interpret the impact of the coherence score on the final ranking. We present these next.

Let B be the baseline ranking score of a document. Let C be the coherence score of a document, computed according to each of our three coherence metrics presented in Section 3. Let R be the reranking score of a document, which should combine both B and C. We compute R as: R = B + C, where C is a transformation of the document coherence score. We transform this document coherence score, in three different and increasingly parameterised ways, known to smooth out the integration of document quality features in general into ranking. Specifically we use the log, satu and sigmoid transformations [START_REF] Craswell | Relevance weighting for query independent evidence[END_REF], shown below:

log(C, w) = w log C ( 5
)
where w is a smoothing parameter.

satu(C, w, k) = w C k + C ( 6
)
where w approaches the maximum as C increases, and k is a parameter controlling the value of C. The function satu can be reformulated as a sigmoid by introducing another parameter:

sigmoid(C, w, k, α) = w C α k α + C α ( 7
)
where α is an extra parameter allowing for more fine smoothing. See [START_REF] Craswell | Relevance weighting for query independent evidence[END_REF] for a discussion of the rationale and behaviour of the log, satu and sigmoid transformations.

Experimental Setup

We compare retrieval performance between 1. a baseline ranking model (query likelihood language model with Dirichlet-smoothing, denoted LM) that does not use coherence, and 2. nine reranked versions of that baseline ranking that use document coherence (the three coherence metrics bipDCC, bipAcc, bipLC presented in Section 3 combined with the three integrations to ranking (log denoted , satu denoted ⊕, sigmoid denoted ⊗) presented in Section 5.1).

Method MRR P@10 ERR@20 NDCG@20 MAP@1000 LM (baseline) [START_REF] Zhou | Document quality models for web adhoc retrieval[END_REF] We retrieve documents from the ClueWeb09 cat. B dataset using queries 150-200 from the Web AdHoc track of TREC 2012. We use the Indri IR system without stemming and without removing stopwords. Following [START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF], we remove spam from ClueWeb09 cat. B using the spam rankings of Cormack et al. [START_REF] Cormack | Efficient and effective spam filtering and re-ranking for large web datasets[END_REF] with a percentile-score < 90. This is a much higher threshold than the < 70 recommended in [START_REF] Cormack | Efficient and effective spam filtering and re-ranking for large web datasets[END_REF], practically meaning that we use much stricter spam filtering than recommended. We evaluate retrieval at different rank positions with MRR, Precision@10 (P@10), ERR@20, NDCG@20, and MAP@1000. The baseline and our reranking methods include parameters µ (for Dirichlet smoothing), and w, k, α that we tune using 5-fold cross-validation. We report the average of the five test folds. We vary µ ∈ [100, 500, 800, 1000, 2000, 3000, 4000, 5000, 8000, 10000], w ∈ [0.0, 2.0] in steps of 0.1, k ∈ [0.0, 2.0] in steps of 0.1, and α ∈ [0.0, 1.0] in steps of 0.1.

Retrieval Findings

Retrieval Effectiveness

Table 3 displays the retrieval effectiveness of our coherencebased reranking experiments and the original ranking baseline. Coherence-based reranking improves over the baseline at all times. The best overall performance differs per evaluation measure: for MRR, ERR@20 and NDCG@20 our strongest coherence metric (as shown in the previous section), bipLC, is the best; for P@10 and MAP, bipACC is the best. All three MRR, ERR@20 and NDCG@20 are evaluation metrics of early precision: MRR measures the rank of the first relevant document, while ERR@20 and NDCG@20 focus in the top 20 ranks (they both consider the rank of a document, but they differ in that ERR conditions the usefulness of a document at rank i on the usefulness of the documents at ranks less than i, whereas NDCG assumes the usefulness of a document to be independent of the documents ranked above it). So it seems that bipLC is best for early precision measures. However, bipACC is best for P@10 (precision in the top 10 ranks), which is also an early precision measure. This could be due to the way P@10 computes precision, namely as the number of relevant documents in the top 10 but regardless of their ranking. In effect this transforms the top 10 into an unordered set of documents, whose measurement is not guaranteed to agree with rank order-oriented measures such as ERR and NDCG.

We also see that the bipDCC coherence metric is never the best. This could be because bipDCC does not account for the number of entities that are shared by sentences. As this is a major indication of coherence (topic transition across sen-tences), it is likely that failing to account for this degrades coherence prediction (as we also saw in Table 2 on average and for the Accidents dataset). As a result, using for reranking a weaker coherence metric (bipDCC) improves retrieval less than when using our other two stronger coherence metrics. Note however that even though bipDCC is not the strongest coherence metric, it still benefits retrieval performance compared to the baseline.

Overall the difference in performance among the coherence runs in Table 3 is relatively small, except for MRR. The MRR exception is because the MRR score tends to change substantially for differences in even one rank position. For instance, when the first relevant document is at rank 1, MRR = 100; when at rank 2, MRR = 50.00; when at rank 3, MRR = 33.33, and so on. Considering this, even the largest difference in MRR among our coherence runs (from 52.82 to 47.63) is not indicative of considerable variation in rank position.

We also see in Table 3 that even though sigmoid (⊗) is more parameterised than the other two combinations, it is never the best. Instead, log ( ) and satu (⊕) take turns at being best, indicating that the coherence-based reranking performance is not a byproduct of additional tuning parameters that smooth out retrieval regardless of coherence.

We further note that improvements over the baseline for MAP@1000 are smaller than improvements over the baseline for the other early precision measures. This is not surprising: typically as the depth of the measured precision increases, for instance from ranks 10-20 to rank positions >500, the actual precision score averaged over all retrieved documents up to that rank progressively deteriorates, because increasingly less relevant documents enter the ranking.

Finally, to contextualise the performance of our coherence metrics, we report that the retrieval performance of the two best non-bipartite coherence metrics in Table 2, out-degree and entity distance, never exceeds the scores of our best bipartite metrics5 .

Coherence and Query Difficulty

An aggregated overview of if and how much coherencebased reranking improves performance for queries of various levels of difficulty can be seen in Table 4. The percentages in Table 4 have been produced as follows. For each retrieval precision measure, we rank all queries decreasingly according to their baseline retrieval score. We then use these scores to sort queries into the four quantiles (Q1-Q4) shown in columns 2- Table 4: Average improvement in retrieval performance over the baseline. Darker cells mark higher improvements.

5.

In effect these quantiles group queries according to their difficulty; Q1 contains those queries that have the highest baseline retrieval score (hence they are perceived as easier queries for the IR system to satisfy), whereas Q4 contains those queries with the lowest baseline retrieval score (which are perceived as the hardest for the IR system to satisfy). For the queries in each quantile, we compute their absolute difference in score between the baseline and each coherence-based reranking and turn this difference into a percentage. The percentages of each quantile correspond to the average improvement in retrieval performance over the baseline per quantile. This is the average over all queries in the quantile, and over all retrieval measures. We see that Q4 gains the most, on average across all coherence runs. As Q4 corresponds to the hardest queries that an IR system has to process, this means that reranking by coherence can improve performance for those queries that standard ranking has the most trouble with. However, the percentages per coherence metric show that our strongest coherence ric, bipLC, benefits mostly Q2 -Q3, and very little or not at all Q4. This very small or no improvement in Q4 for bipLC is in fact an artefact of how we computed the percentages: because it is not possible to compute a percentage improvement over zero, we removed from Q4 those queries that had a zero baseline score. These were on average 10.5 queries per evaluation measure. Removing these highly difficult queries has the effect of underestimating the impact of coherence-based reranking in particular in Q4, and especially for bipLC.

Overall, the smallest improvement for all coherence-based reranking is in Q1, which corresponds to queries that baseline IR ranking can cope with satisfactorily. This indicates that the margin for improvement over the baseline may be smaller for those queries.

Error Analysis

To gain more insight into the type of contribution that coherence makes to retrieval, we look at those cases that benefit the most from coherence-based reranking. For query 174 (rock art), the documents ranked in the top two places by the baseline retrieval model receive a coherence score of 0.0 by all of our coherence metrics. These top two documents have no TREC relevance assessments (hence most IR evaluation metrics will treat them as non-relevant). Even though these documents have stayed in the dataset after we filtered out spam (using very strict spam thresholding, as discussed above), manual inspection reveals these documents to be largely non-informative. The first few lines of these documents are included below: For documents like these, the baseline ranking function (which considers solely single term frequencies) has no way of detecting low document informativeness. The extremely frequent and uninformative (almost spam-like) repetition of the same terms, not only goes undetected in the baseline ranking, but can also result in the documents being ranked very high when they contain query terms (this is what happened for query 174). Our coherence metrics are particularly useful in these cases, because they can detect the low quality of these documents.

Of interest is also the document ranked by the baseline in position 4 for the same query 174. This document also has no TREC relevance assessments, and receives the following coherence scores: bipDCC=0.009, bipACC=0.022, bipLC=0.0. This document is a wikipedia listing of museums in Maryland:

[clueweb09-enwp01-26-04667]: List of museums in Maryland [• • • ] encompasses museums, defined for this context as institutions (including nonprofit organizations, government entities, and private businesses) that collect and care for objects of cultural, artistic, scientific, or historical interest and make their collections or related exhibits available for public viewing. Museums that exist only in cyberspace (i.e., virtual museums) are not included. Lists of Maryland institutions which are not museums are noted in the "See also" section, below. Both our clustering-based coherence metrics (bipDCC and bipACC) give to this document weights that concentrate on the dense clusters of entities. On the contrary, the bipLC metric emphasises more the transition of entities across sentences (which is extremely low in this document, as new entities (museum names and themes) keep on being introduced, mentioned in 1-2 sentences, and then quickly dropped). This is a specific discourse feature of text (to list or enumerate themes without linking them into the discourse), which goes undetected by clustering (bipDCC and bipACC), but not by bipLC. Note that this document was ranked as the fourth most relevant document for the query rock art. After manual inspection, we consider it neither very relevant, nor very coherent.

The above are examples of relatively low quality documents that are ranked (erroneously) high by the baseline but receive a very low coherence score (correctly) by our coherence metrics. Next we display examples of the opposite: high quality documents that are ranked (correctly) higher by coherencebased reranking than by the baseline.

[clueweb09-enwp00-52-08632]: Rock art of the Chumash people. The above documents are both coherent and relevant to query 174. Coherence-based reranking moves these documents three and two positions higher up in the ranking, respectively. Interestingly, for both of these documents bipACC gives the highest coherence score. This is because both these documents first list an index of subtopics that they contain and then discuss each of them under different specialised subheadings. This type of discourse, which is characterised by several local clusters that are however closely linked to each other by an underlying common theme (rock art in this case) is best modelled by bipACC, which focuses on local clusters (unlike bipLC) while also accounting for the number of entities that are shared by sentences (unlike bipDCC).

DISCUSSION

In Section 3 we present three bipartite metrics for approximating document coherence. Our metrics are not the only tailor-made metrics for bipartite graphs. There is substantial work in the field of network science aiming at defining metrics that highlight certain topological features of graphs, several of which may be related to coherence, but to the best of our knowledge this has not been done so far. For example, several techniques exist for community detection [START_REF] Fortunato | Community detection in graphs[END_REF], which may potentially be used in combination with bipartite graph distance to afford more precise coherence scores. The rationale is that, if a document is coherent, sentences being identified as belonging to a particular community should be close in the document. Similarly, several techniques exist for detecting maximal bicliques [START_REF] Kayaaslan | On enumerating all maximal bicliques of bipartite graphs[END_REF] (i.e., maximal subsets of vertices where all and ⊥-vertices are connected). Intuitively, maximal biclique detection could be used to detect document sentences and entities so related that there is no doubt they represent a coherent flow of discourse.

Regarding the integration of document coherence into ranking, we treat our document coherence metrics as a queryindependent type of document quality score that we combine linearly with the retrieval status value of the baseline ranking to rerank retrieved documents. This is a straightforward reranking approach; more involved reranking functions [START_REF] Craswell | Relevance weighting for query independent evidence[END_REF] may be used to possibly improve retrieval effectiveness. For instance, studying the distribution of the document coherence scores as well as the distribution of the document relevance scores can inform functions that aim at fitting the former to the latter more closely. Another integration method that can be used is rank fusion. The idea here is to the turn the baseline and the coherence scores into two rankings, which are then fused, e.g. using CombMNZ, voting algorithms, or Bayesian inference [START_REF] Beitzel | Disproving the fusion hypothesis[END_REF]. This has the advantage of ignoring the coherence score distributions, so for example heavily skewed distributions of document coherence cannot be allowed to have too much impact upon the final ranking. Alternatively, document coherence can also be turned into a prior probability of relevance and combined with the language modelling baseline probability, which would produce a seamless "coherence-enhanced language model". All of the above directions are interesting to pursue in the future.

CONCLUSIONS

We presented three novel bipartite graph metrics of document coherence. Our metrics extend the state of the art in unsupervised coherence modelling by approximating coherence directly on bipartite graphs of discourse entities and sentences (unlike previous methods that use their one-mode projections). We experimentally evaluated the accuracy of our metrics in modelling coherence. Our bipartite metrics incurred no additional efficiency cost over existing one-mode graph metrics. One of our metrics was found to be much more accurate approximation of document coherence than the state of the art computed from one-mode projections [START_REF] Guinaudeau | Graph-based local coherence modeling[END_REF][START_REF] Petersen | Entropy and graph based modelling of document coherence using discourse entities: An application to IR[END_REF]. We also experimentally evaluated the usefulness of our document coherence metrics to IR, and found them overall successful, and in particular for early precision and "difficult" queries. Our results can be seen as another piece of evidence in a long string of results showing that algorithmic approximations of document quality can be exploited in IR to obtain better retrieval performance.

ICTIR ' 16 ,

 16 September 12-16, 2016, Newark, DE, USA c 2016 ACM. ISBN 978-1-4503-4497-5/16/09. . . $15.00 DOI: http://dx.doi.org/10.1145/2970398.2970413

Figure 1 :

 1 Figure 1: Bipartite graph (middle) and its two projections (top and bottom), from [30]. A-D and 1-7 denote two different types of vertices.

Figure 2 :

 2 Figure 2: An example of a bipartite graph of an entity grid. Sentences are represented by squares, entities by circles. Syntactic roles are omitted for readability.

Figure 3 :

 3 Figure 3: Coherence accuracy (vertical axis) vs. number of sentence re-orderings (horizontal axis) per document, for our bipDCC (+), bipACC (o) and bipLC (•) metrics, for Accidents, Earthquakes.

[

  clueweb09-en0009-40-30672]: Music Democracy :: Unchain You Art username: Damn! I forgot my password password: The Music Democracy Team is attending MIDEM 09 in Cannes. If you're interested in a meeting, please contact us (link at the bottom of the page) Tests are underway and certain features could be unavailable punctually.We apologize for these inconveniences. HOME URBAN ROCK ELECTRO POP BLUES WORLD VARIOUS Registration as Musician * Username * Email * Retype email * Password (at least 6 characters) * Retype Password * Country (included province) Select Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba [• • • ] [clueweb09-en0000-95-09794]: Outline of Art History -Ancient Art Search Art History Home Education Art History Email Art History Artists Styles Works of Art Filed In: Art History Outline of Art History -Ancient Art 30,000 BC -c. 400 AD Outline of Art History Part 1: Ancient Art Part 2: Medieval Art Part 3: Renaissance Art Part 4: Modern Art Part 5: Contemporary Art Related Resources Ancient Art Resources Prehistory Paleolithic (Old Stone Age) [• • • ]

1 [

 1 The Justice Department] s is conducting an [anti-trust trial] o against [Microsoft corp.] s with [evidence] x that [the company] s is increasingly attempting to crush [competitors] o . 2 [Microsoft] o is accused of trying to forcefully buy into [markets] x where [its own products] s are not competitive enough to unseat [established brands] o . 3 [The case] s revolves around [evidence] o of [Microsoft] s aggressively pressuring [Netscape] o into merging [browser software] o . 4 [Microsoft] s claims [its tactics] s are commonplace and good economically. 5 [The government] s may file [a civil suit] o ruling that [conspiracy] s to curb [competition] o through [collusion] x is [a violation of the Sherman Act] o . 6 [Microsoft] s continues to show [increased earnings] o despite [the trial] x .

Table 1 : Entity grid example from [1]. Discourse entities are inside square brackets, marked

 1 s, o, x for

subject, object and other grammatical role, respectively.

Table 2 : Average coherence accuracy of baselines (top 4 rows) and our metrics (bottom 3 rows). The highest score in each column is shown in bold.

 2

		Earthquakes Accidents Average
	Entity-grid	69.7	67.0	68.4
	(no graph)
	HMM	60.3	31.7	46.0
	(no graph)
	Out-degree	78.0	80.0	79.0
	(one-mode projection)
	Entity distance	76.0	75.0	75.5
	(one-mode projection)
	bipDCC	55.6	69.8	62.7
	(bipartite graph)
	bipACC	55.5	70.1	62.8
	(bipartite graph)
	bipLC	80.9	94.0	87.5
	(bipartite graph)

Table 3 : Retrieval performance of coherence-based reranking. Improvements over the baseline are shaded and single best scores per evaluation measure are in bold.

 3

		.08	31.19	15.78	15.68	09.67
	LM bipDCC	49.09	34.00	16.89	16.53	10.15
	LM ⊕ bipDCC	48.62 34.00	18.63	16.61	10.07
	LM ⊗ bipDCC	47.66 33.60	18.38	16.26	10.01
	LM bipACC	49.14	34.20	16.94	16.60	10.18
	LM ⊕ bipACC	48.89	34.40	18.11	16.52	10.09
	LM ⊗ bipACC	47.76	33.20	17.02	16.20	10.01
	LM bipLC	52.82 32.80	18.69	16.67	10.05
	LM ⊕ bipLC	47.63	33.41	16.50	16.76	10.12
	LM ⊗ bipLC	50.52	32.60	17.28	16.48	09.92

  To use the sortable table, click on the icons at the top of each column to sort that column in alphabetical order; click again for reverse alphabetical order. Name Location Region Area of study Summary Aberdeen Room Archives & Museum Aberdeen Local history website Academy Art Museum Easton Art website, works on paper and contemporary works by American and European masters Adkins Historical Museum Mardela Springs Open air website, eight historic buildings and the gravestones of a Revolutionary War patriot and his wife, buildings open by appointment African-American Heritage Society Museum [• • • ]

  [• • • ] Chumash Rock Art is a type of artwork created by the Chumash people, mainly in caves or on cliffs in the mountains in areas of southern California. Contents: Chumash people, Rock Art Locations, Shamans and Visions, Shamans and Rock Art, Rock Art Characteristics, Meanings of Rock Art, Conclusion, References [• • • ] Chumash Rock Art is almost invariably found in caves or on cliffs in the mountains, although some small, portable painted rocks have been discovegray by Campbell Grant. The rock art sites are always found near streams, springs, or some other source of permanent water. In his research of southern California rock art, Grant recorded numerous sites from different areas that were all close to a water source. He found twelve painted sites in the highest parts of the mountainous Chumash territory, the Ventureno area [• • • ] [clueweb09-en0009-97-31173]: The Heilbrunn Timeline of Art History. The Metropolitan Museum of Art. African Rock Art. African Rock Art. Thematic Essay Categories. Recent Additions. All Thematic Essays. African Art. Central Africa. Eastern Africa. Southern Africa. Western Africa [• • • ] Africa's oldest continuously practiced art form. Depictions of elegant human figures, richly hued animals, and figures combining human and animal features called the rianthropes and associated with shamanism continue to inspire admiration for their sophistication, energy, and direct, powerful forms. The apparent universality of these images is deceptive; content and style range widely over the African continent. Nevertheless, African rock art can be divided into three broad geographical zones southern, central, and northern. The art of each of these zones is distinctive and easily recognizable, even to an untrained eye [• • • ]

A dual projection can be defined for ⊥ nodes.

The original definition of the entity grid allows to model the succession of only identical entities. This is the definition we adopt here. However, our coherence metrics also work for extensions of the entity grid that capture similar but not identical entities[START_REF] Zhang | Encoding world knowledge in the evaluation of local coherence[END_REF].

Limiting the reranking to the top 1000 is more efficient than reranking all documents with a nonzero baseline score, without making a large difference to system effectiveness[START_REF] Craswell | Relevance weighting for query independent evidence[END_REF].

The respective maximum scores of either out-degree or entity distance are MRR: 34.18, P@10: 22.40, ERR@20: 15.86, NDCG@20: 14.66, and MAP@1000: 07.22.


domain: phys math

text:
Peng Yang

Dongzhe Li

Vincent Repain

Cyril Chacon

Yann Girard

Sylvie Rousset

Alexander Smogunov

Yannick J Dappe

Cyrille Barreteau

Jeŕome Lagoute

C 60 as an Atom Trap to Capture Co Adatoms

C 60 molecules were used to trap Co adatoms and clusters on a Au(111) surface using atomic/molecular manipulation with a scanning tunneling microscope. Two manipulation pathways (successive integration of single Co atoms in one molecule or direct integration of a Co cluster) were found to efficiently allow the formation of complexes mixing a C 60 molecule with Co atoms. Scanning tunneling spectroscopy reveals the robustness of the π states of C 60 that are preserved after Co trapping. Scanning tunneling microscopy images and density functional theory calculations reveal that dissociated Co clusters of up to nine atoms can be formed at the molecule-substrate interface. These results open new perspectives in the interactions between metal adatoms and molecules, for applications in metal-organic devices.

■ INTRODUCTION

Building artificial nanostructures by atomic/molecular manipulation with a scanning tunneling microscope (STM) offers the opportunity to unravel the physical phenomena that govern the matter at the nanometer scale. [START_REF] Eigler | Positioning Single Atoms with a Scanning Tunnelling Microscope[END_REF][START_REF] Bartels | Basic Steps of Lateral Manipulation of Single Atoms and Diatomic Clusters with a Scanning Tunneling Microscope Tip[END_REF][START_REF] Heinrich | Molecule Cascades[END_REF][START_REF] Nazin | Visualization and Spectroscopy of a Metal-Molecule-Metal Bridge[END_REF][START_REF] Yamachika | Controlled Atomic Doping of a Single C 60 Molecule[END_REF][START_REF] Gross | Trapping and Moving Metal Atoms with a Six-Leg Molecule[END_REF][START_REF] Zhao | Controlling the Kondo Effect of an Adsorbed Magnetic Ion through Its Chemical Bonding[END_REF][START_REF] Krull | Site-and Orbital-Dependent Charge Donation and Spin Manipulation in Electron-Doped Metal Phthalocyanines[END_REF][START_REF] Perera | Controlled Clockwise and Anticlockwise Rotational Switching of a Molecular Motor[END_REF][START_REF] Dujardin | Dissociation of Individual Molecules with Electrons from the Tip of a Scanning Tunneling Microscope[END_REF][START_REF] Lee | Single-Bond Formation and Characterization with a Scanning Tunneling Microscope[END_REF][START_REF] Hla | Inducing All Steps of a Chemical Reaction with the Scanning Tunneling Microscope Tip: Towards Single Molecule Engineering[END_REF][START_REF] Repp | Imaging Bond Formation between a Gold Atom and Pentacene on an Insulating Surface[END_REF][START_REF] Liljeroth | Single-Molecule Synthesis and Characterization of Metalligand Complexes by Low-Temperature STM[END_REF] The rise of molecular electronics and spintronics has motivated a growing interest in molecule-metal interactions. STM experiments have been performed on individual manipulated molecule-metal conjugates [START_REF] Yamachika | Controlled Atomic Doping of a Single C 60 Molecule[END_REF][START_REF] Gross | Trapping and Moving Metal Atoms with a Six-Leg Molecule[END_REF][START_REF] Repp | Imaging Bond Formation between a Gold Atom and Pentacene on an Insulating Surface[END_REF] providing a physical understanding of the interaction between molecules and metal atoms which is critical to build new generation molecular electronic devices and molecular machines. Being highly symmetrical, chemically reactive and produced easily in large amount, C 60 is one of the most important members in the nanocarbon family [START_REF] Lopez | Materials Chemistry of Fullerene C 60 Derivatives[END_REF] and is a natural candidate for the study of model systems. The electronic spectrum and spatial mapping of molecular states of C 60 adsorbed on different metallic substrates have been investigated by STM/STS [START_REF] Lu | Spatially Mapping the Spectral Density of a Single C 60 Molecule[END_REF][START_REF] Lu | Charge Transfer and Screening in Individual C 60 Molecules on Metal Substrates:A Scanning Tunneling Spectroscopy and Theoretical Study[END_REF] and the interaction between a C 60 molecule and K adatoms has been measured using lateral manipulation and revealed a charge transfer from K atoms to C 60 . [START_REF] Yamachika | Controlled Atomic Doping of a Single C 60 Molecule[END_REF] The interaction between C 60 molecules and transition metals has also attracted many attentions. [START_REF] Balch | Reactions of Transition Metal Complexes with Fullerenes (C 60 , C 70 , etc.) and Related Materials[END_REF][START_REF] Kurikawa | Formation of Cobalt-C 60 Clusters: Tricapped Co(C 60 ) 3 Unit[END_REF][START_REF] Nakajima | A Novel Network Structure of Organometallic Clusters in the Gas Phase[END_REF][START_REF] Sakai | Comparative Study of Structures and Electrical Properties in Cobalt-Fullerene Mixtures by Systematic Change of Cobalt Content[END_REF][START_REF] Sakai | Effect of Cotunneling and Spin Polarization on the Large Tunneling Magnetoresistance Effect in Granular C 60 -Co Films[END_REF][START_REF] Miwa | Tunnel Magnetoresistance of C 60 -Co Nanocomposites and Spin-Dependent Transport in Organic Semiconductors[END_REF][START_REF] Sakai | Giant Tunnel Magnetoresistance in Codeposited Fullerene-Cobalt Films in the Low Bias-Voltage Regime[END_REF][START_REF] Avramov | Theoretical DFT Study of Atomic Structure and Spin States of the Co x (C 60 ) n (x = 3-8, n = 1,2) Complex Nanoclusters[END_REF][START_REF] Gobbi | Room-Temperature Spin Transport in C 60 -Based Spin Valves[END_REF][START_REF] Li | Effect of Substrate Temperature on the Spin Transport Properties in C 60 -Based Spin Valves[END_REF][START_REF] Cheng | Deep Co Penetration and Spin-Polarization of C 60 Molecules at Hybridized Co-C 60 Interfaces[END_REF] Significant magnetoresistance values have been reported for devices of C 60based spin valves with an electrode of cobalt. [START_REF] Gobbi | Room-Temperature Spin Transport in C 60 -Based Spin Valves[END_REF][START_REF] Li | Effect of Substrate Temperature on the Spin Transport Properties in C 60 -Based Spin Valves[END_REF] Furthermore, mixed thin films of Co and C 60 exhibited large magnetoresistance. [START_REF] Sakai | Effect of Cotunneling and Spin Polarization on the Large Tunneling Magnetoresistance Effect in Granular C 60 -Co Films[END_REF][START_REF] Miwa | Tunnel Magnetoresistance of C 60 -Co Nanocomposites and Spin-Dependent Transport in Organic Semiconductors[END_REF] In such organometallic films, a charge transfer of 0.2 electrons/Co atom to the C 60 molecule was measured, and a saturation composition was found for Co 5 C 60 above which Co dense clusters are formed. [START_REF] Sakai | Polymeric Co-C 60 Compound Phase Evolved in Atomistically Mixed Thin Films[END_REF][START_REF] Lavrentiev | Polymeric Chains in C 60 and Co Mixture[END_REF] In this work, using a low temperature STM, we manipulate atoms and molecules to build C 60 -Co x complexes and study their electronic properties by scanning tunneling spectroscopy (STS). We reach an x value of 9, which is beyond the abovementioned saturation value of 5 in mixed films and is larger than previous manipulated metal-molecule complexes. We perform dI/dV spectroscopy and conductance mapping to measure the electronic properties of the complexes. We find that although the interaction between C 60 and Co is strong enough to obtain a C 60 -Co x that can be moved on the surface as a single entity, the π states of C 60 are totally preserved; i.e., their energy position and wave function are not noticeably modified by the interaction with Co atoms and no evident charge transfer to these states is measured.

■ EXPERIMENTAL METHOD

The experiments were performed using a commercial Omicron low temperature STM operating under ultrahigh vacuum (UHV) (<10 -10 mbar) and at low temperature (5 K). We used a chemically etched tungsten tip for the STM measurement. The differential conductance (dI/dV) measurements were performed using the lock-in technique. The clean Au(111)/mica substrate was prepared by several cycles of Ar + sputtering (900 eV) followed by annealing at 600 K under UHV. The Co atoms were deposited by thermal evaporation of a 99.99% pure Co rod. C 60 molecules were deposited from a C 60 powder sublimated in a crucible heated at 600 K. These depositions were made in situ on the Au(111)/mica surface maintained at low temperature (5 K). Atomic and molecular manipulation were performed using lateral manipulation with the STM tip. [START_REF] Hla | Scanning Tunneling Microscopy Single Atom/ Molecule Manipulation and Its Application to Nanoscience and Technology[END_REF] In a typical molecular manipulation process, at first the tip is moved around the molecule and the scanning is stopped. Then the tip height is modified in order to reduce the tip-sample distance with the goal to increase the tip-molecule interaction. Then the tip is moved laterally along a straight line to the final position while the molecule moves under the influence of the tip. Finally the tip is retracted vertically to the initial height and the scanning is restarted. The molecule is then left at the final position on the surface. The tunneling resistance is used to estimate the tip-molecule distance and interaction strength. The larger the tunneling resistance is, the stronger is the tip-molecule interaction. In our experiment, molecular manipulation could be achieved either in constant current or in constant height mode. In the constant current mode the feedback loop was active during the manipulation with a typical tunnel resistance of 5 MΩ. In the constant height mode, the tip was first placed on top of the molecule (typical imaging parameter 1 V, 10 pA), then the feedback loop was turn off and the tip-sample distance reduced by about 5 Å before performing the manipulation with the tip maintained at constant height.

■ RESULTS AND DISCUSSION

After depositon of Co and C 60 on Au(111) at 5 K, single molecules and adatoms are clearly observed on the surface as shown in Figure 1a. Using the STM tip we performed molecular manipulation and moved a C 60 molecule toward a Co adatom, as shown in Figure 1a,b. In order to gain some insight into the cohesion of the C 60 -Co ensemble we performed an additional manipulation step (indicated by the arrow in Figure 1b) and moved the molecule away from the initial position of the Co adatom. After this manipulation, the Co adatom is no more observed on the surface, as shown in Figure 1c, indicating that it has been displaced together with the C 60 and is now attached to the molecule. This moleculeatom ensemble will be called complex in the following. This C 60 -Co complex was in turn successively moved toward individual adatoms, as shown in Figure 1b-f, in order to build C 60 -Co x and explore the scalability of the process.

By this lateral manipulation 6 Co atoms were taken by one C 60 to build a C 60 -Co 6 complex. Another way to build a C 60 -Co x complex is to move a molecule toward a Co x cluster. To do this, we built a Co 6 cluster by atomic manipulation and then moved a C 60 molecule toward the cluster as shown in Figure 2a,b. Then we displaced away this molecule by an additional manipulation step from the initial position of the Co 6 cluster (Figure 2b,c). After this manipulation, the Co 6 cluster is no more observed on the surface suggesting that it is attached to the molecule and in turn formed a C 60 -Co 6 complex. In order to show the complex mobility and put more Co atoms into the complex, this C 60 -Co 6 complex was moved successively by the STM tip toward the surrounding Co adatoms (Figure 2c). Finally, we have been able to add up to nine Co atoms to the C 60 molecule (Figure 2d). It has to be noted that it was more difficult to move the complex on the surface when more Co atoms were contained in the complex.

The methods described above are both efficient to obtain the C 60 -Co x complex although the building pathway is very different. The structure of these complex is therefore an open question that we address in the following. We studied the apparent height of C 60 and C 60 -Co x measured from the topographic STM image. Various apparent heights have been measured for C 60 organized on different metals. [START_REF] Grobis | Local Electronic Properties of a Molecular Monolayer: C 60 on Ag(001)[END_REF][START_REF] Altman | Growth, and Structure of Fullerene Films on Au(111)[END_REF][START_REF] Giudice | Morphology of C 60 Thin Films Grown on Ag(001)[END_REF] The apparent height of a C 60 molecule measured by STM depends on the orientation of the molecule, the STM tip state, the adsorption site on the surface, and electronic differences caused by surface interaction. [START_REF] Altman | The Interaction of C 60 with Noble Metal Surfaces[END_REF][START_REF] Fasel | Orientation of Adsorbed C 60 Molecules Determined via X-Ray Photoelectron Diffraction[END_REF] Therefore, the height of a molecule cannot be explained by a purely geometrical model as electronic effects must be taken into account. The electronic effects will be discussed below and we first address the expected geometric height. Because of its atomic structure, a fullerene C 60 exhibits five typical orientations: (a) hexagone, (b) pentagone, (c) 6:6 bond, (d) 5:6 bond, and (e) apex atom, which correspond to the configurations of a hexagonal ring, a pentagonal ring, a bond joining two adjacent hexagonal rings, a bond joining a hexagonal and a pentagonal ring, and an apex atom riding on the surface, respectively. The geometric height (without considering the substrate) of pure C 60 with different orientations is in the range of 6.48-7.05 Å as given by an atomic model with a C-C bond length of 1.43 Å. A van der Waals distance of about 2.5 Å 37 should be added to estimate the geometric height of an adsorbed molecule. Here, for a C 60 molecule or C 60 -Co x complex on Au(111) surface, the apparent height is measured as the vertical distance between the top of the molecule and the substrate along a scan line parallel to the reconstruction line (inset of Figure 3). As The Journal of Physical Chemistry C Article illustrated in Figure 3, the apparent height of C 60 is measured in the range of 4.9-7.3 Å. This dispersion of the apparent height can be due to the molecular orientation, the adsorption sites or more complex effects. We measured that for a given orientation the height of C 60 on a given adsorption site (fcc or hcp) can vary by about 1.6 Å. Therefore, the effect of orientation or adsorption site on the apparent height can not be clearly identified. However, the measured height is clearly smaller than the expected geometric height which may be due to electronic effects. It is clear that the C 60 -Co x complexes also exhibit apparent height distributions. Despite this distribution, the average apparent height of C 60 -Co x complex increases when the number of Co atoms increases from 0 to 9 as shown in Figure 3. This is also another evidence for the formation of the complex as the variation of the height reveals a difference between each structure. However, this increase does not correspond to the sum of C 60 and Co clusters taken separately. For example, comparing the apparent height of C 60 -Co 6 and pure C 60 , there is an increase of ∼2 Å, which is slightly larger than the height of a Co adatom (∼1.6 Å) and much smaller than the apparent height of Co 6 cluster (∼5.2 Å). As will be discussed below, the electronic spectrum of the molecule is not strongly modified after the formation of a C 60 -Co x complex, and therefore we expect that electronic effects will not play a major role in the height variations that are measured. It is worth to note that the complexes fabricated by either one-by-one (black triangle in Figure 3) or cluster (red circle in Figure 3) manipulation show the same trend in the apparent height. It suggests that the two methods, one-by-one and cluster manipulation, lead to complexes with the same structure. This can be understood as the typical time constant of the manipulation process (typically 1 ms between two successive tip displacements during manipulation) is much larger than the typical time constant of atomic relaxation, [START_REF] Bouju | Single-Atom Motion During a Lateral STM Manipulation[END_REF] therefore the system can be considered as being in equilibrium during the process and independent of the pathway followed to build the complex.

In order to investigate the electronic interaction between C 60 and Co atoms, we measured the influence of complex formation on the molecular orbitals of C 60 . We recorded dI/ dV spectra with the STM tip located above the center of C 60 molecules and different C 60 -Co x complex obtained separately. As illustrated in Figure 4a, three main resonance peaks, corresponding to the highest occupied molecular-orbital (HOMO), the lowest unoccupied molecular-orbital (LUMO), and LUMO+1 states, respectively, are observed in the differential spectrum of C 60 molecules. Similar features are found for the C 60 -Co x complex with slight shifts of peak position toward both high and low energies (Figure 4a). For the energy of the HOMO state, we determined the energy position after numerical derivation of the spectrum allowing us to measure the zero-slope point. Therefore, no charge transfer can be clearly evidenced between Co and C 60 . As illustrated by Xinhua et al., there is no obvious dependence of peak position on molecular orientation of C 60 on Au(111). [START_REF] Lu | Charge Transfer and Screening in Individual C 60 Molecules on Metal Substrates:A Scanning Tunneling Spectroscopy and Theoretical Study[END_REF] The average energies of the HOMO, LUMO, and LUMO+1 states are around -2.0, +1.1, and +2.4 eV as shown in Figure 4b for C 60 molecule and C 60 -Co x complex.

Simultaneously to the topographic STM image, we measured conductance maps on C 60 molecule and C 60 -Co x complex with different orientations. Such conductance maps allow to visualize the molecular orbitals at given bias voltage. As shown in Figure S1 in the Supporting Information, no clear difference is observed between the molecular orbitals of single C 60 and those of complexes. This shows that although the interaction between C 60 and Co is strong enough to capture single atoms or cluster, the influence of the hybridization between Co orbitals and C 60 π states is rather weak, so that the molecular orbitals remain unchanged. If the Co atoms were on the top of or beside the C 60 molecule, a difference should be observed on the conductance map. Considering the fact that the difference between the apparent height of C 60 -Co 6 and pure C 60 is slightly larger than the apparent height of Co adatom and much smaller than that of Co 6 cluster, it is possible that the Co cluster dissociates when C 60 -Co x complex is formed.

■ FIRST-PRINCIPLES CALCULATIONS

In order to interpret the experimental results, we performed DFT (density functional theory) calculations using a plane wave electronic structure package Quantum-ESPRESSO. [START_REF] Giannozzi | Quantum Espresso: A Modular and Open-Source Software Project for Quantum Simulations of Materials[END_REF] Local density approximation in Perdew and Zunger parametrization [START_REF] Perdew | Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems[END_REF] was used for exchange-correlation functionals. The plane-wave cut-offs were set to 30 and 300 Ry for the wave functions and for the charge density, respectively. A Marzari-Vanderbilt broadening scheme with a broadening width of 0.15 eV was used. The Au(111) substrate was simulated by a 5 layers Au slab with a bulk lattice parameter found to be 4.06 Å, close to experimental value of 4.08 Å. The first three Au layers were fixed while two other layers and C 60 -Co x complex were relaxed until atomic forces become smaller than 0.001 eV/Å. A (4 × 4) in-plane periodicity was adopted for Co/Au(111), C 60 / Au(111), and C 60 -Co/Au(111) in order to avoid unphysical interactions between adsorbates and the 2D Brillouin Zone (BZ) was sampled with (4 × 4 × 1) k-points mesh. For a bigger C 60 -Co 9 /Au(111) complex, a bigger (5 × 5) in-plane supercell was employed.

To provide a simple energetic reasoning for a possibility to drag a single Co atom by a C 60 molecule we present in Table 1 binding energies of Co atom to free C 60 molecule as well as to Au surface at two different adsorption sites: at "fcc-hollow" and "bridge". The difference between the two latters gives an estimate for the diffusion barrier of Co atoms along a Au surface, E diffusion =E hollow b -E bridge b , which was found to be ≈0.13 eV. Since the binding energy of Co/C 60 is much bigger than E diffusion , but, from another side, is substantially smaller than the binding energy of Co/Au(111), the Co atom will bind to C 60 and slide with it along the Au surface, remaining, however, always in contact with the surface, exactly as it is found in experiment. Note that the spin magnetic moment for Co/C 60 was found to be m S ≈ 1 μ B which is twice smaller than that for Co/Au(111), m S ≈ 2.4 μ B .

Next, we have studied the geometry and electronic structure of C 60 /Au(111), C 60 -Co/Au(111), and C 60 -Co 9 /Au(111) complexes (Figure 5). The lowest-energy configuration of C 60 / Au(111) corresponds to a C 60 hexagon placed right above an hcp-hollow site of a Au surface, in a good agreement with previous DFT calculations. [START_REF] Wang | Density Functional Study of the Adsorption of a C 60 Monolayer on Ag(111) and Au(111) Surfaces[END_REF] In the case of C 60 -Co/Au(111), the Co atom was found to bind at hollow site to a Au surface and at 6:6 bond to a C 60 molecule, in agreement with our results for Co/Au(111) and Co/C 60 presented above. The total spin moment of C 60 -Co/Au(111) was found to be around 1.42 μ B . This value is much smaller than that for Co/Au(111) (2.42 μ B ) and reflects thus a general result of suppression of the Co magnetism due to binding to C 60 . For the C 60 -Co 9 / Au(111) complex, we performed atomic relaxations with two different initial configurations: (i) Co atoms were distributed in some random fashion around C 60 molecule (no any statistics was done since calculations are rather heavy); (ii) Co atoms form a compact 2D monolayer island on Au(111) with a C 60 placed on top of it. We found that the first configuration is much more energetically favorable with respect to the second one, with an energy gain of about 0.97 eV. The Co atoms prefer thus to form a noncompact structure around C 60 , as shown on inset of Figure 5c, which points to a strong tendency to dissociation of Co clusters due to the interaction with the C 60 molecule. The total spin moment for this big complex was found to be around 13.71 μ B which corresponds roughly to 1.52 μ B per Co atom.

We next check out the height change of C 60 molecule due to the presence of Co adatoms on a Au surface, taking as a reference the topmost C 60 atom of C 60 /Au(111). The measured heights were found to be increased by ∼0. complexes, respectively, which is in a relatively good agreement with experimental data presented in Figure 3.

To simulate theoretically the STS spectra presented in Figure 4 we have used the well-known Tersoff-Hamman's expression for the tunneling differential conductance:

= ∝ + G I V n R E eV d /d ( , ) S T F (1)
where n S (R T , E F + eV) is the total (spin up plus spin down) vacuum LDOS of the sample (the surface with adsorbate) calculated at the tip position R T and at the energy corresponding to the applied voltage V. In practice, the vacuum LDOS is integrated over a small cubic box of the size which we choose here to be 0.4 Å. In Figure 5 In order to identify various features in vacuum LDOS, we also show in Figure 5a the DOS of C 60 /Au(111) projected onto different molecular orbitals of a free C 60 molecule. This allows us to ascribe clearly the two LDOS peaks at ∼0.55 eV and ∼1.55 eV to LUMO and LUMO+1 derived states, respectively, and a small feature at ∼-1.25 eV (hardly visible for C 60 -Co 9 / Au(111)) to HOMO orbitals. Interestingly, a broad feature at E <-1.5 eV, seen in all LDOS curves, originates from the Au surface states, since, as we have checked, the similar structure was also observed for a clean Au(111) surface (without adsorbates). It should be noted however that the DFT is generally known to underestimate a LUMO-HOMO gap which was found here to be ≈1.8 eV while the value of ≈2.6 eV can be extracted from experimental STS spectra (see Figure 4). Overall, no significant change in vacuum LDOS curves was found among C 60 /Au(111), C 60 -Co/Au(111) and C 60 -Co 9 / Au(111) complexes, which confirms the experimental results on STS spectra (Figure 4). Finally, we note that in Figure 5

n S

, could be probed separately by changing the direction of the tip polarization. We did not find, however, significant spin polarization of vacuum LDOS (Figure S2 in the Supporting Information).

■ CONCLUSIONS

Through atomic and molecular manipulation of C 60 molecules and Co adatoms on clean Au(111) surface at low temperature (5 K) using scanning tunneling microscopy, the C 60 -Co x complex can be formed in two different ways: the molecule is successively moved toward individual adatoms, or a Co x cluster is built by atomic manipulation then the molecule is moved toward the cluster. We have been able to add up to nine Co atoms to a C 60 molecule, which is, to our knowledge, the largest number achieved in such molecule-metal atom complex. The C 60 -Co x spectrum exhibit the main features of the C 60 single molecule suggesting that the π states are at most only slightly affected by the interaction between the molecule and the Co atoms. This is furtherly confirmed by the similarity between the conductance maps of C 60 and C 60 -Co x . The conductance map and the apparent height measurement suggest that the Co cluster is dissociated between the C 60 molecule and the Au (111) surface. These experimental results were explained and supported by DFT electronic structure simulations.

■ ASSOCIATED CONTENT * S Supporting Information Conductance map, spin-polarized vacuum LDOS, and molecular dynamics simulations. This material is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author *(J.L.) E-mail: jerome.lagoute@univ-paris-diderot.fr.

Notes

The authors declare no competing financial interest.

Figure 1 .

 1 Figure 1. Series of STM images obtained during successive manipulations of a C 60 molecule toward Co adatoms that are taken one by one to build C 60 -Co x complex. Note that the C 60 -Co 4 complex has taken two nearby individual Co adatoms by one manipulation to form C 60 -Co 6 . To guide the eyes, the arrows indicate the moving direction of the molecule. All the STM images are taken with a bias voltage and current set point of 2 V and 20 pA, respectively.

Figure 2 .

 2 Figure 2. Series of STM images obtained during successive manipulations of a C 60 molecule toward a Co cluster and Co adatoms. (a) A group of 6 Co adatoms (marked by a rectangle) is manipulated to form a Co 6 cluster (b). (b to c) A C 60 molecule is moved onto this cluster to fabricate C 60 -Co 6 . Three neighbor Co adatoms are taken by C 60 -Co 6 and finally a C 60 -Co 9 complex is built (d). To guide the eyes, the arrows indicate the moving direction of the molecule. All the STM images are taken with a bias voltage and current set point of 2 V and 10 pA, respectively.

Figure 3 .

 3 Figure 3. Apparent height (h) of C 60 and C 60 -Co x measured by STM. The dotted line fits the average height at every x value. The black triangle and red circle symbols correspond to one by one and cluster manipulation, respectively. Inset: the profile of a C 60 molecule. All the apparent height measurements were carried out from STM images taken with a bias voltage of 2 V.

  14 and ∼0.75 Å for the C 60 -Co/Au(111) and C 60 -Co 9 /Au(111)

Figure 4 .

 4 Figure 4. (a) Tunneling spectra for C 60 and C 60 -Co x showing three peaks around -2.03, 1.12, and 2.38 V corresponding to the HOMO, LUMO, and LUMO+1 states, respectively. (b) Energies of HOMO, LUMO, and LUMO+1 for C 60 and C 60 -Co x measured by tunneling spectroscopy. The dotted lines correspond to the average energies of HOMO, LUMO, and LUMO+1 states for all the x values. The colored symbols identify complex obtained with the same C 60 molecule.

Figure 5 .

 5 Figure 5. DFT calculations: vacuum LDOS at 6 Å above the C 60 for (a) C 60 /Au(111), (b) C 60 -Co/Au(111), and (c) C 60 -Co 9 /Au(111) complexes, and (d) the corresponding relaxed geometries. The LDOS for two different lateral positions are presented with solid and dashed lines. For the case of C 60 /Au(111) also the DOS projected onto molecular orbitals of the free C 60 molecule is shown. The height change Δh of C 60 molecule (see text) and the total spin moments are also provided on each panel.

Table 1 .

 1 Binding Energies, Atomic Bonds, and Spin Magnetic Moments for a Co Atom on Au(111) Surface (at Two Different Adsorption Sites: "fcc-hollow" and "bridge") and on Free C 60 Molecule (above 6:6 Bond, the Lowest Energy Adsorption Site)

		Co/Au(111) fcc-hollow	Co/Au(111) bridge	C 60 /Co, 6:6 bond
	E b (eV)	4.10	3.97	2.69
	d Co-Au (Å)	2.42	2.37	-
	d Co-C (Å)	-	-	1.86
	d C-C (Å)	-	-	1.46
	m S (μ B )	2.42	2.43	1.03

  such vacuum LDOS are presented for all three molecular complexes and for two different boxes (solid and dashed lines). These boxes are both placed at 6 Å above C 60 molecule but at slightly different lateral positions. One can see that the curves of LDOS correspond pretty well to the STS spectra shown in Figure4. Their shape however depends somewhat on the lateral box position. In particular, LUMO+1 derived states (at ∼1.55 eV, see discussion below) are almost unvisible for the box represented by dashed lines.

J. Phys. Chem. C 2015, 119, 6873-6879

DOI: 10.1021/jp512723c J. Phys. Chem. C 2015, 119, 6873-6879

■ ACKNOWLEDGMENTS

The authors express thanks for the fruitful discussion with Dr. Xavier Bouju. The calculations in this work was performed using HPC resources from GENCI-CINES (Grant Nos. x2013096813).