Céline Mougenot
email: celine.mougenot@paris.ensam.fr

Carole Bouchard
email: carole.bouchard@paris.ensam.fr

Ameziane Aoussat
email: ameziane.aoussat@paris.ensam.fr

Steve Westerman
email: s.j.westerman@leeds.ac.uk

Inspiration, images and design: an investigation of designers' information gathering strategies

Keywords: creativity, design, design cognition, design computing, images, information retrieval, inspiration, kansei, sectors of influence

Computational tools should efficiently support, and even enhance, designers' creativity. As a ground for such developments, design cognition studies aim at describing designers' mental strategies within the design process. So far, most researches have been focused on the idea generation phases, e.g. sketching activity, which is explicit enough to be observed and described. However, the early stages of design remain incompletely understood, while the informational phase is identified as a crucial step of the design process. In this context, our objective is to identify and evaluate inspirational information used by designers before generating ideas, and to describe how inspirational information is used. In this article, we report a two-part study (interviews and experimental protocol) carried out with professional designers. The main outcomes demonstrate that traditional and electronic resources are not used in the same way by designers. We also show that information gathering strategies are strongly influenced by designers' preference.

Introduction

Context: developing tools to enhance creativity in early stages of design

Computational tools can now support most human activities, including design. A special focus on early phases of design, as the informational phase, would be extremely useful for developing computational tools that efficiently support designers' creativity [START_REF] Schneiderman | Creating creativity: user interfaces for supporting innovation[END_REF]. We think that designers' creativity can be enhanced by computational support. As suggested by [START_REF] Nakakoji | A framework that supports collective creativity in design using visual images[END_REF], computational systems help to provide designers with huge databases of visual and textual materials relevant in creative design activities. Some tools have been developed to support inspiration, based on the idea that designers need large databases containing images of precedents, i.e. previously designed artifacts, to support the evocation process [START_REF] Keller | TRI: inspiration support for a design studio environment[END_REF][START_REF] Keller | For Inspiration Only: Designer Interaction with Informal Collections of Visual Material[END_REF] [START_REF] Guénand | A reference system of semantic characterisation of products based on an ontology[END_REF]) [START_REF] Pasman | Designing With Precedents[END_REF] [START_REF] Restrepo | Information Processing in Design (Design Science Planning)[END_REF]. Based on the same vision, our research context is TRENDS project, a three-year project supported by the European Union whose objective is to design an image-retrieval software dedicated to designers. Designers intensively use images in their professional activities and the TRENDS computational tool will support the image-retrieval activity in design and its cognitive aspects, including evocation, analogy-making and concept generation [START_REF] Bouchard | TRENDS: a content-based information retrieval system for designers, DCC'08[END_REF]. A pre-requisite to the development of digital inspiration-support tools is to understand the inspirational process in design, especially involving a cognitive approach. [START_REF] Bonnardel | Towards supporting evocation processes in creative design: a cognitive approach[END_REF] studied the evocation process in creative design and proposed two ways of leveraging designers' creativity with digital tools: to support designers in taking advantage of inter-domain sources of information and to support designers in adopting various points of view. The study presented here especially addressed the first issue, by comparing magazines and websites in the way they support designers in retrieving sources of inspiration. Today's computational tools support detailed design phases better than conceptual design phases, mostly because conceptual phases in design are not so explicit, they are 'hidden' in designer's mind and thus, difficult to describe, model and support. Therefore, design research with a cognitive approach is still necessary when aiming at developing breakthrough digital tools to support designers' inspiration and creativity.

A cognitive approach to design early stages

Design thinking has been attracting more and more attention from researchers since Donald [START_REF] Schön | The Reflective Practitioner. How Professionals Think in Action[END_REF] and his contribution to the understanding of what practitioners do and think and the development of 'reflection-in-action' and 'reflection-on-action' notions. Lawson's (1980) work was more specifically focused on architectural activities; in an attempt to 'demystify the design process'. [START_REF] Lawson | How Designers Think: The Design Process Demystified[END_REF] observed architectural activities and demonstrated the importance of sketching within the design process, as a tool for an iterative idea formalisation. In 1995, the Delft protocol laid the foundations for research dedicated to design thinking (Cross, Christiaans and Dorst, 1996) and the research community became aware that creativity in design was a research issue in itself, with particular features. To get an understanding of the creative process in the design context (see also Nagai, Candy and Edmonds, 2003; Visser, 2006) the inspirational process was studied by [START_REF] Eckert | Sources of inspiration: a language of design[END_REF], who stressed that designers need to devote some of their working time to browse inspirational materials, and also by [START_REF] Ansburg | Creative and analytic thinkers differ in their use of attentional resources[END_REF] who showed that creative designers use their attentional resources to cover a wide range of sources of information.

Creativity in design also involves a specific cognitive feature: analogical reasoning; many studies demonstrated that designers make an intensive use of analogies in order to adapt design features from other fields to their own design problem. From a more descriptive point of view [START_REF] Leclercq | 5.8 Analogies per hour -a designer's view on analogical reasoning[END_REF] described the way designers use analogies. [START_REF] Bonnardel | Towards supporting evocation processes in creative design: a cognitive approach[END_REF] showed that the most creative analogies are those made between the most distant domains and that analogies can be performed at various levels (functional, structural, and affective). Analogical thinking is often triggered by visual stimulation, it has been shown that pictures and images are a major way of stimulating designers creativity [START_REF] Casakin | Expertise and the use of visual analogy: implications for design education[END_REF][START_REF] Goldschmidt | Variances in the impact of visual stimuli on design problem solving performance[END_REF]. Besides visual materials, the importance of words was emphasised by (Dong, 2006); to him, 'language serves as representations of ideas and concepts through linguistic behaviours that represent the structure of thought during the design process'. Today, visual materials and linguistics materials have been identified as major vectors of design creativity. However, we still lack an acute description of the roles of pictures, words and pictures-and-words relationships within the designers' cognitive process.

Some studies have attempted to create links between the visual characteristics of products and descriptive words, in the frame of design, by building design precedents classifications [START_REF] Keller | For Inspiration Only: Designer Interaction with Informal Collections of Visual Material[END_REF]. Subjective experience, either on the part of designers or product users' can be taken into account and design characteristics can be linked to abstract notions, such as feelings or emotions. Kansei studies (Bouchard, Lim and Aoussat, 2003) aim to describe the role of designers' feelings in relations to product development.

Recent studies in Kansei were reported by [START_REF] Levy | Towards a definition of Kansei[END_REF]. However, so far these studies mainly focus on the idea generation phase or in the design evaluation phase. An emergent trend is to study the relationships between the information provided to the designers and the generated design solutions. A recent study by [START_REF] Perttula | The idea exposure paradigm in design idea generation[END_REF] focused on the impact of exposure to design solutions and demonstrated that showing images of original design solutions to a problem would support designers in finding other original solutions. We propose that the relationships between information content/format and idea generation in design require further investigations.

Research question

To develop user-centred creativity-support systems, including image-retrieval systems, we need to investigate designers' cognitive activity and, in our case, how inspirational resources are used by designers. Our global research agenda aims to assess the impact of inspirational information onto design creativity; in this framework, the goal of the study presented in this article is to investigate the nature of the inspirational resources collected by designers in the early stages of the design process and the strategies followed in their information-retrieval activity.

In the 1990s, a major visual reference for designers was 'MTV's video style' [START_REF] Kolli | Some considerations for designing a user environment for creative ideation[END_REF]. Since this time, professional activities have been deeply transformed with the introduction of the internet in most countries. Most design agencies use online tools and websites [START_REF] Keller | For Inspiration Only: Designer Interaction with Informal Collections of Visual Material[END_REF], and one of the most popular imageretrieval tools among designers is Google Images (http://images.google.com/). One of its most appealing characteristics is a 5-billion-image database, the largest in the world as of May 2008. The internet is the biggest provider of visual information, but, in its current state, is it really relevant for use in professional design activity? Does it provide a sufficiently inspirational medium for designers? Thus, an important research issue concerns the influence of inspirational materials, mainly visual materials, on designers' subjective impressions/experiences of design features and their creativity.

In the investigation reported here, we address designers' activity in the information gathering phase (collecting images), with a special focus on the way they select inspirational materials from 'traditional' resources, such as printed magazines versus new resources, such as websites. In addition, we examined the level of 'abstraction' of images retrieved from magazines and from the web. It can be argued that visual inspiration/images provide information 'on-demand', at the level of abstraction wanted by designers, from a low-level of abstraction (colour, texture) to a high-level of abstraction (emotion, atmosphere, value). However, it is possible that the medium will influence the selected level of abstraction.

To investigate these issues we carried out a study in two phases. First we organised interviews with designers to investigate the early phases of the design process (March 2006) and to get an overview of the inspirational process in design. Then we designed an experimental protocol for an on-site qualitative study (July 2006), to get a more detailed understanding of the inspirational resources and inspirational strategies used by designers. This focused on a comparison between the inspirational resources found from magazines and the ones found from websites, and the strategies followed by designers when retrieving inspirational images. This study was performed with the participation of professional designers from two automotive design companies located in Italy, namely FIAT and Stile Bertone.

2 Phase 1: overview of the inspirational process in design

Protocol: interviews

To investigate the inspirational process, a first phase consisted in interviews that were carried out with 32 professionals from FIAT and Stile Bertone. The objective of the interviews was to describe the nature of the inspirational resources that are collected and used by designers in their daily activities. The participants belonged to departments in charge of design early phases. Twenty-one participants were from the Design department; six participants were from the Marketing department; and five participants were from the Innovation department. The participants were interviewed in groups of two. The interviews were semi-structured and each lasted approximately 1 hour. To be ready for the interviews, the participants had to complete in advance a 13-page printed booklet with sketches and/or text, the booklet questions were the same as the interview questions. Questions included:

Where do you catch sources of information and/or inspiration (places, media, favourite magazines, favourite websites…)?

In which fields/sectors do you search for inspiration (organic shapes, aeronautics…)?

Where do you keep and organise your visual materials? Describe the steps of exploration of your collections of images.

Outcomes

Browsing magazines was seen as a usual and daily activity by designers. The designers claimed that reading magazines is the 'traditional' way of being kept informed about trends and design news. However, they also acknowledged that the internet is becoming more and more widely/frequently used in information gathering/monitoring activities. All of the designers used it on a daily basis as well. We were interested in knowing whether internet and pictures search engines, such as Google Images, are used differently from the printed media in the informational phase of designers' jobs.

About the inspirational process

The inspirational process is continuousgathering information is a continuous preparation for the designers, in order to be highly creative once the brief is announced. Between the reception of a design brief and concept generation, the 'spare' time available for collecting information is very tight. Most of the time is spent in creative activities; so designers use experience and knowledge gained before the project to direct information gathering. In this way, when the project has started, they are able to restrict gathering to relatively small amounts of 'external' information. Most of the designers stressed the fact that inspiration does not fit the constraints of a '9-to-5-job', but is rather a continuous, and almost unconscious, activity that may take place while watching cars on the street, taking a stroll in the countryside or visiting buildings. Capturing information from the everyday life, and storing it mentally, is part of the designers' job. A manager sees the continuous update of cultural knowledge as a keystone for design work, because 'the idea will always be the outcome of [our] experiences'.

Design briefs vary in the types and quantity of information providedoften the brief focuses on key demographics of anticipated users (car owners) and technical details. A design brief can be as short as two A4-pages, or sometimes as long as a book, containing information about the dimensions (car packaging), the targeted market sector, what the design should not be like (e.g. 'not like such or such car model'), required technologies, competition (or anticipated competition), a functional description, regulations… Sometimes additional material is given relating to specific design directions that are preferred or design directions to be avoided. This is often done with specific reference to car images. More detailed information can be given, including images describing semantic concepts or emotions that the design should convey (e.g. pictures of a 'happy family'), or images illustrating key characteristics of the demographic group(s) which the design is targeted.

The early steps of creative activities are mainly individualafter receiving the brief, designers would start to develop individual designs, for a period of approximately one week, up to three weeks. Once initial designs are completed, they would be brought to a design meeting at which a small number, possibly one, of design proposals would be selected by managers for further development. At this point, some of the designers might make use of images illustrating sources of inspiration, through building trend boards for instance. After final concept(s) selection, designers would drop the non-selected design proposals and work collectively on the selected design proposal(s).

An incubation time is essentialconcept generation is carried out over a few days only.

In this timeframe, designers' creative activities reach their peak of intensity. During this time the importance of an 'incubation' period was mentioned by several designers, who find it useful to go away from materials/designs for a while and then come back to them with a fresh view. They deliberately take a break and come back to the design later.

Junior designers rely on inspirational resources more than senior designersexpert designers claimed that their experience and their inner knowledge were sufficient when they had to generate new concepts. Having received the brief proficient, designers were 'sure to be able to produce new concepts, because of long experience'; another reported that he just 'looks into [myself]'. 'Experience is enough; I don't need to go to a special place to get information'. For these reasons, the gap between young designers and expert designers is obvious: they manage inspiration and information with a different level of easiness. 'Young' designers might feel less self-confident than their expert colleagues. It seems there is a greater need for novice or young designers to have access to information and inspirational materials. This may occur as they attempt to compensate for their lack of experience. However, in the case of electronic resources, it is also possible that it occurs due to greater familiarity and liking for new technologies.

About inspirational media and computational tools

Visual sources are predominantinspiration comes to designers through their five senses; however, some senses are predominant over the others. According to the designers, the design process is image-oriented rather than text-oriented, and that is why magazines, books and the internet are the most used sources of information.

Magazines and design books are still the main sources of inspirationmagazines are often used as a source of information. They can be accessed more flexibly than the internet (anyplace, anytime) and designers seem better able to memorise what they saw in magazines. Besides, five participants clearly expressed that reading a magazine is a pleasurable moment, which is not the case while browsing the internet. They seem to enjoy the fact that they have to manipulate physically something and find it pleasant to touch. Designers also stress on the fact that magazine information is always linked with a date, so they easily know whether the information is up-to-date.

Internet: a promising outsider -the internet has become the most commonly used electronic tool in design offices and design agencies. Designers use it on a daily basis, as a complementary tool to books or magazines, but also as an inspirational tool in itself. For all the participants interviewed, the internet is now a natural extension of their working environment. However, low resolution can be a problem when using images from the web (Figure 1).

Computers as design-supporting tools -all participants used the internet in their everyday design job. In parallel to the internet development, we observe that designers use digital cameras a lot, to keep visual records of motor shows, of architecture, and so on. In fact, most of the designers have electronic databases of images that they use. However, these are not particularly structured for the project they are working on. Some designers reported having no need for storing information or collecting images after a project ended. We interviewed people from their 20s to their 50s; they all see internet as a useful tool for finding information. Internet as a brainstorming tool -the Google search engine is often said to be used as part of 'brainstorming'. A rather 'loose' Google search can be useful in retrieving items that the designer did not have in mind but that are inspirational in relation to the design brief. When using the internet, many designers find interesting things they were initially not looking for. This approach to information gathering seems to be particularly useful in the first phase of design projects, when the research benefits from being as 'wide' as possible. Then, in a second phase, the research is more focused in order to find relevant materials in more specific sectors of influence.

Inspirational sectors

Car-design precedents are major influences for automotive designers -Figure 2 shows a representative case (from one designer) of sources of inspiration used in car-design projects: car-design precedents (previous creations) and car-related fields (races, motorways) are the major influences. Some designers assemble images of cars that are consistent with the brief to get an idea of what has being done. The main information search by designers is focused on their own car-design precedents and those of competitors. They may find examples of cars that they do not like. These images would mainly be used as a 'benchmark' for quality/direction, as well as sources of inspiration for design. For this purpose, the information should be relevant to the target (cars) but not too similar. However, some projects at FIAT were based on a sense of history of a particular car (e.g. 'FIAT 500'), in which case, images of the specific car would become more central to the process.

Panorama of inspirational sectors -although car-design precedents have a huge impact on car design projects (see Figure 3), designers also get inspiration from other fields: e.g. architecture, furniture, animals. Participants often quote similar sources of information when asked about inspirational sectors, with 'car design' and 'architecture' being the most quoted. Fields of inspiration were sometimes influences by the brand of the design. According to one participant, FIAT designs tended to be inspired by architecture, ALFA ROMEO by sculpture and LANCIA by fashion. x-axis: percentage of participants quoting the domainy-axis: domains quoted by participants

The interviews provided an understanding of the activity of collecting inspirational materials and the sources used by designers and innovation-related professionals. They also enabled us to draw up a list of inspirational materials, magazines and websites that would be used in the experiment that is described below.

Phase 2: comparison of inspirational resources

After getting an overview of the inspirational process using semi-structured interviews, the second phase of this study was a laboratory-based investigation of designers' ways of selecting inspirational materials retrieved from magazines and websites, and of associating words and pictures. The goal of this experimental component was twofold:

1 To describe the cognitive process of designers when searching for images and texts in the frame of their inspirational process.

2 To compare the ways magazines on one hand and websites on the other hand contribute to supporting designers' creativity.

This study was based on the following premises: in the early phases of design, the activity of browsing is largely based on individual strategies that relate to designers' feelings towards the product (or Kansei). It was also assumed that new digital tools, such as the internet, would impact the informational phase in design projects.

Protocol: exploration and categorisation of visual resources

The sample comprised four male designers who participated in Phase 1 (interviews). The nationality of the designers was Italian (2), German (1) and French (1). Ages of participants ranged from 27 to 33 years old (mean = 29.8 years). Professional design experience ranged from 3 to 7 years (mean = 5.3 years). All participants were proficient in English, the language that was used for giving experimental instructions. In this article were refer to the participants as 'Designer 1', 'Designer 2', 'Designer 3' and 'Designer 4'.

Each experimental session was carried out by one experimenter who interacted with one designer for approximately 120 min. The sessions were video-taped. In this article, we present two assignments that were performed by the participants. Both assignments were designed as to be as close as possible to a real professional activity. The experiments were performed in a lab-like room, inside the designers' usual environment (company facilities). The designers were asked to complete the experiment as if they were performing their usual activities of trends and design information watching (Figure 4).

Identification and categorisation of inspirational content

The exploration of visual resources consisted of participants freely browsing inspirational materials that were provided, i.e. six printed magazines dealing with automotive design, fashion, interior design, art and architecture and 10 websites dealing with automotive design, fashion, product design, as listed in Table 1. All magazines and websites used in the experiment dealt with creative sectors that were identified as usual sectors of reference by car-designers in the semi-structured interviews (e.g. car-design, architecture, interior design). In this first step, designers were asked to identify inspirational content, but the search did not have to target any specific issue. This was intended to simulate a situation close to the usual continuous monitoring of trends and designs. Without any brief or any directions, designers were invited to browse freely magazines first, and then websites. All retrieved images were recorded, as well as the search terms that participants used. Participants were then asked to identify which components of each image led to their decision on inspirational content. Prompts of shape, colour, texture, and semantics were given. The participants wrote down this information on sticky notes that were associated with the selected pictures. When the pictures collecting task was over, designers were invited to categorise the pictures and to choose words to name the categories (Figure 5). The total duration of this task was about 1 hour for each participant.

Constrained exploration of visual resources

In the second stage of the experiment, participants completed a focused image-search; the search was so-called 'focused' because it was constrained by a design brief which gave conditions about sociological and emotional values that needed to be integrated into the targeted design. The design brief is detailed in Figure 6. At first, participants had to write down the keywords that came to their mind when reading the design brief. Then participants were invited to browse a selection of pictures from websites, most of them being designed for professional users (Corbis, Fotolia, Getty, Google Images, Inside, Masterfile). They could use the words that first came to their mind as keywords for their requests. While browsing these websites, participants had to select pictures to illustrate the design brief as if they would use these pictures for a trend board illustrating a design proposal. The selected pictures were saved by the participants on the computer hard disk. During the process of picture selection, participants verbally explained their choices and notes were taken by the experimenter. See Figure 7 for an overview of this component of the experiment. The total duration for this task was about 40 min for each participant.

Outcomes

Magazines and websites unconstrained exploration by designers

Number of retrieved images -while browsing magazines and websites, participants selected the pictures they found inspirational. The first observation concerns the total number of pictures retrieved either from printed medium, i.e. 55 pictures, or in online medium, i.e. 31 pictures. While the participants were given the same time allocation for both browsing tasks, it is obvious that they found a greater quantity of inspirational materials through the magazines than on websites (Figure 8). Commonalities between sets of selected pictures -Figure 9 shows the only picture that was selected by more than one participant (two participants picked this picture, both describing it with the concept of 'simplicity' and both classifying it in a 'shape'-related category. Designer 1 used this picture description to name a whole category. This is an interesting finding: given a finite and rather small images database made of six printed magazines, participants make images selections that are very different from one to another.

Type of images selected -in the magazines browsing tasks, 55 pictures were retrieved by the four participants. Most of the selected pictures were A4-magazine page format (cf. Table 2). The selected pages showed a very clear focus on a specific subject, without any text most of the time. Pages full of small details were not popular: only five images (out of 55) were a selection within a page full of details (graphical or shape details). Six selected images were A3-format (magazine double-pages). All were selected by the same designer who also created many categories linked with feelings and 'atmospheres'. An explanation for this selection could be that large-format images better involve the observer in the atmosphere of the picture.

Sources of influence -from the six magazines proposed by the experimenters, the participants selected between three and five magazines to be browsed during a limited time (30 min). The participants selected inspirational pictures in quite similar sets of magazines among the proposed magazines: FRAME and DAM were the most popular magazines for the pictures selection, while ELLE and VANITY FAIR were the most often left aside. The four participants selected a total of 55 pictures. The overall selection of pictures is broken down as described in Figure 10, with respect to each source.

The content of the selected images can be described as intra-domain sources, close interdomain sources and far inter-domain sources, depending on the amount of shared properties with the products to be designed (in our case: cars). The definitions of these categories are given in Table 3, along with the examples of content as would apply in this study Following these definitions, the experimenters allocated the retrieved images to the three domain categories, as shown in Figure 11. At this stage, the analysis was mainly based on the content of the images, as judged by the experimenters and independent from the participants' perception of the images.

In both cases of retrieval, magazines and websites, the relative preference for domains is similar. It is noticeable that the least numbers of image were selected from intradomain sources and remote inter-domain sources, while the greatest number of images was selected from close inter-domain sources (88% of magazines selection and 71% of websites selection). Table 3 Definition of sources domains [Adapted from [START_REF] Bonnardel | Towards supporting evocation processes in creative design: a cognitive approach[END_REF]]

Type of sources Definition Example content

Intra-domain

The source is from the same semantic domain as the product to be designed.

Car and transportation design.

Close inter-domain

The source has some common properties with the product to be designed.

Product design. Architecture

Far inter-domain The source is obviously different from the product to be designed.

Fashion. Lifestyle. People. x-axis: reference domainy-axis: percentage of retrieved images Abstraction level of the image content -participants had to group their retrieved images and to give names to the created categories. The category names given by all four participants can be found in Table 4. At one extreme, design descriptions can be 'lowlevel' and linked to the physical characteristics of a product. At the other extreme, design descriptions can be 'high-level' and related to designer interpretation of affective and semantic image content. He we consider three levels of abstraction to describe image content: high, mid and low. Definitions are given in Table 5, as well as some examples of the categories created by the participants in this experiment. Following these definitions, the images retrieved by the participants were distributed by the experimenters to one of the three levels of abstraction, as shown in Table 4. Some images could belong to several levels of abstraction; for instance, an image of the 'Shape simplicity' group could be allocated to both the low abstraction level (shape) and the high abstraction level (simplicity). At this stage, the analysis was mainly based on the names given by the participants to the images groups, thus it is based on the participants' perception of the images they retrieved.

As shown in Figure 12, the content of the images was very different depending on whether the images were retrieved from magazines or websites. When assessing the level of abstraction for each categories created by the designers, it appeared that 41.4% of the pictures found in the magazines were classified in the 'high-level' category, i.e. linked to an affective or a semantic description, while only 25% of the pictures found on the internet fell into this category level. The high-level category often refers to an atmosphere triggered by the visual information. Actually, the internet seems to provide pictures that are very often categorised at a mid-level of abstraction, more than 60%, linked to a product or to a creative sector (Car, Furniture).

Table 4

Categories created by the designers and associated number of pictures 1 x-axis: level of abstraction of the image contenty-axis: number of images 'Designer 3' found pictures with the following keywords: BMW Z4, Lotus Exige, Zidane, Football; he was satisfied with the associated findings. To designers 1, 2 and 4, most of request results were not satisfying. The pictures they selected were found by chance, and not thanks to the keywords that were keyed in the search engine dialog box. With the internet, most requests retrieved images that did not fit the participants' expectations.

Discussion

Web tools transform designers' activityin the free browsing tasks, we observed that the designers did not retrieve the same materials when they browse printed magazines as when they browse websites. For instance, the pictures retrieved from the magazines mainly belonged to an 'affective and semantic' level (41.4%), while the pictures selected on websites mainly illustrated 'Products' and 'Sectors' (61.3%). In addition, when fulfilling a design brief, we observed a gap between the designers' intention (keywords) and the web request results/picture selection. Three of the four designers were not satisfied with the results provided by image-search engine, because they felt the retrieved images did not correctly illustrate the ideas behind the keyword used in their requests. We also notice that the designers adapted their searching strategies to compensate for perceived limitations of the web. For instance, to illustrate a rather abstract idea (Competition), a participant used other keywords that he thought would be more likely to be understood by the web engine (Footwear, then Footwear + Sport, then Footwear + Sport + Design).

Individual strategies based on common design culture -consistent with [START_REF] Visser | Both generic design and different forms of designing[END_REF], we found that the design process comprises commonalities and individual specificities.

Our study demonstrates this in the frame of the information gathering phase. All four designers were provided with the same set of information sources; within these sources, they made some common global selections, for instance, they all rejected VANITY FAIR magazine and they all spent a long time flickering through FRAME magazine. The sectors the designers refer to, in their informational search, were quite similar; all of them were targeting product design sector and architecture sector. While there is a common ground for the inspirational materials retrieval, i.e. common 'sectors of reference', only one image out of the 55 selected out of the magazines was selected by more than one participant. Consistent with this emphasis on individuality are results relating to the types of categories designers created to classify the pictures they found inspirational. These varied from low-level categories (Colours, Textures) to high-level categories (Cool, Simplicity) through sectors names (Architecture, Garage). This classification seemed to be very personal. 'Designer 4' created only 'sectors' categories (Architecture, Product Design) while 'Designer 2' named four among his five categories with high-level descriptions (Cool, Style, Impressions, Atmospheres); 'Designer 1' and 'Designer 3' provided a mixed classification. When asked to illustrate a 'Zidane roadster' with any picture of their choice, all designers first started by giving a car-design reference, respectively, Smart, Renault, BMW Z4 and BMW Z4. Referring to car-design precedents seemed to be a shared characteristic of our participants. However, in the following steps of the assignment participants followed rather individual strategies. For instance, they either tried to illustrate high-level characteristics (Popular, Versatile, Fun) or launched requests about concrete elements (Zidane, BMW Z4, Lotus Exige). The participants performed searching sequences very dissimilar from each other.

To summarise, the participants shared common interest for specific domains (e.g. car design, architecture) and for specific media (e.g. architectural magazines, cardesignnews website) but they followed very individual strategies when they had to search for inspirational pictures (e.g. they used different keywords in the pictures search engines, and they classified magazines images at different abstraction levels).

Designers' Kansei in the informational activity -41.4% of the pictures selected in the magazines were described with lexical terms linked to a feeling or an atmosphere. A significant part of the information gathering phase of the design process is concerned with the feelings of the designer. The designers' feelings relating to the productare possibly integrated in information searches made with traditional tools (printed media) but not fully expressed when surfing the internet. The internet provides images that are mainly described by mid-level descriptors, as if neither detailed enough for providing low-level descriptors (colours, shapes) nor subjective enough for bringing feelings, emotions, or a sensation for atmospheres. From the very first results of our analysis, this might be caused by the images formats (images on the web are often of very small size) and by the images quality (images on the web might not have been taken by professional photographers and might not be displayed correctly). Previous studies showed the importance of designers' subjectivity (kansei) within the design process. Our study specifically demonstrates the importance of designers' kansei in the informational phase, as designers search for inspiration and design information.

Conclusions

This two-part study was performed in a car-design context, yet some generic elements of the results may be useful for all design-related activities that include searching information for design.

First, it seems that there are differences in the way that different media are used in the context of the design process. When designers search for inspirational materials, we observed that they use the internet, in a different way to printed magazines.

Second, there may be limitations in current electronic tools that constrain their use. For example, in the study reported it was apparent that designers altered their requests (the keywords used) to adapt to limitations of the computational tools available. This may be because they were not well suited to designers' requirements for expressing and locating images based on feeling-related concepts that were considered inspirational with regard to the design subject.

Third, today's computational tools could allow more effective control, such that individual differences in information gathering strategy can be more effectively pursued. For example, in this study it was apparent that designers differed in their preference for locating inspirational materials at various levels of abstraction. When browsing images some designers would rather look for 'high level' constructs, such as atmospheres, while others would rather look for low-level constructs such as specific colours or shapes: Computer tools that effectively support this type of flexibility would be advantageous.

In summary, we suggest that designers' creativity will be more efficiently supported by computational tools when these tools take better account of differences in image content as it pertains to the design task. This includes providing search facilities that are more flexible with respect to the specification of level of abstraction in image content and that provide greater emphasis on emotional content. On this basis future research should deal with designers' kansei and creativity, not only in the phases of ideas generation, but in the early information gathering and inspirational phases as well. This challenging topic will impact the way computational tools for creativity support will be developed and provide a better understanding of fruitful sources of information and inspiration.

Figure 1

 1 Figure 1 Booklet sample/'Where do you find sources of inspiration'

Figure 2 Figure 3

 23 Figure 2 Booklet sample/'Where do you find sources of inspiration'

Figure 4

 4 Figure 4 A participant annotating and grouping images (see online version for colours)

Figure 5 Figure 6 Figure 7

 567 Figure 5 Steps of the exploration and categorisation of visual resources

Figure 8

 8 Figure 8 Samples of images from magazines that were found inspirational by designers (see online version for colours)

Figure 9

 9 Figure 9 Description by participants about the only image selected more than once (see online version for colours)

Figure 10

 10 Figure 10 Distribution of the amount of selected pictures with respect to the source magazines (e.g. 29% of the total number of selected images came from 'Frame') (see online version for colours)

Figure 11

 11 Figure 11 Number of retrieved images (magazines/websites) for each source domain (see online version for colours)

Figure 12

 12 Figure 12 Number of retrieved images (magazines/websites) for each abstraction level (see online version for colours)

Table 1

 1 Magazines

	Website Name	URL (all websites version from	Sector
		July 25, 2006)
	Ads of the world adsoftheworld.com	Advertising
	Car Design News www.cardesignnews.com	Automotive Design
	Design Goodness www.frederiksamuel.com/blog/	Design -Advertising
	Design*sponge www.designsponge.blogspot.com	Design
	Inside-photo.com www.inside-photo.com	Architecture
	MoCo Loco	www.mocoloco.com	Product Design
	My Fashion Life www.myfashionlife.com	Fashion and People
	Style 4 Cars	www.style4cars.com	Automotive Design
	Truc design	www.trucdesign.com	Product Design
	Wallpaper*	www.wallpaper.com/architecture	Architecture and Design

and websites provided to the participants for a shuffle exploration Magazine name Issue reference Sector Carl*s Car N° 16 -July 2006 Issue (131 pages) Automotive Design and Lifestyle DAM N° 7 -July/August 2006 Issue (168 pages) Design, Art and Architecture ELLE August 2006 Issue (218 pages) -UK Edition Fashion, Lifestyle and People ESTETICA DESIGN N° 6 -July 2006 Issue (102 pages) Architecture and Interior Design FRAME N° 51 -July/August 2006 Issue (209 pages) Interior Design, Product Design VANITY FAIR August 2006 Issue (148 pages) -UK Edition Fashion, Lifestyle and People

Table 2

 2 Format types for images selected by the participants (over 55 selected pictures) (see online version for colours)

	Format	A4-format picture A4-format	A3-format picture
	Visual information	One single subject More than 1 subject One single subject
	Lexical information No text	Lot of text	No text
	% of this type in	80%	9.1%	10.9%
	the selection
	Example given

Table 5

 5 Definition of abstraction levels

	Abstraction level	Types of features	Examples from our case study
	High	Emotions, atmospheres and feelings	Cool, Provocation
	Mid	Products or sectors	Architecture, Products
	Low	Materials, colours, textures	Colours, Shapes

Acknowledgement

The authors are grateful to the European Commission who supported this research and the related project called TRENDS, through the 6th Framework Program for Information Society Technologies (FP6-27916). They also would like to thank Stile Bertone and FIAT designers for their useful and friendly participation to the experiments.

Image-search constrained by a design brief

Sector of reference: car-designafter having received the design brief, all designers started their search task with a very clear idea of a car-model that would fit the brief requirements. All four designers named car brands or car-models aloud, Smart, Renault and BMW Z4 by two of them. Two participants started the task by sketching the car model they were thinking of (inspired by Smart and by Renault brands) and two others initiated an internet search with requests about BMW Z4. Without any brief, participants tended to look for images that were not specifically related to car-design sector, while with the brief constraint, all participants seemed to head spontaneously toward intradomain sources, in their case: car-design.

Subjectivity integration into web requestthe brief dealt with Zinedine Zidane spirit. In consequence it was expected that designers would try to find pictures to illustrate abstract elements, such as sociological values, emotions or personality features. The key results for this task were twofold: firstly the designers wrote down a list of lexical terms they spontaneously associated with the brief statement, secondly the designers launched internet searches based on the list of words they wrote down. It is interesting to look at the gap between the first ideas that came to the participants' mind right after listening to the brief and the actual results of the internet requests that were meant to illustrate their first ideas. When focusing on the strategy adopted by 'designer 1', we noticed that, after listening to the brief, 'designer 1' wrote down the following words: versatile, accessories, fun, 2-sear car, city, zainetto; he also sketched a zainetto car model. He then started a search with picture-search engines, with a strategy described in Table 6.

Note

1 Some of the pictures were allocated to several categories.


David Gianazza

Jean-Marc Alliot

Optimal combinations of Air Traffic Control sectors using classical and stochastic methods

Keywords: Genetic Algorithm, Branch&Bound, A *, Air Traffic Flow Management, Sector Configuration 1

This paper introduces several algorithms which build optimal configurations of Air Traffic Control sectors, taking into account traffic prediction, sector capacities and the number of available control positions.

Introduction

The first step of the Air Traffic Flow Management (ATFM) process is to define the predicted schedule for each Air Traffic Control Center one or two days ahead. This is done by forecasting the traffic and by comparing this estimation to the available resources, in order to determine what sector configuration would be the most adapted to the predicted traffic and if some overloads can be foreseen.

In Europe, the ACC schedule is elaborated by the Flow Management Position (FMP) of each ATC Center. Some automated tools are available to help the operators to perform this task. For example the French FMP operator can choose a sector configuration among a set of pre-defined configurations, and match it with the traffic demand so that traffic overloads appear immediately. But apart from his own experience, he has no way of knowing if the chosen configuration is the most adequate, or if another one could better balance the traffic between the manned control positions. An additional drawback of the current method is that it is limited to a set of statically defined configurations, which is a fairly small subset of all the possible ways to combine sectors, as we will see later.

The present paper describes two classical tree search algorithms and a genetic algorithm that take as input the traffic flows and build optimal sector configurations considering the airspace capacity constraints and also the maximum number of con-trol positions that can be manned at each time of the day. This optimization is made in a realistic context, using the airspace description data, the traffic data, the number of available control positions, and the sector capacities of the French ATC centers.

Related work

The problem of optimizing sector configurations has already been addressed in [START_REF] Delahaye | Genetic algorithms for automatic regroupement of air traffic control sectors[END_REF], although with a less realistic model, and also in [START_REF] Verlhac | Optimization of opening schemes[END_REF]. In [START_REF] Delahaye | Genetic algorithms for automatic regroupement of air traffic control sectors[END_REF], genetic algorithms were used in a toy ATC network to balance workloads by combining sectors, with a chosen number of control positions. Only convex sectors were considered.

In [START_REF] Verlhac | Optimization of opening schemes[END_REF], integer programming techniques were used in a realistic context to minimize the sum of traffic overloads (called deficits of capacity) by selecting patterns among a reduced set of statically defined configurations. A pattern is a configuration associated to a time period. The number of control positions is an input parameter, as in [START_REF] Delahaye | Genetic algorithms for automatic regroupement of air traffic control sectors[END_REF]. An attempt is made to consider the traffic throughput as a variable, by allowing some macroscopic shifting of traffic loads along the time axis or from a sector to another. The convergence of the iterative algorithm which is used in that case seems not sure. However, the results show significant improvements when compared to the current manual methods.

The optimization problem addressed in the present paper is different : the optimum we are trying to reach is the sector configuration for which the traffic load is as close as possible to the capacity of each sector or group of sectors of the configuration, so traffic overloads as well as traffic under-loads are considered. The search of an optimal configuration is not restricted to a subset of manually entered configurations, but explores the whole set of possible configurations which can be obtained by combining operational ATC sectors. The number of control positions is a variable of the cost function we are trying to minimize, constrained by an upper limit as there may not always be enough ATC controllers to man all the positions that would be needed.

Model

A "good" configuration is a configuration for which there are no traffic overloads (or the smallest possible ones), and for which the traffic load is balanced as well as possible between the manned control positions, while arming the minimum number of positions. Let us formulate this as a minimization problem.

Let us define the function ∆ by

∆(x, t) = workload(x, t) -capacity(x, t)
where x is a sector or group of sectors, t is the time, workload is the traffic load (for example N aircraft entering sector x between t and t + w, where w is a chosen time window), and capacity is the threshold value for the workload. The capacity of each sector or group of sectors may also depend on specific criterions (like military activity...). The operator may allow some tolerances around the value of the capacity. These lower and upper tolerances l and u are taken into account in the evaluation of a configuration. For this, we will need to define the overloads and underloads as follows :

∆ ++ (x, t) = ∆(x, t) if ∆(x, t) > u 0 otherwise ∆ + (x, t) = ∆(x, t) if 0 ≤ ∆(x, t) ≤ u 0 otherwise ∆ -(x, t) = |∆(x, t)| if l ≤ ∆(x, t) ≤ 0 0 otherwise ∆ --(x, t) = |∆(x, t)| if ∆(x, t) < l 0 otherwise
Let us then define the following functions :

N pos (t) the number of control positions in the configuration

C ++ (t) = x∈conf ig (∆ ++ (x, t)) 2 C + (t) = x∈conf ig ∆ + (x, t) C -(t) = x∈conf ig ∆ -(x, t) C --(t) = x∈conf ig (∆ --(x, t)) 2
The problem will then consist in minimizing the following cost function :

cost conf ig = a.C ++ +b.N pos +c.C --+d.(C + +C -)
(1) while respecting the constraint : N pos (t) ≤ M pos (t) where a, b, c, and d chosen factors of decreasing value and M pos is the maximum number of control positions available at each time of the day.

Instead of minimizing cost conf ig , and in order to take better account of the relative weights of the different costs, we will in fact maximize eval conf ig , such that the k 1 most significant digits of eval conf ig (x, t) refer to the cost C ++ , the next k 2 digits refer to N pos , and so on:

xxxxx k 1 xx k 2 xxxxx k 3 xxx k 4 eval conf ig = 10 k 2 +k 3 +k 4 × N (k 1 , C ++ ) +10 k 3 +k 4 × N (k 2 , N pos ) +10 k 4 × N (k 3 , C --) +N (k 4 , C + + C -) (2
) where N is a function such that

N (k i , C) = max(0, (10 k i -1) -C)
and k 1 , k 2 , k 3 , and k 4 are chosen such that (10 k i -1) is an upper bound of the corresponding cost, if possible.

Problem complexity

The difficulty of the problem is mostly due to the high number of possible configurations which can be built from a set of sectors. A configuration is the mapping of n sectors onto k control positions.

Let us first try to find how many ways there are to part a set of n elements into k subsets. If P (n, k) is this number, it verifies the following equations :

∀n ≥ 1 P (n, 1) = 1 (one group of n elements) P (n, n) = 1
(one partition of n groups of one element)

P (n, k) = 0 if k > n (we cannot make more than n groups) P (n, k) = k * P (n -1, k) + P (n -1, k -1) if 1 < k < n
The number of all possible partitions will then be P (n) = n k=1 P (n, k). For 17 sectors (Brest ATCC), this would give around 83 billion possibilities. However, this value is not realistic : many of the partitions could not be used in an operational context. For example, a partition containing a group in which one sector is a neighbor of no other sector in the group is not a valid configuration. The set of all possible partitions (that we have counted above) could theoretically be obtained by exploring the tree of all possibilities , although this would become quickly impractical when the number of sector increases.

In order to estimate the difficulty of the real problem, let us consider only the operational sectors and groups of sectors defined in each ACC database. We will obtain all operational configurations by exploring a tree which nodes are lists of couples (g, G) (cf figure 1 illustrating the Branch&Bound), where g is a group under construction and G is the set of valid groups compatible with g in the context of the configuration under construction. An element h of G is "compatible" with g if it contains all the sectors of g, but no sector of the other groups in the configuration (the other "g"'s of the node). If one of the G sets is empty, then there is no need to continue the search from the considered node : it will lead to no valid configuration. The methods presented above allow us to count the number of configurations and estimate the difficulty of the problem. The results for the French ATC centers are shown in table 1, which highlights the combinatorial relation between the number of partitions and the number of sectors.

The number of operational configurations which we can build with the sectors or groups of sectors described in the ATCCs airspace data goes from a few hundreds to a half million. So, we can expect that the use of exhaustive tree search techniques will lead to optimal configurations within a reasonable computation time, at least for relatively small ATC centers and with sector combinations restricted to the groups described in the ATCCs airspace data. However, as the sector configuration optimization problem may be extended to larger ATCCs, and as we may wish to use a wider range of sector combinations, genetic algorithms were also experimented to solve the problem.

Classical algorithms

A basic algorithm: In the previous section, we have mentioned an algorithm which builds all the possible operational configurations.

A basic optimization method consists in evaluating the cost (cf definition 1) of each configuration in order to find the best one. The basic algorithm explores all the configurations. It is memory and time consuming, but complete : we can be sure that it returns the optimum of the evaluation function. So it will be used as a reference for the other algorithms presented hereafter. & bound algorithm illustrated in figure 1 is to avoid exploring every branch of the tree. To do so, it needs to evaluate the nodes in order to decide, by comparison with the best configuration found so far, whether to continue or not the search along a given branch. The cost (resp. evaluation) of a node must be a lower bound (resp. an upper bound) of all the costs (resp. evaluations) of configurations which can be reached from that node. A node of our tree search algorithm is a configuration under construction (see figure 1), i.e. a list of couples (g, G), where g is a group under construction and G is the set of valid groups compatible with g in the context of the configuration under construction.

For a better understanding of this notion of compatibility, let us consider node 6 of the example shown in figure 1. This node is represented by : ({1}, {s, d}) ({2}, {s, a}).

The valid groups compatibles with the group under construction {1} are the singleton s, which is {1}, and the group d = {1, 5}. These groups are the only ones which contain {1} but not {2}.

The cost function for a node is similar to the cost of a configuration. Let us define a function best such that best(G) returns the element h (a sector or group of sectors) of G, for which the difference workload(h, t)capacity(h, t) is the smallest possible underload, or the smallest possible overload if all groups of G are overloaded. We will then define the cost (resp. evaluation) of a node as in definition 1 (resp. 2), except that N pos will be the number of couples (g, G) in the node, and that only ∆ ++ and ∆ + will be considered, taking best(G) as input instead of an operational sector x of a configuration.

An algorithm inspired from A * : Like the Branch & bound, the A * is a tree search algorithm. However, instead of simply storing the best leaf found so far, all the explored nodes are stored and sorted by valuation.

In order to do so, the A * as described in [START_REF] Pearl | Heuristics[END_REF] needs a cost function defining the cost of each state transition, and a function (called heuristic) underestimating the cost of the remaining transitions between the current node and the end of the search.

For our sector configuration problem, we will try to minimize the cost conf ig function described in definition 1, by searching a path in the tree illustrated in figure 1. But instead of comparing the node evaluation with the evaluation of the best configuration found so far like in figure 1, the nodes already explored are stored into a priority queue sorted according to the node eval-uation. The A * will then iteratively consider the node with lowest cost, evaluate its children nodes and insert them in the priority queue, until a leaf of the tree is reached. This leaf is then the optimal sector configuration. The evaluation of a configuration and a node is the same as in 1 and the Branch & bound algorithm respectively.

Genetic algorithm

A genetic algorithm has also been tested to solve the sector configuration problem. The genetic algorithm considers a population of chromosomes, which evolves by crossover, mutation, and selection of the fittest individuals, as described in [START_REF] Goldberg | Genetic Algorithms[END_REF] and [START_REF] Michalewicz | Genetic algo-rithms+data structures=evolution programs[END_REF].

A chromosome will be a sector configuration. Each chromosome is composed of several genes. A gene is either an elementary sector or a group of sectors. A fitness value is assigned to each chromosome. The raw fitness f of a configuration will be given by eval conf ig (see definition 2).

A clusterized sharing operator is applied to the raw fitnesses. The aim of sharing is to avoid that a chromosome with a good fitness reproduces itself to the detriment of the other chromosomes, thus narrowing the search to a single optimal or suboptimal mode. The chromosomes clustering of this sharing operator is based on distance criteria. For our problem, the difficulty to implement sharing lies in the definition of a "distance" between sector configurations. Like the distance of Hamming which uses the number of genes that differ between two chromosomes, the pseudo-distance that was chosen for our problem is based on a gene comparison, except that the two chromosomes may not have the same number of genes. Let n i (respectively n j ) be the number of genes of the chromosome i (respectively j). The chosen pseudo-distance is defined by d(i, j) = min(n i , n j )n where n is the number of identical genes between the two chromosomes. In addition to the sharing operator, a scaling operator (sigma truncation) is applied, in order to smooth the differences between fitnesses of good chromosomes and bad ones. This way, the selection will let a better chance to bad chromosomes to reproduce themselves, and the domain will be more widely explored.

The crossover operator splits the two parent configurations and completes each half configuration with the other parent's genes. The resulting incomplete chromosome is then completed with valid groups or sectors. A local fitness is associated to each gene in order to select the parents genes in decreasing order of local fitness. It was shown in [START_REF] Durand | Genetic crossover operator for partially separable functions[END_REF] that an adapted crossover operator using local fitnesses increases the convergence rate for the optimization of partially separable functions. In our problem, the local fitness is similar to the raw fitness of the chromosome, although it takes account of the overloads and underloads of a single gene. The mutation operator first randomly chooses one gene of the chromosome. Another gene is randomly chosen among a list comprising the first chosen gene and its neighbors (sectors or groups of sectors of the configuration which have a common border with the first chosen sector or group of sector). The sectors of the chosen genes are then recombined into one or several new genes (up to three). The splitting of a single group would allow only mutations towards less loaded configurations with an increasing number of control positions, whereas the recombination of two neighbors may lead to configurations with less items, which may be interesting when the traffic is low.

Results

A graphical interface has been developed to display the results of the optimizations. The languages Ocaml and OcamlTk were used to code respectively the algorithms and the interface. The program runs on a PC Pentium IV (1.8 GHz), with Linux as operating system.

The input parameters are the date, the selected ATCC, the type of traffic (raw demand, final demand...), the capacity tolerances, the maximum number of available control positions, the chosen time step and time horizon (for the computation of traffic flows). The program displays an optimized sector configuration for each time subdivision of the day. The color code is : Green (grey) when the traffic load is under the capacity minus the lower tolerance for the capacity ; Yellow (white) when the traffic load is between the margins of tolerance ; Red (dark grey) when the traffic load is over the capacity plus the upper tolerance.

The upper part of figure 2 shows the result of the optimization for Bordeaux ATCC, with the raw traffic demand and with no constraint on the available number of control positions. In this case, the remaining overloaded sectors are necessarily elementary sectors, or operational groups which cannot be split (some elementary sectors are defined and used only to improve flexibility by choosing different ways to combine two of them into an operational group).

The lower part of figure 2 shows the same optimization but with constraints on the available number of positions. These constraints are taken into account in the evaluation functions by dividing by two the evaluation when the number of control positions in the configuration is greater than the available maximum, thus penalizing these configurations. The constraints used in the right part of figure 2 are directly issued from the ACC schedule that was sent to the CFMU by Bordeaux FMP for that day. These constraints induce additional overloads (like between 4 and 5 o'clock in the example) on combined sectors which the al-gorithms are unable to split because there are not enough available control positions.

By comparing the two schedules we see that Bordeaux ATCC was under-capacitive in the early morning, and over-capacitive at other times of the day.

The tree search algorithms provide optimal sector configurations for each ATCCs, verified with the basic algorithm when possible (for Brest, Paris and Reims ATCCs). The table 2 shows the computation times for these algorithms, with the raw traffic demand and no constraint on the number of maximum positions. Although there are more possible configurations for Bordeaux ATCC than for Aix ATCC (see table 1 about the problem complexity), the computation time for Aix ATCC is higher than for Bordeaux as there are more sectors in Aix than in Bordeaux. The tree of all possible configurations is searched "depth first", and the depth depends on the number of sectors.

For the genetic algorithm, 10 different values of the random seed were tested for Bordeaux ATCC, with a crossover probability of 0.6 and a mutation probability of 0.2. Table 3 shows for each time step of the day the number of configurations which where different from the optimum. The lines labelled (+1) show the number of occurrences when there was exactly one more control position in the configuration found by the GA than in the optimal configuration. The lines labelled (> +1) show the number of occurrences when the difference was greater than one control position.

When they were not optimal, the solutions found were qualitatively close to the optimum.

The genetic algorithm is slower than the tree search methods, but provides several optimal or near-optimal solutions. It is not very significant

Step 0 1 2 3 4 5 6 7 8 9 10 11 220 gen. fails 0 0 0 0 0 0 0 0 2 0 1 5 120 elem. +1 0 0 0 0 0 0 0 0 0 0 0 2 > +1 0 0 0 0 0 0 0 0 0 0 0 0 220 gen. fails 0 0 0 0 0 0 0 0 3 0 0 3 130 elem. +1 0 0 0 0 0 0 0 0 0 0 0 1 > +1 0 0 0 0 0 0 0 0 0 0 0 1 300 gen. fails 0 0 0 0 0 0 0 0 0 0 0 0 220 elem. +1 0 0 0 0 0 0 0 0 0 0 0 0 > +1 0 0 0 0 0 0 0 0 0 0 0 0 Step 12 13 14 15 16 17 18 19 20 21 22 23 220 gen. fails 2 0 1 3 0 1 0 0 1 0 0 0 120 elem. +1 0 0 1 0 0 1 0 0 1 0 0 0 > +1 0 0 0 0 0 0 0 0 0 0 0 0 220 gen. fails 3 0 2 2 0 0 0 0 1 0 0 0 130 elem. +1 0 0 2 0 0 0 0 0 1 0 0 0 > +1 0 0 0 0 0 0 0 0 0 0 0 0 300 gen. fails 0 0 1 0 0 0 0 0 0 0 0 0 220 elem. +1 0 0 0 0 0 0 0 0 0 0 0 0 > +1 0 0 0 0 0 0 0 0 0 0 0 0 Table 3: GA results for Bordeaux ATCC to compare the overall computation times of the genetic algorithm and the tree search algorithm when the minimization problem is easily solved. In such cases (at night for example), the genetic algorithm will run the same number of generations whatever the difficulty of the problem, whereas the B&B will find an optimal solution among the first branches it explores. Table 4 compares for Bordeaux ATCC the computation times of each time step between 5 a.m and 7 p.m., for 220 generations and a population size of 120 configurations:

Step

Conclusion

The tree search algorithms as well as the genetic algorithm provide optimal sector configurations, using the same parameters and constraints than in the current FMP/CFMU process. The results are computed in a time short enough for an operational use. The tree search algorithms are faster than the genetic algorithm when applied to the French ATC centers and while restricting the ways to group sectors to a set of operational groups (issued from each ATCC airspace description database).

However, the combinatorial relation that we have shown between the number of sectors and the number of partitions and configurations is such that the tree search algorithms may prove impractical in the context of larger ATC Centers or if a wider set of operational groups is used. In such a context, the genetic algorithm is a good alternative. It provides several optimal or near-optimal configurations in a chosen computation time.

So far, we have considered the sector configuration optimization only in the context of the pre-tactical ACC schedule estimation, based on the traffic flows and the capacity constraints. The proposed algorithms could as well be envisioned, with adapted workload and constraints definitions, to tactically propose sector configurations to control room managers.

Figure 1 :

 1 Figure 1: Branch & bound search for an optimal sector configuration

Figure 2 :

 2 Figure 2: Optimal sector configurations with (up) or without (down) constraints on the number of available positions (example of Bordeaux ACC)

Table 1 :

 1 Number of possible sector configurations for the French ATCCs (in 1999)

		Number of sectors Number of Number of
		elem.	groups	partitions	configs
	Aix	24	42	4.4610 17	123,965
	Bordeaux	22	65	4.4510 15	551,032
	Brest	17	52	8.2810 10	14,832
	Paris (West) 11	17	678,570	192
	Paris (East)	12	22	4,213,597	399
	Reims	12	17	4,213,597	249

Table 2 :

 2 The fastest is the branch & bound. The A * is slower because the chosen heuristic is not a very good estimate of what it really costs to reach the best configuration achievable from a given node, thus inducing high backtracking. Computation times (in seconds) for the deterministic algorithms

		Aix	Bord.	Brest	Paris(E) Paris(W)	Reims
	Basique	n.t.	n.t.	14.44	0.06	0.03	0.02
	B&B	34.06	6.06	1.45	0.08	0.07	0.04
	A *	134.88	10.12	10.05	0.08	0.04	0.02

Table 4 :

 4 .21 0.66 0.59 0.58 0.35 0.56 GA 16.42 15.62 17.41 16.85 15.65 14.98 13.70 GA and B&B detailed computation times for Bordeaux ATCC

	5	6	7	8	9	10	11
	B&B 0.23 0.05 0.17 0.55 0.95 0.21 0.38
	GA 15.69 14.88 17.19 16.08 15.37 15.80 15.75
	Step 12	13	14	15	16	17	18
	B&B 0.54 0


Andrzej Łapiński
email: lapinski@ifmpan.poznan.pl

Damian Jankowski

Roman Swietlik

Eric W Reinheimer

Roman Świetlik

Marc Fourmigué

Electron-molecular vibration coupling in (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ] salts studied by vibrational spectroscopy

Keywords: DMtTTF and DMTTF salts, IR and Raman spectroscopy, electron-molecular vibration (EMV) coupling effect, dimer model -----------

come

Electron-molecular vibration coupling in (DMtTTF)Br and (o-DMTTF)2[W6O19] salts studied by vibrational spectroscopy

Introduction

Within the field of organic conductors, it was very early realized that electrons in these materials couple strongly with intramolecular vibrations. This interaction is very important for understanding the physical properties of these systems which can display both activated and non-activated conductivity as well as superconductivity [1]. Infrared (IR) spectroscopy is a powerful method whereby molecular parameters, such as the EMV coupling constants, might be determined [2][3][4].

The first experimental determination of the EMV coupling constants was performed on quasi-one-dimensional conductors containing the organic donor TCNQ (TCNQ = tetracyanoquinodimethane). For TCNQ salts possessing uniform or dimerized stacks, the phase phonon or isolated dimer models respectively were successfully applied in order to estimate the EMV coupling constants [5][6][7][8]. Originally developed for the salt K-TCNQ, with its well-isolated (TCNQ) 2 2-dimers, the latter isolated dimer model provided a means by which the experimental determination of the coupling constants in this material could be achieved [7]. In addition to doubly-charged TCNQ dimers, the model also found utility in salts having TCNQ dimers containing one electron as the totally symmetric TCNQ vibrations were found to couple to the charge transfer between the charged and neutral molecules [9].

Subsequently, the isolated cluster model was also successfully applied to systems having greater than two TCNQ molecules [10][11][12]. Fitting the IR spectra of various TCNQ salts via multiple models afforded the unique opportunity to experimentally determine fundamental molecular parameters such as the EMV coupling constants and compare them to those obtained through theoretical calculations [13].

As mentioned above, models of EMV coupling are universal and were successfully applied to IR spectra of charge-transfer salts formed by TTF (TTF = tetrathiafulvalene) and its derivatives with various acceptors [14]. More specifically, the dimer model has proven especially useful in determining the coupling constants for charge transfer materials containing TTF derivatives. For example, reliable values for the EMV constants were obtained for the salt (BEDT-TTF) 2 [Mo 6 O 19 ] (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) which contained well-isolated (BEDT-TTF + ) 2 2+ dimers [15].

According to symmetry considerations, in linear approximation for non-degenerated molecular orbital only the totally symmetric vibrational modes can couple with electrons [6,[16][17]. For other symmetry modes, the electron-vibrational interaction is forbidden by the selection rules and is only correct if the molecules within the dimer have the same symmetry [16]. When considering the dimer, where the molecules are asymmetric with respect to one another, if those molecules are different or inequivalent, their modes are no longer degenerate and couple both in-phase and out-of-phase. In this case, the lack of an inversion center suppresses the mutual exclusion rule leading to all of the modes for the constituent molecules within the dimer becoming both IR and Raman active. Additionally, all of their symmetric modes can then couple to the CT electron [18]. Moreover, if we consider the sufficiently fast charge transfer between the dimer molecules due to electromagnetic radiation, their nuclear configurations do not have time to change in response to the charge transfer and their molecular vibrations arise as the result of the relaxation to each molecule's respective equilibrium configuration. In this case, the symmetry type of the arising vibrational modes depends not only on the final and initial state symmetries, but also on that of the intermediate states from which the transferred charge among the neighboring molecules belongs. These facts suggest that in some cases non-totally symmetric modes can be also coupled [19].

Herein, we describe a new 1:1 charge transfer salt formed via electrochemical oxidation of the unsymmetrical donor DMtTTF (Scheme 1) in the presence of Br -anions.

Within the structure of this salt, the donors are arranged into well-isolated (DMtTTF + ) 2

2+

dimers intimating that the dimer model for EMV coupling should be very well applicable.

Subsequently, we also used the dimer model for fitting the IR spectrum of the (o- 25. The low-frequency data were extrapolated to zero frequency assuming a constant value. For frequency values above the highest point, the reflectance data were approximated by R~ω -2 while those above 10 6 cm -1 by R~ω -4 . Single crystal Raman spectra of (DMtTTF)Br were measured in a backward scattering geometry using Labram HR Horiba Jobin Yvon with a He-Ne laser ( exc = 632.8 nm). The Raman spectra were recorded in the frequency range 150 -3500 cm -1 with a spectral resolution better than 2 cm -1 . In order to avoid sample overheating, the power of the laser beam was reduced to ~0.1 mW.

The quantum chemical calculations of the DMtTTT •+ and o-DMTTF •+ cations were carried out using the Gaussian 03 program with the 6-311++G(d,p) basis set [START_REF] Gaussian | Gaussian[END_REF]. The hybrid gradient-corrected exchange functional proposed by Becke was combined with the gradientcorrected correlation functional of Lee, Yang, and Parr [START_REF] Becke | [END_REF][29]. The initial geometry in the optimization process was taken from X-ray data. The geometries of the radical cations were fully optimized at the B3LYP/6-311++G(d,p) level of theory and those structures were checked by analysis of the harmonic vibrational frequencies to verify whether they are at minima, saddle points or stationary points of higher orders. Only positive eigenvalues of the Hessian matrix were obtained, proving that the calculated geometry was at a minimum on the potential energy surface. DFT orbitals were obtained by solving the Kohn-Sham equation which included both exchange and correlation terms. Recently, a normal mode analysis for neutral DMtTTT and o-DMTTF molecules as well as their cations was already performed [START_REF] Gaussian | Gaussian[END_REF]29].

Results and Discussion

Crystal structures of (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ]

The crystal structure data for the 1:1 salt (DMtTTF)Br collected at room temperature is presented in Table I. This salt crystallizes in the monoclinic pace group P2 1 /c and contains both cations and anions on general positions. As shown in Figure 1, the oxidized molecules are organized into strongly-dimerized chains with very short intradimer S•••S contacts at 3.386(7) and 3.502(7) Å, while the contacts between the sulfur atoms within their interdimer analogues exceeds 3.9 Å. Furthermore, the stacks are oriented perpendicular to each other, an orientation similar to those observed in TMTTF salts that prohibits any sizeable lateral S•••S contacts. In addition, no C-H•••Br hydrogen bonds were observed upon closer inspection. As a result of these structural features, the (DMtTTF) 2 2+ dimers can be considered well-isolated from one another and that the unpaired electrons are strongly localized within the dimeric unit. The intramolecular bond lengths for the TTF core of the DMtTTF [20]. In this salt, the donor molecules aggregate in a head-to-tail manner, forming strong faceto-face doubly charged (o-DMTTF + ) 2 2+ dimers that lie nearly parallel to the ab plane (see Fig. 2). Given the size of the [W 6 O 19 ] 2-anion within the structure, the dimers are effectively well isolated from one another in the solid state. The detailed X-ray structural analysis, including a description of its array of hydrogen bonding interactions, was discussed in Ref. 20.

Raman and IR spectra

The single crystal Raman spectrum for (DMtTTF)Br is shown in Fig. 3. Within the region of C=C stretching, one observes three bands at 1412, 1507, and 1587 cm -1 assigned to the stretching of the central C=C bond, and the out-of-phase and in-phase stretching of the ring bonds, respectively. As DMtTTF has no center of symmetry, the mode related to the outof-phase C=C ring stretching can be viewed in the Raman spectrum. Other bands are assigned as follows: 1034 and 933 cm -1 (CH 3 wagging), 960 cm -1 (C-S and C-C stretching), 510 and 451 cm -1 (in-phase and out-of-phase fulvalene ring breathing) and 221 cm -1 (deformation).

Single crystal IR reflectance spectra of the (DMtTTF)Br salt for two polarizations (parallel and perpendicular to the a-axis) are displayed in Fig. 4a. Within these spectra, we observe a strong electronic absorption centred at ~7700 cm -1 assigned to the charge transfer transition between the fully ionized DMtTTF •+ molecules and an intense narrow vibrational feature at ~1338 cm -1 assigned to the electron-molecular vibration (EMV) coupling of the C=C stretching mode with the charge transfer transition at 7700 cm -1 . It has been well established in spectroscopic studies on TTF derivatives that the largest EMV coupling constants are attributed to coupling with the central C=C bond stretching vibration. As the band at 1338 cm - 1 constituted the largest such vibrational feature based on magnitude, it was assigned to this coupling mode; however in comparison with the Raman data it is shifted towards lower wavenumbers by ~74 cm -1 due to this strong coupling. It is also important to note that within the IR spectrum, at the E//a orientation, we also observed smaller vibrational features at 1436 and 1498 cm -1 corresponding to the electron-molecular vibration (EMV) coupling of the C=C ring anti-phase and in-phase stretching, respectively

The IR reflectance spectra of (o-DMTTF) 2 [W 6 O 19 ] single crystals show also a clear evidence of interaction with the charge transfer transition at ~10250 cm -1 (Fig. 4b): within the region of C=C stretching we observe a strong vibrational feature at 1345 cm -1 as well as much weaker bands at 1465 and 1553 cm -1 , which correspond to the C=C central, and C=C ring anti-phase and in-phase stretching modes respectively (see Fig. 6). It is important to note that by comparison, the charge transfer band of (o-DMTTF) 2 [W 6 O 19 ] lies at much higher energy than its analogue within (DMtTTF)Br. The energy of this transition is proportional to the onsite repulsion energy between two charges (Hubbard U parameter). By a first approximation, the higher energy of the transition, in comparison to other TTF derivatives, could be associated with a larger U. However, it is also possible that the presence of hydrogen bonding between the donors and the anions is also having an effect. For the Raman spectrum of (o-DMTTF) 2 [W 6 O 19 ], within the region of C=C stretching vibrations, three bands at 1417 cm -1 , 1483, and 1556 cm -1 were found and assigned to the stretching of central C=C bond, as well as the out-of-phase and in-phase stretching of ring bonds respectively [20].

In the investigated salts, the shifting of vibrational bands toward lower wavenumbers with respect to the Raman data and, moreover, with a characteristic antiresonance dip, provide evidence of their interaction with the charge transfer transition. This effect is quite visible for (DMtTTF)Br salt where antiresonance dip at 1326 cm -1 was noted (see Fig. 5); the band at 1338 cm -1 displays a characteristics reminiscent of an asymmetric Fano lineshape [30]. When the electric field is polarized along a chain of molecules, the interaction between the electronic absorption and phonon frequencies gives rise to an asymmetric Fano lineshape of bands [30]. The analysis of the Fano-effect, in conjunction with the Raman data, can lead to quantitative predictions for the various electron phonon couplings [31].

Calculation of EMV coupling constants

Much like the IR spectra for the recently published (o-DMTTF) 2 [W 6 O 19 ] whose structure contained quasi-isolated dimers [20], the IR spectra for (DMtTTF)Br can also be analyzed in terms of the isolated dimer model. For both salts, due to the coupling, the vibrational modes borrow intensity from the nearby CT electronic transition and occur at frequencies lower than their corresponding Raman bands. The IR spectra of the investigated salts are dominated by the occurrence of very strong electronic bands (CT transitions) that are polarized perpendicularly to the molecular planes.

Using the Rice's model for both compounds, we calculated the frequency-dependent conductivity for the isolated dimer [8]. For the electronic part we have only considered the ground and charge-transfer states, disregarding the presence of excitonic intramolecular states. Furthermore, the coupling between electrons and the molecular vibrations is assumed to occur through the phononic modulation of the on-site energy. Using linear-response theory, the frequency-dependent conductivity in the direction of the CT transition is given by the formula [8] ( ):

1                     D V N a e i 1 4 2 2    ( 1
)
where e is the electronic charge, a the intradimer distance, N/V the number of dimers per unit volume,

    e CT CT i c          2 2 2 1 8
the CT electronic susceptibility and

      0 ~     
its reduced form; c 1 is the expansion coefficient of the eigenstate. The EMV coupled phonons are described by the phonon propagator:

                   i D 2 2 2 (2)
where ω α and γ α are the frequencies and natural widths of the uncoupled modes. The constant λ α is a dimensionless coupling constant related to the electron-molecular vibration (e-mv) coupling constant g α by

      CT g c 2 2 1 8  (3)
The real part of the scalar conductivity σ(ω) yields the CT excitation spectrum of the ionradical dimer, which consists of the primary CT excitation mode and a series of absorption bands in the region of the molecular frequencies {ω α }. The latter are oscillations in the radical electron dipole moment driven by the antisymmetric vibrational modes q α [8]. In order to obtain the microscopic parameters for the dimer, we have fitted Re the same frequency within their spectra. However, given that those bands might be influenced by the presence and magnitude of on-site Coulombic interactions, the actual frequencies for their charge transfer bands can be quite different [34]. For (o-DMTTF) 2 [W 6 O 19 ], observed at 10250 cm -1 is comparable to those found for salts based on DOEO [25], M(dddt) 2 (M=Pd II , Pt II and Ni II [35][36][37] and BEDT-TTF [25,[35][36][37][38][39][40]. Meanwhile, the considerably lower value of 7700 cm -1 , observed in (DMtTTF)Br, is akin to those measured in Ni(dmit) 2 and selected BEDT-TTF salts [41][42][43].

In order to investigate the differences between CT bands, we computed the highest occupied molecular orbitals (HOMO) for the DMtTTF •+ and o-DMTTF •+ radical cations. is not only responsible for different intradimer distances but also the position of chargetransfer band. For example, it is well known that strong anion-donor interaction can induce a shift of π-hole density and thus contribute to charge ordering effects in organic conductors based on TTF derivatives [44]. Therefore, it is possible that the charge density distribution on the o-DMTTF •+ radicals in (o-DMTTF) 2 [W 6 O 19 ] can be strongly affected by hydrogen bonding and that the evaluated molecular parameters for o-DMTTF •+ cations can be distorted by the anion-donor interaction. Additionally, on the basis of the DFT calculations, we observed that even for isolated o-DMTTF •+ cations, a large amount of positive charge is transferred from the TTF core to the outer part of the molecule (see Table V). This may in turn also influence the position of charge-transfer band, i.e. yield a shift toward higher frequencies.

Conclusions

In this paper, we have presented and discussed the infrared spectra of two recently

Table IV

The EMV coupling constants, g α (meV) of the C=C stretching modes ω (cm -1 ) for several TTF-based radical cations.

DMTTF) 2 [Scheme 1 .

 21 Scheme 1. Molecular structure of the DMtTTF and o-DMTTF donors In the IR spectra for salts formed by unsymmetrical TTF derivatives such as o-DMTTF, DMtTTF, EDO-TTF, and DOEO, one observes vibrational features suggestive of EMV coupling to intramolecular vibrations of donors, especially those related to C=C

  [σ(ω)] to the experimental spectra of (DMtTTF)Br and (o-DMTTF) 2 [W 6O 19 ]. Figures5 and 6show the conductivity spectra obtained by a Kramers-Kronig transformation of the experimental reflectance spectra (upper panels) and the conductivity spectra calculated within the framework of the dimer model (lower panels). In Table3, the model parameters for the fit to the E//a conductivity spectra of (DMtTTF)Br and (o-DMTTF) 2 [W 6O 19 ] are presented and illustrate that the coupling constants for all three C=C stretching modes were evaluated. In Table4, one can see that EMV coupling constants for TTF and its derivatives BEDT-TTF, DOEO (DOEO =(1,4dioxane-diyl-2,3-ditio)ethylenedioxytetrathiafulvalene), TMTTF (TMTTF = tetramethlytetrathiafulvalene) and TTP (TTF = bis-fused TTF) compare closely to those determined for DMtTTF and o-DMTTF [2,3,15,25,32,33]. One can also see that the most strongly coupled modes are those assigned to vibrations of the TTF skeleton, i.e. the modes related to the stretching vibrations of both central and ring C=C bonds. From the frequency and intensity of the CT transition we can also extract the values of the intradimer transfer integral t and the effective Hubbard energy U eff . For (DMtTTF)Br, we find t = 0.358 eV and U eff = 0.418 eV, while for (o-DMTTF) 2 [W 6 O 19 ] t = 0.307 eV and U eff = 0.974 eV. As mentioned previously, the charge transfer band in (o-DMTTF) 2 [W 6 O 19 ] lies at larger frequency than that observed for (DMtTTF)Br, a fact that has an important consequence for both the U eff and EMV coupling parameters. When considering salts based on TTF derivatives, one might expect their charge transfer bands related to intermolecular electronic transitions between neighboring fully charged molecules occur at approximately

Figure

  Figure 7a reveals that the electron density distribution on atoms within the HOMO is

  synthesized charge-transfer salts (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ] in which the donors form strongly dimerized stacks isolated from each other due to effective separation by their co-crystallized anions. Analysis of their IR and Raman spectra allowed us to obtain important information regarding their electronic and vibrational structure. Spectral features related to the electron-molecular vibration-coupling phenomena were analyzed in terms of the model for isolated doubly charged dimers and suitable coupling constants were estimated. The values of coupling constants obtained for (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ] salts are comparable to those obtained for other TTF derivatives. We have shown that the most strongly coupled modes are due to the stretching vibrations of both central and ring C=C bonds. Nevertheless, in the case of (o-DMTTF) 2 [W 6 O 19 ], the evaluated parameters can be distorted by hydrogen bonding interactions between the o-DMTTF •+ radicals and the [W 6 O 19 ] 2-anions.

Figure captions Figure 1 .

 captions1 Figure captions Figure 1. Structure of (DMtTTF)Br: (a) projection view of the unit cell along the a axis, showing the absence of inter-stack interactions and (b) side view of the strongly dimerized stacks running along the a-axis.

Figure 2 .

 2 Figure 2. Crystal structure of (o-DMTTF) 2 [W 6 O 19 ].

Figure 3 .

 3 Figure 3. Raman spectrum of the 1:1 salt (DMtTTF)Br recorded for the electrical vector of

Figure 4 .

 4 Figure 4. Room temperature reflectance spectra of (DMtTTF)Br (a) and (o-DMTTF) 2 [W 6 O 19 ] (b) salts recorded for polarization parallel (E//a) and perpendicular (Ea) to the stacking a-

Figure 5 .

 5 Figure 5. Experimental and calculated conductivity spectra of (DMtTTF)Br salt. Note that the electric vector is parallel to the stacking axis and the logarithmic wavenumber scale.

Figure 6 .

 6 Figure 6. Experimental and calculated conductivity spectra of (o-DMTTF) 2 [W 6 O 19 ] salt. Note that the electric vector is parallel to the stacking axis and the logarithmic wavenumber scale.

Figure 7 .

 7 Figure 7. Sketch of the HOMO orbital of the DMtTTF •+ and DMTTF •+ cations computed at the B3LYP/6-311++G(d,p) level of theory (a). Packing arrangements within the stacks observed for the (o-DMTTF) 2 [W 6 O 19 ] and (DMtTTF)Br salts (b).

Figure 1 .

 1 Figure 1. Structure of (DMtTTF)Br: (a) projection view of the unit cell along the a axis, showing the absence of inter-stack interactions and (b) side view of the strongly dimerized stacks running along the a-axis.

Figure 2 .

 2 Figure 2. Crystal structure of (o-DMTTF) 2 [W 6 O 19 ].

Figure 3 .

 3 Figure 3. Raman spectrum of the 1:1 salt (DMtTTF)Br recorded for the electrical vector of

Figure 4 .

 4 Figure 4. Room temperature reflectance spectra of (DMtTTF)Br (a) and (o-DMTTF) 2 [W 6 O 19 ] (b) salts recorded for polarization parallel (E//a) and perpendicular (Ea) to the stacking a-

Figure 5 .

 5 Figure 5. Experimental and calculated conductivity spectra of (DMtTTF)Br salt. Note that the electric vector is parallel to the stacking axis and the logarithmic wavenumber scale.

Figure 6 .

 6 Figure 6. Experimental and calculated conductivity spectra of (o-DMTTF) 2 [W 6 O 19 ] salt. Note that the electric vector is parallel to the stacking axis and the logarithmic wavenumber scale.

Figure 7 .

 7 Figure 7. Sketch of the HOMO orbital of the DMtTTF •+ and DMTTF •+ cations computed at the B3LYP/6-311++G(d,p) level of theory (a). Packing arrangements within the stacks observed for the (o-DMTTF) 2 [W 6 O 19 ] and (DMtTTF)Br salts (b).

  •+ cation are given in TableII. Given the donor's unsymmetrical nature, for clarification, those bonds from the fulvalene ring having only hydrogen atoms is denoted by an 'R' while those from the ring possessing methyl groups are denoted by 'Me'.

Recently, a charge transfer salt containing radical cations of the unsymmetrical donor o-DMTTF and the closed shell, dianionic Lindquist polyoxometalate [W 6 O 19 ] 2-was reported

Table I .

 I Room temperature crystallographic data of the salt (DMtTTF)Br

	Tables
	Compound	(DMtTTF)Br
	Formula	C 11 H 12 BrS 4
	FW (g•mol -1 )	352.39
	Crystal color	Black
	Crystal size (mm)	0.3×0.3×0.1
	Crystal system	Monoclinic
	Space group	P2 1 /c
	T (K)	293(2)
	a (Å)	7.0259(8)
	b (Å)	12.4074(11
	c (Å)	15.4574(16)
	 (º)	90.0
	 (º)	101.684(9)
	 (º)	90.0
	V (Å 3 )	1319.6(2)
	Z	4
	Dcalc (g•cm -3 )	1.774
	 (mm -1 )	3.717
	Total refls.	6878
	Absorption correction	multi-scan
	T min , T max	0.647, 0.690
	Unique refls.	2977
	Rint	0.0316
	Unique refls. (I > 2(I))	2311
	Refined param.	146
	R 1 (I > 2(I))	0.0503
	wR 2 (all data)	0.1355
	Goodness-of-fit	1.117
	Res. dens (e -Å -3 )	-0.616, 0.614

Table II .

 II Intramolecular bond lengths (averaged) within the TTF core. C i represents the inner carbon atoms of the TTF core, C o the outer ones; R the fivemembered ring side; Me the methyl side). Dimer model parameters for the fit to the polarized conductivity spectrum of (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ] obtained by Kramers-Kronig transformation from the reflectance spectra. a = 3.311 Å, N = 2, V = 1319.62 Å 3 , c 1 = 0.600, ω CT = 7700 cm -1 , γ e = 2900 cm -1 (DMtTTF)Br a (o-DMTTF) 2 [W 6 O 19 ] b a = 3.498 Å, N = 1, V = 802.10 Å 3 , c 1 = 0.435, ω CT = 10250 cm -1 , γ e = 3310 cm -1 (U eff /4t equals xa=0.292 and xb=0.793 for (DMtTTF)Br and (o-DMTTF) 2 [W 6 O 19 ] salts, respectively)

	Table III
	C i =C i (Å)	C i -S (Å)		C o -S (Å)		C o =C o (Å)
	1.389(7)	1.731(5)(R)	1.721(5) (R)		1.349(7) (R)
			1.720(5) (Me)	1.752(6) (Me)		1.329(9) (Me)
	ω α (cm -1 )	g α (meV)	λ α	ω α (cm -1 )	g α (meV) λ α	Assignment
	1587	12	0.002	1556		60	0.022	in-phase ring C=C stretch
	1507	20	0.006	1483		80	0.042	anti-phase ring C=C stretch
	1412	74	0.095	1417		100	0.068	central C=C stretch

(a b

Table V .

 V Charge distribution (Mulliken) on atoms of TTF core calculated at the B3LYP/6-311++G(d,p) for DMtTTF •+ and o-DMTTF •+ cations. Note: the numbering of atoms is shown in Fig.2

	TTF Atom	•+ [2,3]	BEDT-TTF DMtTTF •+ •+ [15] o-DMTTF TMTTF •+	•+ [37]	TTP	•+ [38]		DOEO	•+ [30]
	ω 1505 C1 S1 S2	g α 42	ω 1460 0.737 -0.615 -0.615	g α 43	ω 0.575 1567 -0.624 -0.624	g α 32	ω 1540	g α 8	ω 1575	g α 23
	C2 C3			0.378 0.378		0.34 0.34		1474	54	1494	31
	1420 133 C4	1414 0.618	71	1418 0.585	133	1423	9	1460	29
	S3			-0.446		-0.177
	S4			-0.446		-0.177
	C5			0.65		-0.075
	C6			0.65		-0.075
	(C 6 S 4 )		1.289		0.088

Acknowledgements

This work was supported by the National Science Centre (Decision No. DEC-2012/04/M/ST3/00774).