Philippe Silberzahn

Renaud Gaultier

Jean-Patrick Peche

HOW DO WE KNOW WE TRAIN INNOVATORS EFFECTIVELY? DEVELOPING THE ASSESSMENT CRITERIA OF A NEW DESIGN THINKING MSC PROGRAM

Keywords: Design Thinking, Entrepreneurship education, Innovation management, Creative Industries, Assessment

Some researchers have proposed that the creative industries (CI) could be a source of innovative management practices. In particular, the integration of design thinking to management education has been increasingly popular with the launch of dedicated programs. Yet, these programs' effectiveness is not measured. Based on the study of such a program, and building on a view of innovation as the transformation of ideas into social artifacts, we develop an assessment framework based on the measure of artifacts created by participants during the program. The two dimensions of measure are the complexity of the artifacts and their social dimension. We contribute to the education, innovation and design thinking literatures.

INTRODUCTION

While innovation regularly appears at the top of CEOs agenda, it is still a challenging task for organizations. Some researchers have proposed that the creative industries (CI) could be a source of innovative management practices because the dilemmas experienced by managers in cultural industries are also to be found in a growing number of other industries where knowledge and creativity are key to sustaining competitive advantage [START_REF] Lampel | Balancing Act: Learning from Organizing Practices in Cultural Industries[END_REF]. According to [START_REF] Howkins | Creative Economy[END_REF], the success of creative industries reflects the growing power of ideasand how people make money from ideas. [START_REF] Landry | The creative city[END_REF] contend that twenty-first century industries will depend increasingly on the generation of knowledge through creativity and innovation. It is in this context that the importance of design in management develops [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF].

Already, [START_REF] Simon | The sciences of the artificial[END_REF] had called for the establishment of a rigorous body of knowledge about the design process as a means of approaching managerial problems. More recently, Boland and Collopy (2004) describe the parallels between the two domains of design and management and explore the intellectual foundations for approaching managing as designing.

Management education is a way to make this link a reality because, as noted by Ackoff, 'the education system deeply affects the workplace, because of how people are taught to think, or not taught, in schools' (1993). Teaching design to managers is not new, however. It was pioneered at the London Business School in 1976, and the first program of design management at a design school was started in the 1980s at the Royal College of Art (RCA) in the UK. Results were disappointing, however [START_REF] Wastell | ARCHARIOS: A dialogue between Socrates and a novice manager on the relevance of design to management practice and education[END_REF]. One of the reasons is that what was taught was design as an addition to other subjects such as marketing or strategy instead of design as a set of principles forming the foundation of an integrated curriculum [START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF][START_REF] Kao | Tapping the World's Innovation Hot Spots[END_REF][START_REF] Stevens | Designing and design thinking in strategy concepts: Frameworks towards an intervention tool[END_REF].

To address this issue, programs combining design thinking and business thinking (socalled 'd-schools') were launched in recent years at Stanford in the US, Aalto University in Finland, Imperial College in London, and other institutions across the world. They constitute a new attempt at a holistic approach to create a management curriculum based on design from the ground up.

Yet, these "new generation" programs' ambition is not matched by a rigorous assessment framework. While significant work has been done on measuring innovation in firms (e.g. [START_REF] Zhuparova | Problems of Measuring Effectiveness of Innovation Performance[END_REF], pedagogical assessment is still an under-researched area in management research [START_REF] Fayolle | From craft to science: Teaching models and learning processes in entrepreneurship education[END_REF] and more so regarding innovation programs. Without an assessment framework, we cannot know if programs based on design thinking are more effective at training innovators.

It is difficult to assess the success of education programs, and research in this area is scarce: the impact of innovation and entrepreneurship education on attitudes or perceptions of entrepreneurship has remained relatively untested [START_REF] Peterman | Enterprise Education: Influencing Students' Perceptions of Entrepreneurship[END_REF]. Most measures are either on attitudes and intention change or post-program intentions (e.g. [START_REF] Rauch | Putting Entrepreneurship Education where the Intention to Act Lies: An Investigation into the Impact of Entrepreneurship Education on Entrepreneurial Behavior[END_REF]). Yet, Katz (1990) pointed out that there is only a weak relationship between intentions and behavior in the area of entrepreneurship.

Programs based on design thinking propose that an important contribution of their approach results from their practical approach of learning by doing during the curriculum. This points to a possible way of evaluating their effectiveness by measuring what is actually created during the program. It is on this basis that we develop our assessment framework.

The rest of the article is structured as follows: First, we review the theoretical background on the role that creative industries, and design thinking in particular, can play in educating innovative managers. Second, we propose an assessment framework and apply this framework on IDEA, a typical design thinking based management program. We then discuss the results and our contribution through this research.

THEORY

Creative industries and design thinking

Scholars have suggested that creative industries can be a source of innovative management practices because the dilemmas experienced by managers in cultural industries are also to be found in a growing number of other industries where knowledge and creativity are becoming key to sustaining competitive advantage [START_REF] Lampel | Balancing Act: Learning from Organizing Practices in Cultural Industries[END_REF]. Managers can learn from the approaches, practices and even techniques being developed by these benchmark organizations [START_REF] Cadin | What Can We Learn from the Video Games Industry[END_REF]. In reviewing the different model relationships between the creative industries and the economy, [START_REF] Potts | Four models of the creative industries[END_REF] identify one model (Model 4) where the creative industries are conceptualized as a higher order system that operates on the economic system. In this model, the significance of the creative industries lies in their contribution to the process of change, and in the development and adoption of new knowledge. It is in accordance to this model that the creative industries can be a driver for change in managerial practices.

Design thinking is one way such change can happen. Design can be understood as material and conceptual innovation, realized through the integration of arts, culture, business and technology, and experienced as beauty, value and meaning. In its practice, design integrates culture and the arts, and one of the reasons why previous attempts to teach design in business schools failed is that such attempts did not integrate this art and culture background. Design thinking, then, refers to the methods and processes for investigating ill-defined problems, acquiring information in a large scope, analyzing knowledge, and positing solutions in the design and planning fields [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF]. Design thinking combines empathy for the context of a problem, creativity in the generation of insights and solutions, and rationality to analyze, fit and test solutions to the context. Design thinking has become part of the popular lexicon in contemporary design and engineering practice, and also in business and management [START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF].

In particular, interest from management researchers has been growing recently, as exemplified by the work of [START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF], [START_REF] Stevens | Designing and design thinking in strategy concepts: Frameworks towards an intervention tool[END_REF], [START_REF] Rylander | Design Thinking as Knowledge Work: Epistemological Foundations and Practical Implications[END_REF], [START_REF] Ajzen | The theory of planned behavior[END_REF], [START_REF] Kimbell | Rethinking Design Thinking: Part 1[END_REF][START_REF] Bjögvinsson | Design Things and Design Thinking: Contemporary Participatory Design Challenges[END_REF] among others. As [START_REF] Kimbell | Rethinking Design Thinking: Part 1[END_REF] notes: "Design as design thinking should provide more than mere design. And yet, this re-assembling of some of the approaches, knowledge and practices of professional designers, first within academic design research, and then within business schools and consultancies, has not brought a happy synthesis".

Reviewing major works on design thinking over the previous three years, [START_REF] Kimbell | Rethinking Design Thinking: Part 1[END_REF] explains that one of the approaches is to view design thinking as an organizational resource [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF][START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF][START_REF] Martin | Design of Business: Why Design Thinking is the Next Competitive Advantage[END_REF]. Here, the focus is on businesses and other organizations in need of change with the purpose of innovation, and how design thinking can contribute to this change. It is this approach, in line with [START_REF] Lampel | Balancing Act: Learning from Organizing Practices in Cultural Industries[END_REF] and Potts and Cunnigham's (2008) model 4, that is of particular interest to this paper.

Benefits of design thinking for management

Design and management have contradictory cultures based on different beliefs, values and success metrics. Historically, design management was the way to address this gap as translator and negotiator between the two sides. According to [START_REF] Buchanan | Wicked problems in design thinking[END_REF], by bringing core ideas and methods of design practice into organizations, "the manager becomes a creative and innovative force, and their actually making a product themselves, the product is the organization. […] To understand good practices of design, to understand what design […] can bring, it opens up better possibilities for organizations." Yet despite repeated attempts, integrating design thinking and management is still a challenge, and education programs are still very much a work in progress.

The d.school (Hasso Plattner Institute of Design at Stanford University) is the most ambitious effort to integrate design thinking with other disciplines such as business or sciences. It is not degree granting, but offers courses and modules to the students of Stanford graduate schools (business, engineering, medicine, etc.) Students learn design thinking in a collaborative manner as a tool to inspire, ideate, and implement solutions. One of the pedagogical principles of the school is to mix students, faculty, and executives, each bringing different, and often conflicting, ways of thinking, working, and solving problems. This melting aims at breaking the silos hampering innovation in firms. Each participant leaving the program is equipped with a changed perspective and the ability to think more globally and differently in his domain.

Beyond proposing an answer to some criticisms against management education, design thinking integration enables new interactions and new perspectives in a curriculum and is of help in understanding, modeling and building systems. As such, it is one of the four foundations of system thinking as developed by [START_REF] Gharajedaghi | Systems Thinking: Managing Chaos and Complexity: A Platform for Designing Business Architecture[END_REF], but it doesn't go much beyond.

Yet most attempts at integration of design thinking in management schools did not have the effects anticipated by [START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF]. One explanation is that design thinking is often taught as a separate module, reduced to a creativity method including brainstorming and story-telling. Such an approach neglects a key idea behind design thinking, the idea of Making. Without making, design thinking is only theoretical.

Problems with evaluation

A closer look at this growing offer claiming to integrate design thinking and creative industries reveals a lack of definition in the performance objectives and measurement criteria of these programs. For example, the fact that the d.school, the emblematic representation of these pedagogic practices, is not degree granting is quite symtomatic of the difficulty to evaluate the performances of such programs. While significant work has been done on measuring innovation in firms [START_REF] Zhuparova | Problems of Measuring Effectiveness of Innovation Performance[END_REF], Sawang 2012), pedagogical evaluation is still an under-researched area in management research, and particularly in innovation and entrepreneurship [START_REF] Fayolle | From craft to science: Teaching models and learning processes in entrepreneurship education[END_REF]. Without evaluation criteria, we cannot know if programs based on design thinking are more effective at training innovators.

The question of evaluation is somehow an echo of the older question about the measurement of effectiveness of design and design thinking [START_REF] Carmel-Gilfilen | Developmental trajectories in design thinking: an examination of criteria[END_REF][START_REF] D׳ippolito | The importance of design for firms׳ competitiveness: A review of the literature[END_REF]. As such, this research lies at the intersection of the three fields of pedagogy, innovation and design thinking by asking how we can develop evaluation criteria to know whether the teaching of design thinking can make business students more innovative.

METHOD Measurement: Artifacts and social interactions

In the case of education programs, there is specific difficulty of measuring effectiveness of education programs because their effect happens after program completion, which poses methodological problems such as causal ambiguity. Accordingly, in the entrepreneurship field which is closest to our interest here, most measures are either on attitudes and intention change or post-program intentions (e.g. [START_REF] Rauch | Putting Entrepreneurship Education where the Intention to Act Lies: An Investigation into the Impact of Entrepreneurship Education on Entrepreneurial Behavior[END_REF]). Yet, Katz (1990) pointed out that there is only a weak relationship between intentions and actual behavior in the area of entrepreneurship.

The fact that a key elements of design thinking is learning by doing, however, provides us with a methodological opportunity to develop an assessment framework by basing it on what is actually done, or produced, by students.

To develop it, we need to rely on a clear definition of innovation. For [START_REF] Schumpeter | The theory of economic development[END_REF], innovation is a novel combinations of resources carried out in practice, i.e. subject to attempts at commercialization. Behind this definition lie the idea of newness, and the idea that this newness is socialized through the process of diffusion and/or adoption [START_REF] Callon | Some Elements of a Sociology of Translation: Domestication of the Scallops and the Fishermen of St Brieuc Bay[END_REF][START_REF] Rogers | Diffusion of Innovations[END_REF]. Building on this and based on Sarasvahty (2001), we define innovation as the successful transformation of ideas into social artifacts such as products, firms or markets. Hence measuring the production of social artifacts is a good proxy to evaluate the innovativeness of a process. This suggests two important dimensions of output to measure: the degree of complexity of the artifact created, and the degree to which this artifact is socially embedded [START_REF] Callon | Some Elements of a Sociology of Translation: Domestication of the Scallops and the Fishermen of St Brieuc Bay[END_REF].

The degree of complexity of an artifact, in the context of design thinking, is the number of dimensions introduced into it. It can range from a simple product that is redesigned, such and eyeglass frame, to a software application and to a firm. At its most complex, an artifact includes the three dimensions of design thinking: feasibility, desirability and viability [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF].

The social dimension ranges from simple interaction (market research) to getting user insights (design thinking and empathy) to complete embeddedness through social commitments. By social commitment, we mean the active involvement of a stakeholder in the project evidenced by the provision of resources (tangible or intangible) to the innovator. Examples of commitments include acceptance into an incubator, involvement of a partner to develop a prototype, a pre-order by a customer, etc. Only when a project has secured significant social commitments can it become a viable innovation and, thus, evidence of success of the pedagogical process in this research.

Hence we can assess the production of an artifact along two axes: 1) The complexity of the artifact in terms of design thinking dimensions; and 2) The social complexity of the artifact, ranging from user observation (brainstorming) to interaction and empathy (market study, ethnography) to actual third-party commitments such as investment, incubation or a first sale.

Empirical setting

In our attempt to develop a measurement framework, we study a two-year graduate degree called IDEA (Innovation, Design, Entrepreneurship and Arts), jointly created by an engineering school and a business school. With IDEA, design as a set of principles forms the foundation of the whole curriculum in an integrated way.

The objective of the program is to train future managers by breaking the existing silos between design, the arts, technology and business as per [START_REF] Dunne | Design Thinking and How It Will Change Management Education: An Interview and Discussion[END_REF]. The program aims at educating students able to create new firms or to manage innovation departments in existing firms.

The program's model takes its roots in the triad developed by [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF]. According to Brown, innovation is the conjunction of three elements: feasibility, viability, and desirability. Feasibility is covered by courses delivered by the engineering school. Viability is covered by courses given by the business school. Desirability, which includes design, and creative and cultural aspects, is covered by a diverse, ad-hoc faculty from both schools and external lecturers.

As such, IDEA is representative of the new generation innovation programs based on design thinking aimed at future managers and entrepreneurs, and can thus be considered an exemplary case [START_REF] Yin | Case study research: design and methods[END_REF]. An important difference with existing programs, however, is the emphasis that the program places on the actual production of artifacts early in the process.

In line with the principles of design thinking, real life projects form the cornerstone of the curriculum. Design thinking seen as project management integrates both with Problem-Based Learning and Project Based Learning. Problem-Based Learning is an instructional learner-centered approach that gives students responsibility for problem definition, research conduct and theory and practice integration. Each phase of the design thinking as project management offers by itself a natural problem-based learning situation. Problem-Based Learning uses design and project experiences to transfer and integrate learning, thus amplifying the experiential learning as described by [START_REF] Kolb | Experiential learning: Experience as the source of learning and development[END_REF]. Hence the approach can be described as small "project-oriented studies" gradually switching to "project-oriented curriculum" [START_REF] Heitman | Project-oriented Study and Project-organized Curricula: A Brief Review of Intentions and Solutions[END_REF] to implement the principles of design thinking.

Accordingly, and while there is learning in the traditional sense of the term during the program, we focus our assessment framework on the students' outputs during the program.

RESULTS

In this section, we review the artifacts created during the IDEA program and propose evaluation criteria for each of them.

First year

The first year of the program is articulated around four projects, P0 to P3. Project P0 is the first step of the project-based learning methodology. Students are given a precise brief for a deliverable that is academic in nature. During this project, students learn how to use the fablab, how to sketch and are initiated to the design thinking approach. A typical project is to 'rethink' glasses: the object, its identity that integrates its user profile, its form, and its materials. With P0, the artifact is not complex (eyeglass frames) and the social dimension is limited to understanding human needs and aspirations with regards to glasses (as a tool, as a fashion accessory, as a symbol, etc.).

Project P1 is also based on a brief by the teaching team but broader in scope. This is in line with one of the key elements in design thinking that the formulation of the problem inherent to all project where problem is initially ill-defined [START_REF] Buchanan | Wicked problems in design thinking[END_REF]. Students have to develop an interactive exhibition1 around a given theme for the annual Festival of Lights in Lyon, France2 (which has millions of visitors). With this project students have two objectives: 1) integrate arts and creativity to create aesthetic and interactive artifacts telling a story to the public; and 2) create, prototype and manufacture the artifacts they have imagined. Compared with project P0, the artifact is therefore more complex as new dimensions are added (aesthetics, storification, etc.) and students go beyond the prototyping stage to the product stage with full meaning. The solidification of the design thinking approach is focused on this project on establishing a meaningful product through a broad (arts, culture, literature and technology) state of the art exploration. Interaction with the public visiting the exhibition is introduced, providing an increased social dimension.

Project P2 is a full proposition that could be issued to any design agency. With P2, students experience the whole design thinking process (including problem definition) and address [START_REF] Brown | Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation[END_REF] three elements of design: feasibility, viability, and desirability. In 2013, the brief was to "Imagine a product or service that takes inspiration from bees as a society and as dissemination vectors in the context of Big Data and Urban Mobility" and the event concluding the project was held in conjunction with Biennale Internationale Design Saint-Étienne and received 15,000 visitors. Six out of seven projects were viable enough to eventually be exposed, and two of them moved to startup phase. Design thinking is fully apprehended since it is the first time that students will manipulate all the dimension of the methodology and experiment all of its freedom dimension aspects. Whereas in project P1, the end-user had ''only'' to understand the sense of the exhibition, with P2 the end-user (visitor of the public exhibition) is a potential adopter of the product or service designed. Hence, the social commitment dimension is higher and deeper with project P2. Desirability is integrated through usage observation but also user involvement and field observations. Feasibility is here broadened since the artifact has to be defined and created by the students. P2 is also the first project where viability is introduced as a dimension as students are given a budget for their project: it is an initiation to the entrepreneurial dimension even if students can develop this aspect and then the social commitment dimension of their project by the integration of sponsoring or external support.

Project P3 has a different nature. It is an internship abroad in an NGO designed to develop students' intercultural awareness. There is no formal artifact involved at this stage besides the result of students' action and the end report. Yet, the social dimension of the project is more developed as it is the first time that students have to deliver on a brief given by a real end-user (as opposed to the pedagogic team) with a real issue to address. A typical project involved teaching uneducated women in Vietnam how to read. The lack of formal artifact, however, makes the assessment difficult beyond a qualitative evaluation of their contribution during the project and, possibly, the measurement of the intentions expressed by students to become involved in social entrepreneurship projects.

Second year

The second year of the program focuses on the viability of the design thinking triad with a strong emphasis of entrepreneurship, i.e. social commitments and value creation. The project begins in Project-Based Learning mode from September to January before becoming either an internship within an existing company or a startup within the associated incubator of IDEA for the following six months. The aim is to significantly increase the ambition of the project along the two dimensions of social and artifact complexity.

Mini-IDEA project

Students first work on a pre-project called "mini-IDEA", which is then converted into the Grand-IDEA, either as a startup project or in a project within a host company as an internship. During this period, each student must review the state of the art of their internship subject that they consider as a brief to be interrogated through the design thinking approach. With regards to the artifact, few new dimensions are explored except the entrepreneurial dimension. In terms of social dimension, the objective is to move from interaction to commitments, by integrating the socio-economic context as expressed by the various stakeholders, such as institutional sponsors and early customers, whose commitment is sought.

Accordingly, the following metrics can be used for evaluating the mini-IDEA phase: how many projects are proposed by the students (as opposed to by the teaching team), how many are validated, how many get converted into Grand-IDEA after completion, and out of these, how many are accepted by the school's incubator through a separate selection process.

Grand IDEA

The Grand IDEA project is the cornerstone of the program. The project can be conducted in two modes: either as a startup project or as an in-company project.

Startup project: In the case of a startup project, there is obviously an artifact, the project itself. Beyond the creation of the project itself, traditional metrics of entrepreneurship, such as jobs, revenue, etc. can not necessarily be applied so early [START_REF] Delmar | Arriving at the high growth firm[END_REF]. However, the tracking of the progress of the project in such an early phase can be made in terms of stakeholders acquisition and artifact progress: product, market, firm, etc.

Metrics to evaluate here the effectiveness of the innovators are inherited from incubators metrics (Center for Strategy and Evaluation Services, 2002), entrepreneurship education metrics [START_REF] Küttim | Entrepreneurship Education at University Level and Students' Entrepreneurial Intentions[END_REF] and incubation pedagogy metrics (currently developed in IDEA program).

In-company project: the artifact here is more difficult to measure due to the intricate aspect of the situation of the student in a group or a firm. Raw results are difficult to obtain since filtered by the firm and by the fact that application of the design thinking methodology can be distorted by the enterprise culture. Sometimes students find it difficult to apply their methodology in a real corporate context. Thus, the evaluation is a more qualitative assessment. Company satisfaction at the end of the internship is one element, but does not necessarily assess innovation. The ability of the students to promote change and innovation within company as well as the ability to create a coalition within the company to promote the project can also be assessed, but it is an approximation at best.

The last measurements that have to be integrated are the impact of the students after graduation. Such measurement poses obvious methodological problems, however, and is not well addressed in the literature. One should measure how many of business units focused on innovation are created inside companies and managed by the graduated and how many companies have been created and the ratio of which that are still alive. The IDEA program being in its second year of existence, this information is not yet available.

The results are summarized in Table 1. In summary, the different projects are represented along the two dimensions of social and artifact complexity in Figure 2 below.

Actual results

The program was launched only in September, 2012, so the first batch of students will only graduate in September, 2014. With regards to the artifacts, we observe that two of the six projects for P2 led to the creation of startups, which joined an incubator in January 2014. More generally, regarding the Mini-IDEA project, 10 students out of 31 applied for entrepreneurship and 6 projects (for 8 students including the two previously mentioned) integrated the incubator in January 2014. The progression in terms of artifact complexity, from simple objects with few dimensions involved to complex service or product offering, is evidenced.

Produced objects have a form related to material or immaterial objects, services or organizations. In line with design thinking, the notion of form is the visible expression of the artifact of any complex project. This expression consists of semantic components, functional components, and emotional components that act as mediators of intrinsic values. This mediation uses little but measurable components, determinants in the success of a project. Building on the social and human sciences, the dimensions of meaning, sense-making, and semantics have been introduced in the artifacts, while design thinking served to build a conscious and controlled form, in relation to the project's objectives (value creation). The learning-by-doing posture allowed a concrete and rapid application development of real artifacts, hence closing the loop of innovation, entrepreneurship, design and art that drives the curriculum.

DISCUSSION AND CONCLUSION

We started with the observation that the creative industries could be a source of innovative management practices. In particular, the integration of design thinking to management education has been increasingly popular with the launch of dedicated programs. Yet, these programs' effectiveness is not measured. Based on the study of IDEA, a typical design thinking program that was launched recently, we developed an assessment framework based on the measure of artifacts created by participants during the program. The two dimensions of measure for these artifacts that we proposed are the complexity of the artifacts and their social dimension. As such, this research lies at the intersection of the three fields of pedagogy, innovation and design thinking by asking how we can develop evaluation criteria to know whether the teaching of design thinking can make business students more innovative.

With regards to pedagogy, the research contributes to a better assessment of innovation education programs based on design thinking. Most measures proposed in the literature which are mostly centered on intentions [START_REF] Fayolle | The future of research on entrepreneurial intentions[END_REF] and planned behavior [START_REF] Ajzen | The theory of planned behavior[END_REF], i.e. the measures apply to what may happen after the program is completed. Because learning by doing is a key notion of design thinking, a program based on design thinking necessarily integrates the creation of artifacts and thus offers a possibility to measure outcomes during the program. This reduces the causal ambiguity between a curriculum and its outcomes, and therefore facilitates the evaluation of the curriculum and its improvement.

With regards to innovation, we contribute to the literature on innovation measurement. While significant work has been done on measuring innovation in firms (e.g. [START_REF] Zhuparova | Problems of Measuring Effectiveness of Innovation Performance[END_REF], it is still inconclusive. Studying the evolution of social artifacts along several dimensions is a way to improve such measurement and constitutes an area of further research.

Finally, with regards to design thinking, we contribute to the development of a measurement system for the effectiveness of design and design thinking, which so far has remained an open issue [START_REF] Carmel-Gilfilen | Developmental trajectories in design thinking: an examination of criteria[END_REF][START_REF] D׳ippolito | The importance of design for firms׳ competitiveness: A review of the literature[END_REF]. While our measurement is developed in the specific context of pedagogy, much can be applied in the broader context of industry innovation.

Clearly the assessment framework we propose only covers some aspects of the impact of an education program, that of the creation of social artifacts, and other dimensions of the program must also be assessed. As such, measuring social artifacts can only be one part of a more general assessment framework in innovation education programs. Further research should aim at refining the dimensions of artifacts we assess and better integrate with other variables that influence the impact of the program, such as work team, emotions, etc.

Figure 1 :

 1 Figure 1:Two dimensions to measure the artifacts created by students

Figure 2 :

 2 Figure 2: The IDEA projects along the two dimensions of artifact and social complexity

Table 1 :

 1 Projects and assessment criteria3 As per Actor Network Theory[START_REF] Latour | Science in action: how to follow scientists and engineers through society[END_REF]

		Social	Artifact complexity	Output	Assessment
		complexity
	Project P0	Minimal (internal	Simple product, few	Internal	Purely academic
		project)	dimensions	report
	Project P1	Users' feedback	Product with	Artifact-	Numbers of visitors,
		post process	meaning, Prototyping	based public	reviews, satisfaction of
		through a public	ability, sense-making	exhibition	the organization
		mediation			committee, quality of
					the mediation, etc.
	Project P2	User integration	From wicked	Full product	Numbers of visitors,
		(survey,	problem (Buchanan,	(prototype)	reviews, quality of the
		observational	1992) to well defined	or service	mediation,
		research), users	problems, axis	concept	transformation in start-
		feedbacks,	development	presented to	ups, number and quality
		empathy	identification,	potential	of the industrial
			prototyping, solution	users	contacts, social
			proposition		commitments
	Project P3	Medium:	Limited. Application	Internal	None / Social
		Interculturality	of design thinking	report	entrepreneurship
		integration,	methodology to real		vocation creation.
		empathy,	life without a
		embeddedness	proximity mentoring
	Mini IDEA	User integration	From wicked	Internship	Quality of the rewriting
	In-company	and enterprise	problem (Buchanan,	proposition	of the initial
		culture	1992) to well defined	rewriting,	proposition, number of
		appropriation	problems, axis	state of the	proposition of
			development	art	internship
			identification
	Grand IDEA	Fully embedded:	Ability to deploy DT	Fulfillment	Difficult quantitatively:
	In-company	Enterprise's	methods in	of the	Mission achievement,
		workers or clients	established	mission	satisfaction of the
		engagement	enterprises or start-		enterprise, employment
			ups.		proposition, stakeholder
					commitments.
	Mini IDEA	User integration,	From wicked	Admission	Quality of the
	startup	stakeholders	problem (Buchanan,	to incubator	admission file in
		research	1992) to well defined		incubator, quality of the
			problems, axis		actors network 3
			development		established
	Grand IDEA	Stakeholders	Integration of the	Firm	Conventional incubator
	startup	integration	entrepreneurship	creation	metrics: business
			dimension to design		model, business plan,
			thinking methodology		actor network, number
					and quality of
					stakeholders.
	Post	Real life without mentoring	Employment	Ratio of employment in
	graduation			or enterprise	innovation field of a
				creation	batch, delay to find a
					job since graduation,
					numbers of firms
					created

http://programme-idea-lumieres2013.tumblr.com/

http://www.fetedeslumieres.lyon.fr/EN_2013


François-Xavier Coudert

Pierre Archirel

Anne Boutin
email: anne.boutin@lcp.u-psud.fr

May

Molecular dynamics simulations of electron-alkali cation pairs in bulk water

The structural, dynamic and thermodynamic properties of an excess electron interacting with an alkali cation (Na + , K + , Li + ) in bulk water were investigated by means of a mixed quantumclassical molecular dynamics simulation technique. This study includes a reparametrization of the electron-cation pseudopotentials. The free energy calculations for all three systems show that a contact electron-cation pair can be observed, which is either as stable as the dissociated pair (Li + ), or more stable by only a few kT (Na + , K + ). Given that the dissociation barrier is also quite small, we suggest that the average cation-electron distance in the experiments at room temperature will not depend on this free energy profile but rather on the minimization of the coulombic repulsive interaction between like charges in the solvent medium. This enables us to compare the present MD simulations with the spectroscopic data obtained for different ionic strengths. The overall trend of the UV-Vis hydrated absorption spectra, namely the shift towards shorter wavelengths at high ionic strengths, is fairly well reproduced. This confirms our hypothesis of statistical distribution of the cations and solvated electrons.

Introduction

Investigations of the structure, dynamics and thermodynamics of the solvated electron in water are of great interest due to the importance of redox reactions in everyday physical chemistry and biophysics.

The reactivity of the hydrated electron towards cations in solution has been extensively studied, mainly by pulse radiolysis. 1,2 Noble metal ions such as Ag + are known to be easily reduced by the hydrated electron. 3 On the other hand, alkaline metal cations (M + ; M = Li, Na, K) do not react with the hydrated electron, since the M + /M couple has a lower redox potential than the hydrated electron. [4][5][6][7][8] In such systems, water mediates the effective interactions between the ion and the excess electron and the formation of contact pairs was suggested. 6,9,10 Electron spin echo spectroscopy studies gave indirect information on the structure of the solvation shell of a solvated electron in alkaline glasses and ice. [11][12][START_REF] Dikanov | Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy[END_REF] Recent resonance Raman spectra in bulk water supported these structural findings. [START_REF] Tauber | [END_REF]15 Numerous investigations of the hydrated electron absorption spectrum were reported in the literature, under different ionic strength conditions and using various counter-ions. The overall trend through a systematic experimental study with different cations at various concentrations 7,8 is the shift of the absorption of the hydrated electron towards shorter wavelengths ("blue shift").

The motivation for the present molecular simulation study is to provide a description, at the atomistic level, of the nature of the non reactive alkali cation-solvated electron pairs in bulk water.

A recently developed mixed quantum-classical molecular dynamics (QCMD) approach, 16 based on adiabatic simulation technique, is used to simulate an excess electron and a cation in bulk water. [17][18][19][20] In this approach only one electron is treated quantum mechanically, while the effect of the surrounding molecules and cation is taken into account through effective pseudopotentials.

The paper is organized as follows. The models and methods are presented in the next section.

In section 3, the force fields are described in some details. A reparametrization of the electroncation pseudopotentials is presented, and the new electron-sodium potential is tested against ab initio calculations of [Na + , e -, (H 2 O) n ] clusters. The solvated electron absorption spectrum, free energy calculations and structural information in presence of a sodium cation are given in section 4. Section 5 is devoted to a comparison between the sodium, lithium and potassium cation behaviors. A simple model is suggested that enables to understand the general trend of the observed absorption blue shift in various ionic strength conditions.

Adiabatic mixed quantum-classical molecular dynamics

We perform a mixed quantum-classical molecular dynamics (QCMD) of an excess electron in bulk water, in presence of different cations. While the water molecules and the cation are treated classically, the excess electron is treated quantum mechanically using the Born-Oppenheimer approximation. A given solvent/cation configuration S generates an effective interaction potential with the excess electron Vint (r, S), where r denotes the electronic coordinates. The wavefunction describing the electron, ψ n (r, S), and the corresponding energy, E n (S), are obtained by solving the stationary Schrödinger equation in this effective potential:

Te + Vint (r, S) ψ n (r, S) = E n (S)ψ n (r, S) (1)
where Te is the electronic kinetic energy operator. Equation 1 is solved by diagonalization for each solvent/cation configuration, i.e. at each time step. The Lánczos iterative algorithm (as implemented in the ARPACK library) was used to solve the electron eigenvalue problem, obtaining only the first 25 eigenstates for each time step.

Once the eigenstates are known, the quantum contribution to the force acting on each classical particle is obtained by the Hellmann-Feynman theorem:

F (q) S,n = -∇ S E n (S) = -ψ n (r, S) ∇ S Vint (r, S) ψ n (r, S) (2)
In the present study, all forces are computed for the ground state of the excess electron (n = 0). The wavefunctions ψ n (r, S) are expanded into a basis of 7 3 = 343 spherical gaussian (s-type) functions, centered on the nodes of a cubic lattice. The basis set parameters are identical to those used in reference16 for the simulation of a hydrated electron: the gaussian exponent α is 0.357 Å-2 and the basis grid extension is 10 Å, which corresponds roughly to the half of the simulation box.

Standard periodic boundary conditions are used with the Ewald summation technique 23 to calculate all classical and quantum long-range interactions. The simulations are performed in the NVT ensemble using the Nosé-Hoover thermostat 24,25 to ensure isothermal conditions. The integration of the equations of motion for translation and rotation is performed using the Gear predictor-corrector algorithm, with a time step fixed at 0.5 fs. Simulations are run typically during a few tens of picoseconds.

Quantum umbrella sampling

Some of the simulations are performed with an electron/cation distance ξ constrained around a given value ξ 0 . This goal is achieved using the umbrella sampling approach, adding a quadratic term U ξ0 to the total Hamiltonian of the system:

U ξ0 = 1 2 k (ξ(S) -ξ 0 ) 2 (3)
Following the method proposed by Borgis and Staib, 26 we adapted the umbrella sampling technique to a system containing a quantum particle. A new quantum umbrella sampling force acts on each classical atom, given by

F US iα = - ∂ ∂S iα U ξ0 = -k(ξ(S) -ξ 0 ) ∂r(S) ∂S iα • r(S) ξ(S) (4)
where the non trivial term ∂r(S)/∂S iα is calculated with a perturbative approach. 26 The free energy profile along the electron-cation distance ξ is given by

F (ξ) = -k B T ln P (ξ) (5)
where P (ξ) is the probability to find the electron at distance ξ from the cation:

P (ξ) = δ(r(S) -ξ) exp(βU ξ0 ) ξ0 exp(βU ξ0 ) ξ0 (6)
Umbrella sampling simulations are run for 50 ps, for ξ 0 values (see Eq. 3) ranging from 1 Å to 15 Å with a 0.5 Å increment. The k value was fixed at 0.01 a.u./ Å2 , allowing fluctuations around ξ 0 of about 0.5 Å.

Absorption spectra

Electron absorption spectra can be calculated by a direct average of the transition dipole moment, or using the cumulant expansion and the vibration-rotation decorrelation hypothesis, 26 leading to the formula

I(E) = E 1 -e -βE ∞ n=1 |µ 0n | 0 exp - (E -E 0n 0 ) 2 δE 0n 2 0 (7)
where E 0n ≡ E 0n (S) is the energy gap between the ground state and the nth excited state, whereas µ 0n ≡ µ 0n (S) is the corresponding transition dipole. 3 Force fields and pseudopotentials

Classical interaction potentials

Water molecules and cations interact via classical interaction potentials consisting of a coulombic and a 6-12 Lennard-Jones term. Water-water interactions are described by the SPC model, [START_REF] Berendsen | In: Interaction models for water in relation to protein hydratation[END_REF] while cationwater interactions are described using parameters from Åqvist 28 for alkaline cations. Water/cation interaction parameters are summarized in Table 1.

Interactions between the electron and the classical particles

For the excess electron-water interaction, we use the pseudopotential developed by Turi and Borgis, 29 based on quantum ab initio calculations for one water molecule plus an additional electron confined in a box in the static exchange theory limit. Details on the use of this pseudopotential with an excess electron described using a gaussian grid basis set can be found in Ref. 16.

The interactions between the excess electron and the cations are modeled using the one-electron semilocal pseudopotentials proposed by Durand and Barthelat 30 for a cation M + :

Ve -/cat = - 1 r + Ŵ ps (8)
where -1/r is the coulombic interaction term and Ŵ ps is a nonlocal term. The analytical form of Ŵ ps is chosen to be

Ŵ ps (r) = l W l (r) Pl (9)
with

W l (r) = exp -α l r 2 n l i=1 c i,l r n i,l (10)
and

Pl = +l m=-l |lm lm| (11)
Pl is the projector on the spherical harmonics Y lm whose secondary quantum number is l. Computational details on the evaluation of these nonlocal terms using a gaussian grid basis set can be found in Ref. 18. The original parameters of the nonlocal terms were optimized together with a basis set of s, p and d gaussians centered on the cation nucleus.

Reparametrization of the electron/cation pseudopotentials

We have tested the electron/cation pseudopotentials on the isolated M 0 atoms in vacuum, using our 7 3 gaussian functions basis set. The energy levels for all (M + + e -) systems were compared to the experimental ionization potentials and excitation energies of M 0 . Neglecting the contribution due to the reorganization of the core orbitals, the ground state energy 0 of the excess electron can be related to the ionization potential of M 0 through 0 = -IP.

For all cations, the original pseudopotentials reproduce the desired experimental properties (ionization potential and first excitation energies) within a 15% range, as reported in Table 2. The differences observed are attributed to the different basis set used as well as to the lack of core-valence correlation and core polarization. Thus, for each cation a new set of parameters was designed by minimization of the difference between calculated and experimental properties. In this article, these reparametrized potentials will be called optimized pseudopotentials. Due to the functional form of the nonlocal term Ŵ ps (r), a separate optimization of the s, p and d parts of the pseudopotentials, corresponding to W 0 (r), W 1 (r) and W 2 (r) in Eqn. 9, was possible.

Taking into account the ionization potential and the energy of the first s → p and s → d transitions, we defined the Relative Root Mean Square (RRMS) error for each part of the pseudopotential,

RRMS(s) = IP -IP exp IP exp (12) RRMS(p) = ∆E ns→np -∆E ns→np exp ∆E ns→np exp (13) RRMS(d) = ∆E ns→nd -∆E ns→nd exp ∆E ns→nd exp ( 14
)
where IP is the first ionization potential of M 0 and ∆E i→j is the transition energy between electronic states i and j of M 0 , while the "exp" subscript denotes the experimental value of a given physical quantity.

We found many minima for each RRMS and chose parameters close to the original ones yielding small RRMS values. The optimized parameters for Li + , Na + and K + cations can be found in Appendix A, as well as the original parameters. In vacuo properties for Li, Na and K with these new parameters are in better agreement with the experimental data, as shown in Table 2.

Validation of the electron/cation pseudopotentials

The electron/cation pseudopotentials have been adjusted and reoptimized for the isolated neutral atoms properties. In order to check their ability to fairly describe the cation-electron pair (i.e. when the electron is localized outside the cation), the electron-sodium pseudopotentials have been compared

to ab initio calculations on sodium-electron pair systems. Several configurations have been selected

from QCMD simulation runs. We have retained a few water molecules around the electron-cation pair thus generating free (Na + ,e -,(H 2 O) n ) clusters with n varying from 14 to 99. We have used the TDSCF 31 method implemented in the Gaussian 03 package. 32 The gaussian basis sets used for these ab initio calculations are given in Appendix B. This crude TDSCF (Time-Dependent Self Consistent Field) calculation has first been compared to a high level MCQDPT (Multi-Configurational Quasi-Degenerate Perturbation Theory) calculation on a much smaller cluster of 5 water molecules (H 2 O) 5 using the MCQDPT method of Nakano 33 implemented in the GAMESS 2003 package. 34 The results are given in Table 3. The TDSCF transition energies are only slightly smaller than the MCQDPT ones (by 0.1 eV). The core-valence correlation, neglected in TDSCF, is small in such systems. The TDSCF method thus appears reasonable in this case.

We present here a comparison between the pseudopotentials approach and the TDSCF one on the (Na + ,e -,(H 2 O) 28 ) system. As shown in Table 4, the transitions energies obtained by the TDSCF and by the two pseudopotentials are very close to each other. In order to discriminate which of the original and optimized pseudopotentials is the most realistic one, we have compared the shape of the ground state orbital along the axis joining the Na nucleus and the excess electron barycenter (see Figure 1).

Since the use of pseudopotentials smooths out the rapid oscillation of the ab initio orbital in the vicinity of the Na nucleus, the comparison between orbital shapes must be made at distance from the cation larger than 1 Å. Figure 1 shows that the orbital obtained using the optimized pseudopotential is closer to the ab initio one, especially in the high probability density region. This shows that on top of ameliorating the Na atom spectroscopy, the reoptimization of the pseudopotential also improves the description of the cation-electron pair.

4 The sodium cation

Influence of the pseudopotential parametrization and finite size effects

As a first step in this work, we investigated the influence of the pseudopotential parameters describing the electron/cation interaction on the thermodynamic results, as well as the influence of the size of the simulation box. Structural, spectroscopic and thermodynamic information on this system was obtained by the mixed quantum-classical technique described earlier, using the two different sets of parameters for the electron/cation pseudopotential discussed in the previous section and two different sizes for the simulation box. The two different cubic simulation boxes used contained 300 and 800 water molecules, one sodium cation and an excess electron. The simulations were performed at temperature T = 298 K, with a density of ρ = 1 g.cm -3 .

The free energy profiles obtained using both sets of pseudopotential parameters are shown in Figure 2, for a system containing the sodium cation, an excess electron and 800 water molecules. In both cases, there is a local minimum of the free energy profile at short distances, corresponding to an electron-cation contact pair, 18,19 and a free energy barrier separating this state from the state where the electron and the cation are separately solvated (large electron-cation distance). But while both sets of parameters for the electron/cation pseudopotential exhibit this same general behavior, they yield quantitatively different results. It can be seen that the simulations using the optimized pseudopotential exhibit a higher free energy barrier between the two states (approximately 6 kT , compared to 3 kT for the original parameters), as well as a shorter equilibrium distance for the electron-cation contact pair (around 1.7 Å, compared to 2.2 Å for the original pseudopotential). This can be related to the fact that the optimized pseudopotential gives a larger value of the ionization potential for the sodium atom in vacuum than the original parameters (see Table 2), thus better reproducing the stability of the electron in the vicinity of the sodium cation. Based on this interpretation, we suggest that the free energy curve using the optimized pseudopotential is closer to reality.

The dependence of the size of the simulation box on the thermodynamic and structural properties of the sodium-electron system in bulk water was also studied. Figure 2 also shows the free energy profiles as a function of the electron-sodium distance for systems containing 300 and 800 water molecules. It can be seen that the size of the simulation box has little influence on the equilibrium distance for the contact pair. Indeed, radial density functions (not presented here) for the sodium-electron contact pair in systems containing 300 and 800 water molecules are very similar, indicating that the behavior of this system at short distances is not much influenced by finite-size effects. The thermodynamic information concerning the large electron-cation distances depends strongly on the size of the system chosen for the study, preventing us to draw definite conclusions about the relative stability of the shortand long-distance states. However, it is interesting to note that the short-distance electron-sodium pair seems to be more stable than the separately solvated species for systems containing 800 water molecules by some 2 kT .

The unconstrained dynamics of the electron-sodium system solvated in water can also shed some light on this important question of the relative stability of the contact pair and the separately solvated species. The evolution of the electron-sodium distance during unconstrained simulations is reported in Figure 3, starting from 4 different configurations with an initial electron-cation distance between 5 Å and 7 Å. It can be seen that three of these trajectories lead to the electron-sodium pair within times ranging from 2 ps to 10 ps, while the fourth simulation does not exhibit electron-cation distances smaller than 5 Å. The fact that we observe a spontaneous formation of the contact pair for three systems while the reverse process never occurs in the timescale of 100 ps supports the conclusion that the electron-sodium pair is the most stable state in our simulation model. It seems clear, however, that in the long timescale (thermodynamic limit) an equilibrium between the contact pair and the dissociated solvated species will take place at room temperature. This is because the free energy difference between these two states is on the order of kT , and the free energy barrier is smaller than 10 kT .

Structural information

In this section, we present structural information about the electron-sodium contact pair and its solvation shell. The Radial Density Functions (RDF) for the sodium-oxygen and sodium-hydrogen pairs are presented in Figure 4, for both the sodium-electron pair and the single sodium cation in bulk water. The main solvation features are found to be the same in both cases, like the first maximum of the Na-O RDF at r ≈ 2.4 Å and its first minimum at r ≈ 3.2 Å. The main difference between these two cases is the relative height of the peaks, yielding a number of water molecules in the first solvation shell of 3.4 for the electron-cation pair, to be compared with the 5.9 water molecules present in the first solvation shell of the single sodium cation in bulk water. Thus, the structure of the solvation shell of the Na + cation is unchanged in presence or absence of hydrated electron. The difference in the number of water molecules in the first solvation shell can simply be accounted for by the volume occupied by the hydrated electron.

On the contrary, electron-oxygen and electron-hydrogen RDF in the sodium-electron pair are very different from those of the solvated electron in bulk water (see Figure 5). The first peak in the electronhydrogen radial distribution function is located at 2.1 Å and 2.2 Å for the solvated electron and sodium-electron pair in bulk water respectively. The MD simulation reveals that the water molecules are strongly oriented towards the electron to form hydrogen bonds. The number of water molecules in the first solvation shell is found to be 4.2 in the case of the hydrated electron and drops to 2 for the solvated sodium-electron contact pair. Moreover, we find that the solvation structure is less clear, indicating that the solvation of the electron in the pair is weaker than that of the electron in bulk water.

Experimental structural studies have mainly been performed at very low temperature on glasses and ice systems. In γ-irradiated 10M NaOH alkaline aqueous glasses analysis of electron spin echo data, that firstly leads to the octahedral model, 11,35,36 suggests that 2 bond-oriented water molecules are located at 2.1 Å from the electron center. 12,[START_REF] Dikanov | Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy[END_REF] Our simulation data agree well with these experimental findings and strongly support that the two hydrogen atoms of the first solvation peak do not belong to the same molecule. This hydrogen bonding like interaction has recently been confirmed by Raman experiments. 14, 15

Absorption spectrum

The UV-Vis absorption spectra of the solvated electron with a sodium cation and 300 SPC water molecules at ambient conditions are shown in Figure 6, for both the separately solvated species and the electron-sodium contact pair. The presence of the cation induces a blue shift of the absorption spectrum of the solvated electron. In the case of the separately solvated species, the maximum of the absorption spectrum is located at E = 1.95 eV, which represents a shift of 0.07 eV from the solvated electron in bulk water, while the shape of the band and its half-maximum width are unchanged. An analysis of the contributions to the total electron-cation interaction shows that such long-distance influence is indeed purely coulombic. The absorption spectrum of the electron in the contact electronsodium pair is located at much higher energy (2.25 eV) and exhibits a slightly different band shape, with a shoulder on its high-energy wing and a half-maximum width +0.1 eV larger than that of the solvated electron. The large shift at small electron-cation distances is mainly explained by the stronger coulombic interaction between the electron and the cation. Moreover, previous work showed that the change in the shape of the spectrum and the existence of a shoulder are due to one of the three p-like excited states of the solvated electron (the one with Σ symmetry, its orbital pointing in direction of the cation) being destabilized by core repulsion. 18 A similar phenomenon has been reported experimentally in the case of earth alkaline cations and an excess electron in THF. 10,37 Furthermore, the presence of this shoulder on the spectrum of the solvated electron near a sodium cation has been reported in an experimental study by Gelabert and Gauduel. 9

Comparing the spectroscopic information obtained from simulation to experimental data is not straightforward due to the importance of many factors such as the concentration of ions and the presence of different counter-ions. [4][5][6][7][8] The concentration effect will be discussed below.

Other cations

To study the behavior of the hydrated electron in the presence of different alkali cations, simulations were performed on systems containing one cation (Li + or K + ), 300 water molecules and an excess electron. For each system, we performed free energy calculations using quantum umbrella sampling as well as 100 ps of unconstrained simulations starting from 4 different initial configurations. All simulations were done with sets of parameters for the electron-cation pseudopotential optimized as described in Section 3.3. The results obtained are compared with the case of the sodium cation presented in details in the previous section.

Free energy profiles

The free energy profiles as a function of the electron-cation distance r for the three alkali cations (Li + , Na + , K + ) are shown in Figure 7. For all three cations, these profiles exhibit two local minima, at short distance (r < 4 Å) and at infinite distance. The height of the free energy barrier separating these minima decreases from the sodium cation (6.2 kT ) to the potassium (3.3 kT ) and the lithium cation (1.5 kT ). The time evolution of the electron-cation distance during unconstrained simulations of systems containing a potassium cation, presented in Figure 8 (left panel), reveals the existence of two metastable states clearly separated. A few crossings of the free energy barrier are observed on the time scale of 100 ps. However, unlike Na + , some crossings of the barrier in the case of K + lead to the separately solvated species. This event is not frequent enough during our simulations to draw a definite conclusion upon the stability of the electron-potassium pair. It is important to note that, due to the finite size of our simulation box (≈ 21 Å), free energy information obtained is limited to distances smaller than 9-10 Å. In the case of the lithium cation, the free energy barrier is approximately 1.5 kT , and unconstrained simulations exhibit frequent crossings of this barrier (see Fig. 8, right panel). No stable Li + -electron pair was observed during our simulations.

We suggest that the existence of an electron-cation pair for Na + and K + can be related to their standard reduction potential, higher than that of Li + : [START_REF] Lide | Handbook of Chemistry and Physics[END_REF] This can be interpreted as a stronger ability of the sodium cation, and to a lesser extent of the potassium cation, to accommodate an electron in its close neighborhood, explaining the formation of stable (Na + , e -) and (K + , e -) contact pairs.

E • Na + /Na -2.71 V while E • Li + /Li -3.04 V and E • K + /K -2.93 V.

Electron absorption spectra

The UV-Vis absorption spectra of an alkali cation plus an excess electron in 300 SPC water molecules at ambient conditions are shown in Figure 9, and their main characteristics are reported in Table 5.

The absorption spectra were obtained by averaging over 85 ps simulations starting from 4 different initial configurations (after a 15 ps equilibration run). For Na + and K + cations, the separately solvated species and the electron-cation pair states were separately averaged and the spectra of both metastable states are shown. The effect of the cation on the absorption band of the hydrated electron is similar for Li + and K + to the effect observed for the sodium cation. However, the maximum of the spectrum for the potassium-electron pair is located at a lower energy than that of the sodium-electron pair, due to the larger electron-cation distance in the contact pair.

A simple model for the ionic strength dependence of the absorption spectra

As stated in the introduction section, several hydrated electron absorption studies have been reported in the literature, using various ionic strength conditions. A way to compare these data with the present MD simulations is to consider the following simple model. The free energy calculations for all three electron-ion systems (sodium, lithium and potassium) clearly show that the contact electron-cation pair is either as stable as the dissociated pair, or more stable by only a few kT . Given that the dissociation barrier is also quite small, the average cation-electron distance d in the experiments will presumably hardly depend on the above mentioned free energy profile but rather on the minimization of the coulombic repulsive interaction between like charges in the solvent medium. The alkali cations are thus considered to be distributed statistically around the solvated electron. This allows to relate the average cation-electron distance d directly to the cation concentration C through the following relation:

d = 1 2 (CN A ) 1/3 (15)
where N A is Avogadro's number.

The hypothesis of a randomly arranged cations with respect to trapped electrons has already been put forward by electron spin echo analysis of various Na concentrations alkaline glasses. 12,[START_REF] Dikanov | Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy[END_REF] For a 10M

NaOH glass the electron-sodium distance is estimated to 2.6-2.9 Å. Our simple model predict a distance of 2.7 Å for a sodium concentration of 10M. This model enables us to compare the experimental absorption data obtained for different ionic strengths with the present MD simulations for various constrained electron-cation distances. The experimental absorption shifts due to the presence of cations, ∆E, are reported in Figure 10 together with the MD results. In this figure, the alkali-cation concentrations were converted to average cation-electron distances using Equation 15. The experimental and simulated spectral shifts were determined by the difference of the absorption spectrum maxima of the solvated electron in the concentrate salt solution and in pure water at the same temperature obtained experimentally and by simulation respectively. This takes into account the fact that experiments have been performed at various temperatures.

The simulation results reveal that a significant shift is observed only at short distance, lower than 5-6 Å. A cation effect is obtained on the absorption spectrum if the first solvation shell of the hydrated electron is modified. The absorption spectrum of a solvent separated cation-electron pair is found to be similar to the single hydrated electron one. This is consistent with the fact that a shift of the absorption spectra is only observed at high salt concentration experimentally. We observed for all three cations a blue shift of the same order of magnitude as in experiments. Given the crudeness of the concentration-distance relation used, the agreement can be considered as fair. It seems clear that a more detailed interpretation of the experiments will have to consider the effect of the counter-ions in the simulations. Whether or not the salts are fully dissociated in the experiments at high ionic strength would also have to be carefully studied.

Conclusions

We have performed MD simulations of an excess electron in bulk water in the presence of Li + , Na + and K + cations in bulk water at ambient conditions. We have developped new one electron pseudopotential parameters for describing alkali cations-electron interactions based on ab initio calculation. In the case of the sodium cation, we observe a contact pair which is more stable than the dissociated pair by a few kT . We have carefully checked the effect of the pseudopotential parameters and the system size and found that the existence of this contact pair is not sensitive to our model parameters. For the potassium cation, the contact electron-cation pair is also a stable state but the free energy barrier is lower than in the case of sodium. We observed spontaneous crossings of the barrier leading to the formation or the dissociation of the electron-cation pair in the MD timescale. In the case of lithium, the more stable state is found to be the separated solvated species. The free energy barriers are however small in all cases and we predict that the equilibrium electron-cation distance in bulk water will not be dominated by the free energy profile.

The structure of the first solvation shell of the solvated electron in presence of a sodium cation in bulk water, i.e. two hydrogen bonding water molecules, has been found to be in agreement with electron spin echo analysis.

The calculated absorption spectrum is dominated by the solvated electron-cation distance. When the electron-cation distance decreases, the absorption spectrum is shifted to higher energy. This is good agreement with experimental evidence of absorption spectrum blue shift with increasing cation concentration. We suggest a relation between the cation concentration and the equilibrium solvated electron-cation distance based on a random cation distribution. This model enables us to compare our single cation simulations with experiments at high salt concentration. We found a qualitatively good agreement between simulations and experiments which supports the conclusion that the equilibrium solvated electron-cation distance is dominated by the minimization of the coulombic repulsive interaction between like charges in the solvent medium.

In this work, we have limited ourselves to simulations with only one cation in the simulation box.

At high salt concentration, the average distance between cations is quite small (lower than 6 Å) and the interaction between cations has to be explicitly taken into account to improve the simulation model.

In order to have a better insight of the salt concentration effect, simulation work on systems containing more than one cation and explicit counter-ions is in progress. The value of the orbital is plotted along the axis joining the cation and the center of the electronic density. Data obtained using the optimized set of parameters for the electron/sodium pseudopotential. (dotted line), Na + (dashed line) and K + (solid line). For Na + and K + , two spectra are shown: the contact electron-cation pair (thick line, at higher energies) and the separately solvated species (thin line, at lower energies); for details, see Sec. 5.2. The absorption spectrum for a hydrated electron without cation is also shown (dash-dot-dot).

Figure 1 :

 1 Figure 1: Comparison of the ab initio orbital (thick line) and pseudoorbitals of the ground state using both the original (dashed line) and the optimized (solid line) parameter sets of the electron-cation pseudopotential in the case of the electron-sodium pair solvated by 28 water molecules in vacuum.

Figure 2 :

 2 Figure2: Free energy profiles as a function of the electron-sodium distance obtained using the original pseudopotential (thin solid line) as well as the optimized set of parameters (thick solid line) for a system containing 800 water molecules. The free energy profile obtained with the optimized pseudopotential and 300 water molecules is plotted as a dashed line.

Figure 3 :

 3 Figure 3: Electron-cation distance as a function of simulation time during unconstrained simulations of Na + and an excess electron with 300 water molecules, starting from 4 different initial configurations.

Figure 4 :Figure 5 :

 45 Figure 4: Radial density functions for the distribution of oxygen (solid line) and hydrogen (dashed line) atoms around the sodium cation in the (Na + , e -) contact pair (thick lines). The radial density functions of Na-O and Na-H for a single sodium cation in pure water are shown for comparison (thin lines).

Figure 6 :

 6 Figure 6: Normalized absorption spectra of the solvated electron with a sodium cation, for the contact pair (thick solid line) and separately solvated species (dashed line). The absorption spectrum for an hydrated electron without cation is also shown for comparison purpose (thin solid line).

Figure 9 :

 9 Figure 9: Normalized absorption spectra for the solvated electron with different alkali cations: Li +

Figure 10 : 6 (

 106 Figure 10: Energy shift of the absorption band maximum of the solvated electron with different cations (Li + , red; Na + , black; K + , green) as a function of the electron-cation distance. Simulations results from this work (solid lines) are compared to experimental results from Refs. 5 (LiCl, triangle up), 6 (Na 2 SO 4 , triangle left, and NaClO 4 , triangle right), 8 (NaCl and LiCl, square and NaClO 4 , diamond) and 41 (triangle down) using the concentration-distance relation from Eqn. 15.

Table 1 :

 1 Lennard-Jones parameters used to model the water oxygen/cation interactions, taken from

	iO (kJ/mol) 0.223 1.16 10 -2 1.37 10 -3
	σ iO ( Å)	0.385	3.33		4.74
	Ref. 28.
	Pseudopotentials	Exp. Relative errors
	(original -optimized)
	Li IP (eV)	4.89 -5.30		5.39	9.4% -1.6%
	∆ (eV)	1.57 -1.90		1.84	14.8% -2.9%
	Na IP (eV)	4.76 -5.11		5.14	7.3% -0.5%
	∆ (eV)	1.84 -2.19		2.10	12.5% -4.1%
	K IP (eV)	3.98 -4.26		4.34	8.3% -1.7%
	∆ (eV)	1.51 -1.65		1.61	6.3% -2.6%

Table 2 :

 2 Ionization potential (IP) and first excitation energy (∆) obtained using original and optimized pseudopotentials. These results are compared to the experimental values from Ref.40.

		MCQDPT	TDSCF	TDSCF
	transition transition energy transition energy oscillator strength
	0 → 1	1.105	0.979	0.324
	0 → 2	1.296	1.172	0.313
	0 → 3	1.647	1.513	0.110
	0 → 4	1.814	1.678	0.224

Table 3 :

 3 Comparison of TDSCF and MCQDPT transition energies (in eV) and TDSCF oscillator

	strengths on a (H 2 O) 5	-configuration.
		TDSCF	TDSCF original pseudo. optimized pseudo. optimized pseudo.
	transition transition oscillator	transition	transition	oscillator
		energy	strength	energy	energy	strength
	0 → 1	2.274	0.289	2.295	2.316	0.335
	0 → 2	2.545	0.247	2.390	2.406	0.330
	0 → 3	2.760	0.235	2.724	2.766	0.334

Table 4 :

 4 One electron solvated by one Na + and 28 H

2 O molecules: Comparison of TDSCF and QCMD transition energies (in eV) and oscillator strengths on a Na(H 2 O) 28 + configuration.

Acknowledgments

We thank the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) of the CNRS for generous allocations of NEC SX-5 computer time. Julien Bonin and Mehran Mostafavi are gratefully acknowledged for fruitful discussions.

A Parameters of the pseudopotentials

Using the notations of Eqn. 10, the parameters of the original pseudopotentials are: The parameters obtained after optimization of the pseudopotential (see Sec. 2.4) are: