Ahmed Abdmouleh #
email: ahmed.abdmouleh@univ-ubs.fr

Emmanuel Boutillon #
email: emmanuel.boutillon@univ-ubs.fr

Charbel Laura Conde-Canencia #
email: laura.conde-canencia@univ-ubs.fr

Abdel Nour

Catherine Douillard
email: catherine.douillard@telecom-bretagne.eu

On Signal Space Diversity for Non Binary Coded Modulation Schemes

Keywords: Coded Modulation, Bit Interleaved Coded Modulation, Rotated Constellation, Signal Space Diversity, Mutual information

In this paper, we study high-spectral efficiency and high-order diversity communications for the next generation broadcasting systems. In this context, rotating a Quadrature Amplitude Modulation constellation with a Signal Space Diversity (SSD) technique is known to improve the decoding performance of the communication system over the Rayleigh fading channel. In this work, we consider the SSD technique applied to coded modulation schemes with the novelty of selecting the rotation angle from the analysis of the mutual information variations. In this context, it is known that coding modulation outperforms bit-interleaved coded modulation, but we show that coded modulation has also an extra advantage: the optimal rotation angle is only marginally impacted by the signal to noise ratio and the erasure rate of the fast Rayleigh fading channel. This opens the door to a robust coded modulation scheme particularly suited for broadcasting applications. Simulation results confirm the theoretical study with a gain of up to 1.2 dB when comparing to the DVB-T2 standard.

I. INTRODUCTION

Next generation broadcast systems such as DVB-T2 [START_REF]Digital Video Broadcasting (DVB); frame structure, channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2)[END_REF] and DVB-NGH [START_REF] Gomez-Barquero | DVB-NGH: The next generation of digital broadcast services to handheld devices[END_REF] must guarantee robust high data rate transmissions in severe channels. A key aspect in this context is the increase of the diversity order while keeping high spectral efficiency. Currently, the Signal Space Diversity (SSD) [START_REF] Boutros | Signal space diversity: a power and bandwidth-efficient diversity technique for the Rayleigh fading channel[END_REF] principle associated to Bit-Interleaved Coded Modulation (BICM) represents the reference in coded modulation over fading channels. BICM was first introduced by Zehavi in [START_REF] Zehavi | 8-PSK trellis codes on Rayleigh channel[END_REF] and later formalised by Caire et al. in [START_REF] Caire | Bit-interleaved coded modulation[END_REF]. Its principle is to serially concatenate a Forward Error Correction (FEC) code and a bit-interleaver prior to the mapping and modulation step. Then, since the channel encoder and the modulator are separated by a bit-level interleaver, they can be chosen independently allowing for a simple and flexible design.

The SSD technique consists of rotating the constellation in the signal space and interleaving one of the In-phase (I) or Quadrature (Q) signal components with respect to the other. The interleaving makes the I and Q components to be sent in different symbol periods, each being affected by a different fading coefficient. This doubles the diversity order of the BICM scheme. These so-called Rotated Contellations (RC) were adopted in the DVB-T2 [START_REF]Digital Video Broadcasting (DVB); frame structure, channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2)[END_REF] and DVB-NGH [START_REF] Gomez-Barquero | DVB-NGH: The next generation of digital broadcast services to handheld devices[END_REF] standards.

In this paper, we investigate the association of q-ary codes to high-order modulations, where the cardinality of the code equals the modulation order. This kind of scheme is called Coded Modulation (CM). We consider the optimization of the SSD technique through the analysis of the mutual information of the channel as a function of the rotation angle. This approach is applied to both BICM and CM schemes to show the interest and advantages of the CM solution. Note that for the BICM we consider a binary FEC code whereas for the CM scheme we adopt a Non-Binary (NB) code defined over a Galois Field GF(q), which allows to directly map a coded symbol to a constellation point. In [START_REF] Ma | Design of signal space diversity based on non-binary LDPC code[END_REF] and [START_REF] Zhou | Optimized rotations and labeling for nonbinary LDPC coded modulation with signal space diversity[END_REF] the authors provide results on the association of NB-LDPC and high-order modulations with rotated constellations to show the interest of the CM scheme. A gain of about 0.15 dB is introduced with the SSD in a NB-LDPC coded modulation scheme [START_REF] Ma | Design of signal space diversity based on non-binary LDPC code[END_REF].

The paper is organised as follows: Section II presents the principle of the SSD technique and its application to the DVB-T2 standard. Then, a theoretical study of the mutual information is presented in Section III. Section IV describes how the analysis of the mutual information can optimize the SSD technique for coded modulations. Simulation results and discussions are presented in Section V. Finally, Section VI draws conclusions.

II. SIGNAL SPACE DIVERSITY

When a constellation symbol x = (x I , x Q ) is directly transmitted in the Rayleigh fading channel, both the I (x I ) and Q (x Q ) components fade identically. In case of severe fading, an irreversible loss of information on both components can be observed. In order to help the demapper to retrieve the transmitted symbol, it is more efficient to send separately x I and x Q in two different time or frequency slots, so that the fading coefficient r I affecting x I is independent of the fading coefficient r Q affecting x Q .

In the SSD scheme adopted in the DVB-T2 standard [START_REF] Nour | Improving BICM performance of QAM constellations for broadcasting applications[END_REF], the encoded symbol is mapped to the constellation to generate a modulated signal x t = (x

t Q = r t Q x t Q + w Q
, where w I and w Q represent the additive noise on the I and Q axes, r t I = r t and r t Q = r t+d . Fig. 1 illustrates the effect of the Rayleigh fading channel on a Quadrature Amplitude Modulation (QAM) with 16 points, with and without rotation: the I axis suffers a severe fading (r I = 0.2) while there is no fading on the Q axis (r Q = 1). In the first case, the reconstructed constellation has points very close one to each other, which increases the error probability. On the contrary, with the rotated constellation, the minimum distance between the points of the reconstructed constellation remains significant.

A. Choice of the rotation angle α in the DVB-T2 standard

As the choice of the SSD rotation angle α depends on different factors, different solutions have been considered in the literature. In [START_REF] Boutros | Signal space diversity: a power and bandwidth-efficient diversity technique for the Rayleigh fading channel[END_REF] the choice of α aims to maximize the so-called product distance in order to minimize the pairwise error probability between two different transmitted sequences. Other criteria are considered in [START_REF]Rotated QAM constellations to improve BICM performance for DVB-T2[END_REF] like the average Hamming distance between any two adjacent constellation symbols in the 2-D constellation and the incidence on the Gray mapping in the projected constellation points after rotation. Unfortunately, in practice, these criteria are in conflict and their simultaneous application leads to different values of α. The angle values adopted in the DVB-T2 standard [START_REF]Digital Video Broadcasting (DVB); frame structure, channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2)[END_REF] represent a compromise between the listed criteria. They are given in

TABLE I VALUES OF THE ROTATION ANGLES IN THE DVB-T2 STANDARD

As already introduced in section I, the novelty of the paper is to select the rotation angle that maximizes the mutual information. The following Section is then dedicated to the theoretical study of the mutual information of the CM and BICM schemes.

III. MUTUAL INFORMATION A. Notations

The considered constellation is denoted by Q. It contains q points x k , k = 1 • • • q, where x k is defined by its in-phase x k I and quadrature

x k Q components, i.e., x k = (x k I , x k Q ) = x k I + jx k Q .
Assuming perfect Channel State Information (CSI) at the receiver side, the received point y = y I + jy Q after transmission of x ∈ Q over the fast flat Rayleigh fading channel with erasures is given by y = r I e I x I + je Q r Q x Q + w where w is a complex Gaussian noise with variance σ 2 , r I and r Q are independent realizations of a Rayleigh fading with unitary standard deviation and e I , e Q are the erasure coefficients. If we consider the Rayleigh channel without erasure then e I = e Q = 1, while for the Rayleigh channel with erasures, P (e I = 0) = P (e Q = 0) = p e and P (e I = 1) = P (e Q = 1) = 1 -p e , where p e is the erasure probability. In the sequel, r will denote the couple (r I , r Q ) and we will consider the channel without erasure for the theoretical equations that follow. At the receiver side, P (x|y; r), the probability that x has been transmitted given y and r is defined as:

P (x|y; r) = P (y|x; r)P (x) q k=1 P (y|x k ; r)P (x k ) (1)
with

P (y|x; r) = 1 √ 2πσ e -(y I -r I x I ) 2 +(y Q -r Q x Q ) 2 2σ 2 . (2)

B. Mutual information computation

Let us define X and Y as the random variables that represent the input and output of the transmission channel. The mutual information I(X; Y ) between X and Y is given by

I(X; Y ) = H(X) -H(X|Y ). (3)
The first term in ( 3) is maximized when all the constellation points have the same uniform probability 1/q of being selected. In that case, H(X) = -

q k=1 P (x k ) log 2 (P (x k )) = m
, where m = log 2 (q). The second term in (3) is more complex to compute. We can derive its expression in the case of CM or BICM.

1) Mutual information in the CM scheme: For CM, the q-ary coded symbol is directly mapped to a constellation point. The second term in (3) is then expressed as

H(X|Y ) = - y∈C p(y) r∈R 2
H(X|y; r)P (r)dr dy, (4) where R is the set of real numbers, C is the set of complex numbers and H(X/y; r) is defined as

H(X|y; r) = - q k=1 P (x k |y; r) log 2 (P (x k |y; r)). (5)
2) Mutual information in the BICM scheme: Let us consider a binary mapping of the constellation Q that associates to each point

x k a binary codeword (b k,1 , • • • b k,m ). Let X 0
i be the set of symbols where the i th bit b i is equal to 0 and X 1 i be the set of symbols where the i th bit b i is equal to 1. Thus,

P (b i = s|y; r) = x∈X s i P (x|y; r), s = 0, 1. (6)
Assuming ideal bit interleaving, which makes the considered channel equivalent to m binary channels ([5] eq. 14), the second term of (3) can be expressed as

H(X|Y ) = m i=1 H(B i |Y ), (7)
where B i represents the i th binary channel associated to the i th bit and H(B i |Y ) is expressed as From these curves we can conclude that, in all cases, the CM scheme presents higher mutual information than the BICM. Also, rotation always provides gain for the CM scheme (unlike for the BICM, where rate loss may appear with rotation). Another point is that the variations on the mutual information are more significant in the erasure channel. Thus, the SSD can potentially provide more gains in the erasure channel.

H(B i |Y ) = - y∈C p(y)
In order to enhance the system performance with the SSD technique, we propose to select the rotation angle that maximizes the mutual information I(X; Y ). For each SNR, the optimal angle value can be expressed as Note that this approach rationalizes the one proposed in [START_REF]Rotated QAM constellations to improve BICM performance for DVB-T2[END_REF], which implies a complex trade-off with several contradictory criteria.

α o (SNR) = arg max{I(α, SNR), α ∈ [0 • -90 • ]}. (10)
Fig. 4 and Fig. 5 show the angles that maximize the mutual information for each SNR value (SNR ∈ [0 . . . 30] dB) using respectively the 16-QAM and 256-QAM modulations. As in [START_REF] Nour | Improving BICM performance of QAM constellations for broadcasting applications[END_REF], for the BICM 16-QAM scheme, the optimal angle value for high SNR (i.e. greater that 25 dB) is α o ≈ 31.7 • . However for practical operating SNR values (between 18 dB and 25 dB), α o ≈ 20 • . If this angle value is considered for lower SNRs, a rate loss of about 0.03 bit/s/Hz would be introduced at SNR = 10 dB with respect to the optimal angle α o (10dB) ≈ 10 • (Fig. 2). For CM, the optimal angle value for high SNR is also α 0 = 31.7 • . However, considering this angle also for lower SNRs barely affects performance (unlike for BICM): at 10 dB, using α 0 = 31.7 • instead of the optimal angle introduces only a rate loss of 0.004 bit/s/Hz for the 16-QAM (Fig. 2) and 0.003 bit/s/Hz for the 256-QAM. In other words, the choice of the same rotation angle for all SNR, introduces negligible rate loss for the CM scheme and a some tenths of rate loss for BICM. This fact was already observed in Figures 2 and3, where the mutual information in the CM scheme is much less sensitive (about a factor of 10) to the angle variation than in BICM. Finally, with the erasure channel (Fig. 4 and5), the optimal angles for the CM are closer to the angles with the channel with no erasure, giving a simple modulation scheme efficient for all channel conditions. This is not the case for the BICM modulation. In fact, for broadcasting applications where each receiver experiments a different level of SNR and erasure, the choice of the rotation angle is always a trade-off for BICM.

B. Mutual information as a function of the SNR

We now consider the mutual information curves as a function of the SNR for the selected angle values. I) and, from Fig. 4 as well, this angle choice is a good compromise for high and low SNRs. From these results, we observe that the CM with SSD outperforms the non-rotated scheme for all SNRs. This does not occur for BICM: at low SNR (up to approximately 12 dB for the 16-QAM), the rotation causes a mutual information loss compared to non-rotated BICM. This can also be observed in Figures 2 and3, where the mutual information curve decreases with rotation. Therefore, the gains displayed by the rotated CM are more significant than for BICM.

The same curves are presented for the 256-QAM modulation in Fig. 7. The considered rotation angles are α o = 31.7 • for the CM and α = 3.6 • for the BICM (see Table I). Using the BICM scheme, the SSD barely changes the mutual information performance and does not offer any significant advantage. However, for the CM scheme, a SNR gain greater than 1 dB can be observed for spectral efficiencies larger than 7 bit/Hz/s. Over the erasure Rayleigh channel (p e = 0.1), the gain introduced with the SSD is more significant than for the no-erasure case, for both 16-and 256-QAM and specially for high SNR values.

V. SIMULATION RESULTS AND PERFORMANCE

COMPARISON

To verify the theoretical results, we ran Monte-Carlo simulations for the different scenarios considered in the previous sections. Because of lack of space, we only show results with the 256-QAM for two coding rates (but the same conclusions can be drawn from the simulation results with the 16-QAM). The BICM scheme considered is the one of the DVB-T2 standard, i.e., rotation angle of 3.6 • , a specific interleaver pattern and an N = 64800 binary irregular LDPC code. For the CM, two specific Non-Binary LDPC codes were designed for rates 3/4 and 9/10. The length of these codes is 64800 bits or 8100 symbols defined over GF(256). These NB-LDPC codes are available at [START_REF] Marchand | Lab-STICC website on Non-Binary LDPC[END_REF]. The decoding algorithm of the NB-LDPC codes is the Extended Min-Sum (EMS) algorithm [START_REF] Declercq | Decoding algorithms for nonbinary LDPC codes over GF(q)[END_REF]. For the BICM, the LDPC decoder implements the Sum-Product algorithm followed by a BCH decoder as in [START_REF]Digital Video Broadcasting (DVB); frame structure, channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2)[END_REF]. We have used a maximum number of iterations equal to 50, same frame length and same channel conditions for both cases. Each point of the simulation curves represents the transmission of data until 100 erroneous frames have been encountered. For the EMS decoding, we have performed simulations with n m = 50, i.e. length of the exchanged messages between check and variable nodes [START_REF] Declercq | Decoding algorithms for nonbinary LDPC codes over GF(q)[END_REF]. Fig. 8 presents results for a code rate of 3/4. As already observed in Figure 3, the SSD technique introduces performance loss in the BICM scheme for spectral efficiencies lower than 7 bit/Hz/s. However, as announced by the theoretical study, a gain of about 0.3 dB is provided by the SSD technique for CM.

For higher spectral efficiencies (9/10-rate in Fig. 9), SSD introduces gain for both the BICM and CM schemes, as certified by a zoom on the right upper zone of Fig. 7. This gain is more significant in the CM scheme (1.3 dB at FER = 10 -2 compared to about 0.15 dB for BICM). Note that these performance results are consistent with the analysis of Fig. 3.

VI. CONCLUSION

In this paper we considered the application of the signal space diversity technique to high spectral efficiency com- ig. 9. FER simulation for 9/10-rate BICM-GF(2) and CM-GF(256) schemes over the the fast flat Rayleigh fading channel, with and without Rotated Constellation munications in the context of next generation broadcasting systems. We proposed to determine the optimal rotation angle as the one that maximizes the mutual information for practical signal-to-noise ratio values. We showed that non-binary coded modulations are more robust than bitinterleaved coded modulations and take better advantage of the signal space diversity technique. The solutions that we proposed can lead to significant performance gains for next generation broadcasting systems.

Fig. 1 .

 1 Fig. 1. 16-QAM constellation, 37.2 • -rotated 16-QAM constellation before transmission and after reception for fading factors of r I = 1 on the I-axis and r Q = 0.2 on the Q-axis.

r∈R 2 H 1 P

 21 (b i |y; r)P (r)dr dy.(8) The entropy H(b i |y; r) is defined as H(b i |y; r) = -s=0,(b i = s|y; r) log 2 P (b i = s|y; r).

( 9 )

 9 Figures 2 and 3 show the mutual information curves as a function of the SSD rotation angle for both the CM and the BICM schemes. Fig. 2 considers a 16-QAM with SNR values of 10, 15 and 25 dB. Fig. 3 considers a 256-QAM for SNR values of 15, 25 and 30 dB. For the BICM scheme a Gray mapping is considered. Both figures show results for the flat fast Rayleigh fading channel with erasures (p e = 0.1) and without erasure.From these curves we can conclude that, in all cases, the CM scheme presents higher mutual information than the BICM. Also, rotation always provides gain for the CM scheme (unlike for the BICM, where rate loss may appear with rotation). Another point is that the variations on the mutual information are more significant in the erasure channel. Thus, the SSD can potentially provide more gains in the erasure channel.In order to enhance the system performance with the SSD technique, we propose to select the rotation angle that maximizes the mutual information I(X; Y ). For each SNR, the optimal angle value can be expressed as

Fig. 2 .

 2 Fig. 2. Mutual information as a function of the rotation angle α for CM and BICM. SNR = 10, 15 and 25 dB. Rayleigh fading channel and 16-QAM modulation.

5

 5 CM and BICM Mutual information=f(α), SNR = 15 dB, 256-QAM α

Fig. 3 .

 3 Fig. 3. Mutual information as a function of the rotation angle α for CM and BICM schemes. SNR = 15, 25 et 30 dB. Rayleigh fading channel and 256-QAM modulation.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Rotation angle that maximizes mutual information, as a function of the SNR, for the Rayleigh channel and Rayleigh channel with 10% erasures. 16-QAM modulation.

  Fig 6 considers the 16-QAM with rotation angles α o = 31.7 • for CM and α o = 16.8 • for BICM. This angle choice for the BICM is the one of the DVB-T2 standards (see Table

Fig. 6 .Fig. 7 .

 67 Fig.[START_REF] Ma | Design of signal space diversity based on non-binary LDPC code[END_REF]. CM and BICM mutual information curves for a 16-QAM modulation over fast flat fading Rayleigh channel (without erasures and with 10% erasures)

  Table-I for different modulation orders.

	Constellation Rotation Angle α value (degree)
	QPSK	29.0 •
	16-QAM	16.8 •
	64-QAM	8.6 •
	256-QAM	3.6 •


Agathe Colléony

Susan Clayton

Denis Couvet

Michel Saint

Anne-Caroline Prévot

Agathe Colleony
email: agathe.colleony@gmail.com

Michel Saint Jalme

Anne-Caroline Prevot

Human preferences for species conservation: Animal charisma trumps endangered status

Keywords: animal adoption program, charisma, conservation status, phylogenetic distance, willingness-to-pay, zoo

est destinée au dépôt

Introduction

The accelerating loss of biodiversity is now widely acknowledged, with a steep increase in the number of species listed as Critically Endangered (e.g. from 168 to 209 mammal species) or Endangered (e.g. from 31 to 810 amphibian species) from 1996 to 2015, according to the International Union for Conservation of Nature Red List of endangered species (IUCN 2015). Ambitious conservation policies depend on people's concern for biodiversity, which determines their commitment. One way of investigating their concern is to analyze their willingness-to-pay (WTP) [START_REF] Balmford | The Worldwide Costs of Marine Protected Areas[END_REF][START_REF] Bateman | Bringing Ecosystem Services into Economic Decision-Making: Land Use in the United Kingdom[END_REF][START_REF] Togridou | Determinants of Visitors' Willingness to Pay for the National Marine Park of Zakynthos, Greece[END_REF][START_REF] Zheng | Benefits, Costs, and Livelihood Implications of a Regional Payment for Ecosystem Service Program[END_REF]. Most studies have focused on the value given to ecosystems [START_REF] Balmford | The Worldwide Costs of Marine Protected Areas[END_REF]). Among the few studies that have explored the value given to species, all of them, to our knowledge, have relied on participants' self-reported hypothetical species choices or intentions to support a program (Gunnthorsdottir 2001[START_REF] Tisdell | Public Choice of Species for the 'Ark': Phylogenetic Similarity and Preferred Wildlife Species for Survival[END_REF], rather than on their actual behaviour (i.e. real money invested). For instance, based on hypothetical species choices and money allocation, Martín-Lopez et al. (2007) found that affectrelated factors (e.g. charisma) have more influence on WTP than ecological or scientific considerations. They also found that respondents with better knowledge of biodiversity and greater experience with nature were more willing to donate for the conservation of non-charismatic species that were locally endangered [START_REF] Martín-López | The Non-Economic Motives behind the Willingness to Pay for Biodiversity Conservation[END_REF]). These results needed to be tested in real-life settings, with actual species valuations.

People also seem to have a preference for conserving animals that are similar to humans [START_REF] Dekay | Probability and Utility of Endangered Species Preservation Programs[END_REF], Gunnthorsdottir 2001[START_REF] Plous | Psychological Mechanisms in the Human Use of Animals[END_REF][START_REF] Samples | Information Disclosure and Endangered Species Valuation[END_REF]). The preference among humans for animal species similar to them has been formalized as the Similar Principle Theory [START_REF] Plous | Psychological Mechanisms in the Human Use of Animals[END_REF]. This theory is supported by the findings of a research team in Australia, which showed that respondents appeared to favour the survival of mammals rather than birds or reptiles [START_REF] Tisdell | Public Choice of Species for the 'Ark': Phylogenetic Similarity and Preferred Wildlife Species for Survival[END_REF]. Another study in the United States showed that physical characteristics (e.g. physical length) were better predictors of government spending decisions for conserving endangered species than more scientific characteristics, such as the level of threat or taxonomic distinctiveness [START_REF] Metrick | Patterns of Behavior in Endangered Species Preservation[END_REF]. This prompts the hypothesis that the chances of survival for many species depend as much on human preferences as on more biological requirements (e.g. minimum population size).

In this study, we wanted to investigate WTP and its determinants more closely at the individual level, in a situation where money for species conservation is actually given. Among the numerous existing conservation programs, zoological institutions have been involved in both ex-situ (e.g. captive breeding) and in-situ programs (e.g. significant financial contributions to field conservation projects) [START_REF] Gusset | The Global Reach of Zoos and Aquariums in Visitor Numbers and Conservation Expenditures[END_REF]. However, the way zoos contribute to conservation is still controversial: for instance, zoos mostly display large-bodied vertebrates and less-threatened species [START_REF] Balmford | Parks or Arks: Where to Conserve Threatened Mammals?[END_REF][START_REF] Conde | An Emerging Role of Zoos to Conserve Biodiversity[END_REF][START_REF] Fa | Zoos Have yet to Unveil Their Full Conservation Potential[END_REF][START_REF] Martin | Mammal and Bird Species Held in Zoos Are Less Endemic and Less Threatened than Their Close Relatives Not Held in Zoos[END_REF]. One reason for such bias toward large vertebrates is the general public preference for large mammals and rare or charismatic species in zoos [START_REF] Angulo | Fatal Attraction: Rare Species in the Spotlight[END_REF][START_REF] Ward | The Relationship between Popularity and Body Size in Zoo Animals[END_REF]. However, endangered species may not be charismatic, and vice versa, so that the relationship between zoo exhibits and biodiversity preservation can be complex. In any case, more information is needed on public preferences in zoos, and how zoos could integrate such preferences to connect the public with biodiversity preservation.

To support in-situ conservation programs, zoos have developed different strategies to raise money. One of them is the worldwide strategy of "Animal adoption" programs: people can donate a certain amount of money to the zoo; in return, they receive various benefits (e.g. the zoo's newsletter, meeting zoo keepers, free entrance tickets). In France, participants of such programs are named "godfathers/mothers" of the animal(s) they chose, whereas they are mostly called "parents" in English speaking countries (e.g. United States). Although there are obviously cultural differences regarding this aspect, we will refer here to participants as "parents", to adopt a more neutral position. Such programs foster a more intimate and privileged relationship between participants and a particular animal, via its adoptive status, compared to non-participants who visit the zoo. However, emotional responses to animals vary widely between and within taxonomic groups [START_REF] Myers | Emotional Dimensions of Watching Zoo Animals: An Experience Sampling Study Building on Insights from Psychology[END_REF]). For instance, primates are more likely to elicit positive emotional responses, because of their close similarities with humans [START_REF] Plous | Psychological Mechanisms in the Human Use of Animals[END_REF]; conversely, invertebrates are expected to elicit more fearful or aversive emotional responses [START_REF] Kellert | Values and Perceptions of Invertebrates[END_REF].

Our study therefore aimed to explore people's willingness-to-pay for species conservation through their actual donations to a zoo animal adoption program, by (1) clarifying whether people consider biological characteristics (e.g. threat level, phylogenetic distance from humans), more affect-related ones (e.g. level of charisma) or the combination of such characteristics in their choice of animal and their willingness-to-pay; (2) assessing whether attitudes toward animals (e.g. emotional responses) are reflected in participants' support for their conservation; (3) exploring the impact of the donor's relationship with nature on their choice of an animal and amount of money donated to the program. We assessed these relationships by exploring individual connectedness with nature (Inclusion of Nature in Self, see [START_REF] Schultz | THE STRUCTURE OF ENVIRONMENTAL CONCERN: CONCERN FOR SELF, OTHER PEOPLE, AND THE BIOSPHERE[END_REF] and childhood experiences of nature [START_REF] Chawla | Childhood Experiences Associated with Care for the Natural World[END_REF] according to how far they spent their childhood in a rural setting.

We are not aware of any previously published research on animal adoption in zoos, despite the relevance of such programs to species conservation. This study therefore makes an important contribution to zoo conservation programs, and will help to clarify the effectiveness of zoo conservation programs in both raising money for field conservation projects and reconnecting people with conservation issues related to endangered species.

Based on previous research findings, we hypothesized (1) that the level of threat and the phylogenetic distance from humans, but also less scientific considerations (e.g. whether the species is charismatic or not) are significant factors in determining the choice of an animal and the amount donated per participant, with larger donations expected for species that are more threatened, more similar to humans and more charismatic; to better understand the impact of the animals' characteristics, we also looked for interactions among them: for example, perhaps charisma only matters when species are not endangered, and perhaps it is sufficient for an animal to be either phylogenetically close to humans or charismatic. We also hypothesized (2) that attitudes toward animals (i.e. emotional responses) reflect the support of participants for their conservation; (3) that a stronger sense of connection with nature and more experience of nature during childhood influence respondents' choices of animal towards species that are less charismatic and less similar to humans.

Materials and Methods

Animal Adoption program

The Paris Zoological Park (PZP) opened in 1934, but closed in 2008 for renovation. It reopened in April 2014, as an "immersive" zoo: the 15 ha Park is now divided into five different biozones, where the enclosures are designed to immerse the visitor in the animal's natural environment. Physical barriers were, as far as possible, either removed or kept out of sight (e.g. glass instead of fences).

In late 2013, the PZP set up an animal adoption program allowing members of the public to adopt one or more animals living in the zoo, for conservation purposes. A list of 29 different named individual animals was proposed (see table 1), and adopters were free to donate as much money as they wanted. However, six amounts ranging from 15€ to 1 000€ were proposed as guidelines, with a sliding scale of benefits offered to the adopter in return. The money donated to the program can be deducted from income tax at a rate of 66% of the amount. The adoption lasts for one year, starting from the day of adoption. Overall, the raw data from the program we had access to included the following variables for each adoption between December 2013 and February 2015: animal chosen, amount of money donated, participant's zip code, age, and the date of adoption. Because the program is explicitly presented as supporting in-situ conservation programs, we used the amount of money donated per person for a particular animal as a measure of their willingness-to-pay for the conservation of this species. These raw data represent 10 066 participants in the adoption program.

Secondly, we sent an email to all the program participants to invite them to fill in an online questionnaire, in French, about their experience with the program. We collected data for 6 months (February -September 2015), and received 2 134 completed questionnaires, which represents a 21.20% rate of participation in our survey.

Survey instrument

In the survey questionnaire, we investigated the components of the adoption, whether the participants visited the chosen animal in the zoo, the emotions they felt towards this animal in the zoo, and personal information on their relationships with nature (connectedness with nature, concern for biodiversity and how far they spent their childhood in a rural setting), their age and gender.

Components of the adoption

We asked the participants whether they adopted the animal for themselves, for someone else or if they had received it as a gift. We recorded the number of adoptions and animal(s) each participant adopted, as well as the amount of money donated per animal. Finally, we asked the participant to rank nine different possible motivations for the adoption, from 1least important reason, to 9 -most important reason. The following nine reasons were listed in random order : "to support the zoo's conservation mission", "to support the zoo's research mission", "for the benefits", "for tax relief", "because I feel a connection with this animal", "because I like the Paris zoo", "to contribute to the renovation of the zoo", "to raise someone's awareness", "because the species is endangered".

Visits to the adopted animal and emotions felt

Participants were asked whether they had visited the zoo since the renovation, and whether they had had a chance to observe their chosen animal. For those who visited the zoo and met the adopted animal, we asked to what extent they felt each of a list of five positive emotions (Interest, Fascination, Pleasure, Pride and Joy) and five negative ones (Fear, Sadness, Anger, Worry and Shame), from 1-not at all, to 5-very much. We restricted the question related to emotions to those who had had a chance to observe the animal because we were interested in their emotional reaction to the animal in the zoo, rather than in their beliefs and emotional reactions towards the species in general. Positive and negative emotions were mixed and presented randomly for each participant.

Personal information

We used an adapted version of the Inclusion of Other in the Self (IOS) scale [START_REF] Aron | Inclusion of Other in the Self Scale and the Structure of Interpersonal Closeness[END_REF]) to measure individual beliefs about how interconnected people feel with the natural world, via a series of overlapping circles labelled "nature" and "self" (Inclusion of Nature in Self scale, see [START_REF] Schultz | THE STRUCTURE OF ENVIRONMENTAL CONCERN: CONCERN FOR SELF, OTHER PEOPLE, AND THE BIOSPHERE[END_REF].

Participants were also asked to what extent they were worried about biodiversity, from 1-not at all, to 5-very much. We asked whether they spent their childhood in a rural or urban setting, from 1-very urbanized, to 5-very rural. Finally, we asked for the gender and provided six age categories (18-30, 31-40, 41-50, 51-60, 61-70 and over 70), which we recoded into a numerical scale of 1 to 6.

Biological and non-biological characteristics of the animals

We assessed two biological characteristics of the animals, as follows:

(1) the level of threat to the species, according to the International Union for Conservation of Nature (IUCN) Red List, which we coded from 1 for least concern (LC), to 5 for critically endangered (CR) (IUCN 2015); (2) the phylogenetic distance from humans, obtained from http://tolweb.org/tree, which we coded from 1 for closest to humans (e.g. primates) to 9 for the more distant species (e.g. tarantula). This coding reflected the respective ranks of the species considered in relation to humans, rather than their theoretical phylogenetic distance from humans. In other words, the closest species to humans, i.e. nonhuman primates, were coded 1, the second closest species to humans, i.e. carnivores, were coded 2, and so on, until the most distant species to humans, i.e. invertebrates, were coded 9.

In addition, we attributed two characteristic non-biological traits to each animal species. The first was the charisma of the species, which we identified by averaging the number of Google™ searches (in France only) from January to December 2014. Charisma has been defined as "a special magnetic charm or appeal" in the Merriam-Webster dictionary (www.merriam-webster.com). Although charisma is a complex notion, difficult to be estimated, Google™ searches were used as a proxy for animal charisma, as it reflects people's interest for the species. We examined such searches over a year, a sufficiently large period to avoid that particular eventslike a media controversy about an animal death in a zoosignificantly influence our estimate. A similar approach has already been used, with newspaper (two-month search period) reports as a proxy for the level of awareness of the public [START_REF] Duarte | The Charisma of Coastal Ecosystems: Addressing the Imbalance[END_REF]. The second was the alphabetical order of the name given to the animals, from 1 for A (e.g. Aramis the jaguar) to 26 for Z (e.g. Zyko the arapaima), because the program's website lists the names of the 29 animals in alphabetical order. We ascertained from zoo staff that the animals were not named with any reference to the alphabetical order.

Statistical analysis

All the analyses were performed using R 3.0.2 (R Core Team 2013). Response variables were log-transformed to make data conform to normality.

Effect of biological and non-biological characteristics of the animal on adoption choices, amounts of money donated and emotions felt for the animal

We found no significant correlation between the four characteristics of the animal considered (i.e. IUCN threat level, phylogenetic distance from humans, charisma according to Google™ searches and alphabetical order of the name), using Pearson's correlation tests (coefficients ranging from -0.33 to 0.32). From the complete data set from the program, we then modelled the determinants of animal choice using linear regression. We assessed the number of adopters (ADP) for each of the 29 animal species studied as the response variable, and the IUCN threat level (THR), phylogenetic distance from humans (PHY), "Google™" charisma (CHA), alphabetical order of the name (ALP) and CHA-PHY, CHA-THR and THR-PHY interactions as independent variables. We then applied a stepwise model selection based on Akaike Information Criterion (AIC) scores to select the best model. We used the same stepwise model selection methodology to build up a second model to analyze the determinants of the amount of money donated. Here, we assessed the amount of money donated per person (INV) as the response variable and the same biological and non-biological variables (i.e. THR, PHY, CHA, ALP and CHA-PHY, CHA-THR and THR-PHY interactions) as independent variables. For this analysis, we selected only the participants who had adopted a single animal (N=9 669), to avoid any bias due to multiple adoptions by a single participant.

Finally, using the questionnaire data, we modelled the determinants of both positive and negative emotions toward the adopted animal using linear mixed-effects models. First, we assessed the average score of positive emotions felt for the animal as the response variable, the same four variables (i.e. THR, PHY, CHA and ALP) as independent variables, and the participant as a random effect to control for multiple adoptions by a single person. The same model was run with the average score of negative emotions felt for the animal as the response variable. For these two models, we only considered those who had adopted an animal for themselves, because we were interested in personal involvement in the adoption. Data on emotional scores were available for 511 people who adopted an animal for themselves. We used the 'nlme' 3.1-125 package [START_REF] Pinheiro | Linear and Nonlinear Mixed Effects Models[END_REF].

Effect of background variables on animal choice and amount of money donated in relation to biological and non-biological characteristics

Using the questionnaire data, we explored whether connectedness with nature, concern for biodiversity, a rural setting during childhood, gender and age had an effect on animal choice, in relation to phylogenetic distance from humans, IUCN threat level and "Google™" charisma. To do so, we used a linear mixed-effect model with phylogenetic distance from humans as the response variable and connectedness with nature, rural setting during childhood, concern for biodiversity, gender and age as independent variables. We applied a random effect to the participant variable. We performed the same linear mixed-effect models with "Google™" charisma and IUCN threat level as the response variables.

Additionally, we explored whether connectedness with nature, concern for biodiversity, a rural setting during childhood, gender and age had an effect on the amount of money donated, by performing the same linear mixed effect model with amount of money donated as the response variable.

Results

Participant profiles

Altogether, 10 066 different people took part in the program, adopting one or several animals (619 persons adopted more than one animal, usually two), resulting in a total of 10 929 adoptions by the end of February 2015. Most of the participants (99%) were living in France. 30% were from Paris, and 16.7% of these were living in the 12 th arrondissement in Paris (i.e. where the zoo is located). Given that in France in 2013, Parisians represented 3.43% of the French population, and people living in the 12 th arrondissement in Paris represented 6.49% of Parisians (INSEE 2013), the proportion of Parisians and 12 th arrondissement inhabitants in our sample was relatively large compared to the population in France.

A total of 613 021.36€ had been collected by the end of February 2015, and most participants donated between 30 and 74€ (a minimum donation of 30€ was necessary to receive the program benefits) (Fig. 1).

Figure 1: Numbers of adoptions for each level of benefits offered by the program. Below 15€, the participant did not receive any benefit in return for participating.

Among the 2 134 respondents to our questionnaire, 868 had adopted an animal for themselves, 826 as a gift to someone else, and 243 had received the adoption as a gift. The remaining 141 respondents were participants who combined some of the previous three types of adoption. 1313 respondents had visited the zoo since it reopened (61.5%) and 1533 had visited the zoo before its renovation (71.8%). 1254 owned a pet (58.8 %), which is similar to the proportion for the French population as a whole (FACCO/TNS SOFRES 2015). 784 respondents were involved in environmental or animal protection organizations (36.7%), which is a much higher proportion than for the French population as a whole (11%) (European Commission 2013).

Based on the three most important reasons cited for participating, respondents mostly adopted an animal for themselves or as a gift to support the zoo's conservation mission (25.09%), to support the zoo's research mission (15.45%), because they felt a connection with the animal they chose (12.66%), to contribute to the zoo's renovation (12.22%) and because the species they chose is endangered (11.43%). The remaining four reasonsbecause they like the zoo, to sensitize someone, for the benefits and for tax reliefaccounted for 9.89%, 9.12%, 2.42% and 1.73% respectively.

Effect of biological and non-biological characteristics of the animal on the adoption choice, amount of money donated and emotions felt for the animal 3.2.1 Number of adopters per animal

All interactions were removed during stepwise model selection process. According to the best model (R-squared value = 0.54), number of adopters per animal was positively associated with level of "Google™" charisma, and negatively associated with alphabetical order (Table 2). These results suggest that the more charismatic the species was, the more it was chosen by participants, and that participants were more likely to choose an animal whose name started with a letter near the top of the alphabet than further down in the alphabet, i.e., at the top of the website page, which gives the names of the animals in alphabetical order. At the opposite, we found no significant relationship between number of adopters per animal and IUCN threat level and phylogenetic distance to humans, suggesting that neither the IUCN threat level nor the phylogenetic distance to humans had any effect on the number of adopters per animal.

Interaction between THR and PHY Removed during stepwise model selection

Removed during stepwise model selection Although the relationship with phylogenetic distance to humans was not significant, removing this variable from the model did not change the AIC; because it was a variable of interest, we decided to keep this variable in the final model. Although the relationship with IUCN threat level was not significant either, removing this variable from the model increased the AIC score (from 59.54 to 62.88), but decreased the p-value associated.

Amount of money donated per animal

The best model from the stepwise model selection explained a very low amount of the total variance (R-squared value=0.002), but it was better in terms of AIC that the null-model. According to this selected model, amount of money donated per animal was negatively associated with "Google™" charisma, phylogenetic distance to humans and alphabetical order (Table 2). These results suggest that the more charismatic the species, the smaller the amount of money donated; the smaller the phylogenetic distance from humans, the greater the amount of money donated; and the participants were also more likely to give more money to animals whose name started with a letter near the top of the alphabet (i.e. first presented in the website) than further down in the alphabet. In addition, the interaction between "Google™" charisma and phylogenetic distance to humans was negatively associated with amount of money donated per animal (Table 2), suggesting that for more charismatic species, phylogenetic distance to humans had a stronger negative effect on amount of money donated. Other interactions were not significant. Finally, we found no significant relationship with IUCN threat level (Table 2).

Emotions felt per animal

These analyses were limited to respondents who had visited the zoo since the renovation and had seen the animal they adopted for themselves or for others (i.e. 511 people). We found that the IUCN threat level was negatively correlated with positive emotions felt for the animal (β=-0.04, SE=0.01, p=0.008), and positively correlated with negative emotions felt for the animal (β=0.04, SE=0.01, p=0.015). No correlation was observed between other variables (phylogenetic distance from humans and alphabetical order) and either positive or negative emotions felt for the animals. Interactions were not significant in the models. These results suggest that IUCN threat level had a significant effect in determining the emotions felt for the animal, lowering positive emotions and strengthening negative emotions.

Effect of background personal characteristics on animal choice and amount of money donated in relation to its biological and non-biological characteristics

We found no effect of connectedness with nature on participants' choices in favour of charismatic, phylogenetically distant or more endangered species (Table 3). Similarly, choice of charismatic, phylogenetically distant or more endangered species was not related to respondents' age, and concern for biodiversity (Table 3). A more rural childhood was negatively correlated with the charisma of animals adopted, and positively correlated with their phylogenetic distance from humans (Table 3). These results suggest that participants who spent their childhood in a rural setting were more likely to choose species that are less charismatic and phylogenetically more distant from humans. Additionally, we found no significant relationship between the amount of money donated and any of the demographic and background variables (Table 3).

Table 3: Results of linear mixed-effect models that included five independent variables to explain animal choice (through "Google™" charisma, phylogenetic distance to humans and IUCN threat level) and amount of money donated. Estimates ± standard errors and level of significance (* p<0.05; ** p<0.01; *** p<0.001) are given.

Discussion

The results of this study confirm some of our working hypotheses, but surprisingly did not support others, particularly in relation to the charisma and endangered status of the species that participants chose to support. This study also suggests that individual relationships with nature tend to gear people's support of conservation towards species that are less charismatic and less similar to humans. We discuss these results below.

Technical effects

Surprisingly, we found that the alphabetical order of the names given to animals had a strong effect on animal choice. However, charismatic species were not significantly high in the alphabetical order. Because animals were listed by name in alphabetical order on the adoption program's website, this result therefore suggests that many participants may have selected the first available animals on the website page. Our interpretation is that the alphabetical order effect shows that people are not willing to spend much time on choosing the species they wish to support, but go for the first animal displayed once they have decided to support a conservation program. Does this indicate a lack of interest, or a feeling of ignorance? Further studies are needed to clarify this point.

Similarity effect

As expected, similarity to humans was found to influence WTP for species conservation: participants were more likely to donate more on average for species that are phylogenetically closer to humans. This result is consistent with previous research giving credit to the Similarity Principle in conservation support [START_REF] Dekay | Probability and Utility of Endangered Species Preservation Programs[END_REF], Gunnthorsdottir 2001[START_REF] Plous | Psychological Mechanisms in the Human Use of Animals[END_REF][START_REF] Samples | Information Disclosure and Endangered Species Valuation[END_REF]).

Charisma effects

Our major result revealed complex effects of animal charisma on support for conservation. We showed first that the level of charisma had a positive impact on animal choice, but a negative impact on the amount donated, or WTP. The positive effect of charisma on animal choice is consistent with previous literature [START_REF] Bennett | Biodiversity Gains from Efficient Use of Private Sponsorship for Flagship Species Conservation[END_REF][START_REF] Skibins | Charisma and Conservation: Charismatic Megafauna's Influence on Safari and Zoo Tourists' pro-Conservation Behaviors[END_REF]; however, its negative effect on WTP is striking, and suggests that those who adopted less charismatic species probably engage more strongly with species conservation, acknowledging the strong selection biases that might exist in favour of charismatic species. In other words, committed people might tend to make a strategic choice, anticipating that some non-charismatic species are likely to attract little support and deciding to compensate accordingly. Indeed, since we found that concern for biodiversity was not related to choice of charismatic species, it seems doubtful that a higher WTP among people who adopted noncharismatic species could be due to them having stronger pro-conservation attitudes.

Additionally, we found that when "Google™" level of charisma increased, the negative effect of phylogenetic distance to humans on amount of money donated increased, suggesting that participants who adopted less charismatic species cared less about phylogenetic distance to humans, compared to those who adopted more charismatic species.

Effects of species conservation status

Another unexpected result is the lack of any effect of the species conservation status on animals chosen and amounts donated. This indicates that people taking part in a program presented as dedicated to species conservation do not consider endangered status criteria when choosing an animal to adopt and deciding on the amount they wish to donate. This was even more surprising given the high proportion of participants who reported being involved in organizations for environmental and animal protection.

On the other hand, we found that the conservation status of the animal had a significant effect in determining emotional responses towards it. Compared to other respondents, people who adopted more threatened species were more likely to express negative emotions, and the animals they adopted were less likely to elicit positive emotions than the less threatened species. Linking this to the result on willingness-to-pay suggests that emotional responses towards animals did not reflect participants' willingness-to-pay for species conservation.

A potential limitation of this result is that we were unsure whether the participant visited the animal after the adoption process, or whether the visit to the animal elicited the desire to adopt it. Nevertheless, all species are displayed similarly in the zoo, regardless of how endangered they are.

Information on conservation status is equally available for all the species (e.g. on the program website and on the species information panels in the zoo). Finally, the more threatened species available for adoption belonged to different taxonomic groups, with primates, which are usually more positively perceived by visitors because of their similarities to humans [START_REF] Plous | Psychological Mechanisms in the Human Use of Animals[END_REF], particularly well represented. We are also aware that although those who responded to the questionnaire were relatively similar in age to the program participants as a whole, those who did not complete the questionnaire survey might have had different attitudes towards the animals. The variance in the response variables explained by our models was relatively low, which means that a large part of the variance is not accounted by our models, and that other factors than chance might matter, e.g. socio-economic variables. Notably, although we did not find a significant relationship between demographic variables and amount of money donated, personal income, not available in our dataset, may explain the amount of money donated. Finally, the species that could be adopted were selected by the program managers and the list of species (Table 1) was therefore imposed to this study. Biases, especially toward mammal species, should therefore be mentioned as potential limitations for these results, and further research would be necessary to confirm our results.

Effects of participants' personal characteristics

As expected, our results suggest that childhood experiences of nature have a strong influence on the choice of animals, with people with more rural experiences during childhood choosing species that are less charismatic and less similar to humans. Indeed, childhood experiences of nature have been found to have a profound effect on the way people experience nature in adulthood [START_REF] Chawla | Childhood Experiences Associated with Care for the Natural World[END_REF], and previous research has also noted that experience of nature tends to influence willingness-to-pay for less charismatic species [START_REF] Martín-López | The Non-Economic Motives behind the Willingness to Pay for Biodiversity Conservation[END_REF]). We did not find any effect of connectedness with nature on the choice of animals to adopt, although it has been suggested that this is associated with childhood experiences of nature [START_REF] Chawla | Childhood Experiences Associated with Care for the Natural World[END_REF]). This could be explained by the fact that we assessed connectedness with nature through a single question, and relied on self-reporting by participants of a conscious personal relationship with nature.

Conclusion

Overall, our survey based on actual monetary donations produced results similar to those from a previous survey based on hypothetical animal choices and willingness-to-pay for species conservation [START_REF] Martín-López | The Non-Economic Motives behind the Willingness to Pay for Biodiversity Conservation[END_REF]). Our study also indicates that people's choices of animals to adopt and their willingness-to-pay were mostly driven by affect-related motivations and arbitrary influences, rather than by more ecological considerations such as the endangered status of a species. We therefore suggest that people participating in such conservation programs mostly look for the intimate relationships they allow with individual animals. Our work has several implications for zoo strategies concerning adoption programs for conservation, regarding the selection of animals proposed for adoption: similarity with humans matters, especially for more charismatic species, but endangered status is a minor concern; with regard to species charisma, zoos could develop a more strategic targeting approach: either favour charismatic species to recruit higher numbers of participants, or favour non-charismatic species to raise higher individual donations from committed people. Zoos might therefore consider developing a discourse on the importance of species in ecosystem functioning or on adaptation to global change, which is an important way of reconnecting people with biodiversity. Finally, zoos should be aware of the importance of certain choices made (especially regarding the alphabetical order used to present their animals) in presenting their strategic objectives. To prevent low-information visitors or visitors who are already informed but with no real preference among species from choosing the first few proposed animals, we suggest zoos to give participants an additional choice to donating to a general conservation cause or to a fund that allows the zoo to distribute the donations to the program of their choice. However, such solution might look as patronizing, suggesting that experts know better than the public what the choice in regards to nature should be.

Finally, the consequences of our results for the conservation policies of zoos are complex, because the effectiveness of adoption programs as a way of raising conservation awareness remains uncertain. We strongly advise managers of species conservation program to provide potential participants with more in-depth information about levels of threat to species, and perhaps to considerably increase the proportion of more threatened and less charismatic species in their selection of animals for adoption programs. The question certainly arises as to whether a large amount of small donations for charismatic species would be more effective than fewer but larger donations for less charismatic species. In parallel with adoption programs, we recommend more studies on how animal collections could be optimized to maximize ex-situ conservation in zoos, since reconciling conservation with their own financial viability requires zoos to work with both charismatic and non-charismatic threatened species [START_REF] Delmas | Etude Théorique de L'optimisation Des Combinaisons D'espèces Dans Le but de Maximiser La Conservation Ex Situ Dans Les Parcs Zoologiques[END_REF]. Nevertheless, to raise people's awareness about conservation issues and because of the urgent need to conserve more threatened but less charismatic species, more recommendations are needed on displaying species according to their charisma and conservation status respectively.

Table 1 :

 1 List of animals available for adoption, with given name, scientific name, taxonomic group, total number of adoptions and amount of money raised per animal (in Euros). The animals are shown in decreasing order of total adoptions.

	Taxonomic group	Name, animal (scientific name)	Total number of adoptions	Amount of money raised for each animal (€)
	Mammal	Aramis, a jaguar (Panthera onca)	1479	152
	Mammal	Adeline, a West African giraffe (Giraffa camelopardalis)	1463	550
	Mammal	Lena, a Scandinavian lynx (Lynx lynx)	999	935
	Mammal	Diablo, the Spanish wolf (Canis lupus signatus)	822	466
	Mammal	Nero, an African lion (Panthera leo)	785	640
	Mammal	Diego, a European otter (Lutra lutra)	688	410
	Mammal	Tinus, a manatee (Trichechus manatus)	466	065
	Bird	Indigo, a hyacinth macaw (Anodorhynchus hyacinthinus)	367	310
	Mammal	Patagonian puma (unnamed) (Puma concolor)	349	510
	Mammal	Azufel, a greater bamboo lemur (Prolemur simus)	345	005
	Mammal	Efatra, a crowned sifaka (Propithecus coronatus)	331	096
	Mammal	Serdtse, a Grévy's zebra (Equus grevyi)	312	670
	Mammal	Zakko, a wolverine (Gulo gulo)	279	305
	Mammal	Wami, a white rhinoceros (Ceratotherium simum)	269	195
	Bird	Pigloo, a Humboldt penguin (Spheniscus humboldti)	259	306
	Mammal	Luca, a common woolly monkey (Lagothrix lagotricha)	235	430
	Mammal	Mojo, a southern pudu (Pudu puda)	206	060
	Amphibian Tana, a false tomato frog (Dyscophus guineti)	185	7
	Mammal	Tabitha, a giant anteater (Myrmecophaga tridactyla)	148	9
	Mammal	Uyuni, a Guinea baboon (Papio papio)	138	8
	Mammal	Zoe, a greater kudu (Tragelaphus strepsiceros)	120	5
	Mammal	Quida, a lowland tapir (Tapirus terrestris)	113	6
	Reptile	Gertrude, a European pond turtle (Emys orbicularis orbicularis)	110	8
	Mammal	Portos, a South American sea lion (Otaria flavescens)	106	5
	Arthropod	Tegu, a curly haired tarantula (Brachypelma albopilosum)	94	3
	Reptile	Mandi, a Madagascar tree boa (Sanzinia madagascariensis)	91	3
	Reptile	Leon, a panther chameleon (Furcifer pardalis)	84	3
	Bird	Satory, a griffon vulture (Gyps fulvus)	60	5
	Fish	Zyko, an arapaima (Arapaima gigas)	26	1

Table 2 :

 2 Results of linear regression analyses that included five independent variables to explain animal choice (through number of adopters per animal) and amount of money donated. Estimates ± standard errors and level of significance (* p<0.05; ** p<0.01; *** p<0.001) are given, for the best model retained using stepwise model selection based on Akaike Information Criterion.

	Independent variables	Number of adopters per animal	Amount of money donated per animal
	"Google™" charisma (CHA)	0.367 ± 0.146 *	-0.043 ± 0.016 **
	IUCN threat level (THR)	0.090 ± 0.144	0.004 ± 0.009
	Phylogenetic distance to humans (PHY)	-0.223 ± 0.156	-0.051 ± 0.017 **
	Alphabetical order (ALP)	-0.314 ± 0.140 *	-0.020 ± 0.009 *
	Interaction between CHA and PHY	Removed during stepwise model selection	-0.045 ± 0.021 *
	Interaction between CHA and THR	Removed during stepwise model selection	Removed during stepwise model selection

Acknowledgements:

We wish to thank the managers of the PZP animal adoption program for allowing us to conduct research on the program data, I. Bossanyi for her help, as a professional translator, on improving the English writing style of our manuscript, and the two anonymous reviewers for their comments. Finally, we thank the two anonymous reviewers for providing feedback that greatly improved this manuscript.


Hazar Guesmi

Noelia B Luque

Elizabeth Santos

Frederik Tielens
email: frederik.tielens@upmc.fr

Does the S-H Bond Always Break after Adsorption of an Alkylthiol on Au(111)?

Keywords: SAM, Thiol, S-H bond, Adatoms, Reaction path

The reaction mechanism for the formation of alkyl thiol SAM on Au(111) is still not clearly understood. Especially, the role of defects on the chemisorption process is an important goal to be addressed. In this work, different minimum energy reaction paths of R-SH dissociation of thiols (with long and short chains and di-thiol species) adsorbed on gold adatom are calculated using periodic density functional theory. Our results show a lower energy barrier for the RSbond dissociation when two thiols are adsorbed per adatom. In addition, in contrast with the formation of an adatom at the Au(111) which has been shown to depend on the alkyl chain length, the activation energy of the RS-H bond dissociation of thiols adsorbed on an adatom was shown to be independent of the alkyl chain length. The presented results and derived hypothesis support the model that thiols with long alkyl chain thiols mainly adsorb molecularly on Au(111), while for short alkyl chain thiols the S-H bond breaks. This result is explained by the fact that short chain thiols have a lower inter-chain interaction energies and are thus more mobile compared to the long alkyl chain thiols on the Au(111) surface. This feature enables the short chains to reach adequate geometries, driven by entropy, which could deform the Au(111) more drastically and probably pull Au atoms out from surface to form adatoms. With these results a new mechanism is proposed for the formation of alkyl chain thiols on Au(111).

Introduction

Due to the vast variety of applications of Self-Assembled Monolayers (SAMs) such as lubrication, electrochemistry, electronic and vibrational spectroscopy, photochemistry, electrical conduction, catalysis, and biological membranes etc., preparation and structural characterization of these interfaces have been of great interest for more than three decades 1 .

Alkanethiol/alkanethiolate adsorbates on coinage metal surfaces are widely exploited, particularly the SAMs on Au(111) surface, being the most well-known [2][3][4][5][6][7][8] . However, the detailed nature of the interface structures starts only now to be revealed by combining experiments and quantum chemical calculations 9 . It is mostly assumed that in the first steps of the formation of SAMs on Au(111), thiolate radicals are involved (after the H-S bond cleavage of the alkanethiol), but how these radicals are formed after releasing an H atom is not yet fully understood. 10,[START_REF]Global Propylene Market[END_REF] First attempts to explain the thiolate radical formation using DFT methods were performed by Busnengo et al. 10 at the molecular level by means of DFT calculations. They showed a reaction pathway for S-H bond breaking of methanethiol on a flat Au(111) surface calculating the associated activation energies. This work, however, only considers the shortest of the alkyl thiols' H-SCH3 bond cleavage on a clean, defect-free Au(111).

The evidenced role of gold surface defects and particularly Au adatoms may hold the key to the characterization of the thiolate geometry. Indeed, several recent experimental and theoretical studies [START_REF] Kondoh | [END_REF][13][14][15][16][17] indicate that thiolate-induced reconstruction may also occur on the Au(111) surface [18][19][20][21][22][23][24] .

Two rather different models of these Au-adatom-thiolate moieties have emerged from different experiments. Low temperature STM imaging conducted at low coverage (only a few % of a monolayer) on the methanethiolate species 15 provides evidence for an Au-dithiolate moiety in which the Au adatom occupies a bridge site relative to the underlying Au(111) surface layer; both S head group atoms are bonded to opposite sides of this adatom such that they occupy near-atop sites relative to the underlying Au surface atoms. Experimental groups observed this Au-dithiolate ordering for propanethiolate 25 and butanethiolate 16 at low or intermediate coverage. In DFT studies, thiolate-induced reconstruction of the Au(111) had also been considered 9,17,26,27 . The preference for an ethanethiolate to adsorb on atop geometry if there is an Au adatom on the surface has also been predicted by calculations by Cometto et al. [28][29][30] . The total energy of this Au-adatom-thiolate moiety was almost identical at the fcc and hcp hollow sites, and the diffusion barrier between these sites is found to be very low, in agreement with experimental results at room temperature. Using combined experimental measurements and DFT calculations, Maksymovych et al. 15 , have shown that Au-adatom-dithiolate moiety surface structure is energetically favored over the lowest energy structure on the unreconstructed surface. Grönbeck and Häkkinen 31 have performed calculations on both of the adatom models discussed by others 17 , and on a third model in which Au adatoms occupy a mixture of fcc and hcp hollow sites while methanethiolate species bridge these adatoms. This last model has shown the lowest energy. These calculations also indicate an energetic preference for the dithiolate adatom model over the monothiolate adatom moiety. Other results are the work of Mazzarello et al. 32 and Cossaro et al. 32 that combines DFT-based molecular dynamic (MD) simulations with experimental surface X-ray diffraction data for the ) 3 3 (  -methanethiolate and

) 3 3 2 (
 rect. hexanehiolate phases, respectively, and photoelectron diffraction data for the methanethiolate phase. The MD simulations favor models with a significant degree of disorder (higher for the methanethiolate species), comprising coexistence of both the Au-adatomdithiolate species and thiolate species bonding to bridging sites on the underlying surface, together with a significant concentration of surface Au vacancies. It was found, with some modification in the relative coverage, to be consistent with the experimental work (Even some discrepancies in the computed relative coverage were found, these results showed a high concordance with experimental observations). In addition, in a recent work combining DFT calculations and XPS experiments, we have confirmed the spontaneous reconstruction of the surface, by formation of a Au adatom on the surface, shared with two thiol chains, structure that was earlier reported by Mazzarello et al. 32,33 . Interestingly, the adatom formation was found to be dependent on the thiol chain length where shorter alkyl chains were found to induce a larger reconstruction, and consequently found to be more reactive. 9 Moreover, the same thiol can form different types of assemblies dependent of the temperature and the coverage, especially for the case of the shortest alkyl chain thiol (methanethiol). 34 In a previous study we have investigated the adsorption energies and different geometries of the propanethiol in its molecular and radical states on three different surface unit cells 27 , and later on we showed that the side chain length is related to the gold surface reconstruction 9 .

However, it is not clear yet, a) how the H-S bond cleavage process of adsorbed thiols occurs, b) what is the effect of the alkyl chain length on the H-S bond cleavage, andc) what is the influence of the presence of gold adatoms on the surface. Based on our previous results we investigated the H-S bond cleavage of thiols on gold adatoms as a function of the thiol alkyl chain length. A study in line with our earlier works on thiol self-assembled monolayers on gold surfaces. 9,27,[35][36][37][38]

Computational Details

Density Functional Theory (DFT) calculations were carried out using the Vienna Ab Initio Simulation Package (VASP) 39,40 . Electron-electron exchange and correlation interactions were described within the Generalized Gradient Approximation (GGA) by employing the functional of Perdew, Burke and Ernzerhof (PBE) 41. The Projector Augmented Wave (PAW) 40,42 method was used for the electron-ion interactions. The electronic one-particle wave functions were expanded in a plane wave basis set, up to an energy cut-off of 400 eV. The metal surface was modeled by a slab consisting of five atomic layers that were separated by a vacuum region of 15 Å. The interlayer spacing in the surface was taken from the theoretical lattice parameter calculated for bulk gold (4.17 Å). According to experimental results, the adsorption of thiols

forms a   30 ) 3 3 ( R
unit cell. For the surface 5 × 5 × 1,  centered k-points were used. As regards the convergence tests of the energy of the model we refer to our previous work 27,43 .

The adsorption energies (vide ultra) are calculated using as reference the corresponding Au(111) slabs, with or without adatom. The energy of the isolated molecules is obtained after optimization of its start geometry as found in the SAM. No spin polarization nor dipole corrections were considered on this metallic system because of their negligible contributions to the total energy 27 and the unproportional needed calculation power. Dispersion corrections were also not included in the NEB calculations, since we consider isolated thiol molecules in our model reactions and it would only slow down the calculations and equally shift the adsorption energy but not the activation energies nor the relative energies 21 . However, in the calculation of the adsorption energies within the SAM the DFT-D3 44 method was used.

The transition states (TS) of the elementary steps were determined using the Nudged-Elastic-Band (NEB) method. 45 Reaction pathways were optimized with a set of eight intermediate geometries (sixteen in complex cases), obtained by linear interpolation with a mixed internal and cartesian coordinate system using the string method 46 as implemented in the Opt'n Path suite. [START_REF] Fleurat-Lessard | ReactionPath[END_REF] The obtained approximate transition states were refined by minimizing the residual forces below 10 -2 eV.Å -1 with the quasi-Newton algorithm implemented in VASP. All potential energy surface (PES) extrema were verified by the calculation of the vibrational frequencies within the harmonic approximation. The Hessian or force constant matrix was computed by finite differences on nuclei forces followed by a diagonalization procedure. The resulting eigenvalues correspond to the harmonic frequencies.

Results and discussion

In order to investigate the effect on the RS-H dissociation reaction mechanism of alkylthiols adsorbed on gold adatom and the effect of the thiol alkyl chain length, three different models Å from the Au adatom (See Fig. 3).

Propanethiol (C3H7SH) adsorbs molecularly (physisorbed) on an adatom with an adsorption energy of -0.87 eV, being in agreement with our former calculation (-0.84 eV) 27 . The studied reaction path includes two activation barriers: a first one (TS1) of 1.13 eV (being + 0.27 eV above the reference energy (slab and isolated thiol), and a second one (TS2), which corresponds to the proton diffusion from Au adatom and Au surface atom (Fig. 2) of 0.30 eV (+0.05 eV above the reference energy value). The calculated activation energy is close to the value of 0.9 -1.1 eV estimated from experiments (see ref. 6 ) and in agreement with earlier experimental data summarized in the review of Vericat et al. 7 . Interesting to mention is that the Eact In the second considered reaction pathway, the model system contains a Au/Au(111)adatomon which two thiol molecules are adsorbed. As reported in Figure 3, the overall reaction path includes two successive steps for the deprotonation of two dipropanetiol molecules. The initial reaction step corresponds to the adsorption of a second propanethiol on the Au adatom for which an adsorption energy of -0.4 eV is obtained. This energy is added to the adsorption energy of the first propanethiol, which is lower (less strongly adsorbed) compared with the first thiol adsorption energy, of -0.87 eV (See Fig. 2). The reaction path includes two activation barriers, a) the breaking of the first RS-H bond (TS1) and b) the second RS-H bond (TS2), respectively. The activation energy corresponding to the first RS-H bond breaking, calculated from TS1 (Fig 3), is equal to 0.75 eV, which is lower than the energy barrier calculated for isolated propanethiol. In addition, the proton transfer process occurring for dipropanethiol is different from the isolated propanethiol case. Indeed, the hydrogen atom does not interact with Au adatom (as for the case of isolated propanethiol) but moves directly to the flat Au(111) surface.

The dissociation activation energy of the RS-H bond of the second propanethiol is found to be lower than for the first propanethiol (Eact = 0.44 eV; TS2, Fig 3 )). This second activation energy is also lower than the activation energy calculated for the RS-H bond breaking in one propanethiol per adatom (Eact = 1.13 eV). A second reaction mechanism was modeled (not reported reaction path) for the case of two propanethiols per adatom, namely the concerted formation of dihydrogen after the adsorption of two propanethiol molecules (See Fig. 4). This reaction shows a high calculated activation barrier of 1.75 eV, hence excluding this concerted molecular hydrogen formation compared with the single propanethiol molecule adsorption on Au/Au(111) adatom (Eact = 1.13 eV).

However, the final chemical state (Figure 4,1c) is thermodynamically stable by 0.40 eV compared with the two dissociated propanethiols chemisorbed on an adatom and two hydrogen atoms adsorbed on the Au(111) surface. The desorption of H2 is thermodynamically favored, as expected. So, one can conclude that the formation of a chemisorbed propanethiol monolayer can be formed starting from the adsorption of two propanethiols on an adatom (in vacuum conditions), leading to the formation of H2.

In the third case the propanethiol molecule in model system (See Fig. 1a) was substituted by an undecanethiol molecule (See Fig. 1c). Undecanthiol adsorbs on an adatom with energy of -1.54

eV. The reaction path for RS-H dissociation (See Fig. 4) is similar to the single propanethiol case (See Fig. 2). The barrier for the S-H bond breaking of undecanethiol is found to be of 1.13 eV, which is equal to the S-H bond breaking of propanethiol. For the hydrogen detachment and diffusion process the system has to overcome a small energy barrier of 0.23 eV which is also similar to the computed value in presence of short chain propanethiol. This result indicates at first sight that the activation energy for RS-H dissociation is independent of the alkyl chain length, but dependent on the surface reconstruction, such as the formation/presence of adatoms. This is in line with the fact that the estimated Au-S binding energy (Ebind) is the same( -2.6 eV) for both alkyl thiols. The cohesive energy of a Au atom is found to be 3.81 eV [START_REF] Kittel | Introduction to Solid State Physics[END_REF] . From this value one can approach the energy needed to pull out a Au atom out of the (111) surface, i.e. since Au has coordination 12 in its bulk and 9 at the surface the energy needed to generate an adatom is at maximum 9/12 3.81eV = 2.86 eV, being in the same energy range as the Au-S binding energy.

In the SAM configuration the Au-S binding energy (Ebind), is calculated as follows (See Table 1, Fig. 6):

Ebind = ½. [E(thiolA/Au(111)) -E(thiolA.SAM) -E(Au(111))] (1)
with E(thiolA.SAM) the single point (not geometrically relaxed) total energy of the thiol radicals With this Ebind one can obtain an approximation for the inter-chain interaction energy Eint.chain as following:

  Eint.chain = Eads -Ebind (2)
Eads,disp.D3 is calculated according to the following equation:

Eads,disp.D3 = ½. [E(thiolA/Au(111)) -2.E(thiolA) -E(Au(111))] (3)
where E(thiolA/Au(111)), E(thiolA), and E(Au( 111)) are the total energies (using the DFT-D3 approach 44 ) of the adsorption complex formed by two thiolA radicals per Au(111) slab, the isolated thiolA under its radical form, and the Au(111) slab, obtained after separate geometry optimization, respectively. The deformation energy is implicitly included in the calculated energies.

Table 1. Adsorption energy, binding energy, and inter-chain interaction energy for C3 and C11 thiolate on defect free Au(111) surface investigated at the PBE-D3 In order to break the S-H bond a surface defect has to be present or has to be formed. In the case the defect has to be formed the short alkyl chains will be privileged in the formation of chemisorbed thiolate species. This result is concluded from our recent results on the selfassembly mechanism of thiol molecules on Au(111), showing a difference depending on the chain length of aminothiols 9 . It was found that short chain aminothiol molecules reconstruct the gold surface more strongly in the self-assembly configuration than long chain aminothiol molecules, probably due to a lower activation barrier for reconstruction. The origin of this lower activation energy might be found in the lower inter-chain interaction energy for the short chains making more mobile on the surface compared with the longer chains. This inter-chain interaction energy was evaluated (See Eq. 2, Table 1).

This observation combined with the present findings unveils a much debated question on the thiol SAM formation: Does the S-H bond break or not? 9,27,38 Taking the above mentioned considerations we propose the following formation pathway for short alkyl chain thiol SAMs (See Fig. 7). A first thiol adsorbs on the surface, and initiates the formation of a protrusion on the Au(111) surface. A second thiol interacts with the adsorption site forming a di-thiol gold species, which subsequently reacts to form a di-thiolate gold species.

The organization of these species to a monolayer forms a SAM. SAMs with conformations such as those that have been studied by Ferrighi et al. 8 For longer alkyl chain thiols the SAM formation might not pass to the formation of an adatom due to the higher interactions between the chains preventing the molecule to relax enough to modify the surface (see higher).

Up to date, it is difficult to ascertain the exact process of the formation of gold adatoms. Are they pulled out from the surface or dragged from an existing step? The real scenario is not yet well established. However, many works agree that the plausible mechanism could be adatoms that are initially taken from the gold surface creating vacancies 51 And to our opinion a dual mechanism should be proposed, combining dragging and pulling gold atoms on/to the surface. Now, concerning the point that it is easier for a shorter chains to pull out a Au atom from the surface, this supposition is based on previous theoretical calculations. For instance, Cometto et al. 28 have calculated the adsorption of thiols (CH3SH and CH3CH2SH species) on Au(111) surface as well as on a surface with gold adatoms. Their results suggested that in the presence of surface adatoms, the radical species adsorb on top of the adatom and decrease its barrier for surface diffusion. This barrier is smaller than the barrier for the diffusion of a single gold atom on Au(111) due to the weakening of the Au-Au bonds as a consequence of the formation of a strong S-Au bond. As a short chain is less sterically hindered than the longer chains its mobility is higher compared to the long chains, the S-Au bond might be stronger than the Au-Au bond (cohesive energy) and by consequence may help to pull out or drag a Au atom more easily. The Au-S bond energy has been shown to be independent of the chain length.

Conclusions

The activation energy for the RS-H dissociation on Au/Au(111) adatoms was investigated using periodic DFT. Three models are investigated based on an adatom containing Au (111) surface:

One propanethiol molecule adsorbed on one adatom, two propanethiol molecules adsorbed on one adatom, and one undecanthiol molecule adsorbed on one adatom. It is found that the chain length has no influence of the RS-H bond breaking barrier and that the Au-adatom-dithiol model is a possible reaction pathway for the propanethiol radical formation on Au(111), concluded from the low activation barrier for the reaction (0.75 eV) compared with the singe alkanethiol adsorption on a adatom (an activation energy of 1.13 eV was found for propanethiol as well as for undecanethiol).

It was found that the chain length is not determining, it is the formation of the defect on the Au(111) surface. So, this result suggests us to propose a new mechanism for the formation of thiol SAMs on Au surfaces. Combined with our recent finding that short chain aminothiols adsorb chemically on Au(111) and are thus more predisposed to reconstruct the surface compared with the long alkyl chain thiols. This result is explained by the fact that short chain thiols have lower inter-chain interaction energy contributions than long chain alkyl thiols do.

Though, the latter being more stabilized by the intermolecular interactions between the alkyl chains. In other words short alkyl chain thiols are expected to restructure the surface more strongly due to their higher mobility and ability to move on the surface to bind with two chains on a surface gold atom, which might become adatoms subsequently. The defects generated will catalyze the RS-H bond breaking more easily. Since there will be more adatoms created when short chain alkyl thiols are adsorbed than long alkyl chain thiols, the long chain alkyl thiols are expected to keep their RS-H bond, at least for a longer time.

Finally, it is not the chain length that will activate the RS-H bond but the defect on Au surface formation energy barrier, and this as a function of the coverage. The next study to confirm this reaction path would be the study of the reaction mechanism for the Au surface restructuration in the presence of alkyl thiols.

Figure 1 :

 1 Figure 1: The three different models investigated: a) One propanethiol molecule adsorbed on gold adatom, b) Two propanethiol molecules adsorbed on gold adatom, and c) one undecanthiol molecule adsorbed on gold adatom. (carbon: light blue, gold: yellow, sulfur: orange, hydrogen: white)

  calculated for the deprotonation of HSCH3 by Lustemberg et al. and reinterpreted by us is 0.90 eV10 on Au(111). Nevertheless, it is known that the methanethiol behaves differently compared with the longer alkyl chain thiols, e.g. the SAM organization is less ordered due to the weaker inter-chain interactions.

Figure 2 .

 2 Figure 2. The reaction path for the S-H bond breaking for propanethiol on an adatom/Au(111). The energies reference (E = 0 eV/thiol) is calculated as the sum of the energies of bare surface, including Au adatom, and the free propanethiol molecule in gas phase. (Energies in eV, distances in Å, carbon: light blue, gold: yellow, sulfur: orange, hydrogen: white).

Figure 3 .

 3 Figure 3. The reaction paths and corresponding geometries studied for the S-H bond breaking for two propanethiol molecules on an adatom/Au(111). The energies reference (E = 0 eV/thiol) is calculated as the sum of the energies of bare surface, including Au adatom, and the free propanethiol in gas phase.. (Energies in eV, distances in Å, carbon: light blue, gold: yellow, sulfur: orange, hydrogen: yellow small spheres)

Figure 4 :

 4 Figure 4: Reaction path with a concerted formation of dihydrogen after the adsorption of two propanethiols on Au adatom. 1a) adsorption of two propanothiols, 1b) transition state, 1c) product. (carbon: light blue, gold: yellow, sulfur: orange, hydrogen: white)

Figure5.

  Figure5. The reaction path for the S-H bond breaking for undecanethiol on an adatom/Au(111).The energies reference (E = 0 eV/thiol) is calculated the sum of the energies of bare surface, including Au adatom, and the free undecanethiol in gas phase. (Energies in eV, distances in Å, carbon: light blue, gold: yellow, sulfur: orange, hydrogen: white).

( 2

 2 in the (2√3×√3)R30º unit cell) in the configuration of the SAM but without considering the Au(111) slab. The SAM unit cell structures are used here, and the energies are referred to the SAM optimized geometry of the isolated thiol molecule.

Figure 6 .

 6 Figure 6. Models for the undecane thiol (a) and propyl thiol (b) SAM on defect free Au(111).

Figure 7 .

 7 Figure 7. Schematic representation of the proposed short alkyl chain thiol SAM formation.

  [START_REF] Grimme | [END_REF]50 level. Eads.disp.D3: the

	Grimme D3 dispersion corrected adsorption energy, Ebind.: the estimated Au-S binding energy
	(Eq. 1), Eint.chain: the estimated inter-chain interaction energy (Eq. 2). Energy values per chain
	in eV, and distances in Å.
	SAMs	Eads.disp.D3	Ebind	Eint.chain
				
	C3	-2.94	-2.63	-0.31
	C11	-3.53	-2.60	-0.93

Acknowledgements

This work was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS] (Grant 2014-[x2014082022]) and the CCRE of Université Pierre et Marie Curie. COST action D36, WG No D36/0006/06 and D36/0006/05, CONICET, DFG (Sa1770/1-1,2), ELCAT and HPC-Europa2 are acknowledged for financial support. The authors thanks Prof. O. Eisenstein from Montpellier University for helpful discussions.