domain: info info

text:
Hussein Al

Haj Hassan

Ali Krayem

Ivan Marino Martinez Bolivar

Laurent Toutain

Alexander Pelov

Ivan Martinez

SCHC over LoRaWAN, a Framework for Interoperable, Energy Efficient and Scalable Networks

Keywords: LPWAN, LoRaWAN, Internet, SCHC, Energy efficiency

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The Internet of things (IoT) is a new paradigm that is shifting industries into smart and connected ones. Based on Cisco [START_REF]Internet of Things at a Glance[END_REF], 500 billion devices are expected to be connected to the Internet by 2030. Furthermore, it is forecasted that the IoT industry will generate a revenue of USD 4.3 billion by 2024 [START_REF] Berthelsen | The global iot market opportunity will reach usd 4.3 trillion by[END_REF]. This is triggered by the evolution of many IoT technologies such as LTE-M, NB-IoT, LoRaWAN, Sigfox and others [START_REF] Chettri | A comprehensive survey on internet of things (iot) toward 5g wireless systems[END_REF][START_REF] Chaudhari | LPWAN Technologies for IoT and M2M Applications[END_REF].

Motivated by its low power consumption, wide coverage, simplicity and ease of management due to its star topology, LoRaWAN offers many advantages compared with other technologies. LoRaWAN is an open-source platform that enables the deployment of both private and public networks [START_REF] Milarokostas | A comprehensive study on lpwans with a focus on the potential of lora/lorawan systems[END_REF]. This leverages LoRaWAN as a strong candidate for diverse IoT applications including but not limited to smart cities, smart buildings, smart metering and intelligent agriculture.

Nevertheless, among the key challenges for LoRaWAN technology are the packet size and the possibility to be integrated within the IP world. For example, the smallest MTU of LoRaWAN is 11 bytes in the US and 51 bytes in Europe [START_REF]LoRaWAN Regional Parameters[END_REF]. This puts restrictions on applications with large payloads. Furthermore, protocols with huge header (e.g. IPv6 takes 40 bytes) would take a significant portion of the available MTU, if it can be actually transfered.

To overcome these restrictions, The IPv6 over Low Power Wide-Area Networks Working Group at the IETF has already produced several documents as follows:

• RFC 8376 provides an overview of the baseline LPWAN technologies [START_REF] Farrell | Low-Power Wide Area Network (LPWAN) Overview[END_REF].

• RFC 8724 describes a Generic Framework for Static Context Header Compression and Fragmentation (SCHC), which provides header compression and three fragmentation mechanisms [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF].

• RFC 9011 specifies the operation of SCHC over Lo-RaWAN networks [START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF]. • RFC 9391 specifies the operation of SCHC over NB-IoT networks [START_REF] Ramos | Static Context Header Compression over Narrowband Internet of Things[END_REF]. In addition, the LoRa Alliance has adopted SCHC as the adaptation layer for IPv6 [START_REF]LoRaWAN IPv6 Adaptation Layer Specification[END_REF]. With SCHC, LoRaWAN devices can send IPv6 packets with sizes more than the LoRaWAN MTU, thanks to its fragmentation mechanisms that allow decomposing the message over several fragments. Furthermore, SCHC's compression framework allows reducing the packet header (and possibly payload) to avoid wasting the bandwidth on static content, which is common in LPWANs use cases.

There exist many studies that investigate and evaluate SCHC performance. To the best of the author's knowledge, none of the work have investigated the possible gains of SCHC on the energy consumption of the device and the capacity of the network, which we tackle in this paper. The paper is organized as follows. Section II presents essential background and existing work on SCHC over LoRaWAN. Section II describes the energy model of LoRaWAN device with SCHC. The gain of SCHC at the levels of device and network is discussed and quantified in Section IV. Section V concludes the paper.

II. BACKGROUND AND RELATED WORK

A. LoRaWAN

Long Range (LoRa) is a radio modulation that is based on Chirp Spread Spectrum (CSS) [START_REF] Mroue | Analytical and simulation study for lora modulation[END_REF][START_REF] Chiani | On the lora modulation for iot: Waveform properties and spectral analysis[END_REF]. While LoRa defines the physical layer, LoRaWAN defines the upper layer protocol. This LPWAN technology is used for long range, low power and low datarate applications [START_REF] Farrell | Low-Power Wide Area Network (LPWAN) Overview[END_REF]. The LoRa Alliance specifies and maintain the LoRaWAN protocol. LoRaWAN networks follows a star topology as shown in Figure 1. Multiple gateways can receive an end-device transmissions, and relay it to a Network Server via standard IP connections. Although uplink communication, i.e. from an end-device to a Network Server, is expected to be the dominant, LoRaWAN allows bi-directional exchange of messages.

LoRaWAN distinguishes between a basic LoRaWAN (Class A) end-devices and optional devices with optional features (Class B, Class C) [START_REF]2 1.0.4 Specification[END_REF]:

• In Class A, an uplink transmission is followed by two short downlink receive windows. As such, downlink communications, i.e. from the network server to end-device, will have to wait an uplink communication initiated by the end-device. [START_REF]2 1.0.4 Specification[END_REF] for the full LoRaWAN L2 specifications.

As a companion to the LoRaWAN MAC Layer Protocol specification [START_REF]2 1.0.4 Specification[END_REF], the LoRaWAN Regional Parameters specification document [START_REF]LoRaWAN Regional Parameters[END_REF] defines the adaptation of the LoRaWAN Link Layer to comply with the regulations enforced throughout the world on the use of various frequency bands of the unlicensed spectrum.

B. SCHC over LoRaWAN

The general framework of SCHC is defined in [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF], while the operation of SCHC over LoRaWAN is defined in [START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF]. In LoRaWAN, SCHC operates between two SCHC entities: 1) application layer of the end-device and 2) SCHC gateway (network side). Compression and fragmentation are applied by the sender, while decompression and applied by the receiving entity.

1) Compression/decompression: SCHC compression is based on using a set of rules that are defined in advance to communication. They describe the context to compress or decompress headers. Since the content of LPWAN packets is usually highly predictable, static contexts can be derived and stored. Indeed, the context must be stored ahead in both the sender (compressor) and receiver (decompressor). Note that the way context is provisioned and shared is not yet standardized.

Once the context is shared by the two sides of communication, the sender transmits a RuleID, which describes the rule used to compress the packet, followed by the compression residue, which consist of the reminder of bits after compression. Note that every rule contains a list of field Descriptors composed of a Field Identifier (FID), a Field Length (FL), a Field Position (FP), a Direction Indicator (DI), a Target Value (TV), a Matching Operator (MO), and a Compression/Decompression Action (CDA). At the other side of communication, the receiver uses the RuleID and residue to retrieve the original packet. For more information on SCHC compression, please refer to [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF].

In LoRaWAN, SCHC compression uses RuleID of 1 byte. The RuleID is placed in the FPort field of LoRaWAN when fragmentation is not applied. Otherwise, it is placed in the beginning of first fragment [START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF].

2) Fragmentation: Three SCHC fragmentation modes are defined in [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF], each with different reliability level and retransmission behavior:

• No-ack: The receiver does not provide any feedback to the sender, thus providing no reliability mechanisms. • Ack-Always: The receiver provides the sender with feedback (positive or negative), thus providing high reliability at the cost of sending acknowledgments. • Ack-on-error: The receiver provides the sender with feedback of only missing parts to be retransmitted. In a SCHC fragmentation session, the packet is fragmented into pieces called tiles. A certain number of successive tiles are handled as a group, which is called a window. Each fragmentation mode defines the way tiles and windows are used. In SCHC over LoRaWAN, Ack-always is used for downlink unicast, Ack-on-error for uplink unicast and Noack for downlink multicast. Please refer to [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF][START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF] for further details on the fragmentation parameters and specifications in LoRaWAN.

C. Existing work on SCHC over LoRaWAN

Although standards of SCHC have been recently published [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF][START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF], several studies started to investigate its applications and performance. For example, SCHC is leveraged to enable autoconfiguring the LPWAN IoT devices to provide an interface with the internet in [START_REF] Moons | Device discovery and context registration in static context header compression networks[END_REF]. Two solutions for IPv6 configuration and Neighbor Discovery are proposed and evaluated. The work in [START_REF] Sanchez-Iborra | Ipv6 communications over lora for future iov services[END_REF] uses SCHC to enable IPv6 connectivity between a moving and an Internet node for vehicular IoT solution. In [START_REF] Hoebeke | A cloud-based virtual network operator for managing multimodal lpwa networks and devices[END_REF], the authors proposed a cloud-based virtual network operator architecture for multi-modal LPWANs and devices leveraging SCHC. The study demonstrates that SCHC is a viable choice for achieving unified communication in the proposed architecture. In [START_REF] Famaey | Flexible multimodal subgigahertz communication for heterogeneous internet of things applications[END_REF], a multimodal IoT network architecture is proposed to employ different wireless communications. In this context, SCHC is proposed to overcome the limitation of several technologies (Sigfox, LoRaWAN) in supporting IPv6. [START_REF] Santa | Lpwan-based vehicular monitoring platform with a generic ip network interface[END_REF] presents a vehicular monitoring platform enabled by LoRaWAN and data compression by using SCHC. By testing the platform in a university campus, high level of reliability in the transmission link is shown, with packet delivery ratios over 95%. Based on SCHC, a solution to support roaming of devices during mobility between different LoRaWAN operators is proposed in [START_REF] Ayoub | Schc-based solution for roaming in lorawan[END_REF]. The authors define a server to manage the context between operators. Results shows that the proposed solution decreases the time delay to handle the transmitted messages before registration.

The above mentioned studies explore the usage and possible applications of SCHC. Other studies focus on tuning the parameters of SCHC and evaluating its performance. For example, the authors of [START_REF] Abdelfadeel | Lschc: Layered static context header compression for lpwans[END_REF] present an implementation and evaluation of SCHC. They found that SCHC is very effective when the network flows are known in advance. [START_REF] Sanchez-Gomez | Impact of schc compression and fragmentation in lpwan: A case study with lorawan[END_REF] addresses the SCHC standard and its performance in terms of latency and delivery ratio improvements and useful payload sent over fragment. The considered SCHC fragmentation reliability in this work is No-ACK, and thus reliability is based on retransmissions of LoRaWAN L2 layer. As such, a re-evaluation is needed so that the results are consistent with the standard in [START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF]. In [START_REF] Aguilar | Performance analysis and optimal tuning of ietf lpwan schc ack-on-error mode[END_REF], the authors develop a mathematical model to compute the most critical performance parameters for SCHC ACK-on-Error mode. The model is used to tune the main parameters used over LoRaWAN and Sigfox. [START_REF] Abdelfadeel | Dynamic context for static context header compression in lpwans[END_REF] proposes a dummy mapping technique to compress/decompress some header fields of unknown flows using SCHC. The impact of the dummy mapping size, the request arrival rate and the LPWAN link layer parameters on the compression are explored. [START_REF] Aguilar | Lorawan schc fragmentation demystified[END_REF] study the trade-offs of SCHC fragmentation/ reassembly modes over LoRaWAN. Results show that No-ACK mode yields the lowest channel occupancy, highest goodput and lower total delay. However, it lacks reliability. ACK-Always and ACK-on-Error modes leads to the same total delay, and similar total channel occupancy, but ACK-on-Error offers greater goodput than Ack-Always.

[26] discusses several solutions in order to run IPv6 over IoT. The applicability over LoRaWAN, DASH7 and NB-IoT is investigated. The authors concluded that CoAP and SCHC provide the best approach for LPWANs technologies. In [START_REF] Gomez | Ipv6 over lpwans: Connecting low power wide area networks to the internet (of things)[END_REF], the authors present SCHC as a proposed IPv6 adaptation layer for LPWANs. The efficiency of SCHC is presented by comparing the residue of compressing the IPv6 protocol in comparison with RoHC and 6LoWPAN. Similarly in [START_REF] Ayoub | Implementation of schc in ns-3 and comparison with 6low-pan[END_REF], the authors shows through simulations with ns3 that SCHC protocol solution is better in term of header compression compared to 6LoWPA, as SCHC leads to lower header size. In [START_REF] Moons | Using schc for an optimized protocol stack in multimodal lpwan solutions[END_REF], the authors study the benefits of using SCHC for multimodal LPWAN solutions. By comparing SCHC's overhead and number of packet exchanges to achieve CoAP blockwise transfer and 6LoWPAN compression and fragmentation, the authors concluded that SCHC is the only protocol that is able to support end-to-end IPv6 connectivity for a multimodal device in LPWAN. Furthermore, the study also showed that SCHC has relative small footprint and is suitable for an embedded device as it requires low-memory needs. In [START_REF] Dumay | Effective interoperability and security support for constrained iot networks[END_REF], the authors shows that SCHC's compression and fragmentation mechanism can be used to enable interoperable and secure communication over constrained IoT networks such as sigfox, LoRaWAN and NB-IoT. While security based internet protocol adds relatively large over-head, SCHC compression is able to significantly reduce it. The study in [START_REF] Pappalardo | Device management at the network edge to support qos-aware iot services[END_REF] evaluated the effectiveness of SCHC in compression considering LWM2M for LoRaWAN devices. Results shows that the compression can bring significant benefits with up to 75% compression ratio. A model for determining the efficiency of channel usage of SCHC on LoRaWAN is presented in [START_REF] Muñoz | Schc over lorawan efficiency: Evaluation and experimental performance of packet fragmentation[END_REF]. Results showed that the efficiency decreases when the probability of error increases, and that there is no linear relationship between the spreading factor and efficiency. The end-to-end latency of IPv6 packets is evaluated for a real world deployment of SCHC in [START_REF] Sisinni | Assessing a methodology for evaluating the latency of ipv6 with schc compression in lorawan deployments[END_REF], where the authors evaluated Acklio's implementation for a class C LoRaWAN device and Acklio SCHC gateway (IP Core). Results showed a latency of less than 1 sec for small packets in uplink.

D. Contribution

As presented above, existing studies showed that SCHC is the most efficient solution in providing IPv6 connectivity for LPWAN's device. SCHC compression provides the lowest compression residue, and its fragmentation is able to provide high reliability. Moreover, existing studies show that SCHC can be adopted for wide range of frameworks and applications. Nevertheless, the gain of using SCHC is not fully investigated. For example none of the studies investigated the impact of using SCHC on the energy consumption of a LoRaWAN device. Moreover, none of the studies explored the impact of using SCHC on the network's level such as capacity, In this paper, we aim at exploring possible gains of using SCHC on both the device and network level. At the level of device, we compute the gain of SCHC compression by calculating the overall energy consumption reduction for a real traffic pattern. At the level of the network, we study the percentage of packet delivery with respect to the number of devices. We then emphasize the gain in terms of capacity of a network with devices using SCHC compression.

III. ENERGY MODEL OF LORAWAN DEVICE

Inspired by [START_REF] Maudet | Refined node energy consumption modeling in a lorawan network[END_REF] and [START_REF] Bouguera | Energy consumption model for sensor nodes based on lora and lorawan[END_REF], we develop the energy model of the LoRaWAN device with SCHC implementation. Figure 2 presents the different states of the device. After wakingup, a device (sensor or meter) goes into the process of sensing/measuring. Then, the device processes the input signal before transferring it to transmission. Note that processing also includes SCHC compression and preparing the fragments in case of fragmentation. After the wake-up of transmission chain, the device transmits the data and start preparing for receiving the data in case of downlink. If no more data (fragments) is to be sent, the device goes back into sleep mode. Otherwise, preparing the new fragment is required before the new transmission. Indeed. the device should wait certain time in idle state depending on the spectrum restriction (e.g. duty cycle). Based on the described model, the energy consumption of the device is as follows:

E T OT = E SLP +E SEN S +E P RO +E T X +E RX +E IDLE
where E SLP represents the energy consumption of the device during sleep mode. It depends on the duration the device is in sleep mode. E SEN S represents the energy required by the device to wake-up from sleep and to sense. E P RO represents the energy consumed by the microcontroller unit (MCU). It includes the energy required by the device to process the measurementand to perform the compression and fragmentation when SCHC is used. Note that the energy required for processing depends on the measured/sensed parameter(s), type of compression used (e.g. rules used to compress / decompress) the headers in case of SCHC and type of fragmentation and size of data (number of fragments). E T X is the energy needed to transmit the data. It includes energy needed for waking up and switching-off the transmission chain respectively. This value depends on several parameters such as the size of data to be sent, the transmitted power, regional parameters and the selected data rate. E RX is the energy needed to receive a frame. It includes the energy needed to turn-on and turn-off the receiveing chain respectively. Indeed, the amount of energy depends on several factors such as the used receiving window (RX1 or RX2) and size of the frames. E IDLE is the energy consumed when the device is idle. This corresponds to the time between transmission of fragments. All of the above values of energy consumption are device dependent. For example, the frequency of the MCU affects the processing time and the power amplifier affects the consumed energy for a specific transmitted power. For more details on calculating the energy consumed by a LoRaWAN device refer to [START_REF] Maudet | Refined node energy consumption modeling in a lorawan network[END_REF][START_REF] Bouguera | Energy consumption model for sensor nodes based on lora and lorawan[END_REF].

IV. SIMULATION AND RESULTS

For both device and network levels, we consider that SCHC compression and fragmentation is applied. While fragmentation profiles follow the profile defined in RFC 9011 [START_REF] Gimenez | Static context header compression and fragmentation (schc) over lorawan[END_REF], we consider three different compression profiles as shown in Figure 3 andTable I: • UDP/IPv6 Compression: Compression of UDP/IP following the example of RFC 8724 [START_REF] Minaburo | Schc: Generic framework for static context header compression and fragmentation[END_REF] with perfect header compression. structured application data from smart metering applications. In this work, we consider a real traffic for electricity meter. An example of the message sizes for different compression types/rules is summarized in Table I.

A. Energy Gain of SCHC on the device level

At this level, we focus on energy consumption as the main parameter. This is because we study the device without taking into consideration the network conditions, which is considered in the following section.

The calculations consider Nucleo F070RB board with an SX1272 LoRa shield. The parameters used in calculation of energy are presented in Table II [START_REF] Maudet | Refined node energy consumption modeling in a lorawan network[END_REF][START_REF] Bouguera | Energy consumption model for sensor nodes based on lora and lorawan[END_REF]. To evaluate the gain of SCHC without the effect of network conditions, we consider that there is no loss of packets. This means that the transmitted packets does not suffer from collisions. We also consider that the downlink happens on RX1 (Reception window 1) and that each fragment is processed before sending. The device goes in sleep mode during idle time.

SCHC Compression leads to reducing the energy consumption as follows:

• Reduce the transmitted data and thus the time on air • The results of compression can fit the LoRaWAN payload and thus remove/reduce the need for fragmentation and its corresponding header. Note that when fragmentation is applied the device needs to enter different states before each transmission (wakeup, tx wakeup...) • Reduce collision probability which leads to reducing retransmissions. The impact of SCHC in collision is shown in the following section. Figure 4 shows the energy reduction ratio for different compression types/rules with respect to no-compression case when the transmission power is 14 dBm. The figure shows that the energy reduction ranges between 30% and 81% depending on the radio conditions (considered datarate) and compression rule/type. Obviously, the compression rule that covers bigger part of the packet (and thus higher compression ratio) leads to higher energy reduction. The figure also shows that the highest gain is achieved when the lowest datarate is used. Based on the results, it is possible to extend the battery life up to 5 times when using SCHC compression.

To illustrate the impact of transmitted power, we present in Figure 5 the percentage of energy savings for different types of compression while considering two different transmitted power for the case highest spreading factor (i.e. SF12) . The figure shows that using the simplest rule (UDP/IPv6 header only compression) will achieve significant energy savings (25%) even if the lowest transmitted power is used (3 dBm), which might not be applicable. Intuitively, increasing the transmit power will lead to higher energy consumption but also higher gain when SCHC is used.

B. Network level

We consider a LoRaWAN network composed of a single gateway, a LoRaWAN network server and an application server. The gateway is serving a number of devices that are distributed randomly with a uniform distribution spreading factor amongst devices. We consider a simple propagation model between the gateway and the device as in [START_REF] Maudet | Refined node energy consumption modeling in a lorawan network[END_REF]. We consider that the collision model takes into account the capture effect [START_REF] Heusse | Capacity of a lorawan cell[END_REF]. When a packet is not received, this will be due to: i) collisions with other packets, ii) no more receiver paths, which is limited by the hardware of the receiver, iii) under sensitivity, i.e. the received power is less that the receiver's sensitivity and iv) out of coverage. We differentiate between packet delivery and data delivery, where the former corresponds to the probability of successful reception of individual transmitted frames (fragments), while all fragments of the same message should be received in order to have successful data delivery.

We consider real traffic pattern corresponding to a real deployment of SCHC over LoRaWAN for electricity metering, where a packet is sent every 15 minutes. We use the model developed in [START_REF] Capuzzo | Confirmed traffic in lorawan: Pitfalls and countermeasures[END_REF] to simulate the network behavior in ns3. We consider a gateway with 8 channels. The gateway is covering a radius of 7 km. We consider that the network operates in the EU868 band as described in the LoRa Alliance regional parameters [START_REF]LoRaWAN Regional Parameters[END_REF]. We simulate the network for different number of devices with same behavior. For fragments of the same message, the delay between fragments is calculated depending on the duty cycle. A random delay before transmission (up 1 sec) is considered to avoid all the devices sending at the same time. In order to achieve a confidence level of 99% percent, the number of iterations is selected. Figure 6 presents the probability of packet delivery with respect to the number of devices in the network. The figure shows that using compression increases significantly the number of devices a gateway can serve. This is due to the fact that compression leads to lower message size and thus lower vulnerable time where collisions may occur. For example, if we consider 90% packet delivery, the number of devices that can be supported by the network is around 900 for both Comp. 1 and Comp. 2, while employing no compression limits it to less than 200 devices. This multiplies by more than 4 times the network capacity. The figure also shows that the packet delivery significantly increases for a specific number of devices. For example, if we consider 900 devices, no compression achieves 65% packet delivery. This percentage increases to 74% and 90% when using UDP/IP Compression and Comp. 1 respectively.

Figure 7 shows the percentage of data delivery with respect to the number of devices for different compression types. In data delivery, a successful transmission of a SCHC packet means that all fragments have been received.

By comparing Figure 7 and Figure 6, we see an important difference between data delivery and packet delivery for the no compression case. The difference is less important for UPD/IP compression and almost negligible for Comp. Comp 2. The difference is due to the impact of compression in reducing the message size, and thus reducing the need for fragmentation (less number of fragments or even no fragmentation at all). For example, when UDP/IP compression is employed, the packet is compressed to 59 bytes, which still requires fragmentation in some spreading factors (e.g. SF 12) while Comp. 1 significantly reduces the size of the message.

V. CONCLUSION

In this paper, we study the impact of using SCHC on a LoRaWAN device and a LoRaWAN Network. SCHC significantly reduces the packet size by compressing headers and structure data, which leads to much lower time-on-air for transmitting messages. On the level of device, this would reduce the energy consumption and thus extend the lifetime of a LoRaWAN device with battery unit. On the level of network, this leads to lower collision rate and thus larger number of served devices. Simulations showed that the energy consumption of the device can be reduced up to 81% while the capacity of the network can be increased more than 4 times.

Fig. 3 .

 3 Fig. 3. Compression Types.

UDPFig. 4 .Fig. 5 .

 45 Fig. 4. Percentage of energy reduction when using SCHC compression for different types of compression.

Fig. 6 .

 6 Fig.6. Percentage of packet delivery with respect to the number of devices for different compression types.

Fig. 7 .

 7 Fig. 7. of data delivery with respect to the number of devices for different compression types.

TABLE I TRAFFIC

 I GENERATED BY EACH DEVICE.

	Compression type No comp UDP/IP Compression Comp 1 Comp 2
	Message size	107	59	26	15
			The size includes header and payload in bytes.

TABLE II PARAMETERS

 II USED FOR CALCULATION OF ENERGY CONSUMPTION.

	Parameter	Duration (ms)	Current (mA)
	Sensing	25	5.2
	Processing	35	0.6
	TX wake-up	1.722	2.268
	TX switch-off	0.3	2.072
	TX	varies	39.43 (14 dBm), 21.86 (3 dBm)
	Sleep	varies	0.001
	Idle	varies	0.0015
	RX wake-up	9	1.996
	RX switch-off	0.3	2.033
	RX	varies	10.5

ACKNOWLEDGMENT

This research has been partially funded by French ANR project DiNS under contract ANR19-CE25-0009-01.


Luis Cardenas
email: luis.cardenas@ircelyon.univ-lyon1.fr

Clément Molinet

Stéphane Loridant
email: stephane.loridant@ircelyon.univ-lyon1.fr

Unraveling the Ce 3+ detection at the surface of ceria nanopowders by UPS analysis

A sequential analysis using Ultra-Violet Photoelectron Spectroscopy (UPS) and X-ray Photoelectron Spectroscopy (XPS) on ceria nanopowders has been implemented to identify the influence of the X-ray beam on the surface of this oxide. For the first time, the UPS analysis evidenced the photoreductive effect of XPS analysis on ceria after an oxidative in situ pretreatment, leading to an overestimation of the Ce 3+ /Ce 4+ ratio obtained by XPS. Based on this spectroscopy methodology, UPS imposes itself as a leading technique for analyzing powders with minimal impact on the authentic chemical state, thus paving the way for identifying the real ratio of Ce 4+ and Ce 3+ of ceria after oxidative and reductive in situ treatments.

Introduction

In the last decades, the electronic properties of ceria have been investigated, particularly the relationships between stoichiometric CeO2 and sub-stoichiometric CeO2-δ, which play a central role in controlling the catalytic activity in different relevant processes. 1 In particular, Ce 3+ cations present in CeO2-δ act as a reservoir of electrons to mediate the reduction of O2 molecules during a catalytic redox reaction, associated with high anionic mobility. The Ce 3+ /Ce 4+ redox couple provides exceptional oxygen storage capacity to ceria. However, this redox couple is widely impacted by the surface area. [START_REF] Aneggi | Shape-Dependent Activity of Ceria in Soot Combustion[END_REF] This catalyst has been characterized through X-ray Photoelectron Spectroscopy (XPS), particularly the Ce 3+ /Ce 4+ ratio, making XPS the workhorse in the semi-quantitative determination of chemical states at the surface of ceria. [START_REF] Paparazzo | Use and mis-use of x-ray photoemission spectroscopy Ce3d spectra of Ce2O3 and CeO2[END_REF] Although XPS provides access to elemental chemical composition and high surface sensitivity with an inelastic mean free-path (IMFP) for CeO2 located between 2.1 nm and 6.3 nm for 1.3 KeV (close to Al kα energy = 1486.6 eV) and 5.1 KeV of incident energy, respectively. [START_REF] Kato | Quantitative depth profiling of Ce 3+ in Pt/CeO2 by in situ high-energy XPS in a hydrogen atmosphere[END_REF] The fitting procedure of the Ce 3d core level requires more than ten components, [START_REF] Holgado | Study of CeO2 XPS spectra by factor analysis: reduction of CeO2[END_REF] including different symmetric and asymmetric fit functions, [START_REF] Skála | Cerium oxide stoichiometry alteration via Sn deposition: Influence of temperature[END_REF] rendering the Ce 3d core level challenging to interpret and quantify. These technical and analytical aspects are at the center of the debate that still exists about the origin and determination of the Ce 3+ /Ce 4+ ratio states by XPS. Furthermore, standard X-ray sources (Al Kα and Mg Kα) used in XPS lab setups emit photons with energies of 1486.6 eV and 1253.6 eV, respectively. Under these conditions, photoreduction effects (photolysis) cannot be excluded, especially at the surface of ceria where Ce 3+ is preferentially formed. [START_REF] Kato | Quantitative depth profiling of Ce 3+ in Pt/CeO2 by in situ high-energy XPS in a hydrogen atmosphere[END_REF] The literature has reported several cases related to photolysis effects during XPS and X-ray Absorption Near-edge Spectroscopy XANES analysis. For instance, Paparazzo et al., [START_REF] Paparazzo | XPS studies of damage induced by X-ray irradiation on CeO2 surfaces[END_REF][START_REF] Paparazzo | X-ray induced reduction effects at CeO2 surfaces: An x-ray photoelectron spectroscopy study[END_REF] revealed the reductive character of ceria during an XPS analysis by highlighting a change in the Ce 3d profile as a function of the X-ray exposure time. Subsequently, El Fallah et al., [START_REF] Fallah | Effect of surface treatments, photon and electron impacts on the ceria 3d core level[END_REF] showed by XPS the different experimental parameters involved in Ce 3+ cations formation, as surface treatments and X-ray damage induced during XPS analysis. The debate on the origin of Ce 3+ during XPS analysis was brought back by Park et al., [START_REF] Park | Effect of Crystallinity on the Photoreduction of Cerium Oxide: A Study of CeO2 and Ce/Al2O3 Catalysts[END_REF] attributing Ce 3+ enhancement to photolysis of the amorphous cerium oxide in cerium-alumina catalysts. Zhang et al., [START_REF] Zhang | Cerium oxidation state in ceria nanoparticles studied with X-ray photoelectron spectroscopy and absorption near edge spectroscopy[END_REF] dealt with the photolysis issue on ceria by combining XPS and XANES. The authors found significant discrepancies between both analyses on ceria nanoparticles, showing a significantly higher concentration of Ce 3+ by XPS analysis than that obtained by XANES in both transmission and fluorescence operating modes, a discrepancy probably caused by the X-radiation. Indeed, Wu et al., [START_REF] Wu | Defect engineering by synchrotron radiation X-rays in CeO2 nanocrystals[END_REF] reported the reduction of ceria during XANES analysis with a photon energy of 7 KeV. In this work, the Ce 3+ cations were followed using the Ce L3-edge as a function of the exposure time to X-rays. Foresee a multi-technique approach is an avenue to be explored to determine the real chemical state of many oxides and photosensitive samples, particularly the ceria Ce 3+ /Ce 4+ ratio. However, to date, the multi-technique implementation of certain laboratory spectroscopies (RAMAN, UV-VIS, XPS, IR) has not allowed reaching a consensus in evaluating the chemical state at the surface of stochiometric and sub-stochiometric ceria. For instance, optical UV-Vis and Raman spectroscopies have been intensively used to characterize ceria. [START_REF] Nottbohm | Investigation of ceria by combined Raman, UV-vis and X-ray photoelectron spectroscopy[END_REF] Particularly Raman spectroscopy, [START_REF] Loridant | Raman spectroscopy as a powerful tool to characterize ceria-based catalysts[END_REF] Raman electronic scattering of Ce 3+ cations can be combined with Raman vibrational scattering to characterize the chemical bonds of ceria. However, Raman spectroscopy is a bulk technique compared to UP spectroscopy, even if surface species such as carbonates, peroxo, and OH groups can be observed. Furthermore, only semi-quantitative measurements can be obtained by Raman spectroscopy, and the photolysis process can be observed. [START_REF] Daniel | Probing reoxidation sites by in situ Raman spectroscopy: differences between reduced CeO2 and Pt/CeO2[END_REF] Photolysis effects can only be minimized by using an expensive violet laser and detection system in UV Raman mode. Finally, UV-Vis spectroscopy has also limitations since broad bands are observed, limiting a fine distinction between different electronic transitions. In parallel, further efforts have been made using synchrotron facilities to determine the Ce 3+ /Ce 4+ ratio. However, extreme caution is required when soft and hard X-ray sources are combined as the impact of the beam received on the surface per unit area (power density =ϕ(hc/λ), where ϕ is the photon flux) leads to photoreduction beam damage. To bypass this potential photoreductive effect and increase the surface sensitivity, a combined approach of low (UPS) and soft energies (XPS or RESPES at 121.5 eV and 124.5 eV) spectroscopies techniques is required to confirm the absence of the photolysis effect, allowing thus to reveal the real electronic state of the ceria. Indeed, whatever spectroscopic method is used should emphasize three factors: (i) surface preparation, (ii) mean depth resolution/excitation energy, and (iii) photon power density.

In this context, to characterize the electronic structure of a catalytic relevant material as ceria nanopowders is essential to reveal the nature of the active sites and redox mechanisms guided by the Ce 3+ /Ce 4+ ratio. For instance, a high electron occupancy in the gap Ce 4f1 (Ce 3+ ) results in the deviation of stoichiometric CeO2 (Figure 1). [START_REF] Khalifi | Electronic and optical properties of CeO2 from first principles calculations[END_REF][START_REF] Maslakov | The electronic structure and the nature of the chemical bond in CeO2[END_REF] The reducibility of CeO2 is facilitated by the electron transition (occupied) O 2p → (unoccupied) Ce 5d and Ce 4f [START_REF] Pedrielli | Electronic excitation spectra of cerium oxides: from ab initio dielectric response functions to Monte Carlo electron transport simulations[END_REF] concomitants with the release of two electrons from O 2-anions, leading to the formation of two Ce 3+ cations. The ionic character of ceria foresees a low degree of hybridization between Ce 5d, O 2p, and Ce 4f occupied states. In this context, DFT calculations forecast a valence band formed mainly by the O 2p state with low electronic occupancy of Ce 4f and Ce 5d orbitals in the region occupied by O 2p orbitals. An extremely low density of electron tails characterizes this occupancy (Ce 4f, Ce 5d) which surrounds the interstitial region between O and Ce atoms represented by nonoverlapping muffin-tin spheres. [START_REF] Skorodumova | Electronic, bonding, and optical properties of CeO2 and Ce2O3 from first principles[END_REF] In stoichiometric ceria (CeO2), the low relative energy between occupied O 2p and unoccupied 4f states may render this transition sensitive to photolysis, which may induce the presence of the Ce 4f state in the valence band. In this context, UPS analysis would be a spectroscopic method intended to identify Ce 4f, especially by de-correlating its detection of undesirable effects such as photolysis and keeping a high surface sensitivity. In this paper, we propose studying the electronic structure of ceria nanopowders to address the debate on the origin of Ce 3+ cations. This is remediated by combining two spectroscopic technics with different mean depth resolutions, such as XPS and UPS. Simultaneously, we established a strategy using UPS as a spectroscopic reference method to pinpoint the true Ce 3+ chemical state at the outermost surface of stochiometric and sub-stochiometric ceria in nanopowder form, especially bypassing undesirable photolysis phenomena like those observed during an XPS analysis. Furthermore, we followed the evolution of the Ce 3+ /Ce 4+ ratio by using Ce 4f, O 2p, and Ce 3d states after oxidative and reductive in situ treatments to estimate the reducibility degree of ceria ranging from shallower (UPS) to deeper layers (XPS). To adequately describe the electronic structure of stoichiometric CeO2, an oxidizing in situ treatment was required previously for the UPS analysis. It has two purposes: (i) remove organic impurities and (ii) fully oxidize ceria to render it nearly stoichiometric. In situ oxidized ceria was analyzed according to a sequence starting with UPS at low energy (21.2 eV) followed by XPS (1486.6 eV) to determine the X-ray beam influence on the sample. Therefore keeping the UPS→XPS sequence was essential to analyze the effect of photolysis on ceria due to the high energy and power density photon flux of X-rays.

Experimental section

Materials and methods:

Ceria nanopowder in colloidal solution: An aqueous solution (10 wt% in 100 ml of water) of pure ceria (Aldrich, ref. 643009, 99.99%, particle size below 25 nm) was used as a precursor. It was ultrasonically dispersed and deposited at RT by dropcasting on Ag foil previously cleaned. This CeO2/Ag sample was immediately introduced under vacuum, inducing thus a rapid drying of the solution.

Ceria foil model system intended to identify the Ce 3d core level transitions during in situ oxidation:

A foil of pure ceria (Aldrich, ref. GF63193013, 99.9%) was used to obtain the spectra of Ce 3d under in situ conditions from full reduced to nearly stoichiometric CeO2. The sample was exposed to Ar + sputtering for 6 hours at 3 KeV under vacuum. This erosion method turned the surface of the ceria into nearly reduced ceria (Ce 3+ ). Subsequently, this surface was exposed to a leak of oxygen (O2) P≈10 -6 Torr during XPS analysis, thus providing a clear view of the evolution of each of the components during in situ oxidation (Figure 2(a)).

Oxidation and reduction of colloidal solution of ceria

CeO2-δ nanopowder on Ag was oxidized/reduced in situ using a catalytic reactor cell connected in situ to the PES analysis chamber under UHV, providing a direct sample transfer without contact with the air. The oxidation treatment of CeO2-δ/Ag was carried out under 50 mL.min -1 O2 flow during 4 h at 600 °C and subsequently analyzed by UPS-XPS. In contrast, the reduction process was carried out on the sample under UHV for 4 h held at 600 °C.

Ultraviolet Photoelectron Spectroscopy

UPS analysis was used to determine the electronic structure of the valence band of ceria nanopowders. Prior to measurements, Ag foil was cleaned by several cycles of 2 KeV Ar + sputtering at RT. Then, several drops were deposited on the conducting Ag foil. This methodology for UPS sample preparation was described by Maheu et al., [START_REF] Maheu | UPS and UV spectroscopies combined to position the energy levels of TiO2 anatase and rutile nanopowders[END_REF] thus minimizing the charging effects during Photoelectron Spectroscopy (PES) analysis and providing a straightforward calibration via an absolute measurement of the Fermi level of Ag pristine foil (Figure 3). XPS and UPS spectra obtained from Ag foil after sputtering confirm the metallic character of Ag by the presence of plasmons in the Ag 3d core level, the near-absence of oxygen, and the step the Fermi in the valence band, respectively (Figure S1). PES measurements were carried out in a commercial AXIS-ULTRA DLD spectrometer using an Al Kα (1486.6 eV) XPS source and a discharge UV lamp delivering photons at 21.2 eV corresponding to the He Iα line typically used in UPS. Under these conditions, the intrinsic spectral resolution was measured at the Fermi edge of the Ag foil at room temperature and estimated to be 0.15 eV. For comparison, the intrinsic resolution of a lab-based XPS setup using a monochromatized source is more than 0.55 eV. The UP spectral analysis was conducted using the Fermi level of Ag as internal calibration energy. Likewise, the background was corrected using a mathematical function developed by Li et al., [START_REF] Li | Inelastic electron background function for ultraviolet photoelectron spectra[END_REF] (Figure S2) for UPS analysis and implemented later by Maheu et al., [START_REF] Maheu | UPS and UV spectroscopies combined to position the energy levels of TiO2 anatase and rutile nanopowders[END_REF] on TiO2 nanopowders. After background subtraction, the signal was fitted by using a Gaussian function. In parallel, XPS analysis on CeO2/Ag revealed well-resolved core levels corresponding to Ce 3d, C 1s, and Ag 3d. Ce 3d core levels were fitted using a combination of Voigt line shapes for Ce 4+ and Ce 3+ , including asymmetric shapes.

Temperature Programmed Reduction (TPR)

The reducibility of CeO2 nanopowder was determined by TPR measurements (Figure S4) using a 9 Omnistar GSD 301 Pfeiffer Vacuum mass spectrometer. The dried sample (100 mg) was loaded into a suitable reactor and heated from room temperature to 600 °C (10 °C min -1 ) for 4 h under 1%O2/He to pre-treated CeO2 and then cooled down to room temperature. Then, it was heated from room temperature up to 650 °C (10 °C min-1) under 1% H2-Ar.

Results and discussion

The complexity of the Ce 3d core level fitting procedure requires a prior determination of the origin of each of its components, for which an XPS analysis on the polycrystalline model foil of ceria was executed under in situ oxidation conditions, starting from an almost fully reduced state (as outlined in the experimental section). Figure 2(a) shows the partial oxidation of polycrystalline ceria foil at low pressure (Pox≈10 -6 Torr). Each Ce 3d XPS spectrum was obtained over the same analysis zone while the surface CeO2-δ was continuously oxidized, achieving thus nearly stoichiometric ceria. This in situ analysis allowed the identification of each of the components of the Ce 3d state linked to the transitions denoted with the labels 4f 0 , 4f 1 , and 4f 2 , as well as the presence of satellites and plasmons, which impact the fit (see arrows in Figure 2a). Although these transitions are known for single-crystal [START_REF] Barth | A perfectly stoichiometric and flat CeO2(111) surface on a bulk-like ceria film[END_REF] and epitaxial growth ceria, [START_REF] Allahgholi | Oxidation-State Analysis of Ceria by X-ray Photoelectron Spectroscopy[END_REF] little is known about their behavior on an amorphous surface, as that of ceria in the form of powder. The bottom of figure 2(a) describes the electronic transitions of the Ce 3d core level corresponding to the nearly fully reduced ceria surface (CeO2-δ), characterized by the missing of u''' and v''' components, corresponding to the 4f 0 fundamental transitition of stoichiometric ceria. Instead, a mixture of the 4f 1 and 4f 2 transitions takes place, which are associated to v0-u0 and v'-u' components .

On the other hand, while the surface is continuously oxidized, the emergence of the electronic transition 4f 0 is remarked, concomitant with the evolution of the 4f 1 and 4f 2 transitions. This is evident on the spectrum at the top of figure 2(a), revealing the coexistence of all the electronic transitions (4f 0 , 4f 1 , 4f 2 ) related to multiplet effects coupling the spin and angular momentum of the f electron in the 3d core hole. [START_REF] Le Normand | Photoemission on 3d core levels of Cerium: An experimental and theoretical investigation of the reduction of cerium dioxide[END_REF] Furthermore, this mixed-valent state was confirmed by an electron 4f occupancy of about 0.6. [START_REF] Fujimori | Mixed-valent ground state of CeO2[END_REF] Therefore, as shown in Figure 2(a), the Ce 3d spectrum imposes a challenge for quantifying Ce 3+ and Ce 4+ species as it combines the presence of multiplet effects and mixed valence states. To further complexify the Ce 3d spectral analysis, some additional structures (marked by arrows) observed at the bottom of Figure 2(a) on the nearly fully reduced ceria spectrum cannot be assigned to the effects mentioned above. Instead, these structures are attributable to collective electronic oscillations of plasmonic type. [START_REF] Allahgholi | Oxidation-State Analysis of Ceria by X-ray Photoelectron Spectroscopy[END_REF] However, under these low oxidative conditions (10 -6 Torr), a high concentration of Ce 3+ is expected, which could explain the coexistence of specific structures in the top spectrum Figure 2(a). The absence of reliable methods of charge compensation for UPS analysis, such as those used during an XPS analysis (electron flood gun, pulsed ion gun), [START_REF] Kim | Absolute work function measurement by using photoelectron spectroscopy[END_REF] precludes this type of solution for measuring the valence band on ceria foil by UPS. In this context, we applied a methodology developed in our previous research work [START_REF] Maheu | UPS and UV spectroscopies combined to position the energy levels of TiO2 anatase and rutile nanopowders[END_REF] in order to minimize the charge effects during a UPS analysis. Ceria in nanopowder form was dropcasted on a cleaned silver foil, O 1s and C 1s core levels (See Figure 1, SI), confirming the absence of contamination. Moreover, the plasmonic structures located in the Ag 3d level and the Fermi level of Ag (Figure 3(a)) confirm the metallic character of treated Ag foil. Therefore, Fermi level, plasmons, and absence of O 1s and C 1s support the metallic character of the Ag foil. Thus, the drop-casted CeO2-δ/Ag was oxidized in an in situ reaction catcell (catalytic reaction chamber) to obtain nearly stoichiometric ceria free of impurities and artifacts. This surface was analytically evaluated by combining asymmetric and symmetric functions, as observed in Figure 2(b). At the bottom (1), the spectrum of Ce 3d corresponds to fully oxidized in situ ceria. To fit this spectrum, in addition to the complexity introduced by the number and position of components, a certain degree of asymmetry must be imposed to fit this with an acceptable standard deviation of the residual values (STD). It is known that the shape of the peak depends on the inverse of the lifetime of the photo-electro-generated core-hole. [START_REF] Wertheim | Least-squares analysis of photoemission data[END_REF] A priori, the carrier lifetime of ceria is about 1.52 ns, [START_REF] Li | Efficient photocatalytic oxygen activation by oxygen-vacancy-rich CeO2based heterojunctions: Synergistic effect of photoexcited electrons transfer and oxygen chemisorption[END_REF] which justifies the use of specific asymmetrical peak shapes in ceria. However, the debate still exists regarding the level of peak asymmetry. Some authors propose asymmetric peaks only in the 4f 1 transition, 6,29 while others propose to impose an asymmetry on the 4f 2 transition. [START_REF] Le Normand | Photoemission on 3d core levels of Cerium: An experimental and theoretical investigation of the reduction of cerium dioxide[END_REF] The discussion of asymmetry extends even to the type of function to be used by proposing an analysis of Ce 3d based on Doniach-Sunjic (DS) lineshapes [START_REF] Romeo | XPS Study of the reduction of cerium dioxide[END_REF] but with an asymmetric parameter α = 0, reducing DS lineshape to a Lorentzian function. [START_REF] Wertheim | Least-squares analysis of photoemission data[END_REF] This choice is because DS is a fit function, which follows the relaxation of electron-hole excitation, particularly the relaxation of the electron conduction gas in metallic systems. [START_REF] Doniach | Many-electron singularity in X-ray photoemission and X-ray line spectra from metals[END_REF] Therefore, it does not apply to insulators such as CeO2. In this context, the oxidized Ce 3d was fitted using a Lorentzian function whose asymptotic form is equivalent to the asymptotic form of the theoretical DS asymmetric lineshape. Several fits were executed in Figure 2(b): (1) was performed with an asymmetric function on v and u peaks without including any Ce 3+ related components. This fit has a poor STD (3.96), where the regions marked with asterisks show the absence of spectral weight. (2) The fit was performed regardless of asymmetric peak shapes but included the components associated with Ce 3+ , the atomic concentration of Ce 3+ here is approx. 25%. In ( 3) with a moderate asymmetry on v and u, the concentration of Ce 3+ decreases to 18%, while (4) with moderate asymmetries in v, u and v'', u'' the concentration of Ce 3+ is about 19%. Therefore, in this scenario, asymmetric lineshapes become a controversial adjusting parameter, usually used to reach a better fit. This analysis shows that regardless of the degree of asymmetry introduced, the Ce 3+ contribution is required in order to fit the spectrum, which should be at least 18%. By this Ce 3d core level analysis, we want to highlight the complexity of the fit procedure, which is quite ambiguous 5,6,24,30 . For instance, Allahgholi et al., [START_REF] Allahgholi | Oxidation-State Analysis of Ceria by X-ray Photoelectron Spectroscopy[END_REF] have evoked the ambiguity of factor analysis procedure proposed by Holgado et al., [START_REF] Holgado | Study of CeO2 XPS spectra by factor analysis: reduction of CeO2[END_REF] essentially due to the presence of satellites in the Ce 3+ contribution, which impact the Ce 3d shape. To date, resonant photoemission remains the most appropriate method for monitoring the Ce 3+ and Ce 4+ states. [START_REF] Matolín | A resonant photoemission applied to cerium oxide based nanocrystals[END_REF] However, tunable soft-xrays are required, and photolysis effects cannot be excluded either. The UP spectral analysis on stoichiometric semiconducting ceria was carried out using the Fermi level of Ag as internal calibration energy. 20, [START_REF] Kim | Absolute work function measurement by using photoelectron spectroscopy[END_REF] The bandwidth and bandgap (Eg) [START_REF] Mullins | Electron spectroscopy of single crystal and polycrystalline cerium oxide surfaces[END_REF] and theoretical studies. [START_REF] Khalifi | Electronic and optical properties of CeO2 from first principles calculations[END_REF][START_REF] Hay | Theoretical study of CeO2 and Ce2O3 using a screened hybrid density functional[END_REF] It is crucial to note that from an experimental point of view, the stoichiometric character of oxidized ceria is associated with the absence of the Ce 4f state located between 1.5 eV and 1.9 eV, this feature, in conjunction with a valence band maximum measured to ≈2.5 eV below the Fermi level reveals the valence band of CeO2 -Ce 4f(0) as reported in the literature for ultra-thin model films of ceria. [START_REF] Skála | Cerium oxide stoichiometry alteration via Sn deposition: Influence of temperature[END_REF][START_REF] Pfau | The electronic structure of stoichiometric and reduced CeO2 surfaces: an XPS, UPS and HREELS study[END_REF] Following the analysis sequence, an XPS Ce 3d level spectrum of on in situ oxidized ceria reveals six visible components containing five 3d5/2-3d3/2 spin-orbit-split doublets fitted according to the method proposed on the spectrum (4) Figure 2(b). This class of multi-doublet XPS spectrum is challenging to adjust due to complex final states and electronhole perturbations. However, from figure 3(b) one can identify the spectral weight associated to Ce 3+ at 881.0 eV and 884.6 eV for Ce 3d5/2 accompanied with 899.2 eV and 902.2 eV for Ce 3d3/2. Surprisingly, the concentration of Ce 3+ on pre-oxidized ceria is relatively high, revealing 19% of Ce 3+ with an STD = 1.54. Several theoretical studies suggest the coexistence of Ce 3+ and Ce 4+ with 4fn (with n approx. 0.5) in most samples, 25,36,37 which could be related to the nano-size of CeO2 particles and the surface/bulk dependence of the Ce 3+ /Ce 4+ ratio. [START_REF] Paun | Polyhedral CeO2 Nanoparticles: Size-Dependent Geometrical and Electronic Structure[END_REF] A subsequent UPS analysis on oxidized ceria verified this discrepancy in Figure 3(c), highlighting a new state close to the Fermi level at ≈1.6 eV. This state is characteristic of substoichiometric ceria CeO2-δ with a state Ce 4f. Its presence is concomitant with a modification between 2 eV and 8 eV where O 2p hybridized orbitals are located, revealing structural changes associated with oxygen atoms. Discrepancies between UPS analysis before and after XPS reveal the photoreductive effect induced by X-rays on ceria, contrary to UPS. The magnitude of the Ce 4f state depends on various parameters such as (i) beam exposure time, (ii) power of the Xray source, (iii) surface treatments, (iv) the intrinsic nature of the material (including the size of particles, electronic configuration) and (v) power density (PD) of the beam. [START_REF] Fallah | Effect of surface treatments, photon and electron impacts on the ceria 3d core level[END_REF] PD is a critical parameter used to estimate the impact of a beam source on a surface (photolysis/beam-damage), as this parameter represents the power received on the surface of the sample per unit area. For instance, at a similar photon flux (ϕ), the power density (PD =ϕ(hc/λ)) induced by the X-rays is one order of magnitude higher than that generated by a UV source at 21.2 eV (UPS) of incident energy. Indeed, other parameters as those mentioned in (iv) should not be underestimated. For instance, the literature reports X-ray beam reduction on other oxides after XPS analysis, such as MoO3. [START_REF] Liao | X-ray irradiation induced effects on the chemical and electronic properties of MoO3 thin films[END_REF][START_REF] Baltrusaitis | Generalized molybdenum oxide surface chemical state XPS determination via informed amorphous sample model[END_REF] Highlighting that X-ray beam damage is not specific to ceria. All these effects can influence the quantification of Ce 3+ through XPS. Therefore special care must be taken in the use of the XPS technique as it contributes to an over-estimation of the Ce 3+ concentration at the surface of ceria induced by photoreduction. This analysis highlights that UPS must be established as a "routine" technique to estimate the Ce 3+ surface concentration on ceria nanopowders, as this spectroscopy exerts a lower degree of photoreduction on the surface of ceria and a straightforward interpretation via the Ce 4f orbital located at the extreme surface. Although it is assumed that Ce 3+ cations are located at the surface, their detection will depend on the depth of the analysis. Therefore, it is expected that following an in situ reduction, the surface of ceria will be densely populated by Ce 3+ cations. Following this strategy, post-analyzed stoichiometric ceria was reduced under ultra-high vacuum (UHV) at 600 °C and characterized in situ. UPS analysis revealed the evolution of the electronic structure before and after reduction (Figure 4(a), (b)), which is concomitant with the presence of an intense Ce 4f state located at ≈ 1.4 eV (arrow) and also with a significant change of color of the sample (see the picture in Figure 4(c): insert). XPS confirms the surface-reduction dependence with a modest increase to 26% (Figure 4(c,d)) for post-reductive ceria versus 19% after UPS-XPS analysis on post oxidative treatment, a mere 7% over oxidized ceria. Although the UPS data presented in this paper allows a qualitative approximation of the evolution of the Ce 3+ /Ce 4+ ratio, the UPS uses is limited as this requires the development of quantitative methods. An alternative would be to get a sample reference totally reduced (Ce2O3). However, it is not apparent to get a pure Ce2O3 sample (without metallic Ce) by reduction at high temperature, as the reduction rate not only depends on temperature 41 Furthermore, compounds containing 100% of Ce 3+ cations such as CeCl3 or cerium nitrate contain orbitals that interfere with O 2p and Ce 4f in the valence band region. To carry out a quantitative analysis to determine the Ce 3+ /Ce 4+ ratio without a reference sample would require several hypotheses to be fulfilled: (i) Hybridization between Ce 4f, Ce 5d, and O 2p orbitals is negligible. Theoretical calculations propose a strong ionic character for stoichiometric CeO2 and sub-stoichiometric CeO2-δ concomitant with a low orbital overlap in the O 2p region located in the valence band. [START_REF] Khalifi | Electronic and optical properties of CeO2 from first principles calculations[END_REF][START_REF] Pedrielli | Electronic excitation spectra of cerium oxides: from ab initio dielectric response functions to Monte Carlo electron transport simulations[END_REF][START_REF] Skorodumova | Electronic, bonding, and optical properties of CeO2 and Ce2O3 from first principles[END_REF] The density of states (DOS) of Ce 4f and Ce 5d inside the O 2p region is extremely low, generally associated with electronic tails or reminiscent states, giving it a strong O 2p character to CeO2 and CeO2-δ. However, this is valid only from a theoretical point of view, as an increase in intensity will be observed if these theoretical states are normalized by the experimental photoionization cross-section (PICS) at 21.2 eV. This explains the shape evolution before and after reduction between 8 and 3 eV in the UPS spectra (see Figure 4(a) and (b)). (ii) Be aware of the true photoionization cross-section values and not approximated values. Since the literature does not provide photoionization cross-section data for sub-stoichiometric ceria (mixed Ce 3+ and Ce 4+ , data available only for neutral ceria atoms), the quantitative concentration obtained is not entirely reliable, although their trend is undoubtedly correct. Despite these limitations, an analytical procedure was carried out on the valence band UPS spectrum of ceria after XPS analysis (Figure 4(a)) and post-reductive treatment (Figure 4(b)), respectively. In both spectra, the subtraction of background was carried out by using the function developed by Li et al. [START_REF] Li | Inelastic electron background function for ultraviolet photoelectron spectra[END_REF] As proposed by Maslakov et al. [START_REF] Maslakov | The electronic structure and the nature of the chemical bond in CeO2[END_REF][START_REF] Maslakov | XPS study of ion irradiated and unirradiated CeO2 bulk and thin film samples[END_REF] the valence band can be adjusted with several components, and the number of fit contributions is limited by the resolution of the technique either ≈0.6 eV for XPS and ≈0.2 eV for UPS [START_REF] Maheu | UPS and UV spectroscopies combined to position the energy levels of TiO2 anatase and rutile nanopowders[END_REF] . In order to determine the area of the O 2p region (2 and 8 eV) and Ce 4f (≈1.6 eV), four Gaussian contributions were applied to adjust the valance band region (O 2p and Ce 4f). Although a UP signal renormalization derived from the PICS may provide a way to quantify Ce 3+ /Ce 4+ , this approach is limited as this method requires valid photoionization cross-section values corresponding to ionized ceria (CeO2-δ). Since the literature does not provide such data for sub-stoichiometric ceria, the quantitative concentration obtained would not be reliable. However, this does not preclude a relative comparison of the O 2p and Ce 4f areas as substoichiometric ceria has a strong ionic character. From Figures 4 (a) and (b), one can verify the relative area increment corresponding to the Ce 4f state, which is doubled after in situ reduction, confirming the effects of surface reduction higher than those observed by XPS. It is worth noting that the presence of oxygen contamination is negligible as all the preparation was carried out in situ without exposing the sample to the air during the transfer. Although this methodology should be taken with caution and only as a starting point toward developing a robust method combining DFT, PICS calculations, and UPS analysis, it should be noted that UPS is sensitive to the outermost surface, giving access to Ce 3+ cations after reduction. In addition, TPR analysis, a bulk technique, was carried out in severe conditions to get an extreme value, which revealed only 2.8% of Ce 3+ after reduction at 600 °C under H2 flow (see Figure S4 in SI). This Ce 3+ value is much lower than the one obtained by UPS, confirming that ceria reduction is mainly happening at the surface, in agreement with the literature. [START_REF] Kato | Quantitative depth profiling of Ce 3+ in Pt/CeO2 by in situ high-energy XPS in a hydrogen atmosphere[END_REF] This low value compared to that deduced from UPS after reduction at 600 °C in UHV can be explained by the penetration depth of UPS (≈ 5 Å), which is much lower than the crystallite size of CeO2 (32 nm, see Figure S3 in SI) and preferential reduction of ceria at the surface leading to a Ce 3+ concentration gradient from the surface to the bulk.

Conclusions

To conclude, we have analyzed the electronic structure of stoichiometric and sub-stoichiometric ceria in the form of nanopowders by UPS and XPS spectroscopies under in situ conditions. A sequential analysis of UPS→XPS highlighted the overestimation of the reduction rate (Ce 3+ ) obtained by XPS and the photoreduction effect during XPS analysis. XPS revealed a low evolution of Ce 3+ concentration before (19%) and after reductive treatment (26%), highlighting thus that photolysis contribution is major. UPS confirmed this photolysis effect by detecting Ce 3+ induced by the X-ray beams. We have demonstrated by UPS the high degree of reduction (doubled of Ce 3+ ) at the outermost surface of ceria after reductive treatment at 600 °C. Therefore, a photoemission analysis under low power density flux UPS at 21.2 eV allows qualitatively estimating the rate of Ce 3+ at the outermost surface of ceria subjected to different oxidative and reductive treatments and in situ reaction conditions.

Fig. 1 :

 1 Fig. 1: Schematic diagram of the electronic structure of: (a) CeO2 and (b) CeO2-δ. The dashed red line corresponds to the Fermi level of Ag foil. The Ce 4f state arises in the occupied gap (valence band) (Eg) of CeO2δ.

Fig. 2 :

 2 Fig. 2: (a) Core level (XPS) evolution. Bottom: Ce 3d spectrum (blue) corresponding to nearly-fully reduced ceria foil under Ar + sputtering.Arrows highlights the presence of plasmonic structures. Subsequently the eroded ceria foil was exposed to O2 (Pox≈10 -6 Torr) under in situ conditions during XPS analysis, reaching a nearly-oxidized ceria at the top of the figure (red). (b) Ce 3d XPS analysis was carried out on nearly stoichiometric CeO2 nanopowders after in situ oxidation O2. Ceria nanopowder was pretreated in a catcell connected with the analysis chamber: (1) fitted with high asymmetric function located in v and u without Ce 3+ contributions, (2) fitted combining Ce 3+ and Ce 4+ with only symmetric functions, (3) fitted with moderate asymmetric function located v and u and Ce 3+ contributions, (4) fitted with moderate asymmetric function located v, u and v'' and u'' including Ce3+

Figure 3 (

 3 Figure 3(a) shows the UP HeI valence band spectrum of in situ oxidized ceria, which exhibits a stochiometric character mainly due to a large band formed mainly by O 2p orbitals with ≈ 4 eV broad. It corresponds to a position of the valence band maximum located at ≈ 2.5 eV below the Fermi level of Ag foil.The UP spectral analysis on stoichiometric semiconducting ceria was carried out using the Fermi level of Ag as internal calibration energy. 20,[START_REF] Kim | Absolute work function measurement by using photoelectron spectroscopy[END_REF] The bandwidth and bandgap (Eg)

Fig. 3 :

 3 Fig. 3: (a) Valence band (UPS) after in situ oxidation and before XPS analysis. (b) Ce 3d core level of in situ oxidized CeO2 nanopowders after UPS. (c) UPS analysis on oxidized ceria after XPS analysis. The arrow points on the Ce 4f state. Insert: reminiscent AgFL

Fig. 4 :

 4 Fig. 4: (a) UPS spectrum on in situ oxidized ceria (600 °C under O2) after XPS analysis fitted by four main components. (c) XPS on in situ oxidized ceria after UPS analysis. (b) UPS fitted by four main components and (d) XPS analysis on reduced ceria (600 °C under UHV). Insert: Photo of oxidized ceria (left) and reduced (right), respectively.

Conflicts of interest

There are no conflicts to declare.

Acknowledgement

C. M. acknowledges the French Ministry of Education for the financial support of his Ph.D. thesis.

Notes and references


Miguel Lara Moreno

Thierry Stoecklin
email: thierry.stoecklin@u-bordeaux.fr

Quantum study of the radiative association of Cl + H 2 and Cl + D 2

Keywords: astrochemistry, radiative association, molecular data, molecular processes, scattering, ISM: molecules

come

Introduction

Since the pioneering work of Ferguson et al [START_REF] Michael | Photoelectron spectroscopy of ClH 2 and ClD 2 : A probe of the Cl+H 2 van der waals well and spin-orbit excited states[END_REF] several studies were dedicated to the Photo electron spectroscopy of the H 2 -Cl complex. These authors showed that it was a good way to probe the reactant Van der Waals well of the endothermic reaction Cl + H 2 ! HCl + H.

At about the same time, [START_REF] Wild | The 35 Cl H 2 and 35 Cl D 2 anion complexes: Infrared spectra and radial intermolecular potentials[END_REF], [START_REF] Alexander | Theoretical investigation of the lower bend-stretch states of the Cl H 2 anion complex and its isotopomers[END_REF] and [START_REF] Buchachenko | Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35 Cl . . . H 2 /D 2 complexes[END_REF] studied the vibrational pre-dissociation dynamics of the 35 Cl-H 2 /D 2 complexes and provided 3D potential energy surfaces for these systems. More recently [START_REF] Wild | Complex formation in three-body reactions of Cl with H 2[END_REF] were able to measure in an ion trap the three-Body rate of formation of the H 2 Cl complex. They also tried to measure the radiative association rate and concluded that it was too small to be measurable. In another related work a combined theoretical [START_REF] Lara-Moreno | Predissociation spectra of the 3 5Cl (H 2 ) complex and its isotopologue 3 5Cl (H 2 )[END_REF] and experimental determination of the pre-dissociation spectrum of the H 2 Cl complex was reported by [START_REF] Dahlmann | Strong ortho/para e↵ects in the vibrational spectrum of Cl (H 2 )[END_REF]. A very good agreement between theory and experiment was obtained allowing to explain the strong ortho/para e↵ects in the vibrational spectrum of H 2 Cl . These studies demonstrated the very good accuracy of both the PES of [START_REF] Buchachenko | Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35 Cl . . . H 2 /D 2 complexes[END_REF] and the computed quasi bound states of the complex. On the other hand, the relationship between three body (3B) and radiative association (RA) rates was explored long ago by [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] aiming to deduce one from the other. The general formula obtained by these authors requires the knowledge of the quasi bound states of the complex computed in our previous work [START_REF] Dahlmann | Strong ortho/para e↵ects in the vibrational spectrum of Cl (H 2 )[END_REF].

In the present study we then perform the first Close Coupling calculation of the H 2 /D 2 + Cl RA . To this aim we use the 3D PES of [START_REF] Buchachenko | Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35 Cl . . . H 2 /D 2 complexes[END_REF] and perform dynamics calculations using the method we developed for N 2 H [START_REF] Stoecklin | A new theoretical method for calculating the radiative association cross section of a triatomic molecule: application to n2-h[END_REF] and applied to many systems [START_REF] Burdakova | Formation of Nacontaining complex molecules in the gas phase in dense molecular clouds: quantum study of the Na + + H 2 and Na + + D 2 radiative association step[END_REF][START_REF] Jones | Formation of Al containing molecular complexes in the gas phase in dense molecular clouds: quantum study of the radiative association of Al + +H 2 and Al + + D 2[END_REF][START_REF] Thierry Stoecklin | On the gas-phase formation of the HCO anion: Accurate quantum study of the H + CO radiative associ-ation and HCO radiative electron attachment[END_REF][START_REF] Thierry Stoecklin | On the gas-phase formation of the HCO radical: accurate quantum study of the H+CO radiative association[END_REF]. We then compare our results with an indirect estimate of the experimental values using the relation ship with the 3B rate measured by [START_REF] Wild | Complex formation in three-body reactions of Cl with H 2[END_REF] .

The manuscript is organized as follows: In section 2 we briefly describe the main features of both the PES and the dipole moment surface calculated by [START_REF] Buchachenko | Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35 Cl . . . H 2 /D 2 complexes[END_REF]. We also summarize the main steps of the method used to calculate the RA rate coefficients and remind how the experimental 3B rate can be used to give an estimate of the experimental RA rate. In section 3 we present and discuss our results . Conclusions can be found in section 4.

Methods

All the calculations are performed in the spaced fixed frame using reactant Jacobi coordinates (R, r, ✓) where R is the intermolecular distance, r the bond length of the diatom and ✓ the angle between r and R.

Potential energy surface and dipole moment

We use the ab initio 3D dipole moment surface (DMS) and potential energy surface (PES) developed by [? ] where all details can be found. Contour plots of this PES are represented in Figure 1where the equilibrium geometry of the H 2 Cl complex ( 835.7 cm 1 ) is seen to be linear shaped with R = 5.75 a 0 and an H This is in contrast with the three systems mentioned for which the rigid rotor approximation was used.

As expected for a charged atom interacting with a non polar molecule the ab initio main component of the dipole moment calculated by [START_REF] Buchachenko | Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35 Cl . . . H 2 /D 2 complexes[END_REF] is found to be along the inter molecular vector. In other words, the radial component of the dipole moment along the intermolecular vector is well . Red and blue curves are respectively associated with negative and positive energies.

represented by a function linear in R as for the three other ionic systems.

Bound and quasi bound states of the complexes and Dynamics

We use to calculate the RA cross section and rate the method initially presented in [START_REF] Stoecklin | A new theoretical method for calculating the radiative association cross section of a triatomic molecule: application to n2-h[END_REF]. All details can be found in that paper and in the following references . It is based on the driven equation space fixed formalism (see [START_REF] Heather | Photodissociation of triatomic molecules: Rotational scattering e↵ects[END_REF] and references therein) which connects the bound and scattering wave functions through the light-matter interaction operator. The bound states energies and wave functions of the formed complex are first calculated using a variational approach as detailed in [START_REF] Lara-Moreno | Predissociation spectra of the 3 5Cl (H 2 ) complex and its isotopologue 3 5Cl (H 2 )[END_REF]. For given initial (J) and final (J') values of the total angular momentum, each of the matrix elements of the dipole moment operator between the complex bound states (↵, J 0 ) and the continuous scattering wave function describing the approach of Cl towards H 2 in a given ro-vibrational state (⌫, j) are then accumulated during the course of the propagation of the initial scattering wave function allowing to obtain the RA cross sections.

v,j (E) = 8⇡ 2 3k 2 vj c 3 X J,J 0 ,↵ ! 3 ↵  M ↵,J 0 v,j,J (E) 2 (1)
where ! ↵ is the angular frequency of the emitted photon and M ↵,J 0 v,j,J (E) are the integrated matrix elements of the dipole operator between an initial scattering state (⌫, j, J) of the fragments and a given bound state (↵, J 0 ) of the complex.

Relationship between 3B and RA rates

As radiative association rates are small and di cult to measure, astronomers developed approaches allowing to deduce them from 3B rates. We will here only briefly resume the results obtained by [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] based on a statistical approach. Within this model, both three body

A + + B + C * ) AB + + C (2)
and radiative association

A + + B * ) AB + + h⌫ (3)
processes are assumed to proceed in two steps:

The first step which is common to the two processes sees a charged atom A + colliding with a molecule B and form an excited complex (AB + ) ⇤ .

A + + B k F * ) k D (AB + ) ⇤ (4)
with the (AB + ) ⇤ formation and destruction rates of this step denoted respectively k F and k D .

In the second step the excited ionic complex relaxes to its fundamental state either by emission of a photon in the case of the RA process:

(AB + ) ⇤ k R ! AB + + h⌫ (5)
or by collision with a third body C in the case of 3B collision:

(AB + ) ⇤ + C k C ! AB + (6)
Within the steady state approximation, [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] demonstrated that the RA and 3B rates are respectively related to those of each elementary step by the following relationship:

k RA = ✓ k F k D ◆ k R and k 3B = ✓ k F k D ◆ k C (7)
It then follows from this expression that the two rates are related by the simple relationship:

k RA = ✓ k R k C ◆ k 3B (8)
In a recent work [START_REF] Lara-Moreno | Predissociation spectra of the 3 5Cl (H 2 ) complex and its isotopologue 3 5Cl (H 2 )[END_REF] we determined the quasi bound state energies " J i and widths J i of the Cl H 2 /D 2 complexes. The unimolecular decay rate of each of these quasi bound states is straightforwardly obtained as:

k Ji R = J i ~.
We then compute for each value of J a rotationally selected unimolecular decay rate of the complex:

k J R (T ) = P i k Ji R exp( "i /k B T ) P i exp( "i /k B T ) (9)
From the value of the rotational constant B C of the Cl H 2 /D 2 complex one then calculate the unimolecular decay rate k R :

k R (T ) = P J (2J + 1)k J R (T ) exp( B C J(J+1) /k B T ) P J exp( B C J(J+1) /k B T ) (10)
In the absence of a full quantum calculation requiring the dtermination of a PES describing the collision of the Cl H 2 complex with an H 2 molecule we rely on approximate methods to estimate the k C collisional rate. The most common one is to use the Langevin rate k L associated with the collisions of Cl H 2 + H 2 when considering the simple case of a charge interacting with a non polar molecule:

k L = 2⇡ r ↵ µ ( 11
)
where ↵ is the polarizability of H 2 and µ is the relative mass of the (Cl H 2 ) H 2 system. The rate coe cient k C is taken to be proportional to the Langevin rate:

k C = C k L ( 12
)
where C is interpreted to be the e↵ective probability that a single collision causes stabilization. A few approximate models were proposed to determine the value of C but their accuracy is questionable. Also we will simply take k C = k L in our application of the model.

Results

Bound states

The variation of the calculated number of bound states of Cl H 2 and Cl D 2 are respectively shown as a function of the total angular momentum quantum number J in Figs. 2 and3 . The total number of bound states is 492 for Cl H 2 and 1111 for Cl D 2 while the largest value of J resulting in a bound state is 25 for the Cl H 2 and 36 for Cl D 2 . This is quite comparable with the results we obtained previously for the Na + H 2 /D 2 [START_REF] Burdakova | Formation of Nacontaining complex molecules in the gas phase in dense molecular clouds: quantum study of the Na+ + H2 and Na+ + D2 radiative association step[END_REF] and Al + H 2 /D 2 complex. [START_REF] Jones | Formation of Al containing molecular complexes in the gas phase in dense molecular clouds: quantum study of the radiative association of Al + +H 2 and Al + + D 2[END_REF], the relative masses of these three systems being also very similar while the Cl H 2 well depth is intermediate between those of Al + H 2 and Na + H 2 .

RA cross sections and rates

The RA cross sections variations as a function of collision energy are presented in figures 4 and 5 for the Cl H 2 and Cl D 2 for various initial rotational states of the diatomic fragments. Not surprisingly, these figures are very similar to those obtained previously for the above mentioned systems. The magnitude of the cross sections is directly proportional to the well depth of each system. A larger well depth leading to lower bound state energies while the cross sections are proportional to ! 3 . The initial rotational state j = 1 gives the largest Al + H 2 /D 2 RA cross sections while the RA cross sections then decrease monotonously as a function of rotational excitation. The linear shaped equilibrium geometry of the complex does not seem to lead to noticeable di↵erences of behavior with the three T shaped systems treated previously.

In Figs. [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] (Cl H 2 ) and 7 (Cl D 2 ) we present j resolved RA rate coe cients as well as the total Boltzmann averaged reaction rates. 2:1 and 3:1 ratios obtained from the spin statistics were included when combining respectively the ortho/para-D 2 and ortho/para-H 2 rate coecients. The Boltzmann averaged rate coe cients are seen to be almost flat at low temperature for both reactions before reaching a maximum close to 80 K for Cl H 2 and 160 K for Cl D 2 formation . Both rate coe cients thereafter decrease monotonously and follow the expected T 1 law predicted by modified thermal theory. This general behaviour was also obtained and analysed for the three other ionic Van der Waals complexes we treated previously .

We compare in Table 1 the maximum values of the RA rates for all the Van der Waals complexes we treated up to now. As can be seen in this table the maximum value of the RA rate is of the same order of magnitude for the four systems compared whatever is the magnitude of the well depth. The Cl H 2 complex which is the only linear at equilibrium gives the lowest value of the rate. The temperature giving the maximum value of the rate is seen to increase as a function of the well depth. This is a direct consequence of the presence of the inelastic scattering resonances which appear for collision energies lower than the well depth. When Boltzman averaged these resonances give birth to a bump of the rate coe cient which maximum is shifted towards larger temperature when resonances also appear at higher collision energy.

In the same table we also report the value of the RA rate of Cl with D 2 . Again ,we obtain a very strong isotope e↵ect for this system as a result of the larger number of bound states. The temperature of the RA rate maximum is also shifted to higher temperature.

Indirect comparison with experiment using the 3B rate

We presented in section 2.3 the relationship [START_REF] Heather | Photodissociation of triatomic molecules: Rotational scattering e↵ects[END_REF] obtained by [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] between 3B and RA rates. The 3B rate of the

Cl + H 2 + H 2 * ) (H 2 Cl ) + H 2 (13)
process was recently measured by [START_REF] Wild | Complex formation in three-body reactions of Cl with H 2[END_REF] between 10 and 26 K where it follows a proposed k 3B (T ) = aT 1 law with a = 1.12(2) ⇥ 10 29 cm 6 Ks 1 . We can then infer an experimental estimate of the

Cl + H 2 ! (H 2 Cl ) + h⌫ (14)
RA rate from the measured 3B rate using equation [START_REF] Heather | Photodissociation of triatomic molecules: Rotational scattering e↵ects[END_REF]. We first need to calculate k R and k C .

k C is taken to be the Langevin rate k L defined in [START_REF] Stoecklin | A new theoretical method for calculating the radiative association cross section of a triatomic molecule: application to n2-h[END_REF]. Using ↵(H 2 ) = 5.44 a 3 0 we obtain:

k C = k L = 1.52 ⇥ 10 9 cm 3 molecule 1 s 1 (15)
In order to calculate k R from expression [START_REF] Lara-Moreno | Predissociation spectra of the 3 5Cl (H 2 ) complex and its isotopologue 3 5Cl (H 2 )[END_REF] we would need both the energies and widths of the (H 2 Cl ) quasi bound states . While the energies were calculated accurately in our previous study [START_REF] Lara-Moreno | Predissociation spectra of the 3 5Cl (H 2 ) complex and its isotopologue 3 5Cl (H 2 )[END_REF] the width were more di cult to converge and are available only for a few quasi bound states. We then take instead for k R a usual typical value recommended by [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] for such process: (18) The statistical model of [START_REF] Herbst | Rate Coe cients in Astrochemistry[END_REF] then allows to obtain from the experimental 3B rate an estimate of the RA rate coe cient which is of the same order of magnitude than the calculated one. This is quite encouraging as we used very approximate values of both k R and k C . We then expect that more accurate determination of these two rates should allow obtaining even better estimate of the RA rate using experimental 3B rate for similar systems.

Conclusion

We investigated theoretically the formation of the Al + H 2 and Al + D 2 complexes through RA at the close-coupling level using available 3D PES and dipole moment surfaces. The total number of Al + D 2 bound states is more than twice as large as the one of Al + H 2 while the largest value of J resulting in a bound state is 25 for Al + H 2 and 36 for the Al + D 2 as expected from the mass di↵erence between the two systems. As a result the RA rate is up to 3 orders of magnitude larger with D 2 than with H 2 . We compared our results with those obtained for three other ionic van der Waals complexes and verified that both the temperature of the maximum and the maximum of the RA rate increases a function of the well depth. The linear shaped equilibrium geometry of the complex does not seem to lead to noticeable di↵erences of behaviour with the three T shaped systems treated previously. We also determined an approximate experimental estimate of the Cl + H 2 ! (H 2 Cl ) + h⌫ RA rate using the relationship between the RA and 3B rate for Cl +H 2 +H 2 (H 2 Cl )+H 2 measured recently. We found that the calculated and approximate experimental estimate of the RA rate are of the same order of magnitude. This encouraging result suggest that experimental estimate of the RA rate could be obtained from existing 3B rate for other systems.

Fig. 1

 1 Fig. 1 Contour plots of the potential energy surface of Cl H 2 obtained by Buchachenko et al. for r = 1.4097 a 0 . The energy is given in cm 1. Red and blue curves are respectively associated with negative and positive energies.

Fig. 2 Fig. 3

 23 Fig. 2 Number of bound states of Cl H 2 as a function of the total angular momentum quantum number of the system.

Fig. 4

 4 Fig. 4 Radiative association cross section of Cl H 2 as a function of collision energy depicted for di↵erent values of j.

Fig. 5

 5 Fig. 5 Radiative association cross section of Cl D 2 as a function of collision energy depicted for di↵erent values of j.

Fig. 6

 6 Fig. 6 Radiative association rate coe cient for forming Cl H 2 as a function of temperature depicted for di↵erent values of j.

Fig. 7

 7 Fig. 7 Radiative association rate coe cient for forming Al + D 2 as a function of temperature depicted for di↵erent values of j.

k R = 10 3 s 1

 1 (16) and obtain an experimental estimate ofk Exp RA (T = 26K) = 3.4 ⇥ 10 20 cm 3 molecule 1 s 1(17) while our calculated value is k Cal RA (T = 26K) = 6.7 ⇥ 10 21 cm 3 molecule 1 s 1

Table 1

 1 Comparison between the RA coe cients given

	in cm 3	molecule 1	s 1	calculated for several ionic Van der
	Waals complexes.
	System	Geometry	De (cm 1	)	Tmax (K)	k RA
	H Na + Al + Cl Cl	N 2 H 2 H 2 H 2 D 2	T-shaped T-shaped T-shaped Linear	349.1 1184 668.4 835.7	4 100 8 7 80 147	4 .3 ⇥ 10 20 6 • 10 20 1 .9 • 10 20 8.1 • 10 21 2.5 • 10 18

AcknowledgmentsThe calculations were performed at the Mesocentre de Calcul Intensif Aquitain computing facilities of the Université de Pau et des Pays de l'Adour.

Data availability

The data underlying this article are available in the article.