Hang Zou

Chao Zhang

Samson Lasaulce

Lucas Saludjian

Patrick Panciatici

Decision-Oriented Communications: Application to Energy-Efficient Resource Allocation

Keywords: Quantization, Resource Allocation, Learning, Neural Networks, Energy-Efficiency

In this paper, we introduce the problem of decisionoriented communications, that is, the goal of the source is to send the right amount of information in order for the intended destination to execute a task. More specifically, we restrict our attention to how the source should quantize information so that the destination can maximize a utility function which represents the task to be executed only knowing the quantized information. For example, for utility functions under the form u (x; g), x might represent a decision in terms of using some radio resources and g the system state which is only observed through its quantized version Q(g). Both in the case where the utility function is known and the case where it is only observed through its realizations, we provide solutions to determine such a quantizer. We show how this approach applies to energy-efficient power allocation. In particular, it is seen that quantizing the state very roughly is perfectly suited to sum-rate-type function maximization, whereas energy-efficiency metrics are more sensitive to imperfections.

I. INTRODUCTION

Since the pioneering and fundamental works of Shannon, the ultra dominant paradigm for designing a communication system is that communications must satisfy quality requirements. Typically, the bit error rate, the packet error rate, the outage probability or the distortion must be minimized. It turns out that the classical paradigm consisting in pursuing communication reliability or possibly security may be not suited to scenarios such as systems where communications occur in order for a given task to be executed. To be more concrete, in many resource allocation problems, some knowledge about the system state is necessary to make a decision in terms of using the available resources but having an accurate or too reliable knowledge about the state might induce a prohibitive amount of signaling, while only leading to a marginal increase of the system performance, say in terms of utility function. This motivates us to develop a new communication paradigm, which we refer to as decisionoriented communications (DOC). In the scope of this paper, more modestly, we restrict our attention to one given operation of the design of decision-oriented transmitters, that is decisionoriented quantization (DOQ).

In this paper, we assume that the task the system should execute can be represented as an optimization problem. We assume that the ultimate objective to be reached is to maximize a function u (x; g) (called the utility function) with respect to the decision variables x while having an imperfect knowledge of the function parameters g. Technically, we want to know how to design a device which has to quantize the actual parameters g before sending them to the decision-making entity which has to choose the decision variables x. A classical instance of such a problem occurs when a receiver has to feedback information (e.g., channel state information CSI) to a transmitter so that the latter adapts its transmission scheme; this is the problem of quantized CSI.

When inspecting the literature of communications, it appears that the problem under consideration has not been explored yet, and definitely not from the concrete perspective approach taken in this paper. There exist some works on goal-oriented communications such as [START_REF] Goldreich | A Theory of Goal-Oriented Communication[END_REF] but those rely on logical aspects of computer science and do not formulate the problem as an optimization problem and do not tackle the problem from the perspective of coding and thus quantization. distortion. Concerning the problem of quantization, there exist some works (e.g., [START_REF] Wang | Boosting Quantization for Lp Norm Distortion Measure[END_REF]) where the performance criterion is not distortion (as originally proposed in [START_REF] Lloyd | Least Squares Quantization in PCM[END_REF]) but a more general Lp-norm. But the approach developed in the present paper is not only more general because it concerns arbitrary utility functions but also corresponds to a new approach of designing a communication system. In particular, both source coding and channel coding should be revisited. Additionally, we tackle the important case where the performance criterion (i.e., the utility function) is not known but only observed through its realizations, which is different from the case studied in [START_REF] Zhang | Payoff-oriented Quantization and Application to Power Control[END_REF].

The paper is structured as follows. In Sec. II we introduce the problem of decision-oriented quantization. In Sec. III, we develop two solutions to determine such a quantizer, the solutions respectively corresponding to the case where the utility function is known and the case where only its realizations can be observed. In Sec. IV, we show how to apply our approach to the problem of energy-efficient resource allocation for a multiband and MIMO communications. The paper is concluded by Sec. VI.

II. PROBLEM FORMULATION

Consider the following utility function u (x; g), where x represents the resources that transmitter can allocate and g is an unknown environment parameter that is only measurable but uncontrollable. The utility function can be for example , the energy efficiency, transmission rate and transmission error rate. Let X be the decision space which is generally R N with N the number of users and G be the parameter space which can be R K or C K depending on the situation with K the dimension of vector g. Obviously, given a fixed g, one is capable to maximize the utility function:

U (g) = max x∈X u (x; g) (1)
and find maximum point of this function:

x * (g) ∈ arg max x∈X u (x; g) (2)
However, knowing all information about the environment e.g., the channel state information may be too demanding in practical application or even consumptive.

C i = G
with some corresponding representatives r 1 , . . . , r M . The quantization rule is :

Q (g) = r k , if g ∈ C k (3)
In this scenario, the optimization procedure can still be performed using a quantized version of the parameter g:

U (Q (g)) = max x∈X u (x; g) = max x∈X u (x; Q (g)) (4)
One can find the maximum point (saying the quantized maximum point ) for the the utility function using a quantized version of g:

x * ( g) ∈ arg max

x∈X u (x; g) (5)
Even if the maximum point is found based on a quantized version of the parameter, the utility function still undergoes a realistic channel. Therefore the realistic maximum of the utility function knowing merely a quantized channel parameter can be written as:

U (Q (g)) = u x * ( g) ; g (6)
The objective of DOQ is to find a quantizer Q * such that:

Q * ∈ arg min Q E g U (g) -U (Q (g)) 2 (7)
The expectation is taken over the probability density distribution (p.d.f) φ (g) of the parameter g.

III. PROPOSED SOLUTIONS FOR ARBITRARY UTILITY

FUNCTIONS

As explained in Section II, the goal of the DOQ is to find the optimal quantizer that minimizes the optimality loss (in terms of maximizing the utility function) which is induced by imperfect knowledge of g. In general, this problem can be too complicated to solve due to the continuity of the decision space X . Assume that the effective decision set is finite due to the fact the feedback information from the receiver is limited:

D = {d 1 , . . . , d M } ⊆ X , M < +∞ (8)
This happens for examples in many power control systems in some cellular communication standards or even an equivalent optimality between D and X proved in [START_REF] Gjendemsjø | Binary Power Control for Sum-rate Maximization Over Multiple Interfering Links[END_REF]. In what follows, only discrete decision space will be considered. Moreover, for the sake of simplicity, we only use vector notation of the decision. The extension to matrix-form decision can be treated in the same way and will be presented in Sec.

IV-B.

Due to this assumption, the desired quantizer is equivalent to find a pair (D, C) that maximizes the expectation of our utility function, where C = {C 1 , . . . , C M } is the quantization region set. A decisional quantizer is just a mapping that maps a given parameter g to a unique decision x:

f : {C 1 , . . . , C M } → D g → d (9)
Therefore a decisional quantizer yields not the quantization value of the parameter but instead a unique decision associated with it. Obviously the optimal pair (D * , C * ) is given by:

(D * , C * ) ∈ arg max (D,C) E g [u (x; g) |(D, C) ] (10)
where

E g [u (x; g) |(D, C) ] = M k=1 C k u (d k ; g) φ (g) dg (11)
A. Model-based solution (known utility function)

We firstly assume that the utility function is known, i.e., an explicit expression of u (x; g) is available.

However, finding (D * , C * ) jointly is complicated, the DOQ problem can be split in two steps as the classical quantization algorithm does:

1) The representative-to-cell step which is essentially finding the optimal quantization region (cells) given the concrete decision space D (representatives):

C * k = g ∈ G u (d k ; g) = max l u (d l ; g) (12)
where C * k is called the decision region corresponding to decision d k .

2) The cell-to-representative step which is essentially finding the optimal decision space (representatives) given the concrete quantization regions (cells) C:

d * k ∈ arg max d∈X C k u (d; g) φ (g) dg (13)
Furthermore, if step 1 and step 2 can be separately solved, designing an algorithm which performs step 1 and step 2 in an iterative manner to find the optimal quantizer will be possible, as the classical quantization algorithm, e.g., Lloyd-Max Algorithm [START_REF] Lloyd | Least Squares Quantization in PCM[END_REF] operates. The algorithm is summarized in Algo. 1. The convergence of Algo. 1 can be proved by induction and is omitted here. However, quiet often, an explicit expression of the utility function is difficult to obtain or maybe never exists. For example, the global performance of a massive cellular network may be too complicated to know an explicit expression. Nevertheless, we are always able to obtain the value of a specific realization. Many Machine Learning tools can kick in in this scenario effortlessly without knowing a priori information about the utility function. Input: error tolerance and max iteration T

do 8: Update iteration index i ← i + 1 9: assFor all k ∈ {1, . . . , M }, update C (i) k from D (i-1) using (12) 10: For all k ∈ {1, . . . , M }, update d (i) k from C (i) k using (13) 11: while M k=1 d (i) k -d (i-1) k > ε and i ≤ T 12: (D * , C * ) ← D (T ) , C (T )

B. Model-free approach (unknown utility function)

As we have explained, providing a systematic analytical procedure to partition the parameter space without knowing the explicit expression of the utility function can be very difficult. In this paper, we propose to solve this problem by using a Feed-forward Neural Network (FNN) based learning procedure. Denoting W (l) i,j the weight between the neuron i in the l-th layer and the the neuron j in (l + 1)-th layer and b (l) j the bias term for neuron j, the basic model for FNN is given by:

o (l+1) j = f b (l) j + N d i=1 W (l) i,j o (l) i (14)
where o (l+1) j is the output of the neuron j and o (l) i is the output of the neuron i or the input signal from neuron i to neuron j and N d is the number of neurons in each layer. f (•) is the activation function. Moreover we define the training set as

T n := {g t , θ * t } n t=1
, where θ * t is the optimal decision label corresponding to parameter realization g t gathered somehow, e.g., the data already collected in the environment, analytical solution given the explicit expression of our utility function or even by exhaustive comparison between all possibles decisions: If the error estimation error (test error) is less than some threshold, the NN trained by this training set can give us a reasonable approximation of the real decisional quantizer. Again, if step 2 can be solved, we can use Alg. 1 to solve the DOQ problem by replacing the original step 1 with our Machine Learning based approach. This procedure can, in fact, be used for any utility function of the form u(x; g).

θ * t ∈ arg max θ∈{1,...,M } u (d θ ; g t ) (15)

IV. APPLICATION TO ENERGY-EFFICIENT COMMUNICATIONS

In this section, we consider a particular utility function, the Energy Efficiency (EE) which characterizes the efficiency of transmission in term of energy for multi-bands scenario and MIMO scenario. The general form of EE is given by:

u EE (x; g) := F (x; g) E (x) (16)
where F (x; g) represents the lossless utility for the pair (x; g) and E (x) is the energy (or power) consumed using policy x.

A. Multi-band Energy Efficiency

We consider the following EE function:

u MB (p; g) = N i=1 w (SNR i ) N i=1 p i (17)
where i ∈ {1, 2, . . . , N } is an index which might represent the band, channel, or user index; g i > 0 is the channel gain of i-th channel, p = (p 1 , . . . , p N ) is the power allocation vector; g = (g 1 , . . . , g N ) is the vector channels used by transmitter i; SNR i is the signal-to-noise ratio associated with channel i chosen as SNR i = pigi σ 2 which suggests no interference appears between bands, where σ 2 is the received noise variance. Furthermore, the payoff function which represents the packet success rate is chosen (see [START_REF] Belmega | Energy-Efficient Precoding for Multiple-Antenna Terminals[END_REF]).

w (s) = exp - c s (18)
where c ≥ 0 is a parameter related to spectral efficiency. We firstly consider the single band scenario, i.e., N = 1, we thus have:

u (p; g) = exp -cσ 2 pg p (19)
Assume that p ∈ {P 1 , . . . , P M } (without loss of generality, we assume that P 1 < • • • < P M ). We pick randomly two decisions P i and P j (assume that P i < P j ). On can obtain the following lemma 1: Lemma 1. The optimal decisional threshold between two decisions P i and P j is:

g * 0 (P i , P j ) = cσ 2 1 Pi -1 Pj ln P j -ln P i > 0, if P i < P j (20)
One may think there will be M (M -1) 2 possible thresholds in this problem. However there are only (M -1) effective thresholds. A threshold is called effective if it is the boundary of a decision region. We have the following proposition 2: Proposition 2. Only the threshold in form of g * 0 (P i , P i+1 ) , i = 1, . . . , M -1 is effective. Proof. One can easily find that:

∂g * 0 (P i , P j ) ∂P i = cσ 2 P 2 i (ln P j -ln P i )
2 ln

P i P j - P i P j + 1 ∂g * 0 (P i , P j ) ∂P j = cσ 2 P 2 j (ln P j -ln P i ) 2 ln P j P i - P j P i + 1 (21)
One can prove that

f (x) = ln x -x + 1 ≥ 0, ∀x > 0 ( 22
)
where equality is only taken when x = 1. Knowing that P i < P j , so we can conclude that ∂g * 0 (P i , P j ) ∂P i < 0 if P i < P j (23)

∂g * 0 (P i , P j ) ∂P j < 0 if P i > P j (24)
Thus we have for any i = j such that P i < P j we always have g * 0 (P i , P i+1 ) > • • • > g * 0 (P i , P j-1 ) > g * 0 (P i , P j ) g * 0 (P i , P j ) > g * 0 (P i+1 , P j ) > • • • > g * 0 (P j-1 , P j ) So the conclusion is obvious.

B. Energy Efficiency in MIMO system

We consider the following single user Multiple Input Multiple Output (MIMO) communication system. The receiving signal is modeled by:

y = Hx + z ( 25
)
where H is the N r × N t channel transfer matrix with N t transmit antennas and N r receive antennas. We assume the entries of H are i.i.d. zero-mean circularly symmetric complex Gaussian distributed according to CN (0, 1). A vector x is the transmitting symbols vector with dimension N t and z is the receiving white Gaussian noise vector distributed as CN 0, σ 2 I Nr . Moreover Q = E xx H denote the covariance matrix of x which determines the power allocation policy. And we have the common maximum total power constraint:

Tr (Q) ≤ P max ( 26
)
Given this matrix-form of the system, we define the Energy Efficiency as follows:

u MIMO (Q; H) = R 0 log 2 I Nr + ρHQH H Tr (Q) + P 0 ( 27
)
where ρ = 1 σ 2 , R 0 is the raw data rate (in bits/s) and P 0 represents the power consumed by the transmitter when the radiated power is zero. For instance, in [START_REF] Betz | Energy Efficient Communications in CDMA Networks: A Game Theoretic Analysis Considering Operating Cost[END_REF] it may represent the computation power or the circuit power.

The existence of P 0 is not only reasonable but also avoids the following fact that the most efficient transmission occurs when p = Tr (Q) = 0. The global decision set is the Equal Gain Transmission (EGT) with antenna selections. Without loss of generality, we only consider diagonal covariance matrix of the transmission signal, i.e., Q = Diag (p) with p = (p 1 , . . . , p Nt ). Where Diag (v) generates the diagonal matrix whose diagonal is exactly the vector v. The decision set is chosen as following form:

D = Q = P max l Diag (e) |e ∈ S l , ∀l ≤ N t ( 28
)
where S l = e ∈ {0, 1}

Nt Nt i=1 e i = l which is the set of N t -dimensional binary vector summing to l. The decision set D k associated to a decisional quantizer with k ≤ 2 Nt -1 decisions can be constructed as follows iteratively:

D k = {Q 1 } Q 1 ∈ D, k = 1 D k-1 ∪ {Q k } Q k ∈ D\D k (29)
The singleton set is chosen among all possible sets randomly. Consider the optimality of the decision set, we choose the maximum total power P max = P * s.t.

P * ∈ arg max P ,Q∈D E H u MIMO (Q; H) (30)
P * can be found by comparison through Monte-Carlo simulation. One can imagine that finding the analytical decisional quantizer for EGT will be very difficult if the dimension of the system is huge. Thus we propose to use a neural network to mimic the real decisional quantizer.

V. SIMULATION RESULTS

In this section, we present several simulations that illustrate the performance by using the proposed approach with neuralnetwork. Here, we choose the 3-hidden-layer FNN with fully connected layers comprising 20 neurons each and using the logistic activation function defined as sig(x) = 1 1+exp(-x) . We use the Levenberg Marquardt Algorithm in [START_REF] Marquardt | An Algorithm for Least-Squares Estimation of Nonlinear Parameters[END_REF] to update the weight matrix. In this FNN model, 100000 Monte-Carlo realizations will be divided into three phases: 70000 realizations for the training phase, 15000 for the validation phase and 15000 realizations for the test phase. The structure of FNN is illustrated in Fig. 2. Subsequently, simulation results will be illustrated in two different scenarios: the multiple band case and the multiple antenna case. Multi-band: Firstly, we focus on the multi-band case. For EE defined in Eq. 17, The number of input neurons for Eq. 17 is obviously the number of bands N . Fig. 3 illustrates the decision regions for the following simulation configuration: there are two bands in the system (N = 2), every band has only two choices to choose: P min = 2mW, P max = 3mW. The noisy level is set to be σ 2 = 10mW and the constant is assumed to be c = 1. The channel gain g i in band i is assumed to be exponentially distributed, i.e., its p.d.f. is φ (g i ) = exp (-g i ). There follows our intuitive explanation. Let us take the orange region (P min , P max ) as an example. In this region, channel gain g 1 is smaller than g 2 which means transmission in band 1 is less efficient than band 2, therefore the transmitter chooses the policy (P min , P max ). Same principle can be applied to the 3 remaining regions. Apart from the EE function, we study the sum-rate utility as follows:

u SR (p; g) = N i=1 log(1 + SNR i ) (31)
To compare the performance of DOQ by using a decisional quantizer approach implemented through a FNN, the relative optimality loss introduced by quantization is defined as following:

∆u (%) = E g u * (g) -u NN (g) u * (g) × 100 (32)
where u * (g) = max p u (p; g) and u NN (g) is the performance achieved by our learning approach. Besides, to compare the influence of the compression between the system with different objectives, Define the compression rate γ (σ) of a Fig. 3. Decision regions of 2-band EE problem. When one channel is dominant, it is better to transmit with higher power levels in that dominant channel. Otherwise, both transmitters choose the same transmit power.

given relative optimality loss σ as γ (σ) := M (1%) M (σ) , where M (σ) is the required number of decisions such that the relative optimality loss σ can be satisfied. Fig. 4 illustrates the compression rate γ in function of optimality loss for two bands in two cases. With the two different utilities, it can be seen that the compression rate increases as the optimality loss grows. For the energy efficiency problem, the compression rate decreases slowly while the optimality loss decreases and the loss is always greater than 1%. As for the sum-rate problem, the compression rate declines rapidly while the optimality loss reduces and the optimality loss is always less than 1%. It can be observed that it is easier to compress the g for the sum-rate problem than the energy efficiency in two-band scenario, i.e., the energy efficient function is more sensitive to the variable g. This can be explained by the fact that the explicit optimal decision function of sum-rate, well known as the water-filling solution, is more concise than the solution of the energy efficiency problem, which is inversely proportional to g.

MIMO:

The simulation results of the MIMO system con-sidered in section IV-B are presented in Fig. 5 (N t = 4 and N r = 1 (MISO), R 0 = 10 6 bits/s, σ 2 = 5mW, P 0 = 10mW and P max = 12mW.) and in Fig. 6, (N t = 3 and N r = 2 (MIMO), R 0 = 10 6 bits/s, σ 2 = 5mW, P 0 = 10mW and P max = 10mW) (We use exhaustive search to find the optimal P max by solving (30)), respectively. The number of neurons in input layer for Eq. 27 is given by 2N t N r because the input vector contains the real part and the imaginary part of each entry of the transfer channel matrix. Given the same parameter samples, a k-means quantizer which aims at minimizing the mean square error between the original signal and the quantized signal, is taken as the reference. All the realizations are divided into k regions and each region is assigned with the optimal decision in D k found through exhaustive research. It is worth noting that this k-means approach can be seen as a special case implementing Algo. 1 by taking u (x; g) = -xg 2 .

In both two cases, the decisional quantizer outperforms than the k-means quantizer. In MISO scenario, NN can achieve very close performance to the optimal average utility in several decision set (D k , k = 2, 5, 6, 7 and k ≥ 9) while the average utility found through k-means quantizer is trite. In MIMO scenario, the performance of NN is still better than k-means quantizer. The utility loss introduced by the FNN is perhaps owing to the scarcity of training. More complicated structure of NN should be used to improve the training accuracy.

VI. CONCLUSION

In this paper, we have introduced in a formal way the problem of DOC, and proposed solutions for DOQ. When applied to the problem of power allocation, it is seen that quantizing the channel gains very roughly only induces a very small optimality loss w.r.t. the case where the gains are perfectly known to the transmitter when the utility is the transmission rate. However, for energy-efficiency, channel gains need to quantized more accurately. Using a classical distortion-based quantization scheme (k-means quantization) number of decisions for this is shown to lead to a quite significant performance loss (about 30%), showing the potential of our approach. To better assess the potential of the proposed approach, it should be generalized to decision-oriented source coding and decisionoriented channel coding. Also, it allows one to reconsider the overarching assumption made in resource allocation problem, that is the resource allocation policy is designed by assuming perfect knowledge of the parameters. Mathematically, a deep study should be developed to identifying the properties of the utility function which represents its sensitivity to being maximized under imperfect knowledge of its parameters.

Algorithm 1

 1 Decisional Quantization Algorithm 1: Input: utility function u (x; g) 2:

3 :

 3 Input: initial decision set D (0) = d decision region C (0) = C decision pair (D * , C * ) 6: Initialization: set iteration index i → 1 7:

Fig. 1 .

 1 Fig. 1. Basic structure of a FNN.

Fig. 2 .

 2 Fig. 2. Feed-forward neural network model for MIMO system (Nt = 3 and Nr = 2). Number of neurons in input layer is 2NtNr.

Fig. 4 .

 4 Fig.[START_REF] Zhang | Payoff-oriented Quantization and Application to Power Control[END_REF]. The compression rate as a function of the optimality loss for single user 2-band scenario for energy efficiency and sum-rate capacity. Compressing the channel gain for sum-rate function is easier than compressing the channel gain for energy-efficiency function.

Fig. 5 .

 5 Fig. 5. The average utility vs. number of decisions for Nt = 4 and Nr = 1 (MISO) , σ 2 = 5mW, P 0 = 10mW and Pmax = 12mW. FNN is better than k-means quantizer and close to theoretical optimal utility.

Fig. 6 .

 6 Fig. 6. The average utility vs. number of decisions for Nt = 3 and Nr = 2 (MIMO) , σ 2 = 5mW, P 0 = 10mW and Pmax = 10mW. FNN is better than k-means quantizer and close to theoretical optimal utility.

ACKNOWLEDGEMENT

This work was funded by the RTE Chair and the PEPS YPSOC project funded by CNRS.


Marcel Bouvet
email: marcel.bouvet@espci.fr

Phthalocyanine -Based Field-Effect Transistors as Gas Sensors

Keywords: molecular materials, phthalocyanine, field-effect transistor, sensor, ozone, nitrogen dioxide

Phthalocyanine-based field-effect transistors as gas sensors

Introduction

Gas sensing by measurement of the electrical property changes in molecular materials following their adsorption on a solid surface has been widely investigated. Most studies have dealt with molecular resistors since the studies of Bott and Jones [1] but only few studies concerned transistors. A very interesting work is that of Laurs and Heiland who studied the effect of oxygen, iodine, bromine and also lithium on the conductivity of various phthalocyanines. [2] Without using the term "transistor" they prepared p and n-type fieldeffect transistors (FETs) and studied their sensitivity to oxidizing gases. They showed that the influence of oxidizing gases like oxygen on the surface conductivity reversed its sign when the field-effect changed from p to n type as a result of lithium vapor exposure. These studies carried out in ultra-high vacuum chamber deal with gas sensing but not with sensors. Indeed, different qualities are required to actually obtain sensors. Among them, sensitivity, selectivity and stability are probably the main, but reversibility, reproducibility, response and paralysis times and their insensitivity to factors of influence (temperature, pressure ...) are also important intrinsic qualities to get a sensor. Depending on their particular applications and on the demand other qualities must be fulfilled. A sensor must be miniature, robust, with a sufficient lifespan, should consume low energy, allow an uninterrupted monitoring, of simple implementation, and deliver easily exploitable signals, all for the lowest possible cost. Demands of gas sensors come from the organisms in charge of the air quality control. Indeed, these sensors would allow multiplying the density of measurements and then to get a more accurate cartography of atmospheric pollution than with the analyzers, which are expensive compared to miniaturized sensors. Another emerging application is the indoor pollution control. [3] In that review we will distinguish the FETs in which the molecular material is used as semiconductor, called hereafter molecular FETs from those made from silicon and where the gate, modified by a molecular material, is exposed to gases. For that second type of device, usually called chem-FET, we will use the term gate-modified FET.

I. Description of field-effect transistors

I.1. MOSFET

The most widely used FET is the Insulated Gate FET (IGFET) based on two opposite n/p junctions. Silicon IGFETs are rather known as MOSFETs (Metal Oxide Semiconductor FETs) because their insulating layer is a silicon oxide film thermally grown upon a silicon substrate.

Let us consider a MOSFET with an n-channel in the enrichment regime (Fig. 1). In the absence of any polarization, the capacity MOS remains in depletion mode and the transistor is normally blocked (Fig. 1a). The application of a positive gate-to-source voltage V GS higher than the threshold voltage V T of the capacity creates an inversion layer of the n-type, called channel, between the source and the drain. If a positive drain-to-source voltage V DS is applied a current I DS circulates in the channel. Because of that polarization, the inversion layer is more pronounced near the source than near the drain. For a high polarization of the drain the electron density in the inversion layer decreases and the current starts to saturate. For a certain value of that polarization, the capacity MOS is not any more in inversion mode near the drain, it is the pinching mode (Fig. 1b). Beyond this polarization, the current is ensured by the free carriers in the conducting channel up to the point of pinching and then propelled towards the drain by the electric field that exists in the space charge region. This transistor works with a nchannel but the equivalent exists with a p-channel with reversed polarizations.

I.2. Molecular FET

The first phthalocyanine -based transistors [4][5][6] were described in the mid to late 1980s, simultaneously with polymers [7][8][9] and a-sexithiophene, [10] then with pentacene [11] and fullerenes. [12,13] Very recently, n-channel transistors were obtained with withdrawing moiety-substituted molecules such as fluorine phthalocyanines, [14] a, a ' -diperfluorohexylsubstituted sexithiophene [15,16] and with perylenetetracarboxylic dianhydride or related molecules. [17][18][19] We will see that p and n-type FETs can be useful to detect different type of chemical species.

An electron-active molecular material thin film is deposited between two gold electrodes (source and drain) on a dielectric material (SiO 2 , Si 3 N 4 or a polymer, thickness typically 1000-3000 Å) covering a metallic electrode (Fig. 2). If a negative gate voltage is applied the positive charge carriers existing in the semiconductor are attracted towards the dielectric material, while the negative charge carriers are repulsed that create a channel where the density of majority charge carriers is higher than in the bulk. Although the mechanisms are totally different the basic equations of classical silicon MOSFETs [START_REF] Sze | Physics of Semiconductor Devices[END_REF] can be adapted to molecular transistors. [START_REF] Guillaud | [END_REF] The variation of the source-to-drain current I DS as a function of the source-to-drain voltage V DS and of the grid voltage V GS is well established (eq. 1). [START_REF] Guillaud | [END_REF] (1

)
where Z is the channel length, L the inter-electrode distance, C i the capacitance of the insulator per unit surface and V T the threshold voltage (eq. 2). V T has another origin than in the classical MOSFETs where it corresponds to the voltage required to get the strong inversion. In molecular FETs V T has been associated to the presence of traps of structural origin, or to ions or other impurities at the semiconductor -dielectric material interface. [22,23] (2

)
where h is the thickness of the molecular layer and n 0 the density of charge carriers without grid voltage.

At V DS = V GS -V T , the I DS = f(V DS ) curve reaches a maximum and a pinch off of the channel occurs. For V DS > V GS -V T the channel is no longer continuous and the corresponding current is called saturation current (eq. 3). The curve allows to deduce the mobility µ, which is called the fieldeffect mobility. V T is deduced from the intersection of this curve with the x-axis (V GS = V T )

Contrary to what happens for classical MOSFETs, in molecular FETs the bulk current, I b , cannot be neglected and has to be taken into account in parallel with the channel current I DS in order to get the total current I t .In the absence of gate voltage and in the ohmic domain, I b is proportional to V DS . So, at saturation (i.e. V DS = V GS -V T ), the I on /I off ratio can be calculated (eq. 4).

(

) 4
According to this model, the I on /I off ratio can be improved by decreasing the free charge carrier density and the thickness of the active part of the FET, and by increasing the capacitance of the insulating material. As a consequence, the field-effect is easier to highlight in an insulator as nickel phthalocyanine NiPc than with a semiconducting material as lutetium bisphthalocyanine LuPc 2 . [START_REF] Guillaud | [END_REF] It has been shown that, contrarily to the macroscopic conductivity, the field-effect observed in a FET is very sensitive to the surface states, particularly at the insulator-molecular material interface.

II. FET as gas sensor

II.1. Origin of the sensitivity

II.1.a. Adsorption processes

The adsorption of molecules on a surface is a key step in any gas sensing process. In many cases the surface is already covered by another type of molecule, usually dioxygen or water that has to be removed to allow the adsorption of molecules to be detected. In physisorption (or physical adsorption) the attraction forces between atoms of the sensing layer and those of the gaseous phase are electrostatic forces of van der Waals type, thus of weak energy (from 2 to 10 kJ mol -1 ). In chemisorption (or chemical adsorption) a chemical bond involving substantial rearrangement of electronic density is formed between the adsorbate and substrate. The involved energies are significant, from 40 to 800 kJ mol -1 . Chemisorption is often a dissociative process, which may be irreversible, whereas physisorption is a nondissociative and reversible process. Chemisorption is often a thermally activated process with kinetics of adsorption very variable whereas physisorption is a non-activated and usually fast process. [START_REF] Gasser | An Introduction to Chemisorption and Catalysis by Metals[END_REF] The Langmuir isotherm established ninety years ago gives the fraction q of occupied sites (0 < q < 1) as a function of the partial pressure P of the adsorbing gas. [START_REF]On physical adsorption[END_REF][START_REF] Hayward | Chemisorption[END_REF] The adsorption of gases onto molecular material films has been largely studied. [START_REF] Wright | [END_REF][START_REF] Wright | Molecular Crystals[END_REF] Experimental data related to the adsorption of gases onto molecular layers show that q varies as a power of the gas concentration. To formalize those results the authors use the Freundlich isotherm, which is close to the Langmuir isotherm, but where all the sites are not considered as energetically equivalent because of the existence of grain boundaries and defects. In fact, the assumptions associated to the development of the Langmuir adsorption represent an ideal form seldom found in thin polycrystalline layers. The Freundlich isotherm is rather an empirical model. However, with a relatively small range of partial pressures, far from saturation of the surface, the curve associated to the Langmuir isotherm between q and P may be described by a power law. After adsorption, diffusion phenomenon is the second important parameter that influences gas sensor responses.

It is well known that structure, morphology and surface chemical composition of molecular films, which depend on preparation conditions, have implications on adsorption and diffusion processes.

II.1.b. Redox processes

Phthalocyanines and related molecules, as porphyrins and naphthalocyanines, can be oxidized and reduced by redox active species. The electrical properties of molecular materials depend on the density of charged species. Consequently, a molecular material in contact with a strong oxidizing gas will become more conductive.

Let us see the relationship between the redox potentials of molecular materials and their electrical properties. The conduction process is due to an electron transfer from molecule to molecule. It has been demonstrated that in a molecular material constituted of molecular units A, the creation of charge carriers corresponds to the oxidation of one molecular unit and the reduction of another one. [START_REF] Bouvet | [END_REF][START_REF] Bouvet | Porphyrin Handbook[END_REF] The elementary steps consist in an electron transfer (E.T.) from one molecule to another follow-up by a separation of the newly created charges (C.C.) (eq. 5). In the intrinsic case the density n (or p) of charge carriers is related to the oxidation and reduction potentials, E ox and E red respectively, of A in the solid state (eq. 6).

AAAAAA

E.T. AAA + A -AA C.C. A + AAAA -A (5) (6)
where [A] 0 is the density of molecular units in the solid state, approximately 10 21 cm -3 .

Conductivity s is the product of the density of charge carriers by their mobility µ and the charge of an electron. Mobility µ is lower in molecular materials that in silicon, usually in the range 10 -4 -10 -1 cm 2 V -1 s -1 , with a maximum of 1 cm 2 V -1 s -1 . For metallophthalocyanines as NiPc, whose E ox -E red value is about 1.9 V, [START_REF] Her | Porphyrin Handbook[END_REF] the calculated intrinsic density of charge carriers is n = p = 10 5 cm -3 . They belong to insulating materials. On the contrary, LuPc 2 , which is a radical species, can be easily oxidized and reduced. Due to its very low E ox -E red value (0.48 V), LuPc 2 exhibits a very high density of charge carriers, 5.10 16 cm -3 (ca. 10 ppm), i.e. more than in silicon. It appears that LuPc 2 was the first intrinsic molecular semiconductor. [START_REF] Bouvet | Porphyrin Handbook[END_REF][START_REF] André | [END_REF] An oxidizing species I A (resp. reducing species I D ) will generate extrinsic positive (resp.

negative) charges (eqs. 7, 8). Then, the extrinsic density of charges is proportional to the

exponential of (E A ox -E IA red ) (resp. (E ID ox -E A red )). A, I A A + , I A - (7)
A,

I D A -, I D + (8)
In most of the molecular materials, a very small amount of impurities is sufficient to increase the conductivity of the material, which is intrinsically an insulator. Even for semiconductors such as LuPc 2 , with a very high intrinsic density of charge carriers (10 ppm), the conductivity can be multiplied by a factor 1000 with a concentration of doping agent of 1 %, if an efficient charge transfer is considered. It means that doping of molecular materials is always easy. In the case of insulators the sensitivity is so high that it becomes extremely difficult to measure the intrinsic conductivity. However, doping effects are of the utmost importance since they are at the origin of the conductimetric sensors. [START_REF] Bouvet | Porphyrin Handbook[END_REF] Oxidation of CuPc at room temperature causes the increase of the conductivity by several orders of magnitude up to a plateau. LuPc 2 showed higher sensitivities to NO 2 than the non-radical phthalocyanines. [33] For radical phthalocyanines, in the first stage the conductivity readily increases as in CuPc, then it goes through a maximum and decreases.

Indeed, because of the low oxidation potential of the radical lutetium compounds, a very high concentration of phthalocyanine molecules can be oxidized. The holes displacement by hopping from one oxidized molecule to another neutral one becomes more and more difficult since there are less and less available neutral molecules left for holes to hop into. In addition, hoping between two oxidized molecules involves a doubly oxidized species, which is very unlikely because it requires too much energy, E = 1.23 eV in the case of LuPc 2 , associated with a new equilibrium (eq. 9).

2 LuPc 2

+ LuPc 2 + LuPc 2 2+ ( 9
)
When the concentration of extrinsic charge carriers increases their mobility decreases and also their conductivity. The existence of a maximum of conductivity occurs for LuPc 2 only with relatively strong oxidizing species. Oxygen gas that presents a small electron affinity value does not induce such effect on the conductivity of all phthalocyanine layers even at high concentrations.

Even though the adsorbed species are not redox active in nature, other physical parameters, such as the dielectric constant of the material and the ionic conductivity for examples can be affected. In the original hydrogen sensor of Lundström [34] with a nonmodified Pd-gate MOSFET, or in the case of gate-modified FETs [35] and Schottky diodes, [36] the variation of the work function of the sensing electrode is at the origin of the current modification of the device.

The information delivered by the sensor will be pertinent if the variation of the signal is a reliable picture of the variation of the gas concentration. Consequently, the reaction between the gaseous species to be detected and molecules of the sensing layer should be reversible. Let us consider the case of nitrogen dioxide, NO 2 . After the adsorption step, oxidation occurs through an electron transfer from NO 2 to the sensing layer S (eq. 10).

S + NO

Reversibility of the phthalocyanine oxidation can occur with desorption of one dioxygen molecule whereas the starting oxidizing species (O 3 ) is decomposed.

II.2. Gate-modified FET

MOSFETs have been modified by deposition of Langmuir-Blodgett (LB) films of substituted cobalt porphyrins [38,39] and octahexyl metal-free phthalocyanine [40] on p-type MOSFETs (Fig. 1). It is worth to mention that two different procedures were applied to acquire data, which can make uneasy a comparison between the devices.

In the first case, no gate voltage is applied and exposure to NO 2 induces a modification of the gate potential by a partial oxidation of molecular material. The variation of I DS as a function of V DS at various concentrations can be compared to the characteristics I DS = f(V DS ) of a non-modified MOSFET at various gate voltages (Fig. 3). At V DS = +5 V, 10 and 20 ppm NO 2 concentrations induce a current I DS equal to 0.3 µA and 0.65 µA, respectively. These values are equivalent to those obtained with gate voltages of 0.80 and 0.90 V. [38] Response time is approximately 10 min, with a recovery time of 1 h for a 5 ppm concentration with a 39 layer LB-MOSFET. However thinner films and higher concentrations provide faster responses. Working at 85 °C, NO 2 can be detected at the ppm level, with no sensitivity to H 2 , NH 3 , CO and H 2 S at 500 ppm levels. When the enhancement n-channel MOSFET is replaced by a MOSFET designed as a depletion p-channel, sensitivity can be improved to 0.1 ppm. [41] Surprisingly, at this concentration NO 2 acts as a negative gate voltage.

In the second case, [40] a determined gate voltage is applied and a delay is observed in the response of the drain current. At first, I DS increases slowly, then rapidly up to a saturation value. Thus, the curve I DS = f(t) has the same shape than the I DS = f(V DS ) curve showed in the previous case. The response of the device, defined in that case as the variation of I DS as a function of time, DI DS /Dt, increases with the NO 2 concentration in the range 2-14 ppm. This approach has been used recently with samarium bis(octa octyloxy-phthalocyanine), [42] but with no apparent advantage due to the radical nature of the molecule.

In any case, sensitivity to NO 2 is higher with gate-modified transistors than with nonmodified metallic gates. Modified from [38].

II.3. Molecular FET

Early in the preparation of molecular FETs, effects of atmosphere appeared. For example, it was shown that with LuPc 2 majority charge carriers could change from n-type under vacuum to p-type in air. [START_REF] Guillaud | [END_REF] In the case of non-radical metallo-phthalocyanines (MPc), a p-type behavior was evidenced under vacuum with a negligible current at zero gate-source voltage (I off ). In air, due to dioxygen or related oxidizing species, extrinsic generation of charge carriers occurs, which increases significantly the conductivity at V GS = 0.

Simultaneously the saturation current increases, but less than I off , leading to a lower amplification factor. In the same time, the threshold voltage increases and the FET mobility decreases. [22] It is important to note that, in air, I DS can be increased by a positive gate-source voltage and decreased by a negative V GS value, the FET working in enhancement mode and in depletion mode, respectively (Fig. 4). In FETs several parameters can be affected by gaseous species and molecular FETs can be considered potentially as multi-parameter gas sensors. [44] After these general considerations let us detail humidity sensors, volatile organic compounds (VOCs) sensors and oxidizing gas sensors. Up to now, phthalocyanines have been used for humidity and VOCs sensing only in resistors and not in transistors, even though they could be used favorably in such devices. It is the reason why the next two sections deal with sensors based on other molecular materials.

II.3.a. Humidity

When a pentacene FET is exposed to humidity its saturation current decreases as well as its FET mobility. [45] Above 30% in relative humidity (RH), a change of 0.7% in the saturation current per 1% change in RH is obtained for a 500 Å -thick film, whereas sensitivity decreases to 0.3% when the thickness of the pentacene layer is increased to 1000 Å. Below 30% in RH, the thicker films seem more sensitive but with memory effects. That is a general behavior for gas sensors due to slow diffusion of molecular species in and out of the sensitive layers. I Dsat and mobility decreasings were also observed with 1,4,5,8-naphthalenetetracarboxylic-dianhydride (NTCDA) that leads to n-type FETs. [46] It means that H 2 O does not act on the generation of charge carriers, but rather as traps of the pre-existing free carriers.

With NTCDA an additional phenomenon occurs, which is its possible hydrolysis. Even though no difference between anhydrous NTCDA and NTCDA exposed to humidity was observed by infrared studies in the same conditions than the FETs exposure, however even 1% hydrolysis corresponds to a high concentration of protons in the molecular layer. Ionic conductivity can occur, which could explain the slight increasing of I off . Moreover, the dynamic range for the variation of I Dsat is only of one order of magnitude for NTCDA FETs.

II.3.b. VOCs

Sensitivity to VOCs has also been studied with various molecular FETs using oligothiophenes, phthalocyanines and fluorinated 1,4,5,8-naphthalene-tetracarboxylic-diimide (NTCDI). [47,48] I D decreases when devices are exposed to saturated vapor of the analyte.

For example, the current I D of an a,w-dihexyl-a-sexithiophene -based FET decreases by 7% due to a 5 s exposure time to 1-hexanol. As for water on pentacene, the FET mobility decreases. The degree of sticking measured with a quartz-coated microbalance does not necessarily correlate linearly with the vapor pressure value, but the current change is in close correlation with the mass uptake of odorant that adhered to the sensitive layer. [47] For example, the response of a poly-dipentoxy-tertiophene FET to 1-hexanol is 10 time higher than to ethyl alcohol. [49] Thanks to an electrical bias cycle recovery is ensured after about 1 min, which is a short time compared to sensor standards but represents 12 times the exposure The derivative dI DS /dt gives a response of the sensor independent of the exact exposure time (Fig. 5). The maximum value of the derivative is linearly correlated to the ozone concentration in air (55 pA ppb -1 min -1 ) between 0 and 150 ppb, that is to say in the range encountered in urban atmosphere. This ozone sensor has been used in real situation (Fig. 6a). The use of a dynamic rest instead of a static rest reduces the duration of the recovery period, but is not necessary to achieve a good reproducibility, contrarily to what happens with more stable gases, as NO 2 .

Another advantage of this device is to work at room temperature. A miniaturization of that ozone sensor has been achieved. [51] Due to its high instability, ozone is not supposed to diffuse inside the molecular film.

However, a negative gate voltage can attract the positive charges created at the air-thin film interface by oxidization of the molecules, and surface sites remain available for new oxidizing processes. [51] Although ozone cannot diffuse into the film as it is the case for NO 2 , oxidation in the bulk can occur. It has been demonstrated that only the superficial layer of the molecular film is degraded by ozone, allowing a long sensor life span. [50] Moreover, it has been shown that application of a positive gate voltage accelerates the recovery of the initial state, as seen for VOCs, suggesting that positive charges involved in the redox processes can migrate away from the dielectric-semiconductor interface. [START_REF] Guillaud | Pauly A unpublished results[END_REF] Sensitivity to NO 2 was found to be approximately 5 times smaller than to O 3 .

[53] However, it is not sufficient to get good results in polluting gas control in atmosphere. Indeed, during a day, the ratio [NO 2 ]/[O 3 ] varies between 10 2 and 10 -2 (Fig. 6b). Thus that sensor is able to give reliable maximum values of the ozone concentration, but when the ratio [NO 2 ]/[O 3 ] is higher than 10 the response of the sensor is more related to the NO 2 concentration (Fig. 6a). It is the reason why new methodologies have been developed, [START_REF] Bouvet | Encyclopedia of Sensors[END_REF] including the use of selective filters [START_REF] Viricelle | [END_REF]56] but not yet applied to molecular FET -based sensors. Measurements of relative humidity were realized to quantify its effect on the sensor. Some results were published on synergy between water vapor and NO 2 at room temperature.

[57] In our conditions, namely temperature, pollution rate and range of measured humidity (between 20% and 40%), very weak influence of relative humidity variations on the sensor signal was observed. Considering other gases like O 2 or CO their action can be neglected compared to that of O 3 and NO 2 . If fluorinated phthalocyanines are used the corresponding molecular FETs, of n-type, are sensitive to reducing species like ammonia, [58] as it is the case for resistors. [59]

Conclusion

Phthalocyanines and related molecules have been used in molecular FET structures as sensing materials for various gases. Dynamic procedures using short exposure periods led to the best results, as for molecular resistors. Several advantages of transistors over resistors exist, namely i) the possibility to use very thin films (200-500 Å) since the gate potential increases the current, ii) the possible measurement of several parameters, more or less independent of each other and iii) the improvement of the reversibility of the adsorption processes when a reverse bias is applied. Such advantages do not exist with gate -modified FETs for which the adsorbed species act on the device current through a modification of the work function of the gate. Whereas water and volatile organic compounds act as traps and lead to a current decreasing, oxidizing species such as ozone and nitrogen dioxide act as true dopants. Sensitivity to humidity is weak compared to that of capacitive humidity sensors already commercialized. [60] Discrimination between different VOCs has been proved using a series of sensors. Nevertheless experimental processes have to be carried out in the absence of strong oxidizing species to allow the use of electronic nose based on molecular FETs. The high sensitivity of molecular FETs to ozone allowed to develop an ozone sensor working for atmospheric pollution control. The use of selective filters or devoted thermal methodologies developed for phthalocyanine -based resistors could be applied to molecular FETs to suppress the interference between NO 2 and O 3 .

In any case, not only the choice of the molecular material and the type of transducer, but also the methodology must be adapted to each particular application.

Figure 1 .

 1 Figure 1. Schematic illustration of a MOSFET with a n-channel in the enrichment regime, in

Figure 2 .

 2 Figure 2. Schematic illustration of a molecular FET with a p-type molecular material in its

[ 43 ]Figure 3 .

 433 Figure 3. Characteristics of a FET where the gate is a LB film (39 layers of CoPorBr) when

Figure 4 .

 4 Figure 4. Variation of I DS as a function of V DS for a NiPc -based FET in an air-containing

  period. The recovery time without reverse bias is approximately 1 h. It was shown that the sensing response of oligothiophene FETs towards alcohols enhanced as the number of grain boundaries increased. A map illustrating the effect of 16 analytes on 11 sensor materials was published, suggesting possible applicability in the field of olfactory sensor arrays.[48] II.3.c. Oxidizing species A sensor that exhibits sensitivity to ozone concentration below 10 ppb has been prepared with a NiPc -based FET.[50,51] A dynamic procedure working out of the equilibrium state allows to get rid of drift phenomena. A process where 2 min exposure alternates with 8 min static rest period leads after a conditioning period to a stable and reproducible signal. The drift of I off is about 0.15 nA per cycle, i.e. only 2% of the current.

Figure 5 .

 5 Figure 5. Response dI DS /dt of a NiPc -based FET exposed to various ozone concentrations (--

Figure 6 .

 6 Figure 6. top) Response (dI DS /dt) max of a NiPc -based FET to ozone during a day in a Paris

Acknowledgements

The author is grateful to Professor Alain Pauly (Université Blaise Pascal, Clermont-Ferrand, France) for helpful discussions and to Dr. Bernard Malézieux for his reading of the manuscript.


M Ibrahim

P Soulard

E Alikhani
email: esmail.alikhani@sorbonne-universite.fr

B Tremblay
email: benoit.tremblay@sorbonne-universite.fr

Infrared Spectroscopic and Density Functional Theory Investigations of PdTi Heterodimer Reactivity with Carbon Monoxide Isolated in Solid Argon

The reactivity of diatomic palladium-titanium toward carbon monoxide has been studied in solid argon by infrared spectroscopy (FTIR) in the carbonyl stretching frequency region. Our technique of sublimation of Ti and Pd atoms from two filaments heated separately allowed the identification of five new molecules.

Small polynuclear carbonyl clusters, PdTi(CO) n (n=1-3) have been characterized on the basis of isotopic substitutions, metal atoms and CO concentration variations and irradiation effects. Selective irradiation in visible leads to conversion between two isomers distinguished by the stretching frequency of the diatomic CO: PdTiCO Ti-eo (ν CO =1908.4 cm -1 ) and PdTiCO Pd-eo (ν CO =2009.3 cm -1 ). The Density Functional Theory (DFT) calculations have been carried out to elucidate the geometrical and electronic structures and support the spectral assignments. The nature of the metal-carbon bonding has been discussed using the topology of the Laplacian of the electron density.

INTRODUCTION

Bimetallic catalysts have attracted great research efforts in the past decades due to their chemical and physical properties different from the individual pure metals and promising applications in chemical conversion, energy technology and environmental protection [START_REF] Yao | In situ IR spectroscopic studies of Ni surface segregation induced by CO adsorption on Cu-Ni/SiO2 bimetallic catalysts[END_REF][START_REF] Rodriguez | The nature of the metal-metal bond in bimetallic surfaces[END_REF][START_REF] Gao | Pd-Au bimetallic catalysts: understanding alloy effects from planar models and (supported) nanoparticles[END_REF][START_REF] Wei | Bimetallic catalysts for hydrogen generation[END_REF] . Since a lot of studies are interested in all these important applications, numerous experimental and theoretical investigations have been focused on the reactions of transition metal atoms and small clusters with carbon monoxide and a variety of transition-metal carbonyl molecules have been characterized [START_REF] Zhou | Spectroscopic and Theoretical Investigations of Vibrational Frequencies in Binary Unsaturated Transition-Metal Carbonyl Cations, Neutrals, and Anions[END_REF][START_REF] Himmel | Reactions of Ground State and Electronically Excited Atoms of Main Group Elements: a Matrix Perspective[END_REF][START_REF] Chertihin | Infrared Spectra of the Reaction Products of Laser-Ablated Titanium Atoms and Oxides with Carbon Monoxide in Solid Argon[END_REF][START_REF] Zhou | Infrared Spectra and Density Functional Calculations of Small Vanadium and Titanium Carbonyl Molecules and Anions in Solid Neon[END_REF][START_REF] Liang | Reactions of Laser-Ablated Ni, Pd, and Pt Atoms with Carbon Monoxide: Matrix Infrared Spectra and Density Functional Calculations on M(CO) n (n = 1-4), M(CO) n -(n = 1-3), and M(CO) n + (n = 1-2)[END_REF][START_REF] Tremblay | The vibrational spectrum of PdCO isolated in solid argon[END_REF] . Rare gas matrix isolation is a well established technique used to stabilize small metal molecules and clusters in large enough quantities to enable detection by electronic or vibrational spectroscopy [START_REF] Andrews | Chemistry and Physics of Matrix-Isolated species[END_REF] , thus providing a first approach to investigate the atomic or molecular reactivities, complementary or preliminary to gas-phase investigations. [START_REF] Clemmer | Kinetics of excited-state titanium(a 5 F) depletion by nitric oxide, oxygen, nitrous oxide, and nitrogen[END_REF][START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] Recently, many works have been reported on polynuclear carbonyls by trapping evaporated M atoms with carbon monoxide in solid argon. As an example, some small metal cluster carbonyls, such as Co 2 CO [START_REF] Tremblay | Experimental and theoretical infrared spectra of Co 2 CO[END_REF] , Fe 2 CO [START_REF] Tremblay | Vibrational Spectrum and Structure of the Fe 2 CO Molecule. An Infrared Matrix Isolation and Density Functional Theory Study[END_REF] , Ti 2 (CO) n (n=1,2) and Ti 3 (CO) n (n=1-3) [START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] , M 2 CO (M= Sc, Y and La) [START_REF] Jiang | Observation of Anomalous C-O Bond Weakening on Discandium and Activation Process to CO Dissociation[END_REF][START_REF] Xu | Infrared-Spectroscopic and Density-Functional-Theory Investigations of the LaCO, La 2 [η 2 (μ 2 -C,O)], and c-La 2 (μ-C)(μ-O) Molecules in Solid Argon[END_REF][START_REF] Jiang | nfrared Spectroscopic and Density Functional Theory Studies on the CO Dissociation by Scandium and Yttrium Dimers[END_REF] , (AgCO) 2 and Ag n CO (n=2-4) [START_REF] Jiang | Infrared Spectra of the (AgCO) 2 and Ag n CO (n = 2-4) Molecules in Rare-Gas Matrices[END_REF] , Au n CO (n=1-5) and Au 2 (CO) [START_REF] Jiang | Reactions of Gold Atoms and Small Clusters with CO: Infrared Spectroscopic and Theoretical Characterization of Au n CO (n = 1-5) and Au n (CO) 2 (n = 1, 2) in Solid Argon[END_REF] have been synthesized and characterized by infrared spectroscopy in the carbonyl stretching frequency region [START_REF] Tremblay | Experimental and theoretical infrared spectra of Co 2 CO[END_REF][START_REF] Tremblay | Vibrational Spectrum and Structure of the Fe 2 CO Molecule. An Infrared Matrix Isolation and Density Functional Theory Study[END_REF][START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF][START_REF] Jiang | Observation of Anomalous C-O Bond Weakening on Discandium and Activation Process to CO Dissociation[END_REF][START_REF] Xu | Infrared-Spectroscopic and Density-Functional-Theory Investigations of the LaCO, La 2 [η 2 (μ 2 -C,O)], and c-La 2 (μ-C)(μ-O) Molecules in Solid Argon[END_REF][START_REF] Jiang | nfrared Spectroscopic and Density Functional Theory Studies on the CO Dissociation by Scandium and Yttrium Dimers[END_REF][START_REF] Jiang | Infrared Spectra of the (AgCO) 2 and Ag n CO (n = 2-4) Molecules in Rare-Gas Matrices[END_REF][START_REF] Jiang | Reactions of Gold Atoms and Small Clusters with CO: Infrared Spectroscopic and Theoretical Characterization of Au n CO (n = 1-5) and Au n (CO) 2 (n = 1, 2) in Solid Argon[END_REF] and in the far infrared [START_REF] Tremblay | Experimental and theoretical infrared spectra of Co 2 CO[END_REF][START_REF] Tremblay | Vibrational Spectrum and Structure of the Fe 2 CO Molecule. An Infrared Matrix Isolation and Density Functional Theory Study[END_REF] .

In our laboratory, by coupling matrix isolation FTIR spectroscopy and DFT calculations, the molecules Pd 2 N 2 [START_REF] Souvi | Pd 2 N 2 a proteiform molecule: Matrix isolation spectroscopy and density functional theory calculations[END_REF] then Pd 2 CO [START_REF] Alikhani | Spectra and structures of the Pd m CO : An Infrared Matrix Isolation and Density Functional study[END_REF] isolated in solid argon and neon were characterized. There are strong similarities between these two molecules since the ground state corresponds to the ligand bridged (br) on the two Pd atoms, Pd 2 (η 2 -L), with a C 2v symmetry. In argon we observed another isomer with the ligand in terminal position (end on, eo), Pd 2 (η 1 -L), with a frequency of about 180 cm -1 higher than the C 2v form. By selective irradiations in the visible, it is possible to convert the molecules of the terminal form to bridged form.

On the other hand, using laser-ablation method for producing metal atoms, Andrews and co-workers showed that titanium atoms react readily with CO molecules in argon [START_REF] Chertihin | Infrared Spectra of the Reaction Products of Laser-Ablated Titanium Atoms and Oxides with Carbon Monoxide in Solid Argon[END_REF] and neon [START_REF] Zhou | Infrared Spectra and Density Functional Calculations of Small Vanadium and Titanium Carbonyl Molecules and Anions in Solid Neon[END_REF] , and infrared spectroscopic evidence with [START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] CO and C [START_REF] Xu | Infrared-Spectroscopic and Density-Functional-Theory Investigations of the LaCO, La 2 [η 2 (μ 2 -C,O)], and c-La 2 (μ-C)(μ-O) Molecules in Solid Argon[END_REF] O substitution is presented for the identification of Ti(CO) n species (n = 1-6).

But using thermal evaporation for producing metals atoms, Manceron and co-workers did not observe the band assigned to TiCO in neon, and they have observed the Ti 2 CO molecule [START_REF] Souvi | Neon-matrix spectroscopic and theoretical studies of the reactivity of titanium dimer with diatomic ligands: comparison of reactions with nitrogen and carbon monoxide[END_REF] . More, Xu and co-workers reported the FTIR spectroscopic characterization and theoretical investigation of side-on-bonded mono and polycarbonyl titanium clusters Ti 2 (CO) n (n=1,2) and Ti 3 (CO) n (n=1-3) [START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] photodissociation spectroscopy in the carbonyl stretching frequency region [START_REF] Zhang | Infrared Photodissociation Spectroscopy of Mass-Selected Heteronuclear Iron-Copper Carbonyl Cluster Anions in the Gas Phase[END_REF][START_REF] Qu | Infrared Photodissociation Spectroscopy and theoretical study of Heteronuclear transition metal Carbonyl Cluster cations in the Gas Phase[END_REF][START_REF] Qu | Infrared Photodissociation Spectroscopy of Heterodinuclear iron-zinc and cobalt-zinc Carbonyl cation complexes[END_REF] . The geometric and electronic structures of these ions are assigned with the support of density functional calculations. Also, a series of heteronuclear metal carbonyl anions have been investigated using photoelectron velocity-map

imaging spectroscopy: CuNi(CO) n -(n = 2-4), MNi(CO) 3 -(M = Mg, Ca, Al), MNi(CO) n -(M = Ti, Zr, Hf; n = 3-7), AgNi(CO) n -(n = 2, 3), V 2 Ni(CO) n -(n = 6-10
), and VNi(CO) n -(n =2-6) [START_REF] Zhiling | Structural evolution of homoleptic heteronuclear copper-nickel carbonyl anions revealed using photoelectron velocity-map imaging[END_REF][START_REF] Xie | Photoelectron velocity-map imaging and theoretical studies of heteronuclear metal carbonyls MNi(CO) 3 -(M=Mg, Ca, Al)[END_REF][START_REF] Zou | Probing the bonding of CO to hereronuclear grouip 4 metal-nickel clusters by photoelectron spectroscopy[END_REF][START_REF] Zhiling | Observation of promoted C-O bond weakening on the heterometallic nickel-silver: photoelectron velocity-map imaging spectroscopy of AgNi(CO) n[END_REF][START_REF] Zhang | Photoelectron velocity-map imaging and theoretical studies of heterotrinuclear metal carbonyls V 2 Ni(CO) n -(n=6-10)[END_REF][START_REF] Yuan | Photoelectron velocity map imaging spectroscopic and theoretical study of heteronuclear vanadium-nickel anions VNi(CO) n -(n=2-16)[END_REF] . In these works, the electron affinities, the C-O stretching modes, and the vertical detachment energies are measured (all the parameters are not determined in each work).

The purpose of the present work is to extend the study of the reactivity of the neutral homonuclear dimer to heteronuclear dimer. We report for the first time the reaction of the PdTi heterodimer with CO in solid argon and the formation of PdTi(CO) n (n=1-3) and Pd x Ti y (CO) 2 , neutral molecules. Each metal is vaporized separately and the PdTi formation occurs in the matrix. We investigated these carbonyl complexes using infrared spectroscopy combined with density functional calculations to obtain the geometrical and electronic properties. The system Pd + Ti has been chosen for the fact that the reactivity of the Ti+CO [START_REF] Chertihin | Infrared Spectra of the Reaction Products of Laser-Ablated Titanium Atoms and Oxides with Carbon Monoxide in Solid Argon[END_REF][START_REF] Zhou | Infrared Spectra and Density Functional Calculations of Small Vanadium and Titanium Carbonyl Molecules and Anions in Solid Neon[END_REF][START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF][START_REF] Souvi | Neon-matrix spectroscopic and theoretical studies of the reactivity of titanium dimer with diatomic ligands: comparison of reactions with nitrogen and carbon monoxide[END_REF] and Pd+CO 9,10,23 systems has been examined in Ar or Ne matrix giving a first approach to the spectral analysis.

EXPERIMENTAL AND COMPUTATIONAL DETAILS

The experimental setup for matrix isolation FTIR spectroscopic investigation has been described in detail previously [START_REF] Danset | Mid-and near-IR electronic absorption spectrum of CoO isolated in solid neon. Vibronic data for low-lying electronic states[END_REF] . Briefly, the samples were prepared by co-condensing Ti and Pd vapors and CO-Ar mixtures (0. In general, after deposition times varying between 15 and 90 min, infrared spectra of the sample were recorded at 0.1 cm -1 resolution in the transmission-reflection mode between 4000 and 70 cm -1 using a Bruker 120 FTIR spectrometer and suitable combinations of CaF 2 /Si, KBr/Ge, Si/Mylar(6m beamsplitters with either liquid N 2 -cooled InSb or narrow-band HgCdTe photodiodes or a liquid He-cooled Si-B bolometer fitted with cooled bandpass filters. Bare mirror backgrounds were used as references for processing the sample spectra. Also, absorption spectra in the near, mid-and far infrared were collected on the same samples through either CaF 2 , CsI or polyethylene windows mounted on a rotatable flange separating the interferometer vacuum (10 -3 mbar) from the cryostatic cell (10 -7 mbar). The spectra were subsequently subjected to baseline correction to compensate for infrared light scattering and interference patterns. The sample was next either annealed in order to increase the abundance of aggregates (if necessary)

or irradiated at various wavelength using broad or narrow band-pass filters with a 200 W Hg-Xe highpressure arc lamp. The most significant results only will be described below.

Molecular geometries were optimized using the DFT B3LYP method with a correlation consistent basis set of triple-zeta quality (cc-pVTZ) for C, O and Ti atoms and the cc-pVTZ-PP basis set with extended relativistic pseudo-potentials for Pd obtained from the Basis Set Exchange (BSE) software and the EMSL Basis Set Library. [START_REF] Feller | The Role of Databases in Support of Computational Chemistry Calculations[END_REF][START_REF] Schuchardt | Basis Set Exchange: A Community Database for Computational Sciences[END_REF] All calculations have been performed with the Gaussian 09 quantum chemical package. [START_REF] Frisch | Revision D.01[END_REF] Vibrational frequeny analysis has been done within the harmonic approximation. The nature of chemical bonds between metal-metal and metal-ligand has been investigated using the QTAIM topological approach [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] with the AIMALL software. 40

EXPERIMENTAL RESULTS

Palladium and titanium vapor were condensed with relatively dilute mixtures of CO in argon (0.1%) at 20 K or at 12 K but at higher CO concentration (between 0.5 and 2%). In the Figure 1, the first spectrum presents the result for the Ti+CO reaction (Figure 1a). We observe a band at 1769.1 cm -1 assigned to Ti 2 (CO) 2 and some bands assigned to Ti x (CO) y species [START_REF] Chertihin | Infrared Spectra of the Reaction Products of Laser-Ablated Titanium Atoms and Oxides with Carbon Monoxide in Solid Argon[END_REF] . For the Pd+CO reaction (Figure 1b), we observe several bands, two at 1856.5 and 1867.9 cm -1 assigned to Pd 2 CO (br), and a band at 1729.4 cm -1 assigned to Pd 3 CO [START_REF] Alikhani | Spectra and structures of the Pd m CO : An Infrared Matrix Isolation and Density Functional study[END_REF] . For Pd and Ti vaporized together with CO (Figure 1c), and by comparison with Fig. 1a and 1b, we detect five new absorptions at 2009.3, 1908.4, 1808.9, 1790.7, 1745.3, and a broad one at 1718.9 cm -1 (Table 1). The new absorptions shown in figure 1.c are indicated by arrows. A series of experiments were performed at 12 K using different CO concentrations (ranging from 0.5% to 2%) with constant concentration of metal. At low CO concentration (0.5%), we observed three absorptions in the CO stretching region (Figure 2a). When we increase the concentration to 1%, the bands observed in Figure 1c appear. Between these two spectra, the intensity of the bands at 1908.4 and 1856.9 cm -1 (Pd 2 CO) increase by factor 2. With a CO concentration of 2%, we observed that the intensity of the band at 1908.4 cm -1 increase by factor 2, but the bands at 1745.3 and 1790.7 cm -1 increase at about factor 4, the band at 1808.9 cm -1 increases by factor 8, and the other two at 1769.1 (Ti 2 (CO) 2 ) and 1718.9 cm -1 by factor 3. This suggests that the molecules which have signatures at 1808.9, 1790.7, 1745.3 and 1718.9 cm -1 have a steochiometry in CO greater than the species observed at 1908.4 cm -1 . Accompanying these absorptions in the C-O stretching region, a much weaker absorption in near-infrared region at 3607.2 cm -1 can be correlated to the strong band at 1808.9 cm -1 , the PdTi(CO) 3 molecule. A series of experiments were performed with a constant concentration of CO of 2% but with different metal concentrations. When the palladium flow rate is increasing by a factor of 2, with the same Ti rate, we observed that the intensities of the bands at 1908.4, 1808.9 and 1745.3 cm -1 are multiplied by 2 (Figure 3a and 3b). On the other hand, by decreasing the titanium flow rate by a factor of 2, with the same Pd rate, we observed that the intensities of the bands at 1908.4, 1808.9 and 1745.3 cm -1 are divided by 2 (Figure 3b and3c). This suggests that these bands belong to molecules that contain one Ti atom and one Pd atom. For the bands at 1790.7 and 1718.9 cm -1 , we can find other conditions (CO concentration, temperature) for which the intensity variation of these bands does not have a linear dependence with respect to the titanium or the palladium concentration. These species probably involve more than one Ti or Pd atom, but no definitive identification is possible. For this reason, these bands appear in the Table 1 with the assignment Pd x Ti y for the metals. Isotopic substitutions were carried out using [START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] Irradiations at different wavelengths in the visible and near-UV were carried out. Only one in the range 450-600 nm giving rise significant effects will be described below. The Pd and Ti concentration remains high, that of CO in Ar is 2/1000. As photoconversion processes are noticeably dependent on the initial state, the results reported below describe irradiation performed just after deposition. The Figure 5 Distances are in Å and angles in degrees.

For the PdTi-polycarbonyl compounds, we optimized six structures for PdTi(CO) 2 and one structure belonging to the C 3v group for PdTi(CO) 3 . The singlet structure in the latter case is calculated to be above the triplet one by 3.8 kcal/mol. The PdTi(CO) 2 and PdTi(CO) 3 compounds are predicted to have spin triplet ground states with C 2v and C 3v symmetry, respectively (Figure 8). All the optimized structures are reported in the Supporting Information. Binding energy corrected for the zero-point energy has been calculated to be -21.2 and -32.0 kcal/mol for PdTi(CO) 2 and PdTi(CO) 3 with respect to E(PdTiCO Ti-eo)+E(CO) and E(PdTi(CO)2)+E(CO). The energy gain relative to the addition of a third carbonyl is most important than that for the first and second one. However, it must be remembered that this energy shift reflects the global geometrical variation in the structure of the studied compounds. For instance, the C-O bond length (just like to Ti-C distance) increases as PdTiCO Pd-eo < PdTiCO Ti-eo < PdTi(CO) 3 < PdTi(CO) 2 , while the Ti-Pd distance varies as PdTiCO Ti-eo < PdTiCO Pd-eo < PdTi(CO) 2 < PdTi(CO) 3 .

Nature of chemical bonding

According to the QTAIM, the positive values of the Laplacian at the bond critical point (BCP) are associated with closed-shell interactions, whereas, ∇ 2 ρ < 0, indicates shared interactions (covalent bonds). In addition, the sign and magnitude of the total electronic energy density at the BCP, H(r), is usually used as another criterion to evaluate the importance of sharing of electrons (when H(r) < 0). In Table 2 A multivariate simultaneous analysis of the variation of two parameters -namely distance and electron density at BCP -for each chemical bonds evolved in compounds, allows us not only to understand the variation of the force constant but also to highlight the distribution of vibrational energy within various bonds. To illustrate such an analysis, we compare the two monocarbonyl species, PdTiCO Pd-eo and PdTiCO Ti-eo In going from Pd-eo to Ti-eo, we note that the Pd-Ti distance decreases while the C-O bond length increases slightly. This is consistent with the change in the electron density on the Pd-Ti and C-O bond critical points. It is therefore expected that the Pd-Ti vibrational frequency is higher in PdTiCO Ti-eo than in PdTiCO Pd-eo. In a similar way, the C-O vibrational frequency is found to be greater in PdTiCO Pdeo than in PdTiCO Ti-eo (see Figure S1). These opposite trendsfor both interatomic distances and vibrational frequencies -make these two species remain substantially isoenergetic.

One can easily note that the presence of a BCP between two metal centers in all the studied compounds, even though its electron density slightly decreases when adding a carbonyl ligand. The bonding between C atom and metal center decreases in going from monoligand to triligand compounds leading to a quasi-identical electron density at Pd -C and Ti -C BCPs in the triple -bridge PdTi(CO) 3 species ( -0.076 e/a 0 3 ). All the observed structures have a triplet spin state. The QTAIM analysis indicates that both alpha electrons are almost localized on the Ti atom. The addition of three carbonyls to the heterodimer could not pairing two single electrons to give a singlet ground state. In contrast, interaction between one carbonyl ligand with the palladium dimer (triplet ground state) leads to a -bridged compound at the singlet state. The localization of one alpha electron per Pd atom makes the spin pairing in the Pd 2 (CO) easy to achieve. 23

Compounds

Vibrational analysis and comparison with calculations

All the experimentally observed vibrational frequencies for various isotopic substitutions as well as the corresponding DFT calculated harmonic wavenumbers are reported in Table 3. However, a complete listing of all the calculated frequencies for all the studied compounds is provided in the Supporting information.

In our experiments, no band has been detected in the far infrared region. have been assigned to PdTiCO Pd-eo, PdTiCO Ti-eo, PdTi(CO) 2 , and PdTi(CO) 3 , respectively, on the basis of concentration effects, isotopic substitution and DFT theoretical predictions. Compared to the free CO complex, the calculated red-shifts are 128, 184, 326, and 400 cm -1 for the PdTiCO Pd-eo, PdTiCO Ti-eo, PdTi(CO) 3 , and PdTi(CO) 2 molecules, respectively, which are close to the experimental ones, 129, 230, 329, and 393 cm -1 . Furthermore, the calculated frequency shifts due to the 12 C/ 13 C and [START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O/ [START_REF] Xu | Infrared-Spectroscopic and Density-Functional-Theory Investigations of the LaCO, La 2 [η 2 (μ 2 -C,O)], and c-La 2 (μ-C)(μ-O) Molecules in Solid Argon[END_REF] O isotopic substitutions agree well with the experimental values and give strong support for the assignation of these bands.

For the PdTi(CO) 3 molecule, we also observe a weak band at 3607.2 cm -1 . The assignment of this band to an overtone can be derived from the position and isotopic shift of the observed fundamental. The 3607.2 cm -1 band has a 12 CO/ 13 CO frequency shift of 79.1 cm -1 , almost twice (39.8 cm -1 ) the one obtained for the frequency at 1808.9 cm -1 . We can thus deduce the anharmonicity of the C-O stretching vibrational frequency (5.4 cm -1 ) which is similar to the typical value for an asymmetric stretching overtone of a transition metal tricarbonyl [START_REF] Manceron | Infrared spectrum and structure of Ni(CO) 2 . A matrix isolation and DFT study[END_REF] . For these reasons, we attributed the 3607.2 cm -1 band to the asym 2 CO of PdTi(CO) 3 .

As shown in the experimental results, the PdTi heterodimer reacts spontaneously with CO to form two PdTi-carbonyl coumpounds: PdTiCO and TiPdCO. Visible irradiation in the 450-600 nm range provides sufficient energy for the PdTiCO Ti-eo molecule to overcome the reaction barrier to give the PdTiCO Pd-eo molecule (Fig. 7). The confirmation of this interconversion is obtained through the kinetic study. Our DFT calculations revealed that this isomerization reaction was 17 kcal/mol, Our DFT calculations show that the energy barrier between PdTiCO and TiPdCO is 17 kcal/mol, and the relative energy values of these two molecules are the same (-24.7 kcal/mol), and the intensities of the CO stretching vibration are close (1254 and 1100 km/mol for PdTiCO Ti-eo and PdTiCO Pd-eo, respectively, Supporting Information). With the same relative energy, the PdTiCO Ti-eo and PdTiCO Pd-eo molecules must be formed in the same amounts in the sample, but the experimental result is different than calculated one since the experimental CO intensity for PdTiCO Ti-eo is 2.5 times higher than for PdTiCO Pd-eo, and the calculated ratio is 1.14 (1254/1100). This experimental observation can be explained by the absence of bridged structure (PdTiCO -bridge) in our experiment. Indeed, the energy barrier between transition state (TS12) and the PdTiCO bridge structure is nearly negligible (1 kcal/mol) it seems that this barrier is not high enough to allow this structure to be stabilized in the Ar matrix, which turns into PdTiCO Ti-eo (Figure 7). We can assume that in the entrance of reaction, the PdTiCO Ti-eo, PdTiCO Pd-eo and PdTiCO -bridge molecules are formed in a same amount, and since all the PdTiCO -bridge molecules turn into PdTiCO Ti-eo molecules, the theoretical intensity ratio between PdTiCO Ti-eo and PdTiCO Pd-eo should be 21.14=2.3, in agreement with the experimental one.

Using laser ablation technique for producing Ti atoms, Andrews et al. observed TiCO molecule in excess argon [START_REF] Marzouk | A Combined Experimental and Theoretical Study of the Ti 2 + N 2 O Reaction[END_REF] , but by thermal evaporation technique, TiCO is not observed [START_REF] Zhang | Infrared Photodissociation Spectroscopy of Mass-Selected Heteronuclear Iron-Copper Carbonyl Cluster Anions in the Gas Phase[END_REF] , and our results on the Ti + CO reaction are in agreement with this late observation. In this case it is impossible to form S1 from the reaction TiCO + Pd. PdTiCO Ti-eo, PdTiCO -bridge, and PdTiCO Pd-eo can be only formed from diatomic Pd-Ti with CO molecule in the excess argon matrix. In fact, with a sample at low CO/Ar concentration, 1/1000, we observe the formation of a small amount of PdTiCO Ti-eo and PdTiCO Pd-eo at 12 K. Annealing the sample at 20, 26 and 30 K after deposition allows the Ti and Pd atoms to diffuse in the matrix. After each annealing we observed the growth of the CO bands for the two isomers. This observation means that PdTi reacts with CO in the ground state.

Since Pd 2 CO end-on and PdTiCO Pd-eo have a similar structure, we can compare these two

CONCLUSION

The study of the Pd + Ti+ CO reaction was performed by coupling matrix isolation FTIR spectroscopy and DFT calculations. New infrared absorption data have been observed for PdTi(CO) n (n=1-3) molecules.

The intense bands of the CO stretching appear in 2010-1700 cm -1 range and another absorption is observed in the near-infrared around 3600 cm -1 for PdTi(CO) 3 . Our technique of sublimation of Ti and Pd atoms from two filaments heated separately allowed the formation of molecules from the ground state reagents. The experimental data obtained in argon, with the help of isotopic effects, are fully supported by theoretical calculations. The most relevant structural and energetic data for the lowest lying structures have been calculated for the PdTi(CO) n ( n=1-3), studied molecules. Selective irradiation in the 450-600 nm range leads to conversion between two isomers distinguished by the stretching frequency of the diatomic CO:

PdTiCO Ti-eo (ν CO =1908.4 cm -1 ) and PdTiCO Pd-eo (ν CO =2009.3 cm -1 ). Finally, unlike to the singlet bridged Pd 2 CO the Ti atom carrying two single -electron is bonded to the Pd atom via a bond critical point within the PdTi(CO) 1-3 molecules.

Figure 1 .

 1 Figure 1. Infrared spectra of titanium, palladium, and palladium-titanium CO reactions after deposition at 12

Figure 2 .

 2 Figure 2. Infrared spectra of palladium-titanium carbonyls after deposition at 12 K: a CO concentration

Figure 3 .

 3 Figure 3. Infrared spectra of palladium-titanium carbonyls after deposition at 12 K: a metal concentration

1 )Figure 4 .

 14 Figure 4. Infrared spectra for PdTiCO (A), PdTi(CO) 3 (B), PdTi(CO) 2 and Pd x Ti y (CO) 2 (C) with a Pd/Ti/Ar concentration of 0.1/0.6/1000 at 20 K. (a) 12 C 16 O, (b) 13 C 16 O and (c) 12 C 16 O+ 13 C 16 O. In C, (c) corresponds

Figure 5 .

 5 Figure 5. Infrared spectra in the 1900-2012 cm -1 region for a Pd/Ti/CO/Ar =0.3/0.3/2/1000 sample

Figure 6 .Figure 7 .

 67 Figure 6. Time development of the areas of the bands of PdTiCO Pd-eo (▲) at 1908.4 cm -1 and of PdTiCO Ti-eo (■) at 2009.3 cm -1 versus the irradiation duration at λ=[450,600] nm.

Figure 8 .

 8 Figure 8. Optimized geometrical parameters (distance in Å and angle in degrees) and ZPE corrected

  are gathered the topological descriptors of bonding in the compounds studied in this work. One can easily note existence of a bond path for C -O, Pd -C, Ti -C and Ti -Pd pairs of atoms. The Laplacian of the electron density is always positive indicating a closed-shell interaction between these bonded atoms with partially covalent character (H(r) < 0). The electron density at the C-O BCP ranges from 0.454 e/a 0 3 in the PdTi(CO) 2 to 0.505 e/a 0 3 in free CO. The negative value of the energy density at the C-O BCP ( -0.88) evidences the polar covalent character of the C-O chemical bonding. The electron density being a local property, its change from one compound to another could be used actually as a measure of the variation of a local spectroscopic property such as force constant for example. Consequently, we expect that the C-O vibrational frequency varies in the same ordering as the electron density at the C-O bond critical point: free CO > PdTiCO Pd-eo > PdTiCO Tieo > PdTi(CO) 3 > PdTi(CO) 2 . That means that the greatest red-shift of the C-O vibrational frequency is expected to be observed for the PdTi(CO) 2 compound. Furthermore, the variation of the electron density at the C-O BCP well correlates with the variation of the C-O bond length with a correlation coefficient close to one (R 2  0.998).

  molecules. Indeed, the Pd-C-O and M-Pd-C (M=Ti or Pd) angles, the C-O length, and the CO frequency are similar for both molecules: 169° versus 161°, 116° versus 125°, 1.15 versus 1.14 Å, 2015 versus 2009 cm -1 , for Pd 2 CO versus PdTiCO Pd-eo, respectively. However, the Pd-C bond length makes the distinction between these two molecules: it changes from 1.87 Å in Pd 2 CO to 1.95 Å in PdTiCO Pd-eo. This lengthening implies a weakening of the Pd-C bond.

  OTi 2 N 2 . Irradiation in the near infrared region results to the N≡N bond breaking and then the formation of a new molecule, OTiNTiN 25 .

	Concerning the heteronuclear carbonyl molecules, many works have been done on bimetallic carbonyl
	anions and cations in the gas phase. Mass-selected CuFe(CO) n	-(n = 4-7), FeM(CO) 8	+ (M = Co, Ni and Cu),
	MCu(CO) 7	+ (M = Co and Ni), FeZn(CO) 5	+ , and CoZn(CO) 7	+ molecules have been studied by infrared

. Another work has experimentally shown that the Ti dimer spontaneously reacts with N 2 O molecule leading to the formation of an adduct complex,

Table 1 . Experimental vibrational frequencies (in cm -1 ) and isotopic shifts for the observed molecules molecules

 1 assignment 12 C 16 O 13 C 16 O ∆ν a 12 C 16 O + 13 C 16 O

	12 C 18 O	∆ν
	b

a ∆ν is the difference between the 12 C 16 O frequency and the

[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF]

C 16 O or 12 C 18 O frequency b Only the new bands obtained with the 12 C 16 O + 13 C 16 O mixture are reported

  C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O,[START_REF] Clemmer | Kinetics of excited-state titanium(a 5 F) depletion by nitric oxide, oxygen, nitrous oxide, and nitrogen[END_REF] C[START_REF] Xu | Infrared-Spectroscopic and Density-Functional-Theory Investigations of the LaCO, La 2 [η 2 (μ 2 -C,O)], and c-La 2 (μ-C)(μ-O) Molecules in Solid Argon[END_REF] O, and a 12 C 16 O +[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O mixture. The results are presented in Figure4and Table1. The band at 1908.4 cm -1 shifts to 1866.3 and 1863.9 cm -1 when 12 C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O is replaced by[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O and 12 C 18 O, respectively. With a 12 C 16 O+ 13 C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O mixture (Figure4.A) no further bands appeared which means this molecule contains a single CO. The band at 1808.9 cm -1 shifts to 1769.1 and 1765.9 cm -1 when 12 C 16 O is replaced by[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] C 16 O and 12 C 18 O, respectively, and with a 12 C 16 O + 13 C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O mixture, two further bands appear at 1790.0 and 1778.2 cm -1 (Figure4. B). These two supplementary bands assigned the presence of three carbonyl groups in this molecule. These observations will be discussed in more details in the section devoted to the vibrational analysis. The bands at 1790.7 cm -1 shifts to 1750.7 and 1748.8 cm -1 when 12 C 16 O is replaced by[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] C 16 O and 12 C 18 O, respectively. With the 12 C 16 O + 13 C 16 O mixture, the corresponding spectral region is congested, essentially by PdTi(CO) 3 , and no absorption can be detected. It is not possible to conclude about the number of carbonyls in this molecule. On the other hand, the bands at 1745.3 and 1718.9 cm -1 shift to 1706.6 and 1680.2 cm -1 when 12 C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O is replaced by[START_REF] Matsuda | On the copper oxide neutral cluster distribution in the gas phase: Detection through 355 nm and 193 nm multiphoton and 118 nm single photon ionization[END_REF] C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O and shift to 1704.9 and 1679.5 cm -1 when 12 C 16 O is replaced by 12 C 18 O, respectively. With a 12 C 16 O + 13 C[START_REF] Xu | cyclo-Ti 3 [η 2 (μ 2 -C,O)] 3 : A Side-on-Bonded Polycarbonyl Titanium Cluster with Potentially Antiaromatic Character[END_REF] O mixture two further bands appeared at 1719.9 and 1689.8 cm -1 (Figure4. C), which is appropriate for the presence of two carbonyl groups in these molecules.

Table 2 . Some local topological properties on the bonded atoms in the studied compounds. All parameters are given in atomic units.

 2

	CO	C -O	0.505, 0.459, -0.941
	TiPd	Pd -Ti 0.103, 0.330, -0.035
		C -O	0.487, 0.350, -0.899
	PdTi(CO)
		Pd -C	0.135, 0.398, -0.057
	Bent Pd end-on
		Pd -Ti 0.062, 0.176, -0.015
		C -O	0.482, 0.344, -0.886
	PdTi(CO)
		Ti -C	0.081, 0.321, -0.015
	Bent Ti end-on
		Pd -Ti 0.107, 0.334, -0.038
	PdTi(CO) 2	C -O	0.454, 0.108, -0.821

Table 3 . Comparison of the experimental frequencies with the theoretical harmonic vibrational data (in cm -1 ) of the observed molecules with the isotopic shifts.

 3 It is in line with our theoretical data that infrared intensities are very small in the far infrared region (see Supporting information). Accounting for the detectivity of the argon matrix setup, only modes with intensities larger than 35 km/mol are likely to be observed. Over all the calculated frequencies for PdTiCO (Pd-eo), PdTiCO (Ti-eo), PdTi(CO) 2 , and PdTi(CO) 3 , only two vibrational frequencies have been calculated to have an IR Intensity greater than 35 km/mol: a band located at 270 cm -1 band (in-plane Pd-C-O bending) for PdTiCO (Pd-eo) and another one at 378 cm -1 (in-phase out-of-plane Pd-C-O bending) for PdTi(CO) 2 , for which the IR intensities are 47 and 49 km/mol respectively. This spectral region (200 -400 cm -1 ) is congested by strong absorptions at 310 and 263 cm -1 which belonged to Pd(CO) 4 and Pd(CO) 2 , 10 respectively. Only the new bands obtained with the 12 C 16 O + 13 C 16 O mixture are reported

	molecules	assignment		12 C 16 O 13 C 16 O	∆ν	12 C 18 O	∆ν
	PdTiCO	 CO	Exp 2009.3 1963.9 45.4 1963.1 46.2
	Pd-eo
			DFT	2083	2035	48	2033	50
	PdTiCO	 CO	Exp 1908.4 1866.0 42.4 1863.8 44.5
	Ti-eo
			DFT	2027	1982	45	1978	49
	PdTi(CO) 3	 CO asym	Exp	1808.9 1769.1 39.8 1765.9 43.0
			DFT	1907	1864	43	1861	46
	PdTi(CO) 2	 CO asym	Exp 1745.3 1706.6 38.7 1704.9 40.4
			DFT	1885	1843	42	1840	45
	As discussed above, four main observed bands, located at 2009.3, 1908.4, 1745.3, and 1808.9 cm -1 ,

a

THEORETICAL CALCULATIONS

Structural and energetic analyses

Quantum chemical calculations have been performed to determine the molecular structures and to support the vibrational frequency analysis of the studied metal-carbonyl clusters. Overall, we calculated three structures for the PdTi(CO) monocarbonyl, 6 structures for the PdTi(CO) 2 dicarbonyl and one structure for the PdTi(CO) 3 tricarbonyl compounds. All the cartesian optimized coordinates are reported in the Supporting Information.

Three bonding modes for PdTi(CO) have been investigated: bent Pd-end-on (Pd-eo), bent Ti-end-on (Ti-eo) and -bridge (-br). These three structures are connected to each other by two transition states (Figure 7). Three minima are labeled as to S1 (bent Ti-end-on), S2 (-bridge) and S3 (Pd-end-on). The binding energies reported on Figure 7 are calculated with respect to free CO ( 1 Σ, r CO = 1.126 Å), and the PdTi ( 3 Σ, r PdTi = 2.197 Å) molecules including the zero-point-energy. On the ground of the energetic results, two bent end-on structures (S1 and S3) are isoenergetic (D 0 = -24.7 kcal/mol), but the -bridge structure (S2) is slightly less stable than two bent structures by about of 5 kcal/mol. We should note that the three structures of PdTi(CO) optimized at the singlet state were found significantly above the triplet states (see the Supporting Information). Two transition states (TS12 and TS23) were found which connect S1 to S2, and S2 to S3, respectively. We note that the S2 conversion to S1 structure occurs by overcoming a small energetic barrier (less than 1 kcal/mol), while the barrier height between S2 and S3 is calculated to be large enough ( 12 kcal/mol) to prevent any thermal conversion at low temperature. Consequently, the triplet S1 and S3 structures corresponding to the global minima are actually candidates to be experimentally observed in cold rare gas matrix.

Supporting Information

Correlation between electron density at BCPs (in a.u.) and CO and PdTi frequencies (in cm -1 ) from the calculated molecules. (Figure S1); The cartesian coordinates and the harmonic B3LYP frequencies (cm -1 ) and intensities (km/mol) for the PdTi(CO) n (n=1-3) molecules are reported for all the studied structures.

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TOC Graphic