Ahmed Omran

Nikolay Nesterenko

Valentin Valtchev
email: valentin.valtchev@ensicaen.fr

Revealing Zeolites Active Sites Role as Kinetic Hydrate Promoters: Combined Computational and Experimental Study

Keywords: Zeolitic ice, Acidic zeolites, Kinetic hydrate promoters, DFT, Promotion mechanism, Methane hydrate, Nucleation sites, Energy storage

Clathrate hydrates are emerging as a novel storage medium for safe and compact methane storage. However, their industrial-scale applicability is hindered by relatively lower gas uptake and sluggish formation kinetics. In this study, we have employed zeolites with acidic (H-Y, FAU-type) and basic (Na-X, FAU-type) surface properties as kinetic hydrate promoters (KHPs). The impact of physical parameters as pressure and the gas-to-liquid ratio has also been studied. In a combined experimental and computational study, we assessed the performance of the two types of zeolites in different concentrations and pressures for binary CH 4 -THF clathrate hydrate synthesis in a non-stirred configuration. The kinetic study results showed that the acidic zeolite (H-Y) exhibited superior performance over the basic one (Na-X), reaching its optimum at 0.5 wt% zeolite, which agreed well with the DFT calculations. The methane conversion reached 94.25% at this concentration and a relatively mild pressure (6 MP). The induction time and t 90 (time to reach 90% of final gas uptake) were reduced by 35% and 31%, respectively. Our results open the door for a better understanding of the role of acidic zeolites as possible environmental benign KHPs that can help the utilization of water as a medium for green energy storage and transportation.

Introduction

The international direction toward cleaner energy resources and the increasing world population have created a strong demand for natural gas as energy source and feed for the petrochemical industry. Moreover, the natural gas is considered a "transition fuel" with cleaner-burning that represents a good compromise between conventional fossil fuels such as coal and oil. Thus there is an increasing demand for safe and long-term methane storage technology [START_REF] Hafezi | Global natural gas demand to 2025: A learning scenario development model[END_REF][START_REF] Omran | Mechanistic insights for dry reforming of methane on cu/ni bimetallic catalysts: DFT-assisted microkinetic analysis for coke resistance[END_REF] . There are several methods and technologies to store natural gas, and each has its advantages and disadvantages. Apart from storing natural gas in underground inventories, the main natural gas storage and transportation technologies are CNG (compressed natural gas), LNG (liquified natural gas), ANG (adsorbed natural gas), and SNG (solidified natural gas). SNG is a new technology for safe, eco-friendly, reversible, compact, and economic methane storage that can be suitable for both large reservoirs and discrete, small, inaccessible, or remote gas resources [START_REF] Gudmundsson | Storing natural gas as frozen hydrate[END_REF][START_REF] Prajwal | Evaluating methane storage targets: From powder samples to onboard storage systems[END_REF][START_REF] Veluswamy | A review of solidified natural gas (SNG) technology for gas storage via clathrate hydrates[END_REF][START_REF] Pellegrini | LNG technology: The weathering in above-ground storage tanks[END_REF][START_REF] Shin | Design of a boil-off natural gas reliquefaction control system for LNG carriers[END_REF] . Despite these advantages, the applications of hydrate-based technology on an industrial scale are limited due to the slow kinetics, poor heat transfer, gas diffusion limitation, lower storage capacity in the presence of promoter, and scale-up challenges. Promoters are additives added to either catalyze the kinetics of hydrate formation (kinetic hydrate promoter or KHP) or reduce the P-T requirements (thermodynamic hydrate promoter or THP). Understanding the kinetic model of hydrate formation is essential for developing potential applications of hydrates [START_REF] Partoon | Effect of Mixed Thermodynamic and Kinetic Hydrate Promoters on Methane Hydrate Phase Boundary and Formation Kinetics[END_REF] . However, it is challenging to model the kinetics as it combines a chemical reaction with phase transition. Above all, it is crucial to increase the rate of gas hydrate formation for feasible gas storage and separation process. The crystallization process can be divided into two main steps: nucleation and growth. In the first step, a crystalline phase appears gradually directly from the liquid state (homogeneous nucleation) or occurs at nucleation sites of foreign particles or surfaces (heterogeneous nucleation) [START_REF] Bergeron | Reaction rate constant of methane clathrate formation[END_REF] . This step is usually slow, distinguished by its stochastic nature [START_REF] Pan | Progress in use of surfactant in nearly static conditions in natural gas hydrate formation[END_REF] . After adsorption of guest molecules in the liquid phase, it is enclathrated within the hydrate precursors, and nucleation then can be detected from the simultaneous rapid pressure decrease and temperature increase due to the exothermic reaction. The time elapsed until the appearance of a detectable volume of hydrate phase or, equivalently, until the consumption of a detectable number of gas molecules is known as induction time (or lag time) [START_REF] Sloan | Clathrate Hydrates Nat. Gases[END_REF] . In the second step, the crystal growth is distinguished by a rapid increase in the particle size up to the full crystalline form. This step is immediate, and the gas is more concentrated in the hydrate cages than those in the vapor [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] .

Well-control of growth step enhances the gas diffusion that may be hindered by'hydrate film' formation at the liquid-gas interface [START_REF] Veluswamy | A review of solidified natural gas (SNG) technology for gas storage via clathrate hydrates[END_REF][START_REF] Taylor | Macroscopic investigation of hydrate film growth at the hydrocarbon/water interface[END_REF] .

To solve the problem of slow kinetics, KHP is added to enhance the rate of hydrate formation without influencing thermodynamics. In other words, the hydrate structure, as well as the P-T conditions of hydrate formation, are not affected. This kind of promoters is predominated by surfactants with all its classes (anionic, cationic and non-ionic) [START_REF] Nasir | A review on the role and impact of various additives as promoters/ inhibitors for gas hydrate formation[END_REF] . The most common example of those surfactants is the anionic surfactant sodium dodecyl sulfate (SDS) which has extensively been studied [START_REF] Najibi | Experimental investigation of methane hydrate formation in the presence of copper oxide nanoparticles and SDS[END_REF][START_REF] Pan | Effect of silica sand size and saturation on methane hydrate formation in the presence of SDS[END_REF][START_REF] Deng | New Insights into the Kinetics and Morphology of CO 2 Hydrate Formation in the Presence of Sodium Dodecyl Sulfate[END_REF] . In a concentration close to or above its critical micelle concentration (CMC), it is observed that SDS increased the hydrate formation rate significantly compared to other surfactants [START_REF] Zhong | Surfactant effects on gas hydrate formation[END_REF] . The surfactant micelles increase methane solubility and thus initiating the nucleation [START_REF] Deng | New Insights into the Kinetics and Morphology of CO 2 Hydrate Formation in the Presence of Sodium Dodecyl Sulfate[END_REF] . Moreover, Zhang et al. explained that SDS increases the hydrate particles' surface area and the gas-liquid interfacial area while reducing surface tension [START_REF] Zhang | Kinetics of methane hydrate formation from SDS solution[END_REF] . Increasing the carbon chain length of sodium alkyl sulfates does not change the kinetics of the reaction, but requires much less surfactant concentration [START_REF] Kwon | Synthesis of anionic multichain type surfactant and its effect on methane gas hydrate formation[END_REF][START_REF] He | Surfactant-based Promotion to Gas Hydrate Formation for Energy Storage[END_REF] . However, the hydrate-based process suffers from foam formation, especially during gas recovery (hydrate dissociation) in pilot-scale laboratory experiments [START_REF] Bhattacharjee | Kinetic promotion of methane hydrate formation by combining anionic and silicone surfactants: Scalability promise of methane storage due to prevention of foam formation[END_REF][START_REF] Pandey | Alleviation of Foam Formation in a Surfactant Driven Gas Hydrate System: Insights via a Detailed Morphological Study[END_REF][START_REF] Pang | Experimental study on the scale-up effect of gas storage in the form of hydrate in a quiescent reactor[END_REF] . Adding this disadvantage to the environmental concerns of surfactant separation or degradation, makes the use them not very attractive for a large industrial scale application. To overcome those drawbacks, other KHPs are suggested, such as porous materials.

Porous materials such as carbon forms (such as activated carbon and carbon nanotubes) and silica in different shapes (silica gel, silica sand, hollow silica, and nano-silica), zeolites, and even MOFs were used to promote hydrate formation [START_REF] Borchardt | Methane Hydrate in Confined Spaces: An Alternative Storage System[END_REF][START_REF] Denning | Promoting Methane Hydrate Formation for Natural Gas Storage over Chabazite Zeolites[END_REF] . In general, these materials can be utilized in two different ways: (1) in low concentrations as nucleation sites for heterogeneous nucleation to reduce the induction time 27 and (2) as host for hydrate using the confinement effect to enable mild hydrate formation conditions [START_REF] Linga | Enhanced rate of gas hydrate formation in a fixed bed column filled with sand compared to a stirred vessel[END_REF] . Each of these two uses has its advantages and disadvantages. The use of porous materials as nucleation sites is relatively cheaper, easier to handle [START_REF] Mimachi | Effect of Long-Term Storage and Thermal History on the Gas Content of Natural Gas Hydrate Pellets under Ambient Pressure[END_REF] , and has higher overall gravimetric storage. However, it may suffer from slower kinetics and relatively higher thermodynamic requirements. On the other hand, the use of porous materials as a confinement medium has been proved to reduce the driving force and increase the water-to-hydrate conversion [START_REF] Both | Gas hydrates in confined space of nanoporous materials: New frontier in gas storage technology[END_REF] . However, the high mass of porous material and complicated packing (or pelletizing) process results in a storage capacity loss [START_REF] Peng | Methane storage in metal-organic frameworks: Current records, surprise findings, and challenges[END_REF] . Recently, pelletizing natural has been considered as a promising option for SNG transportation in many pilot plants. While they provide more flexiblibilty to transfer different quantities of solid hydrates, they add capital cost overhead due to the associated energy consumption, gas recycling and pellet dewatering processes [START_REF] Veluswamy | A review of solidified natural gas (SNG) technology for gas storage via clathrate hydrates[END_REF] .

The use of porous material as nucleation sites at low concentrations is the main focus of this article. In this approach, the porous material increases the surface area by adding another interface (or surface) that facilitates gas diffusion and crystallization [START_REF] Cha | A third-surface effect on hydrate formation[END_REF] . Although most relevant studies showed that porous material improved the kinetic performance [START_REF] Said | A study on the influence of nanofluids on gas hydrate formation kinetics and their potential: Application to the CO2 capture process[END_REF][START_REF] Choi | CO2 hydrate formation at atmospheric pressure using high efficiency absorbent and surfactants[END_REF][START_REF] Pan | Effect of silica sand size and saturation on methane hydrate formation in the presence of SDS[END_REF][START_REF] Wang | Accelerated nucleation of tetrahydrofuran (THF) hydrate in presence of ZIF-61[END_REF][START_REF] Rungrussamee | Comparative study of methane hydrate formation and dissociation with hollow silica and activated carbon[END_REF][START_REF] Zhang | How porous surfaces influence the nucleation and growth of methane hydrates[END_REF] , SDS is still added to get acceptable results when the conditions tested were near ambient conditions [START_REF] Inkong | Innovative Approach to Enhance the Methane Hydrate Formation at Near-Ambient Temperature and Moderate Pressure for Gas Storage Applications[END_REF] .

Despite their practical advantages, such as stability, large surface area, tunable acidity, and low cost, few studies investigated the use of zeolites for that purpose. For example, Xiaoya et al. has tested for zeolite 3A for CH 4 -THF hydrate formation and concluded that it enhanced the formation rate [START_REF] Zang | Influence of 3A molecular sieve on tetrahydrofuran (THF) hydrate formation[END_REF] . In 2009, the same group studied the gas storage in LTA-type zeolite (3A and 5A) in the presence and absence of SDS. They concluded that the promotion effect on hydrate formation of 3A zeolite was much more obvious than that of 5A zeolite when both zeolites are used at concentrations of 0.033 and 0.067 wt% [START_REF] Zang | Influence of A-type Zeolite on Methane Hydrate Formation[END_REF] . However, the authors had to add also 0.067 wt% SDS to the initial mixture to get satisfactory kinetic performance and gas uptake. Kim et al. showed zeolite 13X (FAU-type) at 0.01 wt% concentration showed higher gas consumption than SDS and LTA-type zeolites, making it the most promising zeolite as KHP. The author attributed that to the small particle size and large pore diameter of 13X compared to the other zeolites studied [START_REF] Kim | An experimental investigation into the effects of zeolites on the formation of methane hydrates[END_REF] . The advantage of using the above porous materials is that they are cheap, used in low concentration, can be easily separated, and above all, they are environmentally friendly. However, a significant kinetic and gas uptake performance drop upon increasing the zeolite concentration above 0.01 wt% was observed, which remained unexplained.

Other zeolites such as RHO [START_REF] Andres-Garcia | Methane hydrates: Nucleation in microporous materials[END_REF] , SSZ-13 [START_REF] Denning | Promoting Methane Hydrate Formation for Natural Gas Storage over Chabazite Zeolites[END_REF] were also studied in the confinement approach as described above, but the methane hydrate kinetic data were not reported.

In contrast with KHP, which does not intervene with thermodynamic conditions, THP shifts the hydrate formation equilibrium condition to milder P-T, lowering the energy requirements. Depending on the promoter, the hydrate nature may vary, but sII or sH structure types are usually obtained. The most common structure II hydrate promoter is tetrahydrofuran (THF), which is a hydrate former by itself [START_REF] Kim | Tuning clathrate hydrates: Application to hydrogen storage[END_REF] . THF is also reported to improve the kinetics either as stand-alone or with SDS [START_REF] Zhang | Coal mine gas separation of methane via clathrate hydrate process aided by tetrahydrofuran and amino acids[END_REF][START_REF] Ricaurte | CO2 removal from a CO2-CH4 gas mixture by clathrate hydrate formation using THF and SDS as water-soluble hydrate promoters[END_REF][START_REF] Prasad | Laser Raman spectroscopy of THF clathrate hydrate in the temperature range 90-300 K[END_REF][START_REF] Talyzin | Feasibility of H2-THF-H2 O clathrate hydrates for hydrogen storage applications[END_REF] . Other sII formers such as cyclopentane [START_REF] Zhong | Recovery of CH4 from coal mine model gas mixture (CH 4/N2) by hydrate crystallization in the presence of cyclopentane[END_REF] , dioxlane [START_REF] Trueba | Phase equilibrium measurements of structure II clathrate hydrates of hydrogen with various promoters[END_REF] , acetone [START_REF] Partoon | Impact of acetone on phase boundary of methane and carbon dioxide mixed hydrates[END_REF] , and others were reported in the literature 52 but showed lower performance than THF. A more comprehensive review of various promoters studies (KHP and THP) can be found in the literature [START_REF] Nasir | A review on the role and impact of various additives as promoters/ inhibitors for gas hydrate formation[END_REF] . The main drawback of using THP is the reduction in methane uptake compared to sI. The main reason behind that decrease is that those promoters occupy the sII or sH large cages while stabilizing the structure. However, the reduction of formation conditions closer to ambient temperatures can significantly offset that storage capacity reduction. For example, it is estimated that compression cost is approximately 70-80% of the total cost of methane hydrate formation in a large-scale reactor of 25 L 53 . Increasing the methane formation temperature from 274.2 K to 293.2 will reduce 80% of the cooling cost as estimated by Veluswamy et al. [START_REF] Veluswamy | Enhanced clathrate hydrate formation kinetics at near ambient temperatures and moderate pressures: Application to natural gas storage[END_REF] . Finally, we have chosen to do experiments in a non-stirring tank reactor which proved to have a higher yield while removing the additional cost of agitation. In fact, as the slurry becomes thicker, mechanical power/energy consumption will not be economical [START_REF] Mori | On the scale-up of gas-hydrate-forming reactors: The case of gas-dispersion-type reactors[END_REF] . Thus, the non-stirring approach will make it easy to adopt this technology for large-scale gas storage systems [START_REF] Inkong | Effects of temperature and pressure on the methane hydrate formation with the presence of tetrahydrofuran (THF) as a promoter in an unstirred tank reactor[END_REF] .

The primary objective of this study was to assess the performance of environmentally benign acidic (H-Y)and basic (Na-X) zeolites, , in concentrations up to 0.5 wt%, in binary methane-THF hydrate formation.

Another important objective of this study was evaluating the effects of gas-to-liquid ratio and pressure on methane hydrate at a high temperature (283.2 K). Moreover, we explored the effect of hydrophobicity, extra framework cation, and acidity of zeolites on their role as kinetic hydrate promoters. To the best of our knowledge, the latter two properties have not been explored in previous studies in that specific area. Finally, we used ab initio DFT calculation to examine the effect of the extraframework cation on hydrate formation.

Experimental Section

Material and apparatus

Methane (99.99% purity) was purchased from Linde Co., Tetrahyrofuran (THF, AR grade 99.99%) from Alfa Aesar, Na-X (Molecular Sieve Union Carbide Type 13X) from Fluka AG; and zeolite Y zeolite was offered by UOP. Deionized water was used in all experiments . The acidic form of zeolite Y (H-Y) was prepared by 5 consecutive exchanges of Na-Y with 10 wt% NH 4 NO 3 and calcination at 450 • C for 4 hours. The zeolite Na-X was used without modifications. The solution THF (5.56 mol%) solution or the mix of 5.56 mol% THF with zeolite was prepared in a volumetric flask. Full description of the apparatus used for methane hydrate formation and dissociation experiments is shown with details at supporting information.

Characterization Methods

The zeolite powders were characterized using powder X-ray diffraction (PXRD), scanning electron microscope (SEM), inductively coupled-atomic plasma emission spectroscopy (ICP-AES), scanning electron microscopy (SEM) equipped with energy dispersive X-ray (EDX), N 2 -adsorption, and IR spectroscopy. The synthesized binary CH 4 -THF hydrate was characterized with PXRD and Raman spectroscopy. Methods, procedures, calculations, and equipment are detailed in the supporting information.

Hydrate formation experiment

The reactor was filled with the required level of solution and sealed. Then, it was purged three times with N 2 and then with methane to ensure air removal from the system. After reaching the target 283.2 K temperature, ( the target pressure was achieved; their values were recorded every 10 sec with the DAQ system. The time period between this starting point and the formation of the first hydrate crystal is referred to as induction time. The induction time was determined by a simultaneous pressure drop and temperature increase due to the exothermic nature of the hydrate formation. As the reaction continues, the pressure drops further, and the hydrate formation process is considered complete when there is no further drop for 1 h. All experiment were conducted at least 3 time and average results are reported. The number of moles of the gas consumed at any time t (∆n H↓ ) is equal to the difference between the number of moles of the gas n H,0 at time =0 (i.e. the start of the experiment) and the number of moles of the gas present n H,t at any time t in the vessel as shown by Eq.( 1):

∆n H↓ = n H0 -n Ht = P V zRT G0 - P V zRT Gt (1)
Subscript G 0 and G t represent the gas phase at the start of the experiment and time t, respectively. Here, P, T, and V are the pressure, temperature, and reactor volume, respectively. R is the universal gas constant, and z is the comprehensibility factor calculated by Pitzer's correction [START_REF] Pitzer | The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization[END_REF] .

Normalized methane gas uptake is calculated by the following Eq.( 2):

N ormalized uptake = ∆n H↓ n H2O (2)
Water-to-hydrate conversion, methane gas conversion as well as methane recovery percentage calculations are detailed in supporting information.

Computational Methods

We performed density functional theory (DFT) calculations 58 using the projected augmented wave (PAW) method and the standard pseudopotentials supplied by Quantum Espresso (QE) software [START_REF] Giannozzi | QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials[END_REF][START_REF] Omran | Ab initio mechanistic insights into the stability, diffusion and storage capacity of sI clathrate hydrate containing hydrogen[END_REF][START_REF] Omran | DFT Study of Copper-Nickel (111) Catalyst for Methane Dry Reforming[END_REF] . Full description of the hydrate-zeolites systems as well as calculation details are shown in supporting information.

Results and discussion

Zeolite Promoters and Hydrate Characterization N 2 -adsorption measurements, PXRD, and SEM images confirmed the crystal structures of Na-X and H-Y zeolites. ICP-AES and EDX revealed that while Na-X zeolite maintained high concentration of sodium, most of the sodium extra framework cation has been exchanged, and Si/Al ratio of H-Y is 2.7 compared to 1.2 in the case of Na-X. The acidity of the H-Y zeolite and of the Na-X zeolite were determined via IR and Pyridine TPD (temperature programmed desorption). For hydrate characterization, we first confirmed sII formation using PXRD analysis. In addition, Raman spectroscopic measurements on the synthesized binary hydrate were performed. Spectroscopic data revealed methane occupancy in 5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] small cages of sII as a sharp peak at ∼ 2911.1 cm -1 . Detailed zeolite promoter and hydrate characterization results are provided in supporting information.

Effect of Reactor Level and Pressure

It is well-known that the hydrates tend to nucleate in the gas-water interface and then grow into the water bulk phase. The first set of experiments was performed with the aim to determine the effect of liquid/gas level on the gas uptake and conversion at 6 MPa and 283.22 K. During that process, the volume expansion due to hydrate growth causes the formation of a thin hydrate layer. It consumes the excess gas via diffusive transport [START_REF] Jung | Hydrate formation and growth in pores[END_REF] . Previous experimental observations showed that the molar liquid water-gas ratio significantly affects methane hydrates' nucleation and growth [START_REF] Ke | The Effect of Molar Liquid Water-Gas Ratio on Methane Hydrate Formation[END_REF] . Recently, Burla and Pinnelli dedicated their study to investigate the effect liquid water-gas ratio on hydrate kinetics and storage capacity. They found that gas uptake gradually increases with the solution volume and then falls after an optimum threshold point [START_REF] Burla | Enrichment of gas storage in clathrate hydrates by optimizing the molar liquid water-gas ratio[END_REF] .

Therefore, we systematically increased the level of THF aqueous solution without the use of any promoter to obtain the optimum uptake. As shown in Figure 1, the normalized methane gas uptake initially increased with increasing the THF solution level. After reaching an optimum level of about 53%, the amount of gas uptake decreased significantly with the increasing solution level. Similarly, the conversion followed the same trend and reached its optimum (≈ 90%) at a liquid level slightly above half. Such a high conversion is important from a technical and economic point of view as it reduces the energy need to recycle that unconverted excess gas. Thus, if well-optimized, such a slight positive pressure of 2-4 bar can be used as a gas preservation blanket above the hydrate for long-term storage without further processing. The above results can be explained as follow. Initially, when there is excess gas, the rapid growth consumes the gas dissolved. Then, as the volume increases, the diffusive transport increases until a certain optimum level at which the gas uptake reaches its maximum. After that, the gas consumption decreases gradually with further solution increase. On the other hand, when there is excess THF aqueous solution, the less uptake is due to the less initial gas volume, and thus the overall gas uptake drops. Based on that, it is important to fill the reactors slightly above half of their volumetric capacity to gain the highest possible uptake, which agrees well with previous experimental observations [START_REF] Sai Kiran | Experimental investigations on tetrahydrofuran -Methane -water system: Rapid methane gas storage in hydrates[END_REF][START_REF] Veluswamy | Rapid methane hydrate formation to develop a cost effective large scale energy storage system[END_REF] . In order to increase the gas uptake and conversion, we examined two approaches: (1) introducing higher pressure (i.e., higher driving force) and (2) using a zeolite as KHP.

in situ Raman showed that it had been observed that increasing the pressure would result in increasing the small cage occupancy in CH 4 -THF binary hydrates [START_REF] Yoon | A theoretical prediction of cage occupancy and heat of dissociation of THF-CH4 hydrate[END_REF][START_REF] Moryama | In situ Raman spectroscopic studies on small-cage occupancy of methane in the simple methane and methane + deuterated tetrahydrofuran mixed hydrates[END_REF] .Accordingly, we conducted experiments at pressures of 6, 7 and 8 MPa at the same temperature (283.2 K). These conditions are selected to reach the phase boundary conditions for CH 4 -THF sII. As we used the same concentration of THF, we expect no change of system equilibrium due to THF composition variation and the only effect came from pressure variation as agreed in literature [START_REF] Inkong | Innovative Approach to Enhance the Methane Hydrate Formation at Near-Ambient Temperature and Moderate Pressure for Gas Storage Applications[END_REF] . Figure S10 reports the gas uptake and conversion for blank THF aqueous solution at different pressures. One can observe that the increase in gas uptake is insignificant when the pressure increases from 6 to 7 MPa. On the contrary, increasing the pressure from 7 to 8 MPa resulted in a slight decline in gas uptake. Noteworthy, the gradual decrease of pressure from 8 to 6 MPa resulted in a significant increase in the gas conversion. The gas conversion increased from 59% to 90% when the pressure decreased from 8 MPa to 6 MPa. Thus, despite the decrease in induction time, as shown in Table S4 and Figure S12 , trying to populate the small cages of (5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] ) with methane molecules by increasing the pressure did not result in the expected increase of final gas uptake or conversion as reported Figure 2. These results indicate that increasing the pressure shorted the reaction time and did not allow methane molecules to diffuse to the majority of bulk THF solution that remained inaccessible for hydrate conversion. Hence, we employed the zeolites as KHPs at different pressures to get the appropriate trade-off between slow kinetics and gas uptake.

Influence of Zeolite Kinetic Promoters

To study the kinetic performance, zeolite Na-X has been initially tested at various concentrations and pressure. Generally, the presence of Na-X zeolite increased the induction time and t 90 compared to blank THF. For example, after adding 0.225 wt% to the THF aquous solution the induction time of hydrate formation at 8 MPa from 7.3 min to 17 min. For instance, using a concentration as low as 0.01 wt% of Na-X to test the hydrate formation at 7 MPa increased the induction time from 19.3 min to 47.3 min while the t 90 increased by 47%. Such an increase is also associated with less conversion and gas uptake. This reduction trend in gas uptake, and conversion persists at 6 MPa despite the reduction of t 90 as shown in Table S4 and Table 1. Increasing the concentration of Na-X zeolite from 0.01 to 0.5% w/v at 7 MPa and 283.2 K, the kinetic performance and gas uptake has been significantly reduced (Figure S11). Those reductions in gas uptake agree with Kim et al. [START_REF] Kim | An experimental investigation into the effects of zeolites on the formation of methane hydrates[END_REF] for sI methane hydrate when Na-X promoter concentration increased slightly above 0.01 wt%. A possible reason for such a behavior could be the presence of sodium as an extra framework cation. It is well-known that hard cations such as sodium strongly bind to water molecules breaking the intermolecular hydrogen bonds and thus causing the intrinsic water network to collapse [START_REF] Nguyen | Hydrophobic Effect on Gas Hydrate Formation in the Presence of Additives[END_REF] . This observation agrees with the experimental studies showing that Na-X act as hydrate inhibitors even at low concentrations [START_REF] Kumar | Influence of Low-Dosage Hydrate Inhibitors on Methane Clathrate Hydrate Formation and Dissociation Kinetics[END_REF] . In addition to the sodium cation, the relatively lower Si/Al ratio resulted in a more hydrophilic nature and electrostatic structure that can reduce the water activity coefficient [START_REF] Sloan | Clathrate Hydrates Nat. Gases[END_REF] and thus ultimately cause thermodynamic inhibition of hydrate formation. Consequently, the inhibiting effect is expected to increase with increasing the zeolite concentration.

To verify such an assumption, we have explored the acidic form of zeolite Y for hydrate formation in different concentrations and pressures, as shown in Table 1. At 8 MPa, an obvious increase in the gas uptake and water-to-hydrate conversion compared to the blank THF aqueous solution at the same pressure is observed.

The raise of zeolite concentration from 0.01 wt% to 0.5 wt% results in a high gas uptake and methane conversion; despite a minor decrease in induction time. The slight increase in t 90 is probably due to the additional time for higher gas uptake. After decreasing the pressure to 7 MPa, we observed a significant reduction in the induction time and t 90 . However, there was no significant effect on the gas uptake or hydrate conversion relative to 8 MPa. At 6 MP, the optimum methane gas conversion of ≈ 94.25% along with high gas uptake could be achieved. Unlike Na-X zeolite, the increasing H-Y concentration at both 6 MPa and 8 MPa did not affect the relatively high conversion and gas uptake that was either maintained or even increased. The increase of storage capacity could be attributed to the removal of sodium cations from Y-54 zeolite and its acidity and higher hydrophobicity. It has been shown that the presence of acidic additives, such as perchloric acid (HClO 4 ), modify the THF sII hydrates flexibility 71 by increasing gas insertion and improving the gas diffusion coefficient [START_REF] Nguyen | Promoting the Insertion of Molecular Hydrogen in Tetrahydrofuran Hydrate With the Help of Acidic Additives[END_REF] . Thus, zeolites can be an excellent alternative to such extremely corrosive additives from environmental, safety, and economic points of view. Moreover, the adsorption involves specific interaction between the water molecule and the hydrophilic centers in zeolite, which can be either a silanol group or a cation associated with the tetrahedrally coordinated aluminum [START_REF] Chen | Hydrophobic properties of zeolites[END_REF] . Nguyen and Nguyen demonstrated that the moderate hydrophobicity of additive results in organizing the surrounding water into a clathrate-like structure and thereby promotes hydrate formation [START_REF] Nguyen | Hydrophobic Effect on Gas Hydrate Formation in the Presence of Additives[END_REF] . Recently, Denning et al. demonstrated that the more hydrophobic SSZ-13 (Si/Al ratio = 20) promoted 2.6 more hydrate growth than the hydrophilic SAPO-34

(Si/Al ratio = 0.6) [START_REF] Denning | Promoting Methane Hydrate Formation for Natural Gas Storage over Chabazite Zeolites[END_REF] . Thus, the absence of soduim cation and the higher Si/Al ratio of H-Y resulted in enhanced hydrophobicity. Along with the additional gas-to-water contact area indicated by the higher S ext compared to Na-X, such hydrophobicity nature improved better orientation of water molecule for hydrate formation.

In addition to the high gas uptake and conversion, the induction time and t 90 have been reduced significantly by 35% and 31% compared to blank THF aqueous solution,respectively. Similar concentrations of both zeolites were used for direct comparison at two different pressures. In all cases, H-Y outperforms Na-X kinetics at all pressures and concentrations, as shown in Figure 3. For example, at 7 MPa and a concentration of 0.255 wt%, the acidic zeolite increased gas uptake by about 30% compared to Na-X.

Similarly, at 6 MPa and 0.5% w/v, the induction time is reduced 3 times in the case of H-Y compared to Na-X. In fact, Na-X showed a rather inhibiting effect at such a relatively high concentration, and the t 90 has been reduced. The latter observation can be explained by the less gas uptake and conversion, which required less reaction time. Moreover, the positive effect of H-Y zeolite on the gas uptake could outperform SDS reported in the literature [START_REF] Sai Kiran | Experimental investigations on tetrahydrofuran -Methane -water system: Rapid methane gas storage in hydrates[END_REF] at same or even lower concentrations and pressures as shown in Figure S13.

To shed light on the molecular level reactions leading to these results, we have utilized DFT calculations.

Recently, ab initio DFT calculations have been commonly used to determine the promoting or inhibiting effect of different additives on hydrate formation [START_REF] Lee | Experimental and computational investigation of methane hydrate inhibition in the presence of amino acids and ionic liquids[END_REF] . In this study, DFT was employed to analyze zeolite- hydrate systems in terms of 5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] hydrate cage energies and geometrical changes upon their interaction with finite zeolite clusters. In addition, the energetic of host-guest cage system was calculated in the presence or absence of the zeolite KHPs. The optimized geometry of CH 4 @5 12 cage is shown in Figure S2. The host-guest interactions are a key property that characterizes the clathrate stability [START_REF] Atilhan | A quantum chemistry study of natural gas hydrates[END_REF] and can be assessed through interaction energy (∆E HG ). This energy can be defined as follow:

∆E HG = E(CH 4 @5 12 ) -[E(CH 4 ) + E(5 12 )] (3)
where E(CH 4 @5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] ), E(CH 4 ), and E(5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] ) are the energies of CH 4 @5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] , methane molecule and the 5 [START_REF] Ozawa | Crystal Growth of Clathrate Hydrate with Methane plus Partially Water Soluble Large-Molecule Guest Compound[END_REF] empty cage, respectively. Weak interactions such as H-bonding van der Waals forces dominate the hydrate and zeolite systems interaction.

Thus, we initially calculated the interaction energy of methane with small cage with revPBE and vdW-DF2 levels of theory. The values were +2.03 and -27.78 kJ/mol for revPBE and vdW-DF2 levels, respectively.

Notably, while revPBE failed to accurately determine the host-guest interactions, the small difference between the value obtained from vdW-DF2 and the previously reported value of -32.55 kJ/mol at the highly accurate MP2/6-311++G(d,p) level [START_REF] Atilhan | A quantum chemistry study of natural gas hydrates[END_REF] emphasized the quality of vdW-DF2 level in describing the hostguest interaction, and thus we had used it for all calculations. The optimized zeolite-cage structures are shown in Figure 4. Two types of interaction energies can be defined. The first one assesses the degree of zeolite-clathrate interactions (∆E Z-C ) and is defined as follow:

∆E Z-C = E(Z-CH 4 @5 12 ) -[E(Z) + E(CH 4 @5 12 )] (4)
where ∆E Z-C and E(Z) are the energy of the optimized Z-CH 4 @5 12 structure and isolated zeolite cluster, respectively. In this case, the more negative interaction energy between a host water molecule and the additive molecule indicates more attractive interaction or inhibitory effect [START_REF] Kumar | Density functional theoretic studies of host-guest interaction in gas hydrates[END_REF] . The second type considers the effect of promoter host-guest interactions as calculated from (∆E HG ) and eq (3) to get insights into the relative stability of hydrate cages in the presence and absence of zeolite promoters. This is achieved by taking into account the new arrangement of CH 4 @5 12 upon interaction with zeolite. For that, single-point potential energy calculations were performed over different filled cages of CH 4 @5 12 using their coordinates obtained from the optimized Z-CH 4 @5 12 systems. The optimized geometries and calculated values of ∆E Z-C are illustrated in Figure 4.

While the value for Na-X zeolite is -136.04 kJ/mol, H-Y showed only -79.12 kJ/mol. The high value in the case of Na-X indicates that the zeolite binding to the clathrate cage is much stronger and thus disturbs the hydrate growth, which is attributed to the presence of sodium cation. The comparison of the optimized cage structured shown in Figure S14 confirms this conclusion. Clearly, the cage structure in the case of zeolite H-Y is kept intact compared to that of Na-X. This is reflected in the relative ∆E HG in the presence and absence of zeolite promoter. The energy values of optimized methane cages for zeolite Na-X and H-Y are +39.56 and +15.44 kJ/mol, respectively. The higher value in the case of Na-X showed that the hydrate cage structure is destabilized. In summary, the interaction of zeolite with clathrate cage determines their function as heterogeneous nucleation sites and thus as KHPs.

The zeolite efficiency as KHP is highly affected by the (1) presence of extra framework cations, (

zeolite hydrophobicity, and (3) acidity. The effect of H-Y zeolite particles as nucleation sites that enhance heterogeneous nucleation prevailed as the hydrophobic acidic zeolite helped the water surrounding molecules to arrange for hydrate formation and promoted further cage growth. On the other hand, the Na-X zeolite strongly binds to the clathrate cage and disturbs the hydrate growth due to sodium cation and higher hydrophilicity. Moreover, increasing the concentration Na-X zeolite makes their electrostatic interaction that restricts water molecule orientation prevails over their promoting role as a nucleation site and results in both delay in induction time and reduction of gas uptake.

Conclusions

The aim presented study is to provide a fundamental understanding of the role of zeolite as a kinetic hydrate promoter for hydrate formation at different pressures from both molecular and macroscopic levels. To achieve that, we have used combined experimental and computational techniques to compare the performance of two zeolites of FAU-type typology: Na-X and H-Y. The effect of liquid-to-gas ratio and initial pressure on CH 4 -THF hydrate formation at 283.2 K was studied. The set of results showed that the maximum conversion and gas uptake can be achieved at 53% liquid level and 6 MPa in a non-stirred tank reactor. While increasing the pressure could reduce the induction time, the gas uptake was not significantly improved, and the gas conversion was reduced. Similarly, we have found that the conversion and gas uptake is maximized at the optimum THF aqueous level at a certain pressure. Below that level, the rapid formation of thin hydrate shell hinder the excess gas diffusion and reduce the normalized gas uptake. Similarly, going above that level will also reduce the normalized gas uptake due to the excess solution and reduced initial gas volume. In the present study we have also revealed the effect of zeolite extra framework cation and surface acidity on their performance as KHPs. Our results show that increasing the Na-X concentration above 0.01 wt% has negatively affected the kinetic and reduced gas uptake and conversion. The DFT calculations showed that the sodium cation and higher hydrophilicity in Na-X zeolite destabilize the hydrate cage and thus negatively impact hydrates formation. On the other hand, the acidic and more hydrophobic H-Y showed excellent performance as KHPs. A gas uptake of 54 mmol gas/mol H 2 O, methane gas conversion of 94.25%, and recovery as high as 96.59% could be achieved using 0.5 wt% H-Y at 6 MPa. Such results show the promising perspective to use zeolites as KHPs and shed light on the hydrate nucleation mechanism.

For Table of Contents Use Only

Synopsis

This study provides fundamental understanding of acidic zeolite as green kinetic promoters for accelerating sustainable methane storage in clathrate hydrates.

Figure 1 :

 1 Figure 1: Effect of THF aqueous solution level on the gas uptake (in red) and conversion (in black) at 6 MPa.

Figure 2 :

 2 Figure 2: Methane uptake profiles during the hydrate formation after hydrate nucleation at 6 MPa (dark blue), 7MPa(orange), and 8 MPa(green) and 283.2 K.

Figure 3 :

 3 Figure 3: Average data of the effect equal concentrations of Na-X and H-Y zeolite promoters on the induction time (in green) and methane conversion (in dark red) of 5.56 mol% THF solution at different pressures (6-8 MPa). All experiments are conducted at 283.2 K.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Figure 4 :

 4 Figure 4: Optimized configurations of small (5 12 ) cage with zeolite clusters of (a) Na-X and (b) H-Y . Sodium, silicon, and aluminum atoms are shown in light blue, brown, and grey colors, respectively.

Table 1 :

 1 Average data for binary CH 4 -THF Hydrate formation at different zeolite concentrations and pressures at 283.2 K.

	System No.	Zeolite Conc.% w/v)	P (MPa)	Induction time(min)	Gas uptake(mmol gas/mol H 2 O) a	Gas Conversion(%) b Hydrate Yield (%) t 90 (min) % Recovery b
	X-255-80	0.255	80	17.0(±5.2)		48.68	60.70(±3.22)	41.37	257(±17)	97.40
	X-001-70	0.01	70	47.3(±10.5)		49.64	72.47(±1.24)	42.19	339(±19)	96.41
	X-225-70	0.255	70	110.3(±17.3)	41.20	71.88(±1.35)	23.37	387(±27)	96.10
	X-500-70	0.5	70	141.2(±24.7)	8.41	12.28(±2.85)	7.15	474(±48)	96.39
	X-500-60	0.5	60	53.8(±12.4)		48.95	85.38(±2.78)	41.61	295(±37)	97.70
	Y-500-60	0.5	60	17.0(±3.8)		54.00	94.25(±1.47)	45.94	320(±9)	96.59
	Y-255-60	0.225	60	20.0(±2.4)		51.98	90.67(±1.92)	44.19	312(±16)	97.02
	Y-001-60	0.01	60	24.2(±4.7)		52.67	91.87(±0.76)	44.78	327(±31)	96.24
	Y-255-70	0.225	70	11.8(±1.8)		53.54	78.18(±3.49)	45.51	218(±12)	95.83
	Y-001-80	0.01	80	8.5(±2.2)		57.54	71.75(±1.33)	48.91	248(±28)	96.12
	Y-255-80	0.225	80	2.5(±1.3)		57.16	71.29(±1.78)	32.41	235(±18)	95.40
	Y-500-80	0.5	80	1.3(±3.5)		59.95	74.76(±1.65)	50.96	257(±25)	95.51

a average results of gas uptake varied within ±0.42 mmol b average results of hydrate yield and %recovery varied within ± 4.17% and ±1.35 %, respectively.

Acknowledgement

The author thanks CRIANN (Centre Régional Informatique et d'Applications Numériques de Normandie) Normandy, France for providing the computing resources.

Supporting Information Available

Textural properties and acidity measurements for zeolite promoters, THF aqueous solution at different pressures, Schematic diagram of hydrate formation setup, SEM images of zeolite promoters and XRD pattern of Na-X, PXRD pattern of H-Y zeolite, IR spectra of zeolite promoters between 1400 -1700 cm -1 range after pyridine adsorption and evacuation under vacuum at 250 • C, PXRD of CH 4 -THF hydrates, Raman spectra of CH 4 -THF, Raman spectra of CH 4 -THF dissociation, Plot of pressure effect on gas uptake and conversion of blank THF solution, Effect of zeolite Na-X concentration on the induction time and gas uptake, Plot of pressure effect on the IT of THF solution, Comparison methane uptake in presence of H-Y and SDS at different pressures and 283.2 K, Representation of optimized configuration of CH 4 @5 12 small cage using vdW-DF2 exchange functional.

The following files are available free of charge.

• Filename: Supporting information


Juan Carlos López
email: juancarlos.lopeza@uva.es.

Ibon Alkorta

Alberto Macario
email: alberto.macario@univ-rennes1.fr.

Susana Blanco
email: susana.blanco@uva.es

Characterizing the n→π* interaction of pyridine with small ketones: a rotational study of

Introduction

Non-covalent interactions (NCIs) determine the structure and properties of molecules, clusters, or materials, and are central forces in supramolecular chemistry [START_REF] Lehn | Supramolecular Chemistry-Scope and Perspectives Molecules, Supermolecules, and Molecular Devices[END_REF][START_REF] Lehn | Toward self-organization and complex matter[END_REF] and biochemistry. While their study in biological systems is difficult due to the existence of interaction networks and the presence of water molecules, isolated molecular complexes are the best source of information to size the different types of interactions. [START_REF] Desfrançois | Weakly bound clusters of biological interest[END_REF][START_REF] Doppert | Intermolecular π-hole/n→π* interactions with carbon monoxide ligands in crystal structures[END_REF][START_REF] Echeverría | The n → π* interaction in metal complexes[END_REF][START_REF] Weinhold | Valency and Bonding[END_REF] Hydrogen bonding (HB), the best-known NCI, is of fundamental importance in both chemistry and biology. Halogen bonding [START_REF] Mulliken | Structures of Complexes Formed by Halogen Molecules with Aromatic and with Oxygenated Solvents[END_REF][START_REF] Cavallo | The halogen bond[END_REF] constitutes another type of NCI that has attracted the interest of researchers in the last decades. Other groups of weak NCIs 9 include those called tetrel bonds, [START_REF] Bauzá | Tetrel-Bonding Interaction: Rediscovered Supramolecular Force?[END_REF][START_REF] Alkorta | Molecular Complexes between Silicon Derivatives and Electron-Rich Groups[END_REF][START_REF] Grabowski | Tetrel bond-σ-hole bond as a preliminary stage of the SN2 reaction[END_REF] pnictogen bonds, [START_REF] Scheiner | A new noncovalent force: Comparison of P...N interaction with hydrogen and halogen bonds[END_REF][START_REF] Zahn | Pnicogen bonds: A new molecular linker?[END_REF][START_REF] Del Bene | Structures, binding energies, and spin-spin coupling constants of geometric isomers of pnicogen homodimers (PHFX) 2, X = F, Cl, CN, CH 3, NC[END_REF] and chalcogen bonds, [START_REF] Wang | Chalcogen bond: A sister noncovalent bond to halogen bond[END_REF][START_REF] Minyaev | Theoretical study of O -> X (S, Se, Te) coordination in organic compounds[END_REF][START_REF] Sánchez-Sanz | Intermolecular Weak Interactions in HTeXH Dimers (X=O, S, Se, Te): Hydrogen Bonds, Chalcogen-Chalcogen Contacts and Chiral Discrimination[END_REF] which were known a long time ago but have received those names only very recently. [START_REF] Alkorta | An Ab Initio Investigation of the Geometries and Binding Strengths of Tetrel-, Pnictogen-, and Chalcogen-Bonded Complexes of CO2, N2O, and CS2 with Simple Lewis Bases: Some Generalizations[END_REF][START_REF] Legon | Tetrel, pnictogen and chalcogen bonds identified in the gas phase before they had names: A systematic look at non-covalent interactions[END_REF] It is accepted that these NCIs arise mainly from the interaction of an electrophilic region associated with an atom, [START_REF] Cavallo | Naming interactions from the electrophilic site[END_REF] identified with hydrogen (hydrogen bond), halogens (halogen bond), or an element of the group 14 (tetrel bond), 15 (pnictogen bond), or 16 (chalcogen bond), with a nucleophilic region, non-bonding or π-bonding electron pairs located in another or the same molecule. [START_REF] Alkorta | An Ab Initio Investigation of the Geometries and Binding Strengths of Tetrel-, Pnictogen-, and Chalcogen-Bonded Complexes of CO2, N2O, and CS2 with Simple Lewis Bases: Some Generalizations[END_REF] Within this perspective, the so-called n→π* [START_REF] Newberry | The n →π* Interaction[END_REF][START_REF] Paulini | Orthogonal multipolar interactions in structural chemistry and biology[END_REF] interactions where the electrophilic region is associated with the carbon atom of carbonyl compounds can be identified as tetrel bonds. n→π* interactions are structure-determinant in small biomolecules [START_REF] Blanco | Conformations of γ-aminobutyric acid (gaba): The role of the n→π* interaction[END_REF][START_REF] Lesarri | Shape of 4(S)-and 4(R)-hydroxyproline in gas phase[END_REF][START_REF] Sanz | The shape of β-alanine[END_REF][START_REF] Bird | Chirped-pulsed FTMW spectra of valeric acid, 5aminovaleric acid, and γ-valerolactam: A study of amino acid mimics in the gas phase[END_REF][START_REF] Cabezas | Unveiling the Shape of Aspirin in the Gas Phase[END_REF] and proteins [START_REF] Bartlett | n→π* interactions in proteins[END_REF][START_REF] Bretscher | Conformational stability of collagen relies on a stereoelectronic effect[END_REF] but despite their interest, only a few rotational spectroscopy studies have shown these interactions to occur in molecular complexes. [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF][START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF][START_REF] Chen | Hydrogen versus tetrel bonds in complexes of 3-oxetanone with water and formaldehyde[END_REF][START_REF] Pérez | Water-Water and Water-Solute Interactions in Microsolvated Organic Complexes[END_REF] In their pioneering works from crystal structure survey analysis, Bürgi and Dunitz [START_REF] Bürgi | Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group[END_REF][START_REF] Bürgi | Stereochemistry of reaction paths at carbonyl centres[END_REF][START_REF] Bürgi | Chemical reaction paths. IV. Aspects of O.C = O interactions in crystals[END_REF] identified those interactions as the experimental basis to map the reaction coordinate for the addition of a nucleophile to a carbonyl group. At large distances, the interaction would occur orthogonally between local dipoles of the nucleophile and the carbonyl group, giving rise to the classification of these NCIs as orthogonal multipolar interactions. [START_REF] Paulini | Orthogonal multipolar interactions in structural chemistry and biology[END_REF] However, at short distances the carbonyl group appears to adopt a pyramidal shape, indicating that for close contacts, orbital overlap becomes important. [START_REF] Newberry | The n →π* Interaction[END_REF][START_REF] Bürgi | Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group[END_REF][START_REF] Derider | Collagen stability: Insights from NMR spectroscopic and hybrid density functional computational investigations of the effect of electronegative substituents on prolyl ring conformations[END_REF][START_REF] Hinderaker | An electronic effect on protein structure[END_REF] This overlap involves the delocalization of a lone pair (n) of the nucleophile donor group into the antibonding (π*) orbital of the carbonyl group, so these contacts are called n→π* interactions. [START_REF] Newberry | The n →π* Interaction[END_REF] The most important signatures reported for these interactions are: (i) a short contact between the donor atom and the acceptor carbonyl carbon atom, allowing for orbital overlap; (ii) the location of the donor atom along the Bürgi-Dunitz [START_REF] Bürgi | Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group[END_REF] trajectory which maximizes n→π* orbital overlap; (iii) pyramidalization of the acceptor carbonyl group (see Figure 1). Rotational spectroscopy studies have shown that n→π* interactions take place in small biomolecules. For example, they stabilize the most stable conformers of the neurotransmitter GABA [START_REF] Blanco | Conformations of γ-aminobutyric acid (gaba): The role of the n→π* interaction[END_REF] or 4(S)-hydroxyproline, [START_REF] Lesarri | Shape of 4(S)-and 4(R)-hydroxyproline in gas phase[END_REF] and have been observed in βalanine, [START_REF] Sanz | The shape of β-alanine[END_REF] 5-aminovaleric acid [START_REF] Bird | Chirped-pulsed FTMW spectra of valeric acid, 5aminovaleric acid, and γ-valerolactam: A study of amino acid mimics in the gas phase[END_REF] or aspirin. [START_REF] Cabezas | Unveiling the Shape of Aspirin in the Gas Phase[END_REF][START_REF] Choudhary | An n→π* interaction in aspirin: implications for structure and reactivity[END_REF] The n→π* interactions between water and the carbonyl group have also been shown to cooperate with the medium and weak HBs to stabilize the microsolvated adducts of β-propiolactone [START_REF] Pérez | Water-Water and Water-Solute Interactions in Microsolvated Organic Complexes[END_REF] and benzophenone. [START_REF] Li | Unlocking the Water Trimer Loop: Isotopic Study of Benzophenone-(H 2 O) 1-3 Clusters with Rotational Spectroscopy[END_REF] Recently the competition between HB and

2 | J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins n→π* tetrel interactions has been studied in the complex 3oxetanone•••formaldehyde. [START_REF] Chen | Hydrogen versus tetrel bonds in complexes of 3-oxetanone with water and formaldehyde[END_REF] Pyridine (PY) or its derivatives can be used as nucleophilic catalysts in acylation reactions [START_REF] Tandon | Annelated Pyridines as Highly Nucleophilic and Lewis Basic Catalysts for Acylation Reactions[END_REF] so the structures of prereactive intermediates of PY with carbonyl compounds can be expected to be located along the Bürgi-Dunitz trajectory for nucleophilic addition to the carbonyl group. The complexes of PY with the two smaller carbonyl derivatives formaldehyde (FA) [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF] and acetaldehyde (AC) [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] have been already been described and show the signatures of the n→π* interactions. In both cases, the observed complex presents an n→π* tetrel bond and a weak CH•••O HB. The adduct PY•••FA 31 was the first observed complex in the gas phase for which the n→π* is the main intermolecular interaction. For the PY•••AC 32 complex, it was observed that the AC methyl group internal rotation induces a phase-locked intermolecular oscillation along the Bürgi-Dunitz coordinate. The delicate equilibrium between weak attractive and repulsive interactions leads the internal rotation of the AC methyl group to modulate the n→π* interaction coordinate. This sort of molecular balance extracts energy from the intermolecular interaction to reduce the size of the internal rotation barrier so this tetrel bond can be considered as a sort of supramolecular dynamics catalyst as observed for halogen bonds. [START_REF] Szell | Halogen bonding as a supramolecular dynamics catalyst[END_REF] In this paper, we present a combined theoretical and rotational study of the complexes of PY with the simplest ketones, acetone (ACE) and 2-butanone (2BU), in order to see if the n→π* interaction observed for the simplest aldehydes prevails in larger size systems where steric forces may contribute to force the geometry of the adducts to be out of the limiting values predicted for the Bürgi-Dunitz geometry. This would allow us to analyze the consequences of the increasing size of the carbonyl compounds on the strength of the intermolecular interactions. A comparison of the experimental and theoretical data of the four complexes of PY with FA, AC, ACE, and 2BU would shed additional light on modelling the N•••C=O n→π* tetrel bond in systems of different size. Both ketones used here have two methyl tops. These are equivalents in the case of ACE with low barrier values of 266 cm - 1 as determined from rotational data that would rise to complex splitting patterns in the rotational spectrum. [START_REF] Vacherand | The rotational spectrum of acetone: Internal rotation and centrifugal distortion analysis[END_REF] For 2BU only the trans-form has been observed [START_REF] Pierce | Microwave spectrum, dipole moment, and internal rotation of trans-2-butanone[END_REF] and the methyl groups present very different internal rotation barriers, 181.5 cm -1 and 763.9 cm -1 . [START_REF] Nguyen | The effects of two internal rotations in the microwave spectrum of ethyl methyl ketone[END_REF] It would be interesting to detect if the formation of the

Methods

Experimental

Commercial samples of PY, ACE, and 2BU were used without further purification. The spectrum was recorded in the frequency range 2-8 GHz, using a chirped-pulse Fourier transform microwave spectrometer (CP-FTMW) [START_REF] Brown | A broadband Fourier transform microwave spectrometer based on chirped pulse excitation[END_REF] described elsewhere. [START_REF] Pinacho | The complete conformational panorama of formanilide-water complexes: the role of water as a conformational switch[END_REF] The supersonic jet was generated by expansion of Ne at backing pressures of about 2 bar through a 0.8 mm diameter pulsed heatable nozzle with molecular pulses of 700 µs duration. PY was located in a reservoir located at the heatable nozzle and ACE, or 2BU, was placed in a reservoir inserted in the gas line just before the nozzle. The spectra were recorded in steps of 2 GHz. Chirp pulses of 4 µs were created by an arbitrary waveform generator and amplified. The polarization signal was radiated from a horn antenna in a direction perpendicular to that of the expanding gas. A molecular transient emission spanning 40 µs is then detected through a second horn antenna, recorded with a digital oscilloscope and Fourier-transformed to the frequency domain.

The accuracy of frequency measurements is estimated to be better than 10 kHz, but given the signal-to-noise ratio of some of the observed lines in the fits, these were given estimated measurement errors of 15 kHz except for overlapped lines for which it increased to 30 kHz. Measurements of the spectra were done using the AABS package [START_REF] Kisiel | Assignment and Analysis of Complex Rotational Spectra[END_REF] available as well as many other useful applications on the PROSPE website. 50

Computational

The potential energy surfaces of the PY•••ACE and PY•••2BU complexes have been explored with metadynamics sampling in the Crest program. [START_REF] Pracht | Automated exploration of the low-energy chemical space with fast quantum chemical methods[END_REF] These geometries have been used as a starting point in the optimization at B3LYP 52,53 /6-311++G(2d,p) [START_REF] Frisch | Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets[END_REF] with the D3BJ 55 empirical dispersion parameters. Further optimizations have been carried out at the MP2 56 /6-311++G(2d,p) level after removing the repeated geometries. Frequency calculations have been carried out at B3LYP and MP2 levels to confirm that the structures obtained correspond to energetic minima. The rotational barrier of the methyl groups was obtained at MP2/6-311++G(2d,p) level by optimization of the TS structures which were confirmed by frequency calculations. The B3LYP and MP2 calculations have been performed with the Gaussian-16 [START_REF] Frisch | Revision A.03[END_REF] program. Although the results obtained at these commonly used levels are enough to assign the rotational spectra, in previous papers [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF][START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] it has been shown that the experimental n→π* Bürgi-Dunitz parameters are not well reproduced at those theoretical levels. In those cases, CCSD/6-311++G(2d,p) calculations lead to angles and distances that better reproduce the experimental data. In this work, we have only measured the parent species so to have more accurate structural data, especially to analyze methyl group internal rotation, the two most stable minima of each complex have been reoptimized at CCSD/6-311++G(2d,p). The obtained geometries have been used to evaluate the energy at CCSD(T)/6-311++G(2d,p) including the BSSE correction [START_REF] Boys | The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors[END_REF] with the Molpro-2012 [START_REF] Werner | Molpro: a general-purpose quantum chemistry program package[END_REF] program. The nuclear quadrupole coupling constants have been calculated at CCSD/6-311++G(2d,p) level Please do not adjust margins Please do not adjust margins with the Gaussian-16 program. The electrostatic characteristics of the isolated compounds have been characterized using the CCSD wave function generated with the Gaussian-16, analyzed with the Multiwfn program, [START_REF] Lu | Multiwfn: A multifunctional wavefunction analyzer[END_REF] and plotted with Jmol. 61 The components of the interaction energy have been analyzed with the DFT-SAPT 62 method with the PBE0 63 functional and the augcc-pVTZ basis set using the geometries obtained at CCSD level. These calculations have been carried out in the Molpro-2012 program. The electron density of the complexes has been studied using the QTAIM methodology [START_REF] Bader | A quantum theory of molecular structure and its applications[END_REF] with the AIMAll [START_REF] Keith | AIMAll (Version 19.10.12[END_REF] program and the NCIPlot approach. [START_REF] Contreras-García | NCIPLOT: A program for plotting noncovalent interaction regions[END_REF] In addition, the charge transfer stabilization between occupied orbitals of one molecule and empty ones of the other has been studied with the NBO methodology. 67

Results and discussion

Preliminary calculations

The molecular electrostatic potential (MEP) of two molecules can be used to locate the complementary regions that could provide clues about the intermolecular interactions. In the present case, PY shows a region with negative values of the MEP on the 0.001 au electron density isosurface associated with the lone pair of the nitrogen (see Figure 2) while the positive regions are associated with the hydrogen atoms. In the case of the carbonyl compounds, the positive region is also associated with the hydrogen atoms and above/below the carbonyl group carbon atom and the negative one with the oxygen atom.

The two most stable conformers found for each adduct, PY•••ACE and PY•••2BU, are similar (Figure 3) and have been labelled A and B. Conformer A, the most stable form of both complexes, shows a tetrel bond n→π* interaction and a weak C=O•••H-C contact. In forms B the interacting molecules appear to be stacked. The calculated parameters for the three levels of calculation used are shown in Tables S1-S6.

Rotational spectra

The recorded spectra are dominated by the rotational transitions of the monomers (see Figures S1 andS2). Any complex of PY with ACE or 2BU is expected to show a characteristic quadrupole coupling hyperfine structure (hfs) due to the presence of [START_REF] Zahn | Pnicogen bonds: A new molecular linker?[END_REF] N in PY [START_REF] Heineking | Nitrogen and Deuterium Hyperfine Structure in the Rotational Spectra of Pyridine and [ 4-D ] Pyridine[END_REF] and the fine structure due to the internal rotation of the methyl tops in ACE [START_REF] Vacherand | The rotational spectrum of acetone: Internal rotation and centrifugal distortion analysis[END_REF] or 2BU. [START_REF] Pierce | Microwave spectrum, dipole moment, and internal rotation of trans-2-butanone[END_REF][START_REF] Nguyen | The effects of two internal rotations in the microwave spectrum of ethyl methyl ketone[END_REF] Although this adds some extra difficulties to the analysis of the spectrum the specific spectral patterns constitute a fingerprint for each rotational transition (see Figures 4 and5).

The nuclear quadrupole hfs arises from the coupling of the nuclear electric quadrupole moment (eQ) of the 14 N atom with the electric field gradient q (qαβ=∂ 2 V/∂α∂β, α,β=a,b,c) created by the molecular charges at the site of this nucleus. The nuclear spin angular momentum of 14 N (I=1) then couples to the overall rotation angular momentum (J) to form a resultant F (F=I+J).

The determinable spectroscopic parameters are the elements of the nuclear quadrupole coupling tensor χ, linearly related to the electric field gradient tensor q by χ = eQq. Usually, for [START_REF] Zahn | Pnicogen bonds: A new molecular linker?[END_REF] N, only the diagonal elements of this tensor (χ aa , χ bb , and χ cc ) are determined.

For molecules with a single methyl top having a threefold barrier, rotational energy levels split into two torsional The first analysis of the spectrum of the A state of 2BU was done with the CALPGM 71 package using a semirigid rotor Hamiltonian [START_REF] Watson | Vibrational Spectra and Structure a Series of Advances[END_REF] in the S-reduction and I r representation supplemented with quadrupole coupling [START_REF] Gordy | Microwave molecular spectra[END_REF] terms. For the assignments of the E state, additional perturbation terms [START_REF] Gerhard | Internal rotation and chlorine nuclear quadrupole coupling of o-chlorotoluene studied by microwave spectroscopy and ab initio calculations[END_REF] taking into account the deviations of the E states from the semirigid rotor behaviour, were included (see Table S7). In a final step, a global fit of the A and E states was done using XIAM program [START_REF] Hartwig | The Microwave Spectrum of trans-2,3-Dimethyloxirane in Torsional Excited States[END_REF] which is a version of the internal axis method (IAM) of Woods, [START_REF] Woods | A general program for the calculation of internal rotation splittings in microwave spectroscopy. Part II. The n-top problem[END_REF] and allows us to determine the rotational, centrifugal distortion, quadrupole coupling constants, and several internal rotation parameters including the angles ∠(i,a), ∠(i,b), ∠(i,c), giving the orientation of the top axis relative to the principal inertial axes (see Figure 6). In this fit, the value of the F reduced rotational constant for the internal rotation was fixed to the value used for free 2BU [START_REF] Nguyen | The effects of two internal rotations in the microwave spectrum of ethyl methyl ketone[END_REF] using the same program.

The determined parameters are given in Table 1 and the observed frequencies are reported in Table S11. No additional A-E splittings due to the effects of the second methyl top of 2-BU were observed. The splittings predicted for transitions in the 2-8 GHz range with the barrier value reported for this top in 2-BU monomer fall below the resolution of our spectrometer. Please do not adjust margins Please do not adjust margins N is the number of hyperfine quadrupole components fitted. σ is the standard deviation of the fit. Iα is the moment of inertia of methyl top. F is the methyl top internal rotational reduced constant, F = F/r (r = 1-Σg(λg 2 Iα/Ig); g = a, b, c; λg= cos(∠(i,g)). ∠(i,a), ∠(i,b), ∠(i,c) are the angles between the methyl top axis and the inertial axes a, b and c (δ=∠(i,a)). b Standard errors are given in parentheses in units of the last digits. c Parameters in square brackets were kept fixed. Iα was assumed to have the same value given for 2-butanone. [START_REF] Nguyen | The effects of two internal rotations in the microwave spectrum of ethyl methyl ketone[END_REF] Starting values for the geometrical parameters were taken from the CCSD/6-311++G(2d,p) optimized geometry.

The first assignments of the rotational spectrum of the AA substate of the complex PY•••ACE were done using a semirigid Hamiltonian but the analysis of the full set of AA, AE, EA, and EE torsion substates was finally done using the XIAM program. The results are collected in Table 2 and the observed frequencies in Table S12. [START_REF] Hansen | A molecular beam Fourier transform microwave study of 0 -tolunitrile: 14 N nuclear quadrupole coupling and methyl internal rotation effects[END_REF] δ is the angle of the internal rotation axis with the a inertial axis. ε is the angle between the principal inertial axis b and the projection of the internal rotation axis onto the bc plane.

N is the number of hyperfine quadrupole components fitted. σ is the standard deviation of the fit. Iα is the moment of inertia of methyl top. F is the methyl top internal rotational reduced constant, F = F/r (r = 1-Σg(λg 2 Iα/Ig); g = a, b, c; λg= cos(∠(i,g)). ∠(i,a), ∠(i,b), ∠(i,c) are the angles between the methyl top axis and the inertial axes a, b, and c (δ=∠(i,a)) ; Iα was assumed to have the same value given for acetone. [START_REF] Vacherand | The rotational spectrum of acetone: Internal rotation and centrifugal distortion analysis[END_REF] Starting values for the geometrical parameters were taken from the CCSD/6-311++G(2d,p) optimized geometry. d The complex has two equivalent tops which share common values for all the parameters except for angles ε and ∠(i,b)/°.

Structural Considerations

Unfortunately, the intensities of the observed spectra did not allow the observation of [START_REF] Scheiner | A new noncovalent force: Comparison of P...N interaction with hydrogen and halogen bonds[END_REF] C isotopologues in their natural abundances to gain experimental information on the structures of the complexes. With the reduced set of experimental data, we cannot do a determination of the complex structures so we have taken the CCSD/6-311++G(2d,p) structures given in Tables S7-S8 as reasonably accurate descriptions. The geometrical parameters relevant to the intermolecular interactions are given in Figure 6. These parameters are compared in Table 3 and in Figure S3 with those of the previously studied complexes PY•••FA [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF] and PY•••AC. [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] The spectroscopic parameters predicted This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins from these structures are compared in Tables 1 and2 S8 andS9). In the same way and as it was observed for PY•••AC [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] we have also a good agreement between the CCSD and experimental internal rotation parameters, especially the angles ∠(i,a), ∠(i,b), ∠(i,c), giving the orientation of the methyl top axis relative to the principal inertial axes (see Figure 6).

Methyl Group Internal Rotation

The analysis of the rotational spectra has allowed the determination of the barrier to internal rotation of the methyl groups in both complexes. In PY 4 with those of the free AC, 77 ACE [START_REF] Vacherand | The rotational spectrum of acetone: Internal rotation and centrifugal distortion analysis[END_REF] , or 2BU. [START_REF] Nguyen | The effects of two internal rotations in the microwave spectrum of ethyl methyl ketone[END_REF] For the isolated monomers the barrier to internal rotation of the methyl group decreases from AC to ACE and finally 2BU. However, the effect of the formation of the complex on the barrier is remarkable. Decreases of ca. 64.0. cm - 1 for AC and 5.7 cm -1 for ACE while an increment of ca. 34 cm -1 is observed for 2BU. The calculated methyl group internal rotation barriers at the MP2 level reproduced the experimental results showing a good correlation coefficient, R 2 = 0.98. It should be indicated that isolated ACE shows similar barriers as in the complex with PY. The experimental results indicate that the barrier is 6 cm -1 smaller in the complex while the calculations predicts that the barrier is larger by 11 cm -1 in the complex.

The decrease of the barrier height in PY•••AC was shown to be related to the modulation of the n→π* bond distance by the internal rotation motion. [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] In the PY•••ACE and PY•••2BU complexes analyzing the origin of the alterations of the internal rotation barriers is not straightforward. This would require a detailed analysis of the potential energy profile and the changes in the molecular, in particular, the r(N•••C) Bürgi-Dunitz distance, along the minimum energy path for the methyl torsion coordinate. In both complexes, internal rotation is a twodimensional problem although for PY•••2BU the coordinates can be approximately separated. The two-dimensional potential energy function calculated at the MP2/6-311++G(2d,p) level for PY•••ACE is shown in Figure S4 along with the one-dimensional profile which shows alterations in the phase and the shape around the minima due to the intermolecular interactions. Similar behavior is predicted for PY•••2BU at the same level. As shown in Figure S5, in both cases the periodical functions resulting from the difference between the one-dimensional profiles for the free and the bonded ketones show interesting phase relations with the predicted r(N•••C) Bürgi-Dunitz distance oscillating profiles. The Bürgi-Dunitz distance is related to the n→π* interaction energy, 31 so these predicted phase relationships suggest this intermolecular interaction is playing an important role in the alteration of the internal rotation energy profiles and barriers upon complexation with PY. Please do not adjust margins Please do not adjust margins

Nature of the intermolecular interactions

The theoretical structures of the complexes PY•••ACE and PY•••2BU are consistent with their formation through an n→π* interaction. The experimental rotational constants and the geometrical parameters derived from the internal rotation analysis (see Tables 1 and2) are in excellent agreement with the CCSD predictions so they can be taken as good descriptions of the structures of the complexes. Two of the signatures of the n→π* interactions are evident from these structures. The N atom is in the plane bisecting the HCH angle (C s symmetry). 3 also includes dissociation energies calculated at CCSD(T)/6-311++G(2d,p)//CCSD/6-311++G(2d,p) computational level including the BSSE correction. The dissociation energy of the complexes is similar for the two smallest complexes (15.9 kJ mol -1 ) while for the two largest, it increases with the size of the carbonyl derivatives up to 19.0 kJ mol -1 in PY•••2BU. These data also suggest a delicate interplay between both the n→π* and weak HBs in these systems under the influence of other weak steric N•••C and N•••O interactions between PY, the C=O group and its substituents. The influence of the interaction between PY and the methyl group of AC on the n→π* bond distance was found to be responsible for the notable decrease in the barrier to internal rotation of the methyl group in PY•••AC with respect to free AC. [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] The components of the SAPT analysis are gathered in Table 5. The binding energy is dominated by the electrostatic and dispersion terms. The electrostatic one is the most important for the PY•••FA (52% of the attractive term) but decreases as the size of the carbonyl derivative increases, being 45 % of all the attractive terms in PY•••2BU. On the contrary, the dispersion increases with the size of the carbonyl derivative from 33 % to 45%. In fact, for the PY•••2BU complex, the electrostatic and the dispersion terms have the same contribution. S10 and Figure S6). [START_REF] Mata | Universal features of the electron density distribution in hydrogenbonding regions: A comprehensive study involving H•[END_REF][START_REF] Sánchez-Sanz | Theoretical study of the HXYH dimers (X, Y = O, S, Se). Hydrogen bonding and chalcogen-chalcogen interactions[END_REF] Based on the NBO analysis the most important stabilizing charge transfer between occupied orbitals of one molecule and empty ones of the other molecule corresponds to the N(lp)→π* CO (Figure 8). They account for 4.9 and 5.6 kJ mol -1 in the complexes of PY with ACE and 2BU, respectively (Table 6). These values are smaller than in the PY•••FA and PY•••AC complexes (14.4 and 7.6 kJ mol -1 , respectively). A clear relationship is found between the N(lp)→π* CO stabilization energy and the intermolecular N-C, which shorter distances imply stronger stabilizations. The contribution of the CH•••O HB (O(lp)→σ* CH) is much smaller than the tetrel bond, between 0.8 to 1.3 kJ mol -1. In this case, the stabilization contribution of this interaction increases with the size of the carbonyl group being the smallest in the PY•••FA complex (0.8 kJ mol -1 ) and the largest in the PY•••2BU (1.3 kJ mol -1 ).

Conclusions

In this work, we have presented the results of a combined theoretical and experimental study of the complexes of PY with two of the simplest ketones, ACE, and 2BU. In both cases, the main intermolecular interaction is an n→π* tetrel interaction from the PY nitrogen to the carbonyl carbon atom of the ketone, involving the nitrogen atom lone pair and the antibonding π* C=O orbital. This interaction is reinforced by a weak C-H•••O HB involving one of the PY C-H groups adjacent to the N atom and the carbonyl oxygen atom. The same interactions were observed previously in the related complexes of PY with FA [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF] and AC. [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] As previously observed, [START_REF] Blanco | Rotational Characterization of an n → π * Interaction in a Pyridine-Formaldehyde Adduct[END_REF][START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] CCSD/6-311++G(2d,p) calculations give very good predictions of the rotational constants, so the geometries predicted at this level of theory can be considered as reasonable estimations close to the experimental ones. A comparison of the structures and bond properties of the complete series of PY complexes with FA, AC, ACE, and 2BU, indicates that the n→π* tetrel interaction energy decreases along with the series FA>AC>2BU≈ACE. This decrease in energy could be related to the size of the PY partner and to the increase in the steric interactions of the carbonyl substituents with PY. These interactions force the carbonyl carbon to move away from nitrogen. At the same time, the C-H•••O HB seems to be not so hampered since the steric repulsions mainly affect the N atom and its strength increases reversely, FA<AC<2BU≈ACE as the n→π* tetrel interaction weakens. This C-H•••O interaction also forces the Bürgi-Dunitz angle ∠N•••C=O to be out of the predicted optimum interval in the ketone complexes, probably another additional contribution to weakening the tetrel bond. Thus, the interaction of PY with aldehydes or ketones is governed by an intricate balance of attractive interactions, such as n→π* and C-H•••O, together with the effects of the internal rotation dynamics and repulsive steric forces, which increase with the ketone size making the complexes presumably less stable than the complexes PY•••FA or PY•••AC. The DFT-SAPT analysis shows how the electrostatic term is dominant in the PY•••FA, decreasing with the size of the carbonyl molecule, while the dispersion increases with the size of this moiety. Thus, In the PY•••2BU complex, electrostatic and dispersion have similar stabilizing contributions. Another interesting fact observed in this work concerns to the internal rotation of the methyl groups in ACE and 2BU. We have shown that the V 3 internal rotation barrier of free AC decreases by 64 cm -1 upon formation of the PY•••AC complex. [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF] The analysis of the internal rotation splittings in the PY•••ACE and PY•••2BU rotational spectra has allowed the determination of the V 3 barriers in those complexes. Upon complexation, the barrier slightly decreases by 5.7 cm -1 for ACE, but increases by 34 cm -1 for 2BU. As was shown for PY•••AC, [START_REF] Blanco | Pyridineacetaldehyde, a molecular balance to explore the n→π* interaction[END_REF]

Figure 1 .

 1 Figure 1. Geometrical parameters associated to the Bürgi-Dunitz trajectory for the addition of a nucleophile, N, to a carbonyl carbon atom.

Figure 2 .

 2 Figure 2. Molecular electrostatic potential on the 0.001 au electron density isosurface. Red and blue colors indicate values > 0.03 au and < -0.03, respectively. The location and values of some of the stationary points in au are indicated.

Figure 3 .

 3 Figure 3. The two most stable forms, labelled as A and B, predicted for pyridine•••acetone (upper images) and pyridine•••2-butanone (lower images). Forms A in both complexes exhibit a tetrel bond n→π* interaction while in B forms the interacting molecules are stacked.

Figure 4 .

 4 Figure 4. The a R-branch J = 3←2 transitions of the complex pyridine•••2-butanone. The excerpt shows in detail the 3 1 , 2 ←2 1 , 1 transition. The quadrupole coupling components due to the presence of a 14 N nucleus in pyridine are labelled with the F quantum number. Each component is further split into the A and E substates due to the coupling between the angular momenta of the overall rotation and the internal rotation of methyl group of 2-butanone bonded to C=O.

Figure 5 .

 5 Figure 5. The 4 0 , 4 ←3 0 , 3 transition of pyridine•••acetone showing the quadrupole coupling structure due to the presence of 14 N in pyridine for each of the AA, AE, EA and EE substates associated to the internal rotation of the two equivalent methyl groups in acetone subunit.

4 . 7 a

 47 A, B, and C are rotational constants. DJ, DJK, DK, d1, and d2 are quartic centrifugal distortion constants. χaa, χbb, and χcc are 14 N nuclear quadrupole coupling constants. V3 is the internal rotation barrier. Dpi2J is an empirical internal rotation-overall rotation distortion parameter.[START_REF] Hansen | A molecular beam Fourier transform microwave study of 0 -tolunitrile: 14 N nuclear quadrupole coupling and methyl internal rotation effects[END_REF] δ is the angle of the internal rotation axis with the a inertial axis. ε is the angle between the principal inertial axis b and the projection of the internal rotation axis onto the bc plane.

  The r(N•••C) distances are 3.089(3) Å for PY•••2BU and 3.126(2) Å for PY•••ACE, both of them shorter than the sum of van der Waals radii, 3.25 Å. The Bürgi-Dunitz angle ∠N•••C=O values are 92.3(7)° and 91.7(2)°, out of the predicted range of 107° ± 10°, but not far from it. A comparison of these parameters with those of PY•••FA (r(N•••C) = 2.855(3) Å, ∠N•••C=O = 102.8(6)°) or PY•••AC (r(N•••C) = 3.012(3) Å, ∠N•••C=O = 96.9(2)°) indicates that the interaction weakens throughout the series FA→AC→ACE≈2BU, so that PY•••FA could be taken as the best reference to characterize this kind of n→π* tetrel interaction. On the other hand, the parameters related to the weak hydrogen contact C-H•••O=C reflect the reverse behavior if we consider the H•••C distance, which progressively decreases from PY•••FA to PY•••2BU, and the ∠C=O•••H angle, which despite being far from a linear arrangement of the bond increases throughout the series from PY•••FA to PY•••2BU. Table

Figure 7 .

 7 Figure 7. AIM and NCIPlot figures of the most stable minima for pyridine•••acetone (PY•••ACE) and pyridine•••2-butanone (PY•••2BU). The ρ values (au) in the intermolecular BCPs are indicated.

Figure 6 .

 6 Figure 6. CCDS/6-311++G(2d,p) geometrical parameters. In the figures on the right the principal inertial axes have been translated to the carbonyl C atom and show the i CH 3 top axes allowing to envisage the definition of the angles ∠(i,a), ∠(i,b),and ∠(i,c), determined from the internal rotation analysis of the spectra given in Tables1 and 2.

  the theoretical calculations on PY•••ACE and PY•••2BU suggest that the geared oscillation of the Bürgi-Dunitz interaction parameters, like the r(N•••C) distance related to the intermolecular interaction strength, may play an important role in modifying the internal rotation energy profiles in the complexes. Please do not adjust margins Please do not adjust margins Autónoma de Madrid (P2018/EMT-4329 AIRTEC-CM) for financial support. JCL, AM, and SB acknowledge the Junta de Castilla y Leon (Grant INFRARED-FEDER IR2020-1-UVa02) Ministerio de Economía y Competitividad (Grant CTQ2016-75253-P). Notes and references This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins TABLE OF CONTENTS ENTRY: The main interactions between pyridine and small ketones are a N•••C=O n→π* tetrel bond and a C-H•••O weak hydrogen bond as shown in this rotational study of the complexes pyridine•••acetone and pyridine•••2-butanone.

Table 1 .

 1 Rotational parameters obtained from the internal rotation analysis of the pyridine•••2-butanone spectrum and their comparison to those calculated at CCSD/6-311++G(2d,p) level. The centrifugal distortion constants and the V 3 barrier have been calculated at MP2/6-311++G(2d,p).

	Param a	Obs	Calc
	A/MHz	1886.3540(13) b	1891.2
	B/MHz	540.40505(24)	539.2
	C/MHz	535.87635(24)	533.7
	DJ/kHz	0.2201(16)	0.18
	DJK/kHz	2.247(15)	2.30
	DK/kHz	-0.88(28)	-2.26
	d1/kHz	-0.0050(13)	-0.0046
	d2/kHz	-0.00842(88)	0.0100
	χaa/MHz	-4.0687(20)	-4.47
	(χbb-χcc) /MHz	2.2580(38)	1.43
	V3/GHz	6624.85(76)	5927
	V3/cm -1	220.981(26)	197.7
	V3/kJ mol -1	2.59946(30)	2.364
	Dpi2J/kHz	12.14(59)
	ε/rad	0.6123(35)	0.58
	δ/rad	1.609925(72)	1.59
	Iα/uÅ 2	[3.1986] c	3.253
	F/GHz	[158.543] c	155.895
	∠(i,a)/°	92.2419(41)	91.2
	∠(i,b)/°	54.95(20)	56.6
	∠(i,c)/°	35.14(20)	33.4
	N	234
	σ/kHz

Table 2 .

 2 Rotational parameters obtained from the internal rotation analysis of the pyridine•••acetone spectrum and their comparison to those calculated at CCSD/6-311++G(2d,p) level. The centrifugal distortion constants and the V 3 barrier have been calculated at MP2/6-311++G(2d,p).

	Param a	Obs	Calc
	A/MHz	2722.6132(14) b	2722.8
	B/MHz	627.32262(26)	630.4
	C/MHz	575.35393(23)	577.3
	DJ/kHz	0.2308(31)	0.22
	DJK/kHz	2.104(48)	1.76
	DK/kHz	[0.0]	-1.75
	d1/kHz	[0.0]	-0.017
	d2/kHz	-0.0106(41)	0.015
	χaa/MHz	-4.1446(86)	-4.47
	(χbb-χcc) /MHz	-2.4688(96)	-2.59
	V3/GHz	7807.3(14)	7183
	V3/cm -1	260.424(47)	239.6
	V3/kJmol -1	3.11537(56)	2.866
	Dc3J/kHz	-1.247(27)
	ε/rad	±2.0968(10) d	±2.12
	δ/rad	1.63341(38)	1.65
	Iα/uÅ 2	[3.215] c	3.201
	F/GHz	[157.1936] c	158.488
	∠(i,a)/°	93.587(22)	94.5
	∠(i,b)/°	120.071(58)	121.4
	∠(i1,c)/° d	30.329(59)	31.8
	∠(i2,c)/° d	149.671(59)	148.2
	N	182
	σ/kHz	7.2

a A, B, and C are rotational constants. DJ, DJK, DK, d1, and d2 are quartic centrifugal distortion constants. χaa, χbb, and χcc are 14 N nuclear quadrupole coupling constants. V3 is the internal rotation barrier. Dc3J is an empirical internal rotation-overall rotation distortion parameter.

  with those experimentally determined. Experimental rotational constants are an excellent benchmark to test the structural data predicted from theory and in this case, are reproduced very well at this level of theory. A comparison between the calculated parameters and other DFT or MP2 methods can be seen in

	Tables S1, S2, S4, and S5, which do not show the same level of
	agreement. Similar results were found for the complexes
	PY•••FA 31 and PY•••AC 32 indicating CCSD/6-311++G(2d,p) level
	gives a reasonable description of the structure and nature of the
	interactions responsible for the formation of PY•••2BU and
	PY•••ACE complexes (see Tables

Table 3 .

 3 Comparison of the experimental (r 0 ) and theoretical (r e , CCSD/6-311++G(2d,p)) geometrical parameters describing the n→π* tetrel bond interaction and the weak C-H•••O=C HB for the series of complexes formed by pyridine (PY) with formaldehyde (FA),

	acetaldehyde (AC), acetone (ACE) and 2-butanone(2BU). The calculated dissociation
	energies (D e ) are listed in the last row.
		PY-FA a	PY-AC b		PY•ACE	PY-2BU
		r0	re	r0	re	re	re
	r(N•••C) /Å	2.855(4)	2.865	3.012(2)	3.012	3.118	3.095
	∠N•••C=O/° 102.8(6)	102.5	96.9(2)	96.7	92.6	91.7
	∠C4•N•••C/° 156.5(8)	157.0	154.27(8)	154.7	153.3	152.2
	r(O•••H)/Å	2.53(2)	2.534	2.474(3)	2.478	2.439	2.435
	∠C=O•••H/° 94.7(6)	94.8	99.8(1)	99.7	103.5	104.5
	De c /kJ mol -1	15.9		15.9		17.2	19.0
	a Taken from reference 31; b Taken from reference 32; Data for PY-ACE and PY-2BU
	taken from this work; c The dissociation energy, De, has been obtained at CCSD(T)/6-
	311++G(2d,p)//CCSD/6-311++G(2d,p) computational level including the BSSE
	correction.

Table 4 .

 4 -Comparison of the V 3 methyl group internal rotation barriers (in cm -1 ) determined for the complexes pyridine•••acetaldehyde (PY-AC), pyridine•••acetone (PY-ACE), and pyridine•••2-butanone (PY-2BU), and the monomers acetaldehyde (AC), acetone (ACE), and 2-butanone (2BU). The barriers obtained at MP2/6-311++G(2d,p) level are also indicated.

		PY-AC a	AC b	PY-ACE c	ACE d	PY-2BU c	2-BU e
	Exp.	343.6	407.5977	260.42	266.10	220.98	183.170
	MP2	348.4	396.0	239.6	228.3	197.7	160.0

a Taken from reference 32; b Taken from reference 77; c This work; d Taken from reference 44 ; e Taken from reference 46.

Table 5 .

 5 SAPT terms (kJ mol -1 ) calculated in this work for the different pyridine(PY)•••RR'C=O observed. R=R'=H, formaldehyde (FA); R=H, R'=CH 3 , acetaldehyde (AC); R=R'=CH 3 , acetone; R= CH 3 , R'=CH 2 CH 3 , 2-butanone (2BU).

	Complex	Elect.	Exch.	Ind.	Disp.	δHF	ESAPT
	PY•••FA	-24.9	30.2	-3.2	-16.0	-3.9	-17.9
	PY•••AC	-22.3	27.5	-3.0	-17.6	-2.5	-17.8
	PY•••ACE	-22.3	28.5	-3.2	-20.2	-2.1	-19.4
	PY•••2BU	-24.0	32.2	-3.4	-24.0	-2.3	-21.3

Table 6 .

 6

		PY-FA a	PY-AC b	PY-ACE c	PY-2BU c
	r(N•••C) /Å	2.865	3.012	3.118	3.095
	N(lp)  π* CO	14.4	7.6	4.9	5.6
	r(O•••H) /Å	2.534	2.478	2.439	2.435
	O(lp)  σ* CH	0.8	1.0	1.2	1.3

-Results of the NBO analysis of the most important charge transfer in the complexes pyridine(PY)•••RR'C=O; R=R'=H, formaldehyde (FA); R=H, R'=CH 3 , acetaldehyde (AC); R=R'=CH 3 , acetone; R= CH 3 , R'=CH 2 CH 3 , 2-butanone (2BU). a Taken from reference 31. b Taken from reference 32. c This work

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Acknowledgments

IA thanks the Ministerio de Ciencia, Innovación y Universidades of Spain (Project No. PGC2018-094644-B-C22) and Comunidad Figure 8. Orbitals involved in the charge transfer between N(lp) and π* CO.

Conflicts of interest

There are no conflicts to declare".