Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Majdi Hochlaf
Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France. E-mail: hochlaf@univ-mlv.fr; Fax: +33 1 60 95 73 20; Tel: +33 1 60 95 73 19

Received 28th March 2017 , Accepted 9th July 2017

First published on 10th July 2017


Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics. Nowadays, outstanding developments, both theoretical and experimental, have been achieved. The most recent results of these achievements are reviewed here. These molecular systems are studied by means of high-resolution spectroscopic techniques in either the frequency or the time domains. However, they still represent complex molecular systems since they may undergo processes that are still not fully understood in sufficient details. Indeed, electronic and nuclear motions may lead to complex features that are observed experimentally. From a theoretical point of view, these features can only be interpreted if the quantum nature of the atomic nuclei is considered together with the possible couplings between nuclear and electronic degrees of freedom. New developments, from both theoretical and experimental sides, are needed for modeling and engineering applications of outstanding importance. Possible future research directions are discussed.


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Majdi Hochlaf

Majdi Hochlaf received his PhD in physical chemistry from the University Pierre et Marie Curie and the Ecole Normale Supérieure in 1997. Since then, he has worked in the field of theoretical chemistry and molecular physics and in particular on the spectroscopy and dynamics of small- and medium-sized molecular species. He is also performing experiments using synchrotron based spectroscopic techniques. He is currently Distinguished Professor at the University Paris-Est Marne-La-Vallée.


I. Introduction

In the last decade, outstanding developments, from both the theoretical and experimental point of view, have been achieved for dealing with the spectroscopy and the dynamics of small- and medium-sized molecules and clusters, because of the importance of these species in diverse domains. For instance, molecules or clusters containing a few atoms play crucial roles in atmospheric chemistry (e.g. greenhouse gases), in biology (e.g. gaseous signaling molecules), in physics (e.g. multi-charged molecular ions, cold matter, plasma and high pressure experiments), in atto- and femto-chemistry (e.g. model systems to probe electronic wave-packet motions), in astrophysics (e.g. cold collisions) and in exobiology (e.g. formation of prebiotic molecules). However, the physical and chemical properties of these molecular entities continue to present great challenges since they undergo processes that are not yet fully understood, where the coupled electronic and nuclear motions may lead to complex structural or dynamical features that can now be observed experimentally. Theoretically, these features can only be described if the quantum nature of the atomic nuclei is considered together with the possible couplings between nuclear and electronic degrees of freedom. A non-intuitive physical chemistry is in action.

The properties of small- and medium-sized molecules provide the basis for our quantitative understanding of chemistry and a testing ground for new theories of molecular structure and reactivity. With modern methods, these molecular systems can be studied in extraordinary detail by high-resolution spectroscopic techniques in the frequency or time domains, and many advances have been made in this direction. In addition, this field is now benefiting from new results emerging from new achievements in experiment (e.g. attosecond probes of electron dynamics, time-resolved XUV and X-ray spectroscopy) and theory (e.g. non-adiabatic quantum dynamics, accurate calculations of global potential energy surfaces). In 2013 and 2015 a collection of articles that highlight some of the activity in this field and its applications were published as themed issues.1,2 Note also that several reviews were recently published on the spectroscopy and dynamics of small- and medium-sized molecular systems (see below). These reviews concerned some specific aspects of the themes that will be treated in this contribution.

This perspective will mainly focus on the up-to-date achievements in this field and on the potential new developments and applications. For instance, the covered topics include the experimental and theoretical innovations capable of fully characterizing small- and medium-sized molecular systems in electronically excited states and/or in highly excited rovibrational levels including those located above the potential barriers. These species can be either in the gas phase or adsorbed on nanostructures or surfaces. State-to-state dynamics is also a powerful tool to understand the structure and the reactivity of weakly bound aggregated systems, of molecules adsorbed on nanostructures, of molecules at cold and ultracold temperatures, molecules in remote space, astrophysics, astrochemistry, biology and long-range particle transfers.

After presentation of the cutting-edge approaches and techniques that are used for isolated molecules and for those embedded into aggregates, we will provide some examples with particular emphasis on atmospheric, astrophysical and environmental applications. Throughout this perspective, we will conduct a presentation and a deep and critical discussion on the approaches employed to study the spectroscopy and the reactivity of small molecular systems, which would pave the way to new experimental and theoretical developments. Also, new and still unresolved challenging problems in molecular sciences will be identified. Among these, many quantum effects still need to be probed.

II. Theoretical methodological achievements

Full understanding of the spectroscopy and the dynamical behavior of molecular systems, either strongly or weakly bound, at different energy domains needs, at first glance, the full exploration of their global multidimensional potential energy surfaces (PESs). These species can be in their electronic ground and/or electronically excited states. These PESs should cover the molecular regions where (meta)stable isomers can be located, the regions of the potential barriers (isomerization) and the asymptotic regions leading to fragmentation. These PESs should be mapped using accurate ab initio post Hartree–Fock methodologies after considering effects beyond the Born–Oppenheimer (BO) approximation such as relativistic, nonadiabatic and quantum electrodynamic (QED) effects. As discussed recently by Tennyson,3 these effects are rather small but they are required to fully explain the measured spectra (both line positions and intensities) and for the identification of new species in astrophysical media such as the ArH+ ion in the ISM.4 Alternatively, McCoy and co-workers developed Diffusion Monte Carlo methodology to treat molecules and complexes that undergo large amplitude vibrational motions even at low-levels of excitation with a focus on the reliable consideration of couplings between rotation and torsional degrees of freedom. Successful applications include the prediction of the rovibronic spectra of important clusters such as H2D+, HD2+, H5+, D5+, H4D+, and HD4+[thin space (1/6-em)]5–7 and D+(D2O)n.8 In the following, we will show that monoconfigurational wavefunctions of molecular systems, either rigid or semi-rigid or weakly bound, in their electronic ground state can be well described using coupled cluster approaches. In particular, the explicitly correlated versions allow for a significant reduction in computational cost without deteriorating the quality of the results. On the other hand, multi-configurational molecular systems should be described with multi-reference CI techniques, which have prohibitive computational costs. In addition to this, the corresponding predicted thermochemical and spectroscopic data are relatively less accurate than those obtained by coupled cluster approaches. New developments to reduce the computational effort and increase the accuracy of multi-reference CI techniques are highly recommended.

(a) Rigid and semi-rigid molecules in their electronic ground states

Accurate molecular structures of small- and medium-sized rigid and semi-rigid molecules with emphasis on their rotational spectroscopy can be obtained using the “composite approach” as described in ref. 9 and 10. Briefly, this scheme is based on the additivity approximation, where basis set, core-valence, higher electron excitations and relativistic corrections to energies and to gradients are considered.11,12 These corrections are evaluated separately at the highest possible level and then combined together. The largest computations are carried out using the CCSD(T)/CBS+CV+fT+fQ method, where the energies are extrapolated to the complete basis set limit (CBS) and where core-valence (CV), triple (fT) and quadruple (fQ) excitation contributions are fully accounted for. This scheme is implemented in the CFOUR code.13 This approach provides the most accurate theoretical predictions of geometrical parameters of molecules formed by up to 15 atoms as attested by the comparison with the corresponding microwave (μw) spectra. It turns out that the distances and the angles are given within 0.001–0.002 Å and 0.05–0.1 degrees accuracy, respectively.9,10 Interestingly, such accuracy is high enough to allow direct search and identification of small- and medium-sized molecular species in astrophysical media and in the atmosphere.

On the other hand, the last decade showed the emergence of explicitly correlated methods and their implementation in Quantum Chemistry codes (e.g. MOLPRO14 or ORCA15). These explicitly correlated based schemes are viewed as the method of choice for effective and accurate predictions, for the mapping of multi-dimensional PESs and for the determination of the rotational, vibrational and energetic properties of medium-sized molecular species in their electronic ground states. Using these methods, there is also effective reduction of basis-set truncation error via the implicit introduction of the interelectronic distance into the wave function expansion. A much rapid convergence to the CBS limit is reached, let's say with an aug-cc-pVTZ basis set quality.16 This approach was first used for computation of thermochemical properties (reaction energies within 1 kcal mol−1) and of spectroscopic parameters (geometry, harmonic frequencies) close to equilibrium.17–19 Afterwards, it was established that this methodology can be used to generate accurate PESs close to and far from equilibrium getting access to the consideration of anharmonic effects in small molecules (e.g. HN2+,20 [F, C, N, X] isomers (X = O, S),21 H2O, HCN, CO2, CH2O, H2O2, C2H2, CH2NH, C2H2O, and trans-isomer of 1,2-C2H2F218). Excellent agreement was found between computed and state-of-the-art experimental rovibrational spectra, where the typical mean absolute deviations from experimental values of the CCSD(T)-F12a/aug-cc-pVTZ anharmonic frequencies do not exceed 4 cm−1. Also, it was established more than once that the explicitly correlated coupled cluster method with single, double and perturbative treatment of triple excitations (CCSD(T)-F12)17,22 in conjunction with either the aug-cc-pVTZ23,24 or the cc-pVTZ-F1225,26 basis sets, together with the MOLPRO default choices for the density fitting and resolution of identity basis sets,27 leads to data close to those one may obtain with the standard coupled cluster (CCSD(T)) approach extrapolated to the CBS limit. Recently, we extended these findings to organic and prebiotic molecules containing 10–15 atoms (e.g. potential detectable molecules in ISM) to predict accurately their spectroscopic parameters.28,29 For this class of molecules, benchmarks showed that CCSD(T)-F12/cc-pVTZ-F12 computed structures have equilibrium and vibrationally corrected rotational parameters close to those deduced using the CCSD(T)/CBS+CV composite scheme and those measured experimentally.30 Moreover, we showed that the energy pattern of vibrational levels located in strongly anharmonic potentials (e.g. torsional levels lying close to the top of torsional barriers) can be evaluated by combining the CCSD(T)-F12/cc-pVTZ-F12 harmonic frequencies and anharmonic corrections evaluated at the CCSD/cc-pVTZ. A good agreement is found when compared to experimental data.30

Apart from vibrational and rotational spectra, both standard and explicitly correlated coupled cluster methodologies are used to determine electron affinities (EAs), ionization energies (IEs) and relative energies of isomers and tautomers. After comparison to experimental measurements, it was established that standard coupled cluster approaches extrapolated to the CBS limit, where basis set superposition error (BSSE), core-valence (CV), scalar relativistic (SR) and zero point vibrational energy (ZPE) corrections are considered, allow prediction of these quantities with accuracy better than 1 meV.31–33 In more recent works, we validated and benchmarked the accuracy of the (R)CCSD(T)-F12(b)/cc-pVTZ-F12 (+CV+SR+ZPVE) technique for future studies of medium-sized molecules with an obvious reduction of computational effort with respect to the previous scheme. For instance, the computed (R)CCSD(T)-F12(b)/cc-pVTZ-F12 (+CV+SR+ZPVE) adiabatic IE of thymine is 8.917 eV, in excellent agreement with the slow photoelectron spectroscopy (SPES) value (of 8.913 ± 0.005 eV).34 For the more challenging cytosine case, Hochlaf and co-workers highlighted the good performance of the less computationally demanding PBE0/aug-cc-pVDZ//CCSD(T)-F12/cc-pVTZ-F12 (+CV+SR+ZPVE) composite scheme, where equilibrium geometries and anharmonic frequencies are computed at the PBE0/aug-cc-pVDZ level, as implemented in GAUSSIAN 09.35 Then, single point computations on these optimized structures are done to evaluate the CCSD(T)-F12/cc-pVTZ-F12, CV and SR contributions. The deduced adiabatic IEs of this biological entity, which presents a dense low-lying pattern of isomeric and tautomeric forms, are within the error bars (0.003 eV) of the measured ones using VUV photoionization of neutral cytosine tautomers and isomers.36 Moreover, this even cheaper scheme allowed identification of five cytosine specific isomers present as a mixture in a molecular beam. Prior to that, Krylov and co-workers37 used the equation-of-motion coupled-cluster approach to compute the properties of the problematic open-shell states, which are described as “excitations” from a well-behaved closed-shell reference wavefunction. This ansatz is implemented for example in the Q-Chem electronic structure package.38 This approach allows, for instance, qualitative assignment of the photoionization spectra of DNA bases and clusters and gives insights into the subsequent unimolecular processes undertaken by the cationic species.39–41

(b) Weakly bound clusters in their electronic ground states

For weakly bound systems, recent theoretical and experimental spectroscopic studies showed that the “equilibrium” structure is not necessarily related to a minimum in the PES but may be governed by dynamics as evidenced for the benzene dimer42 and for the CO2–N243,44 cluster. These effects are not intuitive and should be studied in depth.

We performed a series of benchmarks where we closely compared PESs obtained using the standard coupled cluster CCSD(T) approach and those generated using explicitly correlated CCSD(T)-F12 methods. As an example, we display in Fig. 1 the 2D-PESs of the O2–He cluster as computed at the RCCSD(T)-F12/aug-cc-pVTZ and at the RCCSD(T)/aug-cc-pVTZ+bond functions. Both PESs coincide for a wide range of R and θ coordinates whereas the cost of a single point computation is strongly reduced using the former level (CPU time by ∼240 and disk occupancy by ∼35). Nevertheless, one needs to correct for the non size-consistency of the RCCSD(T)-F12 method.17,47 We showed that it is enough to uniformly shift the whole explicitly correlated potentials by the corresponding asymptotic value to force the potential to vanish at large intermonomer separations. This procedure has been validated after comparison with experimental data including the rovibrational spectra of some clusters or some macroscopic properties of the corresponding monomers (e.g. pressure broadening coefficients, temperature dependence of the second virial coefficient, temperature variations of interaction-induced rototranslational spectral moment) (see ref. 48–50 for more details). Nowadays, CCSD(T)-F12 multi-dimensional PESs, along both intra- and intermonomer coordinates, are generated “routinely” for accurate spectroscopic and dynamical calculations of medium-sized van der Waals and charge transfer molecular systems at low computational cost. Afterwards, close coupling (CC)51,52 or coupled states (CS)53 dynamical computations are carried out to deduce the rotational and vibrational excitation cross-sections of colliding systems. Faure et al.54 showed that full-dimensionality in low-energy molecular scattering calculations is not mandatory, since reduced dimensional quantum scattering calculations to compute state-to-state cross-sections provide good agreement with low-energy crossed-beam experimental data. This finding is important since full dimensional treatments are only possible for some benchmark molecular systems containing a few atoms, such as the scattering of H2 on CO. Reduced dimensionality theoretical investigations can be used hence for systems still lacking experimental characterization and to treat molecular collisions with more than 4 atoms.


image file: c7cp01980g-f1.tif
Fig. 1 2D-PESs of O2–He computed using RCCSD(T)-F12/aug-cc-pVTZ (left)45 and RCCSD(T)/aug-cc-pVTZ+bond functions (right).46 These PESs are given in Jacobi coordinates R and θ.

(c) Electronically excited molecular systems

Molecular electronic states can be valence, valence-Rydberg or Rydberg in nature. Valence electronic states are lying relatively close in energy with respect to the ground electronic state. They possess usually a pronounced multiconfigurational character that needs to be accounted for. Rydberg states are lying in energy just below the ionization energies. They are characterized by an ionic core and an electron located far away, providing a diffuse nature to the respective wavefunctions. In ref. 55, Little and Tennyson used scattering calculations, performed at negative energy using the UK molecular R-matrix method, to characterize all Rydberg states of N2 having n ≤ 6 and l ≤ 4. Interestingly, this technique provides also higher states located above the cation ground state (N2+ X2Σg+) and associated with the first excited A2Πu state of N2+. Valence-Rydberg states are located between valence and Rydberg states. They have combined and mixed characteristics of both of them. Whatever the energy or space domain, a high density of electronic states is accompanied by a rapid increase of the multiconfigurational character of the wavefunctions of the corresponding molecular systems.

Apart from the description of new still unknown molecules in their valence or Rydberg states, the last developments concerned the identification and the characterization of valence-Rydberg states and of their reactivity. Indeed, VUV photochemical studies of atmospherically important molecules (e.g. N2,56 CO257) pointed out the crucial roles played by this sort of electronic states in diverse media. Also, the focus was the consideration of several spin-multiplicities and the deduction of their mutual spin–orbit and vibronic couplings using highly correlated wavefunctions. These multi-dimensional potentials and couplings may be probed by atto/femtosecond laser-based spectroscopy (see below).

Theoretically, the recent developments58,59 showed that valence-Rydberg electronic states should be treated using multiconfigurational approaches such as the internally contracted reference configuration interaction (MRCI) approach60–62 or the recently developed explicitly correlated version (MRCI-F12),63–65 subsequent to Complete Active Space Self Consistent Field (CASSCF) calculations,66,67 as implemented for instance in MOLPRO.14 Diffuse atomic basis sets are needed to describe the atoms and active spaces must go beyond the valence molecular orbital (MO) space.

Afterwards, the PESs of these electronic excited states are incorporated into either exact quantum dynamical computations using, for instance, the MCTDH package (Multi Configuration Time Dependent Hartree)68 or semi-classical approaches.69 MCTDH is designed for treating multi-dimensional problems, in particular those that are difficult or even impossible to solve in a conventional way. It is well adapted to study the photochemistry of molecules containing tenth of atoms at high energies. The up-to-date achievements using pure quantum approaches are those described by Guo and Yarkony in their perspective article published last year,70 where they showed the necessity to take into account Renner–Teller, vibronic, non-adiabatic and spin–orbit couplings to fully address the dynamics of the wavepacket promoted into the electronic excited states after photon absorption from the corresponding ground states. Within a quantum formalism, these authors showed that the ammonia à band photodissociation state-to-state nonadiabatic dynamics71 can be treated in full dimensionality, whereas phenol photodissociation can only be studied in reduced dimensionality. Instead, semi-classical (or quantum-classical) and quasi-classical approximation techniques represent good enough alternatives for molecular systems up to 6–8 atoms in full dimensions (see ref. 69, 71 and 72 for more details). For even larger systems, the corresponding thermal rate coefficients can be evaluated using conventional transition state theory, with tunneling factor estimated assuming an asymmetric Eckart potential.73 Anyway, the achieved data accuracy for a molecular system of a given size is high enough to allow for a direct comparison with the results from up-to-date experiments. This gives insights into the underlying state-to-state mechanisms taking place after promotion of a wavepacket into an excited state PES.

III. Experimental technical developments

Nowadays, studies of photoexcitation, photodissociation and the subsequent unimolecular processes can be achieved at very high sensitivity. The last experimental developments concern the selective state-to-state promotion of a wavepacket and the probing of its evolution at short timescales. These transitions occur in the infrared (IR), ultra-violet-visible (UV-Vis), vacuum ultraviolet (VUV) or even X-ray energy domains. For standard spectroscopy, the corresponding photon sources with extremely narrow bandwidths are available either in laboratories74,75 or in synchrotrons (e.g. IR, Vis, UV and XUV beamlines at Synchrotron SOLEIL,76 or at the Advanced Light Source,77 or at the Swiss Light Source78). The recent advances in this domain and their applications to high-resolution photoionization, photoelectron and photodissociation studies, based on single-photon VUV and two-color IR–VUV, Vis–UV, and VUV–VUV laser excitations, have been nicely reviewed and illustrated by Ng in ref. 75. For detection, these laser source excitations are coupled with high sensitive detectors for photoelectrons or photoions. State-to-state spectroscopy and dynamics of small molecular ions and neutral species of atmospheric, planetary and astrophysical relevance are performed using these experiments. I refer to this review for further details.

Meanwhile, fast and ultra-fast sources have been set up to explore the ultrafast evolution of the electronic wavepacket a few tens of attoseconds after photon absorption. This allowed time resolved study of photodissociation processes using a pump–probe experimental scheme. Most common sources correspond to isolated or trains of attosecond laser pulses, which are based on high harmonic generation (HHG)79–83 (Fig. 2). For probing, velocity map imaging (VMI) detectors84 are used. By combining both techniques, a new field in molecular physics emerged in the last decade which is qualified by Vrakking80 as “Attosecond imaging”. For few body molecular systems, these pump–probe experiments are used for the observation of electron localization in dissociative molecular photoionization.85 The newly developed sources should provide enough energy to couple this pump wavelength with a probe capable of characterizing molecules formed after photo-excitation. The tunability of the pump laser is required to address all identified absorption bands of the system under study, and the high repetition rate is mandatory to explore, in a reasonable timescale, a wide panel of excitation bands. Such sources will offer interesting perspectives to explore the physical chemistry processes occurring at these time and energy scales. In the following we will detail some of these laboratory based techniques and their application for imaging the molecular species wavefunction dynamics.


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Fig. 2 Upper trace: Schematic representation of the pump/probe ultrafast experimental setup at Milano (Italy). Lower traces: IR/Vis and XUV photon spectra pulses. After courtesy of ref. 79.

(a) Attosecond/femtosecond laser source pump–probe based techniques

Pump–probe experimental setups are based on the successive interaction of two lasers with gas phase molecules. The first laser photoexcites a molecule whereas the second one probes the dynamics of the resulting photoexcited system. Applied to an isolated molecule in the time-resolved domain, the first laser, which is typically a fs laser (∼35 fs time duration), will photo-initiate a molecular process. The second laser, delayed in time by several tens, hundreds, or thousands of femtoseconds, photoionizes the molecule. The photoion and/or the photoelectron produced are collected (Fig. 3). The evolution of the ion signal as a function of time informs on the decays (e.g. a unimolecular dissociation). The electron energy is measured using a VMI spectrometer84 and addresses the electronic state populated in the excited molecule at the interaction time with the probe laser.87 Thus, the pump–probe method applied to isolated molecules informs on the dynamical pathway followed by the molecules to relax their electronic energy and helps to build an accurate picture of the underlying processes. For example, relaxation of 1,4-diazabicyclo[2.2.2]octane (DABCO) deposited on argon clusters showed that such an approach is promising88 (see below).
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Fig. 3 Ultrafast pump/probe FEMTO experimental set-up installed in the Saclay area (France). The left part is a versatile source that may serve to generate doped rare gas clusters. The right part is a versatile detection apparatus. After permission of Poisson and co-workers.86

Instead of scanning the pump–probe delay, tunable ns or ps lasers can be used to perform experiments in the energy domain. Then, measuring the signal intensity from the VMI while scanning the excitation energy gives an action spectrum documenting each of the observed outgoing channels. Nowadays such experiments are “routinely” conducted and lead to the cartography of the final excited states versus the excitation wavelengths.57,89–91

(b) Synchrotron based spectroscopic techniques

Studies of the spectroscopy and the further state-to-state evolution of ionic species or of neutral states close to and above ionisation thresholds can be carried out using molecular beam jets coupled to third generation synchrotron sources. As an example, we display in Fig. 4 the multipurpose SAPHIRS setup combined with the DELICIOUS III VMI device installed on the DESIRS beamline of SOLEIL Synchrotron93,94 as a monochromatic VUV light source (8–26 eV). In this energy range, most of the small- and medium-sized molecules and clusters can be ionized. Prior to that, they need to be promoted into gas phase either by vaporization or using aerosol sources. Cooling by embedding into supersonic molecular beams is needed for high resolution purposes (spatial and temporal focusing of the photoemitted particles). Charged particles (electrons and ions) are detected using VMI techniques and in coincidence (Fig. 4).
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Fig. 4 DELICIOUS III Photoion Photoelectron spectrometer installed at the DESIRS beamline at SOLEIL Synchrotron. Images in the bottom are those of the photoions and photoelectrons as recorded at the position sensitive detectors (PSDs). Adapted with permission from ref. 92. Copyright (2013) American Institute of Physics.

The analysis of the resolved photoelectron and photoion spectra vs. the incident photon wavelength enables one to probe the ionic states and the process mechanisms occurring after photon absorption, including photoionization and unimolecular decomposition. These have been widely discussed in the perspective by Baer and Tuckett.95 For instance, applications include studies of the photoionization spectroscopy of nucleobases and analogues in the gas phase96 or rare gas clusters.97 Particularly, we showed that these techniques can be used for specific identification of cytosine isomers and tautomers.36 When close to zero kinetic energy photoelectrons are collected, state-to-state molecular ionic dynamics may be also addressed.98,99

(c) Bimolecular collisions experimental set-ups

For unraveling molecular collisions, devising and setting up experiments devoted for reactive and non-reactive collisions, especially at low energies, is an extremely active field of research. Several groups around the world mounted such set-ups with outstanding performances. The reasons for that are numerous. They include checking physical and chemical laws at different regimes, simulation of the interstellar cold chemistry (at T = 5–100 K), and finding new routes to produce exotic atomic or molecular species. For instance, cold and ultra-cold atom–molecule, molecule–molecule or ion–molecule collision experiments are run to probe and test the accuracy of PESs and their mutual couplings. For detection, these experiments take advantage of the new performances of imaging techniques, where VMI detectors are installed beyond the collision regions either directly or after (multiple)-ionization of the species present therein.

In the last decade, the challenge was to cool down the reactants in a specific rotational–vibrational level for state-to-state reaction dynamics investigations. To reach low collision energy regimes, experimentalists made use of molecules in micro-chips,105 or skimmed beams coupled to Stark decelerators (Fig. 6) or special nozzles (e.g. Laval nozzle (Fig. 7) or Even–Lavie valves) or pulsed nozzles106 in crossed beam configurations. Temperatures down to 5–10 K are reached. To go further in cooling, Narevicius and co-workers100 set up an experiment in 2014, where they demonstrated the possibility of studying reactive collisions at the sub Kelvin energy ranges. This experimental set-up is composed of a merged supersonic beam originating from two supersonic beams, which are produced by pulsed Even–Lavie valves107 and subsequent skimming (Fig. 5). The reactive collisions occur in a curved magnetic quadrupole guide. At these very low energy collisions, magnetic fields are driving this reactivity and guiding the interaction between the partners. Detection consists in measuring the absolute Penning ionization reaction rates. For illustration they examined the case of collisions involving hydrogen isotopologues and metastable helium down to 0.01 K, where strong quantum kinetic isotope effects were observed. For chemical reactions between more common reactants (OH, NO, CO,…), such temperatures are hard to reach because of the dissipation through the dense manifold of rotation–vibration states of these molecules. For these studies, small polar molecules are decelerated by electric fields in multi-stage Stark decelerators as the one shown in Fig. 6,101 allowing one to cool down the molecules down to 5 K. More complex molecular systems (e.g. organic compounds) are cooled down to 20 K using a Laval nozzle where a uniform supersonic flow reigns. Nevertheless, this technique suffers from low sensitivity, which has been recently remediated by the use of chirped μw laser probes (Fig. 7). Briefly, Suits and Sims groups102–104 established the use of broadband rotational spectroscopy for the simultaneous detection and structural characterization of the products of multichannel reactions, whatever the number of reactive open channels. Thus, they irradiated the reactant mixture present in the pulsed uniform flow following the Laval nozzle by a chirped laser (ArF excimer laser) that propagates down the axis of the nozzle. Among the advantages of these new experiments, we can cite the following: (i) the time acquisition is typically reduced by a factor of ∼50 since the same reaction evolution is reached after a few minutes of irradiation instead of several hours, (ii) there is no need for step cavity dimensions, and (iii) the pulse duration and the power are independent. Obviously, this permits the study of multichannel reactions at low temperatures which are commonly found, for instance, in astrophysical media.102


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Fig. 5 Experimental set-up of Narevicius and co-workers100 used for studying sub Kelvin reactions between two reactants (one in blue and one in red). Reprinted after permission of ref. 100. Copyright (2014) Nature Publishing Group.

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Fig. 6 Up-to-date crossed-beam scattering machine containing a 2.6 meter long 3 stage Stark decelerator (only the last stage is shown) at Radboud University (The Netherlands). The pulsed molecular beam of radicals (e.g. NO) is cooled down by passing through the decelerator. The scattering gas is produced by the pulsed valves at three incident angles (45°, 90° and 180°) with respect to the decelerated beam. The scattered particles are first state-selectively ionized using two pulsed lasers, and then detected using a VMI detector. After permission of ref. 101.

image file: c7cp01980g-f7.tif
Fig. 7 Upper trace: Schematic representation of the chirped-pulse μw set-up coupled with a pulsed uniform flow source followed by a Laval nozzle. The chirped laser (ArF excimer laser) propagates down the axis of the Laval nozzle. Lower trace: Schematic representation of the Laval nozzle and of the uniform supersonic molecular beam generated inside this nozzle. Images taken from ref. 102–104. Copyrights (2014 and 2015) American Institute of Physics and American Chemical Society.

Cutting-edge data consist of recording specific rotational, translational and vibrational distributions of the products and of their branching ratios and of measuring resonances, which are of quantum nature. Achievements include studies of molecular systems up to full dimensionally in close connection with quantum scattering approaches.108–111 Prior to that, cold radical–radical bimolecular collisions were performed using skimmed molecular beams passed through either a Stark decelerator or a hexapole in a crossed beam configuration.109 The feasibility of this experiment was illustrated in the case of the prototypical OH (X2Π3/2, v = 0, j = 3/2, f) + NO (X2Π1/2, v = 0, j = 1/2, f) colliding system, where the spatial distributions of both reagent molecular wavepackets were imaged. Subsequently, these authors deduced the absolute rotational and spin–orbit inelastic scattering cross-sections for collision energies from 70 to 300 cm−1.

For studying anion–neutral collisions at low energies, specific experimental set-ups are available, for instance at UC Berkeley,112 UC San Diego113,114 and U. Innsbruck.115 Detection of the products makes use of photoelectron coincidence measurements112–114 or, after confining both the negative ion and the neutral into a high-order multipole trap, photodetachment probing.115 Again, imaging techniques helped a lot in increasing the sensitivity and the resolution of such complicated measurements. As for the chirped pulse laser case, multichannel reaction products were probed simultaneously.

IV. Isolated molecular systems

In this section, several examples and applications of the latest developments in the field of characterization of isolated small molecular systems are given. Emphasis will be put on molecules in rovibrational levels located close to or above potential barriers or close to dissociation limits or to ionization thresholds. New advances in the investigation of quantum localization will be detailed. We will also consider the possibility of interplay between electronic and nuclear motions and their control by advanced laser (μw, IR, UV or VUV) or free laser-based techniques currently used to study molecular photodissociation with potential production of cold atoms and molecules. The wavepacket evolution at ultra-short and short timescales will be also presented to illustrate the instantaneous dynamics of electrons within molecules following photon absorption. We will also show that multicharged molecular species may be the source of new physical and chemical applications. Highly resolved molecular spectroscopy of heavy atom-containing molecules allow going beyond the standard model.

(a) Molecular spectroscopy as a probe for fundamental physics at the molecular scale

H2+ and HD+ are the simplest molecules in nature. They represent benchmark molecular systems to test chemical bonding and quantum electrodynamics (QED) models, fundamental physical constants and laws as performed recently by Koelemeij and co-workers.116 This group measured the frequency of a vibrational overtone transition in ultra-cooled trapped HD+ ions (∼10 mK) by laser spectroscopy. The analysis of their resonance-enhanced (1 + 1′) multiphoton dissociation (REMPD) spectrum confirmed the validity of high-order QED in molecules and enabled determination of the proton-to-electron mass ratio from a molecular system. Spectra of more complicated molecular diatomics formed by heavy atoms are used for the determination of fundamental quantities, such as the permanent electric dipole moment (EDM) of the electron, which is estimated after analysis of the laser-induced fluorescence spectrum of a pulsed supersonic beam of tungsten carbide (WC) molecules in the ground rovibrational level of the X3Δ1 component.117 Larger molecular systems, such as odorant organic molecules118,119 or atmospheric relevant clusters,120 are used for probing the nuclear quadrupole couplings through the analysis of their complex and rich μw spectra. This goes through the accurate description of the conformer structures of these molecules121 and the interplay between their internal large amplitude motions.122 Let's cite also the active field of measuring and computing parity violating weak nuclear interactions of chiral medium-sized molecules and the possible link of this parity violation to biomolecular homochirality.123,124

(b) Rovibronic levels close to dissociation

The beryllium dimer, Be2, puzzled both theoreticians and experimentalists for more than 70 years. In 2009, a definitive explanation of the unexpected relatively deep potential well of this dimer was given,125,126 which is found to be due to strong bonding between the two closed shell Be atoms. The most controversial point was whether this potential supports 11 or 12 vibrational states. The challenge resided in the accurate description of this dimer’s potential energy curve (PEC) close to dissociation, where standard theoretical methodologies used for the computation of potentials and for the treatment of nuclear motions are useless because of anharmonicity effects since this potential exhibits a strong anharmonic behavior for large internuclear separations. The problem was solved after sampling all 11 vibrational levels of Be2 by Merritt et al.125 and explained by Patkowski et al.126 The latter group established also the existence of a 12th level using up-to-date ab initio calculations at the full configuration interaction level. This case goes beyond what was described by Császár et al.127 as the fourth age of quantum chemistry, where variational nuclear motion programs are used to deduce rovibronic levels and wavefunctions of small molecular systems.

(c) Rovibrational levels outside the Franck–Condon region

When ionizing neutral van der Waals clusters, the ground state vibrational level of the ionic cluster is commonly located outside the Franck–Condon (FC) region accessed by direct photoionization of the corresponding neutral dimer. This is the case of the Ar2 dimer (Fig. 8). Obviously, the energy of this level with respect to that of Ar2 (X1Σg+, v = 0) is an important fundamental quantity since it corresponds to the ionization energy of Ar2. To overcome this difficulty, Briant et al.97 took advantage of the slow photoelectron spectroscopy (SPES) coupled to synchrotron radiation128 to record the full set of vibrational states of Ar2+ from v+ = 0 till v+ = 52. The admitted mechanism responsible for the population of such large manifold of states, despite FC limitations, consists of two steps: (1) VUV excitation of an intermediate Rydberg state; (2) autoionization to a lower-lying vibrational state. The latter step contributes to the intensity enhancement of the cationic vibrational bands whether they are FC active or not. Further insights into the ionization dynamics can be also revealed by the dependence upon the photon energy of the photoelectron and photoion signals. Moreover, Briant et al. showed that the projections of the vibrational wave functions of the autoionizing states over the Ar2+ functions may be extracted from the SPES matrices. After RKR reconstruction, the PECs of the neutral Rydberg states and those of the ground cationic state can be derived. The comparison of these precise empirical PECs to those deduced by theoretical calculations represents critical tests of ab initio methodologies. For Ar2+, this revealed that, as in Be2, non-Born–Oppenheimer effects are in action. Note that the procedure established by Briant et al. is general and not specific to the Ar2 dimer case. When applied to larger clusters, it should help in the characterization of their electronic states close to the ionization threshold. For heavy atom-containing clusters (e.g. Xe2 dimer), where spin–orbit interactions are large, such analysis should help in understanding the nature of the couplings (electronic, nuclear, spin–orbit) and their interplay well above the ground state of the system. Moreover, Briant et al. showed that the potential energy curve of Ar2+ computed using up-to-date theoretical techniques cannot fully account for the experimental measurements. They concluded that new theoretical methodologies should be developed for remediation.
image file: c7cp01980g-f8.tif
Fig. 8 Upper trace: SPES spectrum of Ar2 (in blue) compared to the standard Ar2 TPEPICO spectrum (in green).97 Lower trace: Outlook of the SPES method applied to Ar2. Dark blue curve: reconstructed RKR potential energy curve. Orange curve: ab initio calculated potential energy curve. After permission of ref. 97.

(d) Rovibronic states close and above potential barriers: vibrational localization

In a recent perspective article,3 Tennyson detailed modern computations of accurate ro-vibrational spectra within the fourth age of quantum chemistry.127 Basically, nuclear motions are treated variationally on very accurate potentials where small effects such as those due to quantum electrodynamics are considered. These highly accurate rotation–vibration theoretical spectra, in both line positions and intensities, are competitive with state-of-the-art measurements as illustrated in Fig. 9 for H2O2. This enables one to establish by theory complete and accurate databases for those bands not measured yet. New developments in this field concerned computations of the dense manifold of molecular levels close to dissociation or on top of potential barriers. In 2017, Papp et al.129 showed that the variational or close-coupling scattering approaches can be used for these purposes. Indeed, these authors computed the rotational–vibrational states of ArNO+, below, above, and well above the first dissociation energy of the complex. In fact, levels located above the dissociation limit are either long-lived quasibound or short-lived resonance states embedded in the continuum. Surprisingly, they found them to exhibit a very similar energy-level structure as that of the bound states.
image file: c7cp01980g-f9.tif
Fig. 9 296 K simulated and measured absorption spectra of H2O2. Copyright (2016) American Institute of Physics.

Molecular systems containing more than three atoms possess complex PESs with a considerable number of stationary points (minima and transition states). These stationary points separate potential wells (local and global), which lead to intricate dynamical behaviors with observable effects on the rotation–vibration spectroscopy of the molecule. First there is tunneling through the potential barriers with splitting of the levels having close energies. This can be either systematic (between two equivalent wells as for the ground electronic state of ammonia, NH3131) or accidental (for non-symmetric double-well potentials as for the ground electronic states of the [H, C, N]132 system, of HONO,133 of H2CO/HCOH134 and of the S1 state of C2H2135,136). Whereas the description of rovibrational levels located below the barriers is well within the reach of the most accurate theoretical models, this is not the case for levels lying above the barriers. Because of the variety of cases, there is no trivial method for their identification. Nevertheless, all these molecular systems have a common point: there are strong perturbations of their rovibrational structure close and above the top of the barrier. Very recently, new tools were developed to characterize them, especially for the non-symmetric potential well systems, which are more complex. For instance, Baraban et al.136 showed that a dip in the spacings of certain barrier-proximal vibrational levels exists in the frequency-domain spectra of isomerizing systems. They demonstrated that this characteristic pattern can be related to the concept of effective frequency, ωeff, and hence they proposed a method for extracting transition state energies and properties from the experimental spectra. Using ab initio methodology, Ajili et al.130 showed that rovibrational wavefunctions of the levels of non-symmetric potential wells located above the barriers are localized as those located below (Fig. 10). As suggested there, this localization may be used to probe these levels, which are also found to preserve the memory of the isomers they originate from. This is a signature of a strong vibrational memory effect above isomerization barriers. In some cases (e.g. acetylene/vinylidene135), going from levels below to above the isomerization barrier can be accompanied by the birth of new vibrational modes and intramolecular vibrational–rotational energy redistribution over multiple timescales as nicely documented by Herman and Perry in ref. 135.


image file: c7cp01980g-f10.tif
Fig. 10 Illustration of the localization of vibrational wavefunctions above and below the potential barriers of SN⋯H (top) and SH⋯N (bottom) complexes. Black horizontal lines are those of a bent and linear triatomic system appearing for J ≥ 0, whereas the red ones are the odd quantum bending mode excitations of a linear system that appear only for J ≥ 1. After permission of ref. 130.

(e) Reactive and non-reactive cold and ultracold collisions

In pioneering works, several groups pictured the reactive and non-reactive collisions of prototype few-atom molecular systems, such as F + H2, CO/NO + He/H2 and F + H2O. These measurements are complemented by scattering theoretical computations for interpretation. The excellent agreement between theory and experiment allows full understanding of the underlying mechanisms taking place during molecular collisions.106,110,113,138–142 These works showed that some features (e.g. cross-section interferences or irregular diffraction patterns) cannot be explained without considering the quantum nature of the colliding partners. Even more, some observed quantum stereodynamics has no classical analogue or interpretation.142 In addition, cold atom–diatom collisions could reveal the change of symmetry (from spherical to non-spherical), which produces quantum scattering resonances.143 Van de Meerakker and co-workers just proposed to use them as powerful tools to probe anisotropy in atom–molecule collisions.144

In the astrophysical context, efforts are made to study cold collisions (E < 100 cm−1) of detected or detectable molecules and ions with H, He or H2, since they are the most abundant gases in the universe. The respective cross sections are needed by Astrophysicists to estimate the abundance of these molecules from spectral line surveys.145 In astrophysical media, reactions at low temperatures are accelerated by quantum effects (e.g. tunneling) as evidenced for the reaction between the OH radical and methanol.146 For the prototype F + n-H2 → HF + H reaction, Sims and co-workers110 showed that the corresponding rate doesn't obey the Arrhenius law at very low temperatures. Instead, an increase of this rate is observed when T decreases (Fig. 11). Scattering calculations confirmed such unexpected behavior and attribute it to the importance of tunneling in this reaction.110 Studies of prototype reactions, such as collisions between He* and H2, at the sub Kelvin regime (down to 0.01 K) clearly show that quantum phenomena in the translational motion of reactants dominate the dynamics of such reactive collisions at these low temperatures.100 Such effects are negligible at room temperature whereas they may lead to the formation of potential barriers (albeit small) that are hard to overcome with few hundredth of K collision energies. Tunneling through these weak barriers is responsible for product formation and results in unexpected increases of the total reaction rates with decreasing temperature. In addition, these works showed that in these reactions isotopic effects going beyond the Born–Oppenheimer approximation occur, with the result that ab initio computations on the reactivity of a given isotope cannot account for the reactivity of other isotopes. For remediation, the kinetic isotope effect in the cold regime should be fully considered.


image file: c7cp01980g-f11.tif
Fig. 11 Computed (blue lines) and measured (symbols) rate coefficient for the F + n-H2 → HF + H reaction. The alternating short-long dashed dark green line is the Arrhenius temperature dependence as established by Persky and Kornweitz.137 Reprinted after permission of ref. 110. Copyright (2014) Nature Publishing Group.

Among the other applications, I can cite the efficient vibrational cooling of molecular ions by ultracold atoms as evidenced by Hudson and co-workers147 for the Ca + BaCl+ system and fully explained by Stoecklin et al.148 using the close coupling dynamical approach. Interestingly, these authors showed that both the less costly quantum defect theory and statistical capture model provide intuitive understanding of such a system, where linear dependence between the vibrational quenching and the statistical capture rates is predicted. Note that rate constants by the statistical model are easily evaluated using available physical parameters of the colliding system. This validated the use of this simple model instead of the costly close coupling dynamical approach for other systems. Further details and examples of cold and ultracold chemistry can be found in the perspective by Balakrishnan published last year,149 which presents also the opportunities and challenges for understanding the chemical reactivity in the ultimate quantum regime. Especially, it should be noted that standard chemical laws (e.g. Arrhenius law) are no more valid at these temperature scales and new ones are in action, which should be determined experimentally and explained using theory.

(f) Roaming in the ground and excited states

Roaming is a non-traditional reaction pathway that has been evidenced by Suits and Bowman groups in 2004.150 It was proposed to explain the unimolecular decomposition of formaldehyde, which cannot be accounted for by conventional pathways, such as simple bond breaking or saddle point-transition state crossing or passage through a conical intersection. As stated in ref. 151, roaming occurs in a flat region of the PESs, where the dynamics involve mostly large amplitude motions, bypassing the saddle point entirely. Consequently, this unusual reaction pathway is associated with non-intuitive product distributions and the thermal rate constant law. To date, roaming has been elucidated in a variety of processes, including unimolecular decompositions in molecular electronic ground and excited states (e.g. H2CO → H2 + CO,150 NO3 photodissociation152), isomerization (e.g. in CH3NO2) and bimolecular collisions (e.g. MgH + H → Mg + H2 reaction). Apart from these benchmark molecular systems, roaming was identified in numerous medium-sized molecular systems, both inorganic and organic, where it competes with the conventional reaction pathways.151

For illustration, Fig. 12 presents the characterization of wavepacket roaming in the S1 state of 2-hydroxypyridine (2-HQ).153 Recently, a combined theoretical and pump–probe femtosecond time experiment on 2-HQ was carried out. For instance, the wavepacket promoted into the S1 state of 2-HQ from the ground state of 2-HQ undergoes relaxation that bypasses the well-known transition state and also the conical intersection (between S1 and S2 states) pathways, which are commonly invoked for electronic excited state evolutions. Instead, this electronic wavepacket roams and gets around this conical intersection in a S1 PES region of high anharmonicity, where the initial (π,π*) character of the PES switches to a (n,π*) character (Fig. 12). The further evolution of the reaction is the roaming of the H-atom bounded to oxygen (OH group of 2-HQ), associated with coupling to other degrees of freedom of the molecule. Experimentally, the timescale of wavepacket roaming on a multidimensional PES is estimated as ∼1 ps. See ref. 151 for further selection of examples and models for roaming. The process described here for 2-HQ S1 should be very common and we expect that it should be occurring in various organic and inorganic medium-sized compounds. Indeed, the high density of electronic states of such molecules should favor the occurrence of conical intersections and flat regions of the PESs where the wavepacket may roam. This strongly influences their photochemistry and the production rates of their photoproducts. For future applications and further investigations on this subject, both theoretical and experimental developments are needed.


image file: c7cp01980g-f12.tif
Fig. 12 Schematic representation of the roaming (blue and violet trajectories) on the S1 PES of the electronic wavepacket promoted into the S1 state of 2-hydroxypyridine. X1 and X2 correspond to two coordinates, which lift the degeneracy at the S1/S2 minimum-energy conical intersection. Reproduced from ref. 153 with permission from the PCCP Owner Societies.

(g) UV and VUV photodynamics

In 2001, Spelsberg and Meyer59 proposed a CASSCF/MRCI based scheme to describe accurately the 1Πu valence-Rydberg states of N2 where the N2 valence active space was augmented by one σg and one πg MOs for better relaxation of the wavefunctions of the N2 electronic states whose configurations differ in their σ and π orbital occupations. Later on, we adapted and extended this scheme to fully characterize the electronic states of N2 located in the 90 × 103–120 × 103 cm−1 energy domain above N2(X1Σg+).58 We also deduced their mutual couplings (radial, spin–orbit and vibronic). Alternatively, Little and Tennyson55 performed scattering calculations at negative energy using the UK molecular R-matrix method. A semi-quantitative agreement was found between the MRCI potential energy curves (PECs) and those obtained using this formalism.

The new sets of theoretical results on N2 electronic states and couplings were used recently to explain the quantum-state dependence of product branching ratios in state-to-state VUV photodissociation of N2 measured by the group at UC Davis and hence to propose the wavepacket evolution following its promotion into the valence-Rydberg states of N2 (cf.Fig. 13). A multistep mechanism is proposed and illustrated in Fig. 13, where spin–orbit and vibronic couplings are in action and where the reactions evolve along the potentials of the 1Σu+, 1Πu, 3Πu and quintet states. Experimentally, the branching ratio to the lowest dissociation fragments (N(4S) + N(4S)) is measured to be zero in spite of being the most thermodynamically favorable channel. Moreover, it was found that the branching ratios depend on the symmetry of the predissociative N2 states instead of the total VUV excitation energy. This is due to a nonstatistical N2 photodissociation.56


image file: c7cp01980g-f13.tif
Fig. 13 CASSCF/MRCI/aug-cc-pVQZ(+3s+2p) potential energy curves of N2 in the energy range of 90[thin space (1/6-em)]000–120[thin space (1/6-em)]000 cm−1. The vertical line marked FC represents the center of the Franck–Condon transition region. The PECs of the 1Πu, 1Σu+, and 3Πu states are shown in red, blue, and green, respectively. (i) Photon absorption from N2(X1Σg+). (ii) Region of vibronic couplings between the lowest 1Σu+ and 1Πu states leading to the population of b1Πu or b′1Σu+. (iii) Predissociation of the b1Πu state after spin–orbit coupling with C3Πu/C′3Πu either directly or after their mutual vibronic couplings. (iv) Region of vibronic couplings between the upper 1Σu+ and 1Πu states together with their spin–orbit conversions to the 3Πu states. (v) Formation of N(2P) + N(4S) after involvement of the quintet states (spin–orbit). (vi) Formation of N(2P) + N(4S) through the vibronic coupling between C′3Πu and III3Πu. (vii) Direct production of N(2D) + N(2D) from the 1Σu+ and 1Πu upper states of N2. Adapted from ref. 56.

Little and Tennyson used also the R-matrix approach to compute the energy of N2 states above the ionization threshold, which is hardly feasible by standard ab initio methods. Among the continuum, well-long-lived electronic states are predicted. Experimentally, the multiple bound and autoionizing electronic states of Rydberg and valence character of N2 lying between 12 and 18 eV above N2(X1Σg+, v = 0) were probed using Attosecond Transient Absorption Spectroscopy154 and by time- and angular-resolved photoelectron spectroscopy.155 In both experiments, interferences/quantum beating with short periods (few fs) are observed that may stabilize the discrete Rydberg states within this continuum.

Such non-intuitive photophysical processes were also noticed for the VUV state-to-state photodissociation of CO2 where a zero branching ratio for the CO2(X1Σg+) + (VUV) → CO(X1Σ+) + O(3P) reaction is measured. Again, this reaction is the most thermodynamically favorable. Such features were explained by the faster dissociation of the electronically excited CO2 through the O(1D) and O(1S) channels rather than the O(3P) channel.57 Prior to that, Ng and co-workers90 identified a spontaneous exit channel to produce C + O2 upon VUV photoexcitation of the CO2 molecule as suggested by the computations of Grebenshchikov.156 They measured a yield of ∼5% for this channel. The proposed mechanism involves the ground and the electronically excited states of OCO and of its exotic isomeric form COO (Fig. 14). These reaction channels are thermodynamically favorable.


image file: c7cp01980g-f14.tif
Fig. 14 VUV CO2 photodissociation leading to CO + O (Pathway 1) and C + O2 (Pathway 2) channels. Reprinted after permission of ref. 90. Copyright (2014) Science.

Another application of the special reactivity of molecular valence-Rydberg states concerns their use as intermediates for the production of vibrationally excited and rotationally cold molecules and cold atoms. This was suggested first after the analysis of the experimental electronic spectra of MgO by Bellert et al.158 These authors showed that the second 3Π state of MgO may serve as a source of cold MgO because of the “odd shape” of its potential, which is far from a Morse-like potential type. This was confirmed by our computations.157 Also, we proposed plausible mechanisms for the production of vibrationally excited and rotationally cold MgO molecules and of cold Mg and O atoms. These mechanisms are illustrated in Fig. 15 and involve the second 3Π state of MgO. The key point in these processes is the predissociation of a 3Π vibrational level the energy of which is as close as possible above the targeted dissociation limit.


image file: c7cp01980g-f15.tif
Fig. 15 Plausible mechanism for the formation of cold Mg and O atoms after absorption of a photon of ∼ 4.6 eV from MgO (a3Π, v = 0). Reprinted after permission of ref. 157. Copyright (2010) American Institute of Physics.

In summary, these benchmark theoretical and experimental studies pointed out that valence-Rydberg states represent new routes for new chemistry occurring upon photon absorption. For instance, this chemistry may lead to the formation of non-metallic cold atoms (e.g. O), which are difficult to produce experimentally otherwise. As shown for N2 and CO2, these processes are most likely occurring in the atmosphere, where they are influencing the local and global concentrations of these species and of their fragments. Because of the importance of such processes in cold chemistry and for atmospheric and environmental applications, it is worth investigating such processes in depth.

(h) Reactivity upon multiple ionization

Positively or negatively multi-charged molecular ions can be obtained after single or multiple photon absorption or electron impact from the corresponding neutral or lower charged species. They may also be obtained from the fission of larger compounds or clusters or sputtering of energetic ion beams on surfaces. The binding interaction results from the competition between coulombic repulsions between charges within the molecule and chemical bonding.159–161 Investigation of the reactivity and characterization of such small multicharged ions is still an active field of research because of their importance in plasma physics, atmospheric and planetary chemistry, and catalysis.162–164 In the recent review by Price et al.162 several examples of bond-forming reactions of di- and tri-cations are given.

In the last decade, the challenge concerned the formation of small sized (diatomic) with charges up to +4 (meta-)stable ions. For instance, Castleman and co-workers and Franzreb and co-workers identified, by time-of-flight mass spectrometry, several tri- and tetra-cations that are formed after either intense femtosecond laser pulse irradiation of metallic oxide nanoclusters (<100 atoms) or energetic ion beam sputtering on surfaces.165–167 Within the small clusters, an enhancement of ionization during their exposure to ultra short (∼100 fs) pulses is also observed.168 Metal carbide ions were also detected169,170 with evident importance for organometallic chemistry. These identifications corroborate several theoretical studies dealing with the spectroscopy, potential energy curves and properties of small multi-charged ions as reviewed in ref. 161. These works showed that isovalent multi-charged molecular ions do not possess necessarily the same pattern of electronic states, where some bound states for one species turn out to be repulsive for the other.171 Consequently, explicit theoretical treatment of each species is necessary.

Upon ionization, both theoretical and experimental works showed that complex intracluster ion–molecule reactions are in action. This reactivity is found to depend also on the size of the corresponding clusters. For instance, the combined theoretical and experimental study of the photoionization of multi-charged small methane clusters and its comparison to photoionization of isolated methane ions or of large ionized methane clusters showed that all these systems undergo different reactions and fragmentation processes.173 The products can be covalently bonded molecules. For molecules (AXq+) embedded into rare gas clusters, we proposed linear dependence of the number of Rg units covalently bonded to the AXq+ moiety on the charge q172 as illustrated in Fig. 16 for ArnBeOq+ (n = 1–3 and q = 0–3).


image file: c7cp01980g-f16.tif
Fig. 16 Linear dependence of the number of argon units covalently bonded to the BeOq+ moiety on the charge q. Reproduced from ref. 172 with permission from the PCCP Owner Societies.

(i) Electronic wavepacket motions

Electronic spectroscopy at the attosecond and femtosecond timescales allows following the molecular electronic dynamics where electronic and nuclear motions are probed at these timescales. Applications are, for instance, in the field of fast and ultrafast chemistry, named sometimes as attochemistry or attophysics. The outstanding recent developments of the excitation sources and of the detection techniques80,174–178 led to elucidation of single and multielectronic motions in small inorganic and organic molecules and the interplay and coupling between electronic and nuclear wavepackets. For instance, Nisoli, Calegari and co-workers used isolated attosecond XUV pulses in combination with few-optical-cycle near-infrared/visible (NIR/VIS) pulses and observed electron localization in dissociative molecular photoionization of a relatively large molecule (phenylalanine85). For N2, they recorded an interference pattern, less than 15 fs after the photon absorption which is due to the dissociation dynamics of N2+ formed by attosecond XUV pulse ionization (Fig. 1779). After ab initio computations, it was proven that these interferences are strongly connected to the slope of the potential energy curves activated by the XUV pulse. Thus, they can be used for a semi-quantitative determination of the repulsive part of these curves. In the case of ionized iodoacetylene, Wörner and co-workers demonstrated that attosecond charge migration may be measured and controlled using lasers.179
image file: c7cp01980g-f17.tif
Fig. 17 Left: Time-dependent N+ kinetic energy spectra illustrating the interference pattern measured after dissociative ionization of N2+ by attosecond XUV pulses in combination with few-optical-cycle near-infrared/visible (NIR/VIS) pulses. Right: Reaction pathway for the fragmentation of N2+ in the 0–15 fs range after absorption of the attosecond XUV pulse. After permission of ref. 79.

For N2+ and apart from the fundamental findings given above, Calegari and co-workers79 measured the following branching ratios upon attosecond XUV pulse ionization of neutral N2(X1Σg+):

N2(X1Σg+) + XUV + NIR/Vis → N2+ → N(4S) + N+(3P) 0%

→ N(2D) + N+(3P) 77.1%

→ N(2P) + N+(3P) 14.0%

→ N(2D) + N+(1D) 8.5%
Surprisingly, the lowest channel is associated with 0% branching ratio. Thus, the N2+ intermediate does not dissociate to populate the most thermodynamically favorable channel. Instead a significant probability is found for the production of neutral and/or ionic electronically excited atomic nitrogen. This joins the recent findings of Ng and co-workers relative to the VUV photodynamics of CO2 and N2. As emphasized above, a new chemistry is taking place at these high energies. It is worth noting that this field of physical chemistry is undergoing rapid and fast developments that are disclosing unrevealed phenomena at short and ultrashort timescales. Nevertheless these techniques are still considered as benchmarks and cannot be performed routinely.

V. Small molecules and clusters in a confined environment

Apart from isolated molecules, small molecular systems can be part of macromolecular systems which may affect their spectroscopy, dynamics and reactivity. This section will cover several aspects of molecular systems (solute/dopant) embedded into aggregates, trapped in cold matrices or in cages or in solvents. We will consider molecules interacting with the host via weak van der Waals interactions and/or hydrogen bonds. We will show that, in spite of the weak nature of these interactions, these small molecules are subject to surrounding effects (e.g. matrix site effects, chirality) which may induce also specific dynamical behaviors. Recent theoretical and experimental developments pointed out the importance of considering these effects at the atomic level where couplings between the solute and the solvent occur. They showed that effects induced by long range interactions may differ from those occurring via hydrogen bonds. In quantum solvents (e.g. He) unexpected effects were observed. Several aspects of these features are still not fully understood. We will also point out the evolution and the link between gas phase and condensed phase molecular properties.

(a) Solute/dopant in clusters and aggregates

In a pioneering experimental work, Grebenev, Toennies and Vilesov180 showed that the IR spectra of single oxygen carbon sulfide, OCS, molecules embedded into large 4He and 3He droplets have quite different shapes (Fig. 18). They convincingly linked these observations to the superfluidity of 4He, where OCS is freely rotating in this liquid. On the other hand, hindered rotations occur in the nonsuperfluid 3He droplets. In ref. 181, Toennies and Vilesov give a wide presentation of several He-droplets-embedded organic and inorganic medium-sized molecules, van der Waals complexes and large metal clusters, which were probed by IR and UV-Vis absorption or laser-induced fluorescence spectroscopy. Then, theoreticians made efforts to describe these effects using pure ab initio methodologies. Ground state studies are also performed using Monte Carlo approaches.
image file: c7cp01980g-f18.tif
Fig. 18 Left: IR spectrum of single OCS molecules inside large superfluid 4He (A) and non-superfluid 3He droplets (B). Right: Schematic representation of OCS inside He nanodroplets. Reprinted after permission of ref. 180. Copyright (1998) Science.

Recent developments include the study of the further evolution, at short and long timescales, of electronic excitation of solutes/dopants within the aggregates/droplets. Among them, I can cite the full-configuration-interaction nuclear orbital approach for bosons182 which is very promising: it gives a pure ab initio explanation of the aggregate spin-dependent apparent scaling of the rotational constant with the number of particles forming the aggregate. This is in line with experimental observations. Briefly, de Lara-Castells and Mitrushchenkov182 showed that the onset of collective rotational levels as minima in the energy spectra of bosonic spin-less aggregates (e.g. para-H2, 4He) marks a reversal from inversely proportional to proportional vs. the number of entities in these aggregates for the axial rotation around the dopant, whereas regular dependence is found in 3He aggregates.

Experimentally, the comparison between the spectra of fs-pump/probe molecules deposited into rare gas clusters and the corresponding spectra of free molecules gave insights into the dynamics inside the aggregates at short timescales. For illustration, Fig. 19 displays the time resolved photoelectron signals for the 265 nm pump/792 nm probe of free or deposited DABCO on Ar clusters (of ∼5000 atoms).88 The analysis of the temporal evolution of the bands showed that they correspond to ground-to-Rydberg transitions. Upon this electronic excitation, DABCO migrates from inside the cluster to the surface as schematically presented in Fig. 19. The timescale for this dynamics is estimated as ∼few hundreds of fs. This timescale is short given the relatively large size of DABCO and the large number of Ar atoms involved during the migration. The origin of such rapid dynamics may be linked to the bound interaction of DABCO in its ground state with Ar to repulsive potentials when DABCO is electronically excited. For confirmation, one needs the development of new pure ab initio methodologies which consider the solute and the aggregate not only in their ground but also in their excited electronic states.


image file: c7cp01980g-f19.tif
Fig. 19 Left: Evolutions of the time resolved photoelectron signals for the 265 nm pump/792 nm probe, parallel polarization of free or deposited DABCO for the whole signal (P0) and the second order Legendre polynomial functions (P2). Right: Schematic representation of the observed dynamical effects. DABCO and Ar cluster are represented by the red dot and the grey circle, respectively. The red dashed (black solid) horizontal lines correspond to the electronic states of free DABCO (DABCO embedded into the Ar cluster). Reproduced from ref. 88 with permission from the PCCP Owner Societies.

(b) From gas phase to liquid

A few months ago, Clary said in ref. 183 “Water plays a central role in scientific disciplines ranging from geology to astronomy to biology. Yet it is an extraordinarily difficult liquid to understand because of its complex, ever-changing patterns of hydrogen bonds”. These sentences summarize the importance of water and the challenges that scientists still face in spite of all efforts and works devoted to this important molecule either isolated or within aggregates, droplets, or in condensed phases. Obviously, the properties of isolated water molecules or small water clusters and the accurate deduction of their pair interacting potentials are crucial for the simulation of liquid water and ice. Both of them serve as solvents or catalysts for chemical reactions of primary industrial, environmental and biological importance such as the formation of building blocks of life in early earth or in interstellar media.

Among the challenges, there is the deduction of neutral and ionic isolated water molecules, water pair and three-body potentials of spectroscopic quality using fully ab initio techniques.185–187 The most recent ab initio water potential is obtained from all-electron, internally contracted multireference configuration interaction computations, including size-extensivity corrections and a large basis set (at least of aug-cc-pCV6Z quality),188 where relativistic and nonadiabatic corrections are considered. However, even such costly computations are not yet capable of providing sufficiently accurate potentials for water. Instead, a semi-theoretical potential is proposed to fit experiment.189 In fact, the recent work by Richardson et al.184 on water hexamer, i.e. the smallest water droplet, shows that our knowledge on the intrinsic dynamics of water molecules in small aggregates is still limited. Prior to that, we commonly admitted, indeed, that hydrogen bonds between water molecules evolve independently from each other in water clusters, liquid and ice. In contrast, Richardson et al.184 evidenced that concerted motions of at least two hydrogen bonds occur in water (Fig. 20) where two hydrogen bonds are broken and then formed simultaneously. Interestingly, this unexpected dynamics is governed by pure quantum effects such as tunneling. This leads to splitting patterns in rotational transitions of the water hexamer that were measured experimentally and explained by concerted geared and antigeared rotations of a pair of water molecules. For determination of the quantum tunneling rates, the recent ring-polymer-based on-the-fly instanton calculations seem very promising190 since they provide tunneling rates at the convergence limit of the electronic-structure theory. For ionic water clusters, charge transfer, in addition to hydrogen bonds and dipolar interactions, should be taken into account for fully interpreting the experimental features and collision cross sections as discussed recently for water dimer cations.191


image file: c7cp01980g-f20.tif
Fig. 20 Illustration of the concerted motions within the water hexamer. After permission of ref. 183 and 184. Copyright (2016) Science.

Even the dynamics of a solute molecule in less complex solvents than water still has a challenging character. To date, there is still a gap between photophysical phenomena observed in gas phase and those occurring in liquid phase. Obviously filling this gap allows understanding the solvent induced structural, spectroscopic and dynamical phenomena with wide ranges of applications in synthetic chemistry and biology. Non-interacting solvents, e.g. perfluorinated solvents, which interact weakly with solutes, represent a simplified liquid environment. They were proposed recently by Orr-Ewing and co-workers192 to probe the relaxation dynamics of a solute molecule in order to understand gas- and liquid-phase dynamics using ultrafast transient absorption spectroscopy. As benchmark systems, they recorded the transient electronic absorption spectra that result from gas-phase BrCN and from solution-phase BrCN photolysis at 220 nm. In solvent, the produced energetic CN radicals are thus found to be subject to translational and rotational cooling in addition to rotational hindering from the surrounding solvent molecules. The microscopic phenomena associated with these observations are still not fully understood. Orr-Ewing and co-workers192 showed that some of them are of non-classical nature.

(c) Spectroscopy of molecules inside pores and cavities

In the last two decades, encapsulated molecules aroused great interest not only from a fundamental point of view, but also for environmental, medical and industrial applications, such as capture and sequestration of gases (e.g. CO2) in Zeolitic Imidazolate Frameworks (ZIFs) or Metal Organic Frameworks (MOFs), and drug delivery (e.g. radioiodine to cancerous tissue in the human body193). These molecules can be in either spherical or non-symmetrical pores or cavities. They behave as confined quantum rotors with hindered rotational and translational motions. This results in quantization of both types of degrees of freedom with strong couplings between them. Unconventional patterns of rovibronic levels, which depend on the anisotropy of the pore or the cavity, are observed. In addition, several encapsulated molecules exhibit spin isomerism and their rotational angular momenta undergo precession and nutation in a magnetic field.

Recent works in this field concerned the understanding of the experimental observations and the elaboration of robust theoretical models for explanation. The critical part is the exploration of the interactions between guest–host molecules through the accurate description of the molecular environment inside the cage. This goes through the computation of realistic interaction potentials and full and rigorous quantum treatment of the translational–rotational motion dynamics. In contrast to free molecules, the size of the molecule inside the cavity/pore is related to its vibrational quantum numbers. Therefore, the host–guest binding potentials should depend on these as well.

Prototype (near-)spherical cavities are those found inside fullerenes. Experimentally, infrared (IR), nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) spectroscopy techniques were used to probe small molecules inside fullerenes.194,195 These works showed that new selection rules with respect to free molecules are in action. In the literature, H2@C60 and H2@C70 are used as prototypes.196 They are well documented and modeled. Indeed, there is an excellent agreement between both predicted and measured spectra.194–200 Briefly, these works showed that one needs four quantum numbers (n, j, λ, l) to label diatomic molecule energy levels instead of a unique j rotational quantum number for a free molecule, where n is the translational principal quantum number, l is the orbital angular momentum quantum number, and λ is the quantum number associated to the translation–rotation coupling between l and j.

For applications, anisotropic cavities are more relevant. They can be found inside metal–organic frameworks (MOFs), zeolitic imidazolate frameworks (ZIFs), coals or hydrates. These porous materials are used for gas separation and sequestration (e.g. N2, CH4, CO2). At the microscopic level, these gases interact with their building blocks by van der Waals long range interactions, hydrogen bonding, π stacking, and charge transfer,201–203 which may induce orientation effects of these small molecules inside the cavities.204 These effects lead to structural and spectroscopic modifications of small molecules that are probed using standard spectroscopic techniques (Raman,205 IR,206 UV-Vis207). These optical measurements have the advantage of being neither intrusive nor destructive. For illustration, Fig. 21 displays the evolution vs. temperature of the Raman spectrum of a copper-based porous MOF, {Cu4[(C57H32N12) (COO)8]}, with and without inclusion of CO2. This spectrum covers the region of the symmetric stretching mode band of CO2 (νCOss) and of the two quanta bending band (2 νCOb). While both transitions are Raman allowed, the intensity of the 2 νCOb band is weak in isolated CO2. Upon adsorption on MOFs, the 2 νCOb band of CO2 gains non-negligible intensity because of Fermi resonance coupling with the νCOss band (Fig. 21), which leads to borrowing of intensities between them. Also, the origins of CO2 bands redshift (by few cm−1) in MOFs. These shifts are not uniform for all bands. To date, the reasons for these sequestration induced shifts and for the enhancement of the intensities of some bands (e.g. the 2 νCOb band) are still unknown. Further investigations and most likely new methodologies for the description of the electronic and rovibrational spectroscopy of gases (e.g. CO2) inside the pores should be proposed. This allows probing their reactivity inside the pores and the photostability of both the guest gas and the host porous material. Multi-scaling approaches with interplay between microscopic and macroscopic studies in combination with light absorption by confined gases should be viewed as valuable and promising tools for that purpose. This represents a hot topic, and new developments, both theoretical and experimental, should be undertaken because of the importance of these findings in environmental (e.g. green house sequestration and capture), energetic (e.g. clathrates) and medical (e.g. drug delivery) domains.


image file: c7cp01980g-f21.tif
Fig. 21 Raman spectrum of a porous MOF, {Cu4[(C57H32N12) (COO)8]}, with and without adsorbed CO2vs. temperature. The band at 1377 cm−1 is assigned to the 2 νCOb band after ab initio computations.201 Reprinted (adapted) with permission from ref. 205. Copyright (2016) American Chemical Society.

(d) Rovibronic spectroscopy of physisorbed molecules

Molecules may interact with 2D-substrates such as metallic surfaces or graphene by either chemisorption or physisorption, which are the main processes occurring in heterogeneous catalysis. In the former, new bonds are created resulting in completely different species. However, physisorbed molecules preserve their chemical nature, and bonding is ensured by long range interactions. Molecules can be found in potential wells of few cm−1 up to few hundreds of cm−1 deep.208 Thus, they are subject to hindered motions with subsequent selection rules and spectra. Challenges reside in the accurate description of the potential wells using first principles and in the treatment of the low energy motion of these molecules. These potentials are strongly anharmonic and only full variational treatments of nuclear motions lead to valuable results. In addition, experimental data are scarce because of the difficulty of probing such effects. These experiments are hard to carry out where one needs ultracold surfaces, ultra vacuum conditions,209 but some convincing answers can be obtained using elaborate theoretical models.

As a benchmark, the study of H2 physisorbed on Cu(100) or Ag(111) surfaces208,210 showed that reliable interacting potentials can be obtained using an embedding approach of a small Cu/Ag cluster interacting with H2 onto a periodic Cu/Ag (Fig. 22). Briefly, highly correlated electronic computations on the cluster model are carried out using the MRCI or the coupled cluster CCSD(T) approaches. Then, periodic calculations (e.g. vdW-DF2 DFT functional) and cluster representations of the system are performed. The full dimensional potential may be obtained using an embedding method such as the one described in ONIOM,211 so that delocalization effects in the metal are corrected. The analysis of the rovibrational spectrum of this system shows that the large rotational constant of H2 associated with the anharmonic and anisotropic van der Waals potential results in a coupling between the rotation of H2 and the stretching along the physisorption well. As detailed above for H2 inside fullerenes, one needs new quantum numbers, compared to free H2, for the description of H2@Cu motions. The comparison between the computed and the measured ro-vibrational energy level patterns shows a satisfactory agreement.


image file: c7cp01980g-f22.tif
Fig. 22 Left: Coordinate system used for the description of H2 physisorbed on copper surface. Illustration of the embedded cluster model (in red) used within the periodic calculations. Right: CCSD(T) V2D(Z,θ) potential in the physisorption well. The step between the contours is 2 meV. Adapted from ref. 208. Copyright (2015) American Institute of Physics.

Another recent benchmark study concerns the determination of the nuclear bound states of H2 physisorbed on a graphene sheet.212 The corresponding interaction potential along the azimuthal coordinates is displayed in Fig. 23. It is evaluated using the vdW-corrected DFT periodic scheme. The depth of this potential is ∼50 meV and it is strongly anharmonic. Then, the bound level energies are computed numerically. They are given in Fig. 23, where they are compared to those computed for H2 physisorbed on graphite (H2@graphite), using the same methodology, and those measured experimentally for H2@graphite. For H2@graphite, the largest absolute deviation is 1.7 meV. This excellent agreement validates the predictive results for H2@graphene and the methodology used for the computations. Again, the assignment of these levels is based on specific quantum numbers (cf.ref. 212 for more details).


image file: c7cp01980g-f23.tif
Fig. 23 Left: 2D contour plot of the interaction potential of molecular hydrogen physisorbed on graphene. Right: Energy levels (black horizontal lines) of the nuclear bound states of H2 physisorbed on graphene (left) and graphite (right) and their comparison to experimental data (red horizontal lines). Reprinted (adapted) with permission from ref. 212. Copyright (2015) American Chemical Society.

VI. Conclusions, further developments and perspectives

In this contribution, we presented several aspects of state-of-the-art experimental and theoretical developments and studies on small molecular systems. We focused mainly on those that occurred in the last 4–5 years. These achievements are due to interplay between experiment and theory. Indeed, this interplay plays a pivotal role in our research field. There are several challenging aspects in high-resolution molecular spectroscopy, since the detection and analysis of spectra as well as the interpretation of the obtained results are not at all straightforward. Quantum chemistry has reached such an accuracy that it can be used to disentangle these challenging situations by guiding the experimental investigation, assisting in the determination of the spectroscopic parameters, and extracting information of chemical interest. On the other hand, thanks to the intrinsic high resolution of rotational spectroscopy, experimental data are well suited for benchmarking theoretical calculations and/or new method implementations.

Through the presentation of several examples at different energies and timescales, we pointed out that new chemistry is occurring at high energies where molecular systems in electronic excited states behave quite differently from those in their electronic ground states. Moreover, we showed that the properties of isolated molecules may be affected by the surrounding environment such as solvent or microporous cavities. We also identified new and still unresolved challenges that will pave the way to new industrial, environmental and medical applications. New challenges in small molecular physical chemistry concern the structure determination and the induced dynamical processes at diverse timescales and energies and especially at low (cold and ultracold) collision energies and at “transient” regimes. The first determines the geometric arrangements of atoms and the distribution of electrons and nuclei within these molecular systems. This is directly linked to the spectroscopic properties of the molecular system under investigation. It is needed in order to characterize the particles during reactive processes (reactants, transition states, products). The second gives insights into how these properties change in time either spontaneously or after photoinduction (by lasers). Different timescales are defined: standard molecular dynamics (ps–ns), ultra-fast molecular dynamics (fs–ps) and ultra-fast electronic dynamics (as). Within the first two regimes, we suppose that the Born Oppenheimer approximation is relevant (electronic structure independent of the nuclear velocity) to simulate the molecular evolution. We have, however, to consider both nuclear and electronic motions together to explore the electronic relaxation dynamics. As shown above, this is necessary, at least, in the attosecond regime where the localization of electrons can no more be described in the framework of orbitals. Subsequently, a hot topic has emerged concerning the charge migration induced chemistry, which represents hence new pathways to investigate. Even in the standard regime, we showed that some products are exclusively formed in an electronically excited state, whereas the branching ratios for the ground state products (i.e. the most thermodynamically favorable channel) are strictly zero. These processes still need to be clarified and fully understood in the future.

In planetary atmospheres and astrophysical sciences, several aspects are still unrevealed and still need to be deeply investigated. Emphasis should be placed on radical–radical and ion–molecule reaction studies at low collision energies where electronic, spin and nuclear effects play important roles. In these media, the reactivity and relative abundances of metal containing molecules or electronically excited species are not yet fully established and implications for the environment are neither well understood nor known. Also, some aspects related to chirality of either the molecular entity or the confining environment represent new development directions towards the structuration and particle and energy transfers as proved recently by Zehnacker and co-workers.248 New insights into the influence of external fields (magnetic or electric) on quantum reactivity of small molecules either isolated or encapsulated were also observed that are worth investigating in depth.249,250 Again, the underlying mechanisms are still not well established.

The full understanding of these processes should lead to the control of the electronic and nuclear motions from the molecular regions up to dissociations at different timescales (ps–ns, fs–ps and as). The outcomes of these studies should contribute to the enhancement of the branching ratios of the formation of some products. Routes to reach these aims include

(i) the coherent control of the relaxation dynamics, by attempting to influence the relaxation in its own dynamics. For that purpose, UV-ns lasers can be coupled with IR lasers to explore the effect of the activation of specific vibrational modes on the molecular relaxation dynamics at various locations of the reaction coordinate through the time-resolved investigation of the reaction dynamics.

(ii) Another possibility targets the neighborhood of the molecule and more specifically the micro solvation of small molecules in quantum liquids (He droplets) or classical clusters (Ne, Ar, Kr, Xe, water) or in cavities, where the dissociation dynamics could be influenced in one or the other side. To address this point, the study of the relaxation dynamics of the isolated molecule and comparison to that of the confined molecule should elucidate the dependence of these dopants on the chemical nature of the droplets, solvents, etc. As illustrated above, He droplets or water clusters, for instance, represent microreactors that force reactivity by quantum effects.

(iii) The study of the fragmentation of multicharged species (either cationic or anionic).

Because of the multi-dimensionality of these problems, experiments and computations have to work together in a complementary approach.

To date, the chemical-physical techniques, theoretical or experimental, used for the studies of few particle molecular systems are well established and have reached outstanding levels. This makes their transfer to other communities (e.g. organic and inorganic chemists, biologists, industrial researchers) timely. For instance, standard spectroscopic techniques (e.g. UV-Vis spectroscopy) are nowadays used to identify and quantify small gaseous molecules in situ and endogenous gaseous signaling molecules in vivo (i.e. NO,213,214 CO215 and H2S216,217) and their reaction bioproducts. These molecules are known to act as biological regulators and cellular signaling molecules, which are involved in and control a wide range of bodily essential functions cardiovascular, nervous and immune and, physiological and pathological processes. Moreover, it is established that CO and H2S are closely connected to the modulation of nitric oxide signaling pathways in animals and in plants.218 Thus, the corresponding pathways are surely intricated and complex, where several key endogenous molecular species were identified (e.g. HSNO,219 OONO[thin space (1/6-em)]220–224 and SSNO[thin space (1/6-em)]225,226). While the role and the endogenous nature of OONO[thin space (1/6-em)]224,227–229 are established, those of HSNO and SSNO are still subject to controversy.225–239 This controversy concerns also their potent key role in the cross-talk signaling pathways. More generally, several mechanistic aspects of the implication of these small molecules still need to be investigated in depth. A major issue concerns the lack of information on small molecular systems that may be involved in these processes since the proposed molecular structures and mechanisms rely only on standard molecules known from lab chemists and biologists. Nevertheless, these species cannot fully account for all experimental observations in vivo and in biological media (e.g. non-equivoque attribution of measured UV-Vis absorption or fluorescence bands). For remediation, several groups undertook systematic studies of small molecules that are strongly suspected to be involved in these bioprocesses. The list of molecules includes HSNO and SSNO and their related species (HNO/HON,242 SSNO, HNS/HSN,241,243 HSN/HNS[thin space (1/6-em)]244 and HNS+/HSN+[thin space (1/6-em)]245). These studies are performed using state-of-the-art theoretical and experimental techniques such as those described above. They concern their spectroscopic (vibrational, rotational and electronic) characterization for comparison with the measured in vivo bands. For instance, the comparison of HNO/HON and HNS/HSN systems showed that the latter are more efficient for NO delivery in vivo.

Nowadays, characterization of small molecules in vivo is an emerging and active field of research with obvious implications for diagnostic or medical purposes. Let's cite for instance light assisted NO delivery medical applications (e.g. cardioprotection240) or linking breath analysis to human health.246 The outputs of such research are important for human health. Developments include applications of modern high-sensitivity experiments in medical research for the generation of small NO containing molecules as bioactive reaction products of the NO/H2S interaction and the simulated NO delivery in vivo.247 Up-to-date achievements show that NO-releasing molecules should possess (i) small dissociation energies if the process is occurring in the ground states; or (ii) repulsive electronic states along the NO releasing coordinates if it is induced by UV-Vis photon absorption; (iii) long-lived electronic states in the Vis domain that may serve as intermediates/precursors for fluorescence.

To go further with the applications, a major step concerns the reduction of the cost of the investigations. Once the reaction pathways are known from laboratory studies, one needs to prepare the appropriate molecular reactants or intermediates. Molecular systems in electronic or (ro)-vibrational excited states, that can be easily prepared by photon absorption specifically, present promising potentialities that need to be explored. Note also that the intrinsic properties of small molecules and clusters at the microscopic level are needed to understand those of macromolecular entities and especially the influence of quantum effects on their spectroscopy, reactivity and dynamics. Complex systems such as those one may encounter during reactions at gas–solid interfaces, in liquid solutions, in enzymes, and for protein folding should also benefit from the developments and the outcomes of our field as discussed by Klippenstein, Pande and Truhlar in ref. 251.

Acknowledgements

This work was supported by the CNRS program “Physique et Chimie du Milieu Interstellaire” (PCMI) co-funded by the Centre National d'Etudes Spatiales (CNES). The support of the COST Action CM1405 (MOLIM: MOLecules In Motion) is acknowledged. I thank R. Linguerri for his comments on the manuscript.

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