Frédéric Guégan
email: frederic.guegan@univ-poitiers.frr

Lynda Merzoud

Henry Chermette

Christophe Morell
email: christophe.morell@univ-lyon1.fr

Chapter 5 Excited States

Keywords: Conceptual DFT, excited states, perturbation theory

In this chapter, inclusion of excited states in Conceptual DFT is discussed. We focus on the study of reactivity, along two axes: either looking for reactivity and selectivity in the excited states themselves, or using excited states as a mere tool to delineate ground state chemical properties.

Introduction

Conceptual DFT [START_REF] Chermette | Chemical reactivity indexes in density functional theory[END_REF][START_REF] Geerlings | Conceptual density functional theory[END_REF][START_REF] Geerlings | Conceptual density functional theory: status, prospects, issues[END_REF], by its explicit dependence over the first Hohenberg-Kohn theorem [START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF], is a ground-state theory. Therefore, the very purpose of this chapter may then seem out of scope of conceptual DFT. How can one include excited states in a ground-state only representation? And for which aim? Several approaches were undertook in the past years to embrace this topic, 1 which we propose to revisit here. Broadly speaking, two axes can be drawn: either one is interested in characterizing the excited states properties, by studying them or conjecturing their properties from the ground state, or either one is interested in using the excited states to improve the representation of the ground state. Illustrations of both ideas are provided in sections 1 and 2, respectively. Note however this chapter does not aim at being exhaustive. Noticeably, many developments were proposed over the years, especially at times when no efficient computational framework for excited states was available (before the advent of TDDFT, so to say). Additionally, some works focused on the development of time-independent DFT models, looking for the definition and construction of either state-specific or generic energy density functionals. [START_REF] Görling | Density-functional theory beyond the hohenberg-kohn theorem[END_REF][START_REF] Ayers | Time-independent densityfunctional theory for excited states of coulomb systems[END_REF] We believe such developments, though precious and meaningful, fall out of the scope of the chapter, and for the sake of clarity and concision we decided not to include them in the following.

Reactivity and Selectivity of Excited

Photochemical reactivity

Study of excited states properties is particularly interesting for photochemical reactions (reactions performed under photoexcitation). [START_REF]Photoreaction", IU-PAC Compendium of Chemical Terminology -The Gold Book[END_REF] Experimentally, it is indeed often observed that the course of a chemical reaction is altered when this reaction is performed under exposition to light. This is for instance the case of the electrocyclic reactions, whose reactivity is explained by the famous In such photochemical reactions one reactant is electronically excited to one of the very first excited states. Following Kasha's rule, [START_REF] Michael | Characterization of electronic transitions in complex molecules[END_REF] light absorption may indeed lead to high excited singlet states, which quickly decay to the lowest excited one (S 1 ). This singlet state may also convert to a lower energy triplet state T 1 through inter system crossing (ISC). Hence, among the excited states manifold, one may restrict the study to states S 1 and T 1 only to explain photochemical reactivity and selectivity.

The case of triplet state T 1 is noteworthy. Formally speaking, this excited state is indeed a ground state for the triplet spin multiplicity. Hence many photochemical reactions can be straightforwardly studied by the means of genuine ground-state conceptual DFT tools. This has been nicely illustrated by a series of publication from Geerlings and de Proft group in the case of photochemical cycloadditions. [START_REF] Pintér | Regioselectivity in the [2+2] cyclo-addition reaction of triplet carbonyl compounds to substituted alkenes (Paterno-Buchi reaction): A spin-polarized conceptual DFT approach[END_REF][START_REF] De Proft | Woodward-Hoffmann rules in density functional theory: Initial hardness response[END_REF] They showed that the sign of the hardness variation at the onset of the reaction is a reliable indicator of the feasibility of the reaction (in connection with Woodward-Hoffmann rules). [START_REF] De Proft | Initial hardness response and hardness profiles in the study of woodward-hoffmann rules for electrocyclizations[END_REF] They also demonstrated, by deriving original spin-polarised descriptors (spin donicity and philicity), that selectivity in the [2+2] photochemical cycloaddition of enones with substituted alkenes is better explained by the differential spin-coupling between reactive sites than by standard charge-transfer arguments. [START_REF] De Proft | Spin-polarized conceptual density functional theory study of the regioselectivity in the [2+2] photocycloaddition of enones to substituted alkenes[END_REF]

Insight from frontier MO theory

Nonetheless, how can one address cases for which ISC is not active, or not leading to chemical reactivity? In such a case, a genuine excited state (S 1 ) needs to be studied and a model for predicting their chemical behavior should be proposed.

At first, one may rely on the formalism of MO theory, and employ "usual" approximations to delineate the chemical behaviour of the first excited state. If one neglects orbital relaxation, the first excitation may be seen as arising from the promotion of one electron from the HOMO to the LUMO. The resulting excited state configuration can then be written as (HO) 1 (LU ) 1 . This approximate electron configuration can then be used to express usual conceptual-DFT (C-DFT) descriptors. Let us for instance consider the electrophilic Fukui function. [START_REF] Parr | Density functional approach to the frontier-electron theory of chemical reactivity[END_REF] Under the finite difference approximation, it is expressed as the following electron density difference

f + ex (r) = ρ N +1 (r) -ρ N (r) (5.1)
where the indices refer to the total number of electrons in the system. Here one has to consider the neutral excited configuration, and a configuration with one additional electron (N+1). Keeping the frozen orbital hypothesis, the lowest N+1 configuration in energy is (HO) 2 (LU ) 1 . Hence, in the excited state and under the previous approximations the electrophilic Fukui function will equal the HOMO density

f + ex (r) = ρ HO (r) = f - gs (r) (5.2)
which is itself equal to the nucleophilic ground state Fukui function. Using the same line of arguments, one has f - ex (r) = f + gs (r). Ultimately one may infer that the dual descriptor (DD) [START_REF] Morell | New dual descriptor for chemical reactivity[END_REF] in the excited state will be the opposite of that of the ground state:

∆f ex (r) = f + ex (r) -f - ex (r) = ρ HO (r) -ρ LU (r) = -∆f gs (r) (5.3)
Sites with positive (resp. negative) values of ∆f (r) will be nucleophilic (resp. electrophilic) in S 1 and electrophilic (resp. nucleophilic) in the ground state.

Such a simple development was used and allowed to retrieve the regio-selectivity of photo-chemically induced cycloaddition (Woodward-Hoffmann rules). [START_REF] Ayers | Understanding the Woodward-Hoffmann Rules by Using Changes in Electron Density[END_REF] Even though this naive model holds and provides results in agreement with experiments, there is room for an improved and more grounded theory. Molecules in the ground state are depicted in red, while molecules in the first excited state are depicted in blue.

Chemical potential locality

So, how can one derive more general knowledge on the excited states, thus without the need to rely on the rather drastic frozen orbital hypothesis? One of the very few proposal relies upon the electronic chemical potential.

Let us recall that the electronic chemical potential µ is defined, according to Parr, as the functional derivative of the energy with respect to the electron density:

µ = δE δρ(r) N = v(r) + δF HK [ρ(r)] δρ(r) . ( 5
λ k (r) = δE δρ k (r) N = v(r) + δF HK [ρ k (r)] δρ k (r) .
(5.5)

The excited state concerned in the above equation is called Hot Excited State as it is both electronically and vibrationally excited. In this approach, λ k is a local quantity, since the excited density does not minimize the ground state energy functional. Indeed, the above formulation uses the universal Hohenberg-Kohn functional that only works for ground states. This non constant chemical potential is thus fitted to translate the tendency of the electron density to relax to the ground state configuration, at fixed geometry through the integrated equation:

dE ≈ λ k (r)δρ(r)dr (5.6)
Levy and Nagy have proposed an excited state formulation of DFT in which the Hohenberg-Kohn fonctional is no longer universal, in the sense that it is a functional of both the electron density and the external potential. [START_REF] Levy | Variational density-functional theory for an individual excited state[END_REF] To reach a stationary state, the external potential need to evolve (geometry relaxation).

E k = ρ k (r)δv(r)dr + F k [ρ k (r), v(r)] (5.7)
λ k would have been global should this excited state formulation has been used.

After some developments, it could be shown that for the low lying excited states one may write

λ k (r) = µ + ρ k (r ′ ) -ρ 0 (r ′ ) |r -r ′ | dr ′ = µ + ∆f k (r ′ ) |r -r ′ | dr ′ (5.8)
with ρ k the k th excited state electron density (0 meaning ground state), and ∆f k the so-called kth state-specific dual descriptor (SSDD). Hence, the difference between the global and local potentials is equal to the difference in the electrostatic potential induced by the electron density distributions in the ground and excited states. A site that lost electron density under excitation will then become attractive to electrons in the excited state (thus become electrophilic). Conversely a site that gained electron density will become repulsive to electrons, thus bear some nucleophilicity.

If we now focus only on the first excited state, then we retrieve our previous results on the signification of the DD sign in the excited states. Indeed, it is often assumed that the first SSDD is equal to the "usual" C-DFT and ground-state DD (vide infra). Thus the ground state DD may indeed be used to retrieve the reactivity and selectivity in the first excited state, but the relation between the sign of the DD and the philicities is reversed (see figure 5.2). Nucleophilic regions will be characterised by a positive sign of the DD in the excited state, while electrophilic regions are associated to a negative DD.

Eventually, this model grounds the naive view that the opposite of the ground state dual descriptor can ascribe the electro/nucleo philicity of molecular regions. This approach has been successsful to recover the Woodward-Hoffmann rules, predict the regioselectivity of Paterno-Buchi reactions, [START_REF] Morell | Characterization of the chemical behavior of the low excited states through a local chemical potential[END_REF] and has also been used for explaining DNA photo-chemically induced lesions.

[19]

In summary

Very few attempts have been made to propose a theory able to predict the reactivity and selectivity of excited states. Generally, the proposed approaches intend to only tackle the low-lying excited states, which are expected to be the major player in photoreactivity. In fact, in several cases these excited states are formally ground states for the triplet multiplicity, hence ground-state descriptors are perfectly working.

Otherwise, the electron densities can be described from a Taylor's expansion of the ground state density, allowing to delineate excited state properties using "standard" C-DFT developments. In this spirit a descriptor based on a local chemical potential was proposed, and successfully applied to predict the regioselectivity of various [2+2] photochemical cycloadditions.

Excited states used to describe the ground state

The use of excited states to understand the reactivity of a ground state electron system goes back to a publication by Walsh in the 1940's. [START_REF] Donald | The structures of ethylene oxide, cyclopropane, and related molecules[END_REF] At that time Walsh was arguing that ethylene oxide and ethylene are more reactive than ethane because the first excited state wavelengths of the former are lower (resp.

1950 Å and 1745 Å) than that of the latter. After this first rough approach, the subject was left almost untouched till Pearson, [START_REF] Ralph | A Symmetry rule for Predicting Molecular Structure and Reactivity[END_REF] Bader [START_REF] Richard | Vibrationally induced perturbations in molecular electron distributions[END_REF] and Salem [START_REF] Salem | Conditions for favorable unimolecular reaction paths[END_REF] revived it up in the 1960's. In three different papers they provided a series of conditions for an excited state to favor a chemical reaction. In this part, starting from their development, it is shown that lot of information about the ground state reactivity, regio and stereoselectivity can be obtained from the excited states.

Reactivity from excitation energy: an early formulation of the Maximum Hardness Principle

In the late 1980's Pearson was working on the physical meaning of the chemical potential and the absolute hardness. His main concern was chemical reactivity and how to compare the stability of molecules. In the following years he was about to propose the Maximum Hardness Principle. In this context he published an article in the journal of the American Chemical Society entitled "Electronic spectra and chemical reactivity". [START_REF] Ralph | Electronic spectra and chemical reactivity[END_REF] In this paper, actually a follow up of the series of original papers published by Bader, Salem and himself, he proposed a reactivity model based upon the wave-function and energy perturbation of a molecular fragment experiencing a modification of its surrounding, due for instance to the approach of another molecule or an internal reorganisation (isomerisation). Its perturbed wave function, as it is common in this theory, was expanded through the set of the unperturbed eigenfunctions.

Following Pearson's notation, let U be the nuclear-nuclear and nuclearelectron potential energy, and Q be the reaction coordinate. The molecular (total) Hamiltonian can be expanded as a Taylor series:

H = H 0 + ∂U ∂Q Q + 1 2 ∂ 2 U ∂Q 2 Q 2 + ... (5.9)
and according to Rayleigh-Schrödinger perturbation theory ground state energy and wavefunction vary according to the perturbation as

E = E 0 + ψ 0 ∂U ∂Q ψ 0 Q + ψ 0 ∂ 2 U ∂Q 2 ψ 0 Q 2 2 + k̸ =0 ψ 0 ∂U ∂Q ψ k Q 2 E 0 -E k (5.10) ψ = ψ 0 + k̸ =0 ψ 0 ∂U ∂Q ψ k Q E 0 -E k ψ k (5.11)
where (E 0 , ψ 0 ) and (E k , ψ k ) are the unperturbed solutions of the Schrödinger equation for, respectively, the ground and k th excited state.

Pearson then used equations 5.10 and 5.11 to deduce simple rules to evaluate the reactivity of a given compound. In the energy response, he noticed that the two first terms basically translate how the energy changes when nuclei move while electron density remains frozen. Obviously, if the refer-ence geometry is a minimum, this contribution is positive (destabilisation).

On the other hand, the last contribution is stabilising, since the numerator is by construction positive, while denominator is negative. This term translates the energy change experienced by the system as the electronic configuration is changed along the perturbation. As such, chemical reaction will take place only in cases where the last term has non negligible values. This

States Specific Dual Descriptors

At the core of Pearson and Bader approaches, one finds perturbation theory, which basically states that response to perturbation of a given system can be developed on the basis of its unperturbed eigenstates. Then, treating chemical interaction as a perturbation, and identifying eigenstates as the set of ground and excited states, it is possible to account for the ground state chemical properties through a careful analysis of the excited states.

In a related approach, it was proposed in 2013 that evolution of the electron density along a chemical process, that is, following a reaction coordinate, could also be extrapolated from a set of excited states electron densities. [START_REF] Tognetti | A proposal for an extended dual descriptor: a possible solution when frontier molecular orbital theory fails[END_REF] More specifically, it was proposed that ground state electron density at a given point P on the potential energy surface, closer to the transition state of interest than the reagent R is, reads

ρ P,0 (r) = i≥0 α i ρ R,i (r) (5.12)
where indices P and R refer to the geometry, and i to the energy state (ith excited state, 0 meaning ground state). From the conservation of the electron number we directly obtain that

i≥0 α i = 1 (5.13)
from which we see that electron density reorganisation from R to P is

∆ρ R→P (r) = i≥1 α i [ρ R,i (r) -ρ R,0 (r)] = i≥1 α i ∆f R,i (r) (5.14)
Thus one gets that electron density reorganisation along a chemical process can be expressed thanks to the electron density reorganisation under excitation of the reagent. Analytical formulas for the coefficients α are unknown, but following Pearson's arguments it may be expected that high lying excited states will not contribute significantly to the ground state reactivity. Following Fukui's development, one may even expect that the first excited state, likely stemming from a HO → LU excitation, will be the principal player. Under a frozen orbital hypothesis, such a transition will indeed yield

∆f R,1 (r) = ρ R,1 (r) -ρ R,0 (r) = ρ R,LU (r) -ρ R,HO (r) ≈ ∆f (r) (5.15)
thus the electron density reorganisation from R to P will be roughly equal to the FMO approximation of the dual descriptor. From this identification, it was proposed to coin ∆f i = ρ i -ρ 0 the i th state specific dual descriptor (SSDD). Interestingly, though in most cases the correct reactivities and selectivities are grasped by the first SSDD (see Figure 5.2), situations arise where higher excitations are required (in line with Pearson's observation). This is obviously expected for cases where Frontier Molecular Orbital theory itself is failing. But more interestingly, this is also often the case when one studies reactant complexes at the onset of a chemical reaction -thus with a rather large separation between reagents. [START_REF] De Proft | Investigation of electron density changes at the onset of a chemical reaction using the state-specific dual descriptor from conceptual density functional theory[END_REF]. An illustrative example is given below. In figure 5.3 are represented on the top and bottom left both the second and third SSDD, and on the top and bottom right the first and second NOCV for a butadiene-ethylene complex. NOCV is an acronym that stands for Natural Orbital for Chemical

Valence. Basically the NOCVs describe the electron density deformation of the most relevant orbital during a chemical reaction. The first SSDD actually consists on an intra-fragment excitation located on butadiene that quite likely suggest that butadiene is more prone to react with itself than with ethylene.

It is in perfect line with the Frontier Molecular Orbital theory as both butadiene HOMO and LUMO are located in between those of ethylene making the [4+2] cyclo-adduct of butadiene with itself the major product of the reaction.

Nonetheless, the first density reshuffling located on one reagent alone does not necessarily bring relevant information about reactivity or selectivity. On the other hand, charge transfers from one reagent to the other may be observed in higher excited states, and thus translate how electron density is likely to distort along the reaction path, especially regarding the direction of the easiest electron flow. SSDD may then ascertain the reagents relative philicities and site selectivities, as expected for a Dual Descriptor avatar. Still on the example of cycloaddition between butadiene and ethylene it can be observed on figure 5.3 that the 1 st SSDD describes the electron donation from the ethylene to butadiene while the 2 nd SSDD pictures the back donation from ethelene to butadiene. Interestingly, these inter-fragment state specific dual descriptors uncannily look like the 1 st and 2 nd ETS-NOCVs density deformations calculated at the transition state structure. [START_REF] De Proft | Investigation of electron density changes at the onset of a chemical reaction using the state-specific dual descriptor from conceptual density functional theory[END_REF] Dewar, [START_REF] Michael | A critique of frontier orbital theory[END_REF] pointed out in his critic of isoquinoline as a usual heterocycle for which the use of Frontier Molecular Orbital Theory (FMOT) fails to predict the correct orientation of Electrophilic Aromatic Substitution (EAS). Using HOMO coefficients, FMOT suggests that the order of reactivity is C4 < C5 < C8, and is not in good agreement with the experimental data. Indeed, the 4derivative has never been observed. All the experimental results are consistent with a high reactivity of carbon C5 followed closely by carbon C8.

Concerning the region-selectivity of the Electrophilic Aromatic Substitution (EAS), it seems that the DFT-based descriptors, such as Fukui functions or the usual dual descriptor, are not better than FMOTs. As can be seen in In a final note, it is interesting to note that resorting to explicit evaluation of excited states has two significant advantages. First, since excited states are not restricted to single MO excitations, SSDDs are expected to incorporate fine details about the electron density reorganisation, e.g. σ relaxation for a reaction involving unsaturated compounds. MO relaxation may thus be grasped, at least partially. Second, as a "side-product" of the excited state calculations, one ends up with charge-transfer excitation energies. These energies could serve as quantitative reactivity indicators, as long as one is interested in comparable chemical systems. Interestingly, this point was overlooked so far.

Electron Polarization rationalized with Excited States

In 2020, some of the present authors retraced Pearson's, Walsh' and Bader's footsteps, and used explicit Rayleigh Schrödinger perturbation theory to study the response of a chemical system. [START_REF] Guégan | Understanding chemical selectivity through well selected excited states[END_REF] The premises are thus known: let H pert a perturbation Hamiltonian, acting on a system whose quantum states (E n , |n⟩) are known. From the first order development of the ground state wavefunction,

|ψ⟩ = c 0   |0⟩ + k̸ =0 ⟨k|H pert |0⟩ E 0 -E k |k⟩   = c 0   |0⟩ + k̸ =0 c k |k⟩   (5.16)
it is possible to express the perturbed electron density

ρ pert (r) = ⟨ψ|ρ(r)|ψ⟩ ≈ ρ 0 (r) + 2 k̸ =0 c k ρ 0 k (r).
(5.17)

In the previous expressions, c 0 is a normalisation constant, which is assumed to be close to unity (small perturbation), and ρ 0 k = ⟨k|ρ(r)|0⟩ is the transition density from the ground state to the excited state k. 1 .

Electron density reshuffling under perturbation will thus be

δρ(r) = ρ pert (r) -ρ 0 (r) = 2 k̸ =0 c k ρ 0 k (r) (5.18)
hence be expressed as a weighted sum of transition densities, which can themselves be obtained from any TD-DFT calculation. Several features of δρ deserve to be delineated. First, if the perturbation is designed to mimic the approach of a reagent, then this quantity translates the electron density polarisation caused by this approach. This is a missing term in usual reactivity developments (Klopman-Salem [START_REF] Klopman | Chemical Reactivity and the Concept of Charge and Frontier-Controlled reactions[END_REF][START_REF] Salem | Intermolecular Orbital Theory of the Interaction between Conjugated Systems. I. General Theory[END_REF] for instance), and relates to soft/hard interactions in the nomenclature of Pearson. Interestingly, it proves more relevant than expected to describe chemical reactivity and selectivity, as various known chemical properties can be grasped from such a quantity.

Second, since transition densities integrate to zero, so does δρ: we indeed work at constant electron count. Regarding the c k coefficients, it may be noted that they are decreasing as excitation energy increases, thus only the lowest excited states need to be computed. Nevertheless, and in perfect line with

Pearson, one cannot rely on the very first excited states alone, since the numerator may be negligible for these states (poor overlap between unperturbed states through the perturbation). In fact, in the case of a simple point charge perturbation, it could be shown that the largest contribution could stem from rather high excited states -up to the 33rd excitation in the case of a cobalt complex! Similarly, energy responses can be defined, up to the second order:

E (1) = ⟨0|H pert |0⟩ (5.19) E (2) = - k̸ =0 |⟨k|H pert |0⟩| 2 E k -E 0 = - k̸ =0 c 2 k (E k -E 0 ). (5.20)
If the perturbation Hamiltonian is the electrostatic potential induced by a point charge at point r, E (1) will then simply be proportional to the electronic component of the molecular electrostatic potential (MEP) at point r. It will be stabilising if the point charge is positive, and destabilising otherwise.

On the other hand, E (2) will always be a stabilising contribution, translat-ing the stabilisation undergone by the system by distorting its electron density within the perturbing potential. Following Pearson, if we consider a perturbation potential mimicking the approach of a reagent, the favored geometry of approach should be associated to the most negative (stabilising) value of E (2) . Hence polarisation energy can bring valuable information on reactivity and selectivity. And indeed, studying the evolution of E (2) for carbonyl compounds perturbed by a negative point charge placed at a constant distance from the C and for various angles of attack on the C=O function, the wellknown Bürgi-Dunitz angle of attack can be retrieved, see In a further study, it could furthermore be shown that the more the system can spread its electron density reorganisation, both through space and among the excited states manifold, the larger the second-order stabilisation. [START_REF] Guégan | A statistical thermodynamics view of electron density polarisation: application to chemical selectivity[END_REF] This could in fact be quantified. Recalling equation 5. [START_REF] Ayers | Understanding the Woodward-Hoffmann Rules by Using Changes in Electron Density[END_REF]

S = -k B k c 2 k ln c 2 k . (5.21)
It may be noted that the same entropy can be defined for the unperturbed system (c k = δ 0k ) but it equals zero. Hence S here can be alternatively seen as the entropy of the perturbed configuration or the entropy change induced by the perturbation.

Strong correlations were observed between E (2) and S values for a given system, confirming that most reactive positions in molecules lead to a maximal response in terms of excited states population. This is for instance illustrated in the case of furan in Figure 5.6: placing a 0.1 e point charge perturber on carbon atom Cα results in a much larger polarisation response, translated either in the transition probabilities for each excited state or in the total entropy, than placing the same charge on carbon atom Cβ. At the same time, polarisation energy is significantly more stabilising in the case of a perturbation at Cα, in the line with the expected higher reactivity on this position. gesting this is a general feature. In the end, external perturbation can be seen as interaction with a "heat source", and polarisation as a heat exchange between the perturber and the system. Said otherwise, interaction of two reagents along a chemical reaction could be understood in terms of heating and cooling; it is then possible to say "how hot" or "how cool" an electron density is expected to become as a consequence of the approach of a reagent.

In summary

To summarise, by its very vocabulary and concepts, chemistry invites to study chemical reactions through a "perturbation perspective". As such, it is not surprising that mathematical expressions derived in this context rely explicitly on excited states. But this is not a mere mathematical coincidence. In fact, as pointed out first by Walsh, a formal connection between reactivity and excitability is expected, since both properties are linked to the propensity of the electron distribution in a system to reorganise under external stress. It is also not surprising that Pearson came to the same idea, since he proposed to analyse reactivity through polarisability, which is also another way to describe the plasticity of the electron distribution. Overall, reactivity can then be conceived as "states-specific" excitation of a molecule induced by the approach of a reagent, or conversely excitation can be seen as a "reagent-specific" distortion of the electron cloud in view of a reaction.

Conclusion and Perspectives

In a more general conclusion, although C-DFT is usually conceived as a groundstate theory, extensions to excited states are possible. As retraced previously, one can either focus on the properties of excited states themselves, or try to extract ground state properties from excitations (through a perturbation framework). Formally speaking, both ideas were already present in early theoretical developments (in Walsh, Bader, Fukui and Pearson papers for instance).

Nevertheless, it is only rather recently -say in the last twenty years or so -that they bloomed, owing to the developments of more and more efficient tools to compute excited states. Nowadays, excited state calculations are rather cheap, and computer developments allows the simultaneous calculation of large sets of excited states for relatively large systems -hence "brute force" evaluations are now feasible.

Because of this, it could be tempting to declare that the perspectives are rather limited, since equations are known and can now be evaluated. Yet, the case of the electron density polarisation illustrates that there is always room for more development. First, this phenomenon proved to be more relevant than expected, although polarisation is the fifth wheel of usual reactivity model.

Second, a quantity displaying the features of a temperature could be constructed from polarisation. What is the actual meaning and extent of this temperature? Could it be used to help developing T-dependent DFT models? 23

Figure 5 . 1 :

 51 Figure 5.1: [2+2] cycloaddition of ethylene explained by the Dual descriptor.

  will be more likely to occur if transition energies E k -E 0 are small, thus easily excitable compounds are expected to be rather reactive. Lot of examples were provided to support Pearson statement that the lower the excitation energy, the more reactive the molecule. As for instance the nucleophilic attack of carbonyl compounds that turn out to be easier in the following order: HCOF(45.5 × 10 3 cm -1 ) > CH 3 COCl(42.6 × 10 3 cm -1 ) > CH 3 COCH 3 (35 × 10 3 cm -1 ) > CH 3 CHO(34 × 10 3 cm -1 ) > CH 2 --CHCHO(26.5 × 10 3 cm -1 ).Another example given was the decreasing bond strength of the following alkylhalides: CH 3 F(75.4 × 10 3 cm -1 ) > CH 3 Cl(59 × 10 3 cm -1 ) > CH 3 Br(50 × 10 3 cm -1 ) > CH 3 I(38.5 × 10 3 cm -1 ). The numbers between brackets are the first excitation wavenumbers. Later, it has been shown byNagy[25] that the first excitation energy is very likely the best way to measure the hardness of a molecule. As a consequence Pearson article can be retrospectively regarded as an early formulation of the Principle of Maximum Hardness. A question naturally follows: would it be possible to get regioselectivity information by pursuing this research axis?

Figure 5 . 2 :

 52 Figure 5.2: The ground state DD and the first SSDD of ethylen.

Figure 5 . 3 :

 53 Figure 5.3: SSDD and NOCV 3D maps pertaining to the [4+2] cycloaddition between ethylene (top) and butadiene (bottom) a) 2 nd SSDD b)1 st NOCV c)E rd SSDD and d)2 nd NOCV, in red regions where both fonctions are posivite, in yellow regions where both fontions are negative.

Figure 5 . 4 ,

 54 Figure 5.4, the usual DD and the first SSDD calculated for isoquinoline are different. As can be seen, the usual DD does not give the correct prediction of regio-selectivity. Therefore, for the usual DD, EAS should occur at carbons 3 and 7, the positions known to be non-reactive with respect to EAS. The first SSDD provides an alternative prediction. It indicates that the electrophiles should target the nitrogen lone pair. This example underline the advantage

Figure 5 . 4 :

 54 Figure 5.4: The usual DD and SSDD for isoquinoline, in red regions where both fonctions are posivite, in yellow regions where both fontions are negative (Isovalue=0.005)

Figure 5 . 5 .

 55 According to the density polarisation sign, the main excited state involved in this charge transfer is associated to the promotion of a small fraction of electron of the π(C -O) bonding orbital to the π * (C -0) anti-bonding orbital. The transition density that allows this electron excitation is represented in Figure 5.5

Figure 5 . 5 :

 55 Figure 5.5: 7 th formol transition density and electron density response for formaldehyde perturbed by a -0.5 a.u. point charge placed at 2 Å from the C atom, represented by the light blue sphere. Colour scheme: δρ > 0, red; δρ < 0, yellow. Isodensity: 0.0004 a.u.

Figure 5 . 6 : 5 . 7 .

 5657 Figure 5.6: Polarisation spectrum when Cα and Cβ are perturbed by a 0.1e point charge.

Figure 5 . 7 :

 57 Figure 5.7: Absolute polarisation energy versus entropy for furane; q=0.1e.

Note this quantity is different from the k th SSDD, ∆f k (r) = ⟨k|ρ(r)|k⟩ -⟨0|ρ(r)|0⟩


S Fernandes
email: sandrina.fernandes@insp.jussieu.fr

I Vickridge

P Jonnard

K Le Guen

I Ismail

P Walter

PIXE-KOSSEL IN A GAAS MONOCRYSTAL

A new methodology was developed to analyse thin films at the nanoscale by combining Kossel diffraction with particle-induced X-ray emission (PIXE). This technique is related to the standing wave method and has already been applied to the study of periodic nanoscale multilayers [1, 2]. The Kossel diffraction of a GaAs single crystal, generated during irradiation with a 1.5 MeV proton beam, is presented. The intensities of the characteristic K emissions of Ga and As of GaAs can be measured as a function of the detection angle with a CCD camera (Andor IKON-M), making it possible to obtain Kossel curves without the use of high precision goniometric systems. An oscillation of intensity is observed when the detection angle varies around the Bragg angle, defined by the energy of the X-ray emission and by the lattice distance of the plane which will diffract. The CCD camera allows the selection of x-ray energy at any angle within a given angular range and the entire experimental setup is fixed.

INTRODUCTION

The interaction of the incident protons with the sample produces X-rays which can have a constructive interference when conditions satisfy Bragg's Law (nλ = 2d sinθ). The Braggdiffracted X-rays will result in the emission of Kossel cones, which will then be intercepted through the CDD screen (13 µm resolution).

Under Bragg conditions, a standing wave having the inter-planar distance period develops and shifts perpendicular to the layers as the angle changes. The variation in the detection angle causes a shift in the nodes of the electric field emitted by the crystal.

RESULTS

Calculations with dynamical theory of diffraction show that the GaAs structures should be very narrow but perhaps observable at various planes.

Ga planes ( 002

  X-ray planar waveguides of Pt/Fe/Pt and Ta/Cr/Pt [3].


domain: spi phys

text:
Wojciech Piotrowski

Linda Dalipi

Karolina Elzbieciak-Piecka

Artur Bednarkiewicz

Benoit Fond
email: benoit.fond@onera.fr

Lukasz Marciniak

A 2D temperature imaging system based on two low-power low-cost LEDs for excitation and a single low speed camera for detection

In this work, benefiting from temperature dependent features of the excitation of YVO4:Eu 3+ , we present a luminescence emission ratiometic approach for 2D phosphor thermometry based on excitation with two different wavelengths and single band collection. Thermal imaging is performed using two low power alternating LEDs peaking at 270 nm and 340 nm for excitation and a single low frame rate camera for detection of the same emission band in subsequent exposures. For demonstration a metal plate was coated with YVO4:Eu 3+ and exposed to a flame on the back side. Despite the low power density of the illumination (<0.3 mW/cm 2 ), this simple approach yielded a high single pixel precision (1.5°C) at a resolution of 160 μm as a consequence of the efficient spectral and temporal collection scheme, the high temperature sensitivity and the good thermal response.

In the last decades, phosphor thermometry has become a versatile optical technique to monitor remotely temperature variations in numerous engineering applications. It relies on the thermal dependence of the spectroscopic properties of inorganic phosphor particles attached to the surface of interest. The two main approaches to measure thermal gradients in 2D are the spectral (emission intensity ratio) and temporal (emission decay time) technique. The spectral method provides temperature information from the temperature dependence emission spectrum by taking a ratio of emission intensities in two different wavelength regions. Therefore, it involves two separate detectors equipped with respective spectral filters, and precise image mapping between the recoded images. Alternatively, the emission decay time approach requires recording multiple exposures to split the decay waveform subsequent to a single excitation pulse using high-speed detectors or interline transfer CCDs. Besides, one limitation of this method when using LEDs for excitation, is the limitation in available energy during the short decay times (<ms). In this work, we introduce an intensity ratio approach that exploits the temperature dependence in the excitation spectrum of phosphors instead. Lanthanide-doped rare-earth orthovanadates (AVO4:Eu 3+ , (A = Lu, Y, Gd, La)) show an interesting thermally induced red-shifting excitation feature within VO 4 3-group, as shown in Figure 1 for the case of yttrium. The system relaxes back to the ground state with the characteristic temperature dependent lanthanide emission, here Eu 3+ . Hence, using two pulsed LEDs for excitation, the ratio of the intensity of the same Eu 3+ emission bands but upon each of the two excitation beam is a function of temperature. By separating the excitation in subsequent exposures of the same camera, 2D thermometry can be performed with a single monochrome camera as proposed here. This method is validated experimentally using YVO4:Eu 3+ , as it offered the highest sensitivity and absolute signal levels at room temperature as characterized in liquid dispersion [START_REF] Piotrowski | Self-Referenced Temperature Imaging with Dual Light Emitting Diode Excitation and Single-Band Emission of AVO4:Eu 3+ (A=Y, La, Lu, Gd) Nanophosphors[END_REF]. To demonstrate temperature imaging, a metal plate was coated with YVO4:Eu 3+ (30 µm yielded coating thickness) and subjected to transient heating by a premixed flame. It was illuminated by subsequent pulses from two LEDs which are separated in time. Two low power LEDs (<1 mW peak power), with emission peaks 270 and a 340 nm respectively, were placed at 90° and overlapped using a UV beam splitter to uniformly illuminate a 3 cm × 3cm area of the phosphor coating plate from a single direction (Figure 1.a ).The LED power density was only 0.3 mW/cm 2 . The luminescence emission was imaged using a single 12 bit interline transfer CCD equipped with a 50 mm (f/1.4) objective lens and a 570 nm long pass filter to avoid scattered excitation light.

The LEDs were each triggered at 2.5 Hz, one after the other, while the camera recording rate was set at 5 Hz to capture the emission upon each excitation in subsequent exposures as illustrated in Figure 2.a. The matching 50 ms excitation pulse and camera exposure, provided efficient excitation and collection of the entire Eu 3+ emission band, which allowed to gather high signal levels despite the low LED power density. The ratio images resulted from a frame pair corresponding to an excitation pair, were white field corrected with ratio images at homogenous temperature distribution performed at RT to correct for illumination differences between the two LEDs. The ratio images were converted to temperature maps using calibration data obtained when the coated plate was maintained at prescribed temperatures on a temperature-controlled unit. The temperature sensitivity was found to be over 1%/°C over the 20 to 70 °C temperature range. A 2D temperature map during flame heating is shown in Figure 2.b. This image consists of 340 x 260 independent temperature readouts per image over a 34 mm by 26 mm region. Using uniform temperature data, a single pixel precision of 1.5 °C at a resolution of 160 μm was estimated.

The demonstration shows the capability of this 2D phosphor thermometry ratiometric method based on dual excitation-single band emission to inspect the dynamics of the thermal processes both spatially and temporally. That a high level of precision can be obtained with such low power excitation is the result of the good photon budget of this measurement scheme combined with the high temperature sensitivity for the selected LED. In fact it is also interesting to note that the total intensity under 340 nm LED excitation at room temperature, is only 45% weaker than for the 270 nm LED illumination, which then shows luminescence intensity enhancement with increasing temperature. This thermal induced feature, therefore, provided a very good thermal response. This setup also offers practical advantages as it minimizes systematic errors due to misalignment compared to two-colour-emission intensity ratio technique, and higher photon harvesting in contrast to decay time-based method. However, potential preferential absorption of one of the two wavelength when semi-transparent medium are present in the detection path (condensation etc…) must be investigated. Additionally, this technique does not involve accurate camera timing or fast frame readout, thus offering simplicity in the detection, which can be carried out even with the camera of a smartphone.

Figure 1

 1 Figure 1 Experimental configuration of dual exactionsingle emission approach: schematic of the experimental setup (a), excitation spectrum of YVO4:Eu3+ at 0 o C and 100 o C and LED emission spectra (b) [1].

Figure 2

 2 Figure 2 Temperature imaging using the dual LEDs excitationsingle camera system: LED and CCD timing scheme (a), thermal imaging under localized heating on a steel plate (b) [1].


PhD Davies Adeloye

Omer Elneima

Luke Daines

Krisnah Poinasamy

Jennifer K Quint

PhD Samantha Walker

Chris E Brightling

Salman Siddiqui

Prof John R Hurst

Prof James D Chalmers

PhD Paul E Pfeffer

Petr Novotny

Thomas M Drake

Prof Liam G Heaney

Igor Rudan

Aziz Sheikh

Prof Anthony De Soyza
email: anthony.de-soyza@newcastle.ac.uk

Daines Mbchb

Prof I Drake Mbchb

Prof A Sheikh MD Rudan Phd

Prof C E Elneima Mrcp

Prof S Siddiqui FRCP Brightling Fmedsci

Poinasamy Llm

Prof J K Quint Frcp

Prof A De Soyza

The long-term sequelae of COVID-19: an international consensus on research priorities for patients with pre-existing and new-onset airways disease

Persistent ill health after acute COVID-19-referred to as long COVID, the post-acute COVID-19 syndrome, or the post-COVID-19 condition-has emerged as a major concern. We undertook an international consensus exercise to identify research priorities with the aim of understanding the longterm effects of acute COVID-19, with a focus on people with pre-existing airways disease and the occurrence of new-onset airways disease and associated symptoms. 202 international experts were invited to submit a minimum of three research ideas. After a two-phase internal review process, a final list of 98 research topics was scored by 48 experts. Patients with pre-existing or post-COVID-19 airways disease contributed to the exercise by weighting selected criteria. The highest-ranked research idea focused on investigation of the relationship between prognostic scores at hospital admission and morbidity at 3 months and 12 months after hospital discharge in patients with and without pre-existing airways disease. High priority was also assigned to comparisons of the prevalence and severity of post-COVID-19 fatigue, sarcopenia, anxiety, depression, and risk of future cardiovascular complications in patients with and without pre-existing airways disease. Our approach has enabled development of a set of priorities that could inform future research studies and funding decisions. This prioritisation process could also be adapted to other, non-respiratory aspects of long COVID.

Introduction

The emergence and rapid spread of COVID-19, caused by SARS-CoV-2, has led to about 180 million confirmed cases and nearly 4 million deaths worldwide as of June 19, 2021.1 The acute phase of SARS-CoV-2 infection results in a range of clinical presentations, from asymptomatic infection to severe illness requiring hospital admission and intensive care.2 Factors associated with increased risk of infection and severe disease include, but are not limited to, age, sex, ethnicity, and socioeconomic status. [START_REF] Williamson | Factors associated with COVID-19-related death using OpenSAFELY[END_REF][START_REF] Brodin | Immune determinants of COVID-19 disease presentation and severity[END_REF] The presence of pre-existing comorbidities, especially pre-existing respiratory disease, is also a major risk factor for severe outcomes. [START_REF] Schultze | Risk of COVID-19-related death among patients with chronic obstructive pulmonary disease or asthma prescribed inhaled corticosteroids: an observational cohort study using the OpenSAFELY platform[END_REF] There is already a high global burden of existing, non-COVID-19-related airways disease: 300-400 million people worldwide are living with chronic obstructive pulmonary disease (COPD),6 and the burden is broadly similar for asthma, which has an increasing global prevalence and affects about 10% of the population in highincome countries.7 Furthermore, individuals with COPD have an increased risk of hospital admission and death from COVID-19.8 Mild and moderate asthma has generally not been associated with increased risk of COVID-19-related hospital admission and mortality,9 although individuals with asthma who have required oral steroids in the preceding year have had increased risk of mortality in acute COVID- 19.3,5 In addition to acute illness, COVID-19 can result in long-term morbidity and a prolonged recovery period.10 This post-acute phase of COVID-19 (now widely known as long COVID, the post-acute COVID-19 syndrome, or the post-COVID-19 condition) has been reported in patients admitted to hospital with severe COVID-19,10 as well as in children and adults who initially experienced mild disease.10-13 In the UK, approximately one in five people are estimated to have COVID-19 symptoms beyond 5 weeks, and one in ten report symptoms persisting for 12 weeks or more. [START_REF]The prevalence of long COVID symptoms and COVID-19 complications[END_REF] As a disease that affects multiple body systems, long COVID can result in wide-ranging symptoms, including breathlessness, chest pain, fatigue, muscle weakness, impaired cognition, anxiety, and depression.10 Studies in the non-COVID-19 literature indicate that the prevalence of many of these symptoms-eg, anxiety, fatigue, and cognitive impairment-is increased in people with airways disease (panel 1).6,7,10-13,15-22 However, whether these symptoms are more common or more severe in patients with pre-existing airways disease after acute COVID-19 illness is uncertain. Similarly, the underlying mechanisms of these chronic health sequelae of COVID-19, particularly in relation to pre-existing and newly developed airways disease, are unkown. [START_REF] Huang | 6-month consequences of COVID-19 in patients discharged from hospital: a cohort study[END_REF][START_REF] Against | Post-COVID-19 global health strategies: the need for an interdisciplinary approach[END_REF] To address these uncertainties and improve long-term health outcomes related to COVID-19, the Posthospitalisation COVID-19 study (PHOSP-COVID) consortium was established. PHOSP-COVID is a UK national multidisciplinary consortium of clinicians and data and basic scientists aiming to create an integrated research and clinical platform to investigate the multidimensional long-term health outcomes in patients who have been admitted to hospital with COVID-19. Within this consortium, expert subgroups have been established, including a working group on airways disease, bronchiolitis, and bronchiectasis (the PHOSP-COVID Airways Diseases Working Group) who commissioned this priority-setting initiative. We sought to identify research priorities to understand the long-term consequences of acute COVID-19, with a focus on airways disease (pre-existing and newly developed after COVID-19), to guide researchers, clinicians, policy makers, and funding organisations to address the burden of long COVID globally.

Methods

Overview of the CHNRI method

We adapted the Child Health and Nutrition Research Initiative (CHNRI) method, which was originally developed for setting research priorities for global child health, to our priority-setting exercise for long COVID in the context of airways disease. The CHNRI method uses the principle of crowdsourcing to independently generate research ideas from a large group of experts, and scores these against a predefined set of criteria. It is a systematic, transparent, and democratic approach that has been used in more than 100 exercises led by national governments (eg, in China, India, and South Africa), funders (eg, The Bill & Melinda Gates Foundation), and multilateral organisations, including WHO and the United Nations Children's Fund. The aim of those exercises was to set research priorities in areas ranging from the reduction of global child mortality, non-communicable diseases, or disability to the efficient execution of national health plans. [START_REF] Rudan | Setting research priorities to reduce global mortality from childhood pneumonia by 2015[END_REF][START_REF] Fontaine | Setting research priorities to reduce global mortality from childhood diarrhoea by 2015[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: VII. A review of the first 50 applications of the CHNRI method[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: V. Quantitative properties of human collective knowledge[END_REF] The main advantages of the CHNRI method include: its systematic nature; transparency and replicability; clearly defined context and criteria; involvement of funders, stakeholders, and policy makers; a structured way of obtaining information; informative and intuitive quantitative outputs; assessment of the level of agreement for each proposed research idea; and independent scoring by many experts, thus limiting the influence of individuals on the rest of the group. [START_REF] Rudan | Setting health research priorities using the CHNRI method: VII. A review of the first 50 applications of the CHNRI method[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: V. Quantitative properties of human collective knowledge[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: VI. Quantitative properties of human collective opinion[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: I. Involving funders[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: II. Involving researchers[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: III. Involving stakeholders[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: IV. Key conceptual advances[END_REF][START_REF] Rudan | Setting priorities in global child health research investments: guidelines for implementation of CHNRI method[END_REF] The quantitative output of the CHNRI method as applied here is based on the collective input of a large group of experts in airways disease. As a result of this process, clinicians, academics, funders, and policy makers can clearly visualise the strengths, weaknesses, and relative rankings of each proposed research topic.

Establishment of expert groups

In September 2020, a subgroup of the PHOSP-COVID Airways Diseases Working Group (LGH, ADS, AS, IR, OE, LD, KP, and DA) established the Expert Management Group. This group defined the aims and context of the prioritisation exercise and drafted guidelines for the application of the CHNRI method to research priorities for airways disease in long COVID. This included defining the final criteria, the approach to scoring, and the timelines, coordinating the steps of the priority-setting exercise, and inviting experts. Revised guidelines for the CHNRI method, based on experience of its use, have recently been published. [START_REF] Rudan | Setting health research priorities using the CHNRI method: V. Quantitative properties of human collective knowledge[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: VI. Quantitative properties of human collective opinion[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: I. Involving funders[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: II. Involving researchers[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: III. Involving stakeholders[END_REF][START_REF] Rudan | Setting health research priorities using the CHNRI method: IV. Key conceptual advances[END_REF][START_REF] Rudan | Setting priorities in global child health research investments: guidelines for implementation of CHNRI method[END_REF] The CHNRI approach involves the selection of experts according to their research impact in previous years. However, as studies of COVID-19 were just emerging in the published literature when the Expert Management Group was established, we used two main approaches to identify international experts. First, experts who contributed to recently completed CHNRI-based prioritisation exercises on asthma or COPD were invited to participate. Their opinions were relevant because their research already focused on chronic airways disease. They were identified in the previous CHNRI exercises through searches of the Web of Science for the most productive authors in the preceding 5-year period or for lead authors (first, last, or corresponding authors) of the top 1% most cited research articles in the relevant area of study. Second, experts were invited from other established research groups working on airways disease and COVID-19, including the PHOSP-COVID consortium and the remainder of the PHOSP-COVID Airways Diseases Working Group, the Severe Asthma Registry Network, the UK Bronchiectasis Network and Biobank, and the International Primary Care Respiratory Group. After excluding duplicate names, a total of 202 experts were identified and invited to participate. Each expert was invited to submit a minimum of three priority research ideas or topics related to COVID-19 and airways disease.

Scoring of research ideas

In the first phase of internal review by the Expert Management Group, submitted research ideas were checked for clarity and to ensure that they met the purpose of the study. The final list of research topics was consolidated during the second phase of review, which involved refining the submitted ideas to clearly identify the new knowledge that would be generated through the proposed research. Topics with a high degree of overlap were merged. Research subthemes were identified from the consolidated list. The experts were then invited to systematically rank the final list of research ideas using five predefined criteria: answerability, feasibility, timeliness, effect on burden reduction, and equity (panel 2). Experts were offered four response options for scoring: 0 (unlikely to meet the criterion); 0•5 (informed, but not sure whether it can meet the criterion); 1 (likely to meet the criterion); or left blank if the expert felt insufficiently informed to make a judgment.

Data analysis

All completed scoresheets from the experts were collated into a final worksheet. First, all entries were checked for consistency and errors by the Expert Management Group. Intermediate scores were then computed for each criterion as the sum of the scores (ie, 1, 0•5, or 0) across the criteria divided by the total number of answers received. The answers that were left blank were not included in the denominator. The overall research priority score (RPS) for each idea was computed as the mean of the scores across the five criteria. Thus, the RPS could theoretically range between 0% and 100% for each scored research idea. To give insight into the level of agreement among all the scorers, we computed the average expert agreement (AEA). This provides an indicator of the average proportion of scoring experts who gave the most common answer when scoring a particular research idea, expressed as: (where 5 represents the five criteria and N is the total number of experts.)

Patient input and weighting

In addition to the experts' scoring, we extended aspects of the exercise to patients who had been admitted to hospital with acute COVID-19 or were experiencing long COVID (including individuals with pre-existing airways disease and individuals who had developed a new airways disease after treatment for COVID-19). To account for patients' views, we developed weights for the selected criteria using a method already established by the CHNRI for involving stakeholders. [START_REF] Yoshida | Setting health research priorities using the CHNRI method: III. Involving stakeholders[END_REF] We contacted patients through the Asthma UK and British Lung Foundation Partnership, a UK-based national charity that aims to foster improvements in outcomes for people affected by lung diseases. We used an online survey to recruit and screen patients. The purpose, context, and criteria specific to this exercise were explained to the patients, who then answered the question: "Which of the criteria (ie, answerability, feasibility, timeliness, burden, equity) do you consider most important to set research priorities for COVID-19 in airways diseases?" The resulting weights were expressed as a percentage and applied to each criterion. This resulted in a weighted RPS, defined by the following equation:

where RPSn and wn are the RPS and weights for each of the five criteria, respectively.

Results

Research ideas, themes, and scoring Among the 202 experts contacted, 88 (44%) accepted the invitation and 59 (29%) contributed research ideas after the CHNRI process had been explained to them. Over a 4-week period, we received 300 research ideas from experts. After the two-phase internal review process by the Expert Management Group, 165 duplicate or unclear ideas were removed and 27 were merged (appendix 1 pp 2-4). Ten research ideas were excluded because they were considered to be out of scope or could not be addressed within the context of PHOSP-COVID research.

The final list of 98 research ideas was organised into five subthemes and sent back to the contributing experts for scoring. The subthemes were: (1) study of associations with or risk factors for the development or exacerbation of airways disease in COVID-19 survivors (36 research ideas); (2) understanding of the role of interventions for COVID-19 on the short-term and long-term outcomes of people with chronic airways disease (22 research ideas); (3) investigation of the long-term physiological effects and disease burden of COVID-19 in patients with chronic airways disease (21 research ideas); (4) investigation of the long-term effects of COVID-19 on quality of life, mental health, and social characteristics in patients with chronic airways disease (6 research ideas); and (5) development of innovative approaches to health care and policy-making initiatives targeting patients with chronic airways disease (13 research ideas). These subthemes were systematically ranked by 48 experts (55% of the 88 participants who accepted the invitation) who returned completed scoresheets within 4 weeks. The process for the CHNRI priority-setting exercise is summarised in the figure.

Overall research priority score

The overall RPS for each of the 98 research ideas ranged from 0•339 to 0•864. The AEA ranged from 0•417 to 0•846, with a median of 0•683. There was a high degree of agreement among experts on the most highly-ranked research ideas, with the AEA decreasing with decreasing RPS (r=0•9334, p<0•001). The 98 ranked research ideas, with RPS and AEA data, are presented in appendix 1 (pp 5-15) and appendix 2 (sheets 6, 7). Of the 20 highest-ranked research ideas, half (including five of the ten highest scoring ideas) were on subtheme 1-ie, identification of associations with or risk factors for developing or worsening airways disease in COVID-19 survivors (table 1). The three highest scoring research ideas involved comparing morbidity after hospital discharge between COVID-19 survivors with and without pre-existing airways disease, with the first (RPS 0•864, AEA 0•838) focusing on the correlation between prognostic scores-using the International Severe Acute Respiratory and emerging Infections Consortium (ISARIC) 4C Mortality Score,34 a risk stratification score used to predict in-hospital mortality for patients with COVID-19-at hospital admission and postdischarge morbidity at 3 months and 12 months in the two groups. The second highest-ranked priority (RPS 0•852, AEA 0•846) was assessment of the extent of post-COVID-19 fatigue, sarcopenia, anxiety, and depression. The third (RPS 0•849, AEA 0•817) was investigation of the risk of future cardiovascular complications in patients treated for severe COVID-19. The ten highest priorities included research ideas relating to hospital admission and symptoms in patients with pre-existing airways disease, such as understanding predictors of hospital readmission and validating tools for remote monitoring of symptoms. Other topics among the ten highest scoring ideas were specific to patients with obstructive airways disease who had COVID-19, including determining the incidence of and risk factors for new-onset airways disease, recovery of current smokers with COPD, and clinical efficacy and cost-effectiveness of exercise rehabilitation. Research ideas to explore the risk of venous thromboembolic events in patients with COVID-19, including estimation of the incidence of pulmonary embolism and study of the effects of treatment with anticoagulants on outcomes of patients admitted to hospital with COVID-19, were among the 20 highest-ranking research topics. The majority of the 20 research ideas with the lowest RPS values were from subthemes 2 and 5 (seven from each subtheme). They focused on understanding the role of interventions for COVID-19 on outcomes and development of innovative approaches to health care and policy-making initiatives for patients with chronic airways disease. The three lowest-ranked research topics related to the evaluation of the role of the private sector in pandemic management (RPS 0•339, AEA 0•638), alternative medicine in patients with COVID-19 with pre-existing airways disease (RPS 0•362, AEA 0•608), and the risk of developing lung cancer from acute or long COVID (RPS 0•446, AEA 0•588). Other low-ranking research ideas included determining priority for vaccination among COVID-19 survivors, exploring opportunities for artificial intelligence and advanced technologies such as xenon MRI in the assessment and treatment of patients with COVID-19, investigating the risk of developing pulmonary aspergillosis in COVID-19 survivors, and studying the perceptions and practices of general practitioners during the COVID-19 pandemic (appendix 1 pp 5-15).

Scores for the priority-setting criteria

Across three of the priority-setting criteria (answerability, feasibility, and timeliness), the highest scoring research idea was investigation of the correlation between prognostic scores at hospital admission and morbidity at 3 months and 12 months after discharge in patients with and without pre-existing airways disease (table 2). The second highest-ranking research idea for both feasibility and timeliness was estimation of the incidence of pulmonary embolism up to 1 year after acute COVID-19. Many of the three highest scoring research ideas for the priority-setting criteria were also among the 20 highest scoring ideas according to their overall RPS (table 2). A notable exception was investigation of whether patients at risk of persisting disability after COVID-19 can be identified and targeted for rehabilitation or nutritional interventions. This idea was ranked highest for both burden and equity criteria, but was ranked 21st in the overall list. Similarly, investigation of the long-term effects of COVID-19 on the mental health of people with COPD was ranked third for the answerability criterion, but 25th in the overall list, and development of scores to predict long-term respiratory disease severity and risk of mortality in survivors of severe COVID-19 was ranked third for the equity criterion, but 28th in the overall list (table 2). The ten highest scoring research ideas for each of the five criteria are presented in appendix 1 (pp 16-25) and the full list of 98 research ideas with scoring data for the five criteria are presented in appendix 2 (sheets 1-5).

Patients' weighting

The patients' contributions offered insights into the overall ranking of the research ideas, providing additional perspectives for clinicians, researchers, and policy makers. 61 patients were recruited through the online survey. We do not have extensive data on the demographics of the patient survey respondents, but nearly half reported a pre-COVID-19 airways disease. Of the 61 patients who responded to the question on weighting of the criteria, 32•8% considered burden the most important criterion for setting research priorities for COVID-19 in airways disease, answerability and equity were each selected by 21•3% of patients, 18•0% chose feasibility, and 6•6% opted for timeliness (appendix 1 p 32).

Applying those weights to generate weighted RPS values led to four research ideas moving up into the weighted list of the 20 highest scoring topics. Of note were the ideas concerning investigation of the long-term effects of COVID-19 on the mental health of people with COPD and development of scores to predict longterm respiratory disease severity and risk of mortality in survivors of severe COVID-19-both already identified among the three highest research priorities according to answerability and equity criteria. The two other research ideas that moved into the weighted list of the 20 highest-ranking topics focused on assessment of the effectiveness of counselling and psychological services in addressing long-term psychological and cognitive effects of COVID-19 in patients with pre-existing airways disease and investigation of whether patients with pre-existing asthma develop an accelerated loss of lung function after severe COVID-19. In summary, the 20 highest scoring overall research priorities according to the weighted and individual RPS values were largely overlapping, although their rankings differed slightly (appendix 1 pp 26-28; the 20 lowest scoring overall ideas according to weighted RPS values are presented in appendix 1 pp [START_REF] Rudan | Setting health research priorities using the CHNRI method: I. Involving funders[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: II. Involving researchers[END_REF][START_REF] Yoshida | Setting health research priorities using the CHNRI method: III. Involving stakeholders[END_REF].

Discussion

As the COVID-19 pandemic progresses into a second year, there is an increasing need to understand the burden of emerging or worsening pre-existing comorbidities. Here, we report the findings of a CHNRI research priority-setting exercise aimed at addressing this burden in relation to airways disease in people who have survived an acute illness due to COVID-19. Although the focus was on airways disease, many of the priorities identified would be broadly applicable to the study of long COVID and its management in patients not admitted to hospital or those with other comorbidities. The considerable diversity in topics covered by the highestranking research ideas-from identification of associated risk factors and assessment of incidence of events to investigation of the effects of interventions both in the acute setting and after hospital discharge-reflects the wide-ranging concerns about the burden of the long-term sequelae of COVID-19.

Key findings

The four highest-ranked research priorities focused on comparisons of the health outcomes of COVID-19 survivors with and without pre-existing airways disease. These priorities included exploration of correlations between prognostic scores (using the ISARIC 4C Mortality Score34) at hospital admission and post-discharge morbidity at 3 months and 12 months, and investigation of the potential risk of developing comorbidities or complications in COVID-19 survivors. Comorbidities and complications include fatigue, sarcopenia, anxiety, depression, cardiovascular complications, and hospital readmission. Investigation of the incidence and risk factors (eg, smoking and ethnicity) associated with developing new symptomatic airways disease or structural airways abnormalities on radiological imaging also featured in the 20 highest-ranked ideas. Additionally, investigation of correlations between imaging findings identified during acute COVID-19 illness and subsequent long-term symptoms and outcomes was ranked highly.

The importance of the increased incidence of venous thromboembolic disease in patients with COVID-19 was reflected in three of the 20 highest scoring ideas, including investigation of the incidence of pulmonary embolism and the role of anticoagulants-both newly administered and previously prescribed-on outcomes. Other ideas of interest among the experts included the role of interventions such as exercise-based rehabilitation programmes, nutritional interventions, and the use of acute non-invasive ventilation in patients with pre-existing airways disease. Research ideas from the subcategories addressing long-term effects of COVID-19 on quality of life, mental health, and social characteristics (subtheme 4), and development of innovative approaches to health care and policy-making initiatives (subtheme 5) for patients with chronic airways disease were less common among the 20 highest priorities, featuring one idea each. Topics regarded as less important by the experts in this exercise were those that involved basic science research, the role of advanced technologies such as xenon MRI and artificial intelligence, and suggestions to develop or amend international guidelines. Other ideas with low scores included understanding perceptions of the private sector and primary care providers during the pandemic, and the prevalence of less frequently observed conditions such as invasive aspergillosis after severe pneumonia. These lower scores might have reflected concerns over deliverability in a pandemic situation (eg, for MRI-based studies) or the perception of low burden of disease (eg, for aspergillosis complicating COVID-19).

Strengths and limitations

The use of the standardised CHNRI method enabled a systematic, transparent, and democratic approach to identification of research priorities for long COVID in the setting of airways disease. Despite the pressures associated with the pandemic on clinicians and researchers, we achieved a return rate of more than 40%, which is similar to that for previous CHNRI exercises. [START_REF] Rudan | Setting research priorities to reduce global mortality from childhood pneumonia by 2015[END_REF]-25 Furthermore, previous experience and statistical simulations have shown considerable convergence of collective expert opinion when the number of scoring experts is 40 or more, ensuring stability and replicability of the final rankings according to CHNRI methods;26,28 consistent with this, we found a high degree of agreement among experts on the most highlyranked research ideas according to the AEA values.

As a result of the good response rate, we were able to include opinions from a range of experts with both clinical and academic expertise, including some from low-income and middle-income countries. Although individuals from 36 nations were invited, we had no responses from experts in South America, and few participants from Africa and Asia, and the identified research priorities might therefore not be directly relevant to these regions. Similarly, although general practitioners with respiratory expertise and International Primary Care Respiratory Group members were invited, only a few experts from primary care took part in the study. The lower RPS values and relative lack of research priorities specific to primary care are likely to reflect the targeted population of COVID-19 survivors who had been admitted to hospital, but the involvement of relatively few primary care experts might have also been a contributing factor. As the burden of COVID-19 shifts from acute to chronic care, greater input from primary care experts in priority setting will be essential. Additional expertise relevant to the symptoms seen in long COVID-including input from neurological, psychological, renal, and cardiac fields-should be sought to capture diversity in research questions to feed into future priority-setting exercises.

The incorporation of patients' priorities was a novel aspect of our method that offers additional benefits for setting the directions for future research by ensuring that researchers, policy makers, and stakeholders are engaging in research that meets the needs of affected individuals. Our rapid, online patient survey allowed us to achieve a good number of respondents, although it is likely that views of certain patient groups were missed. A limitation of this exercise was the large number of ideas that were unclear or that could not be addressed within the context of PHOSP-COVID research, which were removed during the internal review process (appendix 1 pp 2-4). Although we endeavoured to carefully rephrase research ideas to reflect the new knowledge they proposed to generate, some might have been poorly reworded, which might have contributed to some ideas being considered as lower priority. Interestingly, few of the proposed research priorities focused on non-respiratory comorbidities, which probably reflects the focus of this initiative on airways disease. Despite the respiratory focus, the absence of high-ranking research ideas relating to cystic fibrosis or sleep-related disorders is important to acknowledge.

Interpretation in the context of published studies

Clinicians and policy makers already recognise the need to follow up patients who have had acute COVID-19. However, understanding which subgroups of patients most need follow-up will be increased by addressing the research priorities outlined here. The development of the ISARIC 4C Mortality Score has helped to identify those at high risk of adverse outcomes during hospital admission. [START_REF] Knight | Risk stratification of patients admitted to hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: development and validation of the 4C Mortality Score[END_REF] The ISARIC 4C Mortality Score is readily available and has been increasingly adopted in clinical practice. [START_REF] Knight | Risk stratification of patients admitted to hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: development and validation of the 4C Mortality Score[END_REF] If subsequent studies show that this acute severity score also helps to identify those with greatest risk of more severe long COVID, it will facilitate service provision and treatment algorithms. Conversely, if correlations with acute illness scores are low, as suggested by some early data,2 then long COVID clinics might need a much larger service provision to provide follow-up to people with long COVID who were not admitted to hospital. This is highly relevant because the COVID-19 pandemic has undoubtedly affected outpatient follow-up for long-term conditions across most medical specialties. Respiratory and infectious diseases are likely to be further disadvantaged owing to the key roles of these specialties in providing acute COVID-19 services. Patients with airways disease have a recognised complex of comorbidities and (pre-COVID-19) clinical patterns that are relevant to COVID-19 and its multisystem disease manifestations. For example, acute COPD exacerbations are associated with a high hospital readmission rate-up to 40% at 3 months-and a long-term increased risk of vascular events, such as myocardial infarction and pulmonary embolism. [START_REF] Alqahtani | Risk factors for all-cause hospital readmission following exacerbation of COPD: a systematic review and meta-analysis[END_REF] Similarly, acute COVID-19, with extrapulmonary disease, widely reported thrombotic events, and other multisystem effects,2,34 can lead to complications after hospital discharge. Understanding the frequency and severity of complications in post-acute COVID-19 and identifying patient subgroups at highest risk of such complications should enable investigation of different intervention strategies, such as anticoagulant treatment after discharge, which might minimise early and late thromboembolism. As the COVID-19 pandemic has progressed, it has become clear that-unlike many other respiratory viruses-SARS-CoV-2 does not cause typical exacerbations of airways disease.36 Observational data have suggested that patients with COPD and selected subgroups with asthma have poorer outcomes than do patients without these pre-existing conditions.3,5,8,9 Research into the role of inhaled steroid use in patients with pre-existing airways disease on COVID-19 disease burden was ranked 12th in our exercise according to its overall RPS. Some studies have suggested that inhaled steroid treatment might be protective against severe COVID-19.37 However, the available observational studies on inhaled steroids are potentially confounded by the effects of behavioural factors such as better adherence to treatments, shielding programmes, and a reduction of exposure to factors related to exacerbation events (eg, other infections and air pollution).

Thus, the effect of COVID-19 on patients with pre-existing airways disease, or with de-novo airways disease, needs to be studied prospectively in large cohorts of patients. These studies will need to have an appropriately matched control group with linked retrospective health-care data to ensure robust assessment of pre-COVID-19 health status. This priority-setting exercise provides a framework to address key research topics in this important patient group.

Implications for policy, practice, and research

This exercise showed a high level of concordance between experts and patients in the 20 highest scoring research topics when weighting of the criteria according to patients' input was included. The weighting led to some differences in the five highest priorities, but in general, the experts' ranks reflected patients' expectations.

As a result, we expect that there will be positive engagement in terms of research participation to address the priority areas identified. Many of the highly-ranked research topics could be addressed within a short time-frame, particularly with national and international coordination. Investigating the potential risk factors identified in the research priorities (eg, socioeconomic status, comorbidities, ethnicity, nutritional status, and medication use) could help to identify patients who are at highest risk of long COVID, which in turn will inform service development during a time of resource constraints and large backlogs in clinical follow-up of patients with long-term conditions. Understanding of the predictors and causes of hospital readmissions after COVID-19 might allow targeted interventions to minimise readmission and reduce the strain on hospital capacity. Care bundles (standardised assessment tools used by the COPD hospital team for patients admitted with acute COPD exacerbations both during the hospital stay and after discharge) to minimise COPD readmissions38 have been widely adopted and could provide the basis to inform post-acute COVID-19 care.

Development of multidisciplinary clinics for long COVID is already encouraged by policy makers and patient advocacy groups.39 These clinics can form the basis for multisite international studies and assessment of interventions to prevent additional morbidity (eg, anticoagulation studies) or enhance return to baseline (eg, rehabilitation studies to tackle sarcopenia).39 However, provision of and access to such multidisciplinary clinics could be challenging in some low-income and middle-income countries where numbers of health-care professionals per capita and resource availability are already lower than in high-income countries and are further stretched by the pandemic. Other challenges could include difficulties in defining caseload where access to COVID-19 testing is limited or there is incomplete or non-systematic assessment of patients-eg, with echocardiography, CT scanning, or lung diffusion capacity testing to identify people who are breathless and have developed myocardial dysfunction or interstitial lung disease, compared with those who are breathless with no radiological changes.

Figure :

 : Figure: Process for setting research priorities CHNRI=Child Health and Nutrition Research Initiative. PHOSP-COVID=Post-hospitalisation COVID-19 study.

Acknowledgments

This study and the Post-hospitalisation COVID-19 study (PHOSP-COVID) consortium are supported by a grant to the University of Leicester from the Medical Research Council (MRC)-UK Research and Innovation (UKRI) and the Department of Health and Social Care (DHSC) through the National Institute for Health Research (NIHR) rapid response panel to tackle COVID-19. The NIHR Leicester Biomedical Research Centre is a partnership between the University Hospitals of Leicester National Health Service (NHS) Trust, the University of Leicester, and Loughborough University. The study was also supported by the UK Health Data Research BREATHE Hub. PHOSP-COVID is registered with the ISRCTN registry (ISRCTN10980107). The funders of the study had no role in study design, data collection, data analysis, data interpretation, writing of the report, or the decision to submit for publication. We acknowledge the contributions of the following experts who submitted research ideas: David Denning, Rachael Evans, Paula Kauppi, Paul Mcnamara, Shoaib Faruqi, Nikos Papadopoulos, Michael Wechsler, George Slavich, Sian Williams, and Neil Fitch. We also acknowledge the support of the following groups to the initiative: the Severe Asthma Registry Network, the UK Bronchiectasis Network and Biobank, the Asthma UK and British Lung Foundation Partnership, and the International Primary Care Respiratory Group. Martha McIlvenny contributed to the administration of the project. The views expressed in this publication are those of the authors and not necessarily those of the NHS, MRC-UKRI, NIHR, or DHSC.

International collaborators

Australia Renae Mcnamara (University of Sydney, Sydney), Andrew Tai (Women's and Children's Hospital, Adelaide). Canada Anthony D'Urzo (University of Toronto, Toronto). Denmark Peter Schwarz, Charlotte Suppli Ulrik (Copenhagen University Hospital-Hvidovre, Copenhagen). France Marcel Bonay (University of Versailles, INSERM, Ambroise Paré Hospital, Boulogne), Arnaud Bourdin (University of Montpellier, CNRS, INSERM, CHU Montpellier, Montpellier). Hong Kong Fanny Wai San Ko (The Chinese University of Hong Kong, Hong Kong). India Dhiraj Agarwal (KEM Hospital Research Centre, Pune), Jagadeesh Bayry (Indian Institute of Technology Palakkad, Palakkad). Iran Mohammad Abdollahi (Tehran University of Medical Sciences, Tehran). Ireland Catherine M Greene (Royal College of Surgeons in Ireland, Dublin). Italy Gaetano Caramori (University of Messina, Messina). Malaysia Ee Ming Khoo (University of Malaya, Kuala Lumpur). Netherlands Louis J Bont (University Medical Center Utrecht, Utrecht), Gerard H Koppelman (University of Groningen, University Medical Centre Groningen, Beatrix Children's Hospital, Groningen). New Zealand Amy Hai Yan Chan (University of Auckland, Auckland). Saudi Arabia Riyad Al-Lehebi (King Fahad Medical City, Riyadh). South Africa Pisirai Ndarukwa (University of KwaZulu Natal, Durban). South Korea Chin Kook Rhee (The Catholic University of Korea, Seoul). Spain Cristóbal Esteban (Hospital Galdakao-Usansolo Hospital, Galdakao, Osakidetza, Bizkaia), Jose Luis Lopez-Campos (Hospital Universitario Virgen del Rocío, Universidad de Sevilla), Miguel A Martinez-Garcia (Hospital Universitari i Politècnic la Fe, Valencia), Marc Miravitlles (Hospital Universitari Vall d'Hebron, Barcelona). Sweden Magnus Ekström (Lund University, Lund), Karin Lisspers (Uppsala University, Uppsala). UK Peter J Barnes, Michael Loebinger (Imperial College

London, London), Thomas Brown (Portsmouth Hospitals University NHS Trust, Portsmouth), David H Dockrell, Michelle C Williams (University of Edinburgh, Edinburgh), Simon Doe (Royal Victoria Infirmary, Newcastle), Jamie Duckers (Cardiff and Vale University Health Board, Cardiff), Atul Gupta, Matthew Maddocks (King's College Hospital, London), Brian J Lipworth (University of Dundee, Dundee), Alison Pooler (Keele University, Keele), Dominick Shaw (University of Nottingham, Nottingham), Michael Steiner (University of Leicester, Leicester), Paul Walker (University of Liverpool, Liverpool). USA Jennifer L Ingram (Duke University School of Medicine, Durham, NC), David Mannino (University of Kentucky, Lexington, KY).

Data sharing

All data for this study were linked, stored, and analysed within a secure online platform. All data have been deidentified where necessary and are available in appendix 2.

Conclusions

In summary, we have undertaken a robust expert consensus process to identify research priorities for long COVID in the context of airways disease, taking into account the views of a large group of international experts as well as those of patients who have had COVID-19 in association with pre-existing airways disease or who have developed airways disease after COVID-19. The rankings of the research priorities are likely to have been influenced by the current stage of the pandemic and the status of vaccine development and roll-out, as well as the knowledge base and backgrounds of the experts and patients. Involving a different group of participants (eg, with expertise in neurology, psychiatry, cardiovascular disease, or digital health) should be considered in future priority-setting exercises as understanding of the burden and symptom complex of long COVID increases. With the COVID-19 pandemic set to continue for the foreseeable future, we recommend that such prioritisation exercises be repeated when the initial priority areas have been addressed and as the knowledge base grows.

Contributors

The International COVID-19 Airways Diseases Group consists of the Post-hospitalisation COVID-19 study (PHOSP-COVID) Airways Diseases Working Group (which is co-led by LGH and ADS and includes all authors of this paper) and the international collaborators. AS, IR, and DA conceptualised the research priority exercise. LGH, ADS, AS, IR, OE, LD, KP, and DA formed the Expert Management Group, a subgroup of the PHOSP-COVID Airways Diseases Working Group. The Expert Management Group defined the aims of the exercise and context, identified and contacted international experts as collaborators, and collected and analysed the results. KP and SW designed and organised the patients' survey. DA, LD, and OE wrote the initial draft of the manuscript. The PHOSP-COVID Airways Diseases Working Group members JKQ, SW, CEB, SS, JRH, JDC, PEP, PN, and TMD oversaw the exercise, contributed to the proposed research ideas, completed the scoresheets, and reviewed, edited, and approved the manuscript. The international collaborators proposed research ideas, completed the scoresheets, and reviewed, edited, and approved the manuscript. All authors were able to access the study data. DA, KP, OE, LD, IR, AS, ADS, and LGH accessed and verified all the data in the study and had final responsibility for the decision to submit the article for publication.

Declaration of interests

CEB reports grants from the Post-hospitalisation COVID-19 study during the conduct of the study. JRH reports personal fees and non-financial support from pharmaceutical companies (AstraZeneca and GlaxoSmithKline) that make medicines to treat chronic obstructive pulmonary disease, outside the submitted work. JDC reports grants and personal fees from AstraZeneca and Boehringer Ingelheim, and personal fees from GlaxoSmithKline, Insmed, Novartis, Chiesi, and Zambon, outside the submitted work. PEP reports personal fees and non-financial support from AstraZeneca, and a grant and non-financial support from GlaxoSmithKline, outside the submitted work. AS reports grants from the Health Data Research UK BREATHE Hub, the Medical Research Council, and the National Institute for Health Research, during the conduct of the study. ADS has received medical education grant support for BRONCH-UK, a UK bronchiectasis network, from GlaxoSmithKline, Gilead, Chiesi, and Forest labs, and his institution receives fees for his work as coordinating investigator on a phase 3 trial in bronchiectasis sponsored by Bayer. All other authors declare no competing interests.