We simulatethe vibrational spectra of BEA accounting for anharmonic contributionsand observe an improved agreement with experimental data comparedto harmonic methods, particularly at wavenumbers below 1500 cm–1. The results demonstrate the importance of incorporatinganharmonic effects in simulations of vibrational spectra, with consequencestoward future characterization and application of zeolitic materials.The characterizationof zeolitic materials is often facilitatedby spectroscopic analysis of vibrations, which informs about the bondingcharacter of the substrate and any adsorbents. Computational simulationsaid the interpretation of the spectra but often ignore anharmoniceffects that can affect the spectral characteristics significantly.Here, the impact of anharmonicity is demonstrated with a combinationof dynamical and static simulations applied to the structures formedduring the synthesis of Sn-BEA  Heteroatom-doped zeolite frameworks, suchas zeolite β (BEA), display potent catalytic ability, especiallywhen Lewis acid elements such as Ti, Sn, or Ge are incorporated inthe BEA framework 1. Of the14 SSI is a “top-down” synthetic approach where readilyavailable zeolite BEA (H-β) undergoes dealumination with a strongacid, creating vacancies in the framework (silanol nests) at the sitespreviously occupied by Al. The dealuminated framework (deAl-β)then undergoes mechanochemical grinding with a Sn precursor (Sn(II)acetate), which induces interaction with the framework, and subsequentheating and cooling steps further incorporate Sn into the BEA frameworkto form the final catalyst  acetate coordination upon grinding,from bidentate to monodentate, and the formation of acetic acid.14Recently, the demonstration of solid-state incorporation(SSI)for synthesizing Sn-β has addressed limitations in wet synthesisthat hinder scale-up, such as high temperatures and pressures andstrong acids.st Sn-β, 1B. A comab initio vibrational simulationsof materials, the calculations often rely on a harmonic approximation,where the potential energy surface (PES), V(R), around the equilibrium positions, R0, is approximated via a second-orderTaylor expansion, i.e., by a parabolic potentialV0 = V(R0) isthe potentialenergy in equilibrium and uiα = Riα – R0,iα are small displacements from equilibrium.Greek letters represent Cartesian directions , i and j are atoms within the lattice, and Φi,jα,β represents the harmonic forceconstants, i.e., the Hessian of the PES evaluatedat R0. The mass-scaled Fouriertransform of Φ yields the dynamical matrix D(q); its eigenvalues and eigenvectors determine the harmonicvibrational modes.When performing 16 In spite of the experimentalagreement, the qualitative validity of the harmonic approximationis therefore severely limited.17 For instance,modeling and understanding material properties such as heat transport,phase transitions, and thermal lattice expansion typically requiresaccounting for so-called anharmonic effects, beyond the harmonic approximation.Similarly, the harmonic approximation only holds for small displacementsfrom equilibrium, e.g., in the low-temperature limit.Under more catalytically relevant thermodynamic conditions, the assumptionsdo not hold true for many materials,18 especiallyfor materials featuring soft bonds and hence quite mobile atoms, suchas zeolites.16 In this case, accountingfor anharmonic effects is essential to reproduce vibrational modesand adsorption free energies.23 Furthermore, exothermic/endothermic catalytic processescan lead to a respective localized increase/decrease of temperaturein such materials and, accordingly, to local changes in anharmonicitythat are desirable to quantify. Developing knowledge of the role ofanharmonic effects in materials such as zeolites can lead to a betterunderstanding of how energy is generated and dissipated and how thisaffects catalytic properties.The harmonic approximation is computationallyadvantageous andformally appealing since the nuclear equations of motion can be solvedanalytically. When applied with semi-local density functional theory(DFT), the harmonic approximation can yield surprisingly good quantitativeagreement with experimental vibrational spectra; however, the agreementwith experiment has been traced back to a benign error cancellationbetween the red shift caused by the too-shallow PES, from semi-localDFT, and the blue shift typically observed due to the deficienciesof the harmonic approximation.24 Additionally, experimental studies have quantified the significanceof anharmonic effects in zeolite systems through observed changesin infrared (IR) signals, which is indicative of anharmonicity, thoughit can be challenging to interpret.26 In the workherein, we aim to computationally quantify the role of anharmonicityat a microscopic level by building on a recently proposed anharmonicitymetric.18 The method improves connectivitybetween experimental and computational methods and facilitates a betterunderstanding of mechanistic steps in chemical processes, which wedemonstrate for the intermediates in the synthesis of Sn-β.The role of anharmonic effectsis typically discussed in termsof macroscopic observables, for instance, these effects have previouslybeen investigated by inspecting adsorption and diffusion of moleculesin zeolites in consideration of thermodynamics.22.1AV(R), are quantified at any given atomic configuration by measuringthe difference between the correct and harmonic PES, V(2) (R), i.e., viaAspreviously mentioned, we seek to better our understanding of SSI throughquantifying anharmonic behavior in zeolite β materials. In thisapproach, anharmonic effects, Theapproach, as represented pictoriallyin 18 the following steps are performed: First, weobtain harmonic force constants Φ, see F and FA = F - Fha arethe total and anharmonic force component α acting on atom I at time t. As this equation highlights,σ quantifies the difference between actual and harmonic forcesTo evaluate anharmonic contributions in zeolitesin terms of theanharmonicity metric, σ proposed by Knoop et al.,via regression27 using hiPhive(ab initio MD (aiMD) simulations at low temperatures (20 K), rather than fromfinite-difference phonon calculations . In this regression approach, Fi(t) and displacements ui(t) observed in the aiMD. The approach isdemonstrated as essentially equivalent to standard phonon approaches,and for zeolites with greater anharmonicity  = Ri(t)–Ri0,, so that theanharmonic contribution to the forces FiA(t) = Fi(t) – Fiha(t), required for the evaluation of σ in Figures S2 and S3 in the SI for aiMD at 300 K.However, as discussed below, zeolitic systems formally exhibit a verystrong anharmonicity at 300 K  owing to the strongly anharmonic lattice distortions present. Thesedistortions are associated with the porosity of the material and theresulting softness of the lattice, as indicated by the low-frequencyacoustic modes exhibiting the highest anharmonicity, c.f.Once low-temperatureforce constants have beenobtained, an assessmentof the anharmonicity requires sampling the fully anharmonic PES andcomputation of the associated forces. The corresponding harmonic forces, 00 K SI, S4 owing 30 For our evaluation of the phonon modes ofBEA, 50 samples were generated, which we find to be converged . For the resulting configurations, FiA(t) is evaluated via DFTso that insights on the acting anharmonic forces can be obtained . Although the harmonic sampling approachis not as systematic as aiMD, it is advantageous for zeolites sincethe phonon picture is inherently retained. Accordingly, the stronglyanharmonic acoustic modes mentioned are effectively constrained, whichfacilitates the disentanglement of the contributions affecting theother, more local phonon modes, and hence allows us to qualitativelyinspect which phonon modes are most affected by anharmonicity, whichwe discuss below. However, in an unconstrained treatment of low-frequencyvibrational modes through aiMD, greater anharmonic contributions areobtained from acoustic phonons, and thus, in the method describedabove, the anharmonicity values obtained serve as a lower estimate.In the harmonic sampling, the nuclear dynamicsare sampled onlyusing the harmonic approximation, rather than the fully anharmonicpotential. The approach means that the thermodynamic average in 2.231 which is an all-electron, full potential code. The general gradientapproximation (GGA) exchange–correlation functional (XC) ofPerdew–Burke–Ernzerhof, reparametrized for solids (PBEsol),was used,32 with dispersion interactionsaccounted for using the Tkatchenko–Scheffler method.33 Calculations were performed using a “light”basis set of the 2010 release, with self-consistent field (SCF) cycleconvergence reached when the sum of eigenvalues and change in chargedensity were below 10-6 eV and 10–6 e/a03, respectively. Calculations were also performedspin-restricted and using the atomic zeroth order regular approximation(ZORA) for relativistic treatments.34DFT calculationswere performed with the Fritz Haber Institute Ab Initio MolecularSimulation (FHI-aims) software package,a, b = 12.643 Å, c =26.182 Å, 192 atoms),35 obtained fromthe database of International Zeolite Association (IZA). The α-quartzunit cell was obtained from the materials project database.36 Models were built and manipulated using theAtomic Simulation Environment (ASE) and FHI-vibes Python packages.38 Electronic structure calculations were performed with a convergedMonkhorst–Pack k-point samplinggrid of 2 × 2 × 2 for BEA and 12 × 12 × 10 forα-quartz. Full unit cell optimizations were performed on allstructures using the Broyden–Fletcher–Goldfarb–Shanno(BFGS) algorithm, with convergence reached when the forces on allatoms are less than a strict criterion of 0.001 eV Å–1,42 as variation in local minima would affect the definition of theharmonic approximation. For the BEA systems studied, geometry optimizationwas performed on Si-β, deAl-β ,Sn(IV)-β (closed site), and H-β (12-membered ring withH oriented toward the pore); these structures can be found on theNOMAD repository (DOI: 10.17172/NOMAD/2023.06.30-1).The BEA unit cell, which contains 9 symmetry inequivalent tetrahedral(T) sites, was optimized from the structure first characterized byNewsam (Ab initio molecular dynamics (aiMD) simulationswere performed with FHI-vibes, FHI-aims, and ASE, using Langevin dynamics.Harmonic force constants from aiMD simulations were obtained by usingthe hiPhive Python package.28 Spectroscopic properties were obtained via thevibrational density of states (VDOS) using a Fourier transform ofthe velocity autocorrelation functionAnharmoniccontributions were calculated using FHI-vibes, whereanharmonicity was defined according to D(ω) isthe VDOS at frequency ωand ν is the velocity at time t.where S, was calculatedfor the harmonic approximation and for anharmonicity at 300 K vian and m are the stoichiometriccoefficients for the reaction. Entropy valueswere obtained through normal mode analysis of aiMD trajectories at20 K (harmonic) and 300 K (anharmonic) using the Phonopy package,43 where S was calculated usingeq 11 in ref  for siliceous BEA (Si-β) is 0.29, meaning that anharmoniceffects contribute 29% of the total forces. Furthermore, σA are slightly greater for BEA frameworks produced during SSI,where the aluminosilicate (H-β), dealuminated (deAl-β),and Sn-containing (Sn-β) frameworks have anharmonicity scoresof 0.35, 0.34, and 0.32, respectively , the anharmonicityper vibrational mode, σsA, can be obtained from the mode-resolvedforce, Fs. Plotting σsA against the modefrequency (ωs) for Si-β, H-β, deAl-β,and Sn-β on the defect site.44 Furthermore, Sn-β has twoadditional vibrational modes that appear in the band gap between 800and 1000 cm–1, which is associated with the vibrationalmodes of Sn–O bonds.46 These modes of Sn–O bonds have moderate anharmonic contributionsof 0.36 and 0.27. Overall, the mode-resolved analysis demonstratesthat anharmonic contributions differ drastically for modes in thevibrational spectrum. Intuitively, the low-frequency acoustic phononmodes, which correspond to soft vibrations of the BEA framework, arethe most anharmonic and are not captured in the harmonic picture atall. More interestingly, we also observe local changes in anharmonicitythat can be attributed to changes in chemical reactivity, as discussedbelow.For H-β, the large anharmonicity of the low-frequencyvibrationalmodes decays more gradually than the other BEA materials, with themodes remaining mostly anharmonic until 400 cm3.3EA, which evaluates anharmonic contributions per chemical element,can also be obtained for each system  nest of the defect in the frameworkhave anharmonic contributions of 0.52, while the hydrogen atom ofthe Brønsted acid site (Al–(OH)–Si) is almost entirelyanharmonic for H-β, with σsE of 0.91. The significant variation inanharmonicity for hydrogen atoms when considering deAl-β andH-β suggests that anharmonicity within BEA materials is drivenby local chemical environment as well as element type.Element-resolvedanharmonicity, σh system 6. The an48 which typically have values >0.90,49i.e., suggesting that O–Hvibrations are predominantly harmonic. The high scaling factor valuesfor O–H vibrations, particularly those obtained with GGA functionals,arise due to the error cancellation between the poor approximationof the energy landscape with semi-local DFT and the inadequacy ofthe harmonic approximation toward vibrations. For instance, an anharmonicmode described by a Morse potential would be “softer”than the harmonic approximation in one direction but “harder”in the other, as depicted in 51 compared to the limited sampling along Cartesian axes that may beused to derive scaling factors for the harmonic approximation. Ourresults demonstrate that anharmonicity is dependent on chemical environment,and therefore another implication is the potential inadequacy of scalingfactors derived for application to results via theharmonic approximation, if these scalars are then applied for thesame bond types in different environments. For instance, in this work,σsE forhydroxyl group H atoms varies drastically depending on its chemicalnature, i.e., whether the O–H bond is a bridginggroup (0.91) or a part of a silanol group (0.52). The results suggestthat to fully account for anharmonicity with scaling factors, exactconsiderations of chemical environment are necessary.The high anharmonicity exhibited by H on the Bronstedacid sitewhen performing element-resolved analysis, especially for H-β,contrasts with the empirical scaling factors applied to O–Hvibrations,3.4Atom-resolvedanharmonicity can provide further insight into localized anharmoniccontributions by spatially resolving onto the unit cell 7. In the3.519 however, there is little consideration for the role ofanharmonic effects on the simulated vibrational modes. In order tounderstand the full impact of anharmonicity for the Sn-β system,we consider the DRIFTS spectrum of Sn(II) acetate adsorbed on deAl-β the harmonic model (finite-differencemethod) and (ii) the aiMD approaches detailed here. Simulations usingthe harmonic model capture key features present in the DRIFTS spectrum,such as vibrational modes at ∼1360–1410 and 1720 cm–1 from carbonyl groups of Sn(II) acetate; however,vibrations containing anharmonic contributions, as obtained the vibrationaldensity of states (VDOS) of aiMD data, are in far better agreementwith DRIFTS spectra for smaller frequencies, ensuring a more completeprofile of the vibrational modes is obtained. Considering the highlyanharmonic behavior displayed by BEA systems and the better low-frequencyrepresentation of the vibrational spectrum obtained from an anharmonictreatment of vibrational modes, caution may be necessary when applyingonly harmonic models toward zeolites for modes <1500 cm–1.Considering the significant anharmonicity displayed by BEA, it isnecessary to consider the validity of harmonic models used for modelingvibrations in BEA and other zeolites. Studies in the literature havecompared experimental IR spectra and VDOS from aiMD simulation tocharacterize the adsorption of alcohol in H-ZSM-5;n deAl-β8, which S, at 300 K is −223.26 J/K/mol when applying a harmonic model,compared to −307.44 J/K/mol when accounting for anharmonicity.The difference in ΔS suggests that includinganharmonicity is important for accurate entropy and free energy calculationswhen studying these zeolite systems.Furthermore, the differences observed in the vibrationalmodeswhen applying the harmonic and anharmonic methodology have a directimpact on the change in entropy that can be calculated for reactionsteps. Considering the adsorption of Sn(II) acetate on deAl-β,as introduced above, the change in entropy, Δ16 An overestimation in the change of frequencies will impactobservables such as zero-point vibrational contributions, entropy,and, subsequently, adsorption enthalpy and free energy. The methodsand systems considered in this work  were confined to the GGA level as higher-level methods werenot computationally tractable; however, with the continued adventof more efficient computing paradigms, we hope that the quality ofthe representation of the PES can be addressed in the near futurealso.While the inclusion ofanharmonic effects yields simulated spectrawith improved agreement to experiment compared to the simple harmonicapproaches, the quality of the representation of the PES remains unaddressedin this work and is important to consider in the future. The PES isdefined by the choice of exchange–correlation functional inDFT, and improvements are necessary for further reconciliation betweensimulation and experiment. The impact of the exchange–correlationfunctional on computational vibrational modes has previously beenreported in the literature. In particular, GGA functionals tend tooverpredict H-bonding interactions, which leads to an overestimationof the change in OH frequencies upon adsorption.4via ananharmonicity score, σA. Si-β has a greateranharmonicity (σA = 0.29) than dense silicate systemssuch as α-quartz (σA = 0.22), indicating thatthe porous nature of the framework and topology contribute to anharmonicbehavior. For the aluminated BEA framework, the anharmonicity is increased,and the anharmonicity then decrease for SSI intermediates with a σA ranking of H-β (0.35) > deAl-β (0.34) >Sn-β(0.32); the result suggests that anharmonic behavior may influenceBrønsted-acid zeolite catalysts more than their Lewis acid counterparts.In summary, anharmoniceffects have been investigated for Si-βand BEA-structured intermediates present during the SSI process toform Sn-β, with the impacts identified EA of 0.53 comparedto 0.38 for aluminum, the latter being broadly similar to σEA displayed by silicon.Hydrogen displays drastically different anharmonic contributions dependingon system type, with deAl-β having σEA for H of 0.53 and H-β beingmuch greater at 0.91. The changes in anharmonicity for H demonstratethat anharmonic contributions are also dependent on local chemicalenvironment.Vibrational mode-resolved analysis indicates that anharmonicitywithin BEA materials is strongest at low-frequency vibrational modes,which are almost entirely anharmonic because the porosity of the materialsallows for flexible lattice distortions that are not included in simpleharmonic models. Furthermore, elements can generate greater anharmoniccontributions that can vary depending on the material. For siliconand oxygen, anharmonic contributions are relatively uniform and low(<0.4) across all BEA materials; however, heteroatoms such as aluminumand tin have varying anharmonic contributions, with tin having a σThe localized nature of the anharmonic effect isfurther supportedby atom-resolved anharmonicity, which maps out anharmonic contributionsacross the BEA unit cell. For Si-β, anharmonicity is uniformlybelow 0.41; however, for H-, deAl-, and Sn-β, strong anharmoniccontributions are concentrated on the T2 site, which is the site ofdealumination and Sn incorporation in our models. The localized anharmonicityhas possible consequences for catalytic activity at the active site.via solid-stateIR, would be a valuable next step. We also emphasize that improvementsin the representation of the potential energy surface would be valuableto quantify the limitations of the semi-local exchange–correlationfunctional used in this work. The described results demonstrate thepotential impact of anharmonicity on mechanistic aspects of appliedzeolite catalysis, which will be investigated further.In evaluating anharmonic effects within BEA systems, the factorsthat contribute toward anharmonicity have been identified. We highlightthat the high degree of anharmonicity displayed by BEA raises questionsabout popular harmonic models used to simulate BEA and zeolites ingeneral. Analysis of vibrational modes obtained from the simulatedVDOS, which accounts for anharmonic effects, are in good agreementwith DRIFTS data obtained from experiment, especially at low frequencies,when compared to vibrational modes obtained from a harmonic approximation.Given the significant anharmonic contributions measured in this work,further experimental analysis, e.g.,


To enhance μ, numerous studies have concentrated on optimizing charge transport within the semiconductor layer. These efforts include: (i) extending π-conjugation, enhancing molecular planarity, and optimizing donor–acceptor structures to improve charge transport within individual molecules; and (ii) promoting strong aggregation, achieving well-ordered structures, and reducing molecular distances to enhance charge transport between molecules. In order to obtain a high charge transport mobility, the charge injection from the electrodes into the semiconductor layer is also important. Since a suitable frontier molecular orbitals’ level could align with the work function of the electrodes, in turn forming an Ohmic contact at the interface. OFETs are classified into p-type (hole transport), n-type (electron transport), and ambipolar-type (both hole and electron transport) based on their charge transport characteristics. As of now, the majority of reported conjugated materials are of the p-type semiconductor category, with research on n-type or ambipolar conjugated materials lagging significantly behind. This review introduces the molecular design concept for enhancing charge carrier mobility, addressing both within the semiconductor layer and charge injection aspects. Additionally, the process of designing or converting the semiconductor type is summarized. Lastly, this review discusses potential trends in evolution and challenges and provides an outlook; the ultimate objective is to outline a theoretical framework for designing high-performance organic semiconductors that can advance the development of OFET applications.In the last two decades, organic field-effect transistors (OFETs) have garnered increasing attention from the scientific and industrial communities. The performance of OFETs can be evaluated based on three factors: the charge transport mobility (μ), threshold voltage (V Field-Effect Transistors (FETs) are active devices that utilize an electric field to regulate the conductivity of solid materials ,2,3. FETth), and current on/off ratio (Ion/off). In these factors, charge transport is the pivotal element driving the performance of OFETs [Generally, OFETs can be categorized into three types: p-type (hole transport), n-type (electron transport), and ambipolar (both hole and electron transport) . The claof OFETs ,35,36,37In recent years, three prominent strategies have emerged for enhancing the charge mobility of organic semiconductor molecules: (i) extending π-conjugation, enhancing molecular planarity, and optimizing donor–acceptor structures to improve charge transport within the individual molecules ,39,40,41In the development of OFETs, although there are many strategies for improving carrier mobility, in fact, there is still a lack of an effective set of guiding rules to assist researchers. Hence, in this review, it introduces a conceptual framework aimed at equipping researchers with the knowledge to enhance the efficiency of OFET device preparation. Herein, we introduce various molecular design concepts aimed at enhancing the charge carrier mobility, including both within the semiconductor layer and during the charge injection. In addition, we provide a summary of how to design or convert the type of semiconductor. Lastly, we discuss potential trends in evolution and challenges and provide an outlook. The ultimate goal is to create a theoretical framework for designing high-performance organic semiconductors while advancing the development of OFETs applications.Enhancing charge mobility needs an appropriate molecular structure as a prerequisite. Charge transport in the semiconductor layer is divided into inter- and intra-charge transport. Regarding the intra-charge carrier’s mobility, the charge mainly transports through the effective conjugate system such as the molecular backbone ,48. Therh value of 0.095 cm2 V−1 s−1 and a μe value of 5.8 × 10−3 cm2 V−1 s−1—which is much higher than that of II-C6 . Recently, Deng et al. [2 V−1 s−1 and 0.09 cm2 V−1 s−1, while oligomers based on NDP show n-type behavior, with an electron mobility of up to 0.26 cm2 V−1 s−1. This work demonstrated that an extension π-conjugation system is not only a useful strategy for increasing the performance of semiconductors but could also alter its charge transport type. Regarding polymers, the effective conjugation system is large due to its long polymer backbone. Extending the π-conjugation of the repeating units is also beneficial for enhancing semiconductor properties. Hou and his colleagues [2 V−1 s−1, whereas P(AzIDT-C6) and P(AzIDT-PhC6) exhibit hole mobilities of only 0.016 cm2 V−1 s−1 and 0.12 cm2 V−1 s−1, respectively. The expanded conjugated system promotes charge transfer within the single molecule, resulting in a significant enhancement of carrier mobility. Based on the above observation as well as the published literature [Tsukasa Hasegawa and his colleagues  synthesig et al.  synthesilleagues  synthesiterature ,55, π-co2 V−1 s−1 and 6.14 cm2 V−1 s−1, which is almost ten times that of BDOPV-2T (μe = 0.96 cm 2 V−1 s−1). In addition, the stability of the device is also improved. After 30 days, the electron mobility of the F4BDOPV-2T device is only 40% lower than the original mobility, while the μe of BDOPV-2T is almost 75% lost. The improved stability is ascribed to the strong interchain interaction of the F…S, F…H, and F…Se results, the more planar backbone, the ordered molecular packing, as well as the small π-π stacking distance, which increase the oxygen penetration barrier. Recently, Liu et al. [h of CTZ is only 0.076 cm 2 V−1 s−1, while the value of PCTZ-T is almost 30 times increased, which is up to 1.98 cm 2 V−1 s−1. Ran et al. [2 V−1 s−1, and the sulfur–oxygen interactions form a more regular plane, whereas the electron mobility of NDTI-BT1C1 is only 0.085 cm2 V−1 s−1. Beside the above-mentioned interaction, some other non-convent bonds are also widely studied, such as N…S, B←N [Besides extending the π-conjugated length, modifying the backbone’s planarity is a simple and useful design strategy in OFETs. This strategy could not only enhance the efficiency of the conjugation length but also improve the order and regularity of molecular arrangement and promote π-π stacking, which results in enhancing charge carrier mobility ,57,58. Bu et al.  designedn et al.  introducN…S, B←N ,63, and h of P-NDF is only 0.55 cm2 V−1 s−1, while that of P-BDF is up to 0.85 cm2 V−1 s−1. This high value of P-BDF is ascribed to the planar backbone resulting in stronger aggregation as well as the short π-π distance. This work indicates that the main chain coplanarity of polymer semiconductors is more essential than the sole extension of π-conjugations  for the design of high-performance OFET materials. The decrease in the volume of the donor or acceptor groups is a simple and useful strategy for designing high-performance semiconductor materials, such as thiophene units, instead of the benzene ring [In most cases, researchers adjust the material’s backbone’s planarity through the non-convent bonds but ignore the volume of the groups. Recently, Zhang’s group  studied ene ring .h value of 1.08 cm2 V−1 s−1 and a μe value of 2.23 cm2 V−1 s−1, while PDPPFT exhibits a μh value of 0.78 cm2 V−1 s−1 and a μe value of 0.24 cm2 V−1 s−1. After the ring closing, the charge transport mobility is significantly increased, typically for the μe. It should be noticed that after the ring closing, the solubility of the polymers is decreased due to the reduction of the alky side chain. Later, Zhuang et al. [−2 cm2 V−1 s−1 for PBDTT-DPPFu and 4.36 × 10−3 cm2 V−1 s−1 for PBDTT-DPP. After the ring closing, the electron transport mobility increased by almost three times. These observations reveal that totally planar structures can be designed through the ring fusion method.Introducing a non-covalent bond and reducing the value of the units can significantly reduce the twisting angle and improve the material’s backbone planarity, but it is difficult to reach 0°. Very recently, Shi et al.  found thg et al.  studied Consequently, the extension of the π-conjugation system and enhancing the planarity of the backbone are simple and useful strategies for building high-performance semiconductor materials with high charge transport mobility. Reducing the volume of the units and ring fusion are effective methods for adjusting the molecular backbone’s planarity. Undoubtedly, these methods have proven effective in the context of current developments, and their potential for significant applications is anticipated in the future advancement of OFETs technology.e = 0.21 cm2 V−1 s−1) and the longest chain molecule NDI-C12 (μe = 0.21 cm2 V−1 s−1) showed the best performance, while the low mobilities semiconductor materials are observed among the intermediate chain lengths . The mobility trends in terms of the competing factors of film uniformity and crystal packing were interpreted. Short side chains promote a more favorable lateral stacking of NDI units within the unit cell, while long side chains promote a more uniform thin-film morphology. This comparison inspires us to refrain from assessing the optimal efficiency based solely on the length of the alkyl chain in the molecular backbone. Instead, it urges us to strike a balance among solubility, intermolecular π-π stacking, and crystallization properties simultaneously. Comparing NDI-C8 and NDI-EH . It is revealed that, with the same number of alkyl chain carbons, the linear side chain can form better intermolecular π-conjugation than the branched side chain.It is widely recognized that conjugated polymers containing aromatic rings exhibit greater rigidity and reduced pliability, resulting in poor solubility. In contrast, alkyl chains offer enhanced pliability, and their judicious incorporation into polymers can significantly improve solubility ,69. In gd NDI-EH b, their −2 cm2 V−1 s−1, which is lower than the 2.3 × 10−2 cm2 V−1 s−1 observed for the branch polymer. The GPC measurement shows that the branch polymer has a high molecular weight, which might be due to the fact that the branch polymer exhibits improved solubility compared to linear ones. This is the reason why the branch polymer’s performed is better than that of the linear polymer. We should consider both molecular packing and molecular weight when we consider using linear or branch alky chains.Although the majority of molecules adhere to this trend, there exist exceptional cases. Zhang and colleagues  synthesi2 V−1 s−1, significantly surpassing the modest 0.79 cm2 V−1 s−1 exhibited by a conventional all-carbon chain. This work reveals that introducing special atoms, such as phosphonate [Besides enhancing the solubility, alky-chain engineering could also endow the martials with some other functional ability. For instance, alkyl chains incorporating silica can offer exceptional flexibility and further optimize intermolecular stacking. Mei and colleagues  synthesisphonate , -S, andsphonate , into thh = 0.06 cm2 V−1 s−1, μe = 7 × 10−3 cm2 V−1 s−1; pDPPTz2T-1:μh = 0.86 cm2 V−1 s−1, μe = 0.014 cm2 V−1 s−1; pDPPTz2T:μh = 1.10 cm2 V−1 s−1, μe = 0.02 cm2 V−1 s−1). This work demonstrates the hydrogen bonding effects on the alky chain. However, if the hydrogen bonding directly worked on the polymer backbone, it will significantly affect the conjugation system as well as the electron cloud distribution.Recently, numerous studies have verified that alky chain engineering incorporating hydrogen bonding interactions is a beneficial strategy, which can result in materials with self-assemble ability. This improves the molecular packing and shortens the π-π distance, resulting in a high charge transport mobility ,79,80,81h = 4.2 × 10−4 cm2 V−1 s−1) was enhanced by two orders of magnitude compared to that of Boc-TATDPP (μh = 3.4 × 10−6 cm2 V−1 s−1). Besides small molecules, oligomers as well as the polymers containing Boc groups also present the same properties with a self-assembling ability, enhancing the charge transport mobility [The alky chain could increase the material’s solubility and enable its solution processing but will result in materials packing disorder. In addition, it cannot enhance the materials’ backbone conjugation systems. In the past few years, researchers found that the Boc unit is broken down during the thermal annealing process. Thus, Boc groups could endow the conjugated materials with a good solubility in most common organic solvents, resulting in a solution processing ability. In most reported articles, the Boc unit is substituted on the amide units (NH). Once the OFET device is prepared, through the thermal annealing processing, the Boc units could be removed; meanwhile, the device based on the materials without any alky-chain is obtained. In addition, the presence of amide units can form hydrogen bonds with the carbonyl groups of neighboring molecules (NH…OC), resulting in materials with self-assembly capabilities. Mula et al.  successfmobility ,85,86. CIn summary, alky chain engineering plays a crucial role in the molecular design concept for high-performance semiconductor materials. Achieving precise control over the alkyl chain’s length and shape (linear or branched), the incorporation of specific groups , or the implementation of a hydrogen bonding system in side-chain engineering offers opportunities to enhance molecular stacking and boost carrier mobility. This also enables the harmonization of semiconductor layer solubility with high efficiency, providing a crucial foundation for the fabrication of efficient OFET devices.The essential components of an OFET device include the semiconductor layer and the electrodes. The organic semiconductor layer is directly in contact with the electrodes, allowing for the transmission of charge between the organic semiconductor layer and the electrodes ,88,89. T−2 cm2 V−1 s−1) and electron (7.27 × 10−2 cm2 V−1 s−1) injection from the Au source-drain electrodes. However, due to the poor alignment Fermi energy levels between the DPPT-DCV and the metal electrode, carriers encounter significant ohmic resistance during migration. As a result, DPPT-DCV exhibits a weak p-type characteristic with an electron mobility of 1.84 × 10−2 cm2 V−1 s−1. Therefore, from the semiconductor layer’s perspective, the design of molecules closely aligned with the Fermi energy level of the metal electrodes can effectively mitigate ohmic resistance during carrier transfer, resulting in enhanced OFET performance.To improve charge carrier injection properties in the organic semiconductor layers, especially in n-type OFETs, the organic semiconductor layers should have suitable HOMO and LUMO. A low LUMO energy level can produce an excellent match with the Fermi energy level of the metal electrode, thus reducing the barrier for electron injection. In general, the introduction of fluorine, cyano, and some other electron-deficient groups into the molecular system can enhance the electron-deficient properties of the materials ,95,96,97In addition, for the purpose of the formation of the Ohmic contact, it is possible not only to ensure a rational alignment of semiconductor molecules with metal electrodes but also to consider the design of diverse electrodes from the metal electrodes’ perspective. This approach aims to achieve superior ohmic contact with the semiconductor layer’s molecules. In the charging process of holes and electrons, organic semiconductors usually support ambipolar transport. However, the charge injection is symmetric due to the inherent misalignment of the electrode work function with both conducting levels of the organic semiconductors ,100,101.While many organic semiconductor layer materials currently exhibit high efficiencies, converting them to high-efficiency OFET devices has significant challenges, primarily in dealing with the ohmic contact problem. Consequently, both from the electrode and semiconductor layer perspectives, there is a pressing need to enhance passivation, minimize ohmic resistance, and mitigate unnecessary carrier losses. This is the primary goal for the efficient preparation of OFET in the future.The performance of the OFETs, as summarized in this review, are provided in OFETs address the shortcomings of inorganic field-effect transistors, including their high cost, environmental impact, and lack of flexibility. Furthermore, the advancement of OFET technology has enabled the creation of flexible electronic devices. In recent years, OFETs have played pivotal roles in our daily lives and have become essential in various fields, including flexible displays, electron-skin technology, and numerous advanced applications. As these fields continue to evolve, the demand for high-performance OFETs with a high charge transport mobility has grown significantly.Despite the long development history of OFETs, several challenges continue to impede their practical application. These challenges include lower charge mobility when compared to that of inorganic field-effect transistors and issues of stability, particularly in the case of n-type and ambipolar OFETs. In addition, environmentally friendly and sustainable materials and manufacturing processes for organic semiconductors are also challenging. Given these challenges, this review focuses primarily on the molecular design concepts for achieving high-performance n-type and ambipolar OFETs. This encompasses considerations related to the backbone, side chains, and electrodes. The ultimate objective is to provide a theoretical framework for designing high-performance n-type and ambipolar OFETs, thereby advancing their development for practical applications.


Hemicentrotus pulcherrimus, comparatively little is known about the specific transcription factors and their spatiotemporal expression patterns that regulate the development of cholinergic neurons. In this study, we establish the requirement of the transcription factor Rx for the development of cholinergic neurons in the apical organ of the species. Furthermore, we investigate the role of the RNA-binding protein Musashi1, known to be involved in neurogenesis, including cholinergic neurons in other organisms, and demonstrate that it is a downstream factor of Rx, and that choline acetyltransferase expression is suppressed in Musashi1 downregulated embryos. Our research also highlights the intricate network formed by neurons and other cells in and around the apical organ of sea urchin larvae through axons and dendrites, providing possibility for a systematic and complexed neural pattern like those of the brain in other organisms.Acetylcholine, a vital neurotransmitter, plays a multifarious role in the brain and peripheral nervous system of various organisms. Previous research has demonstrated the proximity of cholinergic neurons to serotonergic neurons in the apical organ of sea urchin embryos. While several transcription factors have been identified as playing a role in the development of serotonergic neurons in this region of a sea urchin,  To gain insights into the nature of organisms, it is crucial to elucidate the organization and functioning of nervous systems, as they play a fundamental role in shaping behaviors. The development of sophisticated nervous systems throughout evolution has undoubtedly contributed to the efficiency and survival capabilities of animals. Notably, human beings possess one of the largest and most complex brains among all animals , leadingHowever, the current body of knowledge regarding the characteristics of nervous systems in non-model organisms remains inadequate for meaningful comparisons with those of model organisms. This limitation hampers our ability to assess the extent of diversification in nervous systems during evolution.Specifically, detailed studies on the nervous system organization in Ambulacraria, including echinoderms and hemichordates, have not been fully reported, similar to other non-model organisms, despite their significant position in the evolutionary tree . While nLytechinus variegatus  with 50 μg/mL kanamycin.Adult in situ hybridization was performed as described previously (H. pulcherrimus genome and transcriptome (foxQ2 (HPU_15608), rx (HPU_04689), hbn (HPU_04688), lefty (HPU_15030), neurogenin (HPU_07864), choline acetyltransferase (HPU_01496), msi1 (HPU_03784) and tryptophan 5-hydroxylase  (Whole-mount eviously  with somcriptome . The samU_21307)  at a finU_21307) .Whole-mount immunohistochemistry was also performed as described previously. The samples were blocked with 1% skim milk in PBST for 1 h at RT and incubated with primary antibodies (dilutions: mouse anti-Synaptotagmin B (SynB) , 1:100; Microinjection was performed according to a previously described method  with injRx-MO1 (1.9–3.8 mM): 5′- GGGTGATGCGCTCCATCCATTGTTA -3′,Rx-MO2 (1.0–1.9 mM): 5′- TTTGTGACTGATCGTCTTTCCAAAC -3′,Msi1-MO1 (0.5–1.0 mM): 5′- AACCCTCAACTAAAAAGGCCCAATA-3′,Msi1-MO2 (1.9 mM): 5′- GAATTGGCAAACGGTCCTTCTTAAC-3′,and Hbn-MO1 (0.7 mM): 5′- AAAATGAACGGAACAAGTCCAGTGT -3’.(previously characterized) .Two non-overlapping translation-blocking morpholinos for Rx and Musashi were used to confirm the specificity of their function . For negLive samples were observed under a light/fluorescence microscope . The fixed and stained specimens were observed using a light/fluorescence microscope  and a confocal laser scanning microscope . All transmission images were taken with an IX70 microscope. The Figure panels and drawings for the Figures were made using Adobe Photoshop and Microsoft PowerPoint.L. variegatus, these neurons were found to be cholinergic  appear in the brains of prism larvae at 36 h (hr) (Previous research has demonstrated the presence of non-serotonergic neurons in the brains of sea urchin larvae . In the linergic . In H. p6 h (hr) . Non-ser6 h (hr) . The num6 h (hr) .H. pulcherrimus are also cholinergic, similar to L. variegatus, we detected the messenger RNA (mRNA) of choline acetyltransferase (ChAT) and tryptophan 5-hydroxylase (TPH), a rate-limiting enzyme of serotonin synthesis, in the larvae and examined the details using a confocal microscope. Besides the previously reported expression of chat in ciliary band neurons in H. pulcherrimus larvae  is a specific transcription factor expressed in the prospective brain region during early development and in some neural progenitor cells in other sea urchin species . Howeverrx was found to be co-expressed with foxQ2 , the expression of rx was completely abolished in the brain region  at 24 h in early gastrula  at 36 h in larvae  is expressed throughout the ciliary band, including the brain, and Lv-ngn is necessary for the specification of cholinergic neurons in the ciliary band . Previous studies have suggested that Musashi is involved in the differentiation of cholinergic neurons, as it is co-expressed with rganisms . Sea urcrganisms ; howeveris study . In 48-hus stage . msi1 wath foxQ2 , a deterth foxQ2 , but notis stage . Furthern region .msi1 and rx. As rx initially expresses in the same region as foxQ2  in the control group and 3.3% (2/61) in the Rx morphant group. In conclusion, Rx regulates msi1 transcription in the brain region of sea urchin larvae, although it remains unclear whether this control is direct or indirect.Next, we focused on the relationship between as foxQ2 , it is phe brain , and theMsi1 plays a crucial role in the expression of Chat in the larval brain and the formation of the neural plexus.chat signal was absent in the brain , and Go-opsin expression patterns in larvae aged 48–96 h , whereas brain neurons show some effects in response to these manipulations. Furthermore, the formation of upper lip neurons is regulated downstream of the dorsal-ventral axis, which is controlled by the Nodal/BMP pathway . In embrRx is a prominent transcription factor known for its role in regulating eye specification in vertebrates. However, in eyeless organisms such as sea urchins, the function of Rx has remained enigmatic despite its reported expression in various species. This study sheds light on the requirement of Rx in the specification of photoreceptor cells. Intriguingly, Rx also plays a role in ocellus development in ascidians, indicating a conserved function related to photoreceptors among deuterostomes . This suOur findings demonstrate the essential role of Rx in the differentiation of neurons, particularly cholinergic neurons, and their axon development in the sea urchin larval brain. Interestingly, the specification of the brain field, as indicated by the pattern of serotonergic neurons, was unaffected in Rx morphants, suggesting that the dorsal-ventral and left-right axes of brain region were preserved. In contrast, Hbn morphants exhibited a completely opposite phenotype, where the size of the brain remained unchanged but serotonergic neurons were absent. Notably, Rx and Hbn are adjacent genes in the sea urchin genome , as obsemsi1 in the brain region occurs significantly later than rx expression, suggesting that early Rx may indirectly control Msi1 transcription probably through Ngn (chat in non-serotonergic neurons of sea urchin brains (chat gene. Additionally, their neural processes extend only along the left-right body axis. Currently, we do not have information about the specific neurotransmitters or neuropeptides produced by these neurons other than acetylcholine in H. pulcherrimus. Furthermore, the absence of a neuroplexus on the ventral side in Msi1 morphants suggests that Msi1 is crucial for axon development in sea urchins (in situ hybridization of Robo or single-cell RNA-seq, along with functional assays in H. pulcherrimus, will unveil the detailed molecular pathway of Msi1 in the brain region of sea urchin larvae.Our data shows that the regulation of axon development by Rx is mediated by Msi1 in sea urchin larvae. The expression of ough Ngn  (Figure ough Ngn , or thatough Ngn . In our n brains . Based o urchins . AlthougIn summary, our findings provide evidence of the conserved expression pattern and functional role of Rx in echinoderm larvae among deuterostomes, suggesting its importance in brain and photoreceptor development across clade. Rx exhibits an initial expression in the prospective brain region, followed by its expression in photoreceptor cells. Its primary function in the brain appears to be involved in specific aspects of neural differentiation, such as axon development, rather than regional brain specification, as depicted in


Surgery to repair pectus excavatum (PE) is often associated with severe postoperative pain, which can impact the length of hospital stay (LOS). While thoracic epidural analgesia (TEA) has traditionally been used for pain management in PE, its placement can sometimes result in severe neurological complications. Recently, paravertebral block (PVB) and erector spinae plane block (ESPB) have been recommended for many other chest and abdominal surgeries. However, due to the more severe and prolonged pain associated with PE repair, it is still unclear whether continuous administration of these blocks is as effective as TEA. Therefore, we conducted this systematic review and meta-analysis to demonstrate the equivalence of continuous PVB and ESPB to TEA.The online version contains supplementary material available at 10.1186/s12871-023-02221-x. Pectus excavatum (PE) is a chest wall deformity  that notOther alternatives to TEA, such as paravertebral block (PVB)  and erecESPB is another type of peripheral nerve block that involves a local anesthetic, with or without other medication, into erector spinae plane space. The anesthetic diffuses into the paravertebral space anteriorly, working similarly to PVB. An interfascial spread that blocks the posterior rami of spinal nerves may also be another mechanism . The sinThis meta-analysis aimed to assess the effects of continuous PVB and ESPB versus TEA on LOS as primary outcome in patients with PE repair. Our study was conducted in accordance with PRISMA guidelines, a commonly used tool to correctly elaborating reviews that evaluate the effects of interventions  Fig. 1)1).The inclusion criteria for studies were as follows: the patients underwent the repair of PE using sterna wedge osteotomy or minimally invasive approach, regardless of the sex, race, age, height, and weight and studies that compared LOS, pain score, and opioid usage between TEA and continuous infusion of ESPB or PVB; both retrospective and prospective studies were eligible.PubMed, EMBASE, and Cochrane Library databases were searched for the eligible studies published from their inception until January 2023. We did not exclude studies by date, region, or language. MeSH terms including “Nerve Block/pharmacology“[Mesh], “Nerve Block/standards“[Mesh], “Nerve Block/therapeutic use“[Mesh], “Nerve Block/therapy“[Mesh], “Analgesia, Epidural“[Mesh], “Analgesia, Epidural“[Mesh], “Analgesia, Epidural/adverse effects“[Mesh], “Analgesia, Epidural/statistics and numerical data“[Mesh], “Analgesia, Epidural/therapeutic use“[Mesh], “Analgesia, Epidural/therapy“[Mesh]), “Funnel Chest/surgery“[Mesh], “Funnel Chest/therapy“[Mesh], “Funnel Chest“[Mesh], “Pain Measurement“[Mesh], “Visual Analog Scale“[Mesh], “Analgesics, Opioid“[Mesh], “Analgesics, Opioid/administration and dosage“[Mesh], “Analgesics, Opioid/therapeutic use“[Mesh] and “Length of stay“[Mesh] were used in combination with plain text to search PubMed. Similar strategies were applied to search the other databases. The search strategies are provided in detail in Supplement 1.Two independent reviewers selected the eligible studies. Any disagreements were resolved by the reviewers; a third reviewer was consulted if the reviewers cannot reach an agreement.Data extracted from each study included: (i) general study characteristics: study design, country, and enrolment period; (ii) study population characteristics: age, preoperative PE severity index ; (iii) characteristics of the intervention: the level of epidural catheters or continued nerve block catheters that were placed and the medication used for TEA or continued nerve block; (iv) primary outcome measure was LOS; (v) Secondary outcome measures were post-operative pain scores, total opioid usage, and post-operative nausea and vomiting (PONV).One reviewer extracted data sets from each eligible study, which were further validated by a second reviewer. Continuous variables reported as mean and standard deviation (SD) were extracted without any changes. If needed, the values were driven from the graphs. However, variables reported as median and interquartile range were converted before extraction. Methods of conversion have been reported before .The methodological quality of the randomized controlled trial (RCT) was evaluated using the updated Cochrane risk-of-bias tool for randomized trials (RoB 2) . The risI2statistic. Outcomes are presented in forest plots. A subgroup analysis was not predetermined. A P-value ≤ 0.05 was considered statistically significant.Meta-analyses were performed by Review Manager Software  using a random-effects model. This model was chosen because the treatment effect can vary across each study due to differences in treatment protocols. The primary and secondary outcomes were estimated by the mean difference (MD) and its 95% confidence interval (CI). Statistical heterogeneity was assessed by the Cochran Q statistic and quantified by the A total of 43 studies were identified from the three databases, PubMed n = 14), EMBASE (n = 24), and Cochrane (n = 5). Of them, 15 duplicates were removed. The title and abstract of the remaining 28 studies were screened for eligibility. Twenty studies were excluded due to being irrelevant, case reports, or conference abstracts, among other reasons listed in Fig. 4, EMBASEAmong the studies, six were retrospective cohorts –25, 34 aTwo studies , 24 repoFive studies reported the LOS –25, 34. Two studies , 34 wereI² = 0%; P = 0.92) were observed. Five studies reported LOS –25, 34. I² = 0%; P = 0.43) were observed on POD1 . There was an insignificant between-subgroup difference  on POD2 and the difference between PVB and TEA was insignificant while TEA group has a lower pain score than ESPB group . There was no significant between-subgroup difference  on POD3 and the difference between PVB and TEA was also insignificant while TEA group still has a lower pain score than ESPB group .All the studies reported pain scores. The synthesis showed a significantly lower pain score in the TEA group by 0.83 , 0.75 , and 0.63  on post-operative days (POD) 1, 2, and 3, respectively see Fig. . No signI² = 0%; P = 0.89, PVB; MD 0.23, 95% CI, -0.11 to 0.56; P = 0.18; ESPB; MD 0.3, 95% CI, -0.65 to 1.25; P = 0.54), on POD2  and on POD3 . However, due to high-level of heterogeneity in test for subgroup differences on POD3, the heterogeneity decreased to low-level  after we removed the study by Walter [Five studies reported opioid usage on post-operative day 1 to day 3 , 24, 25.I² = 70%; P = 0.03).Three studies reported events of PONV , 18, 24.This systematic review and meta-analysis compared continuous ESPB and PVB with TEA about LOS as the primary outcome. However, no RCT was found in this regard. Seven non-randomized studies were included, with a total of 644 patients. The synthesis of the result reported that continuous nerve blockage reduced LOS by 1.24 days compared to TEA with statistical significance in patient with PE repair Fig. . SeveralPain scores were significantly lower in TEA group from POD 1 to POD 3 compared to nerve block group , 40 (FigOpioid usage was not significantly different in the first two days after the operation. However, on POD 3, there was a significant difference in opioid usage Fig. . This phOur analysis found a higher risk of PONV needing treatment in the TEA group Fig.  which maAlthough TEA provides better pain control compared to continuous ESPB and PVB, catheter placement is considered a technical skill  and has TEA is currently the most common method of pain control for patients undergoing major thoracic and abdominal surgery , 48, 49.The main limitation of this study is the low number of included studies. In addition, none of the studies were RCTs, and there was a moderate to serious risk of bias in the included trials. Furthermore, the use of data conversion methods may have introduced some limitations to our analysis.Continuous PVB and ESPB use is associated with reduced hospital stay and PONV, and thus, may be considered alternative to thoracic epidural analgesia in patients with PE repair. However, because of the low quality of studies, well-designed RCT are required to verify the evidence.Below is the link to the electronic supplementary material.Supplementary Material 1


COVID-19 is a multi-systemic disease which can target the lungs and the cardiovascular system and can also affect parts of the brain for prolonged periods of time. Even healthy athletes without comorbidities can be psychologically affected long-term by COVID-19.This study aimed to investigate athletes’ perceived mental stress and recovery levels in daily life, and their maximal aerobic power, at three different time points, post COVID-19.max)) at the initial screening (t1: 4 months after infection). Follow-up assessments occurred three  and seven months after t1 .In total, 99 athletes , who had been infected by COVID-19, filled out the Recovery Stress Questionnaire for Athletes (REST-Q-Sport) and completed cardiopulmonary exercise testing , p = 0.020, r = 0.224) was significantly above the reference value of two at t1, while all other Stress subgroups were not significantly different from the reference value or were significantly below the maximum threshold of two at t1, t2 and t3. Spearman’s ρ revealed a negative association between Pmax and the subcategories of stress , and positive correlations between Pmax and “Somatic Recovery”  and “General Recovery”  at t1. Pmax (t1: 3.83 (± 0.99), t2: 3.78 (± 1.14), β = 0.06, p < 0.003) increased significantly from t1 to t2. In addition, REST-Q-Sport indicated a decrease in "Sleep" (t2 = 2.35 (± 0.62), t3 = 2.28(± 0.61), β = -0.18, p < 0.023) at t3, when compared to t2.Subgroup means from the Recovery category were significantly below the reference value of four at all three time points, except “General Recovery” (3.76 (± 0.96), p = 0.275, d = 0.968) at tThe perceived recovery seems to be negatively affected in post COVID-19 athletes. Physical performance post COVID-19 correlates with both “Emotional and Somatic Stress” and “Somatic and General Recovery”, indicating potential mental and physical benefits of exercise. While it is evident that COVID-19, like other viral infections, may have an influence on physical performance, monitoring stress and recovery perceptions of athletes is critical to facilitate their return-to-sports, while minimizing long-term COVID-19 induced negative effects like the athletic objective and subjective perceived recovery and stress levels. The Coronavirus disease 2019 (COVID-19) has spread globally and resulted in a global health emergency and pandemic. To date, the long-term health repercussions of this pandemic , dealing with and healing symptoms like fatigue, concentration problems) are not yet completely understood –5. ConseCOVID-19 is a multi-systemic disease  which caAdditional stressors experienced by athletes include competitions, social and environmental factors, and imbalances between training and regeneration, which can all lead to stress and an altered stress resilience . This caThe three aims of this study focused on the investigation of the altered stress and recovery perception of athletes in relation to their maximal aerobic power after COVID-19. The first aim was to investigate the relationship between physical performance and the subgroups of stress and recovery in daily life of athletes post COVID-19. Secondly, we examined which covariates influence the variables of REST-Q-Sport, and the correlation between maximal aerobic power and the REST-Q-Sport variables. Subsequently, in a long-term observation up to seven months, the development of the subgroups of stress and recovery, and athletic performance was analyzed.The study was conducted at the Division of Sports and Rehabilitation Medicine, Centre of Internal Medicine of University Hospital Ulm, Germany. All data were collected as a part of the CoSmo-S study (COVID-19 in German Competitive Sports) at the University Hospital Ulm .The data was collected between December 2020 and May 2022. Inclusion criteria were the following: 1) age ≥ 18 years, 2) regular physical training with a minimum of three training sessions per week (minimum of 20 METs/week), 3) post COVID-19 state (verified by result of positive smear-PCR and/or positive antigen testing). A detailed description of all inclusion and exclusion criteria, as well as the study design, can be found in the study protocol by Nieß et al. .All patients who filled out the Recovery Stress Questionnaire for Athletes (REST-Q-Sport) by Kellmann et al.  and compIn total, 99 participants  were included for initial assessment. A detailed description of the study population, including, sport type, pre-disease training volume, symptoms during acute phase as well as persistent symptoms at each examination are shown in 1) was 3.93 (± 4.41) months, with a median value of 2.5 months. The second examination (t2) took place three months later (3.08 ± 0.30). The third examination t3 was seven months after t1 (6.92 ± 0.25). In total, 37 athletes were included in the analysis considering t1+t2, and n = 19 when including t3. Only athletes with complete data sets were included in the follow-up evaluations , displayed as W/kg Body Mass (BM), which was measured on a bicycle ergometer .Additionally, all participants conducted cardiopulmonary exercise testing (CPET). CPET was used to determine the relative maximal aerobic power , SPSS ), and R version 4.1.2  software.Descriptive values were displayed as mean values and standard deviations (± SD). Differences between the means and the corresponding reference values were determined using T-test or Wilcoxon test. Effect size was calculated with Cohen’s d or r, respectively.max was performed using Spearman’s ρ. The influence of the covariates , which showed a significant correlation to Pmax and Stress subgroups, was considered in the partial correlation.Correlation analysis between the subgroups of Recovery and Stress and P1 to the first follow-up t2 and from t1 to t3, a multilevel mixed models were used. The calculations were corrected for multiple testing using fdr-correction.To calculate whether the parameters changed from the initial screening tRobust linear regression was calculated to capture the influence of time since acute infection on the Recovery and Stress subgroups.The significance level for all tests was set at p<0.050.All athletes were provided with information about the content of the study and the use of the data, and provided written consent. The study was conducted in compliance with the Declaration of Helsinki. The study was approved by the ethics committee of Ulm University (EK-408/20).3. Thus, a large part of the questionnaire data given by the athletes were not in the desirable range. The effect size varies from medium to strong |-0.356–1.231|.Tables 1, whereas “Overtiredness” (r = 0.224 (p = 0.020)) was increased at t1. At t2 “Emotional Stress” (d = -0.415 (p = 0.016)) was significantly lower than the reference value. Thus, this value is within the desired range. At t3, there were no significant differences between the subgroups of Stress and the reference value.The values of the Stress subgroups “General Stress” (r = -0.341 (p < 0.001)), “Emotional Stress” (r = -0.358 (p < 0.001)), “Social Stress” (r = -0.476 (p < 0.001)) and “Performance Pressure” (r = -0.254 (p = 0.012)) were significant lower compared to the reference value of two at tmax were between 3.5 and 3.9 W/kg BM (t1: 3.83 (± 0.99), t2: 3.78 (± 1.14), t3: 3.50 (± 1.10)). Significant differences between genders were not observed. The mean and median values of the subgroups in the Injury category were all within the reference range, while the mean and median values of the subgroups in the Performance category were below the reference values. Additional results of the Injury and Performance categories are provided in S1 and S2 Tables in The values of Pmax and”Somatic Recovery” and “General Recovery”, and Pmax “General Stress”, “Emotional Stress”, “Performance Pressure”, “Overtiredness”, “Lack of Energy” and “Somatic Stress”, were displayed in Figs max showed significantly higher “Somatic Recovery”  and “General Recovery” . No significant association between “Success”, “Social Recovery”, and “Sleep” and Pmax. was found. Negative correlations were observed between Pmax and “Emotional Stress” , “Performance Pressure” , “Overtiredness” , “Lack of Energy”  and “Somatic Stress” . After correcting for multiple testing, all results remained unchanged. A detailed analysis of the correlation between each subgroup can be found in S3 Table in Spearman’s rank correlations between P1 were shown in Significant correlations between the covariates age, BMI, LBM, sex, body mass and time since infection at t1 and t2, a significant change of Pmax was observed with an improvement in Pmax over the three-month period (β = 0.06 (0.02–0.10), p < 0.003). The parameters of the REST-Q-Sport did not show any significant changes over the first three months.For the 37 athletes with complete data sets at tmax could be shown. Moreover, there was no significant change in the subcategories of Stress. Participants did not show a significant change in the perception of recovery besides “Sleep”. The perception of “Sleep” decreased between the first and the third appointment .A complete data set over a period of seven months was collected from 19 athletes. No significant change in Pmax. Higher values of Pmax correlated positively with the Recovery subgroups “Somatic Recovery” and “General Recovery”. When examining changes over three and seven months, an improvement of Pmax between t1 and t2 and a decrease in “Sleep” after a period of seven months could be observed.In the present study, higher levels of decreased perceived recovery were observed among individuals who had recently COVID-19. Furthermore, correlations were found between the subgroups of the REST-Q-Sport and the maximum aerobic performance. Higher values in “General Stress”, “Emotional Stress”, “Performance Pressure”, “Overtiredness”, “Lack of Energy” and “Somatic Stress” were associated with lower P3. On the other hand, only "Overtiredness" from the Stress category significantly exceeded the threshold of two. These results suggest that perceived recovery is frequently disturbed. Small disturbances occur in daily life [On the one hand, all mean values of the Recovery subgroups were below the desirable range. Only "General Recovery" was not significantly below the threshold at tily life . Healthyily life . COVID-1max values and improved perception of “General Recovery” in post COVID-19 athletes. We also found that an increased perception of “Somatic Recovery” correlated with enhanced physical performance.Kalda et al.  observedIn the present study, elevated “General Stress”, “Emotional Stress” and “Performance Pressure” negatively impacted performance after four months of infection. To date, there are no official recommendations for athletes suffering from long-term symptoms post COVID-19 . Wilson A further study group compared the mental health status of athletes and non-athletes and did not find any differences in stress and anxiety levels during the pandemic . HoweverSteinacker et al.  have alrmax, we found a negative correlation between “Overtiredness” and Pmax. It was already observed that, among athletes where the training intensity decreased during the lockdowns, the sleep quality also simultaneously decreased [Another health concern of COVID-19 is sleep disturbance, which may have its origin in mental health problems, which leads to poor sleep quality and thus to overtiredness ,37. Althecreased . These rmax in our study.Brink et al.  showed iIn general, Long-COVID or Post-COVID challenges mental well-being, and the return to sport can add challenging circumstances, especially when long-term symptoms occur . With thAs presented in this study, body composition influences maximal aerobic power. Our athletes with adequate lean body mass showed better performance capability, when compared to athletes below or above reference values. In addition, we showed a negative correlation between LBM and General Stress. These results are in line with previous literature, where it is well established that inadequate body composition can be associated with mental health problems like depression, especially in women . HoweverIt is important to note that the pandemic interrupted social interactions, togetherness, and familiar  routines. Additionally, for our athletic sample in particular, these restrictions can be a striking experience, as sport always has a strong social component, which was largely eliminated in the pandemic.It is well established that COVID-19 can lead to long-term sequela –45. Thesmax and no change in the perceptions of Stress and Recovery.After the first follow-up, our results showed a significant improvement of Pmax could be determined. Generally, after the acute phase of a disease, performance increases to the level before infection, when restarting with sport. This may explain the increase in performance between the first and the second appointment. Over time, the influence of the original infection becomes smaller, and the influence of regular training becomes greater. The results of the study suggest that in this population there may no progressive training, or that a leveling off of performance had already been achieved and the effects of the infection were minor.Over the seven-month period, however, no significant change of PBetschart et al.  showed dAfter the second follow-up, a decrease in perceived “Sleep” was observed. Sleep is a crucial factor when monitoring general recovery and should be assessed with associated parameters , especially within the field of sports . FurtherDonzella et al.  showed tTo our knowledge, there are no comparable studies that have investigated the relationship between physical performance and mental parameters in post COVID-19 athletes. The short time span in the questionnaire that we focused on is also a strength of our study because it highlights even small changes in perceptions of stress and recovery, rather than focusing on states that are quite stable and change only slowly over time. Nevertheless, the results of the study cannot establish a direct connection between the illness and the altered perceived stress and recovery, as no measurement data were available before the disease. Furthermore, the sport type and weekly training volume differed within the study population. In general, however, these individuals were more physical active than the average German population compared to our study population in the same age group (33.0 yrs). Therefore, we could assume that this study population was fitter and had fewer comorbidities.Our results indicate that especially the perceived recovery is affected. Due to an increasing dropout rate over time, the power of the results decrease. In addition, it should be noted that the willingness to participate in the study was probably greater among individuals with existing symptoms than symptom-free athletes. However, the percentage of athletes who were symptom-free at examination increased slightly at each examination. This fact may explain why there were almost no significant changes over time. With a larger study population, group divisions  and comparisons would be possible.Furthermore, we did not take weekly training hours, sleep time, or inflammatory biomarkers into account, which could be confounding components when detecting perceived stress and recovery. Furthermore, we did not investigate whether athletes had COVID-19 again, and we did not monitor their exercise behavior over time.In our post COVID-19 athletic study population, a relationship between maximal aerobic power and perceived stress and recovery was observed. Furthermore, insufficient recovery and slightly increased stress parameters were observed at all examination points. Together with the detrimental effects of “Sleep” for a long-term decrease in performance, the importance of monitoring not only physical but also psychological parameters post COVID-19 athletes is highlighted and should be further integrated in continuous routine documentation by athletes and physicians. The combination of 1) performance testing (CPET), 2) mental state assessment (REST-Q-Sport) and 3) molecular biomarkers  may support in the assessment of the respective athlete’s health status. In addition, this combination may assist in the development of individualized training plans which also consider mental well-being, to help the athletes to return to sport, improve their performance, and attenuate long-term consequences.S1 File(DOCX)Click here for additional data file.


During the final proofreading step of this paper , an erroLast paragraph of Section 3.2, “In another study by the same group and recruiting from the same pool of participants, Hu et al. [69] used a longitudinal design to investigate changes in functional connectivity after a month of excessive SNS use.” The reference number is now [70].7th paragraph of Section 3.3, “Analysing data from the same sample as a previous resting-state fMRI study [66].” The reference number is [67]. 8th paragraph of Section 3.3, “that were extracted from their own account as well as six generalised recommended videos for new users [79].” and “In an extension of this work, the same group published further analyses of the same dataset using graph theory to investigate the functional connectivity between seven networks [80].”. The reference numbers are [80] and [81], respectively. Last paragraph of Section 3.3, “In a study by Leménager et al. [81],” and “A more recent study used a similar self-concept paradigm in which participants had to make self-judgements on academic, physical and prosocial traits from their own perspective and from the perspective of others [82].” The reference numbers are now [82] and [83], respectively. In Table 2, the reference number Hu, Cui et al. [69] is now [68].In Table 3, the references to Meshi, Morawetz and Heekeren (2013) [72], Sherman et al. (2016) [73], Sherman, Greenfield et al. (2018) [74], Sherman, Hernandez et al. (2018) [75] are incorrect . References numbers are now [73], [74], [75], and [76], respectively.In Section 4.1, “Indeed, there is evidence that problematic SNS users show heightened activity in the ventral striatum when responding to SNS cues [71].” The reference number is now [63].In Section 4.1, “and even regular users show greater activity in this region when performing tasks that simulate SNS use especially when the task involves cues related to social reward  [72–74].” References number are now [73–75], respectively.In 3rd paragraph of Section 4.2, “Sherman et al. [75] also reported increased OFC activity when participants ‘liked’ another’s Instagram post.” The reference number is [76].In 4th paragraph of Section 4.2, “It is likely that the DLPFC is recruited to manage the cognitive and emotional demands of sharing personal and emotionally valenced content online .” and “However, contrary to what might be expected, fMRI studies employing tasks of executive function have reported no abnormalities in PFC activation for problematic SNS users .” The references numbers are now  and , respectively. Last paragraph of Section 4.2, “increased medial PFC activity in response to viewing SNS photos with many ‘likes’ ” and “However, more problematic SNS users have been found to show reduced medial PFC activity when viewing cues depicting risky behaviours which might indicate impaired decision making abilities [76].” The reference number are now  and [77], respectively.Last paragraph of Section 4.2, “or when receiving negative SNS comments [78] may also reflect the processing of content relevant to the self.” The reference number is [79]. In Section 4.3, “Nonetheless, Sherman et al. [75] did find increased amygdala activity in regular SNS users when ‘liking’ another’s post”. The reference number is [76].First paragraph of Section 4.4, “In line with this, Sherman et al. [73] found that teenaged Instagram users showed deactivations of regions in the cognitive control network”, “Although this effect appears to be age-specific [74]”, and “The finding of increased ACC activity when ‘liking’ a peers Instagram post [75]”. The reference numbers are now [74], [75], and [76], respectively.In Section 4.5, “Other research has shown that the precuneus is also engaged during decisions to repost emotionally valenced messages online ”. The reference numbers are now .In Section 4.5, “and when viewing posts with many (vs. few) likes [73]”. The reference number is now [74].In Section 4.5, “As reviewed above, only one study implicated the precuneus in problematic SNS use during exposure to Instagram photos, suggesting a role for this region in cue reactivity and the transmission of visual information to motivational systems [76]”. The reference number is now [77].In Section 4.6, “As reviewed above, the TPJ has also been implicated in regular (non-addicted) SNS reposting behaviours .” The reference numbers are now .In Section 4.7, “Nonetheless, as reviewed above, in regular users, insula activity and its connectivity with the TPJ has been associated with reposting emotionally valenced messages, ‘liking’ SNS photos and receiving valenced SNS comments ”. The reference numbers are now .The authors would like to reorder references [83–85] in the References list. The correct order should be the following:83.Dev. Cogn. Neurosci.2021, 48, 100921.Peters, S.; Van der Cruijsen, R.; van der Aar, L.; Spaans, J.; Becht, A.; Crone, E. Social media use and the not-so-imaginary audience: Behavioral and neural mechanisms underlying the influence on self-concept. 84.J. Addict. Res. Ther.2012, 6, 003.Wölfling, K.; Beutel, M.; Müller, K. Construction of a standardized clinical interview to assess internet addiction: First findings regarding the usefulness of AICA-C. 85.J. Comput.-Mediat. Commun.2007, 12, 1143–1168.Ellison, N.B.; Steinfield, C.; Lampe, C. The benefits of Facebook “friends:” Social capital and college students’ use of online social network sites. The references list and corresponding citations throughout the manuscript have been revised.The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.


The growth-optimization hypothesis suggests that diurnal and seasonal patterns of stomatal conductance are driven by a dynamic carbon-use strategy that seeks to maintain homeostasis of carbohydrate reserves.Stomata have recently been theorized to have evolved strategies that maximize turgor-driven growth over plants’ lifetimes, finding support through steady-state solutions in which gas exchange, carbohydrate storage and growth have all reached equilibrium. However, plants do not operate near steady state as plant responses and environmental forcings vary diurnally and seasonally. It remains unclear how gas exchange, carbohydrate storage and growth should be dynamically coordinated for stomata to maximize growth. We simulated the gas exchange, carbohydrate storage and growth that dynamically maximize growth diurnally and annually. Additionally, we test whether the growth-optimization hypothesis explains nocturnal stomatal opening, particularly through diel changes in temperature, carbohydrate storage and demand. Year-long dynamic simulations captured realistic diurnal and seasonal patterns in gas exchange as well as realistic seasonal patterns in carbohydrate storage and growth, improving upon unrealistic carbohydrate responses in steady-state simulations. Diurnal patterns of carbohydrate storage and growth in day-long simulations were hindered by faulty modelling assumptions of cyclic carbohydrate storage over an individual day and synchronization of the expansive and hardening phases of growth, respectively. The growth-optimization hypothesis cannot currently explain nocturnal stomatal opening unless employing corrective ‘fitness factors’ or reframing the theory in a probabilistic manner, in which stomata adopt an  Stomatal behaviour has long been interpreted as an eco-evolutionary optimization strategy that maximizes fitness. Various theories have postulated different proxies for fitness to explain stomatal conductance, traditionally expressing fitness as photosynthetic carbon assimilation with some hydraulic cost or constraint on the optimization, typically soil moisture. A recent growth-optimization hypothesis proposed carbohydrate- and turgor-limited whole-plant growth as a better proxy for fitness. We examine its predictions under dynamic conditions in which whole-plant carbohydrate storage and sink demand vary diurnally and seasonally. Our dynamic simulations suggest that stomatal behaviour is closely linked to sink demand and whole-plant carbohydrate storage, especially the latter, and seeks to balance photosynthetic carbon supply and sink demand, maintaining homeostasis of whole-plant carbohydrate storage. However, the growth-optimization hypothesis was unable to explain why stomata open at night without incorporating either empirical corrective factors or a probabilistic perspective. An; see An in relation to some metric of water stress (e.g. gw) as the conductance at which the marginal carbon profit of water  and marginal carbon cost of water (χw) are equal, unless the maximum χw exceeds the maximum λ, in which case gw = 0  are modelled  are high, leading to more conservative use  reserves (C) and turgor-driven growth (G). Though some AOHs are conceptually founded upon growth maximization, they mathematically couple growth to photosynthesis . Spending NSCs to grow at one instance depletes the NSCs required for growth at later times, potentially hampering future growth as a legacy effect. Hence, stomata should maximize growth by storing NSCs when the potential for C accumulation is high and η is low  to be used when the potential for C accumulation is low and η is high . Like the water-use strategy, the GOH suggests a carbon-use strategy, by which stomata open to slow the depletion of NSCs, especially when NSCs are valuable . NSC depletion is slowed in two ways. First, stomatal opening increases An, accumulating NSCs. Second, stomatal opening reduces plant water potentials (ψ) (χw) should decline and stomata should open under low NSCs and/or high demand (low C and/or high η in ψ and water content in NSC-depleted plants (2 concentrations (eCO2) at the beginning of the growing season when NSC demands are high  that are typically 5–40 % of daytime conductances  to predict nocturnal stomatal opening from χw,D , where χw,D was predicted by ff ≈ 0.15 at 25 °C when ignoring NSLs and HRR. Their pragmatic approach cannot explain why ff < 1 or how ff should respond to environmental conditions. Justifying nocturnal stomata opening as optimal requires a theory for why night-time carbon costs of water are less than that of daytime .Additionally, we interpret the existence and environmental responses of nocturnal stomatal movements through the GOH. Stomata typically close during the first few hours of night and then open, reaching a maximum nocturnal conductance just before dawn  with noct-time λ , predictχw and λ . Wang etχw declines from day to night. First, χw scales with extensibility  and thus should decline at night when most volumetric growth typically occurs  and the NSC storage (C) as control and state variables, respectively. This maximization is subject to the constraint that C must be balanced by its supply and demand:where aL is the leaf area, An is the leaf area-specific net assimilation, RM is the stem and root maintenance respiration, RG is the construction respiration and fc is the constant fraction of G + RG diverted to RG. Environmental conditions include the soil–water potential (ψsoil), air temperature (Ta), the air’s relative humidity (RH), irradiance on a surface normal to the solar beam (Is) and solar elevation below the zenith (Φ). The difference in the temporal bounds over which growth is maximized (t2 − t1) is the timescale of optimization. The GOH suggests that the timescale of optimization spans an individual’s lifetime. Pragmatically, we approximate an infinitely long timescale by reducing it to its smallest repeated units, solving Equation (1) over a cyclic annual period  and (2) through the calculus of variations  with gw η is the NSC-use efficiency, representing sink demand and the cost to growth of depleting NSCs (0 < η ≤ 1 − fc), and ∂G/∂E < 0, since transpiration causes ψ and turgor to decline, slowing growth. Their solution also describes how η changes in time,where η is dynamic, they presented solutions in which η was either a known, instantaneous constant or in steady state (η as described by Equation (4).For the full derivation of Equations (3) and (4), please see carbon-use strategy that opens stomata to conserve NSC is apparent from Equations (3) and (4). By Equation (4), the η∙∂RM/∂C term is responsible for elevating η over time when C is small, since η∙∂RM/∂C is always positive and greatest at low C . Meanwhile, the negative −(1 − η/(1 − fc))∙∂G/∂C term is responsible for diminishing η over time when either C is small or conditions are favourable for growth, either of which causes large ∂G/∂C . Their net effect of C on η is unclear from Equation (4) without a priori knowledge of the magnitudes of ∂RM/∂C and ∂G/∂C. Nonetheless, we later show C is small and C is large . This negative feedback suggests that the carbon-use strategy seeks to maintain homeostasis of NSCs, which is indeed supported by past studies , and G and RM are temperature dependent and NSC limited following Michaelis–Menten kinetics tions [ψ .gw, An, E, λ, η, C, ψL and G that maximize growth under cyclic environmental conditions. Parameters for new processes are shown in η and C dynamics (Equations 3 and 4) are simulated by explicit finite difference with 0.5-h time step with cyclic boundary conditions (η(t1) = η(t2), C(t1) = C(t2), We applied the GOSM and parameters of t1 = 0, t2 = 365 days), reflecting environmental conditions that vary within and among days and seasons, but not across years [t1 = 0, t2 = 24 h) and to C and η are constant within a day instead of being solved by Equations (2) and (4), and boundary conditions are not defined in steady-state simulations.We present cyclic year-long simulations over an average year . Values of 0.005 and 0.04 mol∙m−2 s−1 were chosen as end members considering that gw,N is typically 5–40 % of daytime gw  based on our year-long simulation . However, the simulated η change between day and night never exceeds 0.2 % and is negative for approximately half of the year , soil water potential (ψsoil) and atmospheric CO2 concentration (ca), keeping C constant. These environmental responses were repeated at elevated (+25 %) and depleted (−25 %) NSC storages to represent delayed responses caused by slower changes in NSC status associated with VPD, drought and eCO2  at these times. Counterintuitively, our GOSM predicts that gw is greatest during the cold, dormant periods at the beginning and end of the year, resulting from high RH, low Ta [gw under low VPD is unsurprising, considering AOHs and other empirical formulations for gw often predict similar results , where gwopt is the optimal solution, and gwmax is the maximum conductance; DL ≥ 0.05 kPa in CLM5; gw had little impact on An and G (C and η dynamics (Equations 3 and 4), since An and G were both temperature limited , 215 and 220 (at peak Ta), respectively, and then decline. During the growing season, midday gw ≈ 0.1 mol∙m−2∙s−1, comparing well to the upper bound of measurements from our site on healthy Scots pine (η (i.e. dη/dt) inversely mirror C with an ~80-day lag , displaying the carbon-use strategy. Nonetheless, η is approximately constant, suggesting that gw is controlled more by NSC dynamics (C) than by variations in sink demand (η).Midday values of η and C (η(t1) = η(t2), C(t1) = C(t2), C was nearly constant across days in the year-long simulation  exceeds the maximum possible midday sink demand (G0/(1 − fc) and Rm,0 in C disparities declined while approaching DOY 172 and 325 when year-long-simulated midday C was nearly constant across days as source- and sink demand were near equal.Day-long simulations satisfied both of our cyclic boundary conditions for An, C and G peak  are shown in gw at dawn predominantly results from low morning VPD . During the early growing season, these large morning gw also result from small χw  or unrealistically small NSCs to simulate realistic gw,N [Ta and C would negate virtually all growth at night. Simulated diel C and η changes are too small to significantly alter χw between day and night  closes stomata, while CO2 concentration has no immediate effect on gw,N . Individual plant traits may operate over different timescales, and they certainly differ in the bounds of integration (t2 − t1) that modellers use to predict them through mathematical optimization. It is common to choose longer bounds for traits that change slower  repeat . Though the timescale for stomata has been theorized as plants’ lifetime  and a full year (t2 − t1 = 365 days) and compared these dynamic simulations to C between days were small in year-long simulations and when maximum possible sink demands exceeded instantaneous carbon input (when steady-state simulations would predict finite C). On these days, year-long, day-long and diel-averaged steady-state simulations generally compared well in terms of An, though not in terms of other predicted variables [C predictions. This suggests that cyclic boundary conditions (C(t1) = C(t2)) and steady state are inappropriate to describe NSC use for an individual DOY, since real NSCs change over multiple days and are thus non-cyclic across days. The amplitude of simulated NSC cycles depends on the duration of the simulation and shrinks as t2 − t1 becomes smaller, approaching the steady-state solution as t2 − t1 approaches zero. In day-long simulations, t2 − t1 is small, and thus day-long and diel-averaged steady-state simulations approximate each other [C for the same reason that steady-state simulations do: they ignore the fact that instantaneous An during the peak growing season exceeds the average An over a year, thereby overestimating C. Sink demands during the peak growing season similarly exceed their annual averages, but to a much lesser extent, since plants respire throughout the entire year, while peak photosynthesis occurs over a smaller window . More appropriate boundary conditions for C in dynamic day-long simulations would set C(t1) to a realistic predetermined value. C(t2) would be treated implicitly . However, the appropriate value for C(t1) is unclear. It could be chosen from measurements of whole-tree NSCs, although these estimates are rare, or it could be taken as the value solved by the full year-long simulation at the specified DOY. The latter choice, however, makes the day-long simulation unnecessary since the year-long simulation makes all of the same predictions over a longer period. The dynamic version of the GOSM presented here is an approvement upon C and η evolve dynamically over hours to seasons. Hence, the dynamic GOSM better describes how stomata respond to environmental variation as modulated by the changes in NSC storage (C) and the cost of sink demand (η).Since stomatal conductance, NSCs, and growth rates follow near-cyclic trends over diel and seasonal timescales , we simuG typically occurs in the late afternoon when air is warmest and C is slightly elevated , most growth indeed occurs at night when ψ and turgor are largest. Volumetric growth  is only one aspect of growth (gw and C. Water-use efficiency (χw) and C would both be higher (resulting in lower gw) than currently predicted (G/∂E term in Equation (3) because of shorter, more-concentrated period of expansion than our current growth scheme) with little NSC deposition, since cell wall hardening would have not begun. Conversely, χw and C would both be lower (with higher gw) in the late growing season as increasingly more developing xylem cells end their expansion (∂G/∂E approaching zero) and transition into cell wall hardening, when most NSC deposition occurs.Both year-long and day-long simulations predicted that maximum diel f growth , suggestredicted  in the ewater-use strategies that moderate current transpiration to save soil–water for future uptake  cannot be explained by most AOHs  impose a constraint to gw in our GOSM. Additionally, NSCs in our GOSM are not leaf specific; all NSCs are relevant regardless of organ. In addition to the direct control of NSCs on gw, NSC demand (represented by η) modifies gw in the GOSM, which no AOH directly considers .The carbon-use strategy and the water-use strategy and identify their relative contributions to stomatal opening and closure. Because we have not constrained the objective (Equation 1) by soil–water, we limited our simulations to scenarios of constant and high soil–water availability. Nonetheless, even without the water-use strategy, the GOH would predict lower gw and G and higher C if transpiration depleted soil–water, since the GOH captures these responses under soil–water stress in steady state . In our modelling scenarios with constant and plentiful soil–water, the dry-down length is effectively zero, leading to infinite gw according to gw under constant and high soil–water content. The inclusion of hydraulic limitations also constrains gw from being excessively large in water-saving AOHs , since these variables control χw  does not. By accurate, we mean the ‘anticipated’ temperature distribution is centred on the actual temperature, and by precise, we mean the variation of the ‘anticipated’ temperature distribution is small. If ‘anticipation’ is accurate and relatively precise, Equation (5) predicts realistic ff only on cool days and nights [accurate, Equation (5) cannot predict realistic ff (~0.05 < ff < ~0.25 at 25 °C) on warm nights regardless of the precision [ff, ‘anticipation’ must be inaccurate, ‘anticipating’ night-time temperatures cooler than actuality [inaccuracy could arise from a selective ‘memory’ and from the fact that leaf temperature (TL) is not the same as temperatures in other growing tissues (approximated here by Ta). If stomata ‘anticipated’ that Ta was always some function of actual TL based on a selective ‘memory’ of only daytime experiences . Alternatively, the thermal inaccuracy might reflect a cautious strategy to safeguard against incurring penalties of cold nights that are unaccounted in the GOH framework.where d nights Fig. S11,d nights Fig. S10.recision Fig. S12.ctuality Fig. S13,plad044_suppl_Supplementary_MaterialClick here for additional data file.