This featis achieved by leveraging our recent developments in analytic spin–phononcoupling calculations in conjunction with a new method for includingthe infinite electrostatic potential in the calculations. Furthermore,we make the first ab initio determination of phononlifetimes and line widths for a molecular magnet to prove that thecommonplace Born–Markov assumption for the spin dynamics isvalid, but such “exact” phonon line widths are not essentialto obtain accurate magnetic relaxation rates. Calculations using thisapproach are facilitated by the open-source packages we have developed,enabling cost-effective and accurate spin–phonon coupling calculationson molecular solids.Molecular materialsare poised to play a significant role in thedevelopment of future optoelectronic and quantum technologies. A crucialaspect of these areas is the role of spin–phonon coupling andhow it facilitates energy transfer processes such as intersystem crossing,quantum decoherence, and magnetic relaxation. Thus, it is of significantinterest to be able to accurately calculate the molecular spin–phononcoupling and spin dynamics in the condensed phase. Here, we demonstratethe maturity of  In the best-performing SMMs, this is driven by high-energy opticphonons.16 At lower temperatures, the populations ofhigh-energy phonons are very low, and the Orbach mechanism is suppressed.In this regime, the spin dynamics are instead dominated by two-phononRaman mechanisms driven by low-energy (pseudo)acoustic phonons, showinga power law temperature dependence of τ in the range of T–1–T–7.17 Other mechanisms pertinent to thespin dynamics of SMMs, such as the direct and quantum tunneling ofmagnetization (QTM) mechanisms,11 are notdiscussed here as they are either not relevant in zero magnetic field(direct) or are only active at very low temperatures .Loss of magnetic memory in SMMs, alsoknown as magnetic reversalor magnetic relaxation, occurs through different processes dictatedby spin dynamics. Single-phonon interactions lead to magnetic relaxation iPr5)][B(C6F5)4](Cp* = pentamethyl cyclopentadienyl)18 andmore recently for the mixed-valence CpiPr5DyI3DyCpiPr5 (CpiPr5 = pentaisopropyl cyclopentadienyl),which shows strong magnetic exchange coupling mediated by the Ln–Lnhalf-σ bond.19 In both cases, a largeaxial magnetic anisotropy is imposed by the cyclopentadienyl ligands,leading to large Ueff values and slowOrbach relaxation. For [Dy(Cpttt)2][B(C6F5)4] ,15 it has been demonstrated that the comparativelyslow spin dynamics in the Raman regime for this class of materialsresults from a separation in energy between the very high-energy opticalphonons (due to the conjugated five-membered rings being the onlyligands in the first coordination sphere) and low-energy pseudoacousticphonons .20 Variationof the cyclopentadienyl substituents can have a significant effecton the spin dynamics21 since it impacts both the magnetic anisotropy and the vibrationalspectrum.22 Despite these successes, controlof the spin dynamics through chemical modification remains an openchallenge for the design of improved SMMs and indeed any molecularspin system, and given the vastness of chemical space, strategiesemploying machine learning are likely to be particularly promising.23Among the current best-performing SMMs, magnetichysteresis hasbeen observed as high as 80 K for  , and excellent SMM performance,although we note that the methodology described herein is equallyapplicable to any other molecular magnet, and numerous other suchpreliminary studies are underway in our group. We perform the first ab initio calculation of the phonon line widths for a molecularmagnet to show that: i)phonon lifetimes are orders of magnitude shorterthan the spin lifetimes in this compound, justifying the commonlyassumed Born–Markov approximation for molecular spin dynamics,31 and ii) the phonon line widths are highly energy- and wavevector-dependent,with full width at half maximum (fwhm) values varying between 0.1and 40 cm–1 at 300 K. We find that the spin dynamicsare relatively insensitive to the choice of line width model, withsimilar results obtained using a fixed line width or a thermodynamicapproximation,25 and thus our work suggeststhat the burden of performing expensive phonon line width calculationsfor other molecules may not be required for accurate spin dynamicssimulations. Furthermore, we show that the use of finite slab methodsleads to significant errors and that accurate treatment of the electrostatic(Madelung) potential of the infinite crystal lattice is essentialto achieve quantitative accuracy. Our open-source tools implementa computationally inexpensive and accurate method to calculate theinfinite crystalline electrostatic potential, including its effecton the spin–phonon coupling terms, which vastly improves theagreement with the experiment. This work thus paves the way for accurateand efficient spin–phonon calculations on solid-state molecularsystems with applicability beyond molecular magnetism.To this end, a number of research groupshave recently startedto develop n)Br] 1, 1,32 chos1 in the gasphase or an infinite perfectly periodic crystal of 1);(2) calculation of the vibrations (gas phase) or phonons ; (3) calculation of the electronic structure of a single moleculeof 1 ; (4) calculationof the spin–phonon coupling between the vibrational/phononmodes and the electronic states in 1 ; and (5) calculation of the magnetic relaxation rates.Abrief overview of the entire method is as follows: (1) geometryoptimization is based on a single configuration wave function and therefore struggleswith the multiconfigurational ground state arising from near-degenerate4f electronic configurations. To avoid this, we substituted Dy(III)for the chemically and structurally analogous Y(III), which has no4f electrons, and used the Stuttgart RSC 1997 effective core potential(ECP) and associated valence basis set for Y and the cc-pVDZ basissets for all other atoms.36 We found aroot-mean-square deviation (RMSD) for all the atomic positions comparedto the experimental crystal structure of 0.13 Å. We then calculatedthe vibrational modes of the gas-phase molecule of 1 usinganalytic methods in Gaussian09d, where the isotopic mass of Y wasset as the isotopic mass of Dy.Geometry optimization of a single neutral molecule of 1 was performed using the primitivecell, with starting atomic positionsand unit cell parameters obtained from the Cambridge Structural Database(CCDC: 1416543), using periodic density functional theory (DFT) asimplemented in VASP 5.4.4.40 The PBE functional34 withthe D3 semiempirical dispersion correction35 was employed to model the electron exchange and correlation. Toavoid the multiconfigurational ground state of Dy(III) in this case,we used a 4f-in-core ECP for Dy(III); we have previously verifiedthat both Y(III) substitution and a 4f-in-core ECP give the same results.All ion cores were modeled with projector augmented wave (PAW) pseudopotentials,42 and the valence electronic structure was modeled using a plane-wavebasis set with an energy cutoff of 800 eV and Γ-point Brillouinzone sampling, with both parameters determined via explicit convergence testing. Starting from the 128-atom primitivecell of the published X-ray structure of 1, the atomicpositions and unit cell parameters were optimized to tight tolerancesof 10–8 eV on the electronic total energy and 10–2 eV Å–1 on the forces. Phononcalculations were then performed with the optimized crystal structureof 1 using the finite-difference method implemented inPhonopy43 and Phono3py.44 In this approach, the Phonopy code is used to generatea series of distorted structures  and the forces on the atoms in each distorted structureare calculated using VASP, where the outputs are combined with Phonopyagain to obtain the Hessian matrix of second derivatives of the energywith respect to coordinates. The Hessian is then “mass-weighted”using the atomic masses to give the dynamical matrix, which is diagonalizedto give the normal modes of vibration and squared frequencies. Theprocess is slightly more involved than this, as the calculations areperiodic, and we refer the interested reader to our recent TutorialReview, which covers this in detail.45 ThePhono3py code is similarly used to generate a sequence of distortedstructures in which pairs of atoms are displaced to obtain the third-orderforce constants, which are combined with the harmonic frequenciesand eigenvectors to determine the phonon lifetimes and line widths.A 2 × 2 × 1 supercell with 512 atoms was employed to determinethe second-order force constants in Phonopy,43 while the third-order force constants were determined for the primitivecell  using Phono3py,44 and the phonon frequencies and line widths wereevaluated on uniform 2 × 2 × 2, 3 × 3 × 3, 4 ×4 × 4, and 5 × 5 × 5 q-point gridsusing Fourier interpolation with Phono3py.Geometry optimization of thecrystalline phase of 22 to take into account thephonon modes in the crystalline phase. We first take each unique moleculein the optimized unit cell (expanded to contain complete molecules)and perform a gas-phase DFT calculation using Gaussian 09d33 with the PBE functional34 to determine the atomic charges required to reproduce the externalmolecular electrostatic potential using the CHELPG method.46 To avoid the multiconfigurational ground stateinherent to Dy(III) in these molecular DFT calculations, we substitutedDy(III) for the chemically and structurally analogous Y(III) and usethe Stuttgart RSC 1997 effective core potential (ECP) and associatedvalence basis set for Y,49 along with the cc-pVDZ basissets for all other atoms.36We have adapted ourestablished protocol for modeling molecularspin dynamics50 Thereis no problem using this method for our single-molecule gas-phasestructural and vibrational model for 1. However, foradapting our method to the crystalline phase, we note that the CASSCFis not compatible with periodic wave functions, and hence, we mustbridge the gap between the phonons described in the infinite periodiccrystal and the electronic structure described with a finite model.The simplest approach is a finite slab of unit cells cropped fromthe infinite periodic crystal (approach 1), but we find that thishas its shortcomings, and hence, we have implemented a more accuratemethod accounting for the infinite crystalline electrostatic potential(approach 2); both methods are implemented in our spin_phonon_suite code (version 1.4.1).51To calculatethe spin–phonon coupling, we must considerhow the vibrational/phononic  degrees of freedominfluence the electronic structure of the Dy(III)-based SMM. Determinationof the electronic structure of a molecule with a multiconfigurationalground state requires explicitly correlated electronic structure methods.Our method of choice is complete active space self-consistent field(CASSCF) theory, which is efficient and accurate for describing themagnetic properties of Ln(III) SMMs.q on a Γ-centered q-point sampling grid with q1 × q2 × q3 subdivisionsis commensurate with a q1 × q2 × q3 finiteslab cell expansion in the real space . For a given q-pointgrid, we build the required q1 × q2 × q3 finiteslab, redefined by translation to position a single molecule of 1 in the center. The electrostatic potential of the finiteslab is accounted for by assigning the remaining atoms  their CHELPG charges determined as outlinedabove.The set of phononwavevectors Figure S1), with the unit cell redefinedby translation to position a single molecule of 1 inthe center of the spherical array. All remaining atoms in the sphericalarray are assigned their CHELPG charges (outlined above), and theentire array is embedded in a perfect conductor reaction field cavitywith a radius of 40 Å using the Kirkwood solvent model with ε= ∞.52 The displacement vectorsfor phonons corresponding to arbitrary q1 × q2 × q3 grids can then be mapped onto the spherical array as required.In this method, we builda finite array of unit cells with an approximately spherical shapeof approximately ∼40 Å radius, chosen by convergence testing for a 9-in-7 active space (4f9 configuration) using the second-order Douglas–Kroll–Hessrelativistic decoupling,54 the Cholesky“atomic compact” resolution of the identity method forapproximating the two-electron integrals,55 and ANO-RCC basis sets for all atoms .57 These 18 spin-free states are then mixed with SO coupling, and thelowest 16 resulting states (the 6H15/2 multiplet)are projected onto a crystal field (CF) Hamiltonian acting in the(2J + 1)-dimensional |mJ⟩ basis, using our angmom_suite code(version 1.17.1).58 The spin–phononcoupling parameters foreach phonon mode, defined by band index j and wavevector q, are the derivatives of the CF parameters along the phononnormal mode vectors.59 To compute these, we first obtain the derivativesof the CF parameters with respect to Cartesian atomic coordinatesusing an analytic linear vibronic coupling (LVC) model60 and then convert to the normal mode basis usingthe linear combination of atomic displacements specified by the modedisplacement vector.45 This is done forall vibrational modes of the gas-phase model and all phonon modesat all q-points in the sampling mesh for the crystalline-phasemodel.In both approaches and for our gas-phase calculations, the electronicstructure of the central molecule is obtained with a state-averageCASSCF spin–orbit (SA-CASSCF-SO) calculation in OpenMolcas23.02 .Tau code (commit e058b24959),61 considering Orbach and Raman rates,62 given by eqs 40, 41, and 46–49 in reference.45 There are two forms of the Raman mechanism,which arise from their derivation using different orders of perturbationtheory:62 the Raman-Imechanism  does not depend on the magnitude of an external magneticfield,63 while the Raman-II mechanism  has a quadraticdependence on the field and vanishes in zero field.20 Since our experiments are performed in zero field, we donot consider the Raman-II mechanism, and we therefore refer to theRaman-I mechanism simply as “the Raman mechanism” throughout.In the context of magnetic relaxation in SMMs, the two-phonon Ramanmechanism concerns coupling between the two states of the ground Kramersdoublet, and our calculations are thus restricted to this pair ofstates. Derivation of the Raman rate expressions adopts the secularapproximation, which assumes that no degeneracies exist in the electroniceigenstates,45 and thus, we must introduce an energy gap between the two statesof the ground Kramers doublet. Indeed, this occurs in experimentsdue to the presence of a dipolar magnetic field and/or the drivingAC magnetic field, and we therefore apply a magnetic field of 2 Oealong the main magnetic axis of the molecule, splitting the grounddoublet by ca. 0.002 cm–1. The Raman mechanism involvespairs of phonons, and the rate is obtained as the double integralover their lineshapes.60 We restrict the domain of the phonon energies to 0 ≤ ω≲ ωcut, where ωcut = 267cm–1 is chosen as the minimum in the phonon densityof states (DoS) above the low-energy pseudoacoustic peak  molecule with a pentagonal bipyramidalcoordination geometry. The molecule crystallizes in the orthorhombicspace group C2221 with half a moleculein the asymmetric unit and two complete molecules in the conventionalunit cell , andwe find an RMSD for all atomic positions of only 0.10 Å. Thisindicates that our chosen methodology is a good approximation to themolecular forces. We then obtain the second derivatives of the energy(first derivative of the forces) with respect to the atomic positionsusing numerical finite differences and construct the dynamical matrixto determine the normal modes of vibration by matrix diagonalization varyas a function of energy and wavevector and are intrinsically temperature-dependentthrough the populations of the modes involved in the scattering processes.44 We have previously treated phonon line widthsas an empirical parameter,22 while Lunghiet al. proposed a simplified model for an effective phonon line widthbased on the NVT canonical ensemble force constants with a similar numerical finite-difference method. Thereis also a marked temperature dependence , arising from larger scattering probabilities asthe phonons are more heavily populated at elevated temperature,44 which above 30 K is well approximated as Γ∝ T, in agreement with the high-temperaturelimit of 25 However, the line widths predicted by ab initio calculated values, especially at lowand high phonon energies (ab initio phonon line widthsfor 1 at 300 K are on the order of 0.1–40 cm–1 (corresponding to lifetimes on the order of 100–0.1ps), and some modes become much longer lived at low temperatures withlifetimes of up to 4.5 ns (line widths of 0.001 cm–1) at 10 K. However, even the longest of these ab initio lifetimes is still orders of magnitude shorter than the experimentalspin lifetimes for this compound, which are seconds to hundreds ofmicroseconds, justifying the commonly assumed Born–Markov approximationfor molecular spin dynamics.31 To the best of ourknowledge, the present study represents one of very few explicit calculationsof the phonon line widths and lifetimes for a molecular crystal andthe only such calculation for a molecular magnet.The low-energy phonon dispersion 2a compri–1 2b, whilear modes 2c. Phonoensemble 1251To obsee the  and modee energy 3a, but we energy S2. Thereq-point grid and applying Gaussian orLorentzian smoothing functions with an arbitrary line width . Given the similar profiles of the line widthsobtained with different grids , the difference in the DoS obtained with the different q-point sampling in –1 gives a smooth DoS evenwith a comparatively sparse 2 × 2 × 2 q-point grid .A central quantity of interest for molecular spindynamics is thephonon DoS. The DoS is often obtained evaluating phonon frequencieson a chosen th e.g., 2b. Here,th e.g., 3b.The rsion cf. 2b. We alsion cf. S5. Givenab initio phonon linewidths on the spin dynamics, we proceeded to calculate the spin–phononcoupling and magnetic relaxation rates . As we have shown previously,the absolute rates show a significant dependence on the choice ofline width,65 with broader line widths leading to faster relaxation rates. Thisbehavior occurs for single-phonon processes because there is onlyone possible phonon energy ℏω = |Ef – Ei| that can cause aspin transition between any pair of states i and f , and alarger line width gives a larger probability of overlap between |Ef – Ei| andthe calculated vibrational energies. We find that the best agreementis obtained with Γ = 1 cm–1 , which is consistent with the approximate centerof the distribution of ab initio phonon line widthsat 50 K . We note that we checked larger slabsup to a 9 × 9 × 9 expansion and still did not observe convergence. The electrostatic potentialcan be converged very quickly in reciprocal space using Ewald summation,67 but this method is not available in OpenMolcas.53 Luckily, there are two methods that can be employedto address this issue: the first uses an extra set of charges externalto the crystalline slab as fitting parameters to replicate the exactinfinite crystalline potential69 and the second placesan approximately spherical array of unit cells in a perfect conductorto screen the charges directly,70 thusapproximating the infinite crystalline potential very closely. Thefirst method is not compatible with our analytic “one-shot”LVC method for obtaining the spin–phonon coupling coefficients,60 and we have therefore used the conductor screeningmethod, which allows us to obtain spin–phonon coupling coefficientscorrected for the infinite crystalline electrostatic potential (seethe Two-phonon Raman rates can only be reliably obtained by consideringthe (pseudo)acoustic phonons in the solid-state, so this calculationcannot be performed using the gas-phase vibrational spectrum. We thereforealso calculated the spin–phonon coupling and magnetic relaxationrates using the solid-state phonon modes and finite slab expansionscommensurate with the  crystal 4 and als seethe .Figure S9). Using even and odd slab expansions yields fasterand slower rates, respectively, which is consistent with smaller (larger)CF splitting for the former (latter). While the nonconvergence ofthe infinite electrostatic potential is indeed well known,66 we were surprised to see the large impact thata small electric potential developed over a finite slab can have onthe spin dynamics of molecular crystals, affecting the magnetic relaxationrates by an order of magnitude. Indeed, it is not the spin–phononcoupling itself that is affected by this approximation,60 but rather the static electronic structure ofthe molecule, and this directly leads to the observed effect. We thereforeadopt a method that allows us to include the infinite crystallineelectrostatic potential  and two-phonon (Raman) ratesusing fixed phonon line widths for four finite slab expansions , and as for the gas-phase calculation, the rates are positivelycorrelated with the choice of the line width. However, the dependenceon line width is far less significant than in the gas phase and decreaseswhen using larger q-point grids: the rates obtainedwith Γ = 0.1 and 10 cm–1 differ by a factorof ∼19 at 60 K in the gas-phase calculations, reducing to factorsof ∼8 and ∼2 for solid-state calculations with 2 ×2 × 2 and 5 × 5 × 5 grids, respectively. We next calculatedthe two-phonon Raman rates with fixed line widths, which are in excellentagreement with the experimental rates . We note that the choice of line width has a larger effectin this region than in the single-phonon Orbach region and that, counterintuitively,the two-phonon Raman rates have a negative correlation with line width,i.e., the rates become slower with larger line widths, which is theopposite behavior to the single-phonon rates. This can be explainedby the fact that for the Raman mechanism, only the difference in thephonon energy ℏω–ℏω′ mustmatch the difference in electronic energy Ef – Ei, which allows many pairsof phonons to cause a transition between the ground doublet states.45 When the line widths are larger, the phononlineshapes extend to higher energies, resulting in smaller Bose–Einsteinoccupation factors and hence a reduction in the magnitude of thesecontributions.With this improved approach, calculationof the single-phonon ratesin the Orbach regime with fixed phonon line widths shows excellentagreement with the experimental rates . We also notethat the increased sensitivity of the magnetic relaxation rates inthe Raman region to the choice of phonon line width compared to theOrbach region could provide an explanation for the increase in thedistribution of magnetic relaxation rates for this compound as thetemperature is decreased, i.e., the presence of crystalline disorder,shown to correlate with the width of the distributions of magneticrelaxation rates,71 has more of an effecton the Raman rates, which tend to dominate as the temperature is reduced.As for the single-phonon Orbach rates, we observethat the dependenceon the fixed line width becomes smaller with improved reciprocal-spaceintegration . In the Raman region, the rates obtainedwith mode- and temperature-dependent line widths are close to thoseobtained with fixed Γ = 10 cm–1 at 60 K butincreasingly approach the smaller fixed line width calculations atlower temperature, crossing the Γ = 0.1 cm–1 rates between 20 and 10 K . As the Raman rates are more strongly affected by the choice ofline width than the Orbach rates, it is unsurprising that the extremenarrowing of some of the ab initio phonon line widthsat low temperatures has a marked impact on the relaxation rates. However,we note that the profile of the relaxation rates calculated using ab initio mode- and temperature-dependent line widths doesnot agree with the experimental data at the lowest temperatures andin particular level off at low temperature, while the experimentalrates continue to decrease. We therefore suggest that the extremenarrowing of the ab initio line widths at low temperaturesis overestimated and that there are likely other sources of phononscattering  in real crystals that would lead to shorter phonon lifetimes,and therefore broader line widths, at lower temperature than thoseestimated by our DFT calculations on a perfect infinite crystal.We now examine the impact of using the –1, Γ = 417 cm–1 at 300 K from –1 as calculated ab initio, Figures S3 and S4) such that the numerical integrationover the phonon lineshapes when computing the Raman mechanism becomesproblematic, and we therefore only report these results for T ≤ 46 K. We have also previously shown that theNVT line widths of the high-energy phonons drastically narrow at lowtemperature, resulting in unphysical Orbach rates,22 which again we find here when using anti-Lorentzian lineshapes.Nevertheless, we find that in both the Orbach and Raman regions, theNVT expression gives rates that are close to those obtained usinga fixed Γ = 10 cm–1  and in fact gives rates nearly identical to thoseobtained by fixing the line widths to their ab initio calculated values at 300 K, which themselves agree well with therates obtained using the mode- and temperature-dependent line widthsabove ca. 30 K . Overall,however, excellent agreement with the experimental rates can be obtainedusing a simple fixed line width of Γ = 0.1 cm–1 .Finally, we compare our results to the effective NVT phonon linewidth proposed by Lunghi et al. 1. During0.1 cm–1 5, but,t16 it is not very well understood which phonon modes drive magneticrelaxation in the Raman regime—this is due to both the inabilityof experiments to probe these two-phonon interactions directly andalso the convoluted nature of the two-phonon process itself.45 Given the excellent reproduction of the experimentaldata using our ab initio methodology, we are in theunique position to reliably decompose our calculations and learn whichphonon modes are important for the Raman mechanism in compound 1. As the Raman rates are calculated as sums over pairs ofmodes involved in the scattering process (eqs 46–49 in reference45), we can examine the contribution that everypair makes to the total rate; here, we do so using the modes obtainedwith the 2 × 2 × 2 q-point grid with fixedΓ = 1 cm–1 for simplicity.While it is well known that high-energy localizedmolecular vibrationsdrive magnetic relaxation in the Orbach regime,Table S2): between ℏω= 19.07 cm–1 at q = Y  and one of the doubly degeneratemodes with ℏω = 19.98 cm–1 at q = T , and between one of the doubly degenerate modes with ℏω = 27.41 cm–1 at q =  and ℏω = 27.66 cm–1 at q = Y . These are all off-Γ acoustic modesthat mix substantially with the low-energy pseudoacoustic spectrum(Table S3),significant contributions arise from scattering between higher energymodes. One pair has ℏω = 154.68 cm–1 , corresponding to an asymmetricNpy–Dy–Npy stretch) and ℏω= 154.74 cm–1 .A second pair has ℏω = 113.65 cm–1 , a twisting of the phenoxide and pyridinerings around their tethers) and ℏω = 114.47 cm–1 , whichis a pinching of the pyridyl N and phenoxide O atoms parallel to theDy–Br axis).At 10 K,Raman relaxation is dominated by scattering between fourmodes (spectrum2a. At hi–1) from our Raman relaxation rate calculations leads to a barely perceptiblechange in the total rate of only <11% (Table S4). Removing all modes listed in Table S3 and their symmetry equivalents leads to a slightly moresubstantial reduction of 27% at 40 K, but it is not until we additionallyremove the pseudoacoustic modes between 25 and 60 cm–1 that contribute to the first peak in the phonon DoS (Table S4). The pseudoacoustic modes involve molecularrotations and twists, some of which are accompanied by wagging ofthe Dy–Br bond, which also occurs at low energies given thelarge mass of Br. The terminal bromide ligand can therefore be associatedwith increasing Raman relaxation rates in 1, along withthe flexible backbone of the bbpen ligand, as described above.While acoustic modes are fundamental phenomenain the structuraldynamics of solids and cannot be engineered to “turn off”,the Raman relaxation enabled by the higher energy optical modes canin theory be tuned with chemistry. However, we find that artificiallyexcluding these six higher energy modes and their symmetry equivalents “have a small amount of low-energy vibrationsin both the lattice and the molecular unit” and (ii) “userigid ligands able to decouple intramolecular motions from low-energyacoustic vibrations”;31 our updatedguidance gives some further context on how this can be achieved, byavoiding single-donor atom ligands and terminal halides.These findings again advocate for rigid, multihapto ligands thatavoid single-donor atom coordination groups in order to suppress theRaman relaxation mechanism.ab initio calculation of the phononlifetimes and line widths and demonstrated that (i) the Born–Markovapproximation is justified for Dy(III) single-molecule magnets, and(ii) that the choice of the phonon line width model is not crucialto describe molecular spin dynamics, given an adequate integrationof reciprocal space. Hence, the large computational burden of obtaining ab initio line widths is not justified for this application,and either the NVT approximation or a simple fixed line width on theorder of Γ = 0.1–10 cm–1 is the mosttransferrable and economic method for molecular spin dynamics calculations.Indeed, we are currently exploring the present method applied to othermolecular magnets, including those based on different metal ions,and find excellent agreement with experiment. The open-source toolswe have developed and used herein thus open the door to quantitativelyaccurate and efficient spin–phonon calculations on molecularsolids.In this work, we have presented our maturemethodology for thecalculation of molecular spin–phonon coupling in the solidstate. Using a case study of a Dy(III) single-molecule magnet, wehave shown that significant errors arise when employing finite crystallineslabs but that these can be corrected by employing a perfect conductorscreening model, which is compatible with our accurate and efficientcalculation of spin–phonon coupling constants. We have alsoperformed an


Oncorhynchus tshawytscha). As part of a larger stress response study, juvenile Chinook salmon  were exposed to stress-inducing treatments and sampled for blood. Laboratory reference glucose concentrations  were positively correlated with the Accu-Check Aviva meter  measurements (2R = 0.79), although glucose values were 1.21 ± 0.21 (mean ± SD) times higher in the laboratory than with the portable meter. Lactate concentrations  of the laboratory reference were also positively correlated (2R = 0.76) with the Lactate Plus meter  and were 2.55 ± 0.50 times higher than portable meter. Our results indicate both meters could be used to measure relative glucose and lactate concentrations in Chinook salmon and provide fisheries professionals with a valuable tool, particularly in remote field settings.Blood plasma analyses can provide researchers, aquaculture facilities and fisheries managers with valuable insights into the physiological state and welfare of fish. For example, glucose and lactate are part of the secondary stress response system, and elevated concentrations are indicators of stress. However, analysing blood plasma in the field can be logistically difficult and typically involves sample storage and transport to quantify concentrations in a laboratory setting. Portable glucose and lactate meters offer an alternative to laboratory assays and have shown to be relatively accurate in fish, but these tools have only been validated for a few fish species. The objective of this study was to investigate if portable meters could be reliably used in Chinook salmon ( The authors determined the meters underestimated both glucose and lactate levels compared with a laboratory reference but could still be used reliably for relative concentrations. Similar studies evaluating rainbow trout (Oncorhynchus mykiss) and Atlantic cod (Gadus morhua) showed comparable findings, with meters underestimating concentrations compared with laboratory methods (Oncorhynchus tshawytscha) has not been conducted.Glucose and lactate are secondary stress response metabolites that can also be effective at measuring stress levels in fishes  and examine any possible relationships. If proven reliable, the meters could provide an additional tool for fisheries researchers and managers. The meters used herein are commercially available and were appropriate for this study based on availability (i.e. in stock), portability (light weight) and cost. Other similar meters have also been used in recent studies . Adding studies . The usen = 70) approximately age-1  were provided by the Oregon State University Wild Fish Surrogate Program. These 70 individuals were a subset of fish that were exposed to dam passage simulations and sampled for a larger fish passage stress response study  Institutional Animal Care and Use Committee (protocol no. 2020–06). Juvenile Chinook salmon  within a 24-h post-treatment period. To sample fish, individuals were placed into 5 l of water dosed with a lethal concentration of anesthesia (250 mg/l MS-222) for 30 s (i.e. until sedation). Once immobilized, a minimum of 0.4 ml of whole blood was removed from the fish via caudal venipuncture using 21-gauge needles  pre-rinsed with a heparin sodium solution (1000 units heparin to 1 ml water) to prevent blood clotting . A smallGlucose  was measured using the Accu-Check Aviva meter . The meter had a test range of 20–600 mg/dl, and the associated test strips contained the enzyme glucose dehydrogenase, which converts glucose in the blood to gluconolactone, and measured glucose as a plasma value. Lactate  was measured using the Lactate Plus Meter . The range of detection was 0.3–25.0 mM, and the meter measured blood samples using a lactate oxidase biosensor that determines lactate concentration as a plasma value. Both meters were calibrated daily using the protocols provided by the manufacturers before analysing fish blood.o-toluidine method and measures absorbance at 630 nm to estimate glucose concentration of the sample. Optical density (OD) of the sample was subtracted from the OD of the blank (water) standard and divided by the slope of the standard curve line to calculate concentration of each sample. Laboratory lactate analyses were conducted using the EnzyChrom L-Lactate Assay Kit . The light intensity of the sample was measured at 565 nm and is directly proportionate to lactate concentration. Because samples potentially contained endogenous enzyme activity, two reactions were conducted: one with an enzyme and one without (control). Following the lactate kit protocol, all samples were diluted (6-fold) and concentrations were calculated as the difference between OD of the reaction with the enzyme and the reaction without and divided by the slope of the standard curve. Because the samples were diluted 6-fold, final lactate concentrations were determined by back calculation of multiplying by 6-fold. All samples and standards were run in duplicate using the BioTek model EON photospectrometer .Laboratory glucose analyses were conducted using the QuantiChrom Glucose Assay Kit . The kit uses the CV) between replicate samples were calculated in the software program Gen5  using the following equation:Glucose and lactate reference intra-assay coefficients of variation , samples with at least 75% (3 of 4) showing ≤5% CV were used for analyses. In addition, only sample glucose and lactate reference concentrations that fell within their respective standard curve range were included in the analyses. Subsequently, mean values of sample and standard assay replicates were used when CV guidelines were met.Laboratory reference sample and standard replicate 2R). In addition, absolute differences between laboratory and meter concentrations were plotted against the mean of the two corresponding measurements to examine the heteroscedasticity and associated Pearson correlation coefficient, R  laboratory glucose replicates had <5% CV (1.5 ± 1.2 [mean ± SD]) and were used in the analyses. The standard curves of the laboratory glucose assays showed a high goodness-of-fit (2R = 0.99 ± 0.001). A simple linear regression analysis showed a positive correlation with an 2R = 0.79 and P < 0.001 . A simple linear regression analysis showed a positive correlation between the laboratory reference and portable meters with an 2R = 0.76 and P < 0.001  and accuracy but involved different species such as Atlantic cod, Nile tilapia (Oreochromis niloticus) and bonefish (Albula vulpes), while testing different meter brands than the ones used for this study (Sander vitreus) and measured an 2R = 0.71, leaving potential use of meters based on 2R values open to interpretation.Measured 2R = 0.72 (presented as Pearson correlation R = 0.85), whereas the reference lactate concentrations were nearly three times that of the meter, with an 2R = 0.69 (presented as Pearson correlation R = 0.83). Interestingly, the One of the few studies that evaluated glucose and lactate meters  in a salmonid species compared glucose and lactate meters with reference laboratory assays in rainbow trout . Wells a2R = 0.99) to whole-blood lactate (mM) and measured significantly higher than blood. Interestingly, whole-blood lactate (mM) was 8% lower than plasma lactate (mM) at ≤4 mM and 17.5% lower from 4 to 10 mM, a pattern also observed in our research (Multiple factors could contribute to the lack of accuracy of our study meters. First, both meters are designed to convert whole-blood sample concentrations to plasma concentrations using equations derived for humans. These correction factors are based on human blood and may not readily translate to Chinook salmon blood, potentially due to differences in temperature (Both meters can be used as field tools for measuring fish stress but are not limited to that alone. For example, glucose meters could be used to evaluate the smoltification process of juvenile salmonids and their readiness to migrate because blood glucose increases as fish transition from parr to smolt (Ultimately, the use of these tools depends on specific research needs. As technology advances and biologists gain more understanding of fish physiology, new tools may arise that can be used across whole taxonomic groups, and for now, devices like the meters tested in this study should be validated on a species-by-species basis to best understand the potential differences in meter readings for a given species . The aut


A critical step in how malaria parasites invade red blood cells (RBCs) is the wrapping of the membrane around the egg-shaped merozoites. Recent experiments have revealed that RBCs can be protected from malaria invasion by high membrane tension. While cellular and biochemical aspects of parasite actomyosin motor forces during the malaria invasion have been well studied, the important role of the biophysical forces induced by the RBC membrane-cytoskeleton composite has not yet been fully understood. In this study, we use a theoretical model for lipid bilayer mechanics, cytoskeleton deformation, and membrane-merozoite interactions to systematically investigate the influence of effective RBC membrane tension, which includes contributions from the lipid bilayer tension, spontaneous tension, interfacial tension, and the resistance of cytoskeleton against shear deformation on the progression of membrane wrapping during the process of malaria invasion. Our model reveals that this effective membrane tension creates a wrapping energy barrier for a complete merozoite entry. We calculate the tension threshold required to impede the malaria invasion. We find that the tension threshold is a nonmonotonic function of spontaneous tension and undergoes a sharp transition from large to small values as the magnitude of interfacial tension increases. We also predict that the physical properties of the RBC cytoskeleton layer—particularly the resting length of the cytoskeleton—play key roles in specifying the degree of the membrane wrapping. We also found that the shear energy of cytoskeleton deformation diverges at the full wrapping state, suggesting the local disassembly of the cytoskeleton is required to complete the merozoite entry. Additionally, using our theoretical framework, we predict the landscape of myosin-mediated forces and the physical properties of the RBC membrane in regulating successful malaria invasion. Our findings on the crucial role of RBC membrane tension in inhibiting malaria invasion can have implications for developing novel antimalarial therapeutic or vaccine-based strategies. RBC membrane tension plays an important role in regulating RBC shape and functionality. In particular, recent experimental studies have shown that elevated RBC membrane tension protects against severe malaria infection. In this study, we sought to identify how different contributions to the effective membrane tension can contribute to this mechanically driven protection against malaria invasion. Using a mathematical model, we derived a relationship between the effective tension of the RBC membrane—comprising a lipid bilayer and a cytoskeleton layer– and the degree of membrane wrapping during malaria invasion. Our model shows that the shear resistance of the RBC cytoskeleton plays an important role in inhibiting malaria invasion. Our findings can be generalized to the role of cell membrane mechanics in many wrapping phenomena providing insight into the crucial contributions of the host-cell membrane in protection against severe infections. Plasmodium family, are small egg-shaped parasites with a diameter of 1–2 µm and are key to infecting red blood cells (RBCs) in the progression of malaria , 7978, 7We model the contact energy between the merozoite surface and erythrocyte membrane with a contact potential, assuming that adhesive strength is homogeneous on the surface of the parasite , 59, 87.We assume that the movement of anchored myosin motors on the polymerized actin filaments inside the parasite pushes the RBC adhered area rearwards and propels the merozoite forward into the target cell  14]. We. We14]. For ease of computation, we assume that a flat circular patch of a lipid bilayer and relaxed cytoskeleton deformed to fit the merozoite contour in the adhesive region  66, 68], 6866, 6E) is a sum of three terms: the energy associated with the bilayer-merozoite interactions (Eb), the work done by the parasite actomyosin forces (Ef), and the energy associated with the cytoskeleton deformation (Ec)The total energy of the system  can be written as . The total energy of the skeleton can be obtained by the integral of the energy density over the adhered area to the parasite given byFor a 2-D triangle spectrin filament network with two different orientations, the spectrin persistence length itten as  70, 92], 92p, thθ is the wrapping angle and H0 is the parasite-induced spontaneous curvature on the bilayer surface.Thus, the total energy of the membrane-cytoskeleton composite is given by the sum of Eqs X2 + Y2 + Z2) = RaX3 + (Ra − Rb)X(Y2 + Z2), with Ra = 1 μm, Rb = 0.7 μm [θ* for any given set of membrane properties. This approach has the advantage of focusing on extent of wrapping without extensive computational overhead. Biologically relevant values for the parameters that have been used in the mathematical model are listed in A key challenge in membrane biomechanics problems is energy minimization associated with mechanical equilibrium. Traditionally, we minimize the membrane energy using the principle of virtual work to obtain the shape of the membrane in response to induced curvatures and external forces , 93–98. = 0.7 μm , we fix θ) for a fixed σbilayer = 0.5 pN/nm and three different magnitudes of adhesion strength (θ) for two different magnitudes of bilayer tension and adhesion strengths  and no interfacial force (γ = 0). We find that depending on the magnitude of adhesion strength, there are three states which minimize the change in the energy; (i) a non-wrapped state (θ* = 0), (ii) a partially wrapped state with a small wrapping fraction (0 < θ* < π/4), and (iii) a completely wrapped state (θ* > π/2) (θ → π (1) and the energy associated with the cytoskeleton resistance diverges for large deformations (Eq S17). Thus, we conclude that the complete merozoite entry into the RBCs requires a local disassembly of the cytoskeleton.Motivated by a recent experimental observation that high RBC membrane tension can inhibit malaria invasion , we askestrength . To answstrength  as a funtrengths . Here, w* > π/2) . As can ) (θ → π . This isσbilayer) and adhesion strength (ω). The orange region denotes a non-wrapped state, the yellow region represents a partially wrapped state, and the blue region indicates a state where a merozoite is completely wrapped by the RBC membrane (σbilayer < ω − 2κ/a2 (shown as a dotted line in a is the radius of the sphere with the same surface area as the egg-shaped parasite (Eq S21) [In membrane . We markmembrane . In the (Eq S21) . As expeσthld . However, our results show that the resistance of the cytoskeleton against deformation shifts the tension threshold to significantly lower values , resting length of the spectrin (L0), maximum length of spectrin (Lmax), and persistence length of spectrin (p), with a fixed adhesion strength, ω = 2.5 pN/nm , the height of the energy barrier becomes 3 times larger, reaching Ebarrier ∼ 3 × 104kBT, as the bilayer tension increases from σbilayer = 0 to σbilayer = 1 pN/nm.To investigate the contribution of the induced tension by the lipid bilayer and the cytoskeleton layer on the energy barrier associated with the complete merozite wrapping, we plotted the change in the energy of the system and the height of the energy barrier for different bilayer tension  can create a large energy barrier for wrapping the merozoite. Particularly, an increase in the resting length of the spectrin can raise the energy barrier to > 105kBT . The resistance to the shear deformation is represented by the shear modulus .5 pN/μm –119. How.5 pN/μm , 70. ForH0 = 0, γ = 0, ω = 2.5 pN/nm, and plotted the wrapping phase diagrams for the egg-shaped merozoite for a range of bilayer tension and natural length of spectrin (L0), the maximum length of spectrin (Lmax), and persistence length of spectrin (p) (μ in Eq. 19 in [σshear). The value of the shear tension is given at the top of each panel in L0 = 25 nm to L0 = 85 nm  . We defiq. 19 in ) as a sh = 85 nm . This isormation . In contormation . This deormation . It shouormation . From thσbilayer < ω − 2κ(1/a − H0)2 (below dotted line in H0 < 1/a), the induced spontaneous tension facilitates merozoite wrapping. However, a large spontaneous curvature (H0 > 1/a) increases the membrane resistance to invasion. To investigate the engulfment of an egg-shaped merozoite by the RBC membrane, we set the physical properties of the membrane cytoskeleton as p = 25 nm, L0 = 35 nm, Lmax = 200 nm) and plotted the wrapping phase diagram for a range of bilayer tension (σbilayer) and induced spontaneous tension (κ is fixed and H0 varies) at a fixed adhesion strength, ω = 2.5 pN/nm (It has been suggested that any asymmetry between the leaflets of the lipid bilayer or surrounding environment can induce a relatively large spontaneous tension in order of 1 pN/nm . We next.5 pN/nm .σspon < 0.5 pN/nm (arrow in θ*) as a function of spontaneous tension at σbilayer = 0.5 pN/nm  is required to impede malaria invasion  Interfacial forces create a large energy barrier (“nucleation barrier”) such that the particle does not attach to the membrane (θ* < 0) [ii) Interfacial forces create an energy barrier that impedes the full envelopment of a partially wrapped particle by the membrane (θ* < π/2) (Eq S23a). (iii) Interfacial forces facilitate the encapsulation process when the membrane wrapping passes the equator of the sphere (θ* > π/2) (Eq S23b) [γ) between two boundaries with different properties can be represented by an interfacial tension defined as σinter = γ2/κ. To understand how interfacial tension impacts the entry of an egg-shaped merozoite into an RBC with a cytoskeleton layer, we plotted the wrapping phase diagram for a range of bilayer tension (σbilayer) and interfacial tension . Here, we considered a wide range of line tension (0 < γ < 50 pN) to mimic line tension at lipid domain boundaries and line tension due to protein phase separation [How do interfacial forces between the membrane at the site of invasion and the free membrane outside of adhered area influence the parasite wrapping behavior? Based on analytical approximation, the effects of interfacial forces on the wrapping process of a spherical particle with no cytoskeletal layer can be classified into three regimes (Eq S23). ((θ* < 0) , 61, 120paration , 108.σbilayer < 0.5 pN/nm), independent of the magnitude of the interfacial tension, the particle is fully wrapped by the membrane. At intermediate bilayer tension (0.5 < σbilayer < 0.7 pN/nm), we observed a distinct contrast with the membrane wrapping of a spherical particle with no cytoskeleton layer (Eq S23b), wherein an increase in interfacial tension results in a discontinuous transition from a completely wrapped state to a non-adhesive state , we found that similar to the membrane wrapping of the spherical particle and the egg-shape merozoite with no cytoskeleton layer  a nucleation barrier that impedes the merozoite attachment to the RBC membrane and (2) a wrapping energy barrier that hinders the full merozoite entry.In  tension . We alsoayer = 0 . InteresFz) required for a full envelopment of a spherical particle with no cytoskeleton layer (Eq S26). Based on our analytical approximation, Fz is linearly proportional to the lipid bilayer bending rigidity (κ), bilayer tension (σ), adhesion strength (ω), and line tension (γ), and it varies as a quadratic function of spontaneous curvature (H0) (Eq S26). For example, in the case of a tensionless bilayer, with no adhesion energy, no spontaneous curvature, and no line tension, a minimum axial force of Fz ∼ 3 pN is required for a full wrapping of a spherical particle (Eq. S26), which is of the order of the reported actomyosin forces needed for a complete merozoite invasion by Dasgupta et al. [While the parasite’s motor forces are known as the primary driving mechanism for malaria invasion –14, we nFz) with respect to bilayer tension and spontaneous tension, and a linear decrease as adhesion strength increases  has a considerable effect –compared to the other length scales of spectrin (Lmax and p)– on the degree of motor forces required for a successful invasion , while at L0 = 50 nm, a minimum axial force of Fz ∼ 8 nN is required to push the parasite into the RBC (Fz ∼ O (1 nN)) are needed to drive the merozoite forward into the RBC, considering the resistance of the cytoskeletal layer against deformation.In invasion . For exa the RBC . This isμm, invade healthy RBCs and asexually reproduce inside them. The invasion process was initially assumed to be solely driven by the parasite actomyosin motor forces. However, recent experiments have shown that the biophysical properties of the RBC membrane, particularly the tension of the RBC membrane, also play an important role in controlling the malaria invasion [During the blood stage of malaria infection, thousands of merozoites, which are the smallest egg-shaped parasites with a typical size of 1–2 invasion , 22, 121invasion , 62.Evans and Skalak initially proposed the empirical constitute elastic energy of the spectrin-actin network at the continuum level, treating the cytoskeleton as an isotropic hyperelastic material with constant shear and stretch moduli . This clIn this study, we present a mathematical framework for investigating the role of tension of the RBC membrane, consisting of a lipid bilayer and a cytoskeleton layer, in governing the energy landscape of merozoite entry. Here, we modeled the lipid bilayer as an incompressible elastic shell that can bend and the cytoskeleton as an incompressible triangular elastic network  that cai) displays an almost linear relationship with the merozoite adhesion to the RBC surface (ii) exhibits a non-monotonic trend with respect to spontaneous tensions, with a slight increase followed by a decrease as spontaneous tension increases (iii) undergoes a sharp transition from large to small values under high interfacial tensions  exncreases , and (iitensions . These rL0), the maximum length (Lmax), and the persistence length of spectrin (p)– in membrane wrapping progression Click here for additional data file.


Semicrystalline polymers are solids that are supposed to flow only above their melting temperature. By using confinement within nanoscopic cylindrical pores, we show that a semicrystalline polymer can flow at temperatures below the melting point with a viscosity intermediate to the melt and crystal states. During this process, the capillary force is strong and drags the polymer chains in the pores without melting the crystal. The unexpected enhancement in flow, while preserving the polymer crystallites, is of importance in the design of polymer processing conditions applicable at low temperatures, e.g., cold drawn polymers such as polytetrafluoroethylene, self-healing, and in nanoconfined donor/acceptor polymers used in organic electronics. Semicrystalline polymers can be made to flow at temperatures below their melting point in pores by capillary action. Tm, e.g., at temperatures as low as ~2/3Tm  and poly(ε-caprolactone)  with molecular characteristics shown in table S1. Main results shown here relate to PEO. Results for PCL5k can be found in the Supplementary Materials. Self-ordered nanoporous alumina templates [anodic aluminum oxide (AAO)] were prepared following the literature procedures    (T = 330 K). As expected, the storage (G′) and loss (G″) moduli are independent of frequency exhibiting elastic response (with G′ > G″). A zero shear viscosity was never reached. These data confirm that the PEO8k film on top of AAO template was in the semicrystalline state. The domain spacing, d, of PEO8k crystals obtained from small-angle x-ray scattering (SAXS) (R). Crystalline lamellae were far smaller than the pore size (400 nm in this case). The superstructure formation in bulk PEO8k was studied by polarizing optical microscopy (POM) in a film that was slowly cooled from the melt to ambient temperature. The thermodynamic, structural, and rheological properties of bulk PEO8k are compiled in g (SAXS)  was in tFollowing a 28-day imbibition of PEO8k in AAO templates with a pore diameter of 400 nm, the sample was cooled to ambient temperature, and scanning electron microscopy (SEM) and atomic force microscopy (AFM) were used to characterize AAO cross sections . There wTm. AFM characterization also applied to the confined PCL5k (figs. S4 and S5). In contrast to the relatively smooth profile in PEO8k, PCL5k shows abundant grain structures densely distributed along the pores. The multigrain structure inherits from the high nucleation density in the bulk sample (fig. S2). It was suggested (The successful imbibition was demonstrated for PCL5k as well (fig. S4). Both cases prove that capillary force is strong enough to drag the polymer crystals in the nanopores at a temperature below the melting point, −1 , we performed nano–infrared (IR) microscopy in the photo-induced force microscopy (PiFM) mode. To obtain images of the surface topography, we excited the second eigenmode of the cantilever resonance frequency and kept a constant amplitude of vibration with an electronic feedback circuit. The first eigenmode of the cantilever resonance frequency was used to record the IR light–induced forces. The incoming IR light was modulated at the difference frequency between the first and second eigenmodes. This difference frequency was fine-tuned to a maximum response amplitude at the first eigenmode, while the tip was engaged on the surface. Spectra in PiFM mode were recorded by ramping the wave number of the IR light from 850 to 1850 cm−1  Control eff, using the Lucas-Washburn equation applicable to Newtonian liquids  is the imbibition length (h = 800 nm), γ is the surface tension (~0.029 N/m), θ is the advancing contact angle (θ ~ 44°) (R is the pore radius (200 nm), and t is the imbibition time (t ~ 2 × 106 s). The equation reflects the balance between two opposite forces: the capillary force that drives the imbibition and the viscous force that provides the friction against imbibition  applicable during imbibition, the bulk viscosity at 330 K  is much higher than 1010 Pa·s . Thus, the semicrystalline polymer flows within the nanopores with a viscosity between the crystalline and melt states, i.e., ηmelt(2 × 103 Pa·s) < ηeff (8 × 109 Pa·s) < ηcrystal (higher than 1010 Pa·s). It suggests that a fraction of crystals are molten during the imbibition process. This is likely, given that the force to pull a single PEO chain out of its single crystal is F ~ 40 pN  of 3 × 10−18 J, i.e., a small fraction of the total energy needed to melt the entire crystal (1 × 10−11 J).Here, 010 Pa·s . On the Fviscous = 8πηeffhv, for the drag force that results to 5 × 10−8 N with a corresponding energy of −14 J. This energy is a minor fraction of the energy needed to melt the crystals (1 × 10−11 J for the main melting peak at 335 K). Hence, the polymer chains enter the pores by capillary action in their folded semicrystalline state.Furthermore, we address the possibility that the magnitude of the capillary force is high enough to actually melt the crystals during flow. In this scenario the chains are molten by the capillary action on entering the pores and the polymer re-crystallize within the pores. To this end we employ f0 is a characteristic frequency in the limit of very high temperatures, and E is the activation energy. Alternatively, for confined PCL, it follows a Vogel-Fulcher-Tammann behavior according to B is the activation parameter, and T0 is the “ideal” glass temperature located below the DSC Tg. For the glass temperature, we use the usual definition as the temperature where the segmental relaxation time equals 100 s. We should mention that the uncertainty in the determination of Tg is high under conditions of confinement for two reasons: First, both polymers are semicrystalline, and the glass temperature refers only to the amorphous segments . Second, under confinement, all dynamic processes become broad increasing the uncertainty. Nevertheless, in both cases, the glass temperature is reduced form the bulk by about 9 ± 4 K and 5 ± 3 K, respectively, for PEO (Tgbulk = 206 K) and PCL (Tgbulk = 201 K). These small reductions in the glass temperature cannot account for the reduced effective viscosity of the semicrystalline polymer since the imbibition temperature is ~110 K above Tg.One could argue that the reason for the reduced viscosity of the semicrystalline polymers is the enhanced segmental relaxation under confinement. A faster segmental dynamics has been observed for a number of confined polymers (c>), (ii) the diffusion of PEO chains over a length scale of lamellar thickness (dc) (time τstem), and (iii) the growth of a unit crystal lamellae (time τlc) (obtained from POM). Processes (i) and (ii) reflect the so-called intracrystalline chain diffusion, which is particularly important for crystal-mobile polymers such as PEO. In the largest field of view  processes, are slower, within the millisecond to 10-s time scales and even cross at 326 K. The imbibition of PEO crystals and the adsorption of polymer chains are, expectedly, the two longest processes (yellow sphere and red dashed line). The latter (adsorption) reflects the continuous exchange between polymer segments/chains at the vicinity of pore walls in which unfavorable conformations  and severe topological constraints  are formed , suggesting slow cooperative diffusion of crystalline lamellae as the main mechanism.Understanding the mechanism of imbibition from the semicrystalline state requires addressing the pertinent dynamics in the crystalline and amorphous domains.  of view , the maiMn = 825 g/mol, Ð = 1.23) enters the pores with a higher speed as compared to PEO8k (fig. S10). The lamellar structure of PEO8k  is composed of folded PEO chains  within the crystal domain of 12.6 nm. Hence, a single chain binds two crystalline domains. On the other hand, PEO1k crystallizes in a fully extended configuration within a single-crystalline domain. The latter effectively comprise brushes that are lubricated and can easily slide one another during the flow. Contrast this with the situation in higher molar mass polymers. There, a single chain “binds” several crystalline domains, making it more difficult for a chain to exit the crystal. PEO with a higher molar mass, PEO500k , could not enter the same nanopores (fig. S10).How does the molar mass of the polymer affect the imbibition process? The results reveal that the imbibition speed is controlled by the molar mass and, in particular, by the chain folding process. PEO1k . Although extremely slow, the successful imbibition shows that the capillary force is strong enough to drag polymer crystallites into pores without melting the crystals. The small reduction in the liquid-to-glass temperature by confinement cannot account for the large decrease in viscosity. Shorter polymer chains in the absence of chain folding accelerate this process because crystalline domains effectively comprise lubricated brushes. The unexpected enhancement in flow while preserving the polymer crystallites is of importance in the design of polymer processing conditions applicable at low temperatures. Applications include cold flow and subsequent bonding of polymers to ceramics or metals via porous adhesion-mediated layers under conditions where polymer degradation is prevented. Another example is cold drawn polytetrafluoroethylene yarns. The latter are used in implantable vascular prostheses and show excellent abrasion resistance strength and lubrication characteristics that closely resemble to a natural body lumen  was used for the enthalpy and melting temperature calibration. As a final step, an empty cell (baseline) measurement verified the successful calibration of the instrument.DSC measurements were made with a Mettler Toledo (DSC-822) calorimeter. Samples  were hermetically encapsulated in an aluminum pan. An empty aluminum pan was used as a reference. The melting temperature of the homopolymers was obtained from the second heating run with a rate of 2 K/min. The temperature protocol involved measurements on cooling and subsequent heating in a temperature range between 273 and 363 K. The instrument was calibrated for best performance in the specific temperature range and heating/cooling rate. A precalibration procedure included (i) cleaning of the cell, (ii) a cell-conditioning step (making an inert atmosphere using helium gas), and (iii) an liquid nitrogen cooling system baseline calibration. The main calibration sequence included a baseline calibration using a sapphire standard. In the next step, an indium standard  AFM in intermittent contact mode, using a cantilever with a nominal tip radius of 5 to 10 nm, a nominal spring constant of 42 N/m, and a resonance frequency of 352 kHz . The AFM tip was located above the AAO region of the sample using the top-view video optics of the AFM. In this procedure, the sample was aligned manually to have the pore axis perpendicular to the scan direction of the AFM tip. The obtained phase and height images were processed by Gwyddion software.−1. One spectrum was typically recorded within 30 to 40 s. The data of each spectrum were exported and loaded into Origin (Origin 9.0). We normalized each spectrum by its maximum response amplitude at the first eigenmode. Then, the data were smoothened by a Savitzky-Golay filter (six points). For display reasons, we added an offset to each spectrum.We performed nano-IR microscopy  in the PiFM mode (G′), loss (G″) shear moduli and viscosity were monitored as a function of frequency, ω, for frequencies in the range from 10−2 < ω < 102 rad/s. The temperature scan on bulk PEO8k sample was made at ω = 10 rad/s following the following thermal protocol: first, by heating the sample above its melting temperature (to T = 348 K), followed by slow cooling to 318 K with a rate of 2 K/min. Subsequently, the sample was reheated to the melting temperature.The viscoelastic behavior of the polymers was measured by a shear rheometer (ARES). Measurements were performed with an environmental test chamber at the respective temperature for imbibition experiments of 330 K (PEO8k) and 323 K (PCL9k). Samples were prepared on the lower plate of the 8- and 25-mm-diameter parallel plate geometry. The storage (−2 to 107 Hz). The measurements were obtained on cooling from the melt in 5-K steps. Measurements were carried out in the usual parallel plate geometry with electrodes of 20 mm in diameter. The sample thickness (50 μm) was held constant by poly(tetrafluoroethylene) spacers. The complex dielectric permittivity ε* = ε′ − iε′′, where ε′ is the real and ε′′ is the imaginary part, was obtained as a function of frequency, ω, and temperature, T, i.e., ε*. The analysis of the DS curves was based on the empirical equation of Havriliak and Negami (HN)∞(Τ) is the high-frequency permittivity, τΗΝ(Τ) is the characteristic relaxation time of the equation, Δε(Τ) = εο(Τ) − ε∞(Τ) is the relaxation strength, m and n  describe the symmetrical and asymmetrical broadening of the distribution of relaxation times, respectively. A term describing the conductivity contribution was included in the fitting procedure as σο(Τ)/iεfω, where σο is the dc conductivity and εf is the permittivity of free space. From τΗΝ, the relaxation times at maximum loss, τmax, were obtained analytically from the HN equation as followsDielectric measurements were performed as a function of frequency for different temperatures using a Novocontrol Alpha frequency analyzer (frequency range from 10f)]. This conductivity contribution has also been taken into account during the fitting process. Except from the dielectric loss data, the derivative of the real part of the dielectric permittivity, ε′, [dε′/dlnω ≈ (2/π)ε′′] was used in the analysis of the dynamic behavior.These relaxation times correspond to the relaxation times of the segmental process. At lower frequencies, ε′′ rises because of the conductivity [ε′′ = σ/(ωε2 using a Cu target). The detection system was a MAR345 image plate area detector, and the sample-to-detector distance was set at 2.24 m. The samples  used in SAXS were prepared with different cooling rates  with a Linkam temperature control unit (THMS600) with built-in TMS94 temperature programmer. The recorded intensity distributions were integrated along the equatorial and meridional axes and are presented as a function of the modulus of the scattering vector, q = (4π/λ) sin(2θ/2), where λ (=1.54184 nm) is the wavelength and 2θ is the scattering angle. Measurements of 3600 s long were made at different temperatures.SAXS measurements were carried out with a Rigaku MicroMax 007 x-ray generator using Osmic Confocal Max-Flux curved multilayer optics (maximum power of 800 W and brightness of 18 kW/mm


In 1967, a diamond polymorph was reported from hard, diamond-like grains of the Canyon Diablo iron meteorite and named lonsdaleite. This mineral was defined and identified by powder X-ray diffraction (XRD) features that were indexed with a hexagonal unit cell. Since 1967, several natural and synthetic diamond-like materials with XRD data matching lonsdaleite have been reported and the name lonsdaleite was used interchangeably with hexagonal diamond. Its hexagonal structure was speculated to lead to physical properties superior to cubic diamond, and as such has stimulated attempts to synthesize lonsdaleite. Despite numerous reports, several recent studies have provided alternative explanations for the XRD, transmission electron microscopy and Raman data used to identify lonsdaleite. Here, we show that lonsdaleite from the Canyon Diablo diamond-like grains are a nanocomposite material dominated by subnanometre-scale cubic/hexagonal stacking disordered diamond and diaphite domains. These nanostructured elements are intimately intergrown, giving rise to structural features erroneously associated with h diamond. Our data suggest that the diffuse scattering in XRD and the hexagonal features in transmission electron microscopy images reported from various natural and laboratory-prepared samples that were previously used for lonsdaleite identification, in fact arise from cubic/hexagonal stacking disordered diamond and diaphite domains.This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 2)'. The low-magnification TEM image of lamella 1 reveals a feathery texture (c), which may reflect previous graphitic layering arranged into bundles [c). However, similar to figure 5a, the pattern displays streaking of reflections from multiple d). The corresponding SAED pattern shows continuous rings and the intensity distribution around the 111 diamond spots reveals a quasi-sixfold symmetry, which can be explained with The structure of a hard carbon grain was investigated from two FIB thinned lamellae, which were prepared from two areas after rotating the grain by 90° c. The lo texture c, which  bundles . The cor diamond c. Howeved spacings previously associated with h diamond. Although discrete c diamond reflections along b) are similar to the calculated patterns based on Understanding the complexity of the samples requires the use of HRTEM images, which reveal abundant (111) c diamond stacking faults and twins along  domains . These d domains . The strthe FFTs b are simtructure .Figure et al. [a,b). Since the corresponding indices for c/h stacking disordered diamond are non-integer numbers, we report c diamond indices of this twin only. Although Németh et al. [b). This twin gives rise to a second set of streaking at 71° with respect to the strong {111} c diamond or the {000l} c/h stacking disordered diamond streaking in FFT, which gives rise to the characteristic ring SAED patterns  and provides an explanation for the prominent sawtooth appearance of the low magnification TEM images . DFT calculations suggest the interlayer spacings of type 2 diaphite are compressed (3.1 Å) by the necessity of coherent bonding between the edges of the graphene layers and the {113} diamond surfaces (c). However, we should note that this 3.1 Å spacing cannot be reliably measured from the experimental HRTEM images.The occurrence of diaphite structures within c and c/h stacking disordered diamond gives rise to additional complexity . These nlections –31. The diaphite a,b. DFT surfaces c. Howevea,b) and is challenging to identify in samples thicker than approximately 20 nm due to the vertically superimposed nanodomains. However, the contributions of d, which displays vertically superimposed diaphites structures with crystallographically intergrown c/h stacking disordered diamond.HRTEM images show the diversity of type 1 and type 2 diaphite, and their various intergrowth structures within the grains . Their pfigure 8 (f)2-bonded structures and the hexagonal reflections were assigned to h diamond  data. Based on the lack of obvious spectral features below 288 eV (the main onset of the diamond peak) in C K-edge core-loss EELS data, it has been claimed that samples did not contain sperial in )). Howevd spacing overlap with those of Our calculated diffraction patterns demonstrate that c/h stacking disordered diamond is indistinguishable from h diamond along ⟨0001⟩ . The con figures –8, thus a shows an intricate lattice fringe image. Its high resolution and the approximately 10° rotation between the cubic and the hexagonal stackings provide evidence for a unique c diamond and c/h stacking disordered diamond intergrowth. In certain areas of the image the 1.26 Å d spacing cross fringes (i) occur together with those of approximately 2.1 Å (ii). The FFT (figure 9b) of the image reveals split reflections having 1.26 Å d spacings with an approximately 10° rotation. We associate the FFT-calculated diffraction data from area i and ii with Ultra-high-resolution TEM (uHRTEM) images provided by aberration-corrected microscopes are necessary to resolve interatomic spacings below 1.3 Å, i.e. the 1.26 and 1.09 Å spacings corresponding to {220} and {113} diamond fringes. In a conventional (non-aberration corrected) HRTEM, only the 2.1 Å sets of {111} diamond fringes are visible. The uHRTEM image of figure 9d spacings  shows that such images are in fact consistent with type 2 diaphite and indicate that these nanostructures correspond to a nanocomposite material consisting of sp2- and sp3-bonded carbon regions. Type 2 diaphite contains c diamond, graphene and interface regions. By changing the volume of these regions, various type 2 diaphite structures can be generated and identified in HRTEM images . Several HRTEM images are dominated by c diamond and interface regions, and they are presumably vertically embedded within c diamond. It is an interesting question how their electronic structure and EELS data differ from c or c/h stacking disordered diamond. As the sample gets thicker, the identification of the c diamond units becomes challenging (figure 10d). However, the d).Similar to spacings . We notespacings . Type 2 surfaces . HRTEM isurfaces  are charh et al.  interpre. 4Lonsdaleite is the mineral name given to the h diamond component in the hard carbon grains from the Canyon Diablo iron meteorite . Since i


S = 1/2 ions are predicted to be isotropic. We investigate a Co(II)complex with two antiferromagnetically coupled 1/2 spins on Au(111)using low-temperature scanning tunneling microscopy, X-ray magneticcircular dichroism, and density functional theory. We find that eachof the Co ions has an orbital moment comparable to that of the spin,leading to magnetic anisotropy, with the spins preferentially orientedalong the Co–Co axis. The orbital moment and the associatedmagnetic anisotropy is tuned by varying the electronic coupling ofthe molecule to the substrate and the microscope tip. These findingsshow the need to consider the orbital moment even in systems withstrong ligand fields. As a consequence, the description of S = 1/2 ions becomes strongly modified, which have importantconsequences for these prototypical systems for quantum operations.The magnetic propertiesof transition-metal ions aregenerallydescribed by the atomic spins of the ions and their exchange coupling.The orbital moment, usually largely quenched due the ligand field,is then seen as a perturbation. In such a scheme,  The effect of theremaining orbital moment may be treated as a perturbation and is atthe origin of magnetic anisotropy, which has been extensively studiedfor atoms and clusters on surfaces.6 The magnetic properties of atoms are consequently often modeledwith a spin Hamiltonian that predicts the absence of magnetic anisotropyfor spin-half ions.The orbital momentum of transitionmetal ions strongly depends on the atom coordination and rapidly quenchesto the negligible values in bulk.7 andWhangbo8 et al. used density functionaltheory calculations to analyzethe magnetic anisotropy of spin-1/2 Cu2+ ions in crystalsand suggested that previous interpretations of the anisotropy in termsof anisotropic exchange coupling or magnetic dipole–dipoleinteractions were not complete. They rather emphasized the importanceof spin–orbit coupling. Exchange coupling in crystals can becomplex and consequently it is desirable to investigate the magneticanisotropy of two exchange-coupled spin-1/2 ions in a fairly simpleligand field. Dinuclear (or polynuclear) molecular compounds, whichare intensively investigated in the gas-phase,13 may serve as model systems. Deposition of such complexeson surfaces has so far led to fragmentation15 or to apparent quenching of the internuclear exchange coupling becauseof excessive interaction with the substrate.18 Magnetic excitationshave been observed for bulky three-dimensional Mn12 andFe420 complexes on ultrathin insulatorlayers.Liu et al.66H86Co2N4O4  subunits connected by a shared phenyl ring 1a. Eighttert-butylsubunits (see overlaid molecules in C2 axis of the molecule that is perpendicularto the line connecting the Co(II) ions to define the orientation ofthe molecule, we observe that the molecules enclose angles of ≈±35° with respect to one of the dense directions of theAu substrate (On Au(111), the complex self-assembles into a well-orderedpattern 1bwith a23 The data indicate that the Co(II) ions each carry a spin1/2 and couple antiferromagnetically. An exchange energy, definedas the energy difference between the singlet and triplet states, of2.5 meV was inferred from the data.Solid-state susceptibility measurementsof di-Co powder using a superconducting quantum interference device(SQUID) have been reported by Shimakoshi et al.V| ≈ 9 mV (with variations of ±2 meV frommolecule to molecule using similar tunneling conditions), symmetricabout the Fermi level at V = 0 (Supporting Information Section 6). The magnetic origin ofthe steps is confirmed by their conversion into a Kondo resonanceupon particular manipulations of the complex as described below. Singlet–triplettransitions of molecules on surfaces have been previously reported,involving the spins of organic compounds,27 the spin of a metal center coupledto that of a ligand,28 the spins of separatemolecules,29 and the spins of differentshells on the same atom.30 Magnetic excitationsof single molecular magnets on insulating surfaces, where severalmetal atoms are connected through oxygen atoms, have been observedas well.20 Therefore, the steps in the dI/dV spectrum may, at first glance, be interpretedas being due to singlet-to-triplet excitations with an exchange energyof ≈9  meV. However, this energy is much larger thanvalues from solid-state measurements (2.5 meV). This discrepancyindicates that further ingredients may have to be considered.Differential conductancespectra of di-Co on Au(111) exhibit marked steps at |at V = 0 2a. These33 essentially gives the average projection of spin⟨μspin⟩ and orbital ⟨μorb⟩ moments per Co(II) ion onto the axis of photon-incidence,along which the magnetic field is applied. These data, acquired undera magnetic field of 6.8 T, are shown in J = 9 meV (dashed blue data). Instead, as shown in the Supporting Information Section 1, the experimentaldata can be reproduced by considering an exchange energy of 1.3 meV.This value is only half that inferred from the SQUID measurements(2.5 meV) performed under a substantially smaller field of50 mT.23 The apparent discrepancyof the exchange energies again suggests that the underlying assumptionof coupled spins is insufficient, despite the fact that it leads tofairly good fits of the experimental data.We performed additional X-ray magnetic circulardichroism (XMCD)measurements see the “”sectionB per Co ion with a strongtemperature dependence , an orbital moment between 0.1 and 0.3 μB, depending on the direction of the applied field, is inferredfrom XMCD , and DFT calculationsindicate an orbital moment of ≈0.3  μB. Similar magnitudes of spin and orbital moments are found for di-Copowder and di-Co/Au(111) indicating that the magnetic properties ofdi-Co are not significantly affected by the adsorption. This is corroboratedby essentially identical X-ray absorption spectra for di-Co powderand di-Co/Au(111) .In addition, theXMCD data reveal a sizable orbital moment of upto ≈0.15  μpendence 2c. This spin⟩ ≈0, Supporting Information Section 2). Incontrast, measurements at an incidence angle of 60° between theX-rays and the surface normal give ⟨μspin⟩≈ 0.2 μB. These measurements show thatthe spins are preferentially oriented in the molecular plane, whichis consistent with our DFT calculations including spin–orbitcoupling. The configuration with spins aligned along the axis connectingthe two Co ions . A field of 5 T at 1.5 Kis insufficient to turn a detectable fraction of the spins out ofthe surface plane  or ina pure yz|Lz|dyz⟩= ⟨dxz|Lz|dxz⟩ = 0). However,if |dyz⟩ and |dxz⟩ states are mixed, e.g., because they are degenerateor through SOC,35 then the eigenfunctionsare no longer pure Cartesian orbitals. The occupation of B along the quantization axis z. A concomitant occupation of the state B, therebyquenching the total orbital moment. Similar conclusionscan be drawn for the mixing of the dxy and Having found sizableorbital moments for di-Coin powder samplesand adsorbed on Au(111), we next discuss their microscopic origin.The orbital moment of metal–organic compounds is usually quenchedby the ligand field. An electron in, e.g., a pure z′ does not coincide with the z axisof the molecule. In such cases, the spin–orbit Hamiltoniancan be rewritten as36z (z′) component and the ladder operators of the orbital (spin)momentum, ζ is the spin–orbit constant, and θ andϕ are the polar and azimuthal angles giving the orientationof z′ in the  coordinate system used to describethe orbital. In the present case, the z axis of di-Cois perpendicular to the molecular plane, while the spin axis appearsto be along x (lz differ by one (Δlz = 1). For example, SOC hybridizes thedyz and x. The degree of hybridizationand hence the magnitude ofthe moment scales with ζ and inversely with the energy splittingbetween the dyz and Thesituation is more complex when the spin quantization axis  along x 3a such tHSO on di-Co. DFT calculations find each Co atomin a 4s23d7 configuration with a projected densityof states PDOS shown in HHyb in a |l, m, sz⟩ base, which hybridizes andshifts |l, m, sz⟩ states with parameters adjustedto approximately reproduce the PDOS . We used ζ = 65 meVas reported for Co(II) ions.37 The compositions andorbital moments of the other orbitals are given in the Supporting Information Section 4. The occupationof other orbitals  decreases the total orbital momentto 0.38 μB. This value is in line with theone given by DFT directly (≈0.3  μB). Our calculations show that a large energy splitting due to a ligandfield does not necessarily quench the orbital moment.In the following, we considerthe impact of J is the exchange-coupling constant, gs the g-factorof the spin, and B⃗ is the external magneticfield. The second term of the Hamiltonian describes spin–orbitcoupling of collinear orbital and spin moments . The third termdescribes the Zeeman energy due to the interaction with the externalmagnetic field. A number of simplifications are made to reduce thecomplexity of the model: (i) We use a single-electron Hamiltonianinstead of handling the 7 d-electrons per Co ion, such that Coulombrepulsion and correlations are not taken into account. (ii) We solelyconsider linear combinations of states with m = ±1for each ion site. This is technically achieved by taking L1 = L2 = 1 and byshifting the m = 0 states 100 meV up in energy.(iii) As simplification (ii) overestimates the orbital moments, thespin–orbit coupling is rescaled by adjusting ζ. The Hamiltonian. Using J = 3 meV and ζ = −8.2 meV,the thermal evolutions of the spin and orbital moments and the differentialconductance spectrum are simultaneously reproduced (dashed red curvesin I/dV spectra.This does not significantly affect the temperature evolutions of ⟨μspin⟩ and ⟨μorb⟩ (Supporting Information Section 8).Havingconfirmed a significant orbital moment on each Co atomsand explained its origin, we construct a single-electron Hamiltonianto describe the coupling between the two Co atoms in the di-Co moleculethat takes into account the effect of the orbital moment and reproducesthe experimental data:iltonian2 is diagB = 0, the degenerateground state ofm1, sz1,, m2, sz2,⟩).For dI/dV spectra, excited statesthat differ from the ground state by the angular momentum of a tunnelingelectron are relevant, hence |ΔmJ| = 0, 1. These states essentially are linear combinationsof |1, ↓, −1, ↓⟩, |−1, ↓, 1, ↓⟩, |1, ↑, −1, ↑⟩, and |−1, ↑, 1, ↑⟩. Steps in the dI/dV spectrummay be understood as a spin flip at one of the Co sites and correspondto a transition from an antiferromagnetic to a ferromagnetic configurationof the Co spins. However, the angular momentum provided by the tunnelingelectron (maximum of 1) is insufficient to change the orbital momentof the Co sites. Consequently, spin and orbital momentum are antiparallelat the excited spin-flipped Co site. The energy of the excited statehas therefore contributions from the unfavorable spin alignment (exchangecoupling) and the unfavorable alignment of the spin and orbital momentumat a Co site (due to SOC), which leads to the large excitation energyobserved in dI/dV spectra. In contrastto excitation by electrons, thermal excitation is not limited to |ΔmJ| ≤ 1. This resultsin the evolutions with temperature shown in Withthe above parameters and 40 For di-Co on Au(111), we observedvariations of the excitation energy  measured on different complexes. Although a clear patternhas not yet been identified, the electronic coupling presumably dependson the location of the complex relative to the reconstruction of theAu(111) surface.The magneticanisotropyof Co(II) ions on surfaces was shown to decrease as the exchange couplingto the substrate is increased.tert-butyl moieties that decouple the Co centersfrom the surface. Three states of the tert-butylgroups  with different apparent heights were obtainedthe obtained4a. Changtion gap 4c. Some tion gap 4d typicatert-butylgroups maybe interpreted in terms of sequential removal of methyl groups. Thecorresponding simulated STM images match the experimental ones quitewell ,while that of the other Co site remains fairly constant . In addition, the interactionwith the substrate appears to affect the exchange coupling betweenthe two sites as well. We speculate that the removal of further methylgroups further decreases the orbital moment and the exchange coupling.The Co ions may then be described as pure spin-1/2 systems interactingwith the conduction electrons of the substrate, leading to a Kondoresonance. The change of orbital moment and exchange coupling affectsthe magnetic anisotropy. Orienting the spins along the y axis (green arrows in x axis (Supporting Information Section 5). That is, the magnetic anisotropyof the molecule is tuned by manipulating the tert-butyl moieties.The manipulation of the itewell 5. OurDFtert-butylsubunits allowsa relatively coarse modification of the magnetic properties with limitedcontrol over the final state. Fine-tuning of the magnetic anisotropyis possible by bringing the STM tip close to a Co center. z. The magnetic excitation energy of ≈11meV for Δz ≥ – 80 pm decreasesas Δz becomes more negative, while the dI/dV increases at the steps developingovershoots. This effect may be attributed to an increased interactionof the Co center with the conduction electrons of the tip and thesubstrate. Further data and fits are shown in Supporting Information Section 7.The manipulation of the S = 1/2 spinsseparated by a benzenetetraimine moiety of a di-Co complex on Au(111)are antiferromagnetically coupled. Differential conductance spectra,XMCD measurements, and DFT calculations reveal large orbital momentscomparable to the spin moments despite the ligand field acting onthe Co ions. The orbital moments, often neglected for spin 1/2 ions,lead in turn to a sizable magnetic anisotropy. The orbital momentand the magnetic anisotropy, may be tuned by manipulating the peripheralgroups of the complex or by bringing the STM tip close the molecule.Our study shows that unquenched orbital moments are relevant in transitionmetal complexes and lead to sizable magnetic anisotropies even forspin-1/2 objects.In conclusion, we found that the two The di-Co powder was synthesized followingthe description of ref .in vacuo. Experiments werecarried out in ultrahigh vacuum with a STM operated at ≈4.6K. The differential conductance dI/dV was measured using a lock-in amplifier with a modulation voltageof 0.5 mVrms at 667.8 Hz. The shown dI/dV spectra were low-pass filtered.The Au(111) surface was prepared by cycles of Arion bombardment (1.5 keV) and annealing to 450 °C. di-Cowas sublimated from a heated crucible (≈260 °C) onto thesubstrate at ≈25 °C. STM tips were electrochemically etchedfrom W wire and annealed 43 at the Swiss light source . X-ray absorptionspectra at the Co L3,2 edges were acquiredunder a magnetic field of 6.8 T at different temperatures.The difference of such spectra, recorded with photons of left andright helicities, gives the XMCD spectra. Sum rules have been appliedto the spectra to extract the average spin and orbital moments alignedalong the magnetic field.33 A 3d7 occupation of the Co ions has been used. The X-ray absorption measurementson di-Co on Au(111) (sample prepared as for STM measurements) wereperformed at the DEIMOS beamline44 of thesynchrotron SOLEIL .Measurements on di-Co powder pressed onto a Tafoil were performed at the EPFL/PSI X-Treme beamline45 Core electronswere treated using the projected augmented-wave (PAW) method46 and wave functions were expanded using a planewave basis set with an energy cutoff of 400 eV. The PBE was used asexchange and correlation functional.47 Thedescription of the Co d-electrons was improved by using the GGA+Umethod as formulated by Dudarev48 with Ueff = 3 eV if not otherwise stated. Missinglong-range dispersion interactions in this functional were treatedusing the Tkatchenko–Scheffler method..49 Magnetic anisotropy energies were calculated by performingtotal energy differences between different configurations after includingspin–orbit coupling as implemented in VASP.50Density functionaltheory (DFT) calculations wereperformed using the VASP code.The Au(111) surface was simulated using the slabmethod with four atomic layers separated by a vacuum region of 21Å. The coordinates of all atoms except the two bottom layerswere relaxed until forces were smaller than 0.02 eV/Å.51 using the method of Bocquetet al.52 as implemented in the code STMpw.53STM simulations were done by applying the Tersoff–Hamannapproximation