Urban exodus? Understanding human mobility in Britain during the COVID-19 pandemic using Meta-Facebook data.

Existing empirical work has focused on assessing the effectiveness of nonpharmaceutical interventions on human mobility to contain the spread of COVID-19. Less is known about the ways in which the COVID-19 pandemic has reshaped the spatial patterns of population movement within countries. Anecdotal evidence of an urban exodus from large cities to rural areas emerged during early phases of the pandemic across western societies. Yet, these claims have not been empirically assessed. Traditional data sources, such as censuses offer coarse temporal frequency to analyse population movement over infrequent time intervals. Drawing on a data set of 21 million observations from Meta-Facebook users, we aim to analyse the extent and evolution of changes in the spatial patterns of population movement across the rural-urban continuum in Britain over an 18-month period from March 2020 to August 2021. Our findings show an overall and sustained decline in population movement during periods of high stringency measures, with the most densely populated areas reporting the largest reductions. During these periods, we also find evidence of higher-than-average mobility from high-density population areas to low-density areas, lending some support to claims of large-scale population movements from large cities. Yet, we show that these trends were temporary. Overall mobility levels trended back to precoronavirus levels after the easing of nonpharmaceutical interventions. Following these interventions, we found a reduction in movement to low-density areas and a rise in mobility to high-density agglomerations. Overall, these findings reveal that while COVID-19 generated shock waves leading to temporary changes in the patterns of population movement in Britain, the resulting vibrations have not significantly reshaped the prevalent structures in the national pattern of population movement. As of 2021, internal population movements sit at an intermediate level between those observed pre- and early phases of the pandemic.

Geographical characterisation of British urban form and function using the spatial signatures framework.

The spatial arrangement of the building blocks that make up cities matters to understand the rules directing their dynamics. Our study outlines the development of the national open-source classification of space according to its form and function into a single typology. We create a bespoke granular spatial unit, the enclosed tessellation, and measure characters capturing its form and function within a relevant spatial context. Using K-Means clustering of individual enclosed tessellation cells, we generate a classification of space for the whole of Great Britain. Contiguous enclosed tessellation cells belonging to the same class are merged forming spatial signature geometries and their typology. We identify 16 distinct types of spatial signatures stretching from wild countryside, through various kinds of suburbia to types denoting urban centres according to their regional importance. The open data product presented here has the potential to serve as boundary delineation for other researchers interested in urban environments and policymakers looking for a unique perspective on cities and their structure.

Functional signatures in Great Britain: A dataset.

The spatial distribution of activities and agents within cities, conceptualised as an urban function, profoundly affects how different areas are perceived and lived. This dataset introduces the concept of functional signatures - contiguous areas of a similar urban function delineated based on enclosed tessellation cells (ETC) - and applies it to the area of Great Britain. ETCs are granular spatial units, which capture function based on interpolations from open data inputs stretching from remote sensing to land use, census and points of interest data. The spatial extent of each signature type is defined by grouping ETCs using cluster analysis, based on similarity between their functional profiles, inferred by the data linked to each cell. This approach results in a dataset that reflects urban function as a composite of aspects, rather than a singular use, and is built up from granular spatial units. Furthermore, the underlying data are sourced from available open data products, which together with a method and code fully available, yields a fully reproducible pipeline and makes our dataset and open data product. Both the final classification composed of 17 types of functional signatures and the underlying data collected on the level of enclosed tessellation cells are included in the release and described in this report.

Cure Kinetics Modeling of a High Glass Transition Temperature Epoxy Molding Compound (EMC) Based on Inline Dielectric Analysis.

We report on the cure characterization, based on inline monitoring of the dielectric parameters, of a commercially available epoxy phenol resin molding compound with a high glass transition temperature (>195 °C), which is suitable for the direct packaging of electronic components. The resin was cured under isothermal temperatures close to general process conditions (165-185 °C). The material conversion was determined by measuring the ion viscosity. The change of the ion viscosity as a function of time and temperature was used to characterize the cross-linking behavior, following two separate approaches (model based and isoconversional). The determined kinetic parameters are in good agreement with those reported in the literature for EMCs and lead to accurate cure predictions under process-near conditions. Furthermore, the kinetic models based on dielectric analysis (DEA) were compared with standard offline differential scanning calorimetry (DSC) models, which were based on dynamic measurements. Many of the determined kinetic parameters had similar values for the different approaches. Major deviations were found for the parameters linked to the end of the reaction where vitrification phenomena occur under process-related conditions. The glass transition temperature of the inline molded parts was determined via thermomechanical analysis (TMA) to confirm the vitrification effect. The similarities and differences between the resulting kinetics models of the two different measurement techniques are presented and it is shown how dielectric analysis can be of high relevance for the characterization of the curing reaction under conditions close to series production.

Versatile Coordination of AgI and CuI Ions towards cyclo-As5 Ligands.

The reactions of the cyclo-As5 complex [Cp*Fe(η5 -As5 )] (B) with the AgI and CuI salts of the weakly coordinating anion (WCA) [FAl{OC6 F10 (C6 F5 )}3 ]- ([FAl]- ) are studied. These reactions allow the synthesis of the mononuclear complexes [M(η5 : η2 -B)2 ][FAl] (M=Ag (1), Cu (2)) when a ratio of B/M(FAl) 2 : 1 is used. Compound 1 shows an unusual disorder of the central AgI cation between two π-coordinating cyclo-As5 ligands, which is absent in 2 pointing to a weak interaction of the Ag center towards the cyclo-As5 ligands in B. When the ratio of B/Ag(FAl) is changed to 3 : 1 or 1 : 1, the respective coordination compounds [Ag(η2 -B)3 ][FAl] (3) and [Ag2 (η2 : η2 -B)2 ][FAl]2 (4) are accessible. The coordination modes of the cyclo-As5 units in 1, 3 and 4 are all different, reflecting the adaptive coordination behavior of B towards AgI ions. The optimized geometries in the gas phase of 1-4 are determined by DFT calculations to support the bonding situation observed in their solid-state structures.

Highly soluble Cu(i)-acetonitrile salts as building blocks for novel phosphorus-rich organometallic-inorganic compounds.

The synthesis of the air-stable and highly soluble Cu(i)-acetonitrile salts [Cu(CH3CN)3.5][FAl] (1) ([FAl] = FAl{OC(C6F10)(C6F5)}3) and [Cu(CH3CN)4][TEF] (2) ([TEF] = Al{OC(CF3)3}4) is presented. Compound 1 reacts with the organometallic polyphosphorus complexes [Cp2Mo2(CO)4(η2-P2)] (A) and [(Cp*Fe(η5-P5)] (B) and salt 2 reacts with B to form one new (3) and three unprecedented (4-6) phosphorus-rich Cu(i) dimers with the general formulas [Cu2(µ,η1:η1-A)2(η2-A)2][FAl]2 (3), [Cu2(µ,η1:η1-A)2(η1-CH3CN)4][FAl]2 (4), [Cu2(µ,η1:η1-B)2(η1-CH3CN)4][FAl]2 (5) and [Cu2(µ,η1:η1-B)2(η1-CH3CN)4][TEF]2 (6).

Dicationic E4 Chains (E=P, As, Sb, Bi) Embedded in the Coordination Sphere of Transition Metals.

The oxidation chemistry of the complexes [{CpMo(CO)2 }2 (µ,η2 :η2 -E2 )] (E=P (A), As (B), Sb (C), Bi (D)) is compared. The oxidation of A-D with [Thia]+ (=[C12 H8 S2 ]+ ) results in the selective formation of the dicationic E4 complexes [{CpMo(CO)2 }4 (µ4 ,η2 :η2 :η2 :η2 -E4 )]2+ (E=P (1), As (2), Sb (3), Bi (4)), stabilized by four [CpMo(CO)2 ] fragments. The formation of the corresponding monocations [A]+ , [C]+ , and [D]+ could not be detected by cyclic voltammetry, EPR, or NMR spectroscopy. This finding suggests that dimerization is fast and that there is no dissociation in solution, which was also predicted by DFT calculations. However, EPR measurements of 2 confirmed the presence of small amounts of the radical cation [B]+ in solution. Single-crystal X-ray diffraction revealed that the products 1 and 2 feature a zigzag E4 chain in the solid state while 3 and 4 bear a central E4 cage with a distorted "butterfly-like" geometry. Additionally, 1 can be easily and reversibly converted into a symmetric and an unsymmetric form.

Strategies for the Construction of Supramolecular Dimers versus Homoleptic 1D Coordination Polymers Starting from the Diphosphorus [Cp2Mo2(CO)4(η2-P2)] Complex and Silver(I) Salts.

The reactions of the tetrahedral diphosphorus [Cp2Mo2(CO)4(η2-P2)] (1; Cp = C5H5) complex with Ag[Al{OC(CF3)3}4] (AgTEF) (A) and Ag[FAl{OC(C6F5)(C6F10)}3] (AgFAl) (B) were studied. The first reaction led to the formation of the [Ag2(η2-1)2(η1:η1-1)2][TEF]2 (2) dimer and the [Ag2(η1:η1-1)3] n [TEF]2n (3) coordination polymer, whereas the second reaction afforded the [Ag2(η1:η1-1)2(η1-CH2Cl2)2(η2-C7H8)2][FAl]2 (4) or the [Ag2(η2-1)2(η1:η1-1)2][FAl]2 (5) dimer and the [Ag2(η1:η1-1)4] n [FAl]2n (6) coordination polymer. In each case, the products obtained depended on the ratio of the reactants and/or the synthetic procedure.

The Diphosphorus Complex [Cp2Mo2(CO)4(η2-P2)] as a Building Block for the Synthesis of Mixed-Hybrid Coordination Polymers.

The three-component reaction of the tetrahedral diphosphorus complex [Cp2Mo2(CO)4(η2-P2)] (1), with Ag[BF4] (2) in the presence of 2,2'-bipyrimidine (3) leads to the formation of the two novel two-dimensional networks 4 and 5. Compound 4 is a new two-dimensional organometallic-organic hybrid polymer, while derivative 5 represents a unique two-dimensional organometallic-inorganic-organic hybrid polymer. These results show the possibility of synthesizing a new class of coordination polymers, which could not be obtained from two-component reactions with organic molecules in addition of metal ions.

Oxidation Chemistry of Inorganic Benzene Complexes.

The oxidation of the 28 VE cyclo-E6 triple-decker complexes [(CpR Mo)2 (µ,η6 :η6 -E6 )] (E=P, CpR =Cp(2 a), Cp*(2 b), CpBn (2 c)=C5 (CH2 Ph)5 ; E=As, CpR =Cp*(3)) by Cu+ or Ag+ leads to cationic 27 VE complexes that retain their general triple-decker geometry in the solid state. The obtained products have been characterized by cyclic voltammetry (CV), EPR, Evans NMR, multinuclear NMR spectroscopy, MS, and structural analysis by single-crystal X-ray diffraction. The cyclo-E6 middle decks of the oxidized complexes are distorted to a quinoid (2 a) or bisallylic (2 b, 2 c, 3) geometry. DFT calculations of 2 a, 2 b, and 3 persistently result in the bisallylic distortion as the minimum geometry and show that the oxidation leads to a depopulation of the σ-system of the cyclo-E6 ligands in 2 a-3. Among the starting complexes, 2 c is reported for the first time including its preparation and full characterization.

Supramolecular adducts based on weak interactions between the trimeric Lewis acid complex (perfluoro-ortho-phenylene)mercury and polypnictogen complexes.

Reactions of the trinuclear Lewis acid perfluoro-ortho-phenylene)mercury [(o-HgC6F4)3] (1) with the polypnictogen complex [CpMo(CO)2(η(3)-P3)] (2) containing a cyclo-P3 ligand and the series of E2 complexes [{CpMo(CO)2}2(µ,η(2):η(2)-E2)] (E = P(3a), As(3b), Sb(3c), Bi(3d)) are reported. In all cases, the reaction products show very weak interactions between the En ligand complexes and the Lewis acid 1, as evidenced by their highly dynamic behaviour in solution and the formation of adducts in the solid state showing HgE contacts below the respective sum of the van der Waals radii. The complexes 2 (P3), 3a (P2) and 3b (As2) show interactions of only one pnictogen atom with all three Hg atoms of 1. The complex 3c (Sb2) forms two adducts with 1 showing either a side-on coordination of the Sb2 dumbbell towards Hg or an end-on coordination of both Sb atoms towards two independent molecules of 1. The Bi2 complex 3d shows an almost parallel alignment of the Bi2 dumbbell situated above the center of the planar Lewis acid 1. The arrangements of the E2 complex series towards 1 are rationalized with the help of electrostatic potential maps obtained by DFT calculations. Finally the structural characterizations of a new modification of the free Sb2 complex 3c, the Bi2 complex 3d, the starting material of its preparation [Bi{CpMo(CO)3}3] (4) and an unprecedented 'Cr4As5' cluster 5 are presented.

Self-Assembly of Reactive Linear Cu3 Building Blocks for Supramolecular Coordination Chemistry and Their Reactivity toward E(n) Ligand Complexes.

This study describes the selective synthesis of linear, trinuclear, halide-bridged Cu(I) complexes [Cu3(µ-X)2(µ-dpmp)2(MeCN)2](+) (1a: X = Cl; 1b: X = Br; 1c: X = I) stabilized by the tridentate dpmp ligand obtained by self-assembly reactions in THF/MeCN. Upon drying, the MeCN ligands can be removed and the complexes are transformed to the reactive parent trinuclear [Cu3(µ-X)2(µ-dpmp)2](+) (2a-c) building blocks with two vacant coordination sites on the terminal Cu atoms. Another synthesis in CH2Cl2 directly yields 2a-c. Additionally, two related isomeric compounds, 2a* and 2c*, and two CH2Cl2-ligated complexes, [Cu3(µ-X)2(µ-dpmp)2(CH2Cl2)2](+) (X = Br (3b), I (3c)), were structurally characterized. The frameworks of the cationic [Cu3(µ-X)2(µ-dpmp)2](+) complexes are stable in solution at low temperatures and show dynamic coordination behavior at elevated temperatures, indicated by new signals arising in the (31)P{(1)H} NMR spectra. This evolution cannot be shifted back by decreasing the temperature again. However, cationic [Cu3(µ-X)2(µ-dpmp)2](+) (X = Cl, Br, I) complexes can be obtained selectively in the solid state upon crystallization. Although reactions of 2a-c with complexes [{CpMo(CO)2}2(µ,η(2):η(2)-E2)] (E = P (A1), As (A2)) led to unsymmetrically substituted [Cu3(µ-X)2(µ-dpmp)2(η(1)-L)](+) (4a-c: X = Cl-I, L = A1; 5: X = Cl, L = A2) complexes, reactions with the cyclo-P3 complex [CpMo(CO)2(η(3)-P3)] (B) afforded zigzag chain polymers [Cu3(µ-X)2(µ-dpmp)2(µ,η(1):η(1)-B)]n[BF4]n (6a: X = Cl; 6b: X = Br) and symmetrically substituted complex [Cu3(µ-I)2(µ-dpmp)2(η(1)-B)2](+) (7). Reactions of 2a-c with cyclo-E5 complexes [Cp*Fe(η(5)-E5)] (E = P (C1), As (C2)) led to the isolation of one-dimensional coordination polymers [Cu3(µ-X)2(µ-dpmp)2(µ,η(1):η(1)-L)]n[BF4]n (8a-b: X = Cl-Br, L = C1; 9: X = Cl, L = C2) and symmetrically substituted complex [Cu3(µ-I)2(µ-dpmp)2(η(1)-C1)2](+) (10). All products exhibit a trinuclear, cationic [Cu3(µ-X)2(µ-dpmp)2](+) complex as the central structural motif. Variation of the intramolecular Cu-Cu distances inside the Cu3 complexes is discussed, and supporting DFT computations for the model complex [Cu3(µ-Cl)2(dmmp)2{(η(1)-A1)}](+) (4a') are presented.

Supramolecular aggregation of Ni(salen) with (C6F5)2Hg and [o-C6F4Hg]3.

As part of our ongoing interest in the supramolecular chemistry of fluorinated organomercurials, we have investigated the interaction of bis(pentafluorophenyl)mercury ((C6F5)2Hg), and trimeric (perfluoro-o-phenylene)mercury ([o-C6F4Hg]3), with nickel(II) N,N'-bis(salicylidene)ethylenediamine) (Ni(salen)). While solution studies monitored by UV-VIS spectroscopy suggest that Ni(salen) interacts with the trinuclear mercury complex in solution, the 1 : 1 adduct (Ni(salen)-(C6F5)2Hg) and the 1 : 1 adducts Ni(salen)-[o-C6F4Hg]3 and [Ni(salen)-[o-C6F4Hg]3-THF-H2O] can be obtained by slow evaporation of solutions containing the two building blocks. While arene-fluoroarene and hydrogen bonding interactions, as well as interactions between mercury and the salen ligand are the predominant forces responsible for the formation of these adducts, Ni(salen)-[o-C6F4Hg]3 and [Ni(salen)-[o-C6F4Hg]3-THF-H2O] also display short Ni-Hg separations consistent with the presence of metallophilic interactions. Quantum theory of atoms in molecules (QTAIM) analyses of the Ni-Hg interactions in these adducts finds that these interactions are dominated by electrostatic and dispersion forces, despite featuring non-negligible covalent contributions.

Molecular Polyarsenides of the Rare-Earth Elements.

Reduction of [Cp*Fe(η(5)-As5)] with [Cp''2Sm(thf)] (Cp''=η(5)-1,3-(tBu)2C5H3) under various conditions led to [(Cp''2Sm)(µ,η(4):η(4)-As4)(Cp*Fe)] and [(Cp''2Sm)2As7(Cp*Fe)]. Both compounds are the first polyarsenides of the rare-earth metals. [(Cp''2Sm)(µ,η(4):η(4)-As4)(Cp*Fe)] is also the first d/f-triple decker sandwich complex with a purely inorganic planar middle deck. The central As4(2-) unit is isolobal with the 6π-aromatic cyclobutadiene dianion (CH)4(2-). [(Cp''2Sm)2As7(Cp*Fe)] contains an As7(3-) cage, which has a norbornadiene-like structure with two short As-As bonds in the scaffold. DFT calculations confirm all the structural observations. The As-As bond order inside the cyclo As4 ligand in [(Cp''2Sm)(µ,η(4):η(4)-As4)(Cp*Fe)] was estimated to be in between an As-As single bond and a formally aromatic As4(2-) system.

Highly dynamic coordination behavior of Pn ligand complexes towards "naked" Cu(+) cations.

Reactions of Cu(+) containing the weakly coordinating anion [Al{OC(CF3 )3 }4 ](-) with the polyphosphorus complexes [{CpMo(CO)2 }2 (µ,η(2) :η(2) -P2 )] (A), [CpM(CO)2 (η(3) -P3 )] (M=Cr(B1), Mo (B2)), and [Cp*Fe(η(5) -P5 )] (C) are presented. The X-ray structures of the products revealed mononuclear (4) and dinuclear (1, 2, 3) Cu(I) complexes, as well as the one-dimensional coordination polymer (5 a) containing an unprecedented [Cu2 (C)3 ](2+) paddle-wheel building block. All products are readily soluble in CH2 Cl2 and exhibit fast dynamic coordination behavior in solution indicated by variable temperature (31) P{(1) H} NMR spectroscopy.

Redox and Coordination Behavior of the Hexaphosphabenzene Ligand in [(Cp*Mo)2 (µ,η(6) :η(6) -P6 )] Towards the "Naked" Cations Cu(+) , Ag(+) , and Tl(.).

Although the cyclo-P6 complex [(Cp*Mo)2 (µ,η(6) :η(6) -P6 )] (1) was reported 30 years ago, little is known about its chemistry. Herein, we report a high-yielding synthesis of 1, the complex 2, which contains an unprecedented cyclo-P10 ligand, and the reactivity of 1 towards the "naked" cations Cu(+) , Ag(+) , and Tl(+) . Besides the formation of the single oxidation products 3 a,b which have a bisallylic distorted cyclo-P6 middle deck, the [M(1)2 ](+) complexes are described which show distorted square-planar (M=Cu(4 a), Ag(4 b)) or distorted tetrahedral coordinated (M=Cu(5)) M(+) cations. The choice of solvent enabled control over the reaction outcome for Cu(+) , as proved by powder XRD and supported by DFT calculations. The reaction with Tl(+) affords a layered two-dimensional coordination network in the solid state.

Organometallic polyphosphorus and -arsenic ligands as linkers between pre-assembled linear Cu(I) fragments.

A simple and straightforward synthesis of a new linear trinuclear Cu(I) cluster with polyphosphine ligands is presented. The reaction of this pre-organized Cu3 precursor with En ligand complexes (E = P, As; n = 2, 5) affords discrete complexes exhibiting end-on η(1)-coordination of the E2 ligands or one-dimensional coordination polymers featuring σ-1,3-bridging E5 rings, respectively.

A comparative study of the coordination behavior of cyclo-P5 and cyclo-As5 ligand complexes towards the trinuclear Lewis acid complex (perfluoro-ortho-phenylene)mercury.

Reactions of the cyclo-E5 sandwich complexes [Cp*Fe(η5-P5)] (1) and [Cp*Fe(η5-As5)] (2) with the planar Lewis acid trimeric (perfluoro-ortho-phenylene)mercury [(o-C6F4Hg)3] (3) afford compounds that show distinctly different assemblies in the solid state. The phosphorus containing ligand 1 forms dimeric coordination units with two molecules of 3, with one P atom of each cyclo-P5 ligand positioned in close proximity to the center of a molecule of 3. In contrast to the coordination behavior of 1, the arsenic analog 2 shows simultaneous interaction of three As atoms with the Hg atoms of 3. A DFT study and subsequent AIM analyses of the products suggest that electrostatic forces are prevalent over donor-acceptor interactions in these adducts, and may play a role in the differences in the observed coordination behavior. Subsequently, a series of [CpRFe(η5-P5)] (CpR = C5H5-ntBu n , n = 1-3, 6a-c) sandwich complexes was prepared and also reacted with [(o-C6F4Hg)3]. In the solid state the obtained products 7a-c with increasing steric demand of the CpR ligands show no significant change in their assembly compared to the Cp* analog 4. All of the products were characterized by single crystal X-ray structure analysis, mass spectrometry and elemental analysis as well as NMR spectroscopy and IR spectrometry.

The approach to 4d/4f-polyphosphides.

The first 4d/4f polyphosphides were obtained by reaction of the divalent metallocenes [Cp*2Ln(thf)2] (Ln = Sm, Yb) with [{CpMo(CO)2}2(µ,η2:2-P2)] or [Cp*Mo(CO)2(η3-P3)]. Treatment of [Cp*2Ln(thf)2] (Ln = Sm, Yb) with [{CpMo(CO)2}2(µ,η2:2-P2)] gave the 16-membered bicyclic compounds [(Cp2*Ln)2P2(CpMo(CO)2)4] (Ln = Sm, Yb) as the major products. From the reaction involving samarocene, the cyclic P4 complex [(Cp*2Sm)2P4(CpMo(CO)2)2] and the cyclic P5 complex [(Cp*2Sm)3P5(CpMo(CO)2)3] were also obtained as minor products. In each reaction, the P2 unit is reduced and a rearrangement occurred. In dedicated cases, a P-P bond formation takes place, which results in a new aggregation of the central phosphorus scaffold. In the reactions of [Cp*2Ln(thf)2] (Ln = Sm, Yb) with [Cp*Mo(CO)2P3] a new P-P bond is formed by reductive dimerization and the 4d/4f hexaphosphides [(Cp*2Ln)2P6(Cp*Mo(CO)2)2] (Ln = Sm, Yb) were obtained.