General Relativistic Magnetospheres of Slowly Rotating and Oscillating Magnetized Neutron Stars

We study the magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with $m=0,1$ are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode $(l,m)=(2,1)$, can be a factor $\sim8$ larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface as small as $\eta=0.05 \ \Omega \ R$. The results obtained in this paper clarify the extent to which stellar oscillations are reflected in the time variation of the physical properties at the surface of the rotating neutron star, mainly by showing the existence of a relation between $P\dot{P}$ and the oscillation amplitude. Finally, we propose a qualitative model for the explanation of the phenomenology of intermittent pulsars in terms of stellar oscillations that are periodically excited by star glitches.Comment: 13 pages, 4 figures, submitted to MNRA

Last Mile Delivery with Parcel Lockers: evaluating the environmental impact of eco-conscious consumer behavior

In recent months, online sales have experienced a sharp surge also due to the COVID pandemic. In this paper, we propose a new location and routing problem for a last mile delivery service based on parcel lockers and introduce a mathematical formulation to solve it by means of a MIP solver (Gurobi).The presence of parcel locker stations avoids the door-to-door delivery by companies but requires that consumers move from home to collect their parcels. Potential location of locker stations is known but not all of them need to be opened. The problem minimizes the global environmental impact in terms of distances traveled by both the delivery company and the consumers deciding the optimal number of stations that have to be opened.How much do the number and location of lockers impact on environment? Is the behavior of consumers a critical aspect of such optimization? To this aim we have solved 1680 instances and analyzed diferent scenarios varying the number of consumers and potential parcel lockers, the maximum distance a consumer is willing to travel to reach a locker station, and the maximum distance we may assume the same consumer is willing to travel by foot or by bicycle.The experimental results draw interesting conclusions and managerial insights providing important rules of thumbs for environmental decision makers.Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/

Addition of alkynes at bridging vinyliminium ligands in diiron complexes: Unprecedented diene formation by enyne-like metathesis

The zwitterionic bridging vinyliminium complex [Fe(2){mu-eta 1: eta 3-C(Tol)]=C(CS2)C] = N(Me)2}(mu-CO)(CO)( Cp)(2)] (5a) undergoes the addition of two equivalents of MeO(2)C-C C-CO(2)Me affording the bridging bis-alkylidene complex [Fe(2){mu-eta 1: eta 3-C(Me)C{C(CO(2)Me)C(CO(2)Me)CSC(CO(2)Me)C(CO(2)Me)S}CNMe(2)}(mu-CO)( CO)(Cp)(2)] (6). One alkyne unit inserts into a C-CS(2) bond of the bridging ligand, with consequent rearrangement that leads to the formation of a diene. The reaction shows analogies with the enyne metathesis. The second alkyne is incorporated into the bridging frame via cycloaddition at the thiocarboxylate function, affording a 1,3-dithiolene. The complexes [Fe(2){mu-eta(1): eta(3)-C(R')]=C(CS(2))C=N(Me)(R)}(mu-CO)(CO)(Cp)(2)] (R = Xyl, R' = Tol, 5b; R = p-C(6)H(4)OMe, R' = Me, 5c; Xyl = 2,6-Me(2)C(6)H(3)), treated with MeO(2)C-C C-CO(2)Me and then with HBF(4), undergo the cycloaddition of the alkyne with the dithiocarboxylate group and protonation of the dithiocarboxylate carbon, affording the complexes [Fe(2){mu-eta 1: eta 3-C(R')]=C{C(H)SC(CO(2)Me)C(CO(2)Me)S}C]=N(Me)(R)}(mu-CO)(CO)(Cp)(2)][BF(4)] (R = Xyl, R' = Tol, 7a; R= p-C(6)H(4)OMe, R' = Me, 7b), respectively. The X-ray molecular structure of 6 has been determined

Reactions of diiron MU-aminocarbyne complexes containing nitrile ligands

The acetonitrile ligand in the mu-aminocarbyne complexes [Fe-2{mu-CN(Me) R}(mu-CO)( CO)(NCMe)(Cp)(2)][SO3CF3] (R = Me, 2a, CH2Ph, 2b, Xyl, 2c) (Xyl = 2,6-Me2C6H3) is readily displaced by halides and cyanide anions affording the corresponding neutral species [Fe-2{mu-CN( Me) R}(mu-CO)(CO)(X)(Cp)(2)] (X = Br, I, CN). Complexes 2 undergo deprotonation and rearrangement of the coordinated MeCN upon treatment with organolithium reagents. Trimethylacetonitrile, that does not contain acidic a hydrogens has been used in place of MeCN to form the complexes [Fe-2{mu-CN(Me)R}(mu-CO)(CO)(NCCMe3)(Cp)(2)][SO3CF3] (7a-c). Attempts to replace the nitrile ligand in 3 with carbon nucleophiles ( by reaction with RLi) failed, resulting in decomposition products. However the reaction of 7c with LiC= CTol (Tol = C6H4Me), followed by treatment with HSO3CF3, yielded the imino complex [Fe-2{mu-CN(Me) Xyl}(mu-CO)(CO) {N(H) C(C= CC6H4Me-4) CMe3}(Cp)(2)][SO3CF3] (8), obtained via acetilyde addition at the coordinated NCCMe3

Addition of protic nucleophiles to alkynyl methoxy carbene ligands in diiron complexes

Different protic nucleophiles (i.e. Ph2C=NH, PhSH, MeCO2H, PhOH) can be added to the C equivalent to C bond of [Fe-2{mu-CN(Me)(Xyl)}-(mu-CO)(CO){C(OMe)C equivalent to CTol}(CP)(2)][SO3CF3] (1), affording new diiron alkenyl methoxy carbene complexes. The additions of Ph2C=NH and MeCO2H are regio and stereoselective, resulting in the formation of the 5-aza-1-metalla-1,3,5-hexatriene [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(OMe)C beta H=C-gamma(Tol)(N=CPh2)}(CP)(2)][SO3CF3](2), and the 2-(acyloxy)alkenyl methoxy carbene complex [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(OMe)C beta H=C-gamma(Tol)OC(O)Me)}(CP)(2)][CF3SO3] (5); the E isomer of the former and the Z of the latter are formed exclusively. Conversely, the addition of PhSH is regio but not stereoselective; thus, both the E and Z isomers of [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(OMe)C beta H=C-gamma(Tol)(SPh)}(CP)(2)][SO3CF3](3) are formed in comparable amounts. Compounds 3 and 5 are demethylated upon chromatography through Al2O3, resulting in the formation of the acyl complexes [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(O)C beta H=C-gamma(Tol)(SPh)}(Cp)(2)](4) and [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(O)C beta H=C-gamma(Tol)OC(O)Me}(CP)(2)](6), respectively, both with a Z configured C-beta=C-gamma bond. Finally, the reaction of 1 with PhOH proceeds only in the presence of an excess of Et3N affording the 2-(alkoxy)alkenyl acyl complex [Fe-2{mu-CN(Me)(Xyl)}(mu-CO)(CO){C-alpha(O)C beta H=C-gamma(Tol)(OPh)}(CP)(2)](7). The crystal structures of 4 center dot CH2Cl2 and 7 center dot 0.5CH(2)Cl(2) have been determined by X-ray diffraction experiments

Diiron-aminocarbyne complexes with amine or imine ligands: C-N coupling between imine and aminocarbyne ligands promoted by tolylacetilyde addition to [Fe2{m-CN(Me)R}(m-CO)(CO)(NH=CPh2)(Cp)2][SO3CF3]

A terminally coordinated CO ligand in the complexes [Fe2{m-CN(Me)R}(m-CO)(CO)2(Cp)2][SO3CF3] (R = Me, 1a; R = Xyl, 1b; Xyl = 2,6-Me2C6H3), is readily displaced by primary and secondary amines (L), in the presence of Me3NO, affording the complexes [Fe2{m-CN(Me)R}(m-CO)(CO)(L)(Cp)2][SO3CF3] (R = Me, L = NH2Et, 4a; R = Xyl, L = NH2Et, 4b; R = Me, L = NH2Pri, 5a; R = Xyl, L = NH2Pri, 5b; R = Xyl, L = NH2C6H11, 6; R = Xyl, L = NH2Ph, 7; R = Xyl, L = NH3, 8; R = Me, L = NHMe2, 9a; R = Xyl, L = NHMe2, 9b; R = Xyl, L= NH(CH2)5, 10). In the absence of Me3NO, NH2Et gives addition at the CO ligand of 1b, yielding [Fe2{CN(Me)(Xyl)}(m-CO)(CO)C(O)NHEt(Cp)2] (11). Carbonyl replacement is also observed in the reaction of 1a-b with pyridine and benzophenone imine, affording [Fe2{m-CN(Me)R}(m-CO)(CO)(L)(Cp)2][SO3CF3] (R= Me, L= Py, 12a; R = Xyl, L= Py, 12b; R= Me, L= HN=CPh2, 13a; R = Xyl, L= HN=CPh2, 13b). The imino complex 13b reacts with p-tolylacetylide leading to the formation of the m-vinylidene-diaminocarbene compound [Fe2-C=C(Tol)C(Ph)2N(H)CN(Me)(Xyl)(m-CO)(CO)(Cp2)] (15) which has been studied by X-ray diffraction