Di ff erent topologies in three manganese-μ-azido 1 D compounds : magnetic behavior and DFT-quantum Monte Carlo calculations †

The syntheses and structural characterization of three new monodimensional azido-bridged manganese(II) complexes with empirical formulae [Mn(N3)2(aminopyz)2]n (1), [Mn(N3)2(4-azpy)2]n (2) and [Mn(N3)2(4-Bzpy)2]n (3) (pyz = pyrazine (1,4-diazine)), 4-azpy = 4-azidopyridine and 4-Bzpy = 4-benzoylpyridine) are reported. 1 is a monodimensional compound with double EO azido bridges, 2 is an alternating monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EOdi-EE and 3 is a monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EO-di-EO-diEO-di-EO-di-EE. The magnetic properties of 1–3 are reported. Periodic DFT calculations were performed to estimate the J values and quantum Monte Carlo simulations were carried out using the calculated J values to check their accuracy in comparison with the experimental magnetic measurements. From this theoretical analysis, two appealing features of the di-EO Mn(II) compounds can be extracted: first, the exchange coupling becomes more ferromagnetic when the Mn–N– Mn bridging angle becomes larger and the spin density of the bridging nitrogen atoms has an opposite sign to that of the Mn(II) centers.


Introduction
In the last few years a plethora of polynuclear Mn(II)-azido bridging compounds have been prepared with the aim to expand the borders of the molecular magnetism field.One of the usual synthetic strategies mixes the S = 5/2 Mn(II) cation with the potentially bridging azido ligand and a terminal L ligand to obtain a large number of compounds with the general formula [Mn(N 3 ) 2 (L) 2 ].L are usually R-pyridine monodentate ligands or (L) 2 a bidentate aromatic N-donor ligand.
][3][4][5][6][7][8][9][10][11][12][13] Furthermore, the azido bridging ligand can show several coordination modes as the μ 1,3 (end-to-end, EE) or μ 1,1 (end-on, EO) modes, which can be present simultaneously in the same compound, generating a great variety of topologies in 1D-3D compounds.Taking into account that the EE coordination mode typically promotes antiferromagnetic, AF, interactions and the EO coordination mode promotes ferromagnetic, F, interactions, the great diversity of dimensionalities and topologies found in the Mn(II)-azido bridging compounds has as a consequence a great diversity in their magnetic behaviour: for example, in the 1D compound with the bulk formula [Mn(N 3 ) 2 (3-Mepy) 2 ] n (3-Mepy = 3-methylpyridine) the sequence of the azido bridges is (EE-EE-EO) n which implies an (AF-AF-F) n interaction pattern and a ferrimagnetic behaviour in a homometallic chain. 14This topological ferrimagnetism is found also in the 2D compound [Mn(4-N 3 py) 2 (N 3 ) 2 ] n (4-N 3 py = 4-azidopyridine) with the same (EE-EE-EO) alternance pattern in two dimensions.15a As a consequence of their rich magnetic and structural variety, the polynuclear Mn(II)-azido bridging compounds have also been extensively used in magneto-structural correlations and theoretical studies. 1 We present in this work three monodimensional compounds which are new good examples of the wide structural and magnetic diversity found in the [Mn (N 3 ) 2 (L) 2 ] compounds: [Mn(N 3 ) 2 (aminopyz) 2 ] n (1), [Mn(N 3 ) 2 (4-azpy) 2 ] n (2)  and [Mn(N 3 ) 2 (4-Bzpy) 2 ] n (3) ( pyz = pyrazine (1,4-diazine)), 4-azpy = 4-azidopyridine and 4-Bzpy = 4-benzoylpyridine.1 is a monodimensional compound with double EO azido bridges, 2 is an alternating monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EO-di-EE and 3 is a monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EO-di-EO-diEO-di-EO-di-EE.A preliminary crystal structure of 2 was published recently 15b but for this work we have obtained new crystals of the compound and the quality of X-ray data is improved.The magnetic properties of 1-3 are reported.The plot of χ M T vs. T for 1 can be fitted as a homogeneous 1D system with J = 1.4(1) cm −1 and the plot of χ M T vs. T for 2 can be fitted as an alternating F-AF 1D system with J 1 = −12.8(1)cm −1 and J 2 = 0.7(1) cm −1 .The exchange coupling constants J have also been calculated for 1-3 by using periodic DFT calculations.In order to check the accuracy of the calculated J values, Quantum Monte Carlo (QMC) simulations were performed to extract susceptibility curves that can be compared with the experimental ones.
In general, such a theoretical approach combining periodic calculations and QMC simulations is an accurate procedure to study the exchange interactions in extended structures due to the limitations of the fitting procedures of the experimental data.

Starting materials
Manganese(II) salts, organic N-donor ligands and sodium azide (Aldrich) were used as obtained.Aqueous hydrazoic acid is obtained with a modified Kipp's generator by decomposition of NaN 3 in H 2 SO 4 /H 2 O (1 : 3, v : v) and subsequent transfer of HN 3 into H 2 O with the aid of an inert gas stream. 16The use of diluted hydrazoic acid allows the formation of an acidic medium with pH value < 5.5 without introducing a foreign salt, thus avoiding impurities.The synthesis of 4-azidopyridine was performed according to the literature. 17aution!Azide compounds and hydrazoic acid (HN 3 ) are potentially explosive!Only a small amount of material should be prepared and it should be handled with care.

Spectral and magnetic measurements
Infrared spectra (4000-400 cm −1 ) were recorded from KBr pellets on a Perkin-Elmer 380-B spectrophotometer.Magnetic susceptibility measurements under several magnetic fields in the temperature range of 2-300 K and magnetization measurements in the field range of 0-5 T were performed with a Quantum Design MPMS-XL SQUID magnetometer at the Magnetic Measurements Unit of the University of Barcelona.All measurements were performed on polycrystalline samples.Pascal's constants were used to estimate the diamagnetic corrections, which were subtracted from the experi-mental susceptibilities to give the corrected molar magnetic susceptibilities.

IR spectra
In addition to the vibrations of the aromatic N-donor ligands, very strong absorption bands corresponding to the ν as of the azido ligands appeared at 2100 cm −1 for 1, at 2093 and 2054 cm −1 for 2, and at 2105 and 2059 cm −1 for 3.

X-ray crystallography
The X-ray single-crystal data of compounds 1-3 were collected on a Bruker SMART APEX CCD diffractometer with graphitemonochromated Mo Kα radiation (λ = 0.71073 Å).The crystallographic data, the conditions retained for the intensity data collection and some features of the structure refinements are listed in Table 1.Data processing, Lorentz-polarization and absorption corrections were performed using SMART, APEX, SAINT, and SADABS 18 computer programs.The structures were solved by direct methods and refined by full-matrix leastsquares methods, using the SHELXTL program package. 19All non-hydrogen atoms were refined anisotropically.The hydrogen atoms were located from difference Fourier maps, assigned with isotropic displacement parameters and included in the refinements by the use of HFIX ( parent C atoms) or DFIX ( parent N atoms) utilities of the SHELXTL program package.Molecular plots were performed using the Mercury 20 program.

Computational methods
The computer code employed for all the calculations is the program SIESTA [21][22][23] (Spanish Initiative for Electronic Simulations with Thousands of Atoms) that allows handling periodic systems like those reported in this study.We have employed the generalized-gradient functional proposed by Perdew, Burke and Erzernhof 24 using the DFT+U option 25 with a U value of 4.0 eV.Only valence electrons are included in the calculations, with the core being replaced by norm-conserving scalar relativistic pseudopotentials factorized in the Kleinman-Bylander form. 26The pseudopotentials are generated according to the procedure of Trouiller and Martins. 27For the Mn atoms we have employed a pseudopotential including the 3s and 3p orbitals in the basis set that we have previously tested to give accurate J values. 28We have also employed a numerical basis set of triple-ζ quality with polarization functions for the manganese atoms and a double-ζ one with polarization functions for the main group elements.Previously, we have studied the influence of two main parameters of the SIESTA code, the energy shift and the mesh cut-off, in the calculated J value for transition metal systems. 29Thus, the values of 50 meV for the energy shift and 250 Ry for the mesh cut-off provide a good compromise between accuracy and computer time to estimate exchange coupling constants.The calculated J values are obtained with the non-spin projected approach [30][31][32][33] and using the following Heisenberg-Dirac-van Vleck Hamiltonian: A detailed description of how to calculate the J values of periodic systems was previously reported by some of us. 34For compound 1, two calculations were performed to extract the unique J value as the energy difference between the high spin solution (both metal atoms in the unit cell with spin up) and the low spin solution (with the spin inversion of one of the paramagnetic centers).For compounds 2 and 3, three and six spin configurations were employed to calculate the J values.A supercell duplicating the length in the direction of the chain must be created to calculate the exchange constants; thus, for compounds 1, 2 and 3 in the periodic calculations the system has 62, 132 and 1060 atoms, respectively.Sets of 462, 12 and 1 k-points were employed, respectively, for 1, 2 and 3 to integrate the k-dependent properties.
The usual procedure to check the accuracy of the calculated J values is by the generation of the χT curves for comparison with the experimental data.The best procedure for obtaining such curves is to perform exact diagonalization of the Hamiltonian.However, such an approach cannot be applied for periodic systems and it is thus necessary to use approximate methods in order to make a comparison with the experimental data.Quantum Monte Carlo methods represent a good alternative.Quantum Monte Carlo simulations based on the directed loop algorithm method developed by Sandvik et al. 35 were performed using the ALPS 2.0 library (dirloop_sse package). 36,37or the susceptibility vs. temperature curve, usually we set 10 7 steps for simulations between 2 and 300 K and a whole simulation must be performed at each temperature.The initial 10% of the steps was employed for thermalization of the system in all calculations.However, 10 9 steps were employed below in  order to reach the convergence of the simulations using the DFT calculated J values.

Results and discussion
Description of the structures Description of the structure of [Mn(N 3 ) 2 (aminopyrazine) 2 ] n (1).Compound 1 crystallizes in the triclinic space group P1 ˉ.
Magnetic data for [Mn(N 3 ) 2 (aminopyrazine) 2 ] n (1).The variable temperature magnetic susceptibility data for the title complex were recorded between 300 and 2 K.The plot of χ M T versus T is shown in Fig. 4. Compound 1 shows a χ M T value of 4.85 cm 3 mol −1 K at room temperature, greater than the expected value for an isolated manganese atom (4.375 cm 3 mol −1 K, g = 2.0), and increases gradually as the temperature decreases to a maximum of 17.25 cm 3 mol −1 K at 5 K and then decreases quickly to 8.15 cm 3 mol −1 K at 2 K.The magnetic susceptibility behaviour of 1 indicates bulk ferromagnetic coupling in good agreement with magnetization experiments which show a quasi-saturated value of Table 3 Selected bond lengths (Å) and angles (°) for (2)  M/Nβ equivalent to five electrons (5.13) under an external field of 5 T at 2 K. Taking into account the 1D structure of 1, the fit of the magnetic data was done by using the appropriate equation 38 for homogeneous S = 5/2 chains derived from the Hamiltonian H = −JS i •S i+1 in the range 300-8 K due to the decrease of the χ M T values after the maximum.The best fit parameters were J = 1.4(1) cm −1 , g = 2.09(1).The positive J value is in accordance with the ferromagnetic coupling expected for end-on azido bridges with Mn-N-Mn bond angles of around 100°(the Mn(1)-N(11)-Mn(1′) bond angle is 101.53(5)°).The found J value is similar to that reported for the related compounds cis-[Mn(μ 1,1 -N 3 ) 2 (2-bzpy) 2 ] n (2-bzpy = 2-benzoylpyridine) 39 and trans-[Mn(μ 1,1 -N 3 ) 2 ( pyzamid) 2 ] n ( pyzamid = pyrazineamide) 40 with J values of 0.8 and 1.1 cm −1 for Mn-N-Mn angles of 100.5°(mean angle) and 97.1°r espectively.The structure of cis-[Mn(μ 1,1 -N 3 ) 2 (2-bzpy) 2 ] n shows well isolated chains but as in the case of trans-[Mn(μ 1,1 -N 3 ) 2 ( pyzamid) 2 ] n , 1 shows H bonds between chains which can be the cause of the weak antiferromagnetic interactions at low temperature as can be seen from the decrease of χ M T in the low temperature region.
Magnetic data for [Mn(N 3 ) 2 (4-Bzpy) 2 ] n (3).The plot of χ M T versus T in the 300-2 K range of temperature for compound 3 is shown in Fig. 6.Compound 3 shows a χ M T value of 4.31 cm 3 mol −1 K at room temperature, similar to the expected value for an isolated manganese atom (4.375 cm 3 mol −1 K, g = 2.0).On cooling, χ M T decreases to 3.72 cm 3 mol −1 K at 60 K. Below this broad minimum, χ M T increases to a maximum of 3.87 cm 3 mol −1 K at 20 K and then falls to 1.18 cm 3 mol −1 K at 2 K.The magnetization measurements show a saturation value close to S = 3/2 per manganese ion (inset of Fig. 6).This value is striking as the ground state of this chain should be S = 0 (Scheme 1).The χ M T decay observed below 20 K corresponds   Table 4 Selected bond lengths (Å) and angles (°) for (3)  to the population of the ground state.Similar behaviour has been observed in the 1D compound 14 trans-[Mn(N 3 ) 2 (Menic) 2 ] n showing the same topology as 3.
Theoretical study.The structural dependence of the exchange coupling in end-on azido-bridged Mn(II) dinuclear complexes was previously studied by using hybrid DFT methods. 42Thus, it is expected that end-on coordination results in ferromagnetic behavior 43 while the opposite is found for end-to-end azido bridging ligands.The calculated values for the three studied systems are given in Table 5.1][32][33] However, computer codes to calculate periodic systems usually have not implemented hybrid functionals in an efficient way; hence, we have employed the PBE functional that usually gives good results for transition metal complexes.The calculated J values show that the PBE functional reproduces properly the sign of the interaction; thus, exchange couplings through end-on azido ligands are ferromagnetic while those with end-to-end coordination are stronger and antiferromagnetic.In order to make a comparison with the experimental data, the calculated DFT J values (see Table 5) were employed along with quantum Monte Carlo simulations (see the Computational methods section) to calculate magnetic susceptibility curves that can be directly compared with the experimental data.Excellent agreement is found in Fig. 7 showing that the employed DFT methodology is able to reproduce the experimental magnetic properties of these systems.
Concerning the strength of the interaction, there is a "general belief" that the increase of the M-X-M angle for bridging ligands with a single atom in the exchange pathway enhances the antiferromagnetic contributions.As mentioned above, previously we performed a theoretical study using the B3LYP functional to analyze the dependence between J and the Mn-N-Mn bridging angle for dinuclear azido ligands, as well as for the equivalent systems with Cu(II) and Ni(II) cations.In the three cases, there is a parabolic dependence showing a maximum of the parabola that corresponds to the strongest ferromagnetic coupling. 42This maximum appears at M-N-M angle values of 85°, 102°and 112°for Cu(II), Ni(II) and Mn(II) complexes, respectively.Thus, as most of the Cu(II) complexes have a Cu-N-Cu angle larger than 85°the tendency is in agreement with the "expected" behavior, larger Cu-N-Cu increases the antiferromagnetic contribution and the complexes become less ferromagnetic.For the Ni(II) complexes, the maximum strength of the ferromagnetic interaction appears for Ni-N-Ni angle values close to those adopted in most of the structures. 44hus, most of the Ni(II) azido bridging complexes show a small dispersion in the J values being ferromagnetic, and only a reported complex with a Ni-N-Ni angle value close to 90°presents antiferromagnetic behavior. 45However, the Mn(II) complexes adopt Mn-N-Mn angle values smaller than that corresponding to the strongest ferromagnetic coupling.Thus, an increase of the Mn-N-Mn angle value enhances the ferromagnetism and such a tendency is just the opposite of the one usually assumed.This fact can be corroborated in Fig. 8 showing the dependence of the fitted J value for the reported EO azido Mn(II) complexes with the Mn-N-Mn angle value.
Table 5 Description of the bridging ligands, Mn⋯Mn and Mn-X distances (in Å) and bond angles (in degrees), and calculated exchange coupling constants J (cm −1 ) for compounds 1-3.The calculated values were obtained using the PBE functional with the SIESTA code (see the Computational methods section) and J fit values are those extracted from the experimental measurements using a ring model  The calculated spin density of compound 1 is represented in Fig. 9. Surprisingly, the spin density of the bridging nitrogen atom of the azido groups shows negative spin density (−0.07 e − ) despite the fact that the d 5 configuration of the Mn (II) cations (spin population 4.8 e − ).Such an electronic configuration implies the occupation of the "e g " antibonding orbitals with a large mixing with the ligand orbitals; thus, it should be expected that such large orbital mixing will provide the same sign in the spin density of all the nitrogen atoms coordinated to the metal (spin delocalization mechanism) as happens with the pyrazine ligands (see Fig. 8). 61,62However, the opposite sign in such atoms indicates (also appears in compounds 2 and 3) that the spin polarization mechanism is predominant; this result is different from that obtained either theoretically or experimentally for similar Cu(II) complexes. 42n order to check if the opposite sign of the spin population of the bridging nitrogen atom is an artifact of the periodic PBE pseudopotential calculations, we performed all electron 63 calculations of one Mn(II) end-on diazido dinuclear complex (FIBJIK, see Table S1 †) 48 with the hybrid B3LYP functional 64 using the Gaussian code. 65Again, such results confirm the negative spin population of the bridging nitrogen atoms (−0.05 e − ).The sign of the spin density in such nitrogen atoms is a subtle interplay between the spin delocalization of the singly-occupied antibonding e g -type orbitals and the spin polarization caused by the singly-occupied t 2g -type orbitals.Usually, in such a case with singly-occupied antibonding e gtype orbitals, the spin delocalization prevails over the spin polarization, as shown in Fig. 9 for the pyrazine ligands.However, the azido ligand has two π frontier orbitals (HOMO and LUMO) that very weakly interact with the in-phase and out-of-phase combinations of the two d x 2 −y 2 metal orbitals. 66hus, the two resulting molecular orbitals remain almost degenerate being consistent with the ferromagnetic character of the complexes with end-on azido bridging ligands.The weak interaction between the metal-azido orbitals results in a poor spin delocalization contribution (also reflected in the high spin population value of the Mn(II) centers around 4.8 e − ) that is overcome by the spin polarization.To corroborate such assumptions, we repeated the DFT calculations for the dinuclear complex replacing the Mn(II) by Ni(II) cations (unpaired electrons in the two e g -type orbitals, only spin delocalization) and V II cations (unpaired electrons in the three t 2g -type orbitals, only spin polarization).In the case of the hypothetical dinuclear Ni(II) complex the spin population in the bridging nitrogen atom is only +0.02 e − while in the equivalent V II system the value is −0.07 e − showing the predominance of the spin polarization.Finally, it is worth pointing out that the spin distribution found in the Mn(II) end-on diazido dinuclear complexes is similar to that proposed by Kahn and coworkers for Cu(II) end-on diazido dinuclear systems based on the so-called "spin polarization mechanism" 67 with opposite spin population in the bridging nitrogen atom while the terminal azido nitrogen atom has a relatively larger spin population with the same sign as the metal centers (see Fig. 8).This spin distribution was ruled out, either experimentally 68 or theoretically, 42 for dinuclear Cu(II) systems but now we have found that it is present in the Mn(II) systems.Despite this fact the presence of ferromagnetic coupling in the family of end-on diazido dinuclear complexes is due to the accidental orthogonality of the orbitals bearing the unpaired electrons. 69 compound with double EO azido bridges, 2 is an alternating monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EO-di-EE and 3 is a monodimensional compound with double end-on and double end-to-end azido bridges in the sequence di-EO-di-EO-diEO-di-EO-di-EE.Periodic calculations using PBE functionals to calculate the J values provide excellent agreement with the experimental data.The comparison was made by using quantum Monte Carlo simulations that allows the calculation of magnetic susceptibility curves for periodic systems.Also, it is worth noting that the theoretical analysis allows one to propose that in the range of experimental Mn-N-Mn bridging angle values, the calculated and observed trend is that larger angles result in stronger ferromagnetic coupling.Such a tendency is just the opposite of that usually expected, and is found in Cu(II) and Ni(II) complexes.The DFT spin density of the bridging nitrogen atoms of the azido ligands has the opposite sign of that of the Mn(II) centers.This result is not common because usually in the cases when the metal centers have unpaired electrons in the antibonding orbitals, the large metal-ligand mixing of orbitals results in that the spin delocalization effects are predominant over the spin polarization.In the studied end-on azido Mn(II) systems, the weak metal-ligand interaction is reflected in that the resulting molecular orbitals are close to the degeneracy, and that the spin polarization effects induced by the three singly-occupied "non-bonding" t 2g -type orbitals of the Mn(II) centers overcome the delocalization effect of the e g -type orbitals.Logically, such "special" behavior cannot be found in Cu(II) or Ni(II) equivalent complexes because the t 2g -type orbitals are doubly-occupied.

Fig. 6 χ
Fig. 6 χ M T vs. T plot in the 300-2 K range of temperatures for 3. Inset: molar magnetization at 2 K for 3.

Fig. 5 χ
Fig. 5 χ M T vs. T plot in the 300-2 K range of temperatures for 2. The solid line shows the best fit as an alternating chain (see the text).

Fig. 4 χ
Fig. 4 χ M T vs. T plot in the 300-2 K range of temperatures for 1.The solid line shows the best fit as a uniform chain (see the text).

Fig. 7 χ
Fig. 7 χ M T vs. T plot in the 300-2 K range of temperatures for 1 (squares), 2 (triangles) and 3 (circles).The χ M T values obtained by means of quantum Monte Carlo simulations using the calculated DFT J values are plotted as continuous lines.

Fig. 9
Fig. 9 Calculated spin density of compound 1. White and blue isodensity surfaces indicate positive and negative spin populations, respectively, with a value of 0.003 e − bohr −3 .

Table 1
Crystal data and structure refinement for complexes 1-3