& Spin Crossover | Hot Paper |

Light-Induced Spin Transitions in Copper-Nitroxide-BasedSwitchable Molecular Magnets: Insights from Periodic DFT + UCalculations

Roc�o S�nchez-de-Armas,[a] Norge Cruz Hern�ndez,[b] and Carmen J. Calzado*[a]

Abstract: The electronic structure and magnetic interactionsof three members of the breathing crystal Cu(hfac)2L

R family(hfac = hexafluoroacetylacetonato, LR = pyrazole-substitutednitronyl nitroxides with R = Me, Et, Pr, iPr, Bu ), mainly Cu(h-fac)2L

Pr (1), Cu(hfac)2LBu·0.5 C8H18 (2) and Cu(hfac)2L

Bu·0.5 C8H10(3), have been analyzed by means of periodic plane-wavebased DFT + U calculations. These CuII-nitroxide based mo-lecular magnets display thermally and optically inducedswitchable behavior and light-induced excited spin statetrapping phenomena. The calculations confirm the presenceof temperature-dependent exchange interaction within thespin triads formed by the nitroxide-copper(II)-nitroxide units,in line with the changes observed in the effective magneticmoment. Moreover, they quantify the interchain interaction

mediated by the terminal nitroxide group of two spin triadsin neighboring polymer chains. This interaction competeswith the exchange interaction within the spin triads at hightemperature, and introduces 1D exchange channels that donot coincide with the polymeric chains. The density of statesreveal that the low-lying conduction states potentially in-volved in the UV/Vis transitions are located on the nitroxideradicals, the hfac groups and the Cu atoms. Then, the densi-ty of states is almost independent of the solvent and the Rgroup. This suggests the possibility of light-induced spinswitching for other members of this family. The 500 nmband of the low-temperature phase can be ascribed to aligand-to-metal charge transfer transition between the nitro-xide and Cu bands.

Introduction

Switchable molecular compounds attracted much attention inthe last several decades, due to their potential applications inmagnetic data storage, quantum computing, spintronics, andrelated areas.[1] Spin-crossover (SCO) complexes are among themost promising candidates, most of them based on iron(II),where the switching between different spin states can be in-duced by different external stimuli such as temperature, pres-sure, or light.[2, 3] To date, the light-induced excited spin statetrapping (LIESST) phenomenon has mostly been observed inSCO complexes of iron(II)[4, 5] and iron(III).[1, 6]

Recently, a family of switchable compounds with SCO-likebehavior and LIESST-like phenomena, based on CuII and nitron-yl nitroxide (NIT) ligands have been reported.[7–14] These com-pounds of formula Cu(hfac)2L

R consist of heterospin polymer-chain complexes of CuII hexafluoroacetylacetonato (hfac) withstable pyrazole-substituted nitronyl nitroxides, LR, with R = Me,Et, Pr, iPr, Bu. Two different motifs of the polymer chains canbe obtained (Figure 1): a head-to-tail motif leading to the for-mation of two-spin CuII-nitroxide clusters, and a head-to-headmotif, resulting in alternating one-spin CuII and three-spin NIT-CuII-NIT clusters (spin triads).

These Cu(hfac)2LR systems present magnetic anomalies that

can be thermally and optically induced, similar to the classicalspin crossover, but different in nature. The crystal undergoesreversible structural rearrangements, that modify the exchangeinteraction between the CuII and the nitroxide spins when thetemperature changes (Figure 2). At high temperatures thespins are weakly ferromagnetically coupled (weakly exchange-coupled state, WS), with J�10–20 cm�1,[15, 16] whereas at lowtemperatures the CuII and the nitroxide spins are coupled by astrong antiferromagnetic interaction,[16] with J��100–200 cm�1, and the spin triad converts to the strongly coupledspin state with a total spin S = 1/2 (strongly exchange-coupledstate, SS). As a result, the effective magnetic moment meff de-creases when the temperature drops (Figure 2). The change ofthe magnetic moment Dmeff can be gradual or abrupt depend-ing on R[17] and the solvent. The impact of the solvent hasbeen associated to the relative orientation of the solvent

[a] Dr. R. S�nchez-de-Armas, Dr. C. J. CalzadoDepartamento de Qu�mica F�sicaUniversidad de Sevilla41012 (Spain)E-mail : calzado@us.es

[b] Dr. N. Cruz Hern�ndezDepartamento de F�sica Aplicada I, Escuela Polit�cnica SuperiorUniversidad de Sevilla41011 (Spain)

Supporting information including structural parameters and unit cell repre-sentation for compounds 1–3, relative energies of the four magnetic solu-tions and interaction parameters for compounds 2 and 3 using different Uvalues, spin density maps of compound 3, DOS for Cu(hfac)2L

Pr obtainedfrom PBE + Ud calculations for LT and HT phases, a VASP input file for theFM solution of compound 1, and the ORCID identification number(s) for theauthor(s) of this article can be found under :https ://doi.org/10.1002/chem.201803962.

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Full PaperDOI: 10.1002/chem.201803962

http://orcid.org/0000-0003-3841-7330http://orcid.org/0000-0003-3841-7330http://orcid.org/0000-0003-3841-7330https://doi.org/10.1002/chem.201803962

molecules with respect to the spin triads.[18, 19] The large differ-ence in Cu�O bond lengths between SS and WS states is re-sponsible for the significant change of the unit cell volumeduring the spin transition, and for this reason these systemshave been called breathing crystals.[10]

The photoswitching in the Cu(hfac)2LR family has been ob-

served for the first time for the Cu(hfac)2LPr complex,[12] and

also documented for Cu(hfac)2LBu, with propyl-benzene and m-

xylene as solvents,[21] using EPR[12, 21] and time-resolved EPR.[22]

The phenomenon has also been reported in a related polymerchain complex of Cu(hfac)2 with a tert-butylpyrazolylnitroxideradical.[23] Illumination with light at very low temperature in-

duced a metastable WS state, where the system remainstrapped for hours. The relaxation to the ground SS state isnonexponential and has a self-decelerating character.[21] Theprocess has been also analyzed by femtosecond optical spec-troscopy for a Cu(hfac)2L

Pr complex.[13] Figure 3 shows the UV/Vis absorption spectra of the WS and SS states of Cu(hfac)2L

Pr,which are dominated by the nitronyl nitroxide bands in thel= 450–700 nm region.[13, 14] Similar UV/Vis spectra have beenreported for the related Cu(hfac)2L

Me and Cu(hfac)2LEt-CP com-

plexes (where LEt-CP = 2-(1-ethylpyrazol-4-yl)-4,5-bis(spirocyclo-pentane)-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl).[14] The mostsignificant difference between both states is a strong band at

Figure 1. Head-to-tail (a) and head-to-head (b) motifs in the heterospin Cu(hfac)2LR polymer-chain complexes. Red, blue, gray and orange tubes represent O,

N, C and Cu atoms, respectively. Orange and blue boxes represent the two-spin Cu-NIT clusters and three-spin NIT-Cu-NIT clusters, respectively. Hydrogenatoms, -CF3 and -CH3 groups have been omitted for clarity.

Figure 2. (a) View along b axis of the Cu(hfac)2LPr complex. H and F atoms are omitted for clarity. Blue and red polyhedra represent CuO6 and CuO4N2 octahe-

dron, respectively. The dotted red lines represent the interchain interactions. (b) Magnetic interactions along the polymer chain. The dotted green and bluelines represent the Cu-NIT interaction within the triad (J) and the interaction between the spin-triad and the one-spin CuO4N2 cluster (J’). Schematic represen-tation of the elongated octahedral CuO6 sites in the spin triad for the LT (c) and HT (d) phases. (e) Temperature dependence of the effective magneticmoment meff(T) of Cu(hfac)2L

Pr (1) (red circles), Cu(hfac)2LBu·0.5 C8H10 (2) (blue squares), Cu(hfac)2L

Bu·0.5 C8H18 (3) (green triangles).Reproduced from Ref. [20] withpermission from the PCCP Owner Societies.

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l= 500 nm observed only at low temperature (SS state), andtentatively assigned to a charge transfer band (metal-to-ligand[13] or ligand-to-metal).[13, 14] A further feature is the dis-placement of the structure band centered at ~650 nm, associ-ated with the nitroxide radicals, to a higher energy.[14] Thebleaching of optical density in the l= 500–600 nm region hasbeen employed to monitor the photoinduced SS$WS conver-sion and provide information about its timescale. A three-statemechanism involving the SS, WS and the photoexcited E*states has been suggested, but the nature of this E* state hasnot been identified, and the mechanism of the ultrafast spinstate photoswitching is far from being fully understood todate.[13, 22, 23]

In this context, information regarding the available electron-ic states that could connect the SS and WS states in the photo-induced transition would be extremely useful. At present, theo-retical studies of breathing crystals are scarce, and have beenmostly oriented to the evaluation of the coupling within thespin triads and the interchain couplings, using different ap-proaches such as the difference dedicated configuration inter-action (DDCI) method,[24] complete active-space second-orderperturbation theory (CASPT2),[25] or broken symmetry DFT-based calculations.[19, 26] Regarding periodic treatments, it isworth mentioning a recent study by Morozov et al. ,[27] in whichthe periodic generalized gradient approximation (GGA + U) ap-proach has been applied to describe the magnetic couplingwithin the spin triads of two related Cu(hfac)2L

Me and Cu(h-fac)2L

Et polymer chains. A reduced crystal symmetry was em-ployed to decrease the number of atoms in the unit cell andconsequently the computational cost, but in doing so the in-terchain interactions are neglected.

Therefore, the aim of this work is to obtain a reliable de-scription of the electronic structure of the breathing crystalfrom state-of-the-art quantum chemistry approaches. We useplane wave-based periodic calculations for three representativemembers of the breathing crystal Cu(hfac)2L

R family : Cu(h-fac)2L

Pr (1), Cu(hfac)2LBu·0.5 C8H18 (2) and Cu(hfac)2L

Bu·0.5 C8H10(3). Our DFT + U calculations on the low and high temperaturephases provide information about the relative stability of dif-ferent spin arrangements in the spin triads and the isolatedCuO4N2 units, estimates of the magnetic coupling interactions

between the nitroxide and CuII spins within the triads, andconfirm the presence of antiferromagnetic interactions be-tween the polymeric chains mediated by the terminal nitronyl-nitroxide groups. Additionally, the density of states furnisheskey features of the low-lying electronic states of the low-tem-perature (LT) and high-temperature (HT) phases that couldhelp in the elucidation of the states involved in the photo-switching process, and could gain insight into its whole mech-anism. The density of states reveal that the low-lying conduc-tion states potentially involved in the UV/Vis transitions aremainly located on the nitronyl-nitroxide radicals, the hfacgroups, and the Cu atoms, that is, located on common compo-nents of all the members of the breathing crystal family. Then,the density of states is almost independent of the solvent andthe R group substituting the pyrazole moiety. Hence, the simi-larities found in the density of states for these three com-pounds suggest the potential occurrence of the LIESST-likephenomenon in other members of the breathing crystal family.

Description of the systems

Three compounds Cu(hfac)2LPr, Cu(hfac)2L

Bu·0.5 C8H18 andCu(hfac)2L

Bu·0.5 C8H10 (1–3) of the breathing crystal family havebeen considered, which have been extensively characterized inthe past by X-ray diffraction, SQUID magnetometry, EPR andUV/Vis spectroscopies.[11–13, 15, 19–21, 28–31] In all cases, the polymerchains present a head-to-head coordination motif with alter-nating one-spin CuII in CuO4N2 units and three-spin nitroxide-CuII-nitroxide CuO6 clusters (Figure 2 a). Compounds 1–3 differon the R substituent of the nitroxide ligand (R = Pr for 1, Bu for2 and 3) and the organic solvent (solv) included into the crys-tal structure (solv = octane C8H18 for 2 and ortho-xylene C8H10for 3), and have been selected as representative examples ofthe differential role of both the substituent[17] and the sol-vent[18, 19] on the magnetostructural transition.

At low temperature the nitronyl-nitroxide radicals occupyequatorial positions in the elongated CuO6 octahedral units(Figure 2 c), whereas they occupy the axial position in the CuO6octahedron in the high temperature structure (Figure 2 d). As aresult of the rotation of the elongated Jahn–Teller axis in theCuO6 octahedron with temperature, the Cu-nitroxide distancesare elongated, and more importantly the Cu 3d and p-nitro-xide orbitals carrying the unpaired electrons adopt a quasi-or-thogonal relative orientation, as demonstrated by the ab initiocalculations carried out by one of us on theCu(hfac)2L

Bu·0.5 C8H18 (2) complex.[24] Table 1 shows the Cu�O

bond distances in the CuO6 octahedron for the two structuresconsidered (LT and HT phases) for each compound. The bondangle between the nitroxide group and the Cu ion is also re-ported for each structure. Additional structural information isreported in Table S1 (Supporting Information) for compounds1–3, together with plots of the unit cell for both phases in Fig-ure S1. Consequently, these structural changes have a dramaticimpact on the exchange interactions between the Cu and ni-tronyl-nitroxide spins in the triad, which are significantly modi-fied during the SS$WS conversion. In contrast, the one-spin

Figure 3. UV/Vis absorption spectra of Cu(hfac)2LPr (1) recorded at 80–300 K.

Reprinted with permission from Ref. [22]. Copyright 2012 American ChemicalSociety.

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CuO4N2 units remain magnetically isolated over the wholerange of temperatures.

The three compounds experience gradual magnetostructuraltransitions, that is, the magnetic susceptibility changessmoothly with temperature (Figure 2 e). The complex Cu(h-fac)2L

Pr (1) presents a gradual transition on a broad tempera-ture range T = 100–250 K.[10] Moreover, a structural phase tran-sition occurs at T = 226 K;[11, 28] the crystal belongs to the P21/cspace group at low temperature, while the space group sym-metry is C2/c at T>226 K. The complex Cu(hfac)2L

Bu·C8H10 (3)has a similar behavior, although the transition region is broad-er (100–300 K), and the transition temperature is shifted by~60 K to lower temperatures. Complex Cu(hfac)2LBu·C8H18 (2)represents an intermediate case between abrupt and gradualspin transition,[11] with a narrower temperature range, 75–175 K, and a transition temperature of ~130 K.[19]

Computational Details

The crystals have been studied within density functional theory(DFT) using the Vienna ab initio simulation package (VASP)code,[32–35] employing the generalized gradient approximation(GGA) with the Perdew–Burke–Ernzerhof exchange-correlationfunctional[36] and projector-augmented wave (PAW) potentials.[37, 38]

Effective Hubbard corrections of 9.8 eV and 5 eV have been usedto describe the localized Cu 3d orbitals and O 2p orbitals, respec-tively, using Dudarev’s approach,[39] as in the previous study by Mo-rozov et al.[27, 40] on the related Cu(hfac)2L

Me and Cu(hfac)2LEt com-

pounds. The PBE + U method is considered as a practical alterna-tive to hybrid methods when plane-wave basis sets are used,where the evaluation of the Fock exchange terms is computation-ally prohibitive.[41–43] The main weakness of the + U correction isprecisely the choice of U. Some attempts have been made in thepast for obtaining estimates of the U value from an unbiased andindependent evaluation, based on extended configuration interac-tion (CI) calculations on representative fragments of the system.[44]

However, this approach does not work for the breathing crystals,due to the p-nature of the active orbitals of the nitronyl-nitroxideradicals, responsible for a frame of low-lying states in competitionwith those required for the evaluation of U. Instead, we havechecked the impact of the U value by a complementary set of cal-culations with U(Cu) = 2, 7 and 9.8 eV.

Valence electrons are described using a plane-wave basis set witha cutoff of 500 eV and a G-centered grid of k-points is used for in-

tegrations in reciprocal space, where the smallest allowed spacingbetween k-points is set at 0.2 ��1.[45] Van der Waals interactionswere taken into account through the Tkatchenko–Schefflermethod.[46] Hereafter, PBE + Ud(n) refers to calculations with U =n eV correction in Cu 3d orbitals and PBE + Ud + Up refers to calcu-lations with Ud = 9.8 eV for Cu 3d and Up = 5 eV for O 2p orbitals,including Van der Waals corrections in all cases.

For each crystal we have considered the experimental struc-ture[11, 20] at two temperatures representative of the LT and HT struc-tures (50 and 240 K, 100 and 295 K, 60 and 240 K for compounds1–3, respectively) and single-point calculations have been done fordifferent magnetic solutions. Electronic relaxation has been per-formed until the change in the total energy between two consecu-tive steps is smaller than 10�6 eV. Unlike the previously reportedperiodic calculations on breathing crystals,[11, 20, 29] in our calcula-tions the experimental space group for each system is employed(P1̄ for compounds 2 and 3 in both temperatures,[11, 20] P21/c andC2/c for compound 1 at low and room temperatures,[29] respective-ly), with unit cells of 552, 170 and 162 atoms for compounds 1, 2and 3 respectively. Hence, our calculations take into account theinterchain interactions, neglected in the works by Morozov et al.[27]

as a consequence of the reduced crystal symmetry used in theircalculations.

Results

Periodic plane wave-based PBE + U calculations have been per-formed to establish the electronic structure at low and hightemperatures of three members of the Cu(hfac)2L

R family. Thegoal is two-fold: first, to establish a reliable procedure for de-scribing the whole crystal, explicitly including the interchain in-teractions, relevant in the description of the spin dynamics,and second, to interpret the origin of the main bands on theUV/Vis spectra with a potential role in the photoswitching pro-cess.

Impact of the U value on the relative energies of the mag-netic solutions

Comparing with calculations on fragments modeling the spintriads,[19, 24–26] the periodic calculations are free of border ef-fects, take into account all the groups and atoms of the realcrystal without any simplification, and explicitly deal with theinterchain interactions, considered as relevant for the spin dy-namics at high temperature. However DFT based periodic cal-culations are functional-dependent and in the case of DFT + Ucalculations, the choice of U is a relevant step. Four different Uvalues are considered, as described above, and their impact onthe a) relative energy of the magnetic solutions for the LT andHT structures, b) density of states, and c) amplitude and natureof the magnetic interactions will be analyzed.

The unit cell for Cu(hfac)2LBu·0.5 C8H18 (2) and

Cu(hfac)2LBu·0.5 C8H10 (3) compounds contains four unpaired

electrons: three on the spin triad and one on the CuO4N2 unit.Hereafter Cu1 and Cu2 represent the copper atom in the spintriad and CuO4N2 units, respectively. Three different magneticsolutions have been calculated, corresponding to different spindistributions jNIT-Cu1-NIT···Cu2 j (Figure 4 for compound 2, Fig-ure S2 in Supporting Information for compound 3). Table 2 re-

Table 1. Main geometrical parameters within the spin triad for the LT andHT structures of compounds 1–3. Cu�OL and Cu�Ohfac represent the bonddistances between the Cu and O atoms in the nitronyl-nitroxide and hfacgroups, respectively. All parameters from X-ray diffraction data.[11, 20]

Cu(hfac)2LR·solv T [K] Cu�OL [�] Cu-OL-N [8] Cu�Ohfac [�] Cu�Ohfac [�]

1 R = Pr 50 1.994 123.3 2.274 1.949240 2.256 127.1 2.018 1.960

2 R = Busolv = octane

100 2.034 123.1 2.201 1.998

295 2.352 125.3 1.971 1.9613 R = Busolv = o-xylene

60 2.003 126.1 2.301 1.963

240 2.206 128.5 2.004 1.975

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ports the results obtained for PBE + Ud + Up. The rest of the ex-plored U values can be found in Tables S2 and S3. At low tem-perature, the ground state corresponds to the antiferromag-netic (AFM) solution with Sz = 0, "#" . . . #j j, where the two ni-tronyl-nitroxide groups present an antiferromagnetic coupling

with the Cu1 center, and the two Cu centers are coupled ferro-magnetically. This solution is almost degenerate with theAFM2 solution "#" . . . "j jwith Sz = 1, differing from the AFMsolution by the relative orientation of the Cu spins. This con-firms that the CuO4N2 clusters are magnetically isolated. Theferromagnetic solution """ . . . "j j with Sz = 2 is high in energy,as expected for the low-temperature strongly-coupled phase.At high temperature, the three solutions are almost degener-ate; the ferromagnetic solution being the most stable one(Table 2). Again this result is in agreement with the experimen-tal data for the high-temperature weakly-coupled phase. Addi-tionally, in the case of Cu(hfac)2L

Bu·0.5 C8H10, it has been possi-ble to isolate an additional solution (AFM4) for the HT struc-ture, corresponding to the distribution ""# . . . "j j (Figure S2).When this distribution is replicated, the interaction betweenthe terminal NO groups of two neighbor spin triads is antifer-romagnetic, while in the rest of considered broken-symmetrysolutions, all the interactions between neighbor spins triadsare ferromagnetic (Figure S2).This solution provides additionalinformation about the amplitude and nature of the interchaininteraction mediated by the terminal nitroxide groups in twoneighbor chains.

In the case of the Cu(hfac)2LPr (1) complex, the unit cell con-

tains four spin triads and four CuO4N2 units. The four consid-ered solutions are schematically represented in Figure 5, to-gether with the projections of the spin density on the acplane. Solution AFM3 differs from AFM2 by the antiferromag-netic interchain interaction, Jchain.

The relative energy of the four solutions with different Uvalues is shown in Table 3. They present a strong dependenceon the U value for the LT structures, whereas the energy gapsare almost insensitive to U for the HT solutions, except forPBE + Ud(2). The relative energies of the explored solutions arein good agreement with the experimental data, except forPBE + Ud(2) where an AFM ground state is predicted at HT, al-though the AFM-FM gap is strongly modulated by the chosenU value. At low temperature, the AFM3 solution is the moststable one, which indicates the presence of an antiferromag-netic interchain interaction, as obtained forCu(hfac)2L

Bu·0.5 C8H10 (3). This AF interchain interaction hasbeen also evidenced in our previous theoretical study onCu(hfac)2L

Bu·0.5 C8H18 (2).[24] Hence, in these systems two neigh-

boring chains are magnetically connected through the terminalnitroxide groups of the three-spin clusters . This intercluster in-teraction gives 1D exchange channels that do not coincidewith the polymeric chains, but rather spread across them.[26]

The presence of this interaction is of vital importance for theinterpretation of the spin dynamics and relaxation of the pho-toinduced WS state at low temperature, as discussed below.Since the NO···NO contacts among the polymer chains areubiquitous to all these compounds, it is reasonable to suggestthat this 1D magnetic ordering is a common feature of thewhole family.

The spin density values on the spin triad atoms are shownin Table 4 for the ground state of each structure at PBE + Ud +Up level and represented in Figures 4 and 5. Regarding the ni-troxide groups, the spin density is not homogeneously

Figure 4. (a) View along the a axis of the unit cell for compound 2, in themiddle the nitroxide-Cu-nitroxide spin triad, and in the corners the one-spinCuO4N2 clusters. (b) Spin density maps of compound 2 for the AFM (top),AFM2 (middle), and FM (bottom) solutions. Four unit cells are represented,delimited by a dashed line. View along the a axis. (c) Schematic representa-tion of the three considered magnetic solutions for compounds 2 and 3.Blue and red arrows represent, respectively, the Cu and nitronyl-nitroxidespins of the three-spin cluster (spin triad). Green arrow represents the one-spin CuO4N2 cluster.

Table 2. Relative stability (per NIT-Cu-NIT…Cu unit) and magnetic cou-pling constants for Cu(hfac)2L

R·solv compounds (1–3) at PBE + Ud + Uplevel. Intracluster coupling J, the interaction between the spin triad andthe CuO4N2 units J’ and the interchain interactions Jchain are reported. Allvalues are in cm�1.

Cu(hfac)2LR·solv Phase AFM AFM2 FM J J’ Jchain

1 R = Pr LT 0.0 0.0 737.0 �368.9 0.0 �2.8HT 27.8 27.8 0.0 13.5 0.0

2 R = Bu, solv = octane LT 0.0 �10.1 520.5 �260.2 �10.1HT 38.5 38.5 0.0 19.3 0.0

3 R = Bu, solv = o-xylene LT 0.0 0.1 644.4 �322.2 0.1HT 48.2 48.2 0.0 24.1 0.0 �5.8

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distributed, being localized with advantage in the terminal ni-troxide groups, in good agreement with the picture providedby our previous calculations at CASSCF/DDCI level,[24] and thespin density maps obtained from polarized neutron diffractionexperiments on similar head-to-head nitroxide-Cu-nitroxidesystems.[47] This distribution favors the interactions amongneighbor chains mediated just by these terminal NO groups.

Evaluation of the magnetic interactions

The evaluation of the interaction parameters from periodicDFT-based calculations relies on the mapping between themagnetic solutions and the diagonal terms of the Heisenberg–

Dirac–Van-Vleck (HDVV) Hamiltonian.[48, 49] The HDVV Hamiltoni-an takes the form in Equation (1):

ĤHDVV ¼ �2X

i

EAFM3 � EFM ¼ 2J þ J0 þ Jchain=2ð Þ ð4Þ

EAFM4 � EFM ¼ J þ JNO þ Jchain ð5Þ

The JNO interaction has been neglected, since our previousDDCI calculations[24] on Cu(hfac)2L

Bu·0.5 C8H18 (2) demonstratedthat this interaction is almost null, regardless of the tempera-ture. The J values obtained at PBE + Ud + Up level for the threesystems in the LT and HT phases are collected in Table 2. In allcases, the periodic calculations predict a strong antiferromag-netic interaction between nitronyl-nitroxide and Cu spins at LT,in line with a strongly exchange coupled state SS, whereas thisinteraction becomes ferromagnetic at HT, as expected for theweakly coupled state WS. The calculations also indicate thatthe CuO4N2 units remain magnetically isolated regardless ofthe phase.

Comparing with the results obtained forCu(hfac)2L

Bu·0.5 C8H18 (2) complex from DDCI calculations onthe spin triad (J =�145.3 cm�1 and 8.7 cm�1 for the LT and HTphases, respectively, using the quartet CASSCF(3/3) molecularorbitals in the configuration interaction expansion),[24] the Jconstants at PBE + Ud + Up level are those in better agreementwith the DDCI ones, although always larger in amplitude forboth phases. This overestimation is a well-known feature ofthe DFT-based evaluations of the magnetic coupling constants,extensively discussed in the past for many magnetic binuclearcompounds,[50–54] and also found for the family of Cu(hfac)2L

R

breathing crystals.[19, 27] The interchain interaction is antiferro-magnetic in nature and of the same order of magnitude as theJ value within the spin triads at high temperature. This impliesthat in the WS state there is not a dominant magnetic interac-tion, but J and Jchain are competing, resulting in a frame of spinstates very close in energy, of vital importance for the interpre-tation of the spin dynamics and the relaxation of the photoin-duced WS state.[21, 24, 26] The amplitude of this interaction isindeed in good agreement with previous independent evalua-tions on isolated nitronyl-nitroxide fragments based on DDCI[24]

and broken-symmetry DFT calculations.[26]

Density of states

The density of states (DOS) for the AFM magnetic solutions ofthe three compounds at low and high temperatures is shownin Figure 6 for PBE + Ud + Up and Figures S3–S6 (Supporting In-formation) for the Cu(hfac)2L

Pr (1) complex with different Uvalues. Although there are no experimental data of the bandgap magnitude or electric conductivity for any compound ofthe Cu(hfac)2L

R family, the EPR data indicate that they do notexhibit a metallic behavior, and thus the presence of a bandgap is implicitly inferred.

For U = 2 eV the system presents no band gap (Figure S3).The three other explored U values for Cu(hfac)2L

Pr at low tem-perature give a band gap of 0.7 eV for U = 7 (Figure S4) andU = 9.8 eV (Figure S5), whereas the gap slightly increases up to1 eV in the case of the PBE + Ud + Up approach (Figure S6).When going to the HT structure, the gap is slightly reduced byabout 0.2 eV. For all the explored values, the valence band has

a major contribution of the nitronyl-nitroxide groups, whereasthe low-lying conduction bands are mainly centered on the Cand O atoms of the hfac ligands, the nitronyl-nitroxide groups,and the Cu atoms.

The DOS of the three compounds resulting from the PBE +Ud + Up calculations (Figure 6) are very similar in both natureand energy of the low-lying bands. At low temperature, twohfac-based conduction bands can be distinguished: one cen-tered on the isolated CuO4N2 units (labeled as hfac2 in

Figure 6. Density of states for the AFM magnetic solution at low (top) andhigh temperatures (bottom) of (a) Cu(hfac)2L

Pr (1) (b) Cu(hfac)2LBu·0.5 C8H18

(2) and (c) Cu(hfac)2LBu·0.5 C8H10 (3) from PBE + Ud + Up calculations (black)

and projected DOS on the NO groups (red), C and O atoms of the hfac1(blue) and hfac2 (green) groups, Cu1 (magenta) and Cu2 (orange) atomsand solvent (grey) atoms. The vertical dotted lines represent the Fermi level.

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Figure 6) at lower energy than the band due to the hfac li-gands of the spin triads (labeled as hfac1). These two bandsalmost collapse at high temperature, giving rise to a singleband at about 1.2 eV above the Fermi level. This could be re-lated to the fact that the Cu1�Ohfac1 and Cu2�Ohfac2 bond dis-tances become quite similar at HT, whereas they differ by upto 0.3 � in the LT phase. The next bands in energy are associat-ed to Cu atoms (Figure 6). These Cu bands suffer a redshift dis-placement of about 0.2–0.3 eV in the HT phase, being placedat ~2 eV above the Fermi level. This redshift displacementcould also be associated to the changes observed in the coor-dination spheres of the Cu atoms when going from the LT tothe HT phases.

The position of the Cu bands depends on the U value (Fig-ures S3–S6). Going from U(Cu) = 7 eV to U(Cu) = 9.8 eV movesthese Cu bands to higher energy. The same effect is observedin the conduction oxygen-centered band when the PBE + Ud +Up approach is employed.

The relative position of the low-lying bands in the DOS pro-vides potentially useful information for the assignment of theUV/Vis absorption spectra, in particular a qualitative picture ofboth the energy and the nature of the electronic transitions inthe UV/Vis absorption spectra, and the bleaching observed inthe 500–600 nm region after photoactivation. Figure 3 showsthe experimental UV/Vis spectrum of Cu(hfac)2L

Pr (1) recordedin the 400–900 nm range at different temperatures.[13, 22] The LTand HT phases present quite similar bands in this region, but adistinctive feature of the LT structure is the presence of an in-tense band at l= 500 nm, assigned to a metal-ligand orligand-metal charge transfer transition,[13, 14] based on the factthat the Cu�O distances in the spin triads are noticeably modi-fied upon SS$WS conversion.

Table 5 reports the energy difference at PBE + Ud + Up levelbetween the centers of the bands close to the Fermi level forCu(hfac)2L

Pr complex, mainly the valence band and the low-lying conduction bands. Although qualitative, these energy dif-ferences give information about the features observed in theUV/Vis spectra and the main changes that could be expectedafter SS$WS conversion. Notice that our calculations do notprovide information about the transition dipole moments,then the relative intensities (if any) of these bands cannot beanticipated and consequently the corresponding wavelength

values in Table 5 are just tentative. The separation betweenbands of the same nature is reduced (the wavelength requiredfor a transition between them increases) when going from theLT to the HT structure, with the exception of the transition be-tween nitroxide bands, where the trend is the opposite one.The first feature can be related to the bleaching observed inthe 500–600 nm region after photoswitching. Particularly re-markable is the energy difference between the nitroxide bandsand the Cu centered ones of 2.5 eV (~500 nm) in the LT phase,whereas the gap between these bands moves to lower energy~2.2 eV in the HT structure, then larger wavelengths(~570 nm) are required to promote a transition between thesetwo bands when temperature increases. These two bandscould be responsible (assuming a non-negligible oscillatorstrength) for the l= 500 nm transition observed at low tem-perature and distinctive of the strongly coupled SS phase. Theperiodic calculations suggest that this band could be ascribedto a ligand-to-metal charge transfer transition, from the nitron-yl-nitroxide groups to the Cu atoms, both intimately involvedin the magnetic properties of the LT and HT structures and theSS$WS conversion. The charge redistribution between metaland ligands has also been invoked as a key ingredient of thespin transition in spin crossover FeII compounds.[55] This is acentral result of this work that could help in clarifying themechanism controlling the photoswitching process.

In the case of the separation between the nitroxide bandsand the corresponding nitroxide-nitroxide transitions, theenergy difference increases somewhat (the wavelength de-creases) when going from LT to HT structures.

The final remark concerns the impact of the + U correctionon the energy and nature of the projected DOS. As occurswith the J values, only the DOS at PBE + Ud + Up level presentssignificant differences between the LT and HT structures thatcould be related to the signatures observed in the UV/Vis ab-sorption spectra. Then, the U correction of both the Cu 3d andO 2p orbitals is required for a correct description of theCu(hfac)2L

R complexes.

Conclusions

The Cu(hfac)2LR breathing crystals family manifests thermal

magnetostructural transitions and LIESST-like phenomenaquite similar to those experienced by the classical spin cross-over compounds. While a large amount of research has beendevoted to the characterization and understanding of the ther-mally induced spin transition, much less is known about theoptical properties of these copper-nitroxide based molecularmagnets.

This work provides information about the electronic struc-ture of the whole crystal of three members of the Cu(hfac)2L

R

family, relevant for the assignment of the UV/Vis spectra andthe rationalization of the photoinduced switching. The resultsof a set of periodic DFT + U based calculations in the two limit-ing phases concern the relative stability of the different spinarrangements in the crystal, and the amplitude and nature ofthe magnetic interaction in these heterospin complexes. Theyare consistent with the EPR data and the observed changes of

Table 5. Energy difference between the center of the valence band andlow-lying conduction bands and wavelengths of the corresponding tran-sition for Cu(hfac)2L

Pr (1) complex at PBE + Ud + Up level.

Assignment LT HTDE [eV] l [nm] DE [eV] l [nm]

a-DOS hfac2 !NO 1.54 805 1.41 880hfac1 !NO 2.23 556 1.55 800Cu2 !NO 2.48 500 2.14 564Cu1 !NO 2.59 479 2.20 580NO !NO 2.99 415 3.12 397

b-DOS NO !NO 2.09 593 2.19 566hfac2 !NO 2.23 556 2.19 566hfac1 !NO 2.90 428 2.30 539

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the magnetic moment with temperature. Additionally, the den-sity of states gives insights on the states potentially accessibleby electronic transitions in the UV/Vis range that could be in-volved in the photoswitching process. The similarities found inthe DOS for the three considered compounds suggest the pos-sibility of light-induced spin switching for other members ofthe breathing crystal family, for which this phenomenon hasstill not been reported. Work is in progress to accurately quan-tify the transition energies and, in particular, the oscillatorstrengths for transitions in the UV/Vis range by means ofCASSCF/CASPT2 calculations on the spin triad.

The study highlights the potential of the PBE + U calcula-tions on the understanding of the optical properties of thesesystems, and its conclusions could be relevant not only for theparticular compounds analyzed, but for many other Cu(hfac)2L

R

complexes.

Acknowledgements

The authors acknowledge the financial support provided bythe Ministerio de Econom�a y Competitividad (Spain) andFEDER funds through the projects CTQ2015-69019-P (MINECO/FEDER) and access to the resources of the Red EspaÇola de Su-percomputaci�n (RES) through project no. QCM-2017-3-0033.R.S.-d.-A. thanks VPPI-US for the financial support.

Conflict of interest

The authors declare no conflict of interest.

Keywords: density functional calculations · exchangeinteractions · LIESST: spin crossover · light-induced spintransitions · switchable magnetic materials

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Manuscript received: August 2, 2018

Accepted manuscript online: September 7, 2018

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& Spin Crossover

R. S�nchez-de-Armas, N. Cruz Hern�ndez,C. J. Calzado*

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Light-Induced Spin Transitions inCopper-Nitroxide-Based SwitchableMolecular Magnets: Insights fromPeriodic DFT + U Calculations

Spinning around : The density of states(DOS) of Cu(hfac)2L

Pr gives insights onthe states potentially accessible by elec-tronic transitions in the UV/Vis rangethat could be involved in the photo-switching process, mainly, LMCT pro-cesses between the nitronyl-nitroxideand the Cu 3d bands. The similaritiesfound in the DOS for the three consid-ered compounds suggest the possibilityof light-induced spin switching for othermembers of the breathing crystal family.

Chem. Eur. J. 2018, 24, 1 – 11 www.chemeurj.org � 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim11 &&

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