Halide ligated iron porphines: A DFT+U and UB3LYP study

Halide Ligated Iron Porphines: A DFT+U and UB3LYP Study

Pooja M. Panchmatia,*,†,‡ Md. Ehesan Ali,†,§ Biplab Sanyal,† and Peter M. Oppeneer†

Department of Physics and Astronomy, Uppsala UniVersity, Box 516, S-751 20 Uppsala, Sweden, Departmentof Chemistry, UniVersity of Bath, Bath, BA2 7AY, U.K., and Theoretische Chemie, Ruhr-UniVersitat,Bochum, D-44780, Bochum, Germany

ReceiVed: July 9, 2010; ReVised Manuscript ReceiVed: NoVember 9, 2010

We apply the density functional theory + U (DFT+U) and unrestricted hybrid functional DFT-UB3LYPmethods to study the electronic structure and magnetic properties of two prototypical iron porphines: iron(III)porphine chloride (FePCl) and difluoro iron(III-IV) porphine. Plain DFT within the generalized gradientapproximation (GGA) implementation fails in describing the correct high-spin ground state of these porphinemolecules, whereas DFT+U and UB3LYP provide an improved description. For a range of U values (4-8eV), we compare the results of the DFT+U approach to those obtained previously with the hybrid functional(B3LYP) and with the CASPT2 approach. The DFT+U and UB3LYP methods successfully predict themolecular high spin (S ) 5/2) ground state of FePCl, and also provide the nontrivial S ) 3 high spin groundstate for FePF2. For the latter six-coordinated Fe porphine, our DFT+U calculations show that the S ) 2, S) 5/2, and S ) 3 states are energetically very close together (differences of 30 meV). Nonetheless, S ) 3 isobtained as the ground state of the whole molecule, in accordance with the spin expected from the electroncount. Our DFT+U calculations show furthermore that the Fe 3d occupancy is similar for FePF2 and FePCl,i.e., DFT+U does not support Fe(IV) for FePF2, but rather an Fe(III) porphyrin π-cation radical species, withan Fe high spin SFe ) 5/2, and an additional S ) 1/2 stemming from spin density distributed over the porphinering. This observation is also supported by our UB3LYP calculations.

I. Introduction

The abundance of porphyrin molecules in nature as well asthe probable use of these type of molecules in various techno-logical applications like optical switches, information storage,and nonlinear optics, emphasizes the importance of determiningthe correct ground state properties of these molecules.1 Thesemolecules have been studied extensively, both experimentallyand theoretically. Discrepancies in the interpretation of the metalion spin occupancies are still present within the experimentaldata2-8 and despite the theoretical attempts9-18 to clarify these,the correct ground-state electronic configuration is an ongoingtopic of discussion. The controversy concerning the electronicconfiguration further grows if the porphyrin is ligated, eitherfive coordinated or six coordinated. The unligated Fe(II)porphyrin (FeP) molecule with about six d electrons can be inan intermediate (S ) 1), low (S ) 0), or high (S ) 2) spinstate. On the other hand, the ligated Fe(III) porphyrin moleculecan exhibit S ) 1/2 (low), S ) 3/2 (intermediate), and S ) 5/2(high) spin states. The existence of the Fe(IV) species is moreuncertain; it is formally expected to exhibit an S ) 2 high spinstate or an S ) 1 intermediate spin state. Several investigations19,20

describe the five-coordinated Fe(III) porphine structure to bein the high spin state. Vital for this description is the displace-ment of the iron atom out of the porphyrin plane due to theaxial ligand. This displacement has been estimated to beapproximately 0.36 Å experimentally.21 Liao and Scheiner22

report a correlation of the spin multiplicity and the out-of-planedisplacement of the metal center in five-coordinated porphine

molecules. Using DFT with Vosko-Wilk-Nusair parametriza-tion and Becke’s23 gradient functional for exchange, Liao andScheiner22 quote 0.22-0.30 Å for S ) 3/2 and 0.53 Å for thehigh spin state S ) 5/2. This correlation can only be possiblein molecules with a single axial ligand, where a C4V symmetryis expected.22 In the case of FePF2, where two symmetricallydisposed axial ligands are present, a D2h symmetry is expected,where the central metal center (Fe) stays in-plane with theporphine ring. Such a property could be unfavorable forachieving a high-spin state. Surprisingly, experimental inves-tigations indicate for various planar tetraphenyl difluoro ironporphyrins a high-spin state.4,7

In the present study, the iron porphine difluoride (FePF2) hasbeen chosen as a prototypical molecule for the six-coordinated“Fe(IV)” species, while the chlorohemin molecule (FePCl) hasbeen chosen to represent the Fe(III) five-coordinated system.In the past few years it has become clear that most, if not all,of the available DFT-GGA functionals do not correctly describethe energetics of the low-lying spin states of transition-metalporphyrin complexes. Recent studies9,11 provide an extensivediscussion on the failure of GGA and meta GGA functionalsin predicting the correct description of the ground-state elec-tronic configuration in ligated porphyrin molecules. Kozlowskiet al.12,13 also describe the low-lying spin states of FeP and five-coordinated FeP, ligated with an imdazole ring [FeP(Im)], andemphasize the need to choose an appropriate functional thatwill predict the correct ground state. The motivation of thecurrent work originates from the uncertainties between experi-ment and theory. The FePF2 molecule is an important test casefor studies of the Fe oxidation and spin states because of itsintricate behavior. Although at first sight one might expect anFe(IV) oxidation state, several investigations suggest rather anFe(III) high spin SFe ) 5/2 state,4,7,24 being thus compatible with

* To whom correspondence should be addressed, [email protected].† Department of Physics and Astronomy, Uppsala University.‡ Department of Chemistry, University of Bath.§ Theoretische Chemie, Ruhr-Universitat.

J. Phys. Chem. A 2010, 114, 13381–13387 13381

10.1021/jp106358m 2010 American Chemical SocietyPublished on Web 12/02/2010

concomitant π-cation radical formation (see ref 8 for a recentsurvey). Jones et al.14 mention furthermore electrochemicaloxidation evidence but refer to an unpublished cross referencefor details. Earlier DFT calculations of Jones et al.,14 employingthe local spin-density approximation (LSDA) in Vosko-Wilk-Nusair parametrization, predicted an Fe(IV), S ) 1ground state for FePF2. Also previous B3LYP calculations failedfor this system in that these, too, predicted an Fe(IV) S ) 1lowest energy state, as shown by Ghosh and Taylor.17 In thesame article, Ghosh and Taylor17 predict successfully a highspin S ) 3 state for the FePF2 molecule, with an SFe ) 5/2Fe(III) configuration, using the more accurate and sophisticatedCASPT2 method.

We have recently performed benchmarking calculations ofthe DFT+U method for Fe porphyrin models.25 The DFT+Umethod has frequently been used for studying strongly correlatedelectron systems in periodic solids.26 A few very recentinvestigations also illustrate the successful use of this methodfor porphyrin molecules.10,18,25,27 The essence of the current workis to apply DFT+U for studying the molecular geometry andground state spin structure of the more problematic FePF2 andFePCl molecules. In recent literature, a value of U ) 4 eV hasbeen used for Fe porphyrin molecules.10,25 In this study, wherewe are dealing with high oxidation states of the iron, we havevaried the value of U from 4 to 8 eV to find out the conditionsunder which we can achieve the correct experimental groundstates for these complex molecules, if at all.

It is worthwhile mentioning that the spin state of thesemolecules can play an important role in determining theinteraction between the molecule and a substrate on which itcan be supported. Delicate indirect magnetic interactions18,28,29

can be vital for the use of ligated FeP molecules in devices formolecular electronics. We also emphasize that the focus of thisstudy is not to compare different DFT-based approaches(DFT+U versus UB3LYP) but to explore the capability of theseapproaches in describing challenging ligated porphyrin speciesand how with a combination of methods we are able tounderstand the complex interactions between the metal centerand the porphine ring.

In the following, we outline the computational approach used(section II) and define the molecular models for which thecalculations were performed. A detailed discussion of the resultsand the effect of U on the electronic structure and a moreinsightful description of the function of U compared to B3LYPand CASPT2 is made in section III. Conclusions are given insection IV.

II. Computational Details

Our calculations have been performed using an ab initio full-potential plane wave code (VASP)30,31 with the projectoraugmented wave (PAW)32 method. A kinetic energy cutoff of600 eV was used for the plane waves in the basis set. Also, asimulation box of 20 Å × 20 Å × 20 Å was used toaccommodate the molecules, and since the distance separatingthe individual molecules is chosen to be large, we used the Γpoint only in reciprocal space (i.e., the single molecule limit).For the DFT part of the DFT+U method, we used the GGAPerdew-Wang (PW91)33 parametrization of the exchange-correlation potential. The DFT+U approach used is the atomiclimit version,34 in which the Coulomb U and exchange J areassumed to be independent of the angular orbital quantumnumbers. Thus, only the effective Ueff, Ueff ) U - J, appearsin the DFT+U formulation. In the present implementation, thesupplementary Coulombic type interaction is only applied to

the open-shell Fe 3d electrons. We note that the DFT+Uapproach enforces both a pure Coulombic interaction betweenelectrons in an open shell and the exchange interaction betweenthem. In the present work the value of U is not calculated abinitio, instead it is varied in the range of 4-8 eV. In an earlierinvestigation25 we obtained good results for Fe porphinemolecules with a U of 4 eV, which is considered to bereasonable for Fe in correlated complexes.26,35 As here theinvestigated ligated Fe porphine molecules are expected to havehigh oxidation states (Fe(III) or Fe(III/IV)), a higher value ofU appears to be reasonable. We determine an optimal value ofU through a comparison to available experimental and theoreti-cal data. The exchange parameter J was fixed to be 1 eV. Wenote that in this implementation projections on pseudoatomicd-orbitals are used. Hence the influence of the U parameterdepends on the radius of the d-projector, which implies thatthe U value is not a universal term and indeed nontransferablebetween different +U implementations. Also, it is known thatDFT+U calculations can give rise to multiple total-energyminima. By performing a series of fixed-spin calculations, wehave avoided such side-minima. Complete structural relaxationsof the molecules were done by optimizing the Hellmann-Feynman forces with a tolerance of 0.02 eV/Å. Local propertiessuch as local density of states and local magnetic moments werecalculated by projecting the wave functions onto sphericalharmonics as described in ref 36.

We also have optimized the molecular geometries usingunrestricted hybrid density functional theory with Becke’s 3parameter exchange functional,23,37 with nonlocal Lee-Yang-Parrelectron correlation (UB3LYP model).38 The calculations areunrestricted, in that the spin-up and spin-down states for eachorbital are treated using independently computed spacial wavefunctions. This hybrid functional includes a mixture of 20%Hartree-Fock (HF) exchange with nonlocal/gradient correctedexchange-correlation functional. The 6-311G(d,p) basis sets forH, C, N, O, and Cl are used for optimization and 6-311+G(d,p)basis sets are used for single-point energy calculations. For thetransition metal Fe atom, the effective core potential basis setLanl2dz (Los Alamos ECP plus double-�) is used for valenceelectrons.39 The core electrons are treated with Lanl2 effectivecore potential for optimization as well as in single pointcalculations. All the UB3LYP calculations are performed usingGAUSSIAN 03.40 For a detailed survey regarding the pros andcons of various DFT-based functionals in transition-metalchemistry, we refer to a recent exhaustive article.41

III. Results and Discussion

A. The Fe Porphine Chloride Molecule. In our calculationswe have first started with a full structural optimization of theFe porphine molecules. The structural optimization has beendone on the UB3LYP level and within the DFT+U method forindividual U values. We find that the FeP and FePF2 moleculesconverge to the planar D4h and D2h symmetry, respectively,whereas the FePCl molecule assumes a nonplanar, C4V tetragonalsymmetry.22 The structures of the investigated molecules areshown in Figure 1. To make sure that we have obtained thecorrect, minimal energy spin state in the self-consistent con-vergence, we have in addition performed fixed spin calculations,which give the energy difference between different spinconfigurations.

To start with, we consider the FePCl molecule, whose S )5/2 ground spin state is experimentally well documented.42-44

Our DFT+U calculations for this molecule with relaxed atomicpositions show that the correct ground spin state can be

13382 J. Phys. Chem. A, Vol. 114, No. 51, 2010 Panchmatia et al.

predicted. In a previous publication we benchmarked theperformance of the DFT+U method using smaller Fe porphinemodels.25,45 While the smaller models indeed could provide goodvalues for integrated properties such as magnetic moments, somediscrepancies were seen in the nonintegrated properties of theelectronic structure. For example, the positions of molecularlevels were not properly found with the consideration of rathersmall models.25 In the present work we also recognize theimportance of modeling the whole porphine molecule: theFe-Cl distance relaxes to 2.22 Å in line with the experimentaldistance of about 2.16 Å.4 The Fe-Np distance is calculated tobe 2.09 Å for the Cl ligated porphine ring; see Table 1. Thecalculated structural data agree very well to the experimentalones.21,15 The out-of-plane distance of the Fe atom from theporphyrin ring is also reproduced well to about 0.4 Å withDFT+U and 0.48 Å with UB3LYP. The ground-state spinscomputed with several approaches are also shown in Table 1.Both the DFT+U and UB3LYP approaches predict the S )5/2 ground-state spin, but DFT in the common GGA imple-mentation predicts the wrong S ) 3/2 spin. Despite the identicalground-state spin, the calculated Fe 3d occupancy of FePCl alsodiffers between the DFT+U and UB3LYP approaches. TheDFT+U predicts a lower occupancy for the Fe 3d, as would beexpected for a Fe(III) high spin configuration. UB3LYP predictsconversely a rather high Fe 3d occupation number for FeP,FePCl, and FePF2 as well. We note that the latter occupationnumbers have been obtained from a charge-density decomposi-tion into localized natural orbitals, which is basis set indepen-dent. The DFT+U occupation numbers however are dependenton the radius of the d-projector and are therefore not directlycompatible with those obtained from the natural orbital analysis.It is important to mention here also the role of the ligandmoment contribution to this high spin configuration where withan Fe(III), one would expect five unpaired d electrons; however,integer electron counts are never expected from these calcula-tions and can be attributed to the strong bonding effects of theligands to the central metal ion. Instead it is more useful tonote the reduction of the Fe-3d occupancy when switching fromFe(II) in the FeP to Fe(III) in the ligated molecules and considerthe spin state as a fingerprint of the oxidation state.

In Table 2 we collect the energy differences (eV) obtainedfor FePCl with the DFT+U method, the B3LYP calculationsof Johansson and Sundholm,46 as well as our own UB3LYPcalculations. DFT+U predicts a wrong, intermediate S ) 3/2spin for U ) 4 and 5 eV. However, when U is increased above5 eV, a spin crossover to the S ) 5/2 spin state occurs. The

earlier B3LYP investigation46 predicted the correct S ) 5/2ground state spin.

The calculated energy differences between the S ) 3/2 andS ) 5/2 spin states are shown in Table 2. For the truncatedFePCl model in ref 25, the S ) 5/2 state was already obtainedat U ) 4 eV. For the full FePCl molecule the difference betweenthe energies for the two spin configurations is relatively smallfor U ) 4 eV, but the correct high spin is reproduced only fora slightly higher value of U (between 5 and 6 eV). The DFT+Uenergy difference computed between the S ) 3/2 and S ) 5/2states for FePCl is 0.32 eV, a value which signifies the stabilityof the high spin state. We mention here that we also investigatedthe possibility of obtaining other minimal energy spin states. Afull range of spin states from S ) 1/2 to S ) 5/2 was investigatedfor the range U ) 4-8 eV; the S ) 5/2 high spin state wasconsistently identified as ground state.

Figure 2 illustrates the density of states (DOS) and the partialDOS for the FePCl at U ) 6 eV for both the S ) 3/2 and S )5/2 spin configurations. The crossover from the intermediate S) 3/2 to S ) 5/2 spin can be recognized clearly from the partialDOS. For the S ) 3/2 state there is one unoccupied, spinmajority Fe state at about 1 eV that is strongly hybridized witha N p orbital. When the high-spin state is created, DOS weightof this state is transferred to the occupied spin-majority 3d states(near -0.8 eV). The stronger Hund’s rule coupling present forS ) 5/2, moreover, leads to a shift of the Fe 3d majority-spinDOS to lower energies, where these states hybridize less withthe N p states. For the intermediate S ) 3/2 spin, the Fe and Norbital energies are closer and, consequently, these orbitalshybridize more in the energy range of -3 to -6 eV. The Cl p

Figure 1. Molecular models adopted for the ligated five coordinated FePCl (left) and six coordinated FePF2 (right) Fe porphine molecules. In thestructures, red, blue, gray, white, yellow, and dark and light green colors indicate Fe, N, C, H, Cl, and F atoms, respectively.

TABLE 1: Comparison of Computed DFT-GGA, DFT+U, and UB3LYP Bond Lengths (in Å), Ground State Spin (S), Fe 3dSpin Magnetic Moments (in µB), and Fe 3d Occupation Numbers for FeP, FePCl, and FePF2 Moleculesa

DFT-GGA DFT+U UB3LYP

molecule Fe- NP Fe-L S Fe 3d mom. Fe occ. Fe- NP Fe-L S Fe 3d mom. Fe occ. Fe- NP Fe-L S Fe 3d mom. Fe occ.

FeP 1.98 1 1.92 6.13 2.00 1 1.92 6.13 2.01 1 2.07 6.59FePCl 2.02 2.26 3/2 2.44 5.90 2.09 2.22 5/2 4.09 5.71 1.99 2.21 5/2 3.94 5.98FePF2 2.08 1.83 1 1.94 5.98 2.09 1.88 3 4.30 5.80 2.10 1.87 3 4.27 6.85

a In the DFT+U calculations a U ) 4 eV has been used for FeP and U ) 6 eV for FePCl and FePF2, respectively.

TABLE 2: Computed Spin States of the FePCl Molecule,Obtained with Different Computational Approachesa

method S ES)3/2 - ES)5/2 (eV)

DFT+U ) 4 eV 3/2 -0.02DFT+U ) 5 eV 3/2 -0.18DFT+U ) 6 eV 5/2 0.32DFT+U ) 7 eV 5/2 0.46DFT+U ) 8 eV 5/2 0.59B3LYP46 5/2 0.33UB3LYP (ours) 5/2 0.19

a Also given are the computed energy differences (in eV)between the total energies for the low lying S ) 3/2 and S ) 5/2spin states. For comparison we include the B3LYP result ofJohansson and Sundholm,46 as well as our own UB3LYPcalculations.

Halide Ligated Iron Porphines J. Phys. Chem. A, Vol. 114, No. 51, 2010 13383

states appear mainly between 0 and -3 eV, where they hybridizewith Fe d states. The high spin state shows a larger energysplitting to the unoccupied iron 3d states as compared to theintermediate spin configuration, at the same U value.

B. The Fe Porphine Difluoride Molecule. The FePF2

molecule is a more difficult test case for the computationalfunctionals. Previous B3LYP calculations17 and DFT-LSDAcalculations14 predicted a wrong S ) 1 ground state spin forthis molecule. The second issue is the oxidation state of the Feion, i.e., whether it is Fe(III) or Fe(IV). Experiments4,7,24 as wellas CASPT217 calculations provide evidence for an SFe ) 5/2high spin state (with π cation radical formation), correspondingformally to an Fe(III) state9,17,46 and not to the Fe(IV) state. Onthe basis of plain ionicity arguments, however, an Fe(IV) statewith S ) 2 or S ) 1 would be expected.

Our calculated results for this molecule are presented in Table1. The DFT-GGA approach predicts an Fe-Np of 2.08 Å whilethe Fe-L (axial ligand) distance is computed to be 1.83 Å.Using the DFT+U and UB3LYP we obtain 2.09 and 1.88 Åand 2.10 and 1.87 Å, respectively. These calculated structuraldata for the Fe and the porphine ring agree very well to theexperimental ones.15,21 The Fe-F distance is not well docu-mented; however, the experimental distance of a typical Fe-Fbond in FeF2 is reported to be about 1.76 Å.47 The calculateddistance is much closer for the fluoride, bringing it closer tothe Fe metal center compared to the Fe-Cl analogue. Spectro-scopic and electrochemical reactivity properties for FePF2 havebeen recorded previously.4,15 Solution magnetic susceptibilitysuggests the difluoro iron(III) porphyrin complex to be in thehigh spin state. The electron spin resonance spectra for thedifluoro iron complexes are also typical for a high spin iron(III)species.4

The problematic issue of the spin state of difluoro ironporphine is evident from the computed spin states and Feoccupation numbers given in Table 1. DFT-GGA predicts awrong S ) 1 spin state with a relatively high Fe 3d occupation,which is unexpectedly even higher than that of FePCl. TheUB3LYP calculation predicts correctly a high spin S ) 3 statehowever with an even higher Fe 3d occupation. DFT+U alsopredicts a high spin S ) 3 state for the whole molecule, as wellas the experimental SFe ) 5/2 for the Fe, with an Fe 3doccupation number almost identical to Fe in FePCl. This issomewhat consistent with F having a lower electron affinitycompared to Cl.

The result of our DFT-GGA calculation is in accordance withthe earlier DFT-LSDA calculation,14 but our UB3LYP calcula-

tion gives a ground state distinct from the earlier B3LYP study.17

The origin of this difference is not immediately evident. In ref17 the molecular geometry was optimized constraining thesymmetry to D4h and also constrained d-orbital configurationswere used. We have conversely carried out a full unconstrainedgeometrical optimization for various spin states. This suggeststhe importance of carrying out a full geometrical optimizationin conjunction with assuming an experimental high spin statefor the π-radical cation species.

To analyze the origin of our DFT+U results, we havecomputed the energies of seven fixed spin configurations withthe DFT+U method for U values ranging from U ) 4 to 8 eV,in order to determine the conditions under which the experi-mental spin state can be obtained; see Figure 3. It can berecognized from this plot that for lower U values (4 and 5 eV)DFT+U predicts an S ) 1 ground state. However, when theCoulomb U is increased above 5 eV, a transition to an S ) 3ground-state spin occurs. As can be seen from Figure 3, thestate with S ) 3 is energetically very close to that with S ) 5/2and S ) 2. The states are nearly degenerate, but the S ) 3 stateis deeper by about 30 meV, as shown in Table 3. Note that wehave also tried to achieve half-integer spin value for the wholeFePF2 molecule with the UB3LYP method, but it was notpossible to converge to any half-integer spin value. Thecomputed DFT+U and UB3LYP energy differences betweenS ) 1 and S ) 3 states and S ) 2 and S ) 3 match well topreviously reported energy differences calculated from CASPT2results.17 Thus, DFT+U does reproduce the experimentallyclaimed SFe ) 5/2 ground state of the Fe ion in FePF2. As

Figure 2. Computed DFT+U (U ) 6 eV) partial DOS of iron porphinechloride, FePCl for the S ) 3/2 spin configuration (top panel) and theS ) 5/2 configuration (bottom panel).

Figure 3. Computed DFT+U total energies plotted against the fixedspin moment (in µB) for different U values for the six coordinateddifluoride iron porphine molecule.

TABLE 3: Results of DFT+U and UB3LYP Calculationsfor the FePF2 Moleculea

method S ES)1 - ES)3 ES)2 - ES)3

DFT 1DFT+U ) 4 eV 1 -0.66 0.01DFT+U ) 5 eV 1 -0.22 0.08DFT+U ) 6 eV 3 0.11 0.03DFT+U ) 7 eV 3 0.50 0.03DFT+U ) 8 eV 3 0.89 0.03UB3LYP (ours) 3 0.49 0.05B3LYP17 1 -0.30 -0.65CASPT217 3 0.31 0.04

a Energy differences (eV) for low lying spin states of FePF2 aregiven at different values of U and compared to those of Ghosh andTaylor17 (B3LYP, CASPT2).


already mentioned, CASPT2 also predicts an SFe ) 5/2 spinstate, ferromagnetically coupled to an S ) 1/2 π-radical cation,giving S ) 3 on the FePF2 to be the most favorable groundstate.17 This state is deeper in energy by a considerable 0.31eV with regard to the Fe(IV) S ) 1 state. CASPT2 is in generalknown to predict an appropriate, qualitative reference value.We observe here that both the UB3LYP and the DFT+U, forU values of 7 eV, do provide a comparable energy difference.Below we investigate further the valency of Fe in FePF2.

An interesting feature that could be related to the near-degeneracy of the S ) 2, 3, and S ) 5/2 spin states can readilybe recognized from the DFT+U results in Table 1. Although ahigher oxidation state of Fe is expected for FePF2 than forFePCl, we find that the Fe 3d occupation number is not toodifferent from FePCl to FePF2; i.e., both Fe porphine moleculeshave an Fe(III) oxidation state. Consequently, the additionalhalide bonding of one more fluorine atom cannot removeelectron density from the metal center; instead, the electrondensity on the ring is redistributed. Our results point to a SFe )5/2 spin on the Fe ion, coupling ferromagnetically to an S )1/2 spin distributed on the ring. The electronic distributions atU ) 6 eV for S ) 2 and S ) 3 are listed in Table 4. Here, asignificant change in the N p and C p occupations is identified,which strongly supports the redistribution of the electron densityon the porphyrin ring, resulting in an S ) 3 high-spin state.Interestingly, for the C p, a change in the spin direction of thefour bridging carbon atoms contributes to the higher spin stateof the FePF2 molecule. The difference in the magnetizationdensity between S ) 2 and S ) 3 distributions has been plotted.This plot explicitly shows the differences in the spin densitybetween S ) 2 (4 µB) and S ) 3 (6 µB) states, revealing theredistribution of the spin density (∆S ) 1) within the porphyrinring. The N pz and bridging C pz play a crucial role in supportingthe higher spin state of the FePF2 molecule. Also, the FePClhas the S ) 5/2 high spin and FePF2 the S ) 3 spin, and thecomputed Fe 3d moment reveals a 4.30 µB 3d moment in FePF2,larger than that of 4.09 µB obtained for FePCl. This impliesthat around the Fe atom, FePF2 has a somewhat higher spin

density than FePCl. In both FePCl and FePF2 there is the spindistribution on the porphyrin ring which, together with thespin distribution on Fe, adds up to the high total spin. Thisobservation bears relevance for the poorly understood originof the sometimes experimentally observed high spin state ofFePF2.7 A local probe of the iron magnetism (Mossbauer orNMR), would observe a high spin state on Fe in FePF2, whichcould be thought to be connected to an Fe(III) valency. TheDFT+U computed Fe 3d moment (4.30 µB) does support thepicture of a SFe ≈ 5/2 spin at the metal site. Nonetheless, italso supports the spin state of the molecule as a whole goes tothe S ) 3 state, through the enhancing effect of the π radicalmagnetization dispersed over the porphine ring.

In Figure 5 we show the partial densities of states (DOS) forthe diflouride molecule for computed three fixed spin states (S) 1, S ) 2, and S ) 3), at U ) 6 eV. The transition from thelow spin S ) 1 state to the intermediate spin S ) 2 can beclearly recognized from the partial DOS: one unoccupiedmajority spin Fe DOS peak becomes shifted to below the Fermilevel, and another unoccupied majority Fe DOS peak becomesan unoccupied minority DOS peak. Due to the stronger Hund’srule coupling, the splitting between the occupied majority spinand the unoccupied minority spin Fe states becomes larger. Ifwe compare the FePCl DOS, Figure 2 and FePF2 DOS, Figure5, there is a difference in the electronic structure of the Fe ion,even though in both molecules the Fe is in a high spin SFe )5/2 state. This could be because of the symmetry differencebetween the FePCl and FePF2, as lower symmetry, in general,shows more splitting in the DOS.

Simultaneously, the hybridization of Fe d states with N andF p states becomes reduced. The modification in the partial DOSfrom the S ) 2 to S ) 3 spin state is more subtle. There is nota pronounced change in the Fe d partial DOS, except for a smallchange of the Fe-N, Fe-F hybridized DOS at the chemicalpotential. Figure 5 reveals that a small hybridized Fe d DOSthat is just above EF for S ) 2 becomes partially occupied forS ) 3. Also, there is an accompanying change in the nitrogenp partial DOS, where an occupied spin minority peak becomesunoccupied and vice versa for an unoccupied spin majority peak.This small effect is responsible for most of the extra spin (asthere are four nitrogen atoms).

Figure 6 shows explictly the computed ml-resolved partialFe DOS of FePF2 at U ) 6 eV for the three spin states inquestion, S ) 1, 2, and 3. From this plot, the transition from S) 1 to S ) 2 and S ) 3 is seen clearly where, the spin-minority

Figure 4. Magnetization density difference for the FePF2, between S) 2 and S ) 3 spin distributions, showing clearly no effect on thecentral Fe atom but significant redistribution of the spin on the N pz

and the bridging C pz. Red, blue, gray, white, yellow, and dark andlight green colors indicate Fe, N, C, H, Cl, and F atoms.

TABLE 4: Given Are the Results from DFT+UCalculations for the FePF2 Molecule Analyzing theElectronic Distribution for U ) 6 eV and S ) 2 and S ) 3Spin States

S ) 2 (4 µB) S ) 3 (6 µB)

Fe d moment 4.27 4.30Fe d occ. nr. 5.71 5.80F p moment 0.14 (×2) 0.16 (×2)F p occ.nr 4.04 (×2) 4.33 (×2)N p moment -0.03 (×4) 0.12 (×4)N p occ. nr. 2.13 (×4) 2.62 (×4)Cbridge p moment -0.11 (×4) 0.10 (×4)Cbridge p occ. nr. 1.84 (×4) 1.75 (×4)

Figure 5. Computed partial DOS of FePF2 at U ) 6 eV for the S )1 (top), S ) 2 (middle), and S ) 3 (bottom) spin states.


dxy state at about -2.8 eV moves to the unoccupied states justover 3 eV for the higher spin configurations. The unoccupiedspin-majority dx2-y2 state at 1 eV moves to 0.5 eV below theFermi energy. Also, a switch in the dz2 and dx2-y2 very close tothe Fermi level is noticeable. The dz2 orbital becomes onlypartially occupied, located very close to the Fermi energy. Onceagain, we can emphasize from Figure 6 that very little changeis seen on the Fe atom between the S ) 2 and the S ) 3,reiterating the importance of the ring, in stabilizing the higherS ) 3 spin state configuration.

IV. Conclusions

In conclusion, we have shown an improvement over the DFT-GGA approach in describing complex, intricate five- and six-ligated prophine molecules using both DFT+U and UB3LYP.The DFT+U, and UB3LYP calculations reproduce the experi-mental bond lengths reasonably well. For FePCl, the Fe(III)high-spin state is more favored and the possible explanantionrather tangible, correlating the out-of-plane displacement witha higher spin state, as shown by Liao and Scheiner.22

More importantly, both methods give a clearer explanationfor the controversal magnetic properties in FePF2, where theDFT+U clearly shows a redistribution of the electron densitywithin the porphine ring resulting in the high-spin state S ) 3for the whole molecule. The difference in the magnetizationdensity shows the largest change in the N pz and the bridgingC pz contributing to the overall high spin S ) 3. The energydifferences between the spin states agree well with previouslyreported CASPT2 results of Ghosh and Taylor17 as well asexperimental reports of an Fe(III) high spin state for the FePF2

species. From this investigation, we also conclude that DFT+Uand UB3LYP do not support the existence of Fe(IV) in FePF2.

DFT-based methods have the advantage that they are com-putationally fast. However when studying complex biomol-ecules, one needs to calibrate against other theoretical resultsand/or experiments. Here we have used earlier CASPT2calculations as an accurate reference to perform such calibration.An implication of our study is that DFT+U and UB3LYP cansuccessfully be used to describe challenging ligated porphinessuch as π radical systems. This may be particularly advantageouswhen studying metallorganic molecules in extended or complexsystems, as periodic boundary conditions are naturally incor-porated in codes developed within a condensed matter frame-work. Our results suggest that the DFT+U technique is a good

choice for studying the interaction of magnetic metallorganicmolecules with surfaces.

Acknowledgment. This work has been supported throughthe EU network “MOT-TEST”48 of the European Commission,the Carl Tryggers Foundation, SIDA, and STINT. We gratefullyacknowledge computer time from the Swedish National Infra-structure for Computing (SNIC).

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Halide ligated iron porphines: A DFT+U and UB3LYP study

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