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Broken-Symmetry DFT Spin Densities of Iron Nitrosyls, Including Roussin’s Red and Black Salts: Striking Differences between Pure and Hybrid Functionals Kathrin H. Hopmann,† Jeanet Conradie,†,‡ and Abhik Ghosh*,† Department of Chemistry and Center for Theoretical and Computational Chemistry, UniVersity of Tromsø, N-9037 Tromsø, Norway, and Department of Chemistry, UniVersity of the Free State, 9300 Bloemfontein, Republic of South Africa ReceiVed: May 4, 2009; ReVised Manuscript ReceiVed: May 19, 2009
Pure and hybrid exchange-correlation functionals, as typified by OLYP and B3LYP, respectively, yield dramatically different spin density profiles for a variety of paramagnetic iron nitrosyls. Not unexpectedly, based on the strongly noninnocent nature of the NO ligand, the strength of metal-NO spin coupling appears to vary widely as a function of the functional chosen. For the diamagnetic Roussin’s red salt, red salt esters, and black salt, OLYP and B3LYP yield very different Fe-Fe spin coupling strengths, with OLYP exhibiting a greater preference for a more spin-coupled description. Introduction One of density functional theory’s (DFT) great strengths is that it generally provides a good description of transition metal complexes, notably their structures, vibrational frequencies, spin densities, and other ground-state properties.1 However, a key area where DFT falters concerns the spin-state energetics of transition metal complexes, a problem that we2 and others3,4 have documented for a variety of complexes. In a recent study, we found that, for certain NO complexes, the spin density too exhibits a disturbing dependence on the exchange-correlation functional chosen.5 Given the importance of metal-NO interactions in biology6 (as well as, of course, in inorganic chemistry7,8), we carried out a systematic exploration of the problem. Thus, we have examined the spin density profiles of a number of S ) 1/2 heme and nonheme {FeNO}7 derivatives, S ) 3/2 nonheme {FeNO}7 derivatives,9 and S ) 1/2 {Fe(NO)2}9 derivatives, as well as broken-symmetry states of the diamagnetic, polynuclear Roussin’s red and black salt anions, using both pure and hybrid functionals. Large differences between pure and hybrid DFT spin density profiles were found to be ubiquitous, as recounted below. Methods The ADF200710 and Gaussian0311 program systems were used in this study. By and large, we will focus on results obtained with OLYP12 and B3LYP13 (as in Table 1), as typifying pure and hybrid functionals, respectively, although in a few instances we will discuss a wider range of functionals to better illustrate a trend. Slater-type triple-ζ plus polarization (STO-TZP) basis sets were used with ADF, and the 6-311G(d,p) basis set was used with Gaussian 03. Throughout, we used fine meshes for numerical integration of matrix elements as well as adequately tight criteria for geometry optimizations. Results and Discussion (a) S ) 1/2 {FeNO}7 Systems. Nitrosylhemes, arguably the most important NO complexes in biology, are invariably low* To whom correspondence should be addressed. E-mail: abhik@ chem.uit.no. † University of Tromsø. ‡ University of the Free State.
TABLE 1: OLYP (in Bold) and B3LYP (in Italics) Mulliken Spin Populations for Selected FeNO Complexes (Ltrans Refers to the Ligand trans to the NO Group) complex Fe(P)(NO) Fe(P)(NO)(ImH) [Fe(P)(NO)(SMe)]FeNO tropocoronand [Fe(CN)4(NO)]2[Fe(StBu)3(NO)]FePS3(NO) [Fe(SMe)2(NO)2]-
S
M
N
O
1/2 1/2 1/2 1/2 1/2 1/2 1/2
1.105 0.702 0.627 0.232 0.313 -0.164 1.206
-0.036 0.207 0.236 0.480 0.337 0.648 -0.202
-0.067 0.100 0.128 0.281 0.189 0.392 -0.150
1/2 1/2 1/2 3/2 3/2 1 1 1/2 1/2
1.759 1.253 1.824 2.953 3.387 1.663 2.219 1.571 3.200
-0.484 -0.125 -0.449 -0.394 -0.631 -0.157 -0.367 -0.261 -0.701
-0.365 -0.104 -0.314 -0.282 -0.462 -0.130 -0.322 -0.184 -0.545
Ltrans
0.028 0.013 0.165 0.092
-0.050 -0.103
spin (S ) 1/2) and feature a strongly bent MNO unit with an MNO angle of about 140°.6,8 This bent geometry is most simply explained in terms of the topology of the SOMO, which involves a σ-bonding interaction between the metal dz2 orbital and an NO π* orbital.8 Figures 1 and 2 present key calculated results (obtained with the OLYP functional) on three different {FeNO}7 heme-NO model complexes: five-coordinate [Fe(Por)(NO)] and the six-coordinate complexes [Fe(Por)(NO)(ImH)] and [Fe(Por)(NO)(SMe)]-. The spin density profiles are consistent with EPR hyperfine parameters, which have long indicated a sharp dependence on the nature of the trans ligand. This effect is readily understood in qualitative molecular orbital terms: As shown in Figure 2, a stronger trans ligand (on account of its stronger antibonding interaction with the metal dz2 orbital) pushes more of the spin density from the Fe over to the NO.14,15 Quantitatively, however, the picture is less clear-cut. As shown in Table 1, the spin density varies greatly between a pure functional (OLYP) and the hybrid functional B3LYP. Thus, for five-coordinate Fe(P)(NO), the Fe spin population is considerably higher for OLYP (1.1) than for B3LYP (0.7), the reverse being true for N and O spin populations. As shown
10.1021/jp904135h CCC: $40.75 2009 American Chemical Society Published on Web 07/01/2009
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Figure 1. Selected DFT (STO-TZP) results on {FeNO}7 porphyrins as a function of different sixth ligands (no ligand, imidazole, and methylthiolate). Bond distances (Å) and angles (deg) are shown with a normal font, whereas Mulliken spin populations are shown in bold. The Fe(P)(NO)(ImH) calculations were performed on the PW91 geometry. The spin density plots use a contour of 0.008 e/Å3.
Figure 2. OLYP/TZP SOMOs of three {FeNO}7 porphyrins, emphasizing the role of the sixth ligand.
in Figure 1, the Fe spin population is much lower for Fe(P)(NO)(ImH) for both functionals; however, note again that the OLYP and B3LYP spin populations are quantitatively quite different. With the very strong-field thiolate as the trans ligand, the OLYP Fe spin population (0.3) is even lower, whereas the B3LYP Fe spin population (-0.16) actually becomes negative; as expected, the effects are opposite for
the N and O spin populations. Lehnert and co-workers have reported B3LYP calculations of the 14N hyperfine parameters of certain of these systems, obtaining fair agreement with experiment.16 However, a detailed comparison of experimental and calculated hyperfine parameters, as a function of different exchange-correlation functionals, is yet to be reported. At this point, therefore, we simply do not know
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Figure 3. Selected OLYP and B3LYP (STO-TZP) results for [Fe(CN)4(NO)]2- (C4V). Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.008 e/Å3 has been used for the spin density plots.
enough about the relative merits of different functionals visa`-vis nitrosylheme spin densities.17-19 To ensure coverage of a variety of electronically diverse iron nitrosyls, we have also examined here two unusual, S ) 1/2, nonheme {FeNO}7 complexes: [Fe(CN)4(NO)]2- (Figure 3) and [Fe(5,5-tropocoronand)(NO)] (Figure 4); their unusual feature is a linear FeNO group, which is rare for low-spin {FeNO}7 complexes.20-22 The linearity of the FeNO units in these species, however, has been addressed in some detail, so here we will simply examine their spin density profiles. Both functionals indicate substantial spatial separation of majority and minority spin densities: roughly speaking, OLYP indicates a spin population of about -0.25 on the NO group in both complexes, while B3LYP indicates a far larger negative spin density of -0.75 (see Figures 3 and 4 and Table 1). In other words, B3LYP indicates an intermediate-spin Fe(III)-NO--like description for both species. (b) Nonheme FeNO Complexes with High-Spin Iron Centers. Numerous nonheme S ) 3/2 {FeNO}7 complexes are known, and there is fair agreement that they are best described as S ) 5/2 Fe(III) centers antiferromagnetically coupled to S ) 1 NO- diradicals. A fairly typical example is provided by the [Fe(StBu)3(NO)]- anion,23,24 for which selected OLYP/STOTZP results are shown in Figure 5. The corresponding B3LYP spin populations are given in Table 1. Observe that the spin density plot, depicting a major spatial separation of the majority and minority spin densities, is consistent with the antiferromagnetically coupled electronic description mentioned above. Table 1 shows that the OLYP and B3LYP spin densities are significantly different, although perhaps not as radically as for the S ) 1/2 {FeNO}7 complexes described above.
Hopmann et al.
Figure 5. Selected OLYP/STO-TZP results for the [Fe(StBu)3(NO)]anion. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.008 e/Å3 has been used for the spin density plot.
Figure 6. Selected OLYP/STO-TZP results for [Fe(PS3)(NO)]. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. The contour for the spin density plot is 0.008 e/Å3.
Koch, Lippard, Ghosh, and their co-workers have recently reported an S ) 1 {FeNO}6 complex, [Fe(PS3)(NO)], where PS33- is a trithiolatophosphine ligand.24 Here, we will not comment on the unique S ) 1 ground state of this complex, except that it follows straightforwardly from a consideration of its three-fold-symmetric structure. This complex is trigonalbipyramidal with an apical NO, and DFT calculations24 (Figure 6) indicate that it is exactly C3V. The calculated spin density (OLYP and B3LYP) is largely confined to the equatorial FeS3 moiety, suggesting a dxz2dyz2dxy1dx2-y21 electronic configuration, which was confirmed by an examination of the Kohn-Sham
Figure 4. Selected OLYP/STO-TZP results for [Fe(5,5-tropocoronand)(NO)]. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.008 e/Å3 has been used for the spin density plot.
Broken-Symmetry DFT Spin Densities of Iron Nitrosyls
J. Phys. Chem. B, Vol. 113, No. 30, 2009 10543 TABLE 2: Selected Optimized 6-311G(d,p) Geometry Parameters (Å, deg) for Roussin’s Red Salt Dianion and Comparison with Experiment X-ray R-B3LYP R-OLYP BS-U-B3LYP BS-U-OLYP (average)30
Figure 7. Selected OLYP/STO-TZP results for the [Fe(SMe)2(NO)2]anion. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.008 e/Å3 has been used for the spin density plot.
MOs. Still, as shown in Figure 6, OLYP results in a significant minority spin density of about -0.3 on the NO moiety. In contrast, with B3LYP (Table 1), the combined NO spin population is about -0.7, i.e., substantially different from that predicted by pure functionals. Dinitrosyl iron complexes (DNICs),25,26 typified by the {Fe(NO}2}9 [Fe(SMe)2(NO)2]- anion, are yet a third type of nonheme iron nitrosyl with a high-spin iron center. Both the OLYP and B3LYP spin density profiles (Figure 7), along with an examination of the Kohn-Sham MOs, indicate a high-spin Fe(III) center antiferromagnetically coupled to a pair of NOdiradicals, resulting in an overall S ) 1/2. Quantitatively, however, the OLYP and B3LYP spin populations are significantly different, with B3LYP exhibiting much greater spatial separation of the majority and minority spin densities. (c) Roussins’s Red Salt. In view of the subtleties delineated above, the performance of different functionals vis-a`-vis Roussin’s red and black salt anions appeared to be of exceptional interest. Both salts have attracted interest as potential lightactivated NO-donating cancer drugs.27 Roussin’s red salt (RRS) and its esters (see below for a discussion of the esters, where the bridging sulfurs are alkylated) are conveniently and, as it
Fe-Fe Fe-S Fe-N N-O Fe-N-O
2.740 2.247 1.616 1.196 162.21
2.786 2.253 1.630 1.205 160.43
2.969 2.322 1.779 1.200 156.97
2.794 2.255 1.631 1.205 160.27
2.703 2.237 1.664 1.162 165.93
turns out, appropriately, viewed as DNIC dimers. Selected MS ) 0, broken-symmetry (BS) DFT/6-311G(d,p) results on the diamagnetic RRS dianion, [Fe2(µ-S)2(NO)4]2- (D2h), are presented in Figure 8 and Table 2. Although both OLYP and B3LYP yield broken-symmetry solutions with the 6-311G(d,p) basis set, the degree of R/β symmetry breaking is very different for the two functionals. Thus, whereas OLYP yields only small excess spin populations,28 B3LYP yields large spin populations typical of openshell mononuclear iron nitrosyls (Figure 8). Not surprisingly, the energetics of the Fe-Fe spin coupling is also strongly functional dependent. With the MS ) 0, broken-symmetry state as zero level, the energy of the ferromagnetically coupled, MS ) 1 state is 0.63 eV with OLYP but only 0.30 eV with B3LYP* and 0.23 eV with B3LYP.29 In the same vein, as shown in Table 2, key geometry parameters such as the Fe-Fe, Fe-S, and Fe-N(O) distances all show a disturbing dependence on the functional used. Thus, spin-restricted and spin-unrestricted calculations yield substantially different geometry parameters. It may surprise some that the spin-restricted structural parameters seem to agree best with experiment,30 whereas the BS-B3LYP geometry appears to be the worst.31 (d) Roussins’s Red Salt Esters. Roussin’s red salt esters are neutral molecules with the general formula Fe2(NO)4(µ-SR)2,
Figure 8. Selected DFT/6-311G(d,p) results for Roussin’s red salt dianion. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.03 e/Å3 has been used for the spin density plot.
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Figure 9. Selected DFT/6-311G(d,p) results for Roussin’s red salt ester. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.03 e/Å3 has been used for the spin density plot.
TABLE 3: Selected Optimized 6-311G(d,p) Geometry Parameters (Å, deg) for the anti (C2h) Conformation of Roussin’s Red Salt Ester and Comparison with Experiment R-B3LYP R-OLYP BS-U-B3LYP X-ray (average)34 Fe-Fe Fe-S Fe-N N-O Fe-N-O
2.659 2.220 1.630 1.162 167.75
2.696 2.228 1.639 1.173 166.35
3.115 2.379 1.729 1.168 165.44
2.72 2.27 1.67 1.17 167.5
where R is an alkyl or aryl group.32 NMR evidence suggests that the red salt esters exist as equilibrium mixtures of syn and anti conformations (which differ in the orientation of the R groups relative to the Fe2S2 plane). Our calculatons, with R ) benzyl, are qualitatively consistent with the NMR results and indicate equienergetic syn and anti conformations. However, the reported X-ray crystal structures of red salt esters show only the anti conformation,32,33 so for brevity’s sake, DFT results for only the anti conformation are presented in Figure 9 and Table 3. The red salt ester results differ in some ways from the red salt results. For example, broken-symmetry OLYP calculations did not prove feasible for the esters as they did for the red salts. As shown in Figure 9, however, BS-B3LYP calculations did succeed and the spin populations are qualitatively similar to those found for the red salt. Obviously, these spin populations are not real (and are simply an artifact of the broken-symmetry method), but they do indicate that the FeNO centers in the esters are locally quite similar to those in the red salt. Second, the thiolate bridges in the red salt esters result in somewhat smaller Fe-Fe spin couplings, relative to the red salt. Thus, for OLYP, the ferromagnetically coupled S ) 1 state is only about 0.5 eV higher than the antiferromagnetically coupled (spin-restricted) S ) 0 state. With B3LYP, this energy difference drops to only
about 0.15 eV. One similarity with the red salt results is that the spin-restricted (OLYP or B3LYP) geometry parameters of the red salt esters are in significantly better agreement with experiment than the BS-B3LYP results (see Table 3). (e) Roussins’s Black Salt (RBS). Like RRS, diamagnetic Roussin’s black salt (RBS), Na[Fe4(µ-S)3(NO)7], is also of interest as a locally applicable, photochemical NO donor against cancer cells, although its general toxicity prevents its use as a systemic drug.35 Broken-symmetry B3LYP calculations on the C3V RBS anion have been reported by Jaworska and Stasicka.36 In this study, we have repeated and extended those calculations. Figure 10 and Table 4 present our most important results. Importantly, a variety of functionals, both pure and hybrid, yielded broken-symmetry MS ) 0 solutions. The overall electronic structure, regardless of the functional, is best described as a central S ) 3/2, tetrahedral {FeNO}7 unit, antiferromagnetically coupled to three S ) 1/2 {Fe(NO)2}9 (dintrosyl iron complex or DNIC) units. The three DNICs are thus forced to adopt a spin-frustrated ferromagnetic configuration. This may be seen visually from the broken-symmetry B3LYP MS ) 0 spin density plot in Figure 10d. The spatial separation of the R and β spin densities, as a function of the exchange-correlation functional, exhibits the same trend as found in the rest of this study; i.e., the separation is much more dramatic with hybrid functionals than it is with pure functionals. The reader may verify this from the brokensymmetry OLYP and B3LYP spin populations shown in Figure 10. Although a detailed analysis of the spin couplings in this remarkable structure has not been accomplished yet, they are expected to be strong. Thus, the ferromagnetically coupled, MS ) 3 state was found to be considerably above the brokensymmetry, MS ) 0 state for both pure and hybrid functionals, the energy difference being 0.51 eV with B3LYP, 0.66 eV with
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Figure 10. Selected DFT/6-311G(d,p) results for Roussin’s black salt anion. Distances (Å) and Mulliken spin populations are indicated in normal and bold fonts, respectively. A contour of 0.03 e/Å3 has been used for the spin density plot.
TABLE 4: Selected Optimized 6-311G(d,p) Geometry Parameters (Å, deg) for the Roussin’s Black Salt Anion and Comparison with Experiment FeA-S FeA-NA NA-OA FeB-S FeB-NB/FeB-NC NB-OB/NC-OC FeA-FeB FeB-FeB FeA-NA-OA FeB-NB-OB/FeB-NC-OC
R-B3LYP
R-OLYP
BS-U-B3LYP
BS-U-OLYP
X-ray (average)30,39
2.135 1.603 1.169 2.235 1.623/1.625 1.173/1.170 2.647 3.697 180.00 165.90/164.61
2.141 1.616 1.180 2.240 1.637/1.632 1.183/1.180 2.637 3.720 180.00 161.82/166.20
2.301 1.737 1.172 2.376 1.743/1.732 1.177/1.175 3.034 3.925 180.00 161.43/164.21
2.201 1.652 1.179 2.277 1.649/1.639 1.183/1.179 2.772 3.777 180.00 158.87/166.29
2.205 1.651 1.159 2.256 1.669 1.160 2.697 3.569 176.5 168.1
B3LYP*, and 1.21 eV with OLYP. In other words, the higher the amount of exact exchange in the functional, the less is the energy cost associated with spin decoupling. To even more clearly illustrate the difference in behavior among different functionals, Figure 11 presents spin density plots and Fe spin populations for the ferromagnetically coupled, MS ) 3 state of the RBS anion for five different functionals: BHandHLYP, B3LYP, B3LYP*,37 OLYP, and PW91.38 Observe how the Fe spin population goes down along this series. Also, observe qualitatively how the spin density on the NO moieties shrinks along the series. In other words, the degree of Fe-NO covalence increases significantly along this series of functionals; i.e., we get a more covalent description as the amount of exact exchange decreases in the functional in question. As in the case of the red salt, the optimized structural parameters of the RBS anion depend significantly on the exact
DFT method chosen (see Table 4). OLYP seems to perform distinctly better than B3LYP, and BS-B3LYP, surprisingly, appears to yield the worst structural parameters, compared with experiment.30,39 The atom labels used in Table 4 are defined in the scheme below.
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Hopmann et al. It would be wrong, however, to conclude that B3LYP is generally better than pure functionals vis-a`-vis spin densities of noninnocent transition metal systems.2 We have already pointed out one of B3LYP’s imperfections: broken-symmetry B3LYP gives a poorer geometry of Roussin’s black salt, relative to pure functionals and spin-restricted calculations. In the same vein, B3LYP unduly favors the S ) 3/2 state for the spincrossover complex Fe(salen)(NO), while OLYP correctly predicts equienergetic doublet and quartet states.5 In conclusion, variations in iron nitrosyl spin densities across different exchange-correlation functionals are both striking and ubiquitous. However, at this point, we are unable to identify any one functional as being distinctly better than most others. Extensive and careful calibrations against experimental EPR and Mo¨ssbauer parameters may allow us to make such an identification. Such studies are now in progress in our laboratory and will be reported in due course. Acknowledgment. This work was supported by the Research Council of Norway (A.G.) and the National Research Fund of the Republic of South Africa (J.C.). Supporting Information Available: Optimized Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 11. Iron spin populations for the ferromagnetically coupled, MS ) 3 state of the RBS anion for different functionals and the 6-311G(d,p) basis set (Gaussian 03). A contour of 0.03 e/Å3 has been used.
Concluding Remarks In conclusion, we must again emphasize that the spin density profiles of transition metal complexes are generally relatively independent of the choice of the exchange-correlation functional. Thus, for the great majority of iron complexes, the spin densities exhibit minor variations, depending on the functional. Against this context, as discussed above, iron nitrosyls and, by extension, transition metal nitrosyls in general are radically different. Large variations in the spin density profile are the rule, rather than the exception. Why does DFT behave so erratically for transition metal nitrosyls? We believe that the divergent behavior of different functionals is related to the noninnocent nature of the NO ligand. Because different functionals have inherently different tendencies to pair up electrons, they result in different degrees of antiferromagnetic coupling between the metal center and the NO ligand. This is reflected in the highly variable spin density profiles as well as the highly functional-dependent spin-coupling energies for Roussin’s red and black salts. Noninnocent behavior is obviously not limited to NO complexes;40 another class of complexes where the spin densities vary significantly with the choice of the exchange-correlation functional is the metallocorrole family. Thus, for the S ) 1 Fe(corrolato)Cl derivatives, both pure functionals and B3LYP suggest an S ) 3/2 Fe(III) center antiferromagnetically coupled to a corrolate•2- radical; however, the degree of separation of the majority and minority spin densities is much greater with B3LYP than with pure functionals.19,41 Which then is better? In a recent study, we found that the B3LYP spin density is in significantly better accord with the ab initio CASSCF spin density, suggesting that it may be better than spin densities obtained with pure functionals.42
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