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Relativistic effects in iron-, ruthenium-, and osmium porphyrins
Chemical Physics 285 (2002) 195–206 www.elsevier.com/locate/chemphys
Relativistic effects in iron-, ruthenium-, and osmium porphyrins Meng-Sheng Liao, Steve Scheiner * Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA Received 8 April 2002
Abstract Nonrelativistic and relativistic DFT calculations are performed on four-coordinate metal porphyrins MP and their six-coordinate adducts MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) with M ¼ Fe, Ru, and Os. The electronic structures of the MPs are investigated by considering all possible low-lying states with different configurations of nd-electrons. FeP and OsP have a 3 A2g ground state, while this state is nearly degenerate with 3 Eg for RuP. Without relativistic corrections, the ground states of both RuP and OsP would be 3 Eg . For the six-coordinate adducts with py and CO, the strong-field axial ligands raise the energy of the M dz2 -orbital, thereby making the MII ion diamagnetic. The calculated redox properties of MPðpyÞ2 and MP(py)(CO) are in agreement with experiment. The difference between RuP(py)(CO) and OsP(py)(CO), in terms of site of oxidation, is due to relativistic effects. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Ground state; Ionization potential; Electron affinity; Orbital energies
1. Introduction Metal porphyrins (MP) represent a particularly important class of biological molecules [1]. Iron porphyrin (FeP) [2], for example, is the functional part of both hemoglobin and myoglobin, which are oxygen carriers in animals. MPs are also highly promising as catalysts for a number of chemical reactions [3,4], as enzyme models, as photosensitizers, and as medicinal preparations. No wonder then that so much experimental and theoretical effort has been directed towards the elucidation of the detailed nature of MPs. *
Corresponding author. E-mail address: [email protected] (S. Scheiner).
While experimental studies of MPs have been expanded by the synthesis of species containing second- and third-row transition metals [5–9], theoretical studies have mainly been devoted to the first-row transition metal porphyrins. Certain special and unusual properties of heavy metal porphyrins are worthy of attention. One example arises from the Fe, Ru, Os series. Electrochemical studies show that osmium porphyrin, with pyridine (py) and CO as axial ligands [OsP(py)(CO)], undergoes metal-centered oxidation to yield an OsIII species [7]. Iron-carbonyl porphyrins such as FeP(imidazole)(CO) behave like OsP(py)(CO) in this regard [7]. In contrast, the related complex of ruthenium undergoes one-electron oxidation at the porphyrin ring [6–8]. The situation is different for
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 8 3 6 - 4
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the dipyridyl systems, where one-electron oxidation of the entire M ¼ Fe, Ru, Os set of MPðpyÞ2 systems is metal-centered [6–8]. The change in the oxidation site from MPðpyÞ2 to MP(py)(CO) has been explained in the Ru porphyrin by stronger back bonding to CO compared to py [7]. The argument continued [7] that for the Fe- and Oscarbonyl complexes, the metal d-orbitals are not sufficiently stabilized, although the same effect occurs for iron and osmium. One is left with the fundamental question as to why Os behaves differently than Ru in the carbonyl porphyrin. It is well known that heavy atomic systems may be greatly influenced by relativistic effects [10]. For the positive MII ion, where the ns-electrons are removed into the electronegative porphyrin from the ionic point of view, ðn 1Þd becomes the outermost shell. The 5d-orbitals of heavy OsII might be strongly expanded and destabilized by relativity, making these electrons easier to remove. Relativistic effects may be an important factor in understanding the different oxidation sites in RuP(py)(CO) and OsP(py)(CO). The observation of oxidation state isomerism, in which the isomers differ with regard to the site of oxidation, serves as the impetus for a more thorough examination of relativistic effects in Fe-, Ru-, and Os porphyrins. It turns out that relativistic effects change not only the oxidation site in OsP(py)(CO), but also the ground state electronic configurations of the unligated, four-coordinate RuP and OsP.
2. Computational method The calculations reported in this work were carried out using the Amsterdam density functional (ADF) program package developed by Baerends et al. [11]. Slater-type orbital (STO) basis sets are employed and inner-shell electrons are treated in the frozen-core approximation [11a]. Two kinds of relativistic approaches have been implemented in the present ADF program: scalar quasi-relativistic (QR) [12] and the scalar relativistic zero-order regular approximation (ZORA) [13]. The QR method is the standard method in relativistic ADF calculations and applications to
the investigation of relativistic effects in heavy element systems have been quite successful [14]. However, it is a shortcoming of the QR method that variational collapse may sometimes occur. Indeed, it was found in the present work that QR results on one of the systems, OsPðpyÞ2 , are wrong, in that the orbital energies are far too low. There are also errors in the QR results for OsP(py)(CO), although the problem in this system is less serious than in OsPðpyÞ2 . (The origin of this variational collapse in the QR method has been explained in [15].) The ZORA method, which has been recently implemented in the ADF program, is a variationally stable relativistic method and gives accurate one-electron orbital energies and densities [13]. Thus, the principal relativistic approach employed here is ZORA. For the sake of comparison, QR results are also presented for the unligated MPs. The exchange-correlation potential used in this work is based on the density parametrized form of Vosko et al. [16]. The nonlocal corrections are based on Becke’s gradient functional for exchange [17] and Perdew’s gradient functional for correlation [18], and treated by a fully self-consistent method. In the nonrelativistic (Nrel) and QR calculations the standard ADF basis set IV was used, which is triple-f for valence orbitals plus one polarization function. In the ZORA calculations, special relativistic (reoptimized) basis set, ZORA/ IV, was used for the metals; it is of the same size as the ADF IV basis set. To obtain accurate results, the valence set on the metals included subvalence ðn 1Þs and ðn 1Þp shells. For C, N, and O, 2s and 2p were considered as valence shells. The other shells of lower energy, i.e. [Ne] for Fe, [Ar3d10 ] for Ru, ½Kr4d10 4f 14 for Os, and [He] for C/N/O, were described as core and kept frozen. For the open-shell states, the unrestricted Kohn– Sham (UKS) spin-density functional approach was adopted.
3. Results and discussion 3.1. MP (M ¼ Fe, Ru, Os) The unligated metal porphyrins (MP) serve as a starting point for examining the effects of axial
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ligands on the electronic structure and redox properties of the MPs. The molecular structure of the simplest metal porphyrin, metal porphine, is illustrated in Fig. 1, along with the definition of a and b positions in the rings. The systems that have been synthesized contain phenyl or ethyl groups as substituents on the periphery of the porphyrin ring. The use of metal porphine as a model for larger and more complicated systems has been justified in our previous calculations [19], which showed that the electronic properties of metal porphyrins are insensitive to the nature of these peripheral substituents. The MP in Fig. 1 has D4h symmetry. Taking the z-axis as perpendicular to the porphinato plane, the five M nd-orbitals transform as a1g ðdz2 Þ, b1g ðdx2 y 2 Þ, eg ðdp , i.e., dxz and dyz ), and b2g ðdxy Þ. Various occupations of the six electrons in the d-orbitals of the MP can yield eight possible lowlying states: one low-spin ðS ¼ 0Þ, four intermediate-spin (S ¼ 1), and three high-spin (S ¼ 2) states. The energies of all these spin states have been computed, along with full geometry optimization of each. Their relative energies are presented in Table 1, along with the M–N bond length of each. Fig. 2 illustrates the valence molecular orbital
Fig. 1. Molecular structure of metal porphine (MP), indicating a and b positions.
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(MO) energy levels for the nonrelativistic (Nrel) and relativistic (Rel) ZORA ground states of the MPs, obtained by spin-restricted calculations. The orbital energies for FeP are nearly unaffected by relativistic corrections. Calculated values of M–P binding energies (Ebind ), ionization potentials (IPs) for several outer MOs, electron affinities (EAs), and Mulliken charge distributions on the M (QM ) are reported in Table 2. Ebind is defined as the energy required to extract the M from the porphyrin: Ebind ¼ EðMPÞ fEðMÞ þ EðPÞg: The atomic ground state configurations for the transition metal atoms Fe, Ru, and Os are 3d6 4s2 , 4d7 5s1 , and 5d6 6s2 , respectively. For the calculations of the atomic energies of M with an open and degenerate dn shell, the n electrons were distributed equally over the five d-orbitals; i.e., occupations of n=5 electrons were chosen for each dxy , dxz , dyz , dx2 y 2 , and dz2 orbital, the ‘‘average-of-configuration’’ (AOC) calculation [20], which can avoid some uncertainties in the DFT energies of systems with a degenerate state. AOC calculations were spin-unrestricted. For the molecular systems with an open and degenerate shell such as ðeÞ1 or ðeÞ3 , the same AOC method was used. The occupations of the AOC orbitals do not correspond to a real Slater-determinant. The IPs and EAs were calculated by the socalled DSCF method which computes each property as the difference in total energy between the neutral and ionized species. Diffuse functions have been suggested to be essential for calculations of EAs. SCF convergence problems were encountered with the extra basis sets in the calculations of the negative ½MP systems, preventing examination of the effects of diffuse functions on the calculated EAs. We believe that the present basis sets of triple-f quality are adequate. For instance, the calculated EA values for FeTPP and NiTPP were found to be in excellent agreement with the available experimental data [19]. 3.1.1. M ¼ Fe The electronic structure of FeP has been the subject of a great deal of interest and intense investigation because of its importance in biological
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Table 1 Calculated relative energies (E) and M–N bond lengths (R) for different configurations in FeP, RuP, and OsP State
Configuration b2g =dxy
a1g =dz2
1eg =dp
) RM–N (A
E (eV)
b1g =dx2 y 2
FeP
RuP
OsP
FeP
RuP
OsP
0 0 0
0 0 0
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.01 2.04
2
2
2
0
3
2
1
3
0
3
Eg (A)
Nrel QR ZORA
0.13 0.12 0.11
)0.10 )0.01 )0.02
)0.12 0.33 0.20
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.02 2.04
1
1
4
0
3
B2g
Nrel QR ZORA
0.26 0.26 0.25
0.26 0.34 0.35
0.31 0.77 0.59
1.99 1.98 1.98
2.07 2.05 2.05
2.09 2.03 2.05
1
2
3
0
3
Eg (B)
Nrel QR ZORA
0.76 0.74 0.74
0.69 0.67 0.70
0.68 0.66 0.61
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.01 2.04
1
2
2
1
5
A1g
Nrel QR ZORA
0.68 0.71 0.72
3.05 3.18 3.16
3.72 4.55 4.05
2.07 2.06 2.06
2.15 2.14 2.14
2.17 2.11 2.14
1
1
3
1
5
Eg
Nrel QR ZORA
0.81 0.85 0.86
3.02 3.24 3.21
3.68 4.87 4.30
2.06 2.06 2.06
2.15 2.14 2.14
2.17 2.12 2.14
2
1
2
1
5
B2g
Nrel QR ZORA
1.00 1.05 1.06
3.04 3.27 3.24
3.64 4.84 4.31
2.06 2.06 2.06
2.14 2.13 2.13
2.17 2.11 2.14
2
0
4
0
1
A1g
Nrel QR ZORA
1.45 1.49 1.47
0.98 1.27 1.22
1.01 2.28 2.02
1.99 1.98 1.98
2.06 2.05 2.05
2.09 2.04 2.06
A2g
Nrel QR ZORA
0 0 0
systems. There have been a spate of experimental and theoretical studies of FeP, including some very recent calculations [19,21–25]. One essential question in FeP concerns the ground state configuration of the FeII ion. From available experimental data, there seems to be little doubt that FeP exists in an intermediate-spin (S ¼ 1) state, due in part to the high energy of the antibonding b1g ðdx2 y 2 Þ orbital which leaves it unoccupied. Among the four possible intermediate-spin states, only 3 A2g arising from the ðdxy Þ2 ðdz2 Þ2 ðdp Þ2 configuration, is compatible with M€ ossbauer [26,27], magnetic [28], and proton NMR [29,30] data. Our calculation supports this experimental assignment. A 3 Eg state, 2 1 3 with occupation ðdxy Þ ðdz2 Þ ðdp Þ , is slightly higher 3 (0.1 eV) in energy and a B2g state lies slightly higher still. Because 3 Eg and 3 A2g are so close in energy, they may mix by spin–orbit (SO) coupling.
A more detailed discussion of the effects of SO coupling on the state energies can be found in [27,28]. The lowest quintet is 5 A1g , lying 0.7 eV above the ground state. The closed-shell 1 A1g singlet is the highest in energy among the eight lowlying states, 1.5 eV above the ground state. As indicated in Table 1, the calculated Fe–N bond lengths for the S ¼ 1 and S ¼ 0 states are nearly . Occupation of the dx2 y 2 orbital the same, 1.98 A for the S ¼ 2 states leads to an expansion of the porphinato core: the Fe–N bond lengths for the longer than the same bonds for quintets are 0.08 A the S ¼ 1 states. It is worth stressing that the energies and bond lengths of FeP in Table 1 are virtually unaffected by relativistic effects. Referring to Fig. 2, the Fe 3d-like orbitals are higher in energy than the ligand p-orbitals. The antibonding dx2 y 2 orbital ðb1g ) is particularly
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Fig. 2. Orbital energy levels at nonrelativistic (Nrel) and relativistic (Rel) ZORA levels. Rel levels are not shown explicitly for FeP as relativistic effects are minimal. Electron occupancies are explicitly shown for frontier MOs. Table 2 Calculated M–P binding energies ðEbind Þ, ionization potentials (IP), electron affinities (EA), and Mulliken charge distributions on the M ðQM Þ Ebind (eV)
IP (eV)
EA (eV)
QM
a1g =dz2
b2g =dxy
a2u
a1u
1eg =dp
10.38 10.25 10.25
6.38 (1st) 6.29 (1st) 6.29 (1st)
6.73 6.63 6.64
6.98 7.00 7.00
7.01 7.01 7.01
7.36 7.26 7.27
)1.66 ð1eg Þ )1.66 )1.66
0.68 0.66 0.67
Nrel (3 Eg Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
10.52 10.97 10.87
8.00 6.25 (1st) 6.27 (1st)
7.06 6.85 6.90
6.96 7.01 7.01
7.03 7.06 7.07
6.36 (1st) 6.87 6.87
)2.45 ð1eg Þ )2.10 ð1eg Þ )2.09
1.40 1.32 1.37
Nrel ð3 Eg Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
12.11 12.70 11.38
7.98 6.34 (1st) 6.26 (1st)
7.09 6.64 6.64
6.97 7.09 7.06
7.05 7.05 7.06
6.33 (1st) 6.49 6.55
)2.51 ð1eg Þ )2.09 ð1eg Þ )2.13
1.46 1.18 1.39
FeP
3
Nrel ð A2g Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
RuP
OsP
destabilized due to its interaction with the porphinato nitrogens. The dp and dz2 orbitals, which are nearly degenerate, are weakly antibonding, higher in energy than the nonbonding dxy , and represent a
group of HOMOs. As the first IP results from a1g ðdz2 Þ ionization, one-electron oxidation of FeP is associated with the central metal, in accord with electron spin resonance (ESR) measurements [31].
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This prediction is buttressed by the observation that the IP from the highest occupied porphyrin orbital (a2u ) is notably larger (0.7 eV) than that from Fe 3dz2 . Relativistic effects decrease the IPs from Fe d-orbitals by 0.1 eV, whereas the IPs from the porphyrin orbitals are scarcely affected at all. The Fe–P binding energy is estimated to be 10.3 eV. The strong interaction between the iron and the porphyrin accounts for its high thermal and chemical stability. A small relativistic destabilization of 0.1 eV is observed for the Fe–P binding. From Mulliken population analysis, 0.7e is transferred from Fe to P. 3.1.2. M ¼ Ru In contrast to FeP’s 3 A2g ground state, the 3 Eg state of RuP lies 0.1 eV below 3 A2g (prior to inclusion of relativity). There has been an earlier nonrelativistic DFT (DMol) calculation of RuP by Matsuzawa et al. [25], who found that the 3 Eg state is 0.2 eV lower than 3 A2g , similar to our value. (However, the DMol calculation predicted a 3 Eg ground state for FeP, which differs from our calculation.) Relativistic effects increase the relative energy of 3 Eg by nearly 0.1 eV, making it essentially degenerate with 3 A2g . The QR and ZORA results for RuP are essentially identical to one another. Consequently, the calculations are unable to unambiguously identify the true ground state of RuP. The three quintets are quite similar in energy, about 3.2 eV higher than the ground state, in contrast to the results for FeP, where the quintets are within about 1 eV of the ground state, and the energy varies in the clear order 5 A1g < 5 Eg < 5 B2g . Relativistic effects on the relative energies vary from one state to the next. Whereas 3 Eg (B) is little affected, the energies of the other states all undergo significant relativistic increases, 0.1 eV for 3 B2g and 5 A1g , 0.2 eV for 5 Eg and 5 B2g , and 0.3 eV for 1 A1g . longer While the Ru–N bond length is 0.06 A than in the Fe analogue, the values of Ebind reported in Table 2 reveal that Ru is more strongly bound than is Fe. The qualitative difference in relativistic effects between Fe–P and Ru–P can be attributed in part to the fact that the calculated binding energies refer to different atomic
ground state configurations for Feð3d6 4s2 Þ and Ruð4d7 5s1 Þ, and to the different relativistic and nonrelativistic electronic states of the RuP complex. The relativistic bond contraction of Ru–N is , slightly greater than in Fe–N. 0.01–0.02 A Fig. 2 reveals that the Ru 4d-like orbitals are destabilized by relativity, but only very slightly. On the other hand, the d-orbital energies and orderings for the 3 Eg state are somewhat different from those in 3 A2g , even though the two states are nearly degenerate at the relativistic level. The antibonding dx2 y 2 orbital in RuP is much more strongly destabilized than in FeP, offering an explanation as to why the quintets are much higher in energy above the ground state for RuP. The relativistic results for RuP in Table 2 refer to the 3 A2g state. Its first ionization occurs at the metal a1g ðdz2 Þ and the calculated IP1 value is nearly the same as that of FeP. However, the electron affinity of RuP is significantly more negative than that of FeP. The metal charge increases greatly from M ¼ Fe to M ¼ Ru, as witnessed by the final column of Table 2. 3.1.3. M ¼ Os At the nonrelativistic level, 3 Eg is the ground state for OsP, similar to the RuP case. However, a considerably larger relativistic energy increase of 3 Eg in OsP, as compared to RuP, raises this state significantly above 3 A2g , making the latter the true ground state. Except for 3 Eg (B), the relative energies of the different states are increased drastically by relativistic effects with respect to 3 A2g . The QR energy corrections are larger than those of the ZORA method, especially for the quintets. The QR method also yields larger relativistic bond contractions than does ZORA. Now, the quintets of OsP are more than 4 eV higher than the ground state in energy, even higher than in RuP. According to the ZORA results, the Os–N bond lengths are very similar to those in Ru–N, consis) and Ru tent with the atomic radii of Os (1.35 A (1.34 A). In the absence of relativistic effects, ROs–N longer than RRu–N . The Os–P bond reis 0.02 A mains stronger than that in Ru–P. There is a clear trend of increasing binding energy in the order FeP < RuP < OsP. The M–P binding energy can reflect the experimental data quite accurately. For
M.-S. Liao, S. Scheiner / Chemical Physics 285 (2002) 195–206
example, the trend in computed M–P binding energies for M ¼ Fe, Co, Ni, Cu, and Zn [19] is consistent with infrared spectral data [32]. The calculated IPs for OsP are similar to those for RuP, although certain discrepancies are connected with relativity, and the electron affinities of OsP and RuP do not differ by much, both being more negative than FeP. The effective atomic charges on Ru and Os are also similar, both being reduced by relativistic effects. 3.2. MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) One of the most important phenomena in metal porphyrins is the coordination of the central metal to molecules in addition to the porphyrin. The MPs with M ¼ Fe, Ru, and Os exhibit particularly strong attraction for additional ligands, to which their electronic structures are in turn sensitive. Experiments have shown that the six-coordinate metal porphyrins, MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) are low-spin, diamagnetic [33,34], in contrast to the four-coordinate species (S ¼ 1). This axial ligation in turn exerts an influence on the oxidation/reduction properties of the metal porphyrins, e.g., the oxidation potential and site are dependent upon the nature of the axial ligands [35]. For RuPðpyÞ2 , one-electron oxidation occurs at the metal ion, but if one py ligand is replaced by CO, it is the porphyrin ring which becomes the oxidation site. For M ¼ Fe and Os, on the other hand, no change in the oxidation site has been observed upon changing the axial ligand. Evidence is presented below that the variations of the oxidation site in RuP(py)(CO) and OsP(py)(CO) are due to relativistic effects. The calculated nonrelativistic (Nrel) and relativistic (Rel) properties of MPðpyÞ2 and MP(py)(CO) are collected in Table 3. The structures of the complexes have been optimized under D2h and C2v symmetries, respectively, where the py ring plane is perpendicular to the porphine and bisects the N– M–N angles of the latter; the M–CO attachment is linear. Effects of the axial ligands (py, CO) upon the various MO levels of FeP are displayed in Fig. 3. The left and right extremes of Fig. 3 represent the energy levels of the unperturbed py and CO ligands. Fig. 4 illustrates valence orbital en-
201
ergy levels for the various MP(py)(CO) complexes both without and with relativistic corrections. (QR results for MPðpyÞ2 and MP(py)(CO) are not presented here; Rel results were obtained with ZORA.) 3.2.1. M ¼ Fe As illustrated in Fig. 3, the repulsive interaction between the ligand HOMO and the M a1g ðdz2 Þ dramatically raises the energy of the latter. This rise removes any ambiguity about the 2 4 ground state configuration which is ðdxy Þ ðdp Þ for all. A subsidiary effect of the axial ligands is a lowering of the symmetry from D4h to D2h (in the case of MPðpyÞ2 ) and to C2v (for MP(py)(CO)) which splits the dxz and dyz degeneracy. The dxy ðb2g Þ orbital of FeP is shifted up enough so that it (transformed to a1g ) becomes the HOMO of the system. The first ionization in FePðpyÞ2 arises from the metal dyz ð1b3g Þ (HOMO-1); ionization from the dxy HOMO requires 0.24 eV more energy, and from b1u ða2u Þ of the porphyrin a further 0.4 eV. Compared to FeP, the IP1 of FePðpyÞ2 is decreased by 0.6 eV, suggesting that the axial ligands of FePðpyÞ2 ease the oxidation. These ligands also slightly increase the positive charge of the metal atom, as each ligand takes on about 0.2e of positive charge themselves. The primary net result is a flow of electron density into the porphyrin ring. The ligands also diminish the electron affinity of the assembly from )1.7 to )1.0 eV. The Ebind entry in Table 3 indicates that the two py ligands are bound to the complex by some 1.4 eV. Addition of the two py ligands elongates the Fe–N distance by a small amount, perhaps . 0.02 A Replacement of one of the py ligands by CO lowers all of the MOs. The dp orbitals are particularly stabilized, which may be attributed to Fe ! Lp back bonding, as illustrated in Fig. 3. The first ionization of FeP(py)(CO), unlike FePðpyÞ2 , occurs from the dxy ða1 Þ HOMO, but requires 0.8 eV more energy than the first IP in FePðpyÞ2 . The latter result is consistent with the experimental observation of an increase in the oxidation potential for MPðpyÞ2 on going to MP(py)(CO) [6]. The IP of the lower a1 , derived from P-a2u , is increased by only 0.25 eV.
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Table 3 Calculated properties of MP with two axial ligands MPðpyÞ2 M ¼ Fe RMNðpÞ
a
) (A
) RMNðaxÞ b (A ) RMCOðaxÞ (A ) RCt
M c (A QM Qpy QCO Ebind d (eV) ½MP–ðLÞ2 IPe (eV)
Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel
Rel
EA (eV)
Nrel Rel
2.00 2.00 2.03 2.01
M ¼ Ru 2.07 2.06 (2.05)f 2.12 2.10 (2.10)
0.72 0.73 0.19 0.19
1.40 1.41 5.94 5.69 6.33 5.92 5.68 6.34 )1.00 )1.01
MP(py)(CO)
1.82 1.96 0.01 )0.01
ða1g =dxy Þ ð1b3g =dyz Þ (1st) ðP-b1u Þ ða1g =dxy Þ ð1b3g =dyz Þ (1st) ðP-b1u Þ ð2b2g Þ ð2b2g Þ
2.57 2.73 6.38 5.90 (1st) 6.38 6.31 5.84 (1st) 6.40 )1.00 )0.99
M ¼ Os 2.09 2.06 2.16 2.10
1.59 1.70 0.08 0.02
2.91 2.91 6.42 5.88 (1st) 6.4 6.13 5.69 (1st) 6.45 )0.99 )1.06
M ¼ Fe
M ¼ Ru
M ¼ Os
2.02 2.01 2.09 2.06 1.76 1.76 0.04 0.04 0.49 0.50 0.24 0.24 0.04 0.03 1.92 1.93 6.51 6.70 6.59 6.49 6.67 6.60 )1.22 )1.22
2.08 2.07 2.23 2.21 1.86 1.87 0.07 0.08 1.54 1.71 0.08 0.07 )0.13 )0.19 3.29 3.37 7.12 6.77 6.62 7.03 6.72 6.62 )1.25 )1.24
2.10 2.07 2.28 2.23 1.93 1.88 0.09 0.10 1.45 1.45 0.15 0.12 )0.19 )0.20 3.55 3.72 7.11 6.74 6.68 (1st) 6.73 6.57 (1st) 6.70 )1.27 )1.25
(2.02)f (2.10) (1.77) (0.02)
ða1 =dxy Þ (1st) ð1b2 =dyz Þ ðP-a1 Þ ða1 =dxy Þ (1st) ð1b2 =dyz Þ ðP-a1 Þ ð2b1 Þ ð2b1 Þ
(2.05)f (2.19) (1.84) (0.08)
(1st)
(1st)
a
N(p) denotes porphinato nitrogen atom. N(ax) represents nitrogen atom of axial ligand (py). c Ct denotes the center of the ring and RCt
M the displacement of the M atom out of the porphinato plane. d Binding energy between MP and two L ligands. e See Figs. 3 and 4 for the orbitals in parentheses. f Values in parentheses represent X-ray diffraction data for related crystal compounds: RuPðpyÞ2 , Ref. [36] [in RuOEPðpyÞ2 ]; FeP(py)(CO), Ref. [34] [in FeTPP(py)(CO)]; RuP(py)(CO), Ref. [37] [in RuTPP(py)(CO)]. b
Therefore, the IPs of the Fe-dxy and P-a2u for FeP(py)(CO) are in fact rather close, within 0.1 eV of one another. There are X-ray diffraction data available for crystalline FeTPP(py)(CO) [34], which are in good agreement with the calculated bond lengths. Fe lies slightly out of the porphyrin plane, toward the CO experimentally, 0.04 A according to group (0.02 A calculations). This displacement is partially responsible for the elongation of the Fe–N(py) , relative to that in FePðpyÞ . distance by 0.05 A 2 Another result of the CO substitution is a reduction of the metal atom’s positive charge by roughly 1/4e, even though the CO itself remains essentially devoid of charge. The py/CO tandem is more strongly bound to the complex by about
0.54 eV than are a pair of py ligands, and makes the assembly more attractive toward an electron by about 0.2 eV. All in all, relativistic corrections are only very minor in the Fe complexes. 3.2.2. M ¼ Ru Replacement of the Fe by Ru stabilizes most of the orbitals, but the dxy -orbital by more. This is clearly shown in Fig. 4. The dxy IP is consequently enlarged more than those associated with the other d orbitals, and is no longer first IP. For RuPðpyÞ2 , the first ionization occurs at the 1b3g ðdyz Þ, similar to the case of FePðpyÞ2 . For RuP(py)(CO), on the other hand, the first ionization no longer occurs at the dxy , but at the a1 ða2u Þ orbital of the porphyrin. This result is in agreement with the experimental
M.-S. Liao, S. Scheiner / Chemical Physics 285 (2002) 195–206
203
Fig. 3. Orbital energy levels of FeP complexed to two axial ligands, as well as uncomplexed FeP and ligands (py, CO) for purposes of comparison. The upper unoccupied a1g of FePðpyÞ2 Þ involves a mixing of 70% FeP-a1g ðdz2 ) and 25% py-a1 . The 1b2 =1b1 of FeP(py)(CO) involves a mixing of 90% FeP-1eg (dp ) and 6% CO-p . The HOMO of CO is located at 9:2 eV.
observation that one-electron oxidation of RuP(py)(CO) is ring-centered [6–8]. Although in RuP(py)(CO) the dxy -orbital lies notably above the dyz in the orbital energy level diagram (see Fig. 4), the IP from the former is nevertheless 0.3 eV larger than that from the latter. (The same is true for M ¼ Os.) This situation contrasts with FeP(py)(CO). The dxy orbital behaves differently in the various MP(py)(CO) systems when an electron is removed from this 1 orbital. The singly occupied ðdxy Þ in [MP(py)þ (CO)] represents the HOMO for M ¼ Fe, but it is stabilized below a number of occupied orbitals for M ¼ Ru and Os. (Fig. 5 illustrates the relative po1 sitions of the ðdxy Þ level in the [MP(py)(CO)]þ ions, after an electron has been removed.) In FeP(py)(CO) the IP from dyz is 0.1 eV larger than that of the P-a1 ða2u Þ. A similar result is also found in RuP(py)(CO). Relativistic effects destabilize the Ru d-orbitals very little and reduce their IPs by about 0.1 eV. Electron affinities of the ligated Fe and Ru complexes are very nearly identical.
X-ray diffraction data are available for both RuOEPðpyÞ2 [36] and RuTPP(py)(CO) [37], which are again in excellent agreement with the calculated bond lengths. The axial ligands slightly elongate the Ru–N(p) bond lengths, compared to unligated RuP. Ru is displaced from the ring plane in RuP(py)(CO) by twice as much as is iron in FeP(py)(CO). The bond lengths from Ru to its two ligands are considerably longer than in the iron analogues. Nonetheless, the calculated M–ðLÞ2 binding energies indicate much stronger bonding of these ligands to Ru than to Fe (consistent with the much lower experimental C–O stretching frequency of the Ru complex [7]). The strongly bound CO ligand causes the Ru to displace out of the . porphyrin plane by 0.08 A 3.2.3. M ¼ Os Prior to relativistic corrections, the calculated orbital energies and IPs for OsPðpyÞ2 and OsP(py)(CO) are very similar to those obtained for
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Fig. 4. Nonrelativistic (Nrel) and ZORA relativistic (Rel) orbital energy levels of MP(py)(CO) for M ¼ Fe, Ru and Os.
Fig. 5. Comparison of the relative position of the singly occupied dxy -orbital in the different [MP(py)(CO)]þ ions.
M ¼ Ru, and would thus lead to much the same expectations. Relativity lowers the IPs of the Os dorbitals by 0.2–0.4 eV, sufficient to change the site of oxidation in OsP(py)(CO) as follows. The IP from the metal dyz is larger than that from the
P-a1 ða2u Þ in this species at the nonrelativistic level. After appropriate correction, the order reverses, and the one-electron oxidation of OsP(py)(CO) occurs from the metal, in agreement with experimental observation [7]. For OsPðpyÞ2 , the IP from the dyz is already significantly smaller than that from the P-a1 , even without relativistic effects (relativity makes the metal oxidation even more facile). The geometrical aspects of the complexes calculated for M ¼ Os are quite close to those obtained for M ¼ Ru, although the former is displaced out of the porphyrin plane in MP(py)(CO) by slightly more than is the latter. There are substantial relativistic bond contractions of Os–N and Os–CO. Replacement of Ru by Os enhances the binding energy of the two ligands by a small amount, but has little effect upon the electron affinities. 4. Conclusions The ground electronic states of FeP and OsP are 3 A2g , with 3 Eg a little higher in energy while
M.-S. Liao, S. Scheiner / Chemical Physics 285 (2002) 195–206
the 3 A2g and 3 Eg states are nearly degenerate for RuP. If relativistic effects are ignored, 3 Eg is computed to be lower in energy than 3 A2g for both RuP and OsP. The high-spin (S ¼ 2) states in RuP and OsP are much higher than the ground state in energy, in contrast to the situation in FeP where the energy separation is on the order of 0.7 eV. The energy by which the central metal is held to the porphyrin varies as FeP < RuP < OsP. The first ionization of all three MPs occurs at the central metal, and with very similar ionization potentials of some 6.3 eV. Relativistic corrections are significant for OsP, but they are, as expected, very small and essentially negligible for FeP. Upon complexation of two axial ligands (py and CO) to MP, the MII ion becomes low-spin (S ¼ 0). As a ligand with strong r-donor but weak p-back bonding ability, py raises the M dxy orbital energy level and slightly decreases the dp orbital energy levels with respect to the porphyrin HOMO a2u . Thus the one-electron oxidation of MPðpyÞ2 occurs at the metal, as in unligated MP, and the ionization potentials are reduced relative to MP. When one py is replaced by the strong pacceptor CO, the M d-orbitals, particularly dp , are greatly stabilized through back bonding. For M ¼ Fe, dxy is only stabilized to a small degree, so the IP from this orbital is still slightly smaller than that from the porphyrin a2u . Hence, the oneelectron oxidation of FeP(py)(CO) is metal-centered. In the case of M ¼ Ru and Os, however, the effect of the back bonding is larger, and the oxidation of RuP(py)(CO) yields a p-cation radical species. Regardless of the metal, the ionization energy is raised slightly as compared to unligated MP. The fact that the oxidation of OsP(py)(CO) takes place at the metal is due to relativistic effects which significantly destabilize the d-orbitals of heavy Os. Ignoring relativistic effects provides the wrong site of oxidation in this complex. Acknowledgement This work was supported by Grant DAAD1999-1-0206 from the Army Research Office.
205
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Relativistic effects in iron-, ruthenium-, and osmium porphyrins Meng-Sheng Liao, Steve Scheiner * Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA Received 8 April 2002
Abstract Nonrelativistic and relativistic DFT calculations are performed on four-coordinate metal porphyrins MP and their six-coordinate adducts MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) with M ¼ Fe, Ru, and Os. The electronic structures of the MPs are investigated by considering all possible low-lying states with different configurations of nd-electrons. FeP and OsP have a 3 A2g ground state, while this state is nearly degenerate with 3 Eg for RuP. Without relativistic corrections, the ground states of both RuP and OsP would be 3 Eg . For the six-coordinate adducts with py and CO, the strong-field axial ligands raise the energy of the M dz2 -orbital, thereby making the MII ion diamagnetic. The calculated redox properties of MPðpyÞ2 and MP(py)(CO) are in agreement with experiment. The difference between RuP(py)(CO) and OsP(py)(CO), in terms of site of oxidation, is due to relativistic effects. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Density functional calculations; Ground state; Ionization potential; Electron affinity; Orbital energies
1. Introduction Metal porphyrins (MP) represent a particularly important class of biological molecules [1]. Iron porphyrin (FeP) [2], for example, is the functional part of both hemoglobin and myoglobin, which are oxygen carriers in animals. MPs are also highly promising as catalysts for a number of chemical reactions [3,4], as enzyme models, as photosensitizers, and as medicinal preparations. No wonder then that so much experimental and theoretical effort has been directed towards the elucidation of the detailed nature of MPs. *
Corresponding author. E-mail address: [email protected] (S. Scheiner).
While experimental studies of MPs have been expanded by the synthesis of species containing second- and third-row transition metals [5–9], theoretical studies have mainly been devoted to the first-row transition metal porphyrins. Certain special and unusual properties of heavy metal porphyrins are worthy of attention. One example arises from the Fe, Ru, Os series. Electrochemical studies show that osmium porphyrin, with pyridine (py) and CO as axial ligands [OsP(py)(CO)], undergoes metal-centered oxidation to yield an OsIII species [7]. Iron-carbonyl porphyrins such as FeP(imidazole)(CO) behave like OsP(py)(CO) in this regard [7]. In contrast, the related complex of ruthenium undergoes one-electron oxidation at the porphyrin ring [6–8]. The situation is different for
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 8 3 6 - 4
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the dipyridyl systems, where one-electron oxidation of the entire M ¼ Fe, Ru, Os set of MPðpyÞ2 systems is metal-centered [6–8]. The change in the oxidation site from MPðpyÞ2 to MP(py)(CO) has been explained in the Ru porphyrin by stronger back bonding to CO compared to py [7]. The argument continued [7] that for the Fe- and Oscarbonyl complexes, the metal d-orbitals are not sufficiently stabilized, although the same effect occurs for iron and osmium. One is left with the fundamental question as to why Os behaves differently than Ru in the carbonyl porphyrin. It is well known that heavy atomic systems may be greatly influenced by relativistic effects [10]. For the positive MII ion, where the ns-electrons are removed into the electronegative porphyrin from the ionic point of view, ðn 1Þd becomes the outermost shell. The 5d-orbitals of heavy OsII might be strongly expanded and destabilized by relativity, making these electrons easier to remove. Relativistic effects may be an important factor in understanding the different oxidation sites in RuP(py)(CO) and OsP(py)(CO). The observation of oxidation state isomerism, in which the isomers differ with regard to the site of oxidation, serves as the impetus for a more thorough examination of relativistic effects in Fe-, Ru-, and Os porphyrins. It turns out that relativistic effects change not only the oxidation site in OsP(py)(CO), but also the ground state electronic configurations of the unligated, four-coordinate RuP and OsP.
2. Computational method The calculations reported in this work were carried out using the Amsterdam density functional (ADF) program package developed by Baerends et al. [11]. Slater-type orbital (STO) basis sets are employed and inner-shell electrons are treated in the frozen-core approximation [11a]. Two kinds of relativistic approaches have been implemented in the present ADF program: scalar quasi-relativistic (QR) [12] and the scalar relativistic zero-order regular approximation (ZORA) [13]. The QR method is the standard method in relativistic ADF calculations and applications to
the investigation of relativistic effects in heavy element systems have been quite successful [14]. However, it is a shortcoming of the QR method that variational collapse may sometimes occur. Indeed, it was found in the present work that QR results on one of the systems, OsPðpyÞ2 , are wrong, in that the orbital energies are far too low. There are also errors in the QR results for OsP(py)(CO), although the problem in this system is less serious than in OsPðpyÞ2 . (The origin of this variational collapse in the QR method has been explained in [15].) The ZORA method, which has been recently implemented in the ADF program, is a variationally stable relativistic method and gives accurate one-electron orbital energies and densities [13]. Thus, the principal relativistic approach employed here is ZORA. For the sake of comparison, QR results are also presented for the unligated MPs. The exchange-correlation potential used in this work is based on the density parametrized form of Vosko et al. [16]. The nonlocal corrections are based on Becke’s gradient functional for exchange [17] and Perdew’s gradient functional for correlation [18], and treated by a fully self-consistent method. In the nonrelativistic (Nrel) and QR calculations the standard ADF basis set IV was used, which is triple-f for valence orbitals plus one polarization function. In the ZORA calculations, special relativistic (reoptimized) basis set, ZORA/ IV, was used for the metals; it is of the same size as the ADF IV basis set. To obtain accurate results, the valence set on the metals included subvalence ðn 1Þs and ðn 1Þp shells. For C, N, and O, 2s and 2p were considered as valence shells. The other shells of lower energy, i.e. [Ne] for Fe, [Ar3d10 ] for Ru, ½Kr4d10 4f 14 for Os, and [He] for C/N/O, were described as core and kept frozen. For the open-shell states, the unrestricted Kohn– Sham (UKS) spin-density functional approach was adopted.
3. Results and discussion 3.1. MP (M ¼ Fe, Ru, Os) The unligated metal porphyrins (MP) serve as a starting point for examining the effects of axial
M.-S. Liao, S. Scheiner / Chemical Physics 285 (2002) 195–206
ligands on the electronic structure and redox properties of the MPs. The molecular structure of the simplest metal porphyrin, metal porphine, is illustrated in Fig. 1, along with the definition of a and b positions in the rings. The systems that have been synthesized contain phenyl or ethyl groups as substituents on the periphery of the porphyrin ring. The use of metal porphine as a model for larger and more complicated systems has been justified in our previous calculations [19], which showed that the electronic properties of metal porphyrins are insensitive to the nature of these peripheral substituents. The MP in Fig. 1 has D4h symmetry. Taking the z-axis as perpendicular to the porphinato plane, the five M nd-orbitals transform as a1g ðdz2 Þ, b1g ðdx2 y 2 Þ, eg ðdp , i.e., dxz and dyz ), and b2g ðdxy Þ. Various occupations of the six electrons in the d-orbitals of the MP can yield eight possible lowlying states: one low-spin ðS ¼ 0Þ, four intermediate-spin (S ¼ 1), and three high-spin (S ¼ 2) states. The energies of all these spin states have been computed, along with full geometry optimization of each. Their relative energies are presented in Table 1, along with the M–N bond length of each. Fig. 2 illustrates the valence molecular orbital
Fig. 1. Molecular structure of metal porphine (MP), indicating a and b positions.
197
(MO) energy levels for the nonrelativistic (Nrel) and relativistic (Rel) ZORA ground states of the MPs, obtained by spin-restricted calculations. The orbital energies for FeP are nearly unaffected by relativistic corrections. Calculated values of M–P binding energies (Ebind ), ionization potentials (IPs) for several outer MOs, electron affinities (EAs), and Mulliken charge distributions on the M (QM ) are reported in Table 2. Ebind is defined as the energy required to extract the M from the porphyrin: Ebind ¼ EðMPÞ fEðMÞ þ EðPÞg: The atomic ground state configurations for the transition metal atoms Fe, Ru, and Os are 3d6 4s2 , 4d7 5s1 , and 5d6 6s2 , respectively. For the calculations of the atomic energies of M with an open and degenerate dn shell, the n electrons were distributed equally over the five d-orbitals; i.e., occupations of n=5 electrons were chosen for each dxy , dxz , dyz , dx2 y 2 , and dz2 orbital, the ‘‘average-of-configuration’’ (AOC) calculation [20], which can avoid some uncertainties in the DFT energies of systems with a degenerate state. AOC calculations were spin-unrestricted. For the molecular systems with an open and degenerate shell such as ðeÞ1 or ðeÞ3 , the same AOC method was used. The occupations of the AOC orbitals do not correspond to a real Slater-determinant. The IPs and EAs were calculated by the socalled DSCF method which computes each property as the difference in total energy between the neutral and ionized species. Diffuse functions have been suggested to be essential for calculations of EAs. SCF convergence problems were encountered with the extra basis sets in the calculations of the negative ½MP systems, preventing examination of the effects of diffuse functions on the calculated EAs. We believe that the present basis sets of triple-f quality are adequate. For instance, the calculated EA values for FeTPP and NiTPP were found to be in excellent agreement with the available experimental data [19]. 3.1.1. M ¼ Fe The electronic structure of FeP has been the subject of a great deal of interest and intense investigation because of its importance in biological
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Table 1 Calculated relative energies (E) and M–N bond lengths (R) for different configurations in FeP, RuP, and OsP State
Configuration b2g =dxy
a1g =dz2
1eg =dp
) RM–N (A
E (eV)
b1g =dx2 y 2
FeP
RuP
OsP
FeP
RuP
OsP
0 0 0
0 0 0
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.01 2.04
2
2
2
0
3
2
1
3
0
3
Eg (A)
Nrel QR ZORA
0.13 0.12 0.11
)0.10 )0.01 )0.02
)0.12 0.33 0.20
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.02 2.04
1
1
4
0
3
B2g
Nrel QR ZORA
0.26 0.26 0.25
0.26 0.34 0.35
0.31 0.77 0.59
1.99 1.98 1.98
2.07 2.05 2.05
2.09 2.03 2.05
1
2
3
0
3
Eg (B)
Nrel QR ZORA
0.76 0.74 0.74
0.69 0.67 0.70
0.68 0.66 0.61
1.99 1.98 1.98
2.06 2.04 2.04
2.08 2.01 2.04
1
2
2
1
5
A1g
Nrel QR ZORA
0.68 0.71 0.72
3.05 3.18 3.16
3.72 4.55 4.05
2.07 2.06 2.06
2.15 2.14 2.14
2.17 2.11 2.14
1
1
3
1
5
Eg
Nrel QR ZORA
0.81 0.85 0.86
3.02 3.24 3.21
3.68 4.87 4.30
2.06 2.06 2.06
2.15 2.14 2.14
2.17 2.12 2.14
2
1
2
1
5
B2g
Nrel QR ZORA
1.00 1.05 1.06
3.04 3.27 3.24
3.64 4.84 4.31
2.06 2.06 2.06
2.14 2.13 2.13
2.17 2.11 2.14
2
0
4
0
1
A1g
Nrel QR ZORA
1.45 1.49 1.47
0.98 1.27 1.22
1.01 2.28 2.02
1.99 1.98 1.98
2.06 2.05 2.05
2.09 2.04 2.06
A2g
Nrel QR ZORA
0 0 0
systems. There have been a spate of experimental and theoretical studies of FeP, including some very recent calculations [19,21–25]. One essential question in FeP concerns the ground state configuration of the FeII ion. From available experimental data, there seems to be little doubt that FeP exists in an intermediate-spin (S ¼ 1) state, due in part to the high energy of the antibonding b1g ðdx2 y 2 Þ orbital which leaves it unoccupied. Among the four possible intermediate-spin states, only 3 A2g arising from the ðdxy Þ2 ðdz2 Þ2 ðdp Þ2 configuration, is compatible with M€ ossbauer [26,27], magnetic [28], and proton NMR [29,30] data. Our calculation supports this experimental assignment. A 3 Eg state, 2 1 3 with occupation ðdxy Þ ðdz2 Þ ðdp Þ , is slightly higher 3 (0.1 eV) in energy and a B2g state lies slightly higher still. Because 3 Eg and 3 A2g are so close in energy, they may mix by spin–orbit (SO) coupling.
A more detailed discussion of the effects of SO coupling on the state energies can be found in [27,28]. The lowest quintet is 5 A1g , lying 0.7 eV above the ground state. The closed-shell 1 A1g singlet is the highest in energy among the eight lowlying states, 1.5 eV above the ground state. As indicated in Table 1, the calculated Fe–N bond lengths for the S ¼ 1 and S ¼ 0 states are nearly . Occupation of the dx2 y 2 orbital the same, 1.98 A for the S ¼ 2 states leads to an expansion of the porphinato core: the Fe–N bond lengths for the longer than the same bonds for quintets are 0.08 A the S ¼ 1 states. It is worth stressing that the energies and bond lengths of FeP in Table 1 are virtually unaffected by relativistic effects. Referring to Fig. 2, the Fe 3d-like orbitals are higher in energy than the ligand p-orbitals. The antibonding dx2 y 2 orbital ðb1g ) is particularly
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199
Fig. 2. Orbital energy levels at nonrelativistic (Nrel) and relativistic (Rel) ZORA levels. Rel levels are not shown explicitly for FeP as relativistic effects are minimal. Electron occupancies are explicitly shown for frontier MOs. Table 2 Calculated M–P binding energies ðEbind Þ, ionization potentials (IP), electron affinities (EA), and Mulliken charge distributions on the M ðQM Þ Ebind (eV)
IP (eV)
EA (eV)
QM
a1g =dz2
b2g =dxy
a2u
a1u
1eg =dp
10.38 10.25 10.25
6.38 (1st) 6.29 (1st) 6.29 (1st)
6.73 6.63 6.64
6.98 7.00 7.00
7.01 7.01 7.01
7.36 7.26 7.27
)1.66 ð1eg Þ )1.66 )1.66
0.68 0.66 0.67
Nrel (3 Eg Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
10.52 10.97 10.87
8.00 6.25 (1st) 6.27 (1st)
7.06 6.85 6.90
6.96 7.01 7.01
7.03 7.06 7.07
6.36 (1st) 6.87 6.87
)2.45 ð1eg Þ )2.10 ð1eg Þ )2.09
1.40 1.32 1.37
Nrel ð3 Eg Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
12.11 12.70 11.38
7.98 6.34 (1st) 6.26 (1st)
7.09 6.64 6.64
6.97 7.09 7.06
7.05 7.05 7.06
6.33 (1st) 6.49 6.55
)2.51 ð1eg Þ )2.09 ð1eg Þ )2.13
1.46 1.18 1.39
FeP
3
Nrel ð A2g Þ QR ð3 A2g Þ ZORA ð3 A2g Þ
RuP
OsP
destabilized due to its interaction with the porphinato nitrogens. The dp and dz2 orbitals, which are nearly degenerate, are weakly antibonding, higher in energy than the nonbonding dxy , and represent a
group of HOMOs. As the first IP results from a1g ðdz2 Þ ionization, one-electron oxidation of FeP is associated with the central metal, in accord with electron spin resonance (ESR) measurements [31].
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This prediction is buttressed by the observation that the IP from the highest occupied porphyrin orbital (a2u ) is notably larger (0.7 eV) than that from Fe 3dz2 . Relativistic effects decrease the IPs from Fe d-orbitals by 0.1 eV, whereas the IPs from the porphyrin orbitals are scarcely affected at all. The Fe–P binding energy is estimated to be 10.3 eV. The strong interaction between the iron and the porphyrin accounts for its high thermal and chemical stability. A small relativistic destabilization of 0.1 eV is observed for the Fe–P binding. From Mulliken population analysis, 0.7e is transferred from Fe to P. 3.1.2. M ¼ Ru In contrast to FeP’s 3 A2g ground state, the 3 Eg state of RuP lies 0.1 eV below 3 A2g (prior to inclusion of relativity). There has been an earlier nonrelativistic DFT (DMol) calculation of RuP by Matsuzawa et al. [25], who found that the 3 Eg state is 0.2 eV lower than 3 A2g , similar to our value. (However, the DMol calculation predicted a 3 Eg ground state for FeP, which differs from our calculation.) Relativistic effects increase the relative energy of 3 Eg by nearly 0.1 eV, making it essentially degenerate with 3 A2g . The QR and ZORA results for RuP are essentially identical to one another. Consequently, the calculations are unable to unambiguously identify the true ground state of RuP. The three quintets are quite similar in energy, about 3.2 eV higher than the ground state, in contrast to the results for FeP, where the quintets are within about 1 eV of the ground state, and the energy varies in the clear order 5 A1g < 5 Eg < 5 B2g . Relativistic effects on the relative energies vary from one state to the next. Whereas 3 Eg (B) is little affected, the energies of the other states all undergo significant relativistic increases, 0.1 eV for 3 B2g and 5 A1g , 0.2 eV for 5 Eg and 5 B2g , and 0.3 eV for 1 A1g . longer While the Ru–N bond length is 0.06 A than in the Fe analogue, the values of Ebind reported in Table 2 reveal that Ru is more strongly bound than is Fe. The qualitative difference in relativistic effects between Fe–P and Ru–P can be attributed in part to the fact that the calculated binding energies refer to different atomic
ground state configurations for Feð3d6 4s2 Þ and Ruð4d7 5s1 Þ, and to the different relativistic and nonrelativistic electronic states of the RuP complex. The relativistic bond contraction of Ru–N is , slightly greater than in Fe–N. 0.01–0.02 A Fig. 2 reveals that the Ru 4d-like orbitals are destabilized by relativity, but only very slightly. On the other hand, the d-orbital energies and orderings for the 3 Eg state are somewhat different from those in 3 A2g , even though the two states are nearly degenerate at the relativistic level. The antibonding dx2 y 2 orbital in RuP is much more strongly destabilized than in FeP, offering an explanation as to why the quintets are much higher in energy above the ground state for RuP. The relativistic results for RuP in Table 2 refer to the 3 A2g state. Its first ionization occurs at the metal a1g ðdz2 Þ and the calculated IP1 value is nearly the same as that of FeP. However, the electron affinity of RuP is significantly more negative than that of FeP. The metal charge increases greatly from M ¼ Fe to M ¼ Ru, as witnessed by the final column of Table 2. 3.1.3. M ¼ Os At the nonrelativistic level, 3 Eg is the ground state for OsP, similar to the RuP case. However, a considerably larger relativistic energy increase of 3 Eg in OsP, as compared to RuP, raises this state significantly above 3 A2g , making the latter the true ground state. Except for 3 Eg (B), the relative energies of the different states are increased drastically by relativistic effects with respect to 3 A2g . The QR energy corrections are larger than those of the ZORA method, especially for the quintets. The QR method also yields larger relativistic bond contractions than does ZORA. Now, the quintets of OsP are more than 4 eV higher than the ground state in energy, even higher than in RuP. According to the ZORA results, the Os–N bond lengths are very similar to those in Ru–N, consis) and Ru tent with the atomic radii of Os (1.35 A (1.34 A). In the absence of relativistic effects, ROs–N longer than RRu–N . The Os–P bond reis 0.02 A mains stronger than that in Ru–P. There is a clear trend of increasing binding energy in the order FeP < RuP < OsP. The M–P binding energy can reflect the experimental data quite accurately. For
M.-S. Liao, S. Scheiner / Chemical Physics 285 (2002) 195–206
example, the trend in computed M–P binding energies for M ¼ Fe, Co, Ni, Cu, and Zn [19] is consistent with infrared spectral data [32]. The calculated IPs for OsP are similar to those for RuP, although certain discrepancies are connected with relativity, and the electron affinities of OsP and RuP do not differ by much, both being more negative than FeP. The effective atomic charges on Ru and Os are also similar, both being reduced by relativistic effects. 3.2. MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) One of the most important phenomena in metal porphyrins is the coordination of the central metal to molecules in addition to the porphyrin. The MPs with M ¼ Fe, Ru, and Os exhibit particularly strong attraction for additional ligands, to which their electronic structures are in turn sensitive. Experiments have shown that the six-coordinate metal porphyrins, MPðpyÞ2 and MP(py)(CO) (py ¼ pyridine) are low-spin, diamagnetic [33,34], in contrast to the four-coordinate species (S ¼ 1). This axial ligation in turn exerts an influence on the oxidation/reduction properties of the metal porphyrins, e.g., the oxidation potential and site are dependent upon the nature of the axial ligands [35]. For RuPðpyÞ2 , one-electron oxidation occurs at the metal ion, but if one py ligand is replaced by CO, it is the porphyrin ring which becomes the oxidation site. For M ¼ Fe and Os, on the other hand, no change in the oxidation site has been observed upon changing the axial ligand. Evidence is presented below that the variations of the oxidation site in RuP(py)(CO) and OsP(py)(CO) are due to relativistic effects. The calculated nonrelativistic (Nrel) and relativistic (Rel) properties of MPðpyÞ2 and MP(py)(CO) are collected in Table 3. The structures of the complexes have been optimized under D2h and C2v symmetries, respectively, where the py ring plane is perpendicular to the porphine and bisects the N– M–N angles of the latter; the M–CO attachment is linear. Effects of the axial ligands (py, CO) upon the various MO levels of FeP are displayed in Fig. 3. The left and right extremes of Fig. 3 represent the energy levels of the unperturbed py and CO ligands. Fig. 4 illustrates valence orbital en-
201
ergy levels for the various MP(py)(CO) complexes both without and with relativistic corrections. (QR results for MPðpyÞ2 and MP(py)(CO) are not presented here; Rel results were obtained with ZORA.) 3.2.1. M ¼ Fe As illustrated in Fig. 3, the repulsive interaction between the ligand HOMO and the M a1g ðdz2 Þ dramatically raises the energy of the latter. This rise removes any ambiguity about the 2 4 ground state configuration which is ðdxy Þ ðdp Þ for all. A subsidiary effect of the axial ligands is a lowering of the symmetry from D4h to D2h (in the case of MPðpyÞ2 ) and to C2v (for MP(py)(CO)) which splits the dxz and dyz degeneracy. The dxy ðb2g Þ orbital of FeP is shifted up enough so that it (transformed to a1g ) becomes the HOMO of the system. The first ionization in FePðpyÞ2 arises from the metal dyz ð1b3g Þ (HOMO-1); ionization from the dxy HOMO requires 0.24 eV more energy, and from b1u ða2u Þ of the porphyrin a further 0.4 eV. Compared to FeP, the IP1 of FePðpyÞ2 is decreased by 0.6 eV, suggesting that the axial ligands of FePðpyÞ2 ease the oxidation. These ligands also slightly increase the positive charge of the metal atom, as each ligand takes on about 0.2e of positive charge themselves. The primary net result is a flow of electron density into the porphyrin ring. The ligands also diminish the electron affinity of the assembly from )1.7 to )1.0 eV. The Ebind entry in Table 3 indicates that the two py ligands are bound to the complex by some 1.4 eV. Addition of the two py ligands elongates the Fe–N distance by a small amount, perhaps . 0.02 A Replacement of one of the py ligands by CO lowers all of the MOs. The dp orbitals are particularly stabilized, which may be attributed to Fe ! Lp back bonding, as illustrated in Fig. 3. The first ionization of FeP(py)(CO), unlike FePðpyÞ2 , occurs from the dxy ða1 Þ HOMO, but requires 0.8 eV more energy than the first IP in FePðpyÞ2 . The latter result is consistent with the experimental observation of an increase in the oxidation potential for MPðpyÞ2 on going to MP(py)(CO) [6]. The IP of the lower a1 , derived from P-a2u , is increased by only 0.25 eV.
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Table 3 Calculated properties of MP with two axial ligands MPðpyÞ2 M ¼ Fe RMNðpÞ
a
) (A
) RMNðaxÞ b (A ) RMCOðaxÞ (A ) RCt
M c (A QM Qpy QCO Ebind d (eV) ½MP–ðLÞ2 IPe (eV)
Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel Rel Nrel
Rel
EA (eV)
Nrel Rel
2.00 2.00 2.03 2.01
M ¼ Ru 2.07 2.06 (2.05)f 2.12 2.10 (2.10)
0.72 0.73 0.19 0.19
1.40 1.41 5.94 5.69 6.33 5.92 5.68 6.34 )1.00 )1.01
MP(py)(CO)
1.82 1.96 0.01 )0.01
ða1g =dxy Þ ð1b3g =dyz Þ (1st) ðP-b1u Þ ða1g =dxy Þ ð1b3g =dyz Þ (1st) ðP-b1u Þ ð2b2g Þ ð2b2g Þ
2.57 2.73 6.38 5.90 (1st) 6.38 6.31 5.84 (1st) 6.40 )1.00 )0.99
M ¼ Os 2.09 2.06 2.16 2.10
1.59 1.70 0.08 0.02
2.91 2.91 6.42 5.88 (1st) 6.4 6.13 5.69 (1st) 6.45 )0.99 )1.06
M ¼ Fe
M ¼ Ru
M ¼ Os
2.02 2.01 2.09 2.06 1.76 1.76 0.04 0.04 0.49 0.50 0.24 0.24 0.04 0.03 1.92 1.93 6.51 6.70 6.59 6.49 6.67 6.60 )1.22 )1.22
2.08 2.07 2.23 2.21 1.86 1.87 0.07 0.08 1.54 1.71 0.08 0.07 )0.13 )0.19 3.29 3.37 7.12 6.77 6.62 7.03 6.72 6.62 )1.25 )1.24
2.10 2.07 2.28 2.23 1.93 1.88 0.09 0.10 1.45 1.45 0.15 0.12 )0.19 )0.20 3.55 3.72 7.11 6.74 6.68 (1st) 6.73 6.57 (1st) 6.70 )1.27 )1.25
(2.02)f (2.10) (1.77) (0.02)
ða1 =dxy Þ (1st) ð1b2 =dyz Þ ðP-a1 Þ ða1 =dxy Þ (1st) ð1b2 =dyz Þ ðP-a1 Þ ð2b1 Þ ð2b1 Þ
(2.05)f (2.19) (1.84) (0.08)
(1st)
(1st)
a
N(p) denotes porphinato nitrogen atom. N(ax) represents nitrogen atom of axial ligand (py). c Ct denotes the center of the ring and RCt
M the displacement of the M atom out of the porphinato plane. d Binding energy between MP and two L ligands. e See Figs. 3 and 4 for the orbitals in parentheses. f Values in parentheses represent X-ray diffraction data for related crystal compounds: RuPðpyÞ2 , Ref. [36] [in RuOEPðpyÞ2 ]; FeP(py)(CO), Ref. [34] [in FeTPP(py)(CO)]; RuP(py)(CO), Ref. [37] [in RuTPP(py)(CO)]. b
Therefore, the IPs of the Fe-dxy and P-a2u for FeP(py)(CO) are in fact rather close, within 0.1 eV of one another. There are X-ray diffraction data available for crystalline FeTPP(py)(CO) [34], which are in good agreement with the calculated bond lengths. Fe lies slightly out of the porphyrin plane, toward the CO experimentally, 0.04 A according to group (0.02 A calculations). This displacement is partially responsible for the elongation of the Fe–N(py) , relative to that in FePðpyÞ . distance by 0.05 A 2 Another result of the CO substitution is a reduction of the metal atom’s positive charge by roughly 1/4e, even though the CO itself remains essentially devoid of charge. The py/CO tandem is more strongly bound to the complex by about
0.54 eV than are a pair of py ligands, and makes the assembly more attractive toward an electron by about 0.2 eV. All in all, relativistic corrections are only very minor in the Fe complexes. 3.2.2. M ¼ Ru Replacement of the Fe by Ru stabilizes most of the orbitals, but the dxy -orbital by more. This is clearly shown in Fig. 4. The dxy IP is consequently enlarged more than those associated with the other d orbitals, and is no longer first IP. For RuPðpyÞ2 , the first ionization occurs at the 1b3g ðdyz Þ, similar to the case of FePðpyÞ2 . For RuP(py)(CO), on the other hand, the first ionization no longer occurs at the dxy , but at the a1 ða2u Þ orbital of the porphyrin. This result is in agreement with the experimental
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Fig. 3. Orbital energy levels of FeP complexed to two axial ligands, as well as uncomplexed FeP and ligands (py, CO) for purposes of comparison. The upper unoccupied a1g of FePðpyÞ2 Þ involves a mixing of 70% FeP-a1g ðdz2 ) and 25% py-a1 . The 1b2 =1b1 of FeP(py)(CO) involves a mixing of 90% FeP-1eg (dp ) and 6% CO-p . The HOMO of CO is located at 9:2 eV.
observation that one-electron oxidation of RuP(py)(CO) is ring-centered [6–8]. Although in RuP(py)(CO) the dxy -orbital lies notably above the dyz in the orbital energy level diagram (see Fig. 4), the IP from the former is nevertheless 0.3 eV larger than that from the latter. (The same is true for M ¼ Os.) This situation contrasts with FeP(py)(CO). The dxy orbital behaves differently in the various MP(py)(CO) systems when an electron is removed from this 1 orbital. The singly occupied ðdxy Þ in [MP(py)þ (CO)] represents the HOMO for M ¼ Fe, but it is stabilized below a number of occupied orbitals for M ¼ Ru and Os. (Fig. 5 illustrates the relative po1 sitions of the ðdxy Þ level in the [MP(py)(CO)]þ ions, after an electron has been removed.) In FeP(py)(CO) the IP from dyz is 0.1 eV larger than that of the P-a1 ða2u Þ. A similar result is also found in RuP(py)(CO). Relativistic effects destabilize the Ru d-orbitals very little and reduce their IPs by about 0.1 eV. Electron affinities of the ligated Fe and Ru complexes are very nearly identical.
X-ray diffraction data are available for both RuOEPðpyÞ2 [36] and RuTPP(py)(CO) [37], which are again in excellent agreement with the calculated bond lengths. The axial ligands slightly elongate the Ru–N(p) bond lengths, compared to unligated RuP. Ru is displaced from the ring plane in RuP(py)(CO) by twice as much as is iron in FeP(py)(CO). The bond lengths from Ru to its two ligands are considerably longer than in the iron analogues. Nonetheless, the calculated M–ðLÞ2 binding energies indicate much stronger bonding of these ligands to Ru than to Fe (consistent with the much lower experimental C–O stretching frequency of the Ru complex [7]). The strongly bound CO ligand causes the Ru to displace out of the . porphyrin plane by 0.08 A 3.2.3. M ¼ Os Prior to relativistic corrections, the calculated orbital energies and IPs for OsPðpyÞ2 and OsP(py)(CO) are very similar to those obtained for
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Fig. 4. Nonrelativistic (Nrel) and ZORA relativistic (Rel) orbital energy levels of MP(py)(CO) for M ¼ Fe, Ru and Os.
Fig. 5. Comparison of the relative position of the singly occupied dxy -orbital in the different [MP(py)(CO)]þ ions.
M ¼ Ru, and would thus lead to much the same expectations. Relativity lowers the IPs of the Os dorbitals by 0.2–0.4 eV, sufficient to change the site of oxidation in OsP(py)(CO) as follows. The IP from the metal dyz is larger than that from the
P-a1 ða2u Þ in this species at the nonrelativistic level. After appropriate correction, the order reverses, and the one-electron oxidation of OsP(py)(CO) occurs from the metal, in agreement with experimental observation [7]. For OsPðpyÞ2 , the IP from the dyz is already significantly smaller than that from the P-a1 , even without relativistic effects (relativity makes the metal oxidation even more facile). The geometrical aspects of the complexes calculated for M ¼ Os are quite close to those obtained for M ¼ Ru, although the former is displaced out of the porphyrin plane in MP(py)(CO) by slightly more than is the latter. There are substantial relativistic bond contractions of Os–N and Os–CO. Replacement of Ru by Os enhances the binding energy of the two ligands by a small amount, but has little effect upon the electron affinities. 4. Conclusions The ground electronic states of FeP and OsP are 3 A2g , with 3 Eg a little higher in energy while
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the 3 A2g and 3 Eg states are nearly degenerate for RuP. If relativistic effects are ignored, 3 Eg is computed to be lower in energy than 3 A2g for both RuP and OsP. The high-spin (S ¼ 2) states in RuP and OsP are much higher than the ground state in energy, in contrast to the situation in FeP where the energy separation is on the order of 0.7 eV. The energy by which the central metal is held to the porphyrin varies as FeP < RuP < OsP. The first ionization of all three MPs occurs at the central metal, and with very similar ionization potentials of some 6.3 eV. Relativistic corrections are significant for OsP, but they are, as expected, very small and essentially negligible for FeP. Upon complexation of two axial ligands (py and CO) to MP, the MII ion becomes low-spin (S ¼ 0). As a ligand with strong r-donor but weak p-back bonding ability, py raises the M dxy orbital energy level and slightly decreases the dp orbital energy levels with respect to the porphyrin HOMO a2u . Thus the one-electron oxidation of MPðpyÞ2 occurs at the metal, as in unligated MP, and the ionization potentials are reduced relative to MP. When one py is replaced by the strong pacceptor CO, the M d-orbitals, particularly dp , are greatly stabilized through back bonding. For M ¼ Fe, dxy is only stabilized to a small degree, so the IP from this orbital is still slightly smaller than that from the porphyrin a2u . Hence, the oneelectron oxidation of FeP(py)(CO) is metal-centered. In the case of M ¼ Ru and Os, however, the effect of the back bonding is larger, and the oxidation of RuP(py)(CO) yields a p-cation radical species. Regardless of the metal, the ionization energy is raised slightly as compared to unligated MP. The fact that the oxidation of OsP(py)(CO) takes place at the metal is due to relativistic effects which significantly destabilize the d-orbitals of heavy Os. Ignoring relativistic effects provides the wrong site of oxidation in this complex. Acknowledgement This work was supported by Grant DAAD1999-1-0206 from the Army Research Office.
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