Interaction of Metal Porphyrins with Fullerene C60: A New Insight

Dispersion-corrected DFT calculations on C60-porphyrin complexes. Meng-Sheng Liao , John D. Watts , Ming-Ju Huang. Physical Chemistry Chemical Physics...
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4374

J. Phys. Chem. B 2007, 111, 4374-4382

Interaction of Metal Porphyrins with Fullerene C60: A New Insight Meng-Sheng Liao, John D. Watts, and Ming-Ju Huang* Department of Chemistry, P.O. Box 17910, Jackson State UniVersity, Jackson, Mississippi 39217 ReceiVed: July 11, 2006; In Final Form: February 5, 2007

The electronic structure and bonding in the noncovalent, supramolecular complexes of fullerene C60 with a series of first-row transition metal porphines MP (MdFe, Co, Ni, Cu, Zn) have been re-examined with DFT methods. A dispersion correction was made for the C60-MP binding energy through an empirical method (J. Comput. Chem. 2004, 25, 1463). Several density functionals and two types of basis sets were employed in the calculations. Our calculated results are rather different from those obtained in a recent paper (J. Phys. Chem. A 2005, 109, 3704). The ground state of C60‚FeP is predicted to be high spin (S ) 2); the low-spin (S ) 0), closed-shell state is even higher in energy than the intermediate-spin (S ) 1) state. With only one electron in the Co-dz2 orbital, the calculated Co-C60 distance is in fact rather short, about 0.1 Å longer than the Fe-C60 distance in high-spin C60‚FeP. Double occupation of an M-dz2 orbital in MP prevents close association of any axial ligand, and so the Ni-C60, Cu-C60, and Zn-C60 distances are much longer than the Co-C60 one. The evaluated MP-C60 binding energies (Ebind) are 0.8 eV (18.5 kcal/mol) for MdFe/Co and 0.5 eV (11.5 kcal/mol) for MdNi/Cu/Zn (Ebind is about 0.2 eV larger in the case of C60-MTPP). They are believed to be reliable and accurate based on our dispersion-corrected DFT calculations that included the counterpoise (CP) correction. The effects of the C60 contact on the redox properties of MP were also examined.

1. Introduction Metal porphyrins (MPors) and fullerenes are both fascinating species. MPors are of importance not only in biological systems, but also perform many useful functions in industry1 and technology.2 Fullerenes have been applied to many research areas such as chemistry, materials science, and biology.3,4 Since its discovery in 1985,5 the C60 species has been extensively studied for its unique properties caused by its three-dimensional shape and electronic structure. Carbon nanoclusters of different sizes have also attracted special attention.6 In recent years, there has been considerable interest in molecular complexes of fullerenes with porphyrins or metal porphyrins. This interest results from the fact that a fullerene and a porphyrin are spontaneously attracted to each other to form a host-guest complex both in the solid state and in solution despite the difference in external shape between the planar porphyrin and the curved fullerene. Sun et al. reported the first structural characterization of a pyrrolidine-functionalized C60 species;7 the crystal packing of the dyad reveals an intermolecular interaction of the C60 ball in remarkably close approach to the porphyrin plane. Later, unique cocrystallites of C60 and C70 fullerenes with various metal octaethylporphyrins (MOEPs) and metal tetraphenylporphyrins (MTPPs) have been reported and they show distinct physicochemical properties.8-28 The intermolecular fullerene/porphyrin contacts range from 2.6 to 3.0 Å, which are shorter than typical π-π interactions (3.0-3.5 Å). In contrast to the great number of experimental studies, theoretical investigations of fullerene/porphyrin conjugates are relatively rare. Schuster et al. performed an empirical molecular mechanics (MM) study of some covalently linked C60-porphyrin dyads,29 devoted mainly to the molecular topologies of the systems. But MM is not readily applicable to molecules with complex electronic structures such as those containing Cr, Mn, Fe, and Co. Using a density functional theory (DFT) method, * Corresponding author. E-mail: [email protected].

Wang and Lin investigated the interaction behaviors of ZnTPP with C60 and C70.30 More recently, Basiuk, using the DMol3 program, performed DFT calculations for the interactions of a number of metal porphines (MPs) with C60.31 For C60‚NiP, C60‚ CuP, and C60‚ZnP systems, where the metal dz2-orbital is occupied by two electrons, the calculated C60-MP binding energies are as large as ∼1.5 eV (34.6 kcal/mol) although the obtained M-C60 distances are all larger than 3.2 Å (see Table 3). That is, the calculated C60-MP binding energies (Ebind) appear to be incompatible with the calculated C60-MP distances (R). Many fullerene/porphyrin structures have been interpreted as indicating no covalent interaction.14 The Ebind values are expected to be much smaller (3.0 Å), the energy differences (∆E) are actually very small (∼0.02 eV) and are negligible. In general, the shorter the M‚‚‚C60 distance is, the larger is this energy difference ∆E. Pure, unsubstituted MP molecules are square planar, having D4h symmetry. Placing the molecule in the xy plane, the five metal 3d-orbitals transform as a1g (dz2), b1g (dx2-y2), eg (dπ, i.e., dxz and dyz), and b2g (dxy). For FeP, different occupations of six electrons in these d-orbitals can yield a number of possible lowlying states that belong to one of the low-spin (S ) 0), intermediate-spin (S ) 1), or high-spin (S ) 2) states. Previous calculations33 show that the ground state of FeP is 3A2g arising from the (dxy)2(dz2)2(dπ)2 configuration, in agreement with experimental assignments. Among the several high-spin states, the 5A1g state arising from the (dxy)1(dπ)2(dz2)2(dx2-y2)1 configuration is the lowest quintet state in FeP. CoP and CuP have the ground states of 2A1g [(dz2)1] and 2B1g [(dx2-y2)1], respectively, whereas both NiP and ZnP are diamagnetic (closed-shell). The calculations on C60‚MP were performed with and without the dispersion correction (Edisp) for the sake of comparison. The quality of the newly added, empirical dispersion correction for the supramolecular complexes of fullerene with metal porphyrins is as yet unclear and needs to be tested. We found that the DFTDisp optimized Fe-C60 and Co-C60 distances are extremely short and cannot be considered as reliable. Therefore, in the calculations for the relative energies of the different spin states in C60‚FeP, no dispersion correction was made (Section 3.1). But in evaluating the C60-FeP binding energy (Section 3.3), the Edisp term is added. In the case of MdNi, Cu, or Zn, the M-C60 distances with and without the dispersion correction are very close to each other. Table 4 reports the DFT-Disp optimized structural parameters for the various C60‚MP systems. The structural parameters given in Tables 2 and 3 are those from the pure DFT calculations (with the TZP basis sets). 3.1. C60‚FeP. We first discuss the C60‚FeP complex. The calculated relative energies (Erelative) for the low-, intermediate-, and high-spin states of C60‚FeP are presented in Table 2, together with results of pure FeP for comparison, where the Erelative of the intermediate-spin state is set as zero. Geometry optimization was performed separately for each state considered. The structural parameters of particular interest are RM-C60, the distance between the metal and the midpoint of the (6:6) C-C bond of C60, RM-C(C60), the distance between the metal and a carbon atom of the (6:6) bond of C60, RCt(N4)‚‚‚N, a measure of the porphyrin core size, RCt(N4)‚‚‚M, the displacement of the metal out of the porphyrin (N4) plane toward fullerene, RCt(N4)‚‚‚Ct(C8) or RCt(N4)‚‚‚Ct(H8), a measure of the doming in the porphyrin. The

Interaction of Metal Porphyrins with Fullerene C60

J. Phys. Chem. B, Vol. 111, No. 17, 2007 4377

TABLE 2: Calculated Relative Energies (Erelative), Structural Parameters (R), and Mulliken Unpaired Spin Densities [∆n(r-β)] on Fe and C60 for the Low-Spin (S ) 0), Intermediate-Spin (S ) 1) and High-Spin (S ) 2) States of Combined C60‚FeP and Isolated FeP Species C60‚FeP BP

∆E(6:6-6:5)f

PBE OLYP OPBE Becke00

Erelative, eV RFe-C60, Åg RFe-C(C60), Åh RCt(N4)...Fe, Å RCt(N4)...N, Åi RCt(N4)...Ct(C8), Åi RCt(N4)...Ct(H8), Åi ∆nFe(R-β), e ∆nC60(R-β), e Erelative, eV Erelative, eV Erelative, eV Erelative, eV

FeP

S ) 0a

S ) 1b

S ) 2c

-0.53 0.07 1.954 2.087 0.343 1.977 0.176 0.259 0.00 0.00 0.01 0.25 0.19 0.18

-0.19 0.00 2.161 2.278 0.320 1.979 0.125 0.173 2.02 -0.05 0.00 0.00 0.00 0.00

-0.28 0.42 2.170 2.286 0.470 2.043 0.099 0.135 3.78 -0.19 0.40 -0.08 -0.04 -0.10

S ) 0a

S ) 1d

S ) 2e

1.47

0.00

0.70

1.989

1.979

2.038

0.00

1.95

3.69

1.46 1.39 1.38 1.39

0.00 0.00 0.00 0.00

0.68 0.25 0.21 0.42

a Configuration: (d )2(d )2(d )2. b Configuration: (d )2(d )2(d )1(d 2)1. c Configuration: (d )2(d )1(d )1(d 2)1(d 2 2)1. d Configuration: (d )2(d )1(d )1(d 2)2. xy xz yz xy xz yz z xy xz yz z x -y xy xz yz z Configuration: (dxy)1(dxz)1(dyz)1(dz2)2(dx2-y2).1 f Energy difference (in eV) between the different contacts of FeP to the (6:6) and (6:5) bonds of the fullerene respectively. g The closest distance between Fe and the midpoint of the (6:6) C-C bond of C60. h The closest distance between Fe and a carbon atom of the (6:6) bond of C60. i Ct(N4), centroid of the mean plane defined by the four pyrrole nitrogen atoms; Ct(C8), centroid of the mean plane defined by the eight peripheral carbon atoms; Ct(H8), centroid of the mean plane defined by the eight peripheral hydrogen atoms.

e

TABLE 3: Calculated Propertiesa for the C60‚MP Complexes (MdFe, Co, Ni, Cu, Zn) at Their Ground State BP/TZP

BP/TZP BP/DZP PBE/TZP PBE/DZP OLYP/TZP OLYP/DZP OPBE/TZP OPBE/DZP results of DMol3 (ref 31) BP results for isolated MP

∆E(6:6-6:5), eV RM-C60, Å RM-C(C60), Å RCt(N4)...M, Å RCt(N4)...N, Å RCt(N4)...Ct(C8), Å RCt(N4)...Ct(H8), Å QM, e Ebind(0), eVb Ebind(1), eVb Ebind(2), eVb Ebind(0), eV Ebind(1), eV Ebind(2), eV Ebind(0), eV Ebind(1), eV Ebind(2), eV Ebind(0), eV Ebind(1), eV Ebind(2), eV Ebind(0), eV Ebind(0), eV Ebind(0), eV Ebind(0), eV RM-C60, Å RM-C(C60), Å Ebind, eV RM-N, Å QM, e

MdFe (S ) 2)

MdCo

MdNi

MdCu

MdZn

-0.28 2.170 2.286 0.470 2.043 0.099 0.135 0.72 -0.04c 0.80 0.72 0.61 1.45 0.94 0.16c 1.00 0.92 0.78 1.62 1.13 -0.61 -0.10 -0.37 0.44 2.10d 2.222d 1.90d 1.979e 0.82

-0.11 2.297 2.405 0.226 1.979 0.095 0.154 0.63 -0.12 0.71 0.62 0.63 1.46 0.81 0.07 0.90 0.81 0.81 1.64 1.01 -0.84 -0.28 -0.72 0.19 3.49 3.560 1.60 1.976 0.75

0.00 3.105 3.182 -0.002 1.966 -0.044 -0.066 0.61 -0.09 0.40 0.31 0.40 0.89 0.45 0.06 0.55 0.47 0.54 1.03 0.61 -0.37 -0.11 -0.36 0.09 3.34 3.414 1.56 1.971 0.63

-0.02 3.084 3.162 -0.002 2.021 -0.038 -0.055 0.66 -0.08 0.41 0.32 0.41 0.90 0.45 0.07 0.56 0.48 0.55 1.04 0.61 -0.36 -0.11 -0.37 0.07 3.23 3.301 1.51 2.020 0.72

-0.02 3.124 3.201 0.007 2.055 -0.059 -0.085 0.79 -0.08 0.39 0.32 0.35 0.94 0.44 0.08 0.55 0.48 0.49 1.11 0.61 -0.32 -0.14 -0.33 0.03 3.25 3.329 1.47 2.053 0.82

a See the footnotes of Table 2. b Ebind(0), the (C60-MP) binding energy without dispersion (Edisp) or counterpoise (∆ECP) correction; Ebind(1), the binding energy with only an Edisp correction; Ebind(2), the binding energy with both Edisp and ∆ECP corrections. c For the BP and PBE functionals, the total energies taken for C60‚FeP are those of the intermediate-spin (S ) 1) state since the high-spin state is not the ground state for both functionals. d These are the results for low-spin state (S ) 0). e The Fe-N distance for S ) 1 state.

RCt(N4)‚‚‚N value given in the table is actually the average distance between the centroid of the mean plane defined by the four pyrrole nitrogen atoms and one of the pyrrole nitrogen atoms. Geometry optimization indicates that the porphyrin core is somewhat warped or saddle-like, owing to intramolecular steric repulsion. When C60 is attached to FeP, significant out-of-plane displacement of Fe is observed. One obvious feature of C60‚ FeP is that double occupation of the dz2 orbital (as in the 3A2g and 5A1g states) results in a very long Fe-C60 distance, implying

that 3A2g and 5A1g are no longer the lowest triplet and quintet in C60‚FeP. The possible low-lying states considered for this molecular complex are 1A′ [(dxy)2(dπ)4], 3A′ [(dxy)2(dπ)3(dz2)1], and 5A′′ [(dxy)2(dπ)2(dz2)1(dx2-y2)1], which correspond to the FeP’s 1A , 3E , and 5B 1g g 2g states, respectively. Large changes of the spin state relative energies are seen from FeP to C60‚FeP. With the BP functional, the ground state of C60‚FeP is calculated to be a triplet (3A′); the closed-shell state (1A′) lies 0.07 eV above 3A′. Even higher relative energies of 1A′ (0.20.3 eV) are obtained with the OLYP, OPBE, and Becke00

4378 J. Phys. Chem. B, Vol. 111, No. 17, 2007 TABLE 4: BP/TZP Optimized Structural Parametersa for the C60‚MP Complexes from the Dispersion-Corrected DFT Calculations C60‚FeP

C60‚CoP C60‚NiP C60‚CuP C60‚ZnP

S)0 S)1 S)2 RM-C60, Å RM-C(C60), Å RCt(N4)...Fe, Å RCt(N4)...N, Å RCt(N4)...Ct(C8), Å RCt(N4) ...Ct(H8), Å a

1.922 2.056 0.299 1.977 0.142 0.213

2.081 2.203 0.290 1.975 0.115 0.141

2.099 2.219 0.448 2.042 0.160 0.202

2.093 2.213 0.247 1.978 0.089 0.111

3.092 3.072 3.114 3.170 3.151 3.192 -0.003 -0.003 0.005 1.966 2.020 2.055 -0.038 -0.034 -0.056 -0.049 -0.042 -0.069

See the footnotes of Table 2.

functionals. But the PBE data show the 3A′ and 1A′ states to be nearly degenerate in energy. The relative energy of the high-spin state is, however, very sensitive to the method used; it is ∼0.4 eV with BP and PBE, but becomes negative (∼-0.1 eV) when the OLYP, OPBE, or Becke00 functional is used. In a recent paper,52 we investigated the behaviors of a large number of GGA, meta-GGA, and hybrid-GGA functionals in describing the spin-state energetics of iron porphyrin and related compounds. On the basis of the experimental ground states and the calculated data, the intermediate-spin/high-spin state energy splitting in FeP is estimated to be 0.1-0.2 eV. Therefore, both BP and PBE functionals overestimate the relative energy of the high-spin state by about 0.5 eV. The Erelative of 5A′′ in C60‚FeP is about 0.3 eV lower than that of 5A1g in FeP, reflecting the effect of the C60 binding to decrease the relative energy of the high-spin state. The OLYP, OPBE, and Becke00 calculations that give a high-spin ground state for C60‚FeP are believed to be reliable. It is clear that all our results differ from Basiuk’s results which give a closedshell state for C60‚FeP. Without electron occupation in the dz2 orbital, the Fe-C60 distance for the low-spin state is calculated to be very short, only 1.95 Å. The intermediate- and high-spin states have considerably longer RFe-C60 than does the singlet state as a result of their dz2 orbital occupancy. Owing to the occupation of the dx2-y2 orbital for S ) 2, the core size RCt(N4)‚‚‚N for the highspin state is about 0.06 Å larger than those for the low- and intermediate-spin states. The high-spin state also has a considerably larger Fe out-of-plane displacement than do the lowerspin states. Another structural feature of the complex is that FeP is domed (see Figure 1c). The doming of the ring for the low-spin state is more significant owing to a shorter M-C60 distance. Finally the Mulliken spin densities on Fe and C60 in C60‚FeP for the S ) 1 and 2 states are also shown in Table 2. The unpaired electrons are almost entirely localized on Fe in both C60‚FeP and isolated FeP. Upon complexation, there is about a 0.1 e charge transfer from FeP to C60. 3.2. C60‚MP with MdCo, Ni, Cu and Zn. In contrast to C60‚FeP, the electronic structures of the other C60‚MP complexes are relatively simple; the multiplicities of the ground state are the same as those of the pure MP moieties. Figure 2 illustrates the ground-state orbital energy level diagram for every C60‚ MP; the left and right extremes of the figure represent the energy levels of the FeP and C60 moieties. Orbitals of MP are combined with orbitals of C60 to form orbitals of the complex. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are associated with MP and C60 components, respectively. On going from FeP to C60‚FeP, the energy levels of the former are all shifted down greatly. This indicates decrease of charge density on the FeP moiety. On the other hand, Mulliken population analysis shows the positive

Liao et al. charge on Fe in C60‚FeP to be smaller than that in pure FeP (see Table 3), which indicates some electron transfer from C60 to FeP. These results support the point of view27 that overall the fullerene moiety acts as the acceptor but locally the electronrich (6:6) juncture bond can donate electron density to the positive center of MP. With a longer M-C60 distance, the downshifts of the MP energy levels are less significant. 3.3. The C60-MP Binding Energies and Distances. The calculated properties for a series of C60‚MP complexes in their ground states are presented in Table 3. In addition to the structural parameters, the C60-MP binding energies (Ebind) and Mulliken charge distributions on the metal (QM) are now reported in this table. Ebind is defined as

-Ebind ) E(C60‚MP) - {E(C60) + E(MP)} where E(C60‚MP), E(C60), and E(MP) are the total energies of the indicated species. (The geometries of C60 and MP are independently optimized.) According to this definition, a positive Ebind reflects a bound complex and a negative Ebind indicates that the complex is unbound relative to its components. To examine the performances of the dispersion correction (Edisp) as well as the counterpoise correction (∆ECP) on the C60-MP binding energy, we have displayed in the table three terms of Ebind, namely Ebind(0), Ebind(1), and Ebind(2) (see below). It was argued30,57,58 that counterpoise corrections for basis set superposition error (BSSE) on Ebind appear not to be applicable to DFT calculations on weakly bound intermolecular systems. But the situation may be different when Edisp is taken into account. The calculated results of Basiuk31 are also listed in the table for comparison. 3.3.1. Ebind(0): The Binding Energy without Edisp and ∆ECP. Accurate predictions of binding energies for weakly bound molecular complexes are a difficult issue. As mentioned in the Introduction, the binding energies calculated by Basiuk31 are too large to be considered as reliable. Our results show that the Ebind value is sensitive to the functional used. The calculations with BP and the (high-quality) TZP basis sets (BP/TPZ) yield a negative Ebind of ∼-0.1 eV for every C60‚MP, implying that C60‚MP is energetically unstable relative to C60 and MP. This is in disagreement with the real situation. Even more negative Ebind values are obtained with the OLYP and OPBE functionals. The Becke00 results of Ebind were not given here as we found that the non-SCF procedure could produce large errors in the calculated Ebind, although it is effective in calculating the relative energies of different spin states in the same molecule. Here Ebind is related to the energies of three different systems. In this case, the non-SCF procedure can no longer be used. Among the various functionals, PBE/TZP produces a positive Ebind value for every C60‚MP, ∼0.2 eV for MdFe and ∼0.1 eV for the other metals, which are much smaller than those obtained by Basiuk31 but consistent with what we expected for the weakly bound systems. Wang and Lin30 performed a calculation on C60‚ ZnTPP with PBE/DZP and obtained 0.70 eV for the binding energy. To examine the effects of basis sets on Ebind, we performed additional calculations with DZP on all the C60‚MP systems as well as on C60‚ZnTPP. It is shown that the smaller DZP basis sets do indeed give significantly larger binding energies than the TZP ones. Now the OPBE values of Ebind become positive, though they may still be underestimated. Particularly, the calculated Ebind shows a good correlation with RM-C60, i.e., a shorter M-C60 distance generally corresponds to a larger C60-MP binding energy. To justify their use of the method and basis sets, Wang and Lin30 also reported in their Supporting Information the results

Interaction of Metal Porphyrins with Fullerene C60

J. Phys. Chem. B, Vol. 111, No. 17, 2007 4379

Figure 2. Orbital energy levels of various C60‚MP complexes, as well as pure FeP and C60 moieties for purposes of comparison.

of PBE/DZP calculations on several difficult, weakly bound intermolecular complexes. They showed that their obtained intermolecular binding energies were all in good agreement with those obtained through high-quality ab initio calculations with large basis sets. Their results are indeed surprising and encouraging. In general, calculations with triple-ζ basis sets are more reliable and more accurate than those with double-ζ basis sets. Here the “good” results obtained with PBE/DZP for weakly bound molecular systems suggest fortuitous cancellations of the errors in the calculations. According to the PBE/DZP results, the C60-MP binding energy varies from 0.5 to 0.8 eV, depending on the identity of the metal. These Ebind values are about 1 eV smaller than those obtained by Basiuk.31 The BP functional gives binding energies which are systematically smaller by about 0.15 eV as compared to those obtained with PBE. To facilitate comparison of the calculated binding energies among different C60‚MP species and the various functionals, plots of Ebind versus M and the DFT method are shown in Figure 3, together with the calculated M-C60 distances. (It should be pointed out that the TZP and DZP basis sets give very close results on structural parameters in C60‚MP). The calculations on C60‚ZnTPP show that the phenyl groups shorten the Zn-C60 distance (by 0.2 Å) and increase its binding energy (by ca. 0.2 eV). 3.3.2. Ebind(1): The Binding Energy with Only Edisp. The DFTDisp calculations have been performed with the BP and PBE functionals and with the TZP and DZP basis sets. According to the data in Table 3, the difference between Ebind(1) and Ebind(0) indicates that the dispersion correction (Edisp) is really large. Depending on the distance R, Edisp varies from 0.47 eV (for C60‚ZnP) to 0.84 eV (for C60‚FeP). (Note that the empirical Edisp is independent of the basis set and functional used; it depends only on R.) With only Edisp, the PBE calculated Ebind is probably too large when the smaller DZP basis set is used. In this case, the CP correction is necessary (see next section), which very much improves the Ebind result. 3.3.3. Ebind(2): The Binding Energy with Both Edisp and ∆ECP. It is interesting to find that for all the systems considered here,

Figure 3. Schematic illustration of the C60-MP binding energies calculated with the DZP basis sets and various density functionals. The line in the upper part represents the calculated M-C60 distances.

the dispersion-corrected DFT (DFT-D) results for Ebind with the larger TZP basis set that include ∆ECP are very close to those obtained from the pure DFT method with the smaller DZP basis set without any correction (especially for C60‚CoP and C60‚ZnP). This indicates that in the DFT/DZP results for Ebind, there is a fortuitous error cancellation between the error of an incomplete atomic orbital (AO) basis set and an otherwise neglected dispersion energy. It is apparent that with only the CP correction (and no dispersion), Ebind is too small and even wrong (negative). This is the reason why some researchers30,57,58 argued that counterpoise corrections are not applicable to DFT calculations. The ∆ECP is much larger with the smaller DZP basis set (0.450.65 eV) than with the larger TZP basis set (0.07-0.09 eV). In

4380 J. Phys. Chem. B, Vol. 111, No. 17, 2007 fact, ∆ECP is insignificant when the TZP basis set is used, and by including ∆ECP, the TZP and DZP results for Ebind become quite close; that is, the calculated Ebind values become stable. Wang and Lin30 also performed DFT calculations on C60‚H2TPP at the PBE/DZP level; a binding energy of 17.33 kcal/mol (0.75 eV) was obtained. Recently, Jung and Head-Gordon35 performed a scaled opposite-spin Møller-Plesset (SOS-MP2) calculation on C60‚H2TPP at the structure optimized by Wang and Lin; they obtained a binding energy of 31.47 kcal/mol (1.36 eV), which is significantly larger than the PBE/DZP value. In the SOS-MP2 approach, there is an adjustable parameter cOS. Different values of cOS will yield rather different results, and for different systems, the cOS values may also be different. The reliability of the SOS-MP2 results, which strongly depend on cOS, is hard to judge here. 3.3.4. The M-C60 Distances. Our calculated M-C60 distances are different from those obtained by Basiuk;31 the former are significantly shorter than the latter, especially for MdCo. Our RM-C60 shows the order of MdFe < MdCo < MdNi ≈ Md Cu ≈ MdZn (see Figure 3), in contrast to the trend in RM-C60 obtained by Basiuk.31 With a long M-C60 distance in C60‚NiP, C60‚CuP, or C60‚ZnP, no notable changes in the geometry of the MP moiety occur. The relatively weak binding between C60 and MP is not able to pull the metal out from the N4-plane. For these complexes, the RCt(N4)‚‚‚Ct(C8) or RCt(N4)‚‚‚Ct(H8) values are given as negative, which means that the four N-atoms are “pushed” out by the fullerene (i.e., they protrude out of the porphyrin plane in the opposite direction). 3.4. Ionization Potentials and Electron Affinities. We also examined ionization potentials (IP) and electron affinities (EA) of the C60‚MP complexes as compared to those of the MP and C60 moieties. IP and EA are dominant factors in the determination of electrochemical redox potentials and so their values are of interest. They were calculated by the so-called ∆SCF method in which separate SCF calculations for the neutral molecule and its ion are carried out and IP ) E(X+) - E(X); EA ) E(X-) - E(X). The results are displayed in Table 5. From Figure 2 we see that the HOMO of C60 is located at a rather low energy, and so the first ionization in C60‚MP occurs invariably from a MP orbital. Also reported as ∆IP in Table 5 are the effects of the C60 contact upon the IP of MP, namely ∆IPdIP (MP) - IP (C60‚MP). Various functionals were tested here. High-spin C60‚FeP has an occupied, high-lying dx2-y2 orbital, which is, therefore, the orbital that is ionized first. However, the calculated IP is sensitive to the functional used; even ∆IP is different for different functional. Since no experimental IP data are available for either C60‚MP or MP, a comparison of the calculation with experiment is impossible here. Previous calculations59,60 have shown that the BP functional is able to yield the IPs for MTPPs and MPcs which are in quantitative agreement with experiment. According to the BP results here, the IP of C60‚FeP is decreased by about 0.6 eV compared to that of FeP, suggesting that the C60 contact eases the oxidation. But the ∆IP obtained with PBE is less than 0.1 eV. The other functionals yield an IP of C60‚FeP which is larger than that of FeP; this trend in the IP values is questionable. With MdCo or Ni, the first ionization in C60‚MP occurs from the dz2 orbital, in contrast to pure MP where the first ionization takes place from a porphyrin orbital (a2u or a1u). In the complex, the repulsive interaction between the C60 HOMO and the M a1g (dz2) raises the energy of the latter. We see that the calculated IPs for both C60‚MP and MP are no longer sensitive to the

Liao et al. TABLE 5: Calculated Ionization Potentials (IP) and Electron Affinities (EA) for Combined C60‚MP and Isolated MP (or C60) with Various Density Functionals BP IP, eV

C60‚FeP (1) FeP (2) ∆IP (2 - 1) C60‚CoP

5.69 (dx2-y2) 6.26 (dz2) 0.57 6.39 (dz2) 6.82 (P-a2u) CoP 7.01 (P-a2u) ∆IP (2 - 1) 0.62 C60‚NiP 6.62 (dz2) NiP 7.01 (P-a1u) ∆IP (2 - 1) 0.39 C60‚CuP 6.68 (P-a2u) 6.79 (dx2-y2) CuP 6.97 (P-a2u) ∆IP (2 - 1) 0.29 C60‚ZnP 6.67 (P-a2u) ZnP 6.95 (P-a2u) ∆IP (2 - 1) 0.28 EA, eV C60‚FeP (1) -2.89 (dxz) -2.67 (C60-t1u) FeP (2) -1.67 (dπ) ∆EA (2 - 1) 1.22 C60‚CoP -2.69 (dz2) -2.68 (C60-t1u) CoP -1.97 (dz2) C60‚NiP -2.71 (C60-t1u) NiP -1.30 (P-2eg) C60‚CuP -2.72 (C60-t1u) CuP -1.38 (P-2eg) C60‚ZnP -2.75 (C60-t1u) ZnP -1.40 (P-2eg) -2.84 (t1u) C60

PBE 6.07 6.16 0.09 6.31 6.99 6.94 0.63 6.54 6.95 0.41 6.61 6.68 6.90 0.29 6.59 6.88 0.29 -2.82 -2.59 -1.59 1.23 -2.60 -2.59 -1.90 -2.59 -1.22 -2.64 -1.30 -2.67 -1.32 -2.76

OLYP OPBE Becke00 6.15 5.79 -0.36 6.12 6.74 6.72 0.60 6.32 6.72 0.40 6.38 6.51 6.67 0.29 6.37 6.65 0.28 -2.53 -2.32 -1.33 1.20 -2.31 -2.33 -1.60 -2.33 -0.99 -2.37 -1.06 -2.41 -1.08 -2.50

6.40 5.81 -0.59 6.33 6.93 6.89 0.56 6.49 6.89 0.40 6.55 6.68 6.83 0.28 6.55 6.82 0.27 -2.70 -2.51 -1.48 1.22 -2.47 -2.51 -1.67 -2.52 -1.15 -2.56 -1.23 -2.60 -1.25 -2.70

6.34 6.01 -0.33 6.31 6.93 6.90 0.59 6.50 6.87 0.37 6.56 6.77 6.84 0.28 6.55 6.83 0.28 -2.65 -2.44 -1.44 1.21 -2.35 -2.46 -1.69 -2.46 -1.09 -2.51 -1.16 -2.55 -1.18 -2.63

functional used; the ∆IP values are about 0.6 and 0.4 eV respectively for MdCo and Ni. In the cases of MdCu and Zn, the first-IP orbitals in both C60‚MP and MP are all the porphyrin a2u orbital. Again, all functionals yield similar IPs and the ∆IPs are about 0.3 eV. Concerning the electron affinities, the character of the electron-accepting orbital is different for different systems. For C60‚FeP, the added electron occupies the low-lying Fe-dxz orbital; the calculated EA of the complex is ∼1.2 eV larger (more negative) than that of FeP and the ∆EA value is independent of the functional used. For C60‚CoP, the added electron may enter either the Co- dz2 orbital or the C60-t1u orbital since their EAs are calculated to be very similar. For the other three C60‚ MP systems, there are no longer low-lying, half-filled Morbitals. (The half-filled Cu- dx2-y2 orbital is located at a high energy.) In this case, the added electron clearly goes into the C60-t1u orbital. 4. Conclusions and Remarks By calculating the energetics of several low-lying spin states, the ground state of C60‚FeP is determined to be high spin (S ) 2). The relative energies for the low-, intermediate-, and highspin states show the order of 1A′ < 3A′ < 5A′′. Since no 1:1 C60‚FePor complexes have been reported so far, the calculated ground state of C60‚FeP is subject to experimental verification. With only one electron in the Co-dz2 orbital, the Co-C60 distance is in fact rather short, about 0.1 Å longer than the FeC60 distance in high-spin C60‚FeP. However, the calculated RCo-C60 (2.30 Å) is found to be notably smaller than those in crystal fullerene/CoPor compounds (2.48-2.95 Å).23 In the crystal structures, there are repulsive interactions between neighboring porphyrins or fullerenes; solvent molecules also exist and occupy the space between porphyrins and fullerenes.

Interaction of Metal Porphyrins with Fullerene C60 Various factors including packing requirement may be responsible for the longer Co-C60 distances in the crystal structures. Double occupation of an M-dz2 orbital in MP prevents close association of any axial ligand, and so the calculated Ni-C60, Cu-C60, and Zn-C60 distances of ∼3.1 Å are much longer than the Fe-C60 and Co-C60 ones. For the site of interaction between MP and C60, the central metal in FeP or CoP prefers lying over an electron-rich (6:6) bond of C60 rather strongly. But this site preference is not obvious when the metal is Ni, Cu, or Zn, where the closest M-C60 contact involving a (6:5) bond shows nearly no difference in energy from that involving a (6:6) bond. Among the several functionals used here, PBE performs best in the calculations for the binding energies of the noncovalent systems. On the basis of the most reliable PBE/DZP results here, the MP-C60 binding energies (Ebind) are 0.8 eV (18.5 kcal/mol) for MdFe/Co and 0.5 eV (11.5 kcal/mol) for MdNi/Cu/Zn. (In the case of MTPP-C60, the peripheral substituents, phenyl groups, can increase the binding energy by about 0.2 eV.) Our additional dispersion-corrected DFT calculations on C60‚MP with counterpoise (CP) correction indicate that the “good” Ebind from PBE/DZP results from a fortuitous error cancellation arising from the incomplete atomic orbital basis set and an otherwise neglected dispersion energy (Edisp). The estimated Edisp is ca. 0.8 eV for C60-FeP/CoP (where the M-C60 distance is short) and ca. 0.5 eV for C60-NiP/CuP/ZnP (where the M-C60 distance is long). It improves the calculated binding energy considerably when using more reliable, large basis sets (e.g., TZP) which give a small basis set superposition error (BSSE). The counterpoise correction (∆ECP) is much larger with the smaller DZP basis set (0.45-0.65 eV) than with the larger TZP basis set (0.07-0.09 eV). It was suggested that DFT methods are too “local” to account for the long-rang, nonlocal dispersion energy.35-38 Our additional calculations seem to support this argument. At present, numerous DFT methods are available in the literature; some of them are designed specially for van der Waals dimers and give satisfactory numerical results. Because in those DFT calculations, no CP corrections are made for Ebind, fictitious additional binding is included in Ebind and the satisfactory results may arise from fortuitous cancellations of the errors in the calculations. On the other hand, some density functionals were tested on only several weakly bound systems and their performance for other systems is unclear and cannot be judged. In fact, it has proven to be very challenging to develop a functional which can perform well for every type of systems. Very recently, Truhlar’s group61 proposed a hybrid meta-GGA functional, called M05, which is claimed to perform well for kinetics, thermochemistry, and noncovalent interactions. This functional has not been implemented in the current ADF program and so it cannot be tested here for the present systems. Although M05 is claimed to belong to the fourth rung of Jacob’s ladder, it does not add new physics to the “local” (or “semilocal”) functional. A further test of the performance of the functional may still be needed. Our calculations show that incorporating the empirical C6R-6 term in standard DFT methods, as suggested by Grimme,38 appears to be a practical and effective method to account for the dispersion interaction, provided that large basis sets (e.g., TZP) are used. Finally, the close contact of C60 with MP makes the oxidation of the latter easier, especially for MdFe and Co. The reduction properties of FeP and CoP can also be changed by the C60 contact. Acknowledgment. We thank one of the reviewers, who suggested that we perform additional dispersion-corrected DFT

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