Fourteen-Electron Ring Model and the Anomalous Magnetic Circular

Article pubs.acs.org/JPCA

Fourteen-Electron Ring Model and the Anomalous Magnetic Circular Dichroism of meso-Triarylsubporphyrins Steven Vancoillie,† Marc Hendrickx,† Minh Tho Nguyen,† Kristine Pierloot,† Arnout Ceulemans,*,† John Mack,‡ and Nagao Kobayashi‡ †

Department of Chemistry and Institute for Nanoscale Physics and Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium ‡ Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan S Supporting Information *

ABSTRACT: The MCD spectra of meso-triarylsubporphyrins show a sign anomaly which is correlated with the acceptor properties of the aryl substituent. From the spectra, magnetic moments of the excited states are determined. In the context of a simplified orbital model, the sign change is attributed to the quenching of the magnetic moment of the LUMO by acceptor orbitals of the substituent. The actual calculation of this moment presents a major challenge to computational methods. It is shown that wave function techniques based on CASSCF underestimate the covalency effects that are responsible for the quenching. In contrast, a CI method based on DFT orbitals yields excellent results, which fully support the orbital model.

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INTRODUCTION Porphyrins and phthalocyanines are paradigmatic 18-electron annulene π-systems.1 They represent the best known n = 4 solutions to the celebrated 4n + 2 Hückel rule for electron counts in aromatic systems. In comparison, the properties of 14-electron annulenes which provide an n = 3 solution to the rule have been documented to a much lesser extent. Although it has long been known that ring-contracted tripyrrole phthalocyanine analogues, such as subphthalocyanines (subPcs) and triazasubporphyrins (subAPs), can be formed in the presence of a central boron atom,2−4 the first successful synthesis of a series of meso-triarylsubporphyrins (subP), with carbon atoms rather than aza-nitrogens at the meso-positions, was only achieved relatively recently.5,6 The donor and acceptor properties of the aryl substituents of subPs have been found to exert a strong influence on the excited state magnetic dipoles of the subP complex, which can be probed by magnetic circular dichroism (MCD) spectroscopy.5 When the aryl substituent has donor properties, two positive A terms with −ve/+ve sign sequences are observed in ascending energy for the two main π → π* electronic transitions in the MCD spectra, as is normally observed in the spectra of high-symmetry porphyrinoids which retain either a C3 or C4 symmetry axis. This can be readily explained in conceptual terms based on the greater angular momentum associated with the excited electron circulating in the LUMO of the cyclic perimeter than with the positive charge created in the hitherto fully occupied MO.7 In the case of aryl substituents with pronounced acceptor properties, however, a negative A term is observed for the higher energy B (or Soret) band with a +ve/−ve sign sequence. This effect points to a differential quenching of the magnetic moment properties of the excited state, due to the delocalization of the frontier © 2012 American Chemical Society

molecular orbitals over the substituents. In this paper we analyze the MCD spectra of a donor−acceptor range of mesoaryl subPs and carry out a theoretical treatment, based on a conceptual model of 14-electron systems. The most challenging part involves the first-principles calculation of the magnetic moments of the excited states, using wave function techniques.

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EXPERIMENTAL AND COMPUTATIONAL METHODS The optical spectra for complexes with trifluorophenyl (TFsubP), 4-pyridyl (4pysubP), 3-pyridyl (3pysubP), phenyl (PhsubP), and 4-methoxyphenyl (MOsubP) aryl substituents have been reported previously.5 A spectral band deconvolution analysis was carried out for the various subP complexes based on the use of the SIMPFIT program.8,9 Simultaneous spectral band deconvolution of MCD and absorption spectra removes much of the ambiguity that is normally associated with band deconvolution analyses. Under the rigid shift assumption, the application of the magnetic field does not alter the Gaussianshaped spectral band curve function within the intensity mechanisms for the spectral bands.10 The A1/D0 ratios were determined using the conventions of Piepho and Schatz.10 Two meso-aryl-substituted boron subPs with an axial OH ligand, (OH)(4pysubP) and (OH)(MOsubP), were chosen as being representative of strong acceptor and strong donor substituents, respectively. Geometry optimizations were carried out on these two subPs systems by using the hybrid B3LYP method in combination with the 6-31G** basis sets as implemented in the Received: March 19, 2012 Published: March 21, 2012 3960

dx.doi.org/10.1021/jp302623q | J. Phys. Chem. A 2012, 116, 3960−3967

The Journal of Physical Chemistry A

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GAUSSIAN03 program.11 These geometries were subsequently used in single-point multiconfigurational perturbation theory (CASPT2) calculations, to simulate the experimental electronic absorption bands. These were performed with ANO-s basis sets12 with the following contractions: [4s3p1d]/[2s1p] on B, C, N, O/H, but with only [3s2p1d]/[2s] for C, O/H of the methoxy groups of MOsubP. Due to the bent conformation of the axial OH ligand, the C3 symmetry is lifted. CASPT2 results are reported for an active space of four electrons distributed over four orbitals, the minimum active space necessary to calculate the singlet ground state and the four lowest energy singlet excited states, which are associated with the main bands in the experimental spectra. Thus, in terms of the electronic configuration of the ground state, this means the two highest doubly occupied orbitals (HOMO−1 and HOMO) and the two lowest unoccupied orbitals (LUMO and LUMO+1). The ground state was optimized separately, while for the calculations of the excited states, one set of average CASSCF orbitals was used. Oscillator strengths between the ground and excited states and the angular momentum matrix elements between the excited states, which are required to simulate the MCD spectra, were obtained using the RASSI method.13 However, it was found that these properties depend heavily on the shape of the orbitals (see further in the Results). Therefore, we also used SCF and DFT orbitals followed by CASCI (i.e., full CI within the active space, keeping the molecular orbitals fixed) calculations to obtain these properties. All CASPT2 and RASSI calculations14 were performed with MOLCAS 7.4. The 14-Electron Ring Model. Electronic ring models have been used to rationalize the electronic structures and optical spectra of conjugated π-systems with considerable success. A prime example is the celebrated Gouterman four-orbital model for the description of porphyrins and phthalocyanines7 and subsequent perimeter model treatments of the MCD spectra of these systems.15,16 When using a perimeter model approach, the electronic levels are characterized by an integer ring quantum number λ, which determines the z-component of the angular momentum: ⟨lz⟩ = ±ℏλ ,

λ = 0, 1, 2, 3, ...

Figure 1. Molecular frame for boron subporphyrin and DFToptimized structure of (OH)PhsubP (bond lengths (Å) and angles (deg)).

apical bond to Cl or OH is required to form a neutral B(III) complex. The coordination geometry of the boron is nearly tetrahedral, suggesting that four sp3 bonds are effectively being formed. Of the aromatic Hückel systems, obeying a 4n+2 electron count, the 14-electron case is less well documented than the 18-electron system. The lowest energy spectral excitations are associated with the 3 to 4 transition. In the context of the perimeter model, both occupied and unoccupied frontier orbitals are degenerate and stem from the cyclic waves exp(±3iφ) and exp(±4iφ), respectively, where φ is the angular coordinate of the ring. The inner perimeter of the π-system is domed and warped, but the cylindrical characteristics of the frontier orbitals are retained. In the molecular frame of Figure 1, a right-handed Cartesian coordinate system is placed so that the x-coordinate is aligned through two opposite carbon atoms, while the apical hydroxyl hydrogen points in the direction of the positive y-axis direction. The angle φ runs from 0 to 2π around the circumference of the inner perimeter with the positive x-axis as the starting point. The idealized molecular symmetry of a subporphyrin would be C3v. The out-of-plane twist of the aryl substituents lowers the symmetry to C3, while the apical hydrogen atom can be viewed as further reducing the symmetry to C1. In spectroscopic terms, however, it is reasonable to assume C3 symmetry for the π-system. Figure 2 shows the four frontier Kohn−Sham (KS) orbitals of 4pysubP, obtained with the B3LYP functional. It should be noted that in CASSCF the orbital order of the HOMO and HOMO−1 is

(1)

The nodal patterns associated with these angular momentum properties are retained even after symmetry-lowering perturbations to the structure of the polyene. In the case of porphyrins and phthalocyanines, the inner ligand perimeter and tetrapyrrole core of the π-system can be described in terms of perturbations to a D16h symmetry 16-membered electronic dianionic ring, containing 18 π-electrons.15,16 In the absence of intruder MOs introduced by structural modifications, the cylindrical parentage of the highest occupied orbitals, HOMO and HOMO−1, is 4, while that of the lowest unoccupied orbitals, LUMO and LUMO+1, is 5. These four frontier orbitals give rise to two characteristic electronic transitions, which are associated with the Q and B bands in the context of Gouterman’s four-orbital model.7 An approximation similar to that used to describe the tetrapyrrole porphyrinoid π-systems can be applied to the tripyrrole ring systems of subPs, Figure 1. As with porphyrins, the outer exobonds have shorter bond lengths, indicating that they contribute less to the annular conjugation, so that the ring model can be restricted to the inner 12-membered ring. This inner perimeter of the system contains 14 π-electrons. Protonation of two out of three pyrrole nitrogens would be required to form a free base heteroaromatic π-system. Since the subP ligand is a dianion, an additional 3961



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For example, a product function that would transform as cos 7φ is given by |cos(3φ1 + 4φ2)⟩ = |cos 3φ1⟩|cos 4φ2⟩ − |sin 3φ1⟩ |sin 4φ2⟩

(3)

where φ1 and φ2 denote the coordinates of the hole left in the previously fully occupied MO and the excited electron, respectively. In accordance with the Pauli principle, these product functions need to be coupled into antisymmetrized singlet excitations. A singlet state originating from an a2b2 → ab2c orbital excitation can be denoted as (a → c)1 =

1 (|abb ̅ c ̅ | − |a ̅ bb ̅ c|) 2

(4)

where the components denote Slater determinants, and the overbars designate β spins. The derivation of the components of the S and B states is straightforward on this basis and yields Figure 2. KS orbitals of 4pysubP (isocontour value: 0.0025, positive amplitudes in green, negative in red).

1

S x = 1/ 2 ((c3 → c4)1 − (s3 → s4)1)

inverted with respect to the standard order of the KS orbitals derived from a DFT calculation (vide infra).17 The HOMO−1 and HOMO orbitals have an angular nodal pattern which is derived from the cos 3φ and sin 3φ parent cylindrical harmonics, respectively. This is especially clear in the case of the HOMO−1, which has nodal points for φ = (2k+1)π/6. In contrast with the D12h symmetry of the parent C12H12, these orbitals are nondegenerate. The HOMO transforms as a1 under C3v symmetry (Figure 2) and has large MO coefficients on the meso-carbon positions, while the HOMO−1 transforms as a2 and has nodal planes at these atoms. The LUMO, however, has e symmetry and remains degenerate in C3 symmetry due to time reversal. The apical hydrogen causes only a very minor energy splitting. The nodal pattern of the LUMO clearly varies as cos 4φ, while the LUMO+1 varies as sin 4φ, since it is zero at φ = kπ/4. The cylindrical parentage of each MO is thus determined as in eq 2.

1

1

S y = 1/ 2 ((s3 → c4)1 + (c3 → s4)1)

B x = 1/ 2 ((c3 → c4)1 + (s3 → s4)1)

1

B y = 1/ 2 ((c3 → s4)1 − (s3 → c4)1)

where c and s denote cos and sin, respectively. The x- and ycomponents of the S band transform as cos 7φ and sin 7φ, respectively, while the x- and y-components of the B band correspond to cos φ and sin φ. The coupled states presented in the above equation describe zeroth-order states. First-order corrections may arise from the splitting of the HOMO levels, as has been described in detail in previous work.16 This results in a hybridization of the S and B bands. Experimental and computational evidence suggests that these corrections are small for subPs (vide infra), and more importantly in the context of this study this does not provide a mechanism for generating an anomalous MCD signal. Having derived the states, a parametric description of the transition dipole strengths and the magnetic moments of the excited states can now also be obtained, which can be tested against those measured experimentally by MCD spectroscopy. The treatment closely follows a previous analysis of MCD spectra in porphyrins.16 The transition dipole lengths for the four-orbital excitations are parametrized by two parameters, R1 and R2, which denote the dipole lengths of the orbital excitations to the unoccupied levels as follows:

HOMO−1 ⇔ |cos 3φ⟩ HOMO ⇔ |sin 3φ⟩ LUMO ⇔ |cos 4φ⟩ LUMO+1 ⇔ |sin 4φ⟩

(5)

(2)

In the perimeter model, the excitation λ → λ + 1 gives rise to two coupled states, with moments Λ = 2λ + 1 and Λ = 1. The transition from the ground state to the 2λ + 1 excited state is forbidden, since an incident photon can provide only one quantum of orbital angular momentum. By analogy with atomic multiplet theory, the state with higher momentum is lower in energy. For the tetrapyrroles this state corresponds to Λ = 9 and is referred to as the Q excited state, based on “kyuu”, the Japanese word for the number 9. Although this terminology has also recently been applied to subporphyrins,5 we propose that the corresponding Λ = 7 state should be labeled as the S state in the future, based on “shichi”, one of the possible Japanese words for the number 7. The upper state with Λ = 1 can still be referred to as the B state as was the case with tetrapyrrole porphyrinoids, however. Orbital products which belong to these states can easily be formed from trigonometric sum and difference relationships.

R1 = ⟨(c3 → c4)1|x|G⟩ = ⟨(c3 → s4)1|y|G⟩ R 2 = ⟨(s3 → s4)1|x|G⟩ = −⟨(s3 → c4)1|y|G⟩

(6)

The R-parameters are defined in such a way that they are positive quantities. The corresponding transition dipole lengths for the S and B states are ⟨1S x|x|1G⟩ = ⟨1S y|y|1G⟩ =

2 (R1 − R 2) ≡ r

⟨1B x |x|1G⟩ = ⟨1B y |y|1G⟩ =

2 (R1 + R 2) ≡ R

(7)

Clearly the S band will be very weak since the dipole strength is the difference between two large quantities of similar magnitude. The parameter r may be positive or negative. On the other hand, the B transition is always intense. The 3962



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corresponding dipole moments for the excitation of a single S or B component are represented as μGS or μGB and are obtained by multiplying the lengths by the charge of the electron (−e).

much larger than that of the HOMO, the MCD spectrum becomes dominated by the angular momentum of the positive charge left in the previously fully occupied MO resulting in +ve/−ve/+ve/−ve for the B terms associated with both the S (or Q) and B transitions.19 This intensity mechanism does not play a significant role in the spectra of subPs, however, since the LUMO can be regarded as being degenerate. Even in the absence of second-order interactions due to zero-field orbital splitting, the effects of structural perturbations to the parent perimeter on the angular momentum properties are severe. For example in the context of porphyrins, where L and l have theoretical values of 9 ℏ and 1 ℏ, respectively, the actual empirically derived values are in the 3−4 ℏ range for the Q band, with a value of 0.75 ℏ being typical for the B band.16 L values in the 2−3 ℏ range would be anticipated for the S band of subPs on this basis, instead of the theoretical value of 7 ℏ. Since L is the average of two large quantities, however, it will definitely remain positive, and there is, therefore, no scope for an anomalous negative A term in the MCD spectrum. In the case of the B band region, since l is the difference between two large quantities, which are both quenched considerably, there is a possibility that this quenching will bring about a sign change in l and hence also in the MCD band. The meso-aryl-substituted subporphyrins appear to be what Michl referred to as “soft MCD chromophores”,15 since even comparatively small structural changes in the aryl substituents can switch the sign of the A term observed in the B band region. As will be described below, the accurate prediction of these effects based on theoretical computations represents a considerable challenge.

μGS = −er μGB = −eR

(8)

The oscillator strength of a transition in the context of randomly oriented molecules in solution is a dimensionless quantity and is given by f=

4πme 3ℏe 2

ν |μ|2

(9)

Calculated values for the Sx and Sy band components strongly depend on the theoretical method used and range from 0.001 to 0.050, while those derived for the Bx and By components range from 0.8 to 2.5. Magnetic dipoles can be attributed to the orbital moments of the perimeter MOs so that mz = μB⟨lz⟩/ℏ. The λ level will be split into two Zeeman components corresponding to exp(±iλφ) at energies ± λμBH by an external magnetic field, H, applied along the z-direction. The angular momentum of the occupied frontier orbitals is denoted by L1. In the context of an idealized high-symmetry perimeter, L1 reaches an upper value of 3ℏ. Similarly, the angular momentum of the unoccupied orbitals is denoted by L2, and its upper limit is 4ℏ. The angular momentum integrals of the single-orbital excitations are then given by L1 = i⟨(c3 → c4)1|lz|(s3 → c4)1⟩

■

= i⟨(c3 → s4)1|lz|(s3 → s4)1⟩

RESULTS MCD Parameters. The optical spectra for complexes with trifluorophenyl, 4-pyridyl, 3-pyridyl, phenyl, and 4-methoxyphenyl aryl substituents have been reported previously.5 More detailed spectra for the two compounds under investigation are given in Figure 4. The intense absorption in the 370−380 nm region is clearly similar to the B band of tetraphenylporphyrin (TPP) and therefore almost certainly arises from a transition

L 2 = i⟨(c3 → c4)1|lz|(c3 → s4)1⟩ L′2 = i⟨(s3 → c4)1|lz|(s3 → s4)1⟩

(10)

Two values for the orbital excitations arising from the HOMO and the HOMO−1 have been introduced, since in C3v these orbitals are no longer symmetry equivalent. Combining these parametric expressions with the coupled states, one obtains the following angular momentum integrals i⟨1S x|lz|1S y⟩ = L i⟨1B x |lz|1B y ⟩ = l

(11)

where L and l are related to the orbital angular moments as L = L1 + 1/2(L 2 + L′2 ) l = −L1 + 1/2(L 2 + L′2 )

(12)

Since in the perimeter model the LUMOs typically possess a higher angular momentum than the HOMOs, both L and l parameters are expected to have positive values. Both excitations create angular momentum, as would be required to obtain the MCD spectrum consisting of two derivative shaped A terms that is normally observed for porphyrinoids with either a C3 or C4 symmetry axis. The standard expected spectral pattern for increasing frequencies thus reads: −ve/+ve/ −ve/+ve. A lifting of the orbital degeneracy of both the HOMO and LUMO of the parent perimeter results in the A terms being replaced by two coupled B terms, which in some circumstances can be considered to be pseudo-A terms if the splitting of the x- and y-polarized component states is relatively small.18 If the splitting of the LUMO of the parent perimeter is

Figure 3. KS orbitals of MOsubP (isocontour value: 0.0025; positive amplitudes in green, negative in red). 3963



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thus reflecting the greater orbital angular momentum associated with the S excited state.5 The MCD spectra of the S band region can be divided into two distinct groups. An intense −ve/ +ve pattern in ascending energy (i.e., a positive Faraday A term) is observed in the spectra of subPs with electrondonating groups, while those with electron-withdrawing groups are more complex with a concomitant decrease in intensity. The B band region MCD spectra can be divided on a similar basis. The spectra of subPs with electron-donating groups such as MOsubP contain a −ve/+ve pattern as in the S band region, while in contrast the spectra of subPs with electron-withdrawing groups such as 3pysubP, 4pysubP, and TFsubP contain a +ve/−ve pattern (i.e., a negative Faraday A term). In addition, careful inspection reveals that the −ve/+ve MCD pattern in the B band region of the MOsubP spectrum changes markedly on going to PhsubP. The relative intensity of the positive envelope at higher energy becomes weaker, so that only the negative trough is observed. On proceeding further in terms of the electron acceptor properties of the aryl substituent to 3pysubP, a positive MCD band emerges at lower energy, and this intensifies further in the spectrum of TFsubP, to the point in the spectrum of 4pysubP that the positive and negative MCD envelopes have almost equal intensities. These drastic changes in the MCD pattern depending on the nature of the aryl substituents are highly unusual in the context of the allowed B band. Michl has demonstrated that the value of l usually remains relatively constant when structural perturbations lower the symmetry of the cyclic polyene π-system, while that of L changes markedly and is more likely to change sign.15 Although, as described above, the MCD signal in the B band region of the PhsubP spectrum is not a typical Faraday A term, the presence of clear derivative-shaped S00 and B bands in the spectra of the other compounds strongly suggests that the excited states remain orbitaly degenerate,10 as would be anticipated based on the effective C3 symmetry of the subPs. The A1/D0 ratios determined using the conventions of Piepho and Schatz are directly comparable to L and l in eq 12. The results are shown in Table 1. The A1/D0 ratio value for the S00

Figure 4. Absorption and MCD spectra of 4pysubP and MOsubP. Note the sign change of the MCD between 400 and 350 nm.

directly analogous to the B transition within Gouterman’s fourorbital model.7 This band appears at a shorter wavelength in the case of compounds with electron acceptor substituents relative to the spectrum of MOsubP. The weaker absorption band in the 400−540 nm region can be assigned by direct inspection as almost certainly arising from a transition directly analogous to the Q transition within Gouterman’s four-orbital model, since it is about an order of magnitude less intense. The B and S bands, therefore, lie at considerably shorter wavelengths (ca. 30−50 and 70−100 nm, respectively) than the corresponding B and Q bands in the spectra of TPP metal complexes (ca. 410−420 and 500−610 nm).7 The absorption coefficient of the B band is ca. 25% that of ZnTPP in the same solvent.5a The absorption spectra of subPs are generally similar in shape, with the exception of the S00 band where there is greater intensity for compounds with electron-donating meso-substituents.5a The weak S00 intensity ( f between 0.01 and 0.07) is related to the fact that the HOMOs and LUMOs are degenerate or near degenerate. In the context of tetrapyrrole porphyrins, this results in a π-system which mimics that of the D16h symmetry cyclic polyene parent perimeter, by having an allowed B and a forbidden Q band based on orbital angular momentum changes of Λ = 1 and 9, respectively. It is known that the Q00 bands of TPPs are generally weaker than those of octaethylporphyrins (OEPs) where there is greater separation of the MOs derived from the HOMO of the parent perimeter. As a result, the Q00 band is generally weaker than the Q01 vibrational band in the spectra of TPPs, while the Q00 and Q01 bands of OEPs have comparable intensities. In contrast with the electronic absorption spectra, the MCD spectra of subPs differ markedly from compound to compound. Although the absorption coefficient ratio of the B band to S band in the absorption spectra is about 10:1, the relative S band intensities in the MCD spectra are much larger,

Table 1. Calculated A1/D0 Ratios for S00 and B00 Bands of a Series of Compounds as a Function of meso-Substituents 4-trifluoromethyl (TFsubP) 4-pyridyl (4pysubP) 3-pyridyl (3pysubP) phenyl (PhsubP) 4-methoxyphenyl (MOsubP)

S00

B00

1.01 1.52 0.83 2.27 1.85

−0.14 −0.21 −0.11 0.22 0.26

acceptor ↓ donor

band of PhsubP lies within the 2−3 ℏ anticipated for L based on the analogous values obtained for TPP complexes relative to the upper limit of 7 ℏ for an ideal high-symmetry perimeter. The values for the allowed B band are significantly smaller than those for the forbidden S00 band as would be anticipated based on the definitions for l and L. When electron-accepting aryl substituents are introduced, the observed quenching of the angular momentum properties, which results in the lower A1/ D0 ratio for the S00 bands of TFsubP, 4pysubP, and 3pysubP, would be anticipated, since electron density is removed from the inner ligand perimeter. The change in sign observed in the B band region is more difficult to explain in qualitative terms and will be explored in greater detail based on theoretical calculations. 3964



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Electronic Structure Calculations. All optimized structures are in close agreement with the available X-ray data.5b Figure 1 shows the optimized DFT geometry of a mesotriphenylsubporphyrin with a hydroxyl axial ligand, (OH−)PhsubP. As is also the case with porphyrin ligands, the bonds of the pyrrole moieties alternate. The exo-bonds have more double-bond character than the adjacent bonds. The heteroaromatic character of the π-system is therefore concentrated on the inner 12-atom ligand perimeter. The NICS (nucleus independent chemical shift) values in the ring centers, at GIAO-B3LYP/IGLO-II/6-31G** level), are −11.4 for the 5-membered pyrrole rings, and −15.1 for the 6membered boron-containing rings. The degree of pyramidality at the boron atom, as measured by the ⟨OBN⟩ angle, was found to be 110°. The threefold axis is retained, since the arylsubstituents at the meso-positions adopt a propeller-like configuration. The dihedral angles formed by the meso-aryl substituents are ca. 50°. In tetrapyrrole compounds this angle is close to 90°. The smaller tilt angle in the context of subporphyrins is of great importance, since it facilitates interaction between π-MOs which are associated primarily with the aryl groups and the inner ligand perimeter. Several methods have been used to calculate the absorption spectra. In Table 2 we compare the results obtained for the S and B bands

Table 3. Orbital Energy (eV) of the LUMO versus Splitting of the HOMO of the Parent Perimeter (ΔHOMO) as a Function of meso-Substituents

S S B B

489 (0.01)

S S B B

496 (0.06)

373 (0.89)

379 (0.77)

TD-DFT (B3LYP) (OH−)4pysubP 450 (0.041) 449 (0.026) 353 (0.794) 352 (0.784) (OH−)MOsubP 466 (0.134) 463 (0.113) 361 (0.798) 359 (0.784)

(0.010) (0.008) (1.369) (1.353)

459 463 352 356

(0.001) (0.001) (1.354) (1.339)

−2.71 −2.68 −2.49 −2.17 −2.00

0.23 0.17 0.27 0.28 0.45

acceptor ↓ donor

subporphyrins than in porphyrins due to the smaller dihedral tilt angle. The splitting of the HOMO indicates the presence of a filled donor orbital which can interact with the HOMO. The HOMO−1 is always the a2 symmetry component which has no density at the meso-positions and therefore is not significantly affected by the presence of the substituents. Detailed inspection of the orbital plots at the meso-sites reveals antibonding phases between the ring orbital and a πorbital on the substituents, which is indicative of the donor interaction. This is especially the case for the methoxysubstituent, as shown in Figure 3. It results in a larger ΔHOMO value, which in turn leads to a more intense S00 band due to hybridization of the S and B excited states. In contrast, for the LUMO the interaction with the π*-orbital on the aryl substituent is in-phase as can most clearly be seen for the pyridyl substituent (Figure 2). The magnetic moments are very sensitive to this orbital composition, as will be shown in the next section. Magnetic Moment Calculations. First-principles calculations of MCD spectra have been reported by different methods,20,21 but it is difficult to reach quantitative agreement with experiment. Instead of calculating the primary MCD parameters, we have focused on the calculation of the excited state magnetic moments, which offer a direct understanding of the experiments. The spectra show a clear dichotomy: a normal positive A term is observed in the S band region of the MCD spectra of both complexes (although the main electronic band is very weak in the 4pysubP spectrum), while A terms of different sign are observed in the B band region. In the case of 4pysubP an anomalous negative A term is observed, while a positive A term is observed in the MOsubP spectrum. Calculations have been carried out for both these compounds as typical representatives of acceptor (4pysubP) versus donor (MOsubP) substituents. The magnetic moments can be derived from the off-diagonal parts of the Zeeman matrix, corresponding in this case to the matrix elements of lẑ between the components of the S and B states. The off-diagonal matrix element between the S components, multiplied by the imaginary unit, directly yields the magnetic moment of the lower energy S band. The results of several methods are shown in Table 4. CASSCF wave functions predict similar negative l values for both donor and acceptor substituents, in contrast to

CASPT2(4,4) 451 453 342 343

ΔHOMO (eV)

TFsubP 4pysubP 3pysubP PhsubP MOsubP

Table 2. Wavelengths λ (nm) of the S and B Bands of the Absorption Spectrum of 4pysubP and MOsubP, Calculated by TD-DFT and CASPT2, with Oscillator Strengths Added in Brackets expt

LUMO (eV)

of (OH−)4pysubP and (OH−)MOsubP. Comparison with the experimental wavelengths clearly demonstrates that both the TD-B3LYP and CASPT2(4,4) calculations provide accurate predictions of the excitation wavelengths. The increase in wavelength of the bands when going from 4pysubP to MOsubP is predicted as well. The energies of the main spectral bands for PhsubP, TFsubP, 3pysubP, 4pysubP, and MOsubP are broadly similar in both the experimental and calculated absorption spectra. For the oscillator strengths, however, CASSCF predicts lower absorption intensity for MOsubP, contrary to the experimental observations where 4pysubP has a much smaller intensity. In this respect TD-DFT scores better. The KS frontier orbitals for both model compounds are shown in Figures 2 and 3. The role of the substituents is clearly illustrated by orbital energies of the HOMO and LUMO. In Table 3 we list the energies of the LUMO and the splitting of the HOMO (ΔHOMO) as calculated by DFT. These quantities are well correlated. The observed trend reflects the donor−acceptor properties of the substituents. The low-lying virtual orbitals in acceptors will stabilize the LUMO through orbital interactions. These interactions are stronger in

Table 4. Calculated Angular Momenta (in Units of ℏ)

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l

CASSCF

CASSCF(5)

CASCI(HF)

CASCI(KS)

expt

4pysubP MOsubP L

−0.192 −0.103 CASSCF

−0.107 −0.050 CASSCF(5)

0.008 0.211 CASCI(HF)

-0.193 0.099 CASCI(KS)

(−) (+) expt

4pysubP MOsubP

3.737 3.709

3.870 3.850

3.996 3.915

3.430 3.295

(+) (+)



Article

and the substituents is bigger for s3 than for the (s4, c4), which is also apparent from the population analysis (see Suporting Information Table S1). The delocalization of the s3 orbital is larger than in the c4 or s4 orbitals, while the c3 orbital is completely localized on the inner structure. Furthermore, while for 4pysubP the delocalization of s3 is only slightly larger than for (c4, s4), the situation in MOsubP is quite different. In the latter compound, the s3 orbital is much more delocalized over inner and outer rings than in 4pysubP, while the delocalization of (c4, s4) is smaller. Analyzing the shape of the orbitals, we can rationalize the observations in the MCD signals. The angular momentum matrix elements will be quenched by delocalization of the orbitals over the substituents. As such, a small L1 value will correspond to delocalized (s3, c3) orbitals, while small L2 and L2′ values will coincide with delocalized (s4, c4) orbitals. Comparing 4pysubP and MOsubP, larger delocalization of s3 and thus smaller L1, combined with a more ionic (s4, c4) and thus larger L2 and L2′, will lead to a more positive l = −L1 + (1/ 2)(L2 + L2′) value in MOsubP compared to 4pysubP. This is true for both the SCF and KS orbitals: the l value is reduced when going from MOsubP to 4PysubP. For L = L1 + (1/2)(L2 + L′2) the changes will partially offset each other. When going from HF to KS orbitals, on the other hand, the delocalization of all orbitals is increased, leading to smaller L1 but also smaller L2 and L2′ resulting in a smaller L value. This time, the changes will partially cancel out for the l value. The orbital composition of the four transitions at RASSCF and CASCI(KS) complies well with the theoretical model and is given in Table S2. The oscillator strengths obtained from the CASSCF (4,4) calculations for the S band (Table 2) do not match the differences in the experimental absorption spectra of 4pysubP and MOsubP, since a much smaller intensity is observed for the former compound. The oscillator strengths obtained with CASCI are shown in Table 5. We can see that while

experiment. To check the stability of the results with respect to the shape of the molecular orbitals, we recomputed these values using CASSCF orbitals which were instead obtained by averaging over all five states (i.e., including the ground state) rather than using two different sets of orbitals for the ground state and the four excited states. The results obtained from this alternative CASSCF calculation are denoted as CASSCF(5) in Table 4. As one can see, the l values obtained with CASSCF(5) are halved with respect to the original CASSCF values, thus indicating a high sensitivity of this property to the orbital shapes. A similar phenomenon has been observed previously when computing EPR g factors for a number of copper complexes. It was found there that different ways of orbital averaging greatly influence the angular momentum values obtained from CASSCF.22,23 The problem was traced back to the description of covalency of the Cu(II)−ligand bonds, as manifested by the extent of mixing between Cu 3d and ligand character in the (antibonding) orbital which is singly occupied in the ground state (the SOMO). Using CASSCF orbitals optimized for the ground state only, the contribution of Cu 3d character in the SOMO is much too high, resulting in too large angular momentum matrix elements.24 The solution was to use instead CASSCF orbitals obtained from an average calculation over the two states which have either the bonding or antibonding combination of the Cu 3d and ligand orbital singly occupied. Along similar lines, Sadoc et al.25 noted that the calculation of the Mössbauer isomer shift was very sensitive to the inclusion of charge-transfer configurations, and hence to covalency. In the present case, however, the value of angular momentum matrix elements cannot be related to the covalency of a single bond, nor are the states involved connected to one singly occupied orbital. More elaborate multiconfigurational calculations (employing larger active spaces) revealed highly fluctuating values for the angular momentum. Thus, we opted to abandon the CASSCF approach and go to a simpler approach instead, closer to the orbital model. Starting from either SCF or Kohn−Sham (B3LYP) orbitals, a CASCI(4,4) calculation was performed, in which the orbitals were not further optimized. Since B3LYP includes dynamical correlation, the orbital compositions should be of good quality. Indeed, when using KS orbitals, l values with the correct sign are obtained, negative for 4PysubP and positive for MOsubP. On the other hand, with SCF orbitals, both values are positive. Following the same procedure for the L values, we find that also in this case the value is very sensitive to the orbital shape, although both the correct, positive sign as well as a decrease in L value from 4PysubP to MOsubP is obtained with all methods. We now continue with the analysis based on the KS orbitals obtained with the B3LYP functional, shown in Figures 2 and 3 for 4pysubP and MOsubP, respectively. The x-axis runs through the central boron atom and two pyrrole α-carbons, while the positive y-axis is oriented along the hydroxyl direction. Although the hydroxyl axial ligand breaks the strict trigonal symmetry, it also forces the orbitals into canonical combinations, with approximate mirror symmetry across the BOH symmetry plane. The a1 HOMO’s (s3) have an antibonding interaction with a π-donor MO on the aryl substituents. The a2 HOMO−1 (c3) on the other hand has nodal planes at the meso-carbon positions and, therefore, does not interact directly with the substituents. While the LUMO orbitals (s4, c4) of 4pysubP have a slight bonding interaction with the substituents, that interaction is nonbonding in MOsubP. The orbital interaction between the inner structure

Table 5. Oscillator Strengths Obtained with CASCI 4pysubP S S B B

MOsubP

(HF)

(KS)

(HF)

(KS)

0.0079 0.0025 2.3721 2.3611

0.0007 0.0035 2.4715 2.4639

0.0002 0.0023 2.3517 2.3517

0.0097 0.0151 2.4912 2.4854

CASCI(HF) also wrongly predicts a lower intensity of the S band in MOsubP, the CASCI(KS) values match the experimental observations.

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DISCUSSION AND CONCLUSION The subporphyrins exhibit a pyramidal structure with lower tilt angles for meso-aryl substituents relative to tetrapyrrole porphyrins. The substituents, therefore, interact to a much more significant extent with the frontier π-MOs, and this results in a larger quenching of the orbital moments. This accounts for the anomalous sign of the A term in the B band region of the spectra of complexes with aryl substituents, which have electron-withdrawing properties. As far as the absorption spectra are concerned, both TD-DFT and CASPT2 calculations yield good results, although the energies of the lowest excitations still exceed the experimental values by about 1500 cm−1 (Table 2). Improvements in this regard can only be expected from extended correlations involving either a specifically tailored active space or a better description of the 3966



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J. Am. Chem. Soc. 2007, 129, 8271−8281. (c) Shimizu, S.; Matsuda, A.; Kobayashi, N. Inorg. Chem. 2009, 48, 7885−7890. (6) (a) Inokuma, Y.; Yoon, Z. S.; Kim, D.; Osuka, A. J. Am. Chem. Soc. 2007, 129, 4747−4761. (b) Inokuma, Y.; Osuka, A. Dalton Trans. 2008, 2517−2526. (7) Gouterman, M. The Porphyrins; Dolphin, D., Eds.; Academic Press: New York, 1978; Vol. III, Chapter 1 (8) Gasyna, Z.; Browett, W. R.; Nyokong, T.; Kitchenham, R.; Stillman, M. J. Chemom. Intell. Lab. Syst. 1989, 5, 233−246. (9) Mack, J.; Stillman, M. J. Coord. Chem. Rev. 2001, 219−221, 993− 1032. (10) Piepho, S. B.; Schatz, P. N. Group Theory in Spectroscopy with Applications to Magnetic Circular Spectroscopy; Wiley: New York, 1983. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (12) Pierloot, K.; Dumez, B.; Widmark, B.-O.; Roos, B. O. Theor. Chim. Acta 1995, 90, 87−114. (13) Malmqvist, P.-Å.; B.O. Roos, B. O. Chem. Phys. Lett. 1989, 155, 189. (14) Molcas 7.4. Aquilante, F.; De Vico, L.; Ferré, N.; Ghigo, G.; Malmqvist, P.-Å.; Neogrády, P.; Pedersen, T. B.; Pitonak, M.; Reiher, M.; Roos, B. O.; Serrano-Andrés, L.; Urban, M.; Veryazov, V.; Lindh, R. J. Comput. Chem. 2010, 31, 224. (15) Michl, J. J. Am. Chem. Soc. 1978, 100, 6801−6811, ibid. 6812− 6818. (16) Ceulemans, A.; Oldenhof, W.; Gö r ller-Walrand, C.; Vanquickenborne, L. G. J. Am. Chem. Soc. 1986, 108, 1155−1163. (17) Pichierri, F. Chem. Phys. Lett. 2006, 426, 410−414. (18) Mack, J.; Stillman, M. J.; Kobayashi, N. Coord. Chem. Revs. 2007, 251, 429−453. (19) Keegan, J. D.; Stolzenberg, A. M.; Lu, Y. C.; Linder, R. E.; Barth, G.; Moscowitz, A.; Bunnenberg, E.; Djerassi, C. J. Am. Chem. Soc. 1982, 104, 4317−4329. (20) (a) Peralta, G. A.; Seth, M.; Ziegler, T. Inorg. Chem. 2007, 46, 9111−9125. (b) Lee, K.-M.; Yabana, K.; Bertsch, G. F. J. Chem. Phys. 2011, 134, 144106. (21) Ganyushin, D.; Neese, F. J. Chem. Phys. 2008, 128, 114117. (22) Bolvin, H. ChemPhysChem 2006, 7, 1575−1589. (23) Vancoillie, S.; Malmqvist, P.-Å.; Pierloot, K. ChemPhysChem 2007, 8, 1803−1815. (24) Vancoillie, S.; Pierloot, K. J. Phys. Chem. A 2008, 112, 4011− 4019. (25) Sadoc, A.; Broer, R.; de Graaf, C. Chem. Phys. Lett. 2008, 454, 196−200.

dynamical correlation. Calculations for the relevant magnetic moments are very demanding, as the multiconfigurational CASSCF wave functions heavily depend on the shape of the orbitals. In contrast we have found that a simplified approach based on Kohn−Sham orbitals yields magnetic moments that correctly predict the MCD sign as well as the correct transition dipole moments. In this context, the CASSCF orbitals are deficient, as has been observed before in the calculation of g factors for copper(II) complexes.23 For the 4pysubP complex, the S band has very weak intensity due to a very small splitting of the HOMO and HOMO−1. The LUMO is also almost degenerate as confirmed by the presence of an almost symmetric A term in the B band region. Hence, higher-order corrections to the ring model are expected to be weak, and the sign change of the B band can be attributed only to the larger quenching of the magnetic moment of the excited electron (L2) relative to that of the positive charge left in the occupied MO’s (L1) due to the electron acceptor properties of the aryl substituents. To confirm this result, we carried out a calculation for MOsubP, where no sign change is observed for the A term in the B band region, and which indeed is calculated to present a normal MCD spectrum. It is encouraging to note that the CASCI(KS) method, which shows the best score, is also the one that is closest to the conceptual orbital tools that are being used to understand the complex reality of heteroaromatic macrocycles.

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ASSOCIATED CONTENT

S Supporting Information *

Orbital energies and delocalization of the HF and KS orbitals; configurational composition of the electronic transitions, calculated by CASCI(HF) and CASCI(KS). This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are indebted to the Flemish Fund for Scientific Research (FWO Vlaanderen) and the KU Leuven Research Council (GOA program) and a Grant-in-Aid for Scientific Research on Innovative Areas (No. 20108007, “pi-Space”) from the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT), for continuing financial support.

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REFERENCES

(1) Cheek, J. ; Dawson, J. In The Porphyrin Handbook; Smith, K. M., Guilard, R., Kadish, K. M., Eds.; Academic Press: New York, 2003; Vol. 7, p 339. (2) Torres, T. Angew. Chem., Int. Ed. 2006, 45, 2834−2837. (3) Kobayashi, N.; Ishizaki, T.; Ishii, K.; Konami, H. J. Am. Chem. Soc. 1999, 121, 9096−9110. (4) Stork, J. R.; Brewer, J. J.; Fukuda, T.; Fitzgerald, J. P.; Yee, G. T.; Nazarenko, A. Y.; Kobayashi, N.; Durfee, W. S. Inorg. Chem. 2006, 45, 6148−6151. (5) (a) Kobayashi, N.; Takeuchi, Y.; Matsuda, A. Angew. Chem. Int. Ed. 2007, 46, 758−760. (b) Takeuchi, Y.; Matsuda, A.; Kobayashi, N. 3967


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