Magnetically Induced Ring Currents from DFT-GIMIC Calculations

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The Antiaromatic Character Of 16#-electron Octaethylporphyrins: Magnetically Induced Ring Currents From DFT-GIMIC Calculations Heike Fliegl, Fabio Pichierri, and Dage Sundholm J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp5067549 • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 22, 2014

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The Journal of Physical Chemistry

The Antiaromatic Character Of 16π-electron Octaethylporphyrins: Magnetically Induced Ring Currents From DFT-GIMIC Calculations Heike Fliegl,∗,† Fabio Pichierri,∗,‡ and Dage Sundholm∗,¶ Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O.Box 1033 Blindern, 0315 Oslo, Norway, Department of Applied Chemistry, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-07, Sendai, 980-8579 Japan , and University of Helsinki, Department of Chemistry, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland. E-mail: [email protected]; [email protected]; [email protected] Phone: +358 (2)941 50176 . Fax: +358 (2)941 50279

∗

To whom correspondence should be addressed Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O.Box 1033 Blindern, 0315 Oslo, Norway ‡ Department of Applied Chemistry, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-07, Sendai, 980-8579 Japan ¶ University of Helsinki, Department of Chemistry, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 University of Helsinki, Finland. †

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Abstract The magnetically induced current-density susceptibility also called current density has been calculated for a recently synthesized octaethyl porphyrin (OEP) zinc(II) dication with formally 16π electrons. Numerical integration of the current density passing selected chemical bonds yields the current pathway around the porphyrinoid ring and the strength of the ring current. The current strengths show that the OEP-Zn(II) dication is strongly antiaromatic as also concluded experimentally. The calculation of the ring-current pathway shows that all 24 π electrons participate in the transport of the ring current, since the current splits into inner and outer branches of practically equal strengths at the four pyrrolic rings. The corresponding neutral octaethyl porphyrinoid without Zn and inner hydrogens is found to be antiaromatic sustaining a paratropic ring current along the inner pathway with 16 π electrons. The neutral OEP-Zn(II) molecule with formally 18 π electrons is found to be almost as aromatic as free-base porphyrin. However, also in this case all 26 π electrons contribute to the ring current as for free-base porphyrin. A comparison of calculated and measured 1 H NMR chemical shifts is presented. The current strength susceptibility under experimental conditions has been estimated by assuming a linear relation between experimental shielding constants and calculated current strengths.

Keywords Magnetically induced current densities, London orbitals, aromaticity, nuclear magnetic resonance shieldings, porphyrinoids

1

Introduction

Synthetic porphyrin chemistry is a very active research field because the electronic properties of the connected conjugated rings can be adjusted to yield porphyrinoids that may


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be employed in technological applications. 1–4 A variety of modifications of the basic freebase porphyrin macroring have been devised to obtain desired molecular properties that can be fine-tuned by introducing substituents, forming porphyrin metal complexes, replacing pyrrole rings with other aromatic rings, expanding the porphyrin macrocycle by increasing the number of pyrrole rings, replacing the methine bridge with longer bridging units, compressing the porphyrin by removing methine bridges, etc. The electronic properties of the porphyrinoid macrocycle are to large extent determined by the number of π electrons participating in the conjugation network. 5–8 Experimental and computational studies have shown that the aromatic properties of porphyrinoids follow almost exceptionlessly the generalized H¨ uckel’s rule for aromaticity, 9–22 whereas the dominating conjugation pathway sustaining the magnetically induced ring-current can be reliably obtained only by performing explicit calculations of the current densities. 23–29 Recently, Hiramatsu et al. 30 synthesized a octaethyl porphyrin (OEP) zinc(II) dication without meso substituents that has formally 16π electrons by oxidizing the corresponding 18π porphyrin Zn(II) complex with AgSbF6 and I2 , see Figure 1. Measurements of the 1 H NMR and UV-Vis spectra as well as calculations of nucleus independent chemical shifts (NICS) suggested that the OEP-Zn(II) dication is antiaromatic, which is also expected when assuming that H¨ uckel’s rule for aromaticity holds. The detected a large blue shift of the UV-Vis spectrum and the missing Q band generally indicate that the porphyrinoid is antiaromatic. 31–35 For meso-unsubstituted porphyrinoids, the degree of aromaticity can also be estimated from the position of the 1 H NMR signal of the meso hydrogens. 30 Judging from those experimental data, Hiramatsu et al. claimed that the OEP-Zn(II) dication is the strongest antiaromatic porphyrin that has been reported so far. They also proposed that the reason for the extraordinary strong paratropicity of the porphyrinoid with formally 16π electrons is the absence of the meso substituents allowing a planar structure of the porphyrin macroring.

Yamamoto et al. have reported a nonplanar 16 π Zn porphyrinoid with eight

isobutyl groups at the β carbons and four phenyl groups in the meso positions in addition to



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an axial Cl ligand coordinated to the metal center. 36 However, the porphyrin ring of axially coordinated 18 π OEP-Zn(II) molecules lacking meso substituents is found to be practically planar. 37 In this work, we computationally study the magnetically induced current density for OEP and OEP-Zn(II) species with 16π and 18π electrons, with the aim to determine the degree of antiaromaticity according to the magnetic criterion as well as the conjugation pathway of the ring-current flow. The article is organized as follows. In Section 2, we present the employed computational methods. The molecular structures of the studied molecules including the nomenclature are described in Section 3. The calculated magnetically induced current densities, current strengths, and current pathways are discussed in Section 4. Calculated and measured 1 H NMR chemical shifts are compared in Section 5. In Section 6, we summarize the obtained results and present our conclusions.

2

Computational methods

The molecular structures were optimized at the density functional theory (DFT) level using Becke’s three-parameter functional (B3LYP) 38,39 as implemented in Turbomole version 6.5. 40 The Karlsruhe triple-ζ quality basis sets augmented with polarization functions (def2TZVP) 41 were employed in the calculations. The initial structures of the different possible conformers were preoptimized with Gaussian 09 at the B3LYP level using double-ζ polarization quality (DGDZVP) basis sets. 42–44 The nuclear magnetic shieldings were calculated at the B3LYP level using split-valence polarization (def2-SVP) basis sets as well as at the B3LYP/def2-TZVP level using the Mpshift module of Turbomole. 45,46 The NMR chemical shifts were obtained from the calculated magnetic shielding constants by using the tetramethylsilane (TMS) value of 31.93 ppm as reference, which has been obtained at the same level of theory. 47 The magnetically induced current densities were calculated at the B3LYP/def2-SVP level


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using the gimic method. 48–50 Since the use of gauge including atomic orbitals (GIAO) leads to a fast basis set convergence of the current densities, the def2-SVP basis set is found to be sufficient for calculating the current densities. gimic is an independent program that uses the atomic orbital density matrix as well as the corresponding first-order magnetically perturbed density matrices from the nuclear magnetic shielding calculations and basis-set information as input data. 48,49 Ring-current strengths and current pathways were determined by numerical integration of the current-density susceptibility (in nA/T) passing through cut planes perpendicularly to selected bonds of the investigated octaethyl porphyrins. The current-density susceptibility is for simplicity also called current density. The molecular pictures of the current pathways were obtained with jmol 51 and gimp. 52

3

Molecular structures and nomenclature

Each pyrrole ring has two ethyl groups in the β positions. Each of them can be oriented either upwards (u) or downwards (d) with respect to the porphyrin plane. The X-ray structure showed that the ethyl conformation of the neutral OEP-Zn(II) complex is uu-ud-dd-du (c1). 37 We calculated the relative energies of the uu-uu-uu-uu (2c), dd-uu-dd-uu (3c), and du-dudu-du (4c) conformers with respect to 1c. Conformer 2c has all its ethyl groups oriented upwards (or downwards), whereas 3c has every second pair of ethyl groups alternatingly oriented downwards and upwards. For 4c, the ethyl groups of each pair on the pyrrole ring are oriented in opposite directions. Thus, the relative energy of the conformers is 4c < 1c < 3c < 2c. Structure optimizations at the B3LYP/DGDZVP level showed that 4c is the most stable conformer, whereas 2c is highest in energy lying 0.42 kcal/mol above 4c. Conformer 1c, which is found in the molecular crystal, is 0.29 kcal/mol above 4c. Conformer 3c lies 0.36 kcal/mol above 4c. Thus, the energy differences between the conformers are very small implying that small perturbations such as packing effects in the crystal or the employed computational



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level might shift the energetic order of the conformers. The final molecular structures were optimized at the B3LYP/def2-TZVP level with the preoptimized 4c conformer as initial structure. The obtained structures were employed in the calculations of the NMR chemical shieldings and current-density susceptibilities, which were calculated for the neutral OEP-Zn(II) complex, the OEP-Zn(II) dication, the neutral metal-free octaethyl porphyrinoid, and the metal-free OEP dianion. The neutral OEP-Zn(II) complex and the metal-free OEP dianion have formally 18π electrons, whereas the OEPZn(II) dication and the neutral metal-free octaethyl porphyrinoid without inner hydrogens have formally 16π electrons. Calculations were also performed on the OEP-Zn(II) dication with phenyl substituents in the meso positions to assess how the meso substituents influence the molecular structure and the current strengths. The porphyrin ring of phenyl-substituted OEP-Zn(II)2+ is almost planar with deviations of less than 12 degrees in the dihedral angles of the porphyrin ring. The Cartesian coordinates of the optimized molecular structures are given in the Supporting Information.

4

Current-density calculations

The calculated current pathways and current strengths for the octaethyl porphyrinoids are shown in Figure 2. The main current pathways are indicated with the pink lines. The integrated current strengths passing selected bonds are also given in the figure. Figure 2a shows that the neutral OEP-Zn(II) complex with formally 18π electrons is aromatic sustaining a ring current of 25.2 nA/T around the porphyrin macroring, which is of the same size as the ring-current strength of 27.2 nA/T that has previously been obtained for free-base porphyrin. 19 Thus, the 18π OEP-Zn(II) complex is almost as aromatic as free-base porphyrin. At the pyrrole rings, the current is rather evenly split into a current of 11.9 nA/T along the inner route and 13.3 nA/T passes the β carbons.


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Current density calculations show that the OEP-Zn(II) dication sustain a very strong paratropic ring-current of -51.7 nA/T around the porphyrin macroring. Figure 2b shows that the ring current flow of the OEP-Zn(II) dication splits at the pyrrolic rings into an inner and outer route the current strengths of which are -29.1 nA/T and -21.1 nA/T, respectively. Thus, the current is rather evenly split into the two branches. The current strength along the inner route is 8 nA/T stronger than for the one via the β carbons. The calculated ring-current strength shows that the OEP-Zn(II) dication is strongly antiaromatic as also suggested by Hiramatsu et al. 30 For both neutral OEP-Zn(II) and the corresponding dication, almost no ring current passes through the metal-nitrogen bond, which is expected because radial currents are classically forbidden. The fact that the current flow splits into two almost equally strong branches at the pyrrolic rings shows that all 24 π electrons of the dication participate in the current transport, whereas for the neutral complex, 26 π electrons sustain the ring current. Previous studies on free-base porphyrin and Mg porphyrin showed that there is almost no difference in the current pathways. 53 The same trend is expected to hold for Zn porphyrins. The calculated ring-current pathways show that the proposed 16π-electron pathway for the OEP-Zn(II) dication is not correct. For the neutral OEP-Zn(II) complex, the current does not flow along the classical 18π-electron pathway either as one has traditionally believed and which is still proposed. 29 The role of the Zn(II) dication at the center of the porphyrin is also investigated. The two zinc-free species shown in Figures 2c and 2d are obtained by removing Zn2+ from the OEP-Zn(II) dication and the neutral complex, respectively. The ring-current strength of the neutral metal-free porphyrinoid is -26.5 nA/T indicating that it is also antiaromatic as the parent OEP-Zn(II) dication. Its ring current strength is though only half the current strength of the dication. The current pathway shown in Figure 2c shows that the paratropic ring current of the metal-free porphyrinoid flows along the inner route at the pyrrolic rings. Thus, in this case only 16 π electrons sustain the ring current around the porphyrin macroring.



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The OEP dianion is on the other hand aromatic sustaining a ring current of 21.1 nA/T. As seen in Figure 2d, all 26 π electrons of the dianion participate in the current transport, since the current strength along the inner route is 13.6 nA/T and 8.2 nA/T flows via the β carbons. The current pattern of the anion is reminiscent of the average current pathway at the pyrrolic rings with and without inner hydrogens for free-base porphyrin. 19 However, the total current strength is 6 nA/T weaker in the anion than for free-base porphyrin. Substitution of phenyl groups to the meso carbon atom did not significantly change the current pathway around the porphyrinoid macroring for the OEP-Zn(II) dication, see Figure 3. Phenyl-substituted OEP-Zn(II)2+ is also antiaromatic according to the magnetic criterion. The total net current strength of -44.6 nA/T is 13% weaker than for the unsubstituted porphyrinoid. Mulliken population analysis indicates that the perpendicular phenyl groups pull electrons from the porphyrin macroring due to the mesomeric effect (-M) resulting in a somewhat weaker antiaromaticity. The phenyl-substituted OEP-Zn(II) dication is also a very antiaromatic molecule. However, the experimental detection of the degree of antiaromaticity is more problematic for phenyl-substituted porphyrins than for the corresponding molecules with hydrogens at the meso carbons, because of the lacking hydrogens at the meso carbons as 1 H NMR probes. Since the ring currents of the aromatic phenyl rings also shift the 1 H NMR signals of the hydrogens of the neighboring ethyl groups, the degree of aromaticity of the porphyrin ring might be difficult to assess from 1 H NMR chemical shifts.

5

1

H NMR chemical shifts

The calculated 1 H NMR chemical shifts of the meso hydrogens are compared to experimental values in Table 1. The calculated nuclear magnetic shieldings of all atoms are reported in the Supporting Information. The calculated and measured 1 H NMR chemical shifts for neutral OEP-Zn(II) agree well with a discrepancy of only 0.55 ppm. The rather small difference between calculated and measured 1 H NMR chemical shifts is due to vibrational effects,


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environmental effects and the employed computational level. For the OEP-Zn(II)2+ complex, the deviation of 4.55 ppm between the calculated and measured values of -1.00 ppm and 3.55 ppm,respectively, is much larger. Thus, the comparison of calculated and measured 1 H NMR chemical shifts for the hydrogens at the meso carbons indicates that the calculated ring-current strength is larger than the experimental one. Solvent and counterion effects are omitted in the calculations. The environmental effects might be larger for the dication than for neutral porphyrins, because of the strong Coulomb interactions between the charged species in the solution. The surrounding solvent molecules and counterions most likely decrease the paratropic ring current as the electron-deficient dication is stabilized by accepting a partial charge from them. However, when neglecting environmental and vibrational effects and assigning the difference between calculated and measured 1 H NMR chemical shifts to induced ring currents, the ring-current strength of the porphyrin under experimental conditions can be estimated. Linear interpolation of the calculated ring-current strengths and 1 H NMR chemical shifts in combination with the measured 1

H NMR chemical shifts yield ring-current strengths of 21.6 nA/T for neutral OEP-Zn(II)

and -21.7 nA/T for the dication. The 1 H NMR chemical shifts of the hydrogens at the meso carbons and the ring current strengths are compared in Table 1. The ring currents of the porphyrinoids also affect the proton shifts of the ethyl groups. The calculations show that the average 1 H NMR chemical shifts of the two hydrogens at the carbons connected to the β carbon of the pyrrolic rings are shifted by -4.66 ppm when oxidizing OEP-Zn(II) to OEP-Zn(II)2+ . The methyl hydrogens of the ethyl groups are more distant from the ring current leading to an average ring-current shift of -2.13 ppm. Experimentally the average shift of the 1 H NMR signals of the ethyl groups due to oxidation are -2.67 ppm and -1.31 ppm. By comparing the calculated and measured 1 H NMR chemical shifts of the hydrogens of the ethyl groups, the ring-current strength under experimental conditions can be estimated. An analogous interpolation procedure as used for the hydrogens at the meso positions suggests that the ring-current strength of OEP-Zn(II) is 18.0-19.1



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nA/T. For the OEP-Zn(II)2+ dication, ring-current strengths of -25.1 nA/T and -29.1 nA/T were estimated from the ethyl hydrogens using the same procedure. The calculated and measured 1 H NMR chemical shifts of the ethyl groups as well as calculated and estimated ring-current strengths are given in Table 2. The uncertainty in the ring-current strength estimated from the ethyl hydrogens is larger than the ones estimated from the hydrogens at the meso carbons, because the ring-current shift is smaller for the ethyl hydrogens than for the hydrogens at the meso carbons. The peripheral hydrogens of the ethyl groups can also be expected to be more exposed to the environment than the hydrogens at the meso carbons. Anyway, one can conclude that the OEP-Zn(II)2+ dication is strongly antiaromatic sustaining a paratropic ring current of about -22 nA/T under the experimental conditions.

6

Summary and conclusions

The magnetically induced current-density susceptibility (current density) has been calculated for a recently synthesized octaethyl porphyrin (OEP) zinc(II) dication with formally 16π. The recent experimental study suggested that the OEP-Zn(II) dication is strongly antiaromatic. 30 In this work, integrations of the current density passing selected bonds show how the ring current flow around the porphyrin macroring. The isolated OEP-Zn(II) dication is found to be very antiaromatic sustaining a paratropic ring current of -51.7 nA/T. Calculated ring-current strengths and the comparison of calculated and measured 1 H NMR chemical shifts indicate that the molecular environment such as the effect of the counter anions and solvent molecules make the molecule less antiaromatic under experimental conditions. However, the computational study confirm that the OEP-Zn(II) dication dissolved in CD2 Cl2 is indeed antiaromatic sustaining a paratropic ring current of about -22 nA/T. The calculations also show that all 24 π electrons participate in the aromatic pathway, because the strengths of the currents via the inner and outer routes at the pyrrolic rings are almost equal. Calculations on the neutral octaethyl porphyrinoid showed that it is also antiaromatic


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sustaining a paratropic ring current. However, its paratropic ring current is weaker and flows mainly along the inner 16 π route. Calculations on the neutral OEP-Zn(II) complex and the OEP dianion yielded diatropic ring currents showing that the porphyrinoids with formally 18 π electrons are aromatic. Since the ring current takes both the inner and outer routes at the pyrrolic rings, all 26 π electrons contribute to the ring current around the porphyrin macroring. We recently performed a similar study on antiaromatic core-modified isophlorins that were synthesized by Reddy and Anand in 2008. 10,22 The same kind of interpolation procedure as used here to estimate the degree of antiaromaticity under experimental conditions yielded paratropic ring-current strengths of -24.8 nA/T and -30.5 nA/T for the thiophene-furan and furan based isophlorins, respectively. Thus, the strength of the paratropic ring current of the core-modified isophlorins are slightly larger than what we obtained for the OEP-Zn(II) dication dissolved in CD2 Cl2 in this work. The OEP-Zn(II)2+ dication might be the most antiaromatic porphyrin. However, when porphyrinoids like the isophlorins are considered to belong to the class of porphyrins, they seem to be somewhat more antiaromatic than OEP-Zn(II)2+ , since the isophlorins sustain a larger paratropic ring current according to our calculations.

Acknowledgement This research has been supported by the Academy of Finland through its Computational Science Research Programme (LASTU). We thank Magnus Ehrnrooth foundation for financial support. CSC – the Finnish IT Center for Science – is acknowledged for computer time. H. F. thanks for support by the Norwegian Research Council through the CoE Centre for Theoretical and Computational Chemistry (Grant No. 179568/V30). This work has received support from the Norwegian Supercomputing Program (NOTUR) through a grant of computer time (Grant No. NN4654K). F.P. thanks the Department of Applied Chemistry of the Graduate School of Engineering (Tohoku University) for financial support 11 ACS Paragon Plus Environment


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Supporting Information Available Cartesian coordinates and nuclear magnetic shieldings of the studied molecules. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Figure 1: Octaethyl Zn(II) porphyrin (Zn(II)OEP) and the Zn(II)OEP2+ dication.



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(a)

(b)

(c)

(d)

Figure 2: Calculated current pathways (pink) and current strengths for selected bonds of (a) neutral octaethyl porphyrin zinc(II) (OEP-Zn(II)), (b) the OEP-Zn(II) dication, (c) the neutral metal-free octaethyl porphyrinoid, and (d) the metal-free OEP dianion.


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Figure 3: Calculated current strengths for selected bonds of the OEP-Zn(II) dication with phenyl substituents at the meso carbon atoms.



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Table 1: Calculated chemical shifts (δ in ppm) for the meso hydrogens as compared to experimental data. The difference in the chemical shifts (∆δ in ppm) between the oxidized and reduced forms are also given. The calculated and estimated experimental ring-current strengths (I in nA/T) are also given. Molecule OEP-Zn(II) OEP-Zn(II)2+ OEP2− OEP

1

Calculated H NMR I 10.66 25.2 -1.00 -51.7 9.24 21.3 3.07 -25.2

∆δ – -11.66 – -6.17

1

Experimental H NMR Ia ∆δ(Exp.) 10.11 21.6 – 3.55 -21.7 -6.56 – – – – – –

a

Estimated from calculated ring-current strengths and calculated and measured 1 H NMR chemical shifts for the meso hydrogens. Table 2: The average of the calculated chemical shifts (δ in ppm) for the hydrogens of the ethyl groups of the OEP-Zn(II) molecules as compared to experimental data. The difference in the chemical shifts (∆δ in ppm) between the oxidized and reduced forms are also given. The calculated and estimated experimental ring-current strengths I are given in nA/T. Calculated Experimental 1 1 Molecule H NMR I ∆δ H NMR Ia ∆δ(Exp.) OEP-Zn(II) ethyl 4.34 25.2 – 3.97 19.1 – 2+ OEP-Zn(II) ethyl -0.32 -51.7 -4.66 1.30 -25.0 -2.67 OEP-Zn(II) phenyl 1.98 25.2 – 1.78 18.0 – 2+ OEP-Zn(II) phenyl -0.16 -51.7 -2.13 0.47 -29.1 -1.31 a 1 Estimated from calculated ring-current strengths and calculated and measured H NMR chemical shifts for the corresponding hydrogen of the ethyl group.


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Graphical TOC Entry

Investigation of the change in aromaticity of octaethyl Zn(II) porphyrin upon oxidation.


Magnetically Induced Ring Currents from DFT-GIMIC Calculations

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