Aromaticity of HÃ¼ckel and MÃ¶bius Topologies involved in

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Aromaticity of Hückel and Möbius Topologies involved in Conformation Conversion of Macrocyclic [32]Octaphyrin(1.0.1.0.1.0.1.0): Refined Evidences from Multiple Visual Criteria Zeyu Liu, Tian Lu, Shugui Hua, and Yi Yu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b06302 • Publication Date (Web): 10 Jul 2019 Downloaded from pubs.acs.org on July 18, 2019

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The Journal of Physical Chemistry

Aromaticity of Hückel and Möbius Topologies involved in Conformation Conversion of Macrocyclic [32]Octaphyrin(1.0.1.0.1.0.1.0): Refined Evidences from Multiple Visual Criteria Zeyu Liu,† Tian Lu,‡ Shugui Hua,§ and Yi Yu† †College

of Biotechnology, Jiangsu University of Science and Technology, Zhenjiang 212018, People’s Republic of China

‡Beijing

Kein Research Center for Natural Sciences, Beijing 100022, People’s Republic of China

§College

of Life Science and Chemistry, Jiangsu Key Laboratory of Biological Functional

Molecules, Jiangsu Second Normal University, Nanjing 210013, People’s Republic of China

 Corresponding

author. Tel: +86 511 85638328. E-mail: [email protected]. 1

ACS Paragon Plus Environment

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Abstract A comprehensive investigation of the aromaticity control process of expanded porphyrins was carried out using a variety of visual criteria for the first time. The results show that the indicators based on magnetic property can be used to inspect the global aromaticity of [32]octaphyrins(1.0.1.0.1.0.1.0), while the methods according to electronic (de)localization are more suitable for assessment of the local aromaticity. The quasi-planar Hückel molecules with 32 π-electrons are shown to be distinctly antiaromatic, which follows the conventional 4n antiaromaticity Hückel's rule. The distortion of molecular skeleton leads to weakening of π-conjugation in macrocycles, making the single-sided Möbius topologies with the same number of π-electron exhibit weak aromaticity. The seriously twisted figure-eight Hückel species are proved to be almost nonaromatic. These results agree well with our previous conclusions on aromaticity characteristic of the same system deduced from some numerical indexes. It is suggested necessary to extract evidence from multiple visual indicators for systematical analysis of the molecular aromaticity.

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Introduction Since Kekulé put forward the concept of aromaticity in 1865 and applied the term to the benzene derivatives,1 the related researches have been one of the hotspots in the field of chemistry.2-11 In fact, the definition of aromaticity is in a certain extent ambiguous because it is not quantum observable and accordingly needs to be described by convention. The molecular aromaticity can be defined as a manifestation of electron delocalization in closed circuits, either in two- or in three-dimensional systems. Besides that, aromaticity is also thought to be related to other physicochemical properties of a molecule, such like bond-length equalization, structure stability, unusual reactivity, induced ring current, and also spectroscopic feature. Is precisely because of this, there are many descriptors to quantify the molecular aromaticity, which can be classified into five main categories: structural, energetic, reactivity-based, magnetic, and electronic.12,13 For a large number of recognized aromatic systems, statistical analysis results show that they do usually exhibit some manifestations of its characters mentioned above at the same time. However, the descriptors of the aromaticity are not necessarily fully correlated for certain individual compound and different metrics give rise to the conflicting conclusions in some cases, which is called multidimensional character of aromaticity.12 Therefore, it was suggested to employ a set of descriptors based on different properties to characterize the aromaticity of compounds. When using a variety 3



of indicators to jugde the aromaticity characteristics, relevant conclusions are much reliable, especially if all criteria provide the same trend. Expanded porphyrins have a very flexible molecular skeleton, which enables them to switch between different π-conjugated topologies (known as Hükel, Möbius, and twisted-Hükel) with diverse electronic properties. The ability to be modulated between various conformers of expanded porphyrins in a controllable manner has open the door for the development of novel molecular switches, which can be applied as conductance switching elements,14 nonlinear optical (NLO) switches,10,15 reversible bithermoelectric switches,16 and so on. In 2013, Kido and co-workers first succeeded in synthesizing the bis-palladium [32]octaphyrin(1.0.1.0.1.0.1.0).17 They confirmed that the complex adopts figure-eight structure with weak antiaromaticity by spectroscopic analyses and density functional theory (DFT) calculations. Our previous theoretical prediction about the aromaticity of this compound is basically in agreement with their assertion.18 Moreover, using freebased [32]octaphyrin(1.0.1.0.1.0.1.0) with multiple conformers involving Hückel and Möbius topologies,19 we have demonstrated that the conclusions from some numerical indexes of aromaticity, such as Julg parameter (Julg A)20, harmonic oscillator model for aromaticity (HOMA)21, magnetic susceptibility exaltations (Λ)22, and nucleusindependent chemical shift (NICS)23, are perfectly matched with each other. In reality however, owing to the rich conformational diversity and extensive πelectron delocalization in expanded porphyrins, the determination of aromaticity in them is more challenging. In recent years, a number of descriptors for quantifying 4


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Hückel and Möbius aromaticity in expanded porphyrins have been proposed continuously, as many as dozens of species now exist.20-39 However, it must be noted that for commonly used quantitative indicator, there is no received threshold to determine exactly whether the molecules are aromatic or not. This will make it arbitrary to apply them in judgment of the aromaticity behavior of a system. By contrast, the advantage of visual criteria over numerical ones is that they can provide very intuitive images to facilitate our understanding of the essential characteristics of molecular aromaticity. So in this paper, research work on the aromaticity feature of macrocyclic [32]octaphyrins(1.0.1.0.1.0.1.0) based on several visual criteria, including isochemical shielding surfaces (ICSS)30, anisotropy of the induced current density (AICD)31, electron localization function (ELF)32, and localized orbital locator (LOL)33, were made.

2. Calculation details Several benchmark studies have indicated that the selection of suitable theoretical levels for describing the topologies, relative energies, and aromatic properties of expanded porphyrins is a complex task.38,40,41 It has been reported that M06-2X functional42 is an appropriate choice to implement reliable theoretical calculations of the topology of expanded porphyrins.41 Considering the compromise between calculation accuracy and time consumed, we make the following selections about the calculation levels of molecular geometries, energies, and related properties in this work. Full geometry optimization for each stationary point was carried out with the M062X hybrid density functional and the 6-311G(d) basis set.43 Vibrational frequency analyses were conducted at the same level on all optimized structures to examine the 5



nature of them. A single point calculation at M06-2X/Def2-TZVP44 was performed and the relative energy of the stationary point was obtained by summation of this single point energy and the thermal correction to Gibbs free energy from the vibrational frequency analysis. ECD spectra for enantiomers were simulated with the timedependent DFT (TD-DFT)45,46 method by using the CAM-B3LYP functional47 at the 6-311G(d) level. The spatial magnetic property known as visual ICSS employing the NICS concept was calculated at the B3LYP/6-31G(d)48 level of theory with the gaugeinvariant atomic orbital (GIAO) approach.49 The continuous set of gauge transformation (CSGT) method50 was applied at the B3LYP/6-311+G(d)43,51-53 level to study the AICD plot in the procedure with the same name. Magnetically induced current density was calculated using the gauge including magnetically induce current (GIMIC) method54 at the same level. Because of the nonplanarity of the macrocyclic molecules studied, it is obviously impossible to determine their planes uniquely. The molecular plane defined in this work is the paper plane corresponding to the standard orientation given in the output files of Gaussian program. For the rules of specific molecular standard orientation, please refer to the Gaussian 16 User's Reference. In fact, we can roughly think it as an approximate plane with the maximum visual angle of the cavity of macrocyclic molecule. We believe that such a definition of the molecular plane is acceptable in this work. A magnetic field is applied orthogonally to the molecular plane with its vector points out of the page, which orientation is coincide with that of the z-axis, in ICSS and AICD analyses. 6


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All calculations were performed with Gaussian 16 program package.55 Electronic wavefunctions were extracted from geometry optimizations to conduct ELF and LOL analyses by means of code Multiwfn 3.5.56,57 The visualization of the isosurfaces for various functions has been realized in VMD software.58 3. Results and Discussion A simple and convenient parameter, called the torsional π-conjugation index (Π), has been employed to characterize properly the different topologies (Table 1, where 1–6 represent the six conformational isomers on the potential energy surface (PES) in turn, and superscripts "H" and "M" denote that the corresponding conformers take Hückel and Möbius topologies, respectively).59 The calculated Π values are positive for 1H, 3H, 4H, and 6H, which reflect that these four isomers present Hückel topology. The 2M and 5M display negative values of Π, revealing that they are definitely Möbius conformers. As an inspection of the macrocyclic geometries further reveals, molecules 1H and 6H are common two-sided systems with quasi-planar structure. 2M and 5M show a single-sided topology with an explicit phase change within their p-orbitals, while 3H and 4H are severely twisted figure-eight species (see Table S1 for Cartesian coordinates of stationary points). It is generally believed that the absolute value of the Π index can be regarded as a rough descriptor of the extent of π-conjugation. One can find that the Π values of the macrocyclic molecules follow the order: 1H/6H > 2M/5M > 3H/4H, which reflects the intensity of their electron delocalization characteristics and hence the strength of the (anti)aromaticity.

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Table 1. Torsion angle between the pyrrolic subunits (ij, i, j = A–H)a and calculated torsional

π-conjugation

index

(Π)b

for

stationary

points

of

[32]octaphyrin(1.0.1.0.1.0.1.0)

AB BC CD DE EF FG GH HA Πa aSubscript bTorsional

1H 2M 3H 4H 5M 11.38 36.95 43.98 23.95 28.22 4.06 23.66 24.28 17.08 23.43 1.56 26.01 28.82 21.06 16.42 14.14 36.2 51.71 43.12 24.23 11.38 14.71 148.63 156.05 18.46 4.07 14.17 9.95 17.08 17.56 1.56 28.83 27.00 21.06 25.26 14.14 157.01 162.55 136.88 135.91 0.90 -0.40 0.25 0.35 -0.42

6H 11.38 4.06 1.56 14.14 11.38 4.07 1.56 14.14 0.90

"A–H" represent pyrrolic subunits in [32]octaphyrins(1.0.1.0.1.0.1.0); π-conjugation index for stationary points,    cos ij (i, j  A- H) . i, j

3.1 Isomerization reactions Conformational isomerizations and consequent changes in properties have been observed by some groups from several types of expanded porphyrin in theoretical and experimental areas.14,15,60-62 Similarly, the free-based [32]octaphyrin(1.0.1.0.1.0.1.0) can also go through facile multistep isomerization involving Hückel and Möbius topologies at the M06-2X/6-311G(d) level (Scheme 1). The order of relative energy of the stationary points under the current calculation level is identical with that obtained by B3LYP functional.19 The transformation from 1H to 2M is a rate-limiting step for the isomerization with a barrier height of 28.41 kcal/mol. Note that the third isomer, named as 3H in this paper, exhibits an unambiguous Hückel configuration, rather than a Möbius topology as 8


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previously reported.19 In addition, the terminal of the isomerization reaction is not 5M, but an enantiomer of the initial 1H, namely 6H. The chirality of 1H and 6H has been confirmed by the electronic circular dichroism (ECD) spectroscopies, where the mirrorimage spectra for them were observed (Figure S1). The chiral inversion can also occur through one-step direct reaction with an activation energy of only 1.96 kcal/mol. Neglectable barrier indicates that the enantiomers may transform each other mutually in normal conditions.

Scheme 1. Potential energy diagram along the isomerization pathway of [32]octaphyrin(1.0.1.0.1.0.1.0).

3.2 Molecular aromaticity New descriptors for assessing aromaticity of organic molecule have been proposed unceasingly in recent years. In this work, we employed four visual criteria to systematically examine the aromaticity of the stable structures involved in the 9



isomerization of [32]octaphyrin(1.0.1.0.1.0.1.0). 3.2.1 Aromaticity criteria based on magnetic property: ICSS and AICD A ring current is expected to be induced by an external magnetic field in the macrocycle containing extensive π-electronic conjugation, and the aromaticity of the molecule can therefore be effectively reflected by investigating the information of it. Here, the zz component of ICSS (ICSSzz) and the AICD plot with π feature (AICD-π) based on the response behavior of the molecules to external magnetic field are discussed. Due to its excellent performance in describing the location and strength of molecular (de)shielding areas in external field, ICSS contour has been utilized as a powerful method to inspect the aromaticity characteristic for a large number of compounds.30,63-65 It can be seen that a bulk of red ICSSzz contour protrudes in the direction perpendicular to the molecular plane of 1H and 6H and a closed blue circular isosurface surrounded it (Figure 1). These images show that the inner part of 1H and 6H are deshielding domains, while shielding areas are located around the molecules. 1H and 6H are thus considered to be typical antiaromatic compounds, which is consistent with their electronic structure characteristics of Hückel topology with 4n π-electrons. The ICSSzz plots of 2M and 5M present roughly opposite feature to those of 1H and 6H. Concretely, there is a red deshielding annulus surrounding the blue shielding region inside the molecules, which show that they are aromatic species. Nevertheless, it seems that the extent of the aromaticitiy of 2M and 5M is less than that of the antiaromaticity of 1H and 6H due to the obvious contraction and split deshielding isosurface in the former two. This can be rationalized by considering that the distorted Möbius structure 10


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destroys the conjugation of the macrocyclic molecule in some degree. Doping and penetrating each other of shielding and deshielding regions can be readily found in the ICSSzz contours of 3H and 4H, which illustrates the nonaromatic properties of these two conformations. The absence of (anti)aromatic features in them may originate from the serious destruction of the effective π-electronic conjugation by their highly skeleton distortion. It is noteworthy that some ICSSzz plots of transition states (TSs) have similar characteristics to those of their adjacent intermediates - TS1/2 vs 2M, TS5/6 vs 5M, and TS1/6 vs 1M/6M, for example (cf. Figures 1 and S2). However, the rest of the TSs do not show much similarity to their associated equilibrium structures in terms of the ICSSzz contour. This illustrates that some properties of TS in the reaction process are difficult to understand because of its complex electronic structure.

Figure

1.

ICSSzz

plots

for

stable

conformations

of

macrocyclic

[32]octaphyrin(1.0.1.0.1.0.1.0). Shielding surfaces at 0.5 ppm are in blue, and deshielding surfaces at 0.5 ppm are in red.

11



AICD is another widely accepted visual function based on magnetic property to investigate the molecular aromaticity, which can describe the density and direction of the induced ring current in a molecule under an external magnetic field.35,66-68 Strong paratropic current density vectors can be clearly observed in 1H and 6H (Figure 2). The violation of the left-handed rule fully demonstrates that the magnetically induced current generated by π-electrons will significantly strengthen the external field in the inner region of macrocycles. Hence, it can be confirmed that these molecules show a considerable antiaromaticity. The current pathways in 1H and 6H determined by AICD analyses are dominated by the flow along the route through the C-N(H)-C moieties, as the studies on heteroannulenic antiaromatic porphyrinoids have shown.35 The same conclusion has been obtained by employing the magnetically induced current density of 1H using the gauge including magnetically induce current (GIMIC) method (Figure S4). Though 2M and 5M do not sustain an obvious global ring current under the action of an external magnetic field, the induced current density vector almost formed a diatropic circulation in individual pyrrolic subunits. The fact implies there is a local aromaticity in some moieties of them, which leads to a weak global aromaticity of the molecules. No obvious magnetically induced currents were observed in conformers 3H and 4H, even if they are localized, implying they might be neither aromatic nor antiaromatic.

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Figure

2.

AICD-π

plots

for

stable

conformations

of

macrocyclic

[32]octaphyrin(1.0.1.0.1.0.1.0). Isovalues for AICD-π surfaces are 0.07 au. The large red and blue arrows denote the vectors of paratropic and diatropic current density, respectively.

The above discussions on aromaticity reveal that a very accordant conclusion can be drawn from ICSSzz and AICD-π analyses of the studied system. Their reliabilities is supported by our previous results deduced from some quantitative indexes19 and the above mentioned torsional π-conjugation index (Π). 3.2.2 Aromaticity criteria based on electronic (de)localization: ELF and LOL Generally speaking, the characteristics of intramolecular induced ring current are directly related to the extent of electron delocalization. ELF and LOL are popular realspace functions served to measure the degree of electron delocalization in molecule at different locations in three-dimensional space. Their solution processes are simple, and whats more, they are convenient for graphic analysis. Therefore, ELF and LOL have become important tools in the field of quantum chemistry to study the characteristics 13



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of electronic structure and been widely used in the research of various properties including molecular aromaticity.69,70 In this section, the contributions of 16 molecular orbitals (MOs) with π-character to the ELF and LOL, which are respectively referred to ΕLF-π and LOL-π, were selected to investigate the electronic (de)localization of the studied system, and then to explore their aromaticity properties. The ELF-π domains display that the π-electrons delocalize over the dipyrrolemethylene moieties and the bridging C-C bonds show a weaker π-electronic population in every stable conformation (Figure 3). This illustrates that each dipyrrole-methylene unit has obvious local aromaticity, while the degree of the grobal aromaticity for each compound can't be easily distinguished with this diagram.

Figure

3.

ΕLF-π

isosurfaces

for

stable

conformations

of

macrocyclic

[32]octaphyrin(1.0.1.0.1.0.1.0). Isovalues for ELF-π surfaces are their respective ringclosure bifurcation values as reported in Table S2. Red arrows denote the positions of this bifurcation.

14


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LOL population analysis, which can provide comparable chemical information as ELF function, was carried out to compare the availability of different descriptor in measuring molecular aromaticity. The electron (de)localization characteristics described by LOL-π function are similar to those of depicted by ELF-π (cf. Figures 3 and 4). The ring-closure ELF-π and LOL-π bifurcations of each conformer all appear on the bridging C-C bond and are located at the same position in macrocycle. However, the morphology of LOL-π isosurface is not as bulky as that of ELF-π. Therefore, it can be inferred that LOL may be more intuitive than ELF in aromaticity research, at least for a system alike to the studied subjects in this work. Recent theoretical study on electron (de)localization functions showed that LOL can provide a clearer, more reliable, and insightful image than ELF,71 which supports our claim.

Figure

4.

LOL-π

isosurfaces

for

stable

conformations

of

macrocyclic

[32]octaphyrin(1.0.1.0.1.0.1.0). Isovalues for LOL-π surfaces are their respective ringclosure bifurcation values as reported in Table S2. Blue arrows denote the positions of this bifurcation. 15



Through topological analysis, the π-conjugated isosurface of ELF and LOL functions can be divided into several electron basins with clear chemical significance. The grade of these basins is directly related to the bifurcation values of their localized domains.72 It is generally true that the region surrounded by ELF-π or LOL-π isosurface with higher value is easier in delocalization for electrons. In other words, the larger the value of a bifurcation, the stronger the conjugation tendency of the two regions connected by it. To investigate the utility of ELF-π and LOL-π functions on evaluation of the global aromaticity, we extracted the ring-closure bifurcation values of the stationary points (Table S2). The bifurcation values of LOL-π correlate fairly well with those of ELF-π with the correlation coefficient (R2) between them up to 0.99 (Figure 5), implying these two criteria has the same effect on evaluating the aromaticity of the titled molecules. Unfortunately, the bifurcation values of present systems show no obvious regularity, that is, they are neither related to the topological structure nor to the global aromaticity descripted by ICSS and AICD. The extracted bifurcation values from ELF-π and LOL-π of TSs are much smaller than those of the stable conformers, except for the quasi-planar TS1/6. It shows again that the electronic structures of the TSs in this reaction are very complex and the properties of them not simply lie between the two intermediates connected.

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Figure 5. Correlation between the ring-closure bifurcations values of ELF-π and LOLπ.

4. Conclusions The conformational isomerization of macrocyclic [32]octaphyrin(1.0.1.0.1.0.1.0) were theoretically investigated at the level of M06-2X/6-311G(d). Precise energy calculations show that the enantiomers locating at the origination and the destination of the reaction are engaged in a constant chiral reversion in configuration, and other conformers may also realize facile isomerization under appropriate conditions. The judgments of the molecular aromaticity by magnetic-based properties (ICSS and AICD) have come to the same conclusion, and the results are consistent with what was inferred from the numerical indexes in our previous work. Whereas, the aromaticity criteria based on electron (de)localization (ELF and LOL) are not suitable for detecting the global aromaticity of the systems, but only qualified for reflecting the aromaticity in local regions of the molecules. It is shown that the determination of the aromaticity for a molecule should be comprehensively considered by refining evidence from multiple 17



descriptors, and the importance of the visual criteria are suggested to be paid special attention.

Acknowledgment This work was supported by the financial supports from The Natural Science Foundation of the Jiangsu Higher Education Institutuios of China (Grant No. 18KJA180005). We are very grateful to Mr. Jingjie Zhou of Jiangsu University of Science and Technology for his help in Table of Contents (TOC) graphic. Dr. Zeyu Liu especially appreciates his wife for her tireless encouragement and urging.

Supporting Information Available: Cartesian coordinates of stationary points; ECD spectra of 1H and 6H; ICSSzz and AICD-π plots for TSs; Magnetically induced current density for 1H; ΕLF-π and LOL-π isosurfaces for TSs; ring-closure bifurcation values of ELF-π and LOL-π plots; full citation for reference 55.

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Scheme 1. Potential energy diagram along the isomerization pathway of [32]octaphyrin(1.0.1.0.1.0.1.0). 271x155mm (300 x 300 DPI)



Figure 1. ICSSzz plots for stable conformations of macrocyclic [32]octaphyrin(1.0.1.0.1.0.1.0).(1.0.1.0.1.0.1.0). 249x214mm (72 x 72 DPI)


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Figure 2. AICD-π plots for stable conformations of macrocyclic [32]octaphyrin(1.0.1.0.1.0.1.0). 196x162mm (300 x 300 DPI)



Figure 3. ΕLF-π isosurfaces for stable conformations of macrocyclic [32]octaphyrin(1.0.1.0.1.0.1.0). 259x215mm (72 x 72 DPI)


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Figure 4. LOL-π isosurfaces for stable conformations of macrocyclic [32]octaphyrin(1.0.1.0.1.0.1.0). 260x216mm (72 x 72 DPI)



Figure 5. Correlation between the ring-closure bifurcations values of ELF-π and LOL-π. 296x209mm (300 x 300 DPI)


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Aromaticity of HÃ¼ckel and MÃ¶bius Topologies involved in

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