#
The Magnetic Response of Starphenes^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{3h}symmetry [1,2]. As with most large PAHs, scientific interest in two-dimensional organic structures increases due to their potential applications as molecular electronic devices [3]. However, because of the difficulty of isolating large acenes, the synthesis and characterization of starphenes are challenging [1,3]. Recently, Holec et al. reported the synthesis of [16]starphenes [4], which contains three pentacene branches. Similar exciting structures based on starphenes have also been isolated, such as cloverphenes and [19]dendriphene [5,6]. Therefore, the race to obtain larger starphenes is intensely competitive, and the description of their physical properties from a theoretical point of view is still scarce.

## 2. Computational Details

**J**

^{ind}) [12,13,14], and the induced magnetic field (

**B**

^{ind}) [27,28,29].

^{pπ}

**J**

^{ind}) and the induced magnetic field (

^{pπ}

**B**

^{ind}). The calculations of

^{pπ}

**J**

^{ind}and

^{pπ}

**B**

^{ind}were performed with the GIMIC [12,13,14] and Aromagnetic [30] programs, respectively. The external magnetic field was applied parallel to the highest-symmetry molecular axis, which coincides with the z-axis. In this orientation, the z-component is the most significant contribution to

^{pπ}

**B**

^{ind}(

^{pπ}B

^{ind}

_{z}). Thus, the

^{pπ}

**B**

^{ind}analysis can focus on the

^{pπ}B

^{ind}

_{z}component. For a unit external field and planar molecules (as in this work), B

^{ind}

_{z}is equivalent to the zz-component of the nucleus-independent chemical shift (NICS

_{zz}) index [31,32,33]. GIMIC also computes the ring-current strengths (J

^{ind}) by integrating the current density flowing through a plane intersecting one or more chemical bonds. The ring-current strength number is commonly used to quantify aromaticity. In addition, the current–density flux in different parts of the plane can be determined by calculating the derivative of J

^{ind}(dJ

^{ind}/dr) with respect to one of the plane coordinates (r) [14]. The plane of integration extends 8 bohr above and below from the molecular plane. Also, the coordinate r can be chosen such that it starts with r = 0 on the horizontal axis at the center of the central ring of starphene, intersects all the C–C bonds, and ends where

^{pπ}

**J**

^{ind}vanishes (ca. 8 bohr away from the last C–C bond). This allows us to screen smooth changes in the ring-current strength and define intervals in the plane corresponding to regions where J

^{ind}changes sign, where it becomes zero, or identify where the current has different local or global circulations [14]. In starphenes, there are current flows that can classify as global and local circulations. Due to the multipath character of the

^{pπ}

**J**

^{ind}in starphenes, the ring-current circulations are plotted with different colors to distinguish each pathway. To quantify the ring-current strengths of these other flows, the intervals where the field lines cross a given subplane are determined and highlighted using the same color code (Figure 1). The units for the pseudo-π ring-current strengths are in nA/T, while

^{pπ}B

^{ind}

_{z}is given in ppm. For visualization purposes, the skeleton shown in the figures depicting the pseudo-π magnetic response corresponds to the original carbon, rather than the all-hydrogen system.

## 3. Results and Discussion

^{pπ}

**J**

^{ind}calculations reveal a diatropic ring current (see Figure 2a). Consequently,

^{pπ}

**B**

^{ind}points in the opposite direction to the external magnetic field, resulting in rather intense negative

^{pπ}B

^{ind}

_{z}values and a long-range shielding cone (Figure 2b).

#### 3.1. [4]Starphene

^{pπ}

**J**

^{ind}shows that the flow lines split into a diatropic peripheral current (global) and local circulations in the outer 6-MRs (see Figure 3a). The integration of

^{pπ}

**J**

^{ind}across a plane intersecting the peripheral current pathway leads to a π ring-current strength of 8.28 nA/T (see Table 1). For the local ring currents, which are also diatropic, the integration of the

^{pπ}

**J**

^{ind}flux at the inner C–C bond provides a strength of 4.12 nA/T. Note that there is no local ring current flow in the CBR. So, from a magnetic response point of view, it cannot be considered an aromatic ring; it is a bridge for peripheral current flow. This explains why the shielding values of the CBR are weaker than those of the outer rings [36,37]. These

^{pπ}B

^{ind}

_{z}negative values inside the CBR arise from the combination of the deshielded zones of the outermost rings and the shielding caused by the flux of the peripheral current. The latter ends ruling the magnetic response of the CBR leading to shielded values inside the ring. This phenomenon changes in larger starphenes. Furthermore,

^{pπ}B

^{ind}

_{z}shows that the outer rings have a slightly larger shielding cone than benzene due to the local and peripheral fluxes (Figure 3b).

#### 3.2. [7]Starphene

^{pπ}

**J**

^{ind}flux lines are branching into peripheral and local naphthalene-like circulations in the arms (see Figure 4a). Also, the CBR maintains the bridging behavior for the weaker peripheral current flow along the starphene. The

^{pπ}B

^{ind}

_{z}isolines also confirm this (Figure 4b). The shielding cones are mainly above (and below) the naphthalene-like arms. The positive

^{pπ}B

^{ind}

_{z}values in the CBR are the result of the combination of the deshielding caused by strong naphthalene-type currents and the shielding due to the peripheral current flowing along the starphene. Unlike [4]starphene, the peripheral current of [7]starphene is considerably weaker (3.81 nA/T), which also leads to weaker shielding that is suppressed by the deshielding cones caused by the adjacent naphthalene-like circulations, giving rise to positive values within the CBR. It is well-known that naphthalene produces diatropic currents of 10π-electron flowing only in the periphery, i.e., there are no individual circulations in each 6-MR [15,16,38]. Reports of

^{pπ}

**J**

^{ind}on naphthalene lead to a fully diatropic pseudo-π ring-current strength of 13.41 nA/T (at the B3LYP level) [10]. However, the naphthalene-like current in [7]starphene is weaker (9.41 nA/T, see Table 1). So, electron delocalization in the arms of [7]starphene is slightly weaker than that of naphthalene.

#### 3.3. [10]Starphene

^{pπ}B

^{ind}

_{z}values inside the rings of the anthracene-like arms. Moreover, traces of an additional current appear in the central 6-MR of the anthracene-like arms because its shielding cone is larger than that of the adjacent rings (Figure 5a).

^{pπ}

**J**

^{ind}shows local and global delocalized pathways in anthracene and larger acenes, with no contamination of the core- and σ-orbitals [10,15,16,17]. This vector field also reveal that the [10]starphene’s arms has a current of 10.46 nA/T, flowing around the anthracene-like perimeters (Figure 5a). In addition, a local circulation of 3.62 nA/T flows in its central 6-MR. This additional local circulation results in a larger shielding cone above (and below) this ring (Figure 5b). This explains why the highest shielded values arise in the center of this ring [8,40]. However, this does not mean that this central 6-MR is more aromatic than the others, but instead there is an overlap of the shieldings from adjacent rings resulting in the fusion of the shielding cones.

^{pπ}

**J**

^{ind}across a C–C bond at the perimeter of the central 6-MR leads to a ring-current strength of 15.37 nA/T, which is practically the sum of the peripheral current, the anthracene-like current, and the local circulation in the central 6-MR. To compare, the sum of the local 6-MR and the anthracene-like currents leads to a cumulative net π ring-current strength of 14.08 nA/T, which is also slightly weaker than the net current of the isolated anthracene (~16 nA/T) [10].

#### 3.4. [13]Starphene

^{pπ}B

^{ind}

_{z}calculations show a large shielding cone above these two innermost 6-MRs, while the CBR exhibits large deshielded values in the molecular plane due to the presence of these strong tetracene-like currents and surpassing the weak shielded values caused by the peripheral current (Figure 6b). For systems such as [13]starphene, addressing aromaticity by B

^{ind}

_{z}(or NICS) calculations highlights the use of several tools to determine the true origin of shielding or

^{1}H-NMR signals. The strengths of the local naphthalene-like currents, the local tetracene-like currents, and the peripheral current flowing along [13]starphene are 5.05, 10.27, and 1.30 nA/T, respectively (Table 1). Note that the peripheral current tends to decrease as the size of the starphene skeleton increases, but so do the local currents. For example, while the isolated naphthalene has a pseudo-π current of 13.4 nA/T, [7]- and [13]starphene have a naphthalene-like current of 9.4 and 5.05 nA/T, respectively. Thus, the ring-current strengths decrease as the number of delocalized π-electrons increases in the starphene, also indicating that its aromaticity decreases with respect to their isolated acene’s arms.

#### 3.5. [16]Starphene

^{pπ}B

^{ind}

_{z}suggests that [16]starphene is highly aromatic due to the formation of long-range shielding cones, of which the central 6-MR pentacene-like arms is the most pronounced (Figure 7). This is explained by the superposition of the shielding caused by several ring currents flowing in the structure. In particular, the

^{pπ}

**J**

^{ind}calculations reveal a weak peripheral current along the starphene, a current running in the perimeter of the pentacene-like arms, an anthracene-like current in the innermost three 6-MRs, and a local current in the central ring of the arms (Figure 7). Like the previous systems, electron delocalization of pentacene-like has been explained in terms of 6π-, 10π-, 14π-, but also 18π-electron circuits [42]. Following the trend, the peripheral current is weaker than that of the previous starphenes (only 1.11 nA/T). The pentacene-like, anthracene-like, and local currents in the central 6-MR are 9.77, 5.61, and 1.73 nA/T, respectively. A comparison between the strengths of the isolated anthracene and the anthracene-like current of [10]starphene indicates that [16]starphene has a weaker anthracene-like current. Therefore, the degree of aromaticity in starphenes decreases as the arms become larger.

#### 3.6. [19]Dendriphene

^{pπ}B

^{ind}

_{z}shows negative values in the CBR and a shielding cone emerges above that ring. Besides, there are three other 6-MRs in which the outer naphthalene-like arms are attached, exhibiting deshielded values.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Pozo, I.; Guitián, E.; Pérez, D.; Peña, D. Synthesis of Nanographenes, Starphenes, and Sterically Congested Polyarenes by Aryne Cyclotrimerization. Acc. Chem. Res.
**2019**, 52, 2472–2481. [Google Scholar] [CrossRef] [PubMed] - Rüdiger, E.C.; Müller, M.; Freudenberg, J.; Bunz, U.H.F. Starphenes and Phenes: Structures and Properties. Org. Mater.
**2019**, 01, 001–018. [Google Scholar] [CrossRef] [Green Version] - Müllen, K.; Rabe, J.P. Nanographenes as Active Components of Single-Molecule Electronics and How a Scanning Tunneling Microscope Puts Them to Work. Acc. Chem. Res.
**2008**, 41, 511–520. [Google Scholar] [CrossRef] [PubMed] - Holec, J.; Cogliati, B.; Lawrence, J.; Berdonces-Layunta, A.; Herrero, P.; Nagata, Y.; Banasiewicz, M.; Kozankiewicz, B.; Corso, M.; de Oteyza, D.G.; et al. A Large Starphene Comprising Pentacene Branches. Angew. Chem. Int. Ed. Engl.
**2021**, 60, 7752–7758. [Google Scholar] [CrossRef] - Alonso, J.M.; Díaz-Álvarez, A.E.; Criado, A.; Pérez, D.; Peña, D.; Guitián, E. [16]Cloverphene: A Clover-Shaped Cata-Condensed Nanographene with Sixteen Fused Benzene Rings. Angew. Chem. Int. Ed. Engl.
**2012**, 51, 173–177. [Google Scholar] [CrossRef] - Vilas-Varela, M.; Fatayer, S.; Majzik, Z.; Pérez, D.; Guitián, E.; Gross, L.; Peña, D. [19]Dendriphene: A 19-Ring Dendritic Nanographene. Chem. Eur. J.
**2018**, 24, 17697–17700. [Google Scholar] [CrossRef] [PubMed] - Yu, D.; Stuyver, T.; Rong, C.; Alonso, M.; Lu, T.; De Proft, F.; Geerlings, P.; Liu, S. Global and Local Aromaticity of Acenes from the Information-Theoretic Approach in Density Functional Reactivity Theory. Phys. Chem. Chem. Phys.
**2019**, 21, 18195–18210. [Google Scholar] [CrossRef] [PubMed] - Portella, G.; Poater, J.; Bofill, J.M.; Alemany, P.; Solà, M. Local Aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9). J. Org. Chem.
**2005**, 70, 2509–2521. [Google Scholar] [CrossRef] [PubMed] - Pino-Rios, R.; Báez-Grez, R.; Solà, M. Acenes and Phenacenes in Their Lowest-Lying Triplet States. Does Kinked Remain More Stable than Straight? Phys. Chem. Chem. Phys.
**2021**, 23, 13574–13582. [Google Scholar] [CrossRef] - Orozco-Ic, M.; Dimitrova, M.; Barroso, J.; Sundholm, D.; Merino, G. Magnetically Induced Ring-Current Strengths of Planar and Nonplanar Molecules: New Insights from the Pseudo-π Model. J. Phys. Chem. A
**2021**, 125, 5753–5764. [Google Scholar] [CrossRef] - Orozco-Ic, M.; Restrepo, A.; Muñoz-Castro, A.; Merino, G. Molecular Helmholtz Coils. J. Chem. Phys.
**2019**, 151, 014102. [Google Scholar] [CrossRef] - Jusélius, J.; Sundholm, D.; Gauss, J. Calculation of Current Densities Using Gauge-Including Atomic Orbitals. J. Chem. Phys.
**2004**, 121, 3952–3963. [Google Scholar] [CrossRef] - Fliegl, H.; Taubert, S.; Lehtonen, O.; Sundholm, D. The Gauge Including Magnetically Induced Current Method. Phys. Chem. Chem. Phys.
**2011**, 13, 20500–20518. [Google Scholar] [CrossRef] [PubMed] - Sundholm, D.; Fliegl, H.; Berger, R.J.F. Calculations of Magnetically Induced Current Densities: Theory and Applications. WIREs Comput. Mol. Sci.
**2016**, 6, 639–678. [Google Scholar] [CrossRef] - Steiner, E.; Fowler, P.W. Patterns of Ring Currents in Conjugated Molecules: A Few-Electron Model Based on Orbital Contributions. J. Phys. Chem. A
**2001**, 105, 9553–9562. [Google Scholar] [CrossRef] - Steiner, E.; Fowler, P.W.; Havenith, R.W.A. Current Densities of Localized and Delocalized Electrons in Molecules. J. Phys. Chem. A
**2002**, 106, 7048–7056. [Google Scholar] [CrossRef] - Fowler, P.W.; Steiner, E. Pseudo-π Currents: Rapid and Accurate Visualisation of Ring Currents in Conjugated Hydrocarbons. Chem. Phys. Lett.
**2002**, 364, 259–266. [Google Scholar] [CrossRef] - Charistos, N.D.; Muñoz-Castro, A.; Sigalas, M.P. The Pseudo-π Model of the Induced Magnetic Field: Fast and Accurate Visualization of Shielding and Deshielding Cones in Planar Conjugated Hydrocarbons and Spherical Fullerenes. Phys. Chem. Chem. Phys.
**2019**, 21, 6150–6159. [Google Scholar] [CrossRef] [PubMed] - Yanai, T.; Tew, D.P.; Handy, N.C. A New Hybrid Exchange–correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett.
**2004**, 393, 51–57. [Google Scholar] [CrossRef] [Green Version] - Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys.
**2010**, 132, 154104. [Google Scholar] [CrossRef] [Green Version] - Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys.
**2005**, 7, 3297–3305. [Google Scholar] [CrossRef] - Lehtola, S.; Dimitrova, M.; Fliegl, H.; Sundholm, D. Benchmarking Magnetizabilities with Recent Density Functionals. J. Chem. Theory Comput.
**2021**, 17, 1457–1468. [Google Scholar] [CrossRef] [PubMed] - Valiev, R.R.; Benkyi, I.; Konyshev, Y.V.; Fliegl, H.; Sundholm, D. Computational Studies of Aromatic and Photophysical Properties of Expanded Porphyrins. J. Phys. Chem. A
**2018**, 122, 4756–4767. [Google Scholar] [CrossRef] [Green Version] - Ditchfield, R. Self-Consistent Perturbation Theory of Diamagnetism. Mol. Phys.
**1974**, 27, 789–807. [Google Scholar] [CrossRef] - Wolinski, K.; Hinton, J.F.; Pulay, P. Efficient Implementation of the Gauge-Independent Atomic Orbital Method for NMR Chemical Shift Calculations. J. Am. Chem. Soc.
**1990**, 112, 8251–8260. [Google Scholar] [CrossRef] - Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Petersson, G.A.; Nakatsuji, H.; et al. Gaussian 16; revision D.01; Gaussian Inc.: Wallingford, CT, USA, 2016. [Google Scholar]
- Merino, G.; Heine, T.; Seifert, G. The Induced Magnetic Field in Cyclic Molecules. Chem. Eur. J.
**2004**, 10, 4367–4371. [Google Scholar] [CrossRef] - Heine, T.; Islas, R.; Merino, G. Sigma and Pi Contributions to the Induced Magnetic Field: Indicators for the Mobility of Electrons in Molecules. J. Comput. Chem.
**2007**, 28, 302–309. [Google Scholar] [CrossRef] [PubMed] - Islas, R.; Heine, T.; Merino, G. The Induced Magnetic Field. Acc. Chem. Res.
**2012**, 45, 215–228. [Google Scholar] [CrossRef] - Orozco-Ic, M.; Cabellos, J.L.; Merino, G. Aromagnetic; Cinvestav-Mérida: Mérida, Mexico, 2016. [Google Scholar]
- von Ragué Schleyer, P.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N.J.R. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc.
**1996**, 118, 6317–6318. [Google Scholar] [CrossRef] - Chen, Z.; Wannere, C.S.; Corminboeuf, C.; Puchta, R.; von Rague Schleyer, P. Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion. Chem. Rev.
**2005**, 105, 3842–3888. [Google Scholar] [CrossRef] - Fallah-Bagher-Shaidaei, H.; Wannere, C.S.; Corminboeuf, C.; Puchta, R.; Schleyer, P.v.R. Which NICS Aromaticity Index for Planar Pi Rings Is Best? Org. Lett.
**2006**, 8, 863–866. [Google Scholar] [CrossRef] - Radenković, S.; Đorđević, S. Relating Nucleus Independent Chemical Shifts with Integrated Current Density Strengths. Phys. Chem. Chem. Phys.
**2021**, 23, 11240–11250. [Google Scholar] [CrossRef] [PubMed] - Monaco, G.; Zanasi, R.; Pelloni, S.; Lazzeretti, P. Relative Weights of σ and π Ring Currents in a Few Simple Monocycles. J. Chem. Theory Comput.
**2010**, 6, 3343–3351. [Google Scholar] [CrossRef] [PubMed] - Papadopoulos, A.G.; Charistos, N.D.; Sigalas, M.P. Aromaticity Variation in BN Substituted Triphenylene: A Theoretical Study. AIP Conf. Proc.
**2012**, 1504, 1223–1226. [Google Scholar] - Lampkin, B.J.; Karadakov, P.B.; VanVeller, B. Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding. Angew. Chem. Int. Ed. Engl.
**2020**, 59, 19275–19281. [Google Scholar] [CrossRef] [PubMed] - Sundholm, D.; Berger, R.J.F.; Fliegl, H. Analysis of the Magnetically Induced Current Density of Molecules Consisting of Annelated Aromatic and Antiaromatic Hydrocarbon Rings. Phys. Chem. Chem. Phys.
**2016**, 18, 15934–15942. [Google Scholar] [CrossRef] [Green Version] - Solà, M. Forty Years of Clar’s Aromatic π-Sextet Rule. Front. Chem.
**2013**, 1, 22. [Google Scholar] [CrossRef] [Green Version] - von Ragué Schleyer, P.; Manoharan, M.; Jiao, H.; Stahl, F. The Acenes: Is There a Relationship between Aromatic Stabilization and Reactivity? Org. Lett.
**2001**, 3, 3643–3646. [Google Scholar] [CrossRef] - Fias, S.; Van Damme, S.; Bultinck, P. Multidimensionality of Delocalization Indices and Nucleus Independent Chemical Shifts in Polycyclic Aromatic Hydrocarbons. J. Comput. Chem.
**2008**, 29, 358–366. [Google Scholar] [CrossRef] - Szczepanik, D.W.; Solà, M.; Krygowski, T.M.; Szatylowicz, H.; Andrzejak, M.; Pawełek, B.; Dominikowska, J.; Kukułka, M.; Dyduch, K. Aromaticity of Acenes: The Model of Migrating π-Circuits. Phys. Chem. Chem. Phys.
**2018**, 20, 13430–13436. [Google Scholar] [CrossRef] [Green Version] - Aihara, J.-I. Circuit Resonance Energy: A Key Quantity That Links Energetic and Magnetic Criteria of Aromaticity. J. Am. Chem. Soc.
**2006**, 128, 2873–2879. [Google Scholar] [CrossRef] [PubMed] - Gershoni-Poranne, R. Piecing It Together: An Additivity Scheme for Aromaticity Using NICS-XY Scans. Chem. Eur. J.
**2018**, 24, 4165–4172. [Google Scholar] [CrossRef] [PubMed] - Bendikov, M.; Duong, H.M.; Starkey, K.; Houk, K.N.; Carter, E.K.; Wudl, F. Oligoacenes: Theoretical Prediction of Open-Shell Singlet Diradical Ground States. J. Am. Chem. Soc.
**2004**, 126, 7416–7417. [Google Scholar] [CrossRef] [PubMed] - Poater, J.; Bofill, J.M.; Alemany, P.; Solà, M. Local Aromaticity of the Lowest-Lying Singlet States of [n]Acenes (n = 6-9). J. Phys. Chem. A
**2005**, 109, 10629–10632. [Google Scholar] [CrossRef] [PubMed] - Jiang, D.; Dai, S. Electronic Ground State of Higher Acenes. J. Phys. Chem. A
**2008**, 112, 332–335. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Starphenes studied and the integration planes intersecting their different C–C bonds. The planes of integration extend 8 bohr above and below the molecular plane.

**Figure 2.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic ring current (in blue) of benzene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of benzene. The white areas surrounded by negative (or positive) values correspond to regions where the shielding (or deshielding) magnitude is larger than the values chosen for the color scale.

**Figure 3.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue) and the local diatropic currents (in purple) of [4]starphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [4]starphene (scale conventions as in Figure 2).

**Figure 4.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue) and the naphthalene-like ring currents (in purple) of [7]starphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [7]starphene (scale conventions as in Figure 2).

**Figure 5.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue), anthracene-like ring currents (in purple), and the local circulation in the anthracene-like’s middle 6-MR (in green) of [10]starphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [10]starphene (scale conventions as in Figure 2).

**Figure 6.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue), tetracene-like ring currents (in purple), and the local circulation in the naphthalene-like’s middle 6-MR (in green) of [13]starphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [13]starphene (scale conventions as in Figure 2).

**Figure 7.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue), pentacene-like ring currents (in purple), the local anthracene-like current (in green), and the local current in the middle 6-MR (in orange) of [16]starphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [16]starphene (scale conventions as in Figure 2).

**Figure 8.**(

**a**)

^{pπ}

**J**

^{ind}vector maps showing the diatropic peripheral ring current (in blue), naphthalene-like ring currents (in purple), and local 6-MR currents (in green) of [19]dendriphene. (

**b**) Isolines of

^{pπ}B

^{ind}

_{z}calculated in the transverse plane (left) and the molecular plane (right) of [19]dendriphene (scale conventions as in Figure 2).

**Table 1.**Ring-current strengths (in nA/T) of starphenes divided into their diatropic and paratropic components calculated using the pseudo-π model at the CAM-B3LYP/def2-SVP level. The position of the integration planes is shown in Figure 1.

Molecule | Plane | Diatropic | Paratropic | Net |
---|---|---|---|---|

Benzene | A | 12.52 | 0.0 | 12.52 |

[4]starphene | A (peripheral) | 8.99 | −0.71 | 8.28 |

B (local 6-MR) | 4.12 | 0.0 | 4.12 | |

[7]starphene | A (peripheral) | 5.20 | −1.40 | 3.80 |

B (naphthalene-like) | 9.41 | 0.0 | 9.41 | |

[10]starphene | A (peripheral) | 3.79 | −1.81 | 1.98 |

B (anthracene-like) | 10.46 | 0.0 | 10.46 | |

C (local 6-MR) | 3.62 | 0.0 | 3.62 | |

[13]starphene | A (peripheral) | 3.22 | −0.01 | 1.30 |

B (tetracene-like) | 10.27 | 0.0 | 10.27 | |

C (naphthalene-like) | 5.53 | 0.0 | 5.05 | |

[16]starphene | A (peripheral) | 2.98 | −1.87 | 1.11 |

B (pentacene-like) | 9.77 | 0.0 | 9.77 | |

C (anthracene-like) | 5.61 | 0.0 | 5.61 | |

D (local 6-MR) | 1.73 | 0.0 | 1.73 | |

[19]dendriphene | A (peripheral) | 6.63 | 0.0 | 6.63 |

B (naphthalene-like) | 9.09 | 0.0 | 9.09 | |

C (local 6-MR) | 4.74 | 0.0 | 4.74 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Orozco-Ic, M.; Merino, G.
The Magnetic Response of Starphenes. *Chemistry* **2021**, *3*, 1381-1391.
https://doi.org/10.3390/chemistry3040099

**AMA Style**

Orozco-Ic M, Merino G.
The Magnetic Response of Starphenes. *Chemistry*. 2021; 3(4):1381-1391.
https://doi.org/10.3390/chemistry3040099

**Chicago/Turabian Style**

Orozco-Ic, Mesías, and Gabriel Merino.
2021. "The Magnetic Response of Starphenes" *Chemistry* 3, no. 4: 1381-1391.
https://doi.org/10.3390/chemistry3040099