Aromatic Pathways of Porphins, Chlorins, and Bacteriochlorins Heike Fliegl* ,†,‡ 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 Chemistry, University of Helsinki, P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014, University of Helsinki, Finland * S Supporting Information ABSTRACT: Magnetically induced current densities have been calculated for free-base porphynoids using the gauge including magnetically induce current (GIMIC) method. Numerical integration of the current density passing selected chemical bonds yields current pathways and the degree of aromaticity according to the magnetic criterion. The ring- current strengths of the porphins, chlorins, and bacteriochlorins are 1.5-2.5 times stronger than for benzene. The calculations show that the 18π [16]annulene inner cross is not the correct picture of the aromatic pathway for porphyrins. All conjugated chemical bonds participate in the current transport independently of the formal number of π electrons. The ring current branches at the pyrrolic rings taking both the outer and the inner route. The NH unit of the pyrrolic rings has a larger resistance and a weaker current strength than the pyrroles without inner hydrogens. The traditional 18π [18]annulene with inactive NH bridges is not how the ring-current flows around the macroring. The porphins have the strongest ring current of ca. 27 nA/T among the investigated porphynoids. The current strengths of the chlorins and bacteriochlorins are 19-24 nA/T depending on whether the ring current is forced to pass an NH unit or not. The current strengths of the 3-fold and 4-fold β-saturated porphynoids are 13-17 nA/T, showing that the inner- cross 18π [16]annulene pathway is not a preferred current route. 1. INTRODUCTION An external magnetic field applied perpendicularly to a planar aromatic molecular ring induces a net diatropic current that flows around the ring. In aromatic molecules consisting of fused conjugated rings, the current can circle around one or several of the individual rings. It can also flow around the entire molecule. Thus, molecules with fused aromatic rings have many feasible current pathways, the routes of which are difficult to determine. It is not possible to determine magnetically induced current pathways experimentally. The only reliable means to elucidate the pathways of the current flow is to explicitly calculate the strength of the currents passing selected chemical bonds of the multiring molecule. Porphyrins, which are aromatic molecules with 26 π electrons, consist of four pyrrole units connected by conjugated C-C bonds to form a larger ring with several possible aromatic pathways. Traditionally, porphyrins have been considered as a bridged 18π [18]annulene with the inner NH groups acting as inert bridges. 1-5 Cyrañ ski et al. 6 studied the aromatic pathway of free-base porphyrin (porphin) using nucleus independent chemical shifts 7 (NICS) and calculations of harmonic oscillator model of aromaticity 8 (HOMA) indices. They concluded that the aromatic pathway of porphins consists of the 18π [16]annulene internal cross implying that the ring current does not pass the outer C 2 H 2 groups of the pyrrolic rings. Using current-density plots, Havenith et al. found more recently that the ring current avoids the outer route at the pyrroles without an inner hydrogen. 9 Other possible pathways for the induced ring current in porphyrins also exist. However, they have to fulfill the Hü ckel rule for aromaticity involving (4n +2) π electrons. 10,11 For porphyrins, Hü ckel-aromatic pathways might involve 18 π or 22 π electrons. Juse ́ lius and Sundholm found that all 26 π electrons play an active role for the aromaticity of porphyrins. 12 Chlorins and bacteriochlorins have 24 π and 22 π electrons as they are free-base porphynoids with one and two of the pyrrole rings saturated in the β positions, respectively. Juse ́ lius and Sundholm calculated long-range magnetic shielding functions and used their aromatic ring current shieldings (ARCS) approach to estimate current strengths and current pathways in such free-base porphynoids. 13 In the ARCS studies, they found that the total aromatic pathways of the porphynoids and of magnesium porphyrin must be considered as a superposition of several pathways. 12,14 Thus, the aromaticity of the classical porphynoids is not yet settled, not to speak of more general porphyrinoids. Modern porphyrinoid chemistry also involves complicated molecules with singly and doubly twisted Mö bius structures, 15-22 whose degree of aromaticity is very difficult to assess. 20,23-37 The aim of this work is to employ the gauge-including magnetically induced current (GIMIC) method to elucidate the aromatic pathways of planar porphins, chlorins, and bacterio- chlorins. 38-40 Compared to the previously employed NICS and ARCS methods, the GIMIC approach is more accurate. Thus, it avoids speculation about the current density, current strengths, Received: January 27, 2012 Published: March 8, 2012 Article pubs.acs.org/joc © 2012 American Chemical Society 3408 dx.doi.org/10.1021/jo300182b | J. Org. Chem. 2012, 77, 3408-3414