Theoretical Study of the Inner Hydrogen Migration in the β-Substituted

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Theoretical Study of the Inner Hydrogen Migration in the β-Substituted 5,10,15,20-Tetraphenylporphyrins Xiaoquan Lu,* Yong He, Jing Chen, Jinfeng Wang, and Haicai Shi Key Laboratory of Bioelectrochemistry and EnVironmental Analysis of Gansu ProVince, College of Chemistry and Chemical Engineering, Northwest Normal UniVersity, Lanzhou, 730070, China ReceiVed: July 30, 2010; ReVised Manuscript ReceiVed: October 31, 2010

In order to investigate the mechanism of the N-H migration in asymmetrical metal-free porphyrins, four porphyrins of electron-withdrawing or electron-donating substituent at the β-position were studied theoretically. For porphyrin 2 (R ) OMe), 3 (R ) Me), and 4 (R ) NO2), four different asynchronous N-H migration pathways exist due to symmetry reasons. The corresponding trans-, cis-, and transition state geometries were analyzed using a normal structure decomposition method. Our data show that the hydrogen migration of porphyrin 2, 3, and 4 in clockwise (A, B) are much more preferred than counterclockwise (C, D) direction. Introduction Porphyrins are known to play important roles in many fundamental biological processes, for example, photosynthesis (chlorophyll), metal coordination chemistry, biological redox reactions (cytochrome), and oxygen transport processes (hemoglobin).1-11 Furthermore, porphyrins have been used in the investigation at the antioxidant property of ascorbic acid in the human body,12 the kinetics of electroactive agents on mimic membrane,13-15 the nature of interactions between Lewis acids and porphines as free bases,16 and the application in molecular electronics device.17-20 Porphyrin compounds have also attracted considerable interest as sensors for the anion recognition, because of advantages such as its high efficiency, good regioselectivity, and compatibility with the reaction environment.21 Therefore, we have an ongoing interest in developing a new type of porphyrin-based sensor for the dihydrogenphosphate anion recognition.22 In the design of porphyrin-based sensor for dihydrogenphosphate anion, a major obstacle must be overcome; that is, the β-substituted group is generally believed to be a great influence on properties of porphyrin.21,23-25 Recently, we found that the hydrogen migration in asymmetrical metal-free porphyrins ignore the nature of the substituent. This result prompted us to reevaluate the effect of the β-substituted group in the porphyrinbased anion sensor. It is well-known that the two inner hydrogen atoms of metalfree porphyrin can migrate in a framework of four nitrogen sites, and the process is referred to as N-H tautomerism. The mechanism of the N-H migration in the metal-free porphyrins has also attracted considerable experimental26-32 and theoretical33-41 interest, especially for the porphyrins that has involved symmetrical systems. In contrast, much less is studied about the asymmetric system. The N-H tautomerism in porphyrins was first demonstrated by Storm and Teklu using variable-temperature NMR spectroscopy,26 and then significant efforts were made to elucidate the proton-exchange mechanism using NMR spectroscopy both in solution27,28,42 and the solid state.32 Maxwell J. Crossley and co-workers reported that the activation parameters for tautom* To whom correspondence should be addressed. Phone: +86-9317971276. Fax: +86-931-7971323. E-mail: [email protected].

erism and an isotope effect in β-substituted porphyrins were essentially the same as those observed in symmetrical porphyrins.42 This suggests that the mechanism of proton migration is similar in both symmetrical and asymmetrical systems. However, structural information about the transition state and cistautomer could not be obtained. To interpret the experimental results obtained for the barriers of N-H migration of porphyrins, theoretical calculations were performed at different levels of theory.33,34,38,41,43-45 Jon Baker et al. provided a comprehensive picture of the inner-hydrogen migration in free base porphyrin, using density functional theory with the hybrid B3LYP exchangecorrelation functional, and both the 6-31G (d) and a triple-ζ double-polarization (TZ2P) basis set. Meanwhile, structural information about the transition state and cis-tautomer had also been obtained.35 Recently, Walewski, £. and co-workers reported that Car-Parrinello molecular dynamics simulations (CPMD) have been carried out to interpret proton-transfer processes observed experimentally in porphycene under thermodynamic equilibrium conditions (NVT ensemble) as well as during selective, nonequilibrium vibrational excitations of the molecular scaffold (NVE ensemble).46 It is now generally accepted that the hydrogen tautomerism occurs via a two-step mechanism involving a metastable cis intermediate rather than a synchronous one-step procedure that have been proposed by some authors.32,35,47 The N-H tautomerism of planar symmetrical metal-free porphyrins is well investigated, but less is researched about the involved cis and transition-state structures of the N-H tautmerism of the asymmetrical β-substituted metal-free porphyrins. In this work, we investigate the substitution effect, core deformation, and preferred tautomeric pathways in a series of β-substituted metal-free porphyrins 1-4 (see Scheme 1), as well as whether the cis-porphyrin could be stabilized by introducing electron-withdrawing or electron-donating substituent at the β-position; finally, the influence of the substituent on the core conformation of the tautomeric transition states is studied as well. The porphyrin core deformation of the calculated structures is analyzed in terms of changes of bond lengths, bond angles, and by means of the normal structure decomposition (NSD) method. The bond critical points (BCPs) and the ring critical points (RCPs) of them are also localized and analyzed.

10.1021/jp107145p  2010 American Chemical Society Published on Web 11/10/2010

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SCHEME 1: Trans Tautomers a (Left) and b (Right)

Computational Details The basic level of theory used throughout our study was DFT with the hybrid B3LYP exchange correlation functional as implemented in the Gaussian 03 program48 on a Dawning 5000 housed at GanSu Province High Performance Computing Centre. Density functional theory (DFT) is currently the most cost-effective method available for including electron correlation, and hybrid functionals are currently the most accurate density functionals.49 B3LYP has been widely used in theoretical studies of the inner hydrogen migration in the pyrrole macrocycles,35,40,41,50-53 and it is expected that the B3LYP calculations would give good results for β-substituted 5,10,15,20-tetraphenylporphyrin as well. The geometry optimizations of ground and transition states were performed (B3LYP/6-31(d)) without any symmetry restrictions and were followed by frequency calculations to verify the character of the stationary point obtained. The default numerical integration grid was employed when using Gaussian 03. The minimum energy path (MEP) was obtained using the intrinsic reaction coordinate (IRC) method at the B3LYP/6-31G (d) level. Further, single point calculations were carried out using the 6-31+G (d, p) basis set at HF, B3LYP, and BPW91 level on B3LYP/6-31G (d) optimized geometries. It is worth noting that no basis set superposition error (BSSE) correction is carried out in this work because hydrogen transfer occurred in the same molecule. The normal structure decomposition (NSD) method37,54 (NSD engine program, version 3.0, http://jasheln.unm.edu/jasheln/ content/nsd/NSDengine/nsd_index.htm) was carried out for the quantitative analysis of the structures involved in the inner hydrogen migration. The atoms in molecules (AIM) calculations were performed using the wave functions generated at the B3LYP/6-31+G (d, p) level with the help of AIM2000 program.55 Results and Discussion 1. Trans Tautomers. Full geometry optimization of the trans tautomers can lead to an approximate D2h structure. The calculated trans tautomers of 2-nitro-5,10,15,20-tetraphenylporphyrin are depicted in Figure 1a, 1e. The two trans tautomers of β-substituted 5,10,15,20-tetraphenylporphyrins (compounds 2, 3, and 4) exhibit a larger contribution for the macrocycle breathing (bre, A1g; 0.249 to 0.307 Å),

Lu et al. stretching in the direction of the nitrogen atoms (N-str, B1g; 0.095 to 0.141 Å), with the minor contribution for the macrocycle stretching in the direction of the meso carbon atoms (mesostr, B2g;; 0.004 to 0. 107 Å), x and y pyrrole translations [Eu; trn(x), 0.001 to 0.045 Å; trn(y), 0.001 to 0.033 Å], and pyrrole rotation (rot, A2g, 0.001 to 0.030 Å) in-plane distortion (see Table S1 in the Supporting Information). This is due to the additional substituent group in position 2. Figure 2 illustrates the results of the in-plane decomposition of 2-methoxy5,10,15,20-tetraphenylporphyrin. Moreover, as a result of the symmetry of 5,10,15,20-tetraphenylporphyrins (TPP) being consistent with the reference structure of the NSD method (see Table S1), the m-str (B2g, 0.004 Å), trn(x) (0.001 Å), trn(y) (0.001 Å), and rot (A1g) (0.001 Å) distortion types are practically absent in the two trans tautomers of it.37 Also, the trn(x) and trn(y) deformation types of compounds 2, 3, and 4 are remarkably larger than 1, probably because the substituent play a role in determining the symmetry of substituent perturbation on the macrocycle ring. Figure 3 displays the out-of-plane displacements of 2-methoxy-5,10,15,20-tetraphenylporphyrin. From the decomposition results in Figure 3, it can be seen that the macrocycle is mainly saddling when β-pyrrolic position of the porphyrin ring is substituted. For the 5,10,15,20-tetraphenylporphyrin, the saddling (sad, B2u, 0.001 Å), ruffling (ruf, B1u, 0.000 Å), doming (dom, A2u, 0.001 Å), and propellering (pro, A1u, 0.000 Å) distortion types are practically absent in the two trans tautomers of it. This phenomenon shows the out-of-plane under the influence of substituent. Besides the amounts of waV(x) (0.151 Å of a) and waV(y) (0.151 Å of b) deformations are also equal, probably because it has a high symmetry. Due to the different substitution pattern in compounds 2-4, up to four nonequivalent and significantly different, asynchronous pathways are possible (see Scheme 2). Each of these pathways includes one cis tautomer (local minimum) and two transition states (first-order saddle point). In the four pathways of the asynchronous tautomeric mechanism, the pathways A and B are much more preferred than C and D. In this study, the structures involved in the inner-hydrogen migration of pathway A are analyzed using the normal structural decomposition method (NSD) for classifying and quantifying their out-of-plane and in-plane distortions. 2. Cis Tautomers. The cis tautomers are characterized by both inner protons being connected to two adjacent nitrogen atoms in one-half of the molecule (see Figure 4). The calculated geometries of the cis and trans tautomers of 2-nitro-5,10,15,20-tetraphenylporphyrin are shown in Figure 1. The bond lengths in the optimized structures of the cis and trans tautomers are very similar. The C-C and C-N bond lengths in both tautomers are approximately in the order CR-Cβ (1.43-1.47 Å) > CR-Cmeso (1.40-1.42 Å) > Cβ-Cβ ∼ CR-N (1.35-1.38 Å). The N-H bond distances of 1.02 Å in the cis tautomers are significantly longer than those in the trans tautomers, which are about 1.01 Å, presumably reflecting a slight weakening of these bonds in the cis tautomers. The CR-N-CR angles are significantly wider in the N-protonated pyrrole rings (∼110°) than in the N-unprotonated rings (∼106°). This structural feature has been observed in many crystal structures of porphyrins and chlorins and is often used in a diagnostic manner to determine the connectivities of the central hydrogens even when they have not been actually located in the crystallographic structure determination.33,44,45 The most significant differences between the skeletal geometries of the cis and trans tautomers are in the bond angles within

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Figure 1. Important B3LYP/6-31G(d) geometrical parameters (bond lengths in angstroms, angles in degrees) for the trans a (a), TS1 (b, 4TS1A), cis (c, 4CISA), TS2 (d, 4TS2A), and trans b (e) of 2-nitro-5,10,15,20-tetraphenylporphyrin on the minimum energy pathway (MEP) relevant to the inner-hydrogen migration.

the macrocycle ring. The approximate D2h symmetry of the trans tautomers dictates that all four CR-Cmeso-CR angles are

approximately equal, with each angle being about 125°. Similarly, the CR-N-H angles in the trans tautomers are also

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Figure 2. In-plane displacements (complete basis) for trans tautomers, cis tautomer, and transition states of 2-methoxy-5,10,15,20-tetraphenylporphyrin. For full details, see the Supporting Information. The error bars represent the maximum displacements of transition states and cis tautomers in the four different, asynchronous pathways.

Figure 3. Out-of-plane displacements (complete basis) for trans tautomers, cis tautomer, and transition states of 2-methoxy-5,10,15,20tetraphenylporphyrin. For full details, see the Supporting Information. The error bars represent the maximum displacements of transition states and cis tautomers in the four different, asynchronous pathways.

approximately equal (∼124°). The two symmetry distinct types of N-CR-Cmeso angles in the trans tautomers are nearly equal (∼126°). In contrast, for the cis tautomers, the CR-Cmeso-CR angles between the two N-protonated pyrrole rings and that between the two N-unprotonated pyrrole rings are each about 128°, which is significantly wider than CR-Cmeso-CR angles of ∼123° between a pair of adjacent N-protonated and Nunprotonated pyrrole rings. In another difference from the trans tautomers, four out of eight N-CR-Cmeso angles in the cis tautomers are significantly wider (∼125°-129°) than the other four (∼123°-125°). In other words, the cis-porphyrin molecule is significantly broader along an axis passing through the two central N-H protons than along the molecular C2 axis, which evidently reflects steric repulsion between the cis imino hydrogens. This repulsion is also reflected in the considerable inequality of the two CR-N-H angles (∼131° and 117°) subtended at each of the two protonated central nitrogens of the cis tautomers. These differences in bond angles between the central macrocycles of the cis and trans tautomers result in significant differences in non-nearest-neighbor internuclear distances between the two tautomers. For instance, distances between nitrogen atoms are significantly different between the two tautomers. In the optimized structure of the cis tautomers of 2-nitro5,10,15,20-tetraphenylporphyrin, the distance between two protonated nitrogens is about 3.18 Å, and that between two

Lu et al. unprotonated nitrogens is about 3.12 Å. In contrast, the nitrogen atoms of an adjacent pair of N-protonated and N-unprotonated pyrrole rings of the cis tautomers are separated by only 2.70 Å. In the trans tautomers, the nitrogen atoms of a pair of adjacent pyrrole rings are separated by about 2.90 Å. Obviously, these differences in internitrogen separations between the two tautomers stem from the response of the macrocycle to better accommodate the closely spaced imino hydrogens in the cis tautomers. However, the energy cost due to this steric repulsion must be quite modest; (see Figure 5 and Table 1) otherwise, the cis tautomers would have been significantly buckled. The overall dominating distortion modes for all investigated local minima cis structures (see Figure 2, Table S1 in the Supporting Information) are the in-plane distortion modes m-str (B2g) and bre (A1g). The bre distortion describes the expansion of the porphyrin core.37,54 However, compared to the m-str (B2g) distortion, the contributions of the bre (A1g) distortion to the structures discussed are rather small. The position of the two inner NH protons in one-half of the molecules results in repulsive interactions that increase the distance between the corresponding nitrogen atoms. As a result, significant stretching (m-str) and modest expansion (bre) of the porphyrin macrocycle can be observed. The degree of the m-str (B2g) (0.53-0.57 Å) and bre (A1g) (0.27-0.30 Å) contribution are nearly the same in all cis tautomers. The m-str distortion results in steric strain for the β-substituted group leading in turn to different degrees of out-of-plane distortions (see Figure 3 and Table S1). 3. Transition-State Structures. In the asynchronous mechanism, shown in Scheme 2, each asynchronous pathway includes two different transition states TS1 and TS2. All tautomeric transition state structures are characterized by two adjacent nitrogen atoms sharing the hopping proton. The calculated geometries of transition states of 2-nitro5,10,15,20-tetraphenylporphyrin are depicted in Figure 4. The bond lengths in the optimized structures of transition states (TS1 and TS2) are similar with cis and trans tautomers (see Figure 1). The C-C and C-N bond lengths in the transition states are also approximately in the order CR-Cβ (1.43-1.47 Å) > CR-Cmeso (1.40-1.42 Å) > Cβ-Cβ ∼ CR-N (1.35-1.38 Å). The N-H bond distances for the hopping protons in the transition states (∼1.29 Å, ∼1.35 Å) are significantly longer than those in the cis tautomers, which are about 1.02 Å, presumably reflecting a weakening of these bonds in the transition states.35 The most significant differences between the skeletal geometries of transition states and the trans tautomers are the bond angles within the macrocycle ring. The approximate D2h symmetry of the trans tautomers dictates that all four CR-Cmeso-CR angles are equal, with each angle being about 125°. Similarly, the CR-N-H angles in the trans tautomers are equal (∼124°). In contrast, for transition states, the CR-Cmeso-CR angles both the two adjacent pyrrole rings sharing the hopping proton are about 119°, the CR-Cmeso-CR angles between one N-protonated pyrrole ring and another N-unprotonated pyrrole ring are about 121°, which is significantly asymmetric. This asymmetric is also reflected in the considerable inequality of the two CR-N-H angles (∼105° and 130°). Obviously, these differences in bond angles of the central macrocycle ring of transition states result in more larger m-str (in-plane) displacement than the cis and trans tautomers (see Figure 2). By examining the NSD results for the series of transition state structures given in Figure 2 and Table S1 in the Supporting Information, one recognizes that the distortions of two different

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SCHEME 2: Four Possible Pathways of the Inner-Hydrogen Migrationa

a 1, R ) H; 2, R ) OMe; 3, R ) Me; 4, R ) NO2. The hydrogen migration of the pathways A and B along the clockwise direction, in contrary, the hydrogen migration of the pathways C and D in the counterclockwise direction.

Figure 4. Top view of the calculated structure of 4CISA (cis tautomer of 2-nitro-5,10,15,20-tetraphenylporphyrin).

transition states TS1 and TS2 are quite similar in appearance. The overall dominating distortion modes for all investigated transition state structures are the in-plane distortion modes m-str (B2g) and bre (A1g).41 However, compared to the m-str (B2g) distortion, the contributions of the bre (A1g) distortion to the structures discussed are rather small. Similar to the local minima cis structures, the steric strain also results in some ruf out-ofplane distortion (see Figure 3 and Table S1), which is the strongest in the 2-nitro-5,10,15,20-tetraphenylporphyrin (see Figure 6).

Figure 5. Calculated potential energy surface of 4 at the B3LYP/631G* level. Energies include ZPE corrections. Curves A-D represent four possible pathways of the hydrogen migration.

4. Minimum Pathway. Table 1 summarizes the relative energies (including Zero-Point-Corrected) of the cis and TS structures with respect to the corresponding trans tautomers for compounds 1-4. A comparison of the energies of the two trans tautomers of porphyrin 2 (R ) OMe) reveals the trans a is (0.8 kcal/mol) lower in energy than the trans b. The reverse situation is found in porphyrin 3 (R ) Me). Namely when R ) OMe, NO2, the dominant trans tautomer is a, where R lies on the isolated double bond. In contrast, when R ) Me, the major trans tautomer is b, where R lies on the aromatic delocalization pathway.28

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Lu et al.

TABLE 1: Relative Energies (Including Zero-Point-Corrected) for the Trans, Cis, and Transition State (TS) Structures on the Minimum Energy Pathway (MEP) Relevant to the Inner-Hydrogen Migrationa HF 6-31+(d,p) 1

2

3

4

a

B3LYP 6-31+G(d, p)

BPW91 6-31+G(d,p)

structure

rel. 0

rel. 1

B3LYP 6-31G(d) rel. 1 + ZPE

rel. 2

rel. 3

1Trans a 1TS1A 1CISA 1TS2A 1Trans b 2Trans a 2TS1A 2CISA 2TS2A 2Trans b 3Trans a 3TS1A 3CISA 3TS2A 3Trans b 4Trans a 4TS1A 4CISA 4TS2A 4Trans b

0.0 27.1 10.6 27.1 0.0 0.0 26.7 10.1 27.0 0.6 0.3 26.2 10.8 25.7 0.0 0 25.4 9.1 26.7 2.2

0.0 17.9 8.7 17.9 0.0 0.0 17.5 9.0 18.1 0.8 0.7 17.8 10.8 17.5 0.0 0.0 17.5 7.7 18.6 2.6

0.0 14.8 8.2 14.8 0.0 0.0 14.5 8.4 15.1 0.8 0.6 14.6 10.4 14.2 0.0 0.0 14.4 7.5 15.4 2.4

0.0 16.9 8.6 16.9 0.0 0.0 16.4 8.6 17.0 0.9 0.7 16.7 8.4 16.3 0.0 0.0 16.2 7.5 17.2 2.5

0.0 15.7 8.4 15.7 0.0 0.0 15.2 8.6 15.8 0.9 0.8 15.6 8.3 15.3 0.0 0.0 15.2 7.5 16.3 2.6

Relative energies in kcal/mol; the global minima trans-porphyrins are taken as the energy zero.

Figure 6. Side view of the calculated structures of (a) 2TS2A, (b) 3TS2A, and (c) 4TS2A.

Each of the possible asynchronous paths A-D includes two transition states that are energetically different. The TS1 and TS2 were calculated to be higher in energy than the respective trans tautomers. The calculated relative energies also show that all calculated transition state structures (TS) are energetically higher than the cis tautomers (CIS) (see Table 1). In order to convert A to B, the transition state of highest energy for the relevant pathway is significant and must be compared with the corresponding transition states of the other pathways. Thus, the transition state of the lowest energy of four ones obtained determines the preferred asynchronous pathway A-D (see Figure 5).41 Following this rationale, for porphyrins 2, 3, and 4, the asynchronous pathways A and B are much more preferred than C and D. Namely, the hydrogen migration in clockwise is much more preferred than counterclockwise direction. When in clockwise direction, the trans-cis or cis-trans barrier of porphyrins, including the significant zero-point correction, is 7.5-10.4 kcal/mol at the B3LYP/6-31G (d) level, which is smaller than the experimental value. Crossley et al. reported that the classical barrier height is 10.6-11.4 kcal/mol.42

Moreover, for porphyrin 1, the trans-cis barrier agrees quite well with the calculated value (8.2 kcal/mol) of the free base porphyrin,35,39 which may reflect the fact that the N-H migration mechanisms of the 5,10,15,20-tetraphenylporphyrin and the free base porphyrin are very similar. To get a more reliable estimation of the barrier height, single-point energy calculations were performed at the optimized B3LYP/6-31G (d) geometries. It is worth pointing out that these are the first high-quality ab initio estimates of the energy difference between cis- and transβ-substituted 5,10,15,20-tetraphenylporphyrin. Geometry optimizations of tetrapyrroles at the HF level result in unrealistic structures with localized double bonds. However, if realistic optimized structures are available from optimizations at correlated levels (e.g., from B3LYP calculations, as in this work), then single-point Hartree-Fock calculations yield reasonable results, for quantities such as ionization potentials, energy differences between tautomers, etc.33,56,57 The trans-cis or cis-trans barrier of porphyrins is 9.1-10.8 kcal/mol at the HF/ 6-31G+(d, p) level; these values agree closely with experimental estimates for the classical barrier height of 10.6-11.4 kcal/mol.42 The calculated DFT trans-cis or cis-trans energy difference is essentially the same with both methods (B3LYP, BPW91); this also agrees closely with the MP2 value, 8.9 kcal/mol.35 It is clear from this table that regardless of the method and basis set used, the barrier height for migration in β-substituted porphyrins is essentially the same as those observed in symmetrical porphyrins. This suggests that the mechanism of proton migration is similar in both symmetrical and asymmetrical systems. All transition states and cis tautomers involved in these pathways reveal strong m-str (B2g, in-planar), weaker sad (B2u, out-of-plane) contributions. Clearly, the change from the transtautomers to the transition states (TS1A and TS2A, TS1B and TS2B) via m-str (B2g), sad (B2u) distortion requires less energy than the change to the other transition states (TS1C and TS2C, TS1D and TS2D). This can be understood by considering that the β-substituent reduces the symmetry from D2h for the ideal planar 5,10,15,20-tetraphenylporphyrin, and the displacements occur along several or all lowest-frequency normal coordinates.

N-H Migration in Asymmetrical Metal-Free Porphyrins Still, the sad (out-of-plane) and m-str (in-plane) deformations are energetically favored to relieve steric strain most efficiently.37 5. AIM Analysis along the Hydrogen Migration Pathway. The theory of Atoms in Molecules (AIM) developed by Bader derives chemically relevant information from the topology of electron density in a molecule.58-60 In particular, it describes chemical bonding in terms of bond critical points (BCPs) and bond paths and provides an unambiguous scheme of partitioning molecules into atoms (atomic basins). The most commonly used measure is the Laplacian of electron density ∇2Fb in conjunction with the Fb value at a bond critical point. In general, Fb is greater than 0.20 au in shared (covalent) bonding and less than 0.10 au in a closed-shell interaction (for example ionic, van der Waals, hydrogen, dihydrogen, H-H bonding, etc.). In covalent bonding the two negative curvatures are dominant and ∇2Fb < 0, for example, ∇2Fb ) -1.1 au for a typical C-H bond. In contrast, in closed-shell bonding, for example ionic, hydrogen-bonding or van der Walls interactions, the interaction is characterized by a depletion of density in the region of contact of the two atoms and ∇2Fb > 0.61 Koch and Popelier have introduced eight criteria based on the theory of AIM to characterize hydrogen bonds.62,63 Three of them are most often applied. The electron density and its Laplacian for the H · · · Y contact within the X-H · · · Y H-bond should have a relatively high value. Both parameters for closed-shell interactions as H-bonds are positive and should be within the following ranges: 0.002-0.04 au for the electron density and 0.02-0.15 au for its Laplacian. Covalency is not expected to dominate homonuclear N · · · HN/N-H · · · N intramolecular resonance-assisted H-bonds (RAHBs), in particular of the double trans tautomers. AIM methods, however, can still be of great help in the present case for assessing the variations in chemical-bond nature occurring along the hydrogen migration pathway. Present results illustrated in Figure 7 provide an example of N · · · H-N/N-H · · · N RAHBs. The plots show the strong symmetrization undergone by the H-bonds when going from one trans tautomer to another through a cis tautomer. According to the criteria, N · · · H-N/N-H · · · N RAHBs are to be classified as rather weak closed-shell interactions. They are characterized by low Fb values in the range 0.013-0.030 au and by slightly positive ∇2Fb values of 0.045-0.094 au (values to be compared with those of the covalent N-H bonds of 0.326 < Fb < 0.337 au and -1.85 < ∇2Fb < -0.202 au, see Table S2 in the Supporting Information). It can be seen that H-bonds have partially covalent nature in all investigated structure.64 From above results, the conclusion can be inferred as follows: When the full range of interactions including the N-H bonds is considered, the variation of the laplacian of Fbat BCPs reveals a continuous transition from the weak hydrogen bonding to the covalent bonding situation. Conclusions Depending on substitution for the asynchronous pathway, four different asynchronous N-H migration pathways have been studied by DFT calculations. Irrespective of the nature of the substituent, for porphyrins 2 (R ) OMe), 3 (R ) Me), and 4 (R ) NO2), the asynchronous pathways A and B are much more preferred than C and D. Namely, the clockwise hydrogen migration is much more preferred than the counterclockwise direction. The theory result is in agreement with experimental kinetic isotope effect data.42 In addition, the macrocyclic conformations obtained were analyzed using the NSD method. The corresponding TS structures exhibited significant m-str and sad distortion, which existed in the lowest-energy TS of 2, 3, and 4. The important role of the m-str and sad distortion can also be found in the corresponding cis-structures.

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Figure 7. H-bond critical-point parameters. (a) Fb (au) and (b) ∇2Fb (au) plotted against the reaction coordinate as calculated by AIM analysis of DFT-optimized stationary points for 2 (2-methoxy-5,10,15,20tetraphenylporphyrin). For full details, see the Supporting Information.

In a more general sense, it can be concluded that the N-H migration studied shows a strong interplay between the in-plane m-str and the out-of-plane sad distortion. In-plane stretching (m-str), occurring in all cis and TS conformations of the porphyrins 1-4, may lead to contributions of the sad mode. In other words, the steric repulsion of the β-substituent group and the adjacent benzene ring, which is based on the m-str in-plane distortion, induces the saddling of the macrocycle. The tautomeric trans-trans system of porphyrins has turned out to be an almost ideal benchmark for the study of homonuclear N · · · H-N/N-H · · · N intramolecular resonance-assisted H-bonds (RAHBs). The pathway of the hydrogen migration can be correlated with topological properties, local kinetic and potential energy densities, interpenetrations of van der Waals spheres, and interpenetrations of CPs with van der Waals spheres. When the full range of interactions including the N-H bonds is considered, the variation of the laplacian of Fb at BCPs reveals a continuous transition from the weak hydrogen bonding to the covalent bonding situation. Acknowledgment. This work was supported by the National Natural Science Foundation of China (No. 20875077, No. 20775060, No. 20927004, and No. 21005063), and the Natural

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