A density functional theory study on the porphyrin isomers: effect of meso-bridge length, relative stabilities, cis - tran s isomerism

B3LYP/6-311+G** calculations are employed to study the structures, stabilities of 1,2 ( syn ) and the 1,3 ( anti ) tautomeric forms of porphyrin isomers with varying meso-bridge lengths. A total of 46 structures obtained by considering the geometrical isomers of 1,2 ( syn ) and the 1,3 ( anti ) tautomeric forms, 44 were characterized as distinct minima on potential energy surface. Among the anti and syn tautomeric form the porphycene isomer 4a and 4a ′ is computed to be the most stable with a strong intramolecular hydrogen bonding. A –(CH) 2 – linker in Z form with significant π -delocalization and the E form isomers are somewhat distorted into bowl-like structure in order to avoid the steric repulsion between the inner protons. In the isomers with trimethine interpyrrole linker, the E forms 7b and 7b ′ are having lower energy than the Z form due to the unstrained bond angles in these isomers and the Z form is destabilized by severe bond angle. In isomer [4.0.0.0], which has connectivity with the maximum possible bipyrrolic, linkage Z isomer is having high energy this is due to possibly strained bonds that are directly connected to the pyrrole rings.


Introduction
The study of porphyrins and related compounds has been developed into a subject of interdisciplinary interest due to their importance and relevance spanning a range of fields such as chemistry, biology and medicine. 1,2,3Porphyrins with their extended π-electron networks and exhibit high stability and have displayed applications in advanced materials as components in organic metals and in photodynamic therapy in the treatment of cancer and dermotological diseases. 3The biological significance and the potential technological applications of porphyrins and related isomers are traced to their unique structural features. 4,5,6ecent successes in the syntheses of porphyrin isomers have opened up a new direction in porphyrin chemistry.The research groups of Vogel, Sessler, Furuta and others have synthesized a wide variety of porphyrin analogues. 7,8,9Many of the porphyrins are of interest as novel ligands for transition metals, and some have potential practical applications. 3Porphycenes, the first porphyrin isomers to be synthesized show promise as drugs in photodynamic cancer therapy. 10tructural variants such as ring or bridge extended, reshuffled, 11,12 inverted 13 , N-and C-fused 14 , contracted and core-modified porphyrins 15 have been synthesized and they continue to exhibit novel physico-chemical properties.Synthetically this endeavor is challenging which is compounded by the fact that these structural variations may lead to configurational isomers.Their relatively large molecular sizes, symmetry, rich light absorption and emission properties have triggered meaningful interplay between theory and experiment. 16,17,18,19 t has been observed that the properties of porphyrin isomers such as, hemiporphycene [2.1.1.0],porphycene [2.0.2.0], isoporphycene [3.0.1.0], 7,12,16corrphycene [2.1.0.1], 8 are akin to those of porphyrin especially in their ability to form a wide range of stable complexes. 20,21,22,23,24u et al. carried out density functional calculations using both the BLYP/3-21G and BLYP/6-31G** methods on free-base porphyrin and its possible isomers with an N 4 -metal coordination core. 20Ghosh et al. examined whether tetrapyrrolic isomers can accommodate trans double bonds. 18while these studies addressed some important issues on the stability ordering of the porphyrin isomers, the structural and stabilities of various other possible porphyrin isomers were not considered.Considering the importance of the understanding the relative stability of the porphyrin isomers, we would like to explore the causative reasons such as angle strain, internal hydrogen bonding, inner proton repulsion, meso bridege length, cis-trans isomerism etc. 20,21,25 In this present study we concentrated particularly on tetrapyrrolic isomers of porphyrin isomers with N 4 cores.Two types of tautomers (a) anti (the imino protons on the I and III ring, Scheme 1); (b) syn (imino protons at II and I ring, Scheme 2) were taken into consideration.In this study, eight classes, depending on the nature of bridging, were considered, viz.freebase porphyrin [1.1.1.1],hemiporphycene

Scheme 2. Continued
Computational details B3LYP/6-31G calculations on all the structures considered in the study were optimized with planar geometries and the resultant stationary points were subjected to frequency calculations.Frequency calculations reveal that most of the planar structures do not correspond to minima.In such cases, following the normal modes of the imaginary frequencies, the minimum energy structures were obtained which display significant out-of-plane distortions.Many of these nonplanar minimum energy structures are highly puckered and in some cases the pyrrolic rings got inverted.This show that the structures have very high strain in the planar geometries, so we intended to calculate the energy difference between the planar structure and the puckered nonplanar structures and reported as distortion energies.The cavity size also large for the puckered structures.The EE isomers are more puckered compared to the EZ isomers.All the minima are characterized by frequencies calculations, which shows all real frequencies.Single point calculations were done using 6-311+G** basis set on B3LYP/6-31G optimized geometries.6-311+G** basis set is a triple ζ basis set with polarization function on the heavy atoms and hydrogens as well as diffuse functions on the heavy atoms.The choice of using a B3LYP/6-31G geometries is entirely due to the economic reasons.As the previous studies 6, [18][19][20] indicate that a better quality basis set is required to get better estimates, single point calculations were done at higher level of theory.All the calculations were performed using Gaussian 98 suite of programs. 26

Results and Discussion
The different types of isomers are possible by varying methine bridges in addition to the parent porphyrin moiety.Considering all the possible geometric isomers, a total of 46 structures of 1,3 (anti) and 1,2 (syn) tautomers were considered in the present study, are given in Schemes 1 and 2. The relative energies were calculated from the energy difference between porphyrin isomer 1 in anti isomers and porphyrin isomer 1′ in syn isomers.

Anti and syn tautomeric forms
The relative energies, enthalpies, Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) energies, distortion energies of anti tautomers of porphyrin isomers obtained at B3LYP level using the 6-31G and 6-311+G** basis sets are given in Table 1.The B3LYP/6-31G optimized geometries of anti tautomeric structures and the relative energies with enthalpy correction are given in Figure 1.The variation in relative energies of anti (1,3) and syn (1,2) tautomeric porphyrin isomers obtained at B3LYP/6-31G and 6-311+G** levels of theory are given in Figure 3. Considering all the possible cis-trans isomers of 1,3 (anti) and 1,2 (syn) tautomers totally 46 porphyrin isomers are resulted.Among 46 isomers 8c collapsed to the EZ isomer 8a and Z isomer 6a′ collapsed to the anti tautomeric structure 6a due to closely presented imido protons.Thus, the total number of isomers reduced to 44.Porphyrin isomer 4a is the most stable isomeric form.The porphyrin isomer 4a is -0.4 kcal/mol more stable than the porphyrin isomer 1.  Isomers 5a, 6a, 7a and 8a are much less stable than porphyrin isomer 4a and 1.In hemiporphycenes [2.1.1.0],the Z isomer 2a is more stable than the E isomers 2b and 2c.Isomer 2c is more stable than 2b by 7 kcla/mol and the isomer 2b undergoes ring inversion due to a highly repulsive interaction between tautomeric carbons and inner proton repulsion.In corrphycenes [2.1.0.1], the Z isomer 3a is more stable than the E isomers 3b and 3c.Isomers 3b and 3c are having energy difference around 0.6 kcal/mol.In porphycenes [2.0.2.0], three different isomeric forms are possible: Z form (4a), EZ form (4b and 4c) and EE form (4d and 4e).Among porphycene isomers, 4a is most stable due to strong hydrogen bonding.In EZ form and EE forms, the EZ form isomers 4b and 4c more stable than the EE form isomers 4d and 4e by 20-30 kcal/mol.The destabilizations of these isomers are traced due to the inner proton repulsion between the imino proton and proton present in the methine bridge.In isomer [2.2.0.0], like porphycene isomers, three different types of isomers are possible for these isomers.In EZ form and EE forms, the EZ form isomers 5b and 5c more stable than the EE form isomers 5d and 5e this is due to the presence of inner CH group.In isomers [3.0.1.0],the Z isomer is strongly favored energetically over the E isomer.The E forms 7b and 7b′ are having lower energy than the Z form due to the unstrained bond angles in these isomers.In isomers [4.0.0.0] which has connectivity with the maximum possible bipyrrolic linkages and all the methine bridging groups are placed together, the EZ isomer 8b is having lower energy than the Z form 8a. Attempts to locate the 8c was futile, the structure is collapsing with the isomer 8a.
The relative energies, enthalpies, HOMO and LUMO energies, distortion energies of syn tautomers of porphyrin isomers obtained at B3LYP level using the 6-31G and 6-311+G** basis sets are given in Table 2.The B3LYP/6-31G optimized geometries of anti tautomeric structures and the relative energies with enthalpy correction are given in Figure 2. The variation in relative energies of anti (1,3) and syn (1,2) tautomeric porphyrin isomers obtained at B3LYP/6-31G and 6-311+G** levels of theory are given in Figure 2. In the syn tautomeric structures of porphyrin isomer, 4a′ is the most stable isomeric form and is about 6 kcal/mol more stable than porphyrin due to its exceptional strong hydrogen bonding.Isomers 5a′, 7a′ and 8a′ are much less stable than porphyrin isomer 1′.Similarly like anti porphyrin isomers, hemiporphycenes [2.1.1.0]and corrphycenes [2.1.0.1], the Z isomer 2a and 3a are more stable than the E isomers 2b and 3b this is due to the inner proton repulsion.In porphycenes [2.0.2.0] and [2.2.0.0], like anti porphyrin isomers there are three different isomeric forms.Isomer 4a′ is most stable than all other porphycene isomers.This is due to strong hydrogen bonding.In EZ form and EE forms, the EZ form isomers 4b′ and 4c′ more stable than the EE form isomers 4d′ and 4e′.The Z isomer 5a is more stable than the EZ isomers 5b and 5c and EE isomer 5d and 5e.In EZ form and EE forms, the EZ form isomers 5b and 5c more stable than the EE form isomers 5d and 5e this is due to the presence of inner CH group.
In isomers [3.0.1.0],attempts to locate the planar form of 6a′ was futile, the structure is collapsing with the anti tautomeric isomer 6a.In [3.1.0.0], the E form is more stable than the Z forms.The E form 7b′ are having lower energy than the Z form due to less steric strain in these isomers.In isomers [4.0.0.0], which have connectivity with the maximum possible bipyrrolic linkages the EZ, isomer 8b is having lower energy than the Z and EE form 8a and 8c due to less angle strain.Comparison of Table 1 and 2 indicates that the trends in the relative energy ordering of the 1,3 (anti) and 1,2 (syn) tautomeric forms are very similar.

Geometrical isomerism
Except for the porphyrin isomers 1 and 1′ geometrical isomerism is possible for all the isomeric forms considered for the syn and anti isomers.The relative stabilities of the geometrical isomers have attracted the theoreticians and experimentalist.The E and Z form especially affects the metal-binding properties of ligand.The important bond lengths and bond angles for all the anti and syn porphyrin isomers obtained at B3LYP/6-31G optimization are given in Figure 3.
In isomers isoporphycene [3.0.1.0]and [3.1.0.0], one E form and one Z form was considered in both syn and anti tautomers.In isomers [4.0.0.0], which have connectivity with the maximum possible bipyrrolic linkages one Z form, one EZ form and one EE form was considered.In [3.1.0.0] the E forms are more stable than Z forms.The E forms 7b, 7b′ are more stable than the Z forms 7a and 7a′ due to the less angle strain in these isomers.Isomers [4.0.0.0] 8a and 8a′ are computed to be least stable compare to all other Z isomers and EZ isomer 8b and 8b′ favored than Z isomers (8a and 8a′) and EE isomers (8c′), this may be due to less angle strain in the EZ form.In isomers porphycenes [2.0.2.0], [2.2.0.0] the EZ isomers are more stable than the EE isomers in both the anti and syn tautomeric forms.
When a -(CH) 2 -linker is in the Z form, isomers are nearly planar with significant πdelocalization.In contrast, the corresponding E isomers have distorted structures with bowl-like geometries, which are traced due to steric repulsive interactions involving the inner protons.But, [3.1.0.0] the E forms are more stable than the Z forms, indicating higher angle strain in the latter.In isomers [4.0.0.0], which have connectivity with the maximum possible bipyrrolic linkages, Z isomer is computed to be relatively unstable.The variation in number of methine groups drastically alters the stability in these class of compounds.

Angle strain
Next to the hydrogen-bonding interactions, the strained bond angles dictate the relative stability ordering of the porphyrin isomers.All skeletal bond angle for the anti and syn structures are given in Figure 1 and Figure 3 respectively.The lower stability of isomers 5a, 5a′, 6a, 7a, 7a′, 8a and 8a′ in both syn and anti forms may directly traced to the severe angle strain in these isomers.The isomers of types [2.2.0.0], isoporphycenes [3.0.1.0],[3.1.0.0], [4.0.0.0] are destabilized due to the absence of bridging methine groups, which results in the angle strain for the tetrapyrroles and possibly due to the strained bonds that are directly connect to pyrrole rings.Bond angle strain is perhaps the most important factor contributing to the high energies in Z form in all [3.0.1.0],[4.0.0.0] isomers.The E isomers 7b and 7b′ are having lower energy than the Z form, due to the unstrained bond angles in these isomers and the Z form is destabilized by severe bond angle strain in the trimethine interpyrrole linker.Isomers 8a and 8c′ are computed to be the least stable among the [4.0.0.0.] isomers.The EZ isomers (8b and 8b′) appear to be much less strained and importantly one of the hydrogens of the methine chain involve in hydrogen bond with the nitrogens.

Distortion energies
The π-delocalization and planarity has been treated as important factors to impart stability to porphyrins.However, as the planar form of a large number of isomers are not minima on the potential energy hypersurface, the puckering is often related to the strain in the planar form.We termed the energy difference between the planar structure and the corresponding minimum energy structure as the distortion energy.The distortion energies, which quantifies the amount strain in the planar geometry of the isomers, of the anti and syn porphyrin isomers are given in Table 1 and Table 2.In anti porphyrin isomers all the Z form isomers except 5a and 8a are planar.All other isomers have positive distortion energies, indicating that the nonplanar structures are more stable.In syn porphyrin isomers all the Z form isomers except 7a′ and 8a′ are planar.Isomers having positive distortion energies, signifying that nonplanar structures are more stable.The distortion energies are more for the EE form isomers than EZ forms.This is due to the inner proton repulsions in case of EE isomers.

Hydrogen bonding
Porphyrin isomers show some strong hydrogen bonds in most of the structures due to the close proximity of the four nitrogen atoms.In anti porphyrin isomer 1, the N---H--N distance is 2.315 Å and in syn porphyrin isomer 1′ the distance is 1.896 Å (Figure 1 and 3).In anti and syn porphycene isomers 4a and 4a′ features strong hydrogen bonding with H---N distances 1.640 Å and 1.565 Å respectively.Strong hydrogen bonding exists in isomers 6a and 3b.Isomers 3a-3c, 2a′, 3a′, 3b′, 4b′, 4c′, 5a′ and 7b′ shows moderate hydrogen bonding.The difference between the stabilities of corrphycenes (3a-3c and 3a′-3b′) and hemiporphycenes (2a-2c and 2a′-2b′) can also to be traced by ring strain, as hemiporphycene is better hydrogen bonded than corrphycene.In general the syn tautomers have strong hydrogen bonds compare to the corresponding anti tautomers.In stability of all the low energy porphyrin isomers is clearly a manifestation of strong NH---N hydrogen bond resulting in short hydrogen bonding distances.Extremely long and unequal H-N-C angles leads to a high energy isomer.

Central cavity
The four adjacent N-N distances of all the syn and anti porphyrin isomers are given in Tables 3  and 4. The sum of the four N-N distances of the individual isomers may be taken as a measure of the effective cavity sizes of the porphyrin isomers.These measures give a straightforward indication of the cavity size of the porphyrin isomers.The inner protons were not considering when estimating the cavity sizes as normally complexation is invariably associated with displacement of the protons.
The porphyrin isomer 1 is having large cavity size with a square geometry (2.937Å).In corrphycenes, isomers 3b and 3c have large N 3 -N 4 distances 4.123 and 4.151 Å respectively.In isomers 4d, 4e, 5b and 5c the imino proton distances are very large due to more puckering of these isomers.In porphycenes, the isomers with EE form (4d and 4e) have large N 2 -N 3 and N 4 -N 1 distances and isomer 4e has similar N 1 -N 2 and N 3 -N 4 distances.Isomers 5b, 5c and 5d (N 3 -N 4 distance also large) have large N 4 -N 1 distances range from 4.207 to 4.246 Å this is due to the distortion into bowl-like structure in order to avoid the steric repulsion between the inner CH group.Isomers with [3.0.

Conclusions
The present study reports density functional calculations on a series of syn and anti tautomeric forms of porphyrin isomers.The relative energy differences seem to critically depend on the length and position of the meso bridges.The isomers The present computational study touches upon a few important aspects of porphyrin chemistry, such as the relative stabilities of tautomers, geometrical isomers.This study provides a good insight about the geometry, energetics and reactivity of various porphyrin isomers and the perturbations that are caused to these isomers upon shuffling hydrogen positions.The variation in number of methine groups drastically alters the stability in these classes of compounds Several factors, such as angle strain, inner proton repulsion, hydrogen bonding, length of the bridge and the type of geometrical isomerism-E or Z, play important roles in deciding the relative stability ordering of the porphyrin isomers.In -(CH) 2 -linkers the Z forms are more stable than E form due to significant π-delocalization and hydrogen bonding, even in the presence of significant angle strain in it.The E form isomers are distorted into bowl-like structure in order to avoid the steric repulsion between the inner CH group.In trimethine interpyrrole linker E forms are having lower energy than the Z form due to the unstrained bond angles in these isomers.In isomers [4.0.0.0], which have connectivity with the maximum possible bipyrrolic linkages, Z isomer is having high energy this is due to possibly strained bonds that are directly connect to pyrrole rings.

Table 2 .
Relative energies (∆E, in kcal/mol), Enthalpies (∆H, in kcal/mol), HOMO (E HOMO , in eV) and LUMO (E LUMO , in eV) energies and the number of imaginary frequencies (NIMG) of The energy computed by taking the difference between the planar structure and the corresponding minimum energy structure.All these values are in kcal/mol.

Table 4 .
The adjacent N---N distances and imino proton distances (Å) of syn tautomer of porphyrin isomers obtained at B3LYP level using the 6-31G basis set