J. Phys. Chem. 1995, 99, 1073-1075
1073
Structure and Stability of &Porphyrin Abhik Ghosh* and Jan Almliifx Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55415 Received: October 26, 1994@
Ab initio Hartree-Fock and second-order Moller-Plesset perturbation theory (MP2) calculations have been performed on the cis tautomer of porphyrin, an intermediate in the process of N-H tautomerism of free base porphyrin. According to our best estimate (MP2), cis-porphyrin is higher in energy than the trans tautomer by about -7.6 kcaymol. The structure of cis-porphyrin exhibits no significant nonplanarity and differs from that of trans-porphyrin mainly in the internal bond angles of the central C12N4 ring.
It is now generally agreed that the N-H tautomerism of free base porphyrins occurs in a stepwise manner, proceeding via transient cis-porphyrin intermediates which quickly tunnel to the trans The proton migration is also believed to be strongly coupled to deformation of the porphyrin skeleton. The complexity of the process has so far precluded a thorough understanding of its dynamics. In particular, knowledge about the portion of the potential energy surface that includes the metastable cis tautomer would be valuable. The following are some of the relevant questions: How does a cis configuration of the central protons affect the skeletal geometry of porphyrin? Does the proximity of central protons in cis-porphyrin result in significant nonplanarity of the skeleton? Is there any significant electronic difference between the cis and trans tautomers of porphyrin? What is the relative stability of the cis and trans tautomers? A number of semiempirical theoretical studies on the molecular geometry of free base porphyrin, using such Hamiltonians as Q C F F / P ~spin-restricted ,~ AMl,5 etc., have predicted a Cz, symmetric structure for the ground state of trans-porphyrin, with the Cz axis coinciding with the N-I+ .H-N vector. Spinunrestricted AM1 optimizations5 did lead to a Dzh symmetric geometry of porphyrin but predicted (unrealistic) nonzero a and /3 spin populations on alternate carbon atoms of the free base porphyrin molecule. Even at the ab initio spin-restricted Hartree-Fock level, geometry optimizations of trans-porphyrin result in unrealistic CzVstructures with alternating single and double These problems are due to a lack of inclusion of electron correlation effects in the methods employed. Second-order Moller-Plesset perturbation theory and density functional theory result in D2h symmetric structures of free base porphyrin, in agreement with experiment.8 This rather long history of confusion in theoretical studies on the structure of porphyrin prompted us to choose fairly high-quality methods and basis sets in this work.g The structures of cis- and trans-porphyrin were optimized with the density functional program DMOL'O using the local exchange-correlation potential due to von Barth and Hedin' and a numerical double-c plus polarization ("DNP")basis set. Only a C2 (as opposed to CzV) symmetry constraint was employed to allow for possible out-of-plane distortions of the macrocycle in cis-porphyrin. A DZh constraint was used for trans-porphyrin.6 Ab initio Hartree-Fock (HF) and secondorder Mgller-Plesset perturbation theory (MP2) calculations were performed on the LDF optimized structures using the direct
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'
@Abstractpublished in Advance ACS Abstracrs, January 15, 1995.
electronic structure code DISC0,12 which obviates extensive storage of electron repulsion integrals. The ab initio calculations used generally contracted basis sets of double-l; plus polarization quality: (6s3pld)/[3s2pld] for C and N and (3slp)/[2slp] for ~.13,14
The calculated geometries of cis- and trans-porphyrin are shown in Figure 1. We have previously established that the structure of the ground state of trans-porphyrin has perfect or near-perfect D2h symmetry.6 The optimization of cis-porphyrin also resulted in a perfectly planar geometry with the highest possible symmetry (CzV). The following are some of the highlights of the optimized structures. The bond lengths in the optimized LDF structures of cis- and trans-porphyrin are very similar. The C-C and C-N bond lengths in both tautomers are approximately in the order CaCg (1.42-1.44 A) > Ca-Cmeso (1.38-1.39 A) > CB-CB w Ca-N (1.36-1.37 A), Note that the Ca-C, bonds are rather long, which is a characteristic structural feature of porphyrins and hydroporphyrin~.'~The N-H bond distances of 1.07 A in cis-porphyrin are significantly longer than those in transporphyrin, which are about 1.03 A, presumably reflecting a slight weakening of these bonds in the cis tautomer. The bond angles within the pyrrole rings as well as the CgCg-Hg angles are very similar between cis- and trans-porphyrin. In both cis- and trans-porphyrin, the Ca-N-Ca angles are significantly wider in the N-protonated pyrrole rings (-1 10') than in the N-unprotonated rings (-105'). This structural feature has been observed in many crystal structures of porphyrins and hydroporphyrin~~~'~ 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. The most significant differences between the skeletal geometries of cis- and trans-porphyrin are in the bond angles within the central 16-membered C12N4 rings. The DZh symmetry of trans-porphyrin dictates that all four Ca-Cmeso-Ca angles are equal, each angle being -127.6 A. Similarly, the Ca-N-H angles in trans-porphyrin are equal (-125"). The two symmetry-distinct types of N-Ca-CmeSo angles in trans-porphyrin are also nearly equal (-125'). In contrast, for cis-porphyrin, the Ca-Cmeso-Ca angle between the two N-protonated pyrrole rings and that between the two N-unprotonated pyrrole rings are each about -130", which is significantly wider than CaCmeso-Ca angles of -123' between a pair of adjacent Nprotonated and N-unprotonated pyrrole rings. In another difference from trans-porphyrin, four out of eight N-Ca-Cmeso angles in cis-porphyrin are significantly wider (-127'- 129")
0022-3654/95/2099-1073$09.00/0 0 1995 American Chemical Society
Letters
1074 J. Phys. Chem., Vol. 99, No. 4, 1995 H
105.7"
H
2L -
H
H
H
H
106.7"
cis
trans
Figure 1. Optimized LDFDNP geometries of cis- and trans-porphyrin. Intemuclear distances and angles are in angstroms and degrees, respectively.
than the other four (-122"-123"). In other words, the cisporphyrin 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 C,-N-H angles (-135" and 115') subtended at each of the two protonated central nitrogens of cis-porphyrin. These differences in bond angles between the central C12N4 rings of cis- and trans-porphyrin 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 cis-poThyrin, the distance between two protonated nitrogens is -3.18 A, and that between two unprotonated nitrogens is 3.09 A. In contrast, the nitrogen atoms of an adjacent pair of N-protonated and N-unprotonated pyrrole rings of cis-porphyrin are separated by only 2.65 A. In trans-porphyrin, the nitrogen atoms of a pair of adjacent pyrrole rings are separated by 2.91 A. Obviously, these differences in inter-nitrogen separations between the two tautomers stem from the response of the C12N4 ring to better accommodate the closely spaced imino hydrogens in cisporphyrin. However, the energy cost due to this steric repulsion must be quite modest; otherwise, cis-porphyrin would have been significantly buckled. Our calculated HF orbital energies of the nitrogen 1s and highest occupied valence orbitals are nearly identical for cisand trans-porphyrin." Using semiempirical CNDO/S calculations, Kuzmitsky and Solovyov calculated nearly identical singlet-singlet transition energies and oscillator strengths of the two tautomers.za This suggests that neither steric nor electronic factors should result in a large energy difference between the cis and trans tautomers of porphyrin, which is confirmed by explicit computed results: cis-porphyrin is higher in energy than the trans isomer by 7.0, 10.6, and 7.6 kcal/mol at the LDF, HF, and MP2 levels, respectively. It is worth pointing out that these are the first high-quality ab initio estimates of the energy difference between cis- and trunsporphyrin. Geometry optimizations of tetrapyrroles at the HF level result in unrealistic structures with localized double bonds.6
However, if realistic optimized structures are available from optimizations at correlated levels (e.g., from LDF 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. The MP2 results, which are presumably the most reliable, are in good agreement with an experimental estimate of -4.8-5.6 kcal/mol for the energy difference between the two porphyrin tautomers.3a In view of the modest magnitude of our calculated energy difference between cis- and trans-porphyrin, it is possible that the cis tautomer may be the energetically preferred structure for certain substitution patterns of porphyrins.'* Overall, our results provide insights into the structural changes that take place in the course of N-H tautomerism of free base porphyrin. Steric repulsion between the central protons of cisporphyrin results in considerable deformations of the bond angles within the central C12N4 ring but is not severe enough to induce any significant buckling of the porphyrin macrocycle. Our best estimate of the energy difference between cis- and trans-porphyrin is about 7-8 kcal/mol.
References and Notes (1) For extensive lists of references on the mechanism of N-H tautomerism in free base porphyrins, see: Braun, J.; Schlabach, M.; Wehrle, B.; Kocher. M.; Vogel, E.; Limbach, H.-H. J . Am. Chem. SOC. 1994, 116. 6593. (2) For theoretical evidence in favor of a stepwise mechanism for the double proton transfer, see: (a) Kuzmitsky, V. A,; Solovyov, K. N. J . Mol. Strucr. 1980, 65, 219. (b) Sarai, A. J . Chem. Phys. 1982, 76, 5554. (c) Sarai, A. J . Chem. Phys. 1984, 80, 5431. (d) Merz, K. M.; Reynolds, C. H. J . Chem. Soc., Chem. Commun. 1988,90. (e) Smedarchina, Z.; Siebrand, W.; Zerbetto, F. Chem. Phys. 1989, 136, 285. (3) For experimental evidence in favor of a stepwise mechanism for the double proton transfer, see: (a) Butenhoff, T.; Moore. C. B. J . Am. Chem. SOC. 1988, 110, 8336. (b) Butenhoff, T.; Chuck, R.; Limbach. H.H.; Moore, C. B. J . Phys. Chem. 1990, 94, 7847. (4) Zerbetto, F.; Zgierski, M. Z.; Orlandi, G. Chem. Phys. Lett. 1987, 139, 401. (5) Reynolds, C. H. J . Org. Chem. 1988, 53, 6061. (6) For ab inirio geometry optimizations of trans-porphyrin at the HF, MP2, and LDF levels, see: Almlof, J.; Fischer, T. H.; Gassman, P. G.; Ghosh, A.; Haser, M. J . Phys. Chem. 1993, 97. 10964. (7) Foresman, J. B.; Head-Gordon, M.; Pople, J. A,; Frisch, M. J. J . Phys. Chem. 1992. 96, 135.
Letters (8) For crystallographic studies on unsubstituted porphyrin, see: (a) Chen, B. M. L.; Tulinsky, A. J. Am. Chem. SOC.1972, 94, 4144. (b) Tulinsky, A. Ann. N.Y. Acad. Sci. 1973, 206, 47. (9) For high-quality a6 initio calculations on porphyrins, see e.g. (a) Ghosh, A.; Almlof, J.; Gassman, P. G. Chem. Phys. Lett. 1991, 186, 113. (b) Gassman, P. G.; Ghosh, A.; Almlof, J. J . Am. Chem. SOC.1992, 114, 9990. (c) Ghosh, A,; Almlof, J. Chem. Phys. Lett. 1993, 213, 519. (d) Ghosh, A.; Gassman, P. G.; Almlof, J. J . Am. Chem. SOC.1994,116, 1932. (e) Merchh, M.; Orti, E.; Roos, B. Chem. Phys. Lett. 1994, 226, 27. ( f ) Ghosh, A. J. Phys. Chem. 1994,98, 11004. (g) Ghosh, A,; Fitzgerald, J.; Gassman, P. G.; Almlof, J. Inorg. Chem. 1994, 33, 6057. (h) Merchh, M.; Orti, E.; Roos, B. Chem. Phys. Lett. 1994, 221, 136. (10) Delley, B. J . Chem. Phys. 1990, 92, 508. (11) von Barth, U.; Hedin, L. J . Phys. C 1972, 5, 1629. (12) (a) Almlof, J.; Faegri, K.; Feyereisen, M. W. F.; Korsell, K.; DISCO, a direct ab initio code. (b) Direct SCF: Almlof, J.; Faegri, K.; Korsell, K. J . Comput. Chem. 1982, 3, 385. (c) Direct MP2: Saebg, S.; Almlof, J. Chem. Phys. Lett. 1989,154, 521. (d) Almlof, J.; Taylor, P. R.In Advanced Theories and Computational Approaches to the Electronic Structure of Molecules; NATO AS1 Ser., Ser. C, 133; Reidel: Dordrecht, 1984; p 107. (e) Almlof, J.; Faegri, K. F., Jr. In Sey-Consistent Field: Theory and Applications; Elsevier: Amsterdam, 1990; p 195. (13) The nonpolarization parts of the basis sets were obtained from: van Duijneveldt, F. B. ZBM Res. Rep. 1971,RJ945. The hydrogen exponents were multiplied by a scaling factor of 1.44. For all basis sets, the outermost
J. Phys. Chem., Vol. 99, No. 4, 1995 1075 primitives were uncontracted so that they could constitute basis functions on their own. (14) The polarization d exponents for C and N were obtained from: Roos, B.; Siegbahn, P. Theor. Chim. Acta 1970, 17, 199. A polarization p exponent of 0.789 was used for H. (15) Barkigia, K. M.; Fajer, J. In The Photosynthetic Reaction Center; Academic Press: New York, 1993; Vol. 2, p 513. (16) For selected crystallographic studies of chlorins, see: (a) Hoppe, V. W.; Will, G.; Gassmann, J.; Weichselgartner, H. Z. Kristallogr. 1969, 128, 18. (b) Pelter, A.; Ballantine, J. A.; Femto, V.; Jaccarini, V.; Psaila, A. F.; Schembri, P. 3. J. Chem. SOC.,Chem. Commun. 1976,999. (c) Pelter, A,; Ballantine, J. A.; Murray-Rust, P.; Femto, V.; Psaila, A. F. Tetrahedron Lett. 1978,2017. (d) Barkigia, K. M.; Chang, C. K.; Fajer, J. J . Am. Chem. SOC.1991,113,7445. (e) Barkigia, K. M.; Fajer, J.; Smith, K. M.; Williams, G. J. B. J . Am. Chem. SOC.1981, 103, 5890. ( f ) Senge, M. 0.;Hope, H.; Smith, K. M. J. Chem. SOC.,Perkin Trans. 1993, 2, 11. (17) For selected HF/DZP orbital energies for an optimized geometry of trans-porphyrin, see Table 1 in ref 9d. (18) Zayats, V. Ya.; Pinchuk, V. M.; Lobanov, V. V. Teor. Eksp. Khim. 1988,24,335; Theor. Exp. Chem. 1988,24,324. This paper also suggests that the cis tautomer may be energetically preferred for certain asymmetrically substitutedporphyrins. However, the theoretical methods used in this work are not accurate enough to definitively support this prediction. JP9428810
