J. Phys. Chem. 1994, 98, 11878-11884
11878
Rigid Fused Oligoporphyrins as Potential Versatile Molecular Wires. 1. Geometry and Connectivity of 1,4,5,8-Tetraazaanthracene-BridgedSystems T.X. Lii: J. R. Reimers,’tt M. J. Crossleyf and N. S. Hush?$* Department of Physical and Theoretical Chemistry, Department of Organic Chemistry, and Department of Biochemistry, The University of Sydney, N.S.W. 2006, Australia Received: June 7, 1994; In Final Form: August 26, 1994@
We investigate theoretically a class of rigid, fused oligoporphyrin molecules proposed as potential “molecular wires”, composed of substituted and/or chelated porphyrins fused together with conjugated bridging units such as 1,4,5&tetraazaanthracene (TA). Our long-term goal is to investigate the effects of porphyrin or bridge substitution, metal chelation, oxidation state, and related properties on the conductivity and spectroscopic characteristics of these molecules, leading to predictions of systems most likely to have useful molecular electronic potential. Here, the primary aim is to develop an accurate empirical method by which the geometry of an arbitrary oligoporphyrin, extending perhaps over say 50-100 8, in length, can be readily constructed. This is achieved through the semiempirical quantum-chemical study of a set of basic “building blocks”, which may be reliably combined by using a deduced set of rules to predict the structure and relative energy of an arbitrary molecule. The most important effects occur for and about the porphyrin-TA fused bond, and the consequences of this for the degree of n delocalization and hence the interporphyrin communication are discussed. We also consider possible isomerization effects associated with the location of the two inner hydrogens per free base porphin unit, including the height of interconversion barriers. Finally, we consider briefly some effects of porphyrin substitution or chelation on the calculated geometries and bond orders.
1. Introduction Rigid, laterally-bridged porphyrin systems, e.g., bisporphyrin’ and tetrakisporphyrin,2have recently been synthesized, and an approach to a new type of molecular wire based on this quasione-dimensional conjugated oligoporphyrin system has been outlined.2 These molecules have porphyrin units linked via aromatic bridges such as1s2 1,4,5,8-tetraazaanthracene (TA). They are presumed to be planar conjugated molecules. Delocalization is a highly desired property since it would permit these molecules to function as efficient “molecular wires”: conjugated x systems facilitate rapid transfer of information from one end of the wire to the other. One such molecule, a porphyrin tetramer2extending over 56 A, is shown in Figure 1; clearly, the presence per porphyrin unit of four nominally equivalent pyrrole rings, 12 sites for skeletal substitution, and a metal chelation center (with possibly other ligands attached to the metal), as well as the possible existence of multiple porphyrin and/or metal oxidation states, allows for considerable diversity in the oligoporphyrin family, and this is being explored synthetically.’s2 This diversity is attractive not only in that it allows for the possibility of building in extra functionality such as that of a “molecular switch” or a “molecular memory” but also because it allows for the possibility of fine tuning of a molecule in order to meet specific requirements. In order to exploit this diversity, its very extent requires that one is confident that a proposed molecule would display some set of desired properties before it is synthesized. This work is the first part of a long-term project aimed at fulfilling this goal; it concentrates on developing methods for the quick and accurate determination of the structure of arbitrary oligoporphyrins. We consider the molecular electronic properties of the oligoporphyrins elsewhere.
’ Department of Physical and Theoretical Chemistry.
* Department of Organic Chemistry.
8 Department of Biochemistry. @Abstractpublished in Advance ACS Abstracts, October 15, 1994.
The geometry of any oligoporphyrin is yet to be determined experimentally; indeed, even the structure of free base porphin itself‘ is not completely beyond question, as discussed below. While extensive ab inito calculation of this, the simplest porphyrin, has recently been it is currently not feasible to apply such techniques for any bridged or significantlysubstituted porphyrin. We thus employ various semiempirical structural determination methods for small substituted oligoporphyrins, but again their use is currently not feasible for molecules as large as that shown in Figure 1. In order to proceed, we consider initially a model system consisting of fused, unsubstituted free base porphin units; specifically, the (nominally planar and aromatic) molecules considered in this work are shown in Figures 2 and 3 and are named P,,TA,, where n and m are the number of free base porphin (P) and TA units in the molecule, respectively. Figure 2 shows one possible isomer of each molecule in detail, while an abbreviated notation is used in Figure 3, which for many isomers shows explicitly only the relative locations of the TA bridges and the internal hydrogens. While it is in principle possible to synthesize these model (Le., peripherally unsubstituted) molecules and determine their isomerization and their functionality as molecular wires, solubility, stability, and other problems make this unlikely. Results predicted for them are important, however, as often effects of peripheral chemical substitution and chelation can be treated as perturbations. Even these model compounds quickly become too large for semiempirical structural determination, however, and hence we develop an empirical scheme which quickly and accurately determines the structure of an arbitrary oligoporphyrin from the explicitly determined structures of the monoporphyrins PITA, (m = 1-4). Among the criteria which a molecular wire needs to meet,2 the first and the most important one is electron conduction, i.e., the mobility of the electrons in the system, which can be characterized for a conjugated system, according to molecular
0022-365419412098-11878$04.50/00 1994 American Chemical Society
J. Phys. Chem., Vol. 98, No. 46, 1994 11879
Rigid Fused Oligoporphyrins
t
15.7
A
I.
6:
15.7
56
I
15.7
a
A
Figure 1. Typical oligoporphyrin: t h i s linear substituted P4TA3 oligoporphyrin has been synthesized,2 along with other linear and bent structures (see, e.g., ref 2). n
v
the modem bond order convention,8defining the n-bond order bi, as .
b.. = 6.2 I I I I
/I..L
where QV is the element of the n-density matrix for neighboring atoms i andj. By use of this definition, the standard Huckel n-bond order for benzene is 419.
2. Geometry and Bond Orders of Free Base Porphin (PI)
Figure 2. Characteristic isomer of each oligoporphyrin P.TA, considered herein; these aromatic molecules are constrained to be planar.
orbital theory, by the extent of the conjugation or the delocalization of the n-electrons. The latter is in tum related to the n-bond orders and therefore to the lengths of relevant bonds. Herein, we consider the bond orders for our model compounds, determining the extent of the electron delocalization. Possible modulation of the delocalization through the use of ligand or metal substitution is considered briefly. Note that we adopt
2a. Comparison of Hamiltonians Implemented in MOPAC. The Hamiltonians implemented in MOPAC9 are AM1,l0 MIND0/3,11 MNDO,’* and PM3,13 of which AM1 and PM3 are indeed the derivatives or the modified models of MNDO. Historically, AM1 aimed to overcome the problem that MNDO overestimates steric effects and fails to describe hydrogen bonds accurately, while PM3 was reported as a reparameterized version of AM1 and was claimed to be a significant improvement over the original. As the molecules considered herein are fused free base porphin and TA units, the quality of geometry prediction given by a theoretical model for these model systems will largely depend on its quality of the geometry description for the basic
P1TA3
/ I
P3TA2
‘ I
@-E$ o*
0.1
C2v 6 . 6
BONO ORDER
--
0
RANGE
.13+,18 .Y3+.51
.69+.72
= .78+.85
Figure 3. Sketches representing the PM3 optimized structures of various oligoporphyrin isomers with their symmetries and energies relative to the lowest-energy isomer found for each molecule. A ring indicates each porphyrin unit and is overlaid by four shaded rectangles indicating the and 1, respectively). The location of the inner Cp-Cp n-bond order bij (for completely single, aromatic, and double bonds this would be 0, hydrogens on the proton-bearing pyrroles is indicated explicitly, and TA bridges are shown by parallel lines connected to the Cp-Cp rectangles.
Lii et al.
11880 J. Phys. Chem., Vol. 98, No. 46, 1994
TABLE 1: Observed Lengths, in di, for Various Bonds (as Defined in Figure 2) on Proton-Bearing or Proton-Free Pyrrole Rings of Free base Porphin (PI) Obtained from Symmetrized Crystal Data: and the Deviations from Them of Calculated ab Initio MPuDZP2 [4] Bond Lengths, and Da-Constrained Semi-Empirical Bond Lengths." Czvdistortion PM3 deviation from experimental offset splitting proton bearing exptl length order PM3 AM1 MNDO MINDOl3 MF'2/DZP2 length order length order Yes
no
Yes no Yes
no
Yes
no
1.380 1.377 1.431 1.452 1.365 1.345 1.387 1.376
1.402 1.384 1.448 1.468 1.371 1.361 1.391 1.389
0.27 0.35 0.19 0.12 0.70 0.79 0.37 0.39
0.013
0.014 0.001 0.033 0.038 0.016 0.023 0.006 0.018
0.017 -0.003 0.029 0.032 0.017 0.023 0.017 0.030
O.Oo0 -0.010 0.030 0.041 0.013 0.016 0.020 0.030
0.014
0.022
0.022
0.023
0.022 0.007 0.017
0.016 0.006 0.016
0.004
-0.02 -0.03 0.00 0.01 -0.02 -0.01 -0.02
0.00 0.017
0.004 0.003 -0.002 0.004 0.004 -0.003 0.003 0.004
-0.02 0.04 0.03 -0.02 -0.02 0.03 0.03 0.03
0.024 0.101 0.055 0.003 0.042
0.14 0.55 0.27 0.01 0.34
0.073 0.080
0.51 0.55
0.003
0.03
0.062
0.39
a Absolute D z PM3 ~ bond lengths and n-bond orders bo, and the offsets and splittings of these which result when the symmetry is reduced to Czvr are also given. Some root-mean-square (RMS) values obtained by averaging over all bonds are indicated.
structure units. In order to choose one Hamiltonian for the present study, we start with a comparison of geometries calculated by using these Hamiltonians for the basic structure unit, free base porphin PI. The geometry of P1 itself has attracted much research interest for a long time. The first experimental description of the geometry of PI, reported by Webb and F l e i ~ c h e r ' in ~ , ~1965, ~ was followed by a more accurate redetermination several years later by Chen and T ~ l i n s k y .According ~ to their description, a P1 molecule is planar with about k0.02 A deviation from the nuclear least-square plane and possesses either C2h or C2, symmetry with the minor planes bisecting the pyrrole rings. The observed molecular distortion from D2h is quite small, however, and is believed to be due to crystal-packing forces; see ref 15. While infrared and Raman spectra16-21are consistent with a DZh assignment, unfortunately no unambiguous structure is available for this, the simplest porphyrin. Theoretical studies on porphyrin geometry and electronic structure have been undertaken for a long time. It is found that the geometries predicted by spin-restricted Hartree-Fock (RHF) and spin-unrestricted Hartree-Fock (UHF)calculations at the AM1 have different symmetries, the former being C2, and the latter D2h. The UHF calculation of course has the lower energy but it predicts incorrectly that the ground state is triplet in nature. AMl/RHF predicts that the optimized DZh structure is in fact a transition state. Similar results are obtained by using self-consistent-field (SCF) STO-3G ab initio23 calculations. Based on a comprehensive ab initio study at the SCF, MP2, and LDF (local density functional) levels, Almlof at aZ.5 recently demonstrated using the extensive DZP2 basis that at the MP2 and LDF levels, the RHF calculations predict that the geometry of P1 is planar with D2h symmetry. While this result may well persist as the level of the ab initio theory increases, such an extrapolation could possibly prove unreliable. Evidence supporting their result comes indirectly from MP2 calculations7for the rate of inner-hydrogen migration in P1 and directly from Merchh, Orti, and Roos' very recent extensive multiconfigurational SCF and multireference configuration interaction calculations. Vibrations, and possibly even distortions, of the particular normal mode in question are, however, known to be important in porphyrin systems: the extremely intense infrared band (at 1250 and 1550 cm-l for tetraphenyl and octaethyl porphyrins, respectively), which is a characteristic signature of a porphyrin x-cation radical,24is a well-known example.25 It is clear that the balance between the forces which favor and disfavor high-symmetry structures is reasonably delicate.7.26,27While both theoretical and experimental evidence favors high-symmetry structures for PI, this result may not apply to oligoporphyrins. Where possible, we consider structures of
both high and low symmetry and seek conclusions which are independent of this symmetry element. In Table 1 we list the D2h-symmetrized expenmental geometry of P14 and the deviations from this as calculated by the PM3, AM1, MNDO, and MND0/3 methods under the constraint of D2h symmetry, together with the unconstrained ab initio MP2/ DZP2 result^;^ the carbon atom types a,3!,, and m (meso) are defined in Figure 2 and differ depending on whether they are on a proton-bearing or proton-free pyrrole ring. The root-meansquare (RMS) deviations are also given and are lowest for the PM3 method, 0.014A, but the ab initio and other semiempirical calculations are of similar quality, 0.017 and ca. 0.022 A, respectively. Noticeably, PM3 gives better results for C-C bond lengths than the other methods, particularly for the C,Cg bonds to which interporphyrin communication in oligoporphyrins is sensitive. Hence, we adopt PM3 for the study of the oligoporphyrins; for reference, PM3-calculated absolute bond lengths and x-bond orders are also given in Table 1. Like AM1, ab initio, and other SCF levels of theory, the PM3/ RHF model predicts that a D2h to C2, distortion occurs for PI. Similarly, PM3AJHF predicts that the ground state is a triplet state free of this distortion, and, to avoid the spin-contamination problems, we use RHF methods throughout. In addition, the PM3/RHF C2, structure also possesses an extra small imaginary frequency corresponding to an out-of-plane distortion, lowering the symmetry even further to C,. The energy lowering associated with this distortion is just 0.4kcal/mol, however, and is insignificantly small. We choose to ignore this distortion as being almost certainly artifactual and constrain all molecules considered herein to be planar. The nature of the D2h to C2, distortion can be quantified by considering the splitting and comoffset of the broken symmetry bond lengths ( j and pared to those of the high symmetry structure ru:
(i,
,
I,
splitting = lru - ri,l and I
,,
The PM3-calculated bond-length splittings and offsets, as well as the corresponding bond-order splittings and offsets, are given in Table 1 for both individual bonds and the RMS values for all bonds. As the RMS bond length offset is just 0.003 A, the high-symmetry structure is to quite a good approximation given as simply the average of the two halves of the low-symmetry structure. Significant splittings do occur, however, with effects
J. Phys. Chem., Vol. 98, No. 46, 1994 11881
Rigid Fused Oligoporphyrins
TABLE 2: PM3, AM1, [37] MNDO, [29] and ab Initio PM2 [7] Classical Relative Energies, in kcal/mol, for Stationary Structures of free Base Porphin (PI) structure
PM3
AM1
MNDO
trans cis TS
0 8 26 45
0 7 35 61
0 6 43 69
MP2 ~
ss
~~
0 10 17 19
being the most severe for the proton-free C-N bond and the Ca-C, bonds. For metal-substituted porphyrins, e.g., the zinc derivative, less ambiguity exists in the structure and it is known to be D4h.28 Again, PM3 predicts a symmetry-broken (C2,,) structure, but its energy is just 0.4 kcaYmol below that of the D4h structure. 2b. Location and Migration of Inner Hydrogens. As the location of inner hydrogens in oligoporphyrins is unknown, a theoretical prediction is needed. To test whether such a prediction is reliable, the location and migration of inner hydrogens in free base porphin, PI, is considered. The location of inner hydrogens and tautomerism in P1 has attracted considerable attention for a long time.7*16.29-41 Briefly, two possible isomers for PI have been postulated, a trans isomer in which the hydrogens are located on opposite pyrrole rings and a cis isomer in which the hydrogens are located on adjacent pyrrole rings. Experimentally, no direct evidence has been found for the existence of the cis isomer, but indirect estimates39 place it ca. 5-8 kcaYmol in energy above that of the trans isomer. At high temperatures, the hydrogens are believed to rotate around the porphyrin ring in an asynchronous f a s h i ~ n , ~ * - ~ with the barrier for each 90" rotation being estimated by different techniques as AG* = 11.5 kcaVmol at 298 K35 and 11.1 k c d mol at 255 K.36 Calculated classical energies relative to that of the trans isomer for different structures of P1 are shown in Table 2 as evaluated by using AMl,37 MND0,29 and ab initio MP27 methods, as well as results obtained here by using PM3. All methods predict the existence of a cis isomer of comparable energy to that inferred e~perimentally,~~ as well as the existence of transition state (TS) linking the trans and cis isomers. Clearly, inner-hydrogen migration is predicted to occur in two asynchronous steps, one trans isomer reacting to form a cis isomer, which subsequently reacts to form the rotated trans isomer. Any synchronous trans to trans conversion must pass over the structure labeled SS, which is found to be a second-order saddle point of much higher energy than the TS. Quantitatively, the ab initio MP2 result for the TS barrier height is comparable to that estimated experimentally after quantum corrections such as zero-point energy and hydrogen tunneling are taken into a c ~ o u n t .All ~ of the semi-empirical methods considered overestimate the relative energies of the TS and SS structures, but from Table 2 the MP3 results are clearly superior to those from both AM1 and MNDO, and the actual error for the TS structure is tolerably small. Thus it is likely that MP3 could provide a reasonable description of inner-hydrogen isomerization in oligoporphyrins. 2c. Bond Lengths, z-Bond Orders, and Conjugation Pathway. As is indicated in Table 1, all four theoretical models predict that for D2h free base porphin the Ca-Cp bonds are the longest, with smallest n-bond order bo of 0.12 and 0.19, while the Cp-Cp bonds are the shortest with the largest n-bond orders of 0.70 and 0.79. Thus, the Ca-Cp bonds are quite localized while the Cp-Cp bonds are moderately so; the C,-C, bonds are quite delocalized with bond orders of 0.37 and 0.39. If we draw a picture in such a way that the width and darkness of a bond are proportional to its n-bond order, we get a pictorial view of the conjugation pathway of the molecule. Figure 4 is
D:
I
enhanced I-f!!$-l delocalization
I
delocalized
I
I
delocalized
I
Figure 4. Pictorial view of the conjugation pathway in (A) free base porphin (PI), (B): 1,4,5,8-tetraazaanthracene(TA), (C) PzTAI, (D) tetrahydro PITA^, and, for reference, (E) benzene and (F) 1,3-butadiene, in which the line width and density is proportional to the n-bond order b ~ In . PzTAI, the weak interunit coupling is apparent; this can be somewhat enhanced by tetrahydro substitution.
such a picture and includes benzene and 1,3-butadiene as standards: very dark and light regions correspond to unconjugated double and single bonds, respectively, while intermediate shading indicates a conjugated aromatic pathway. Results for the PM3 D2h structure of P1 indicate that, while the molecule is conjugated as a whole, the four outer Cp-Cp bonds are more or less isolated; a 16-atom 18-electron (11:;) conjugation pathway, which actually is the free base porphin inner ring, is immediately recognizable. In an alternate description, the moderately localized Cp-Cp bonds on the proton-bearing pyrrole rings could also be included, forming a 20-atom 22electron (11:;) conjugation pathway; this system reduces to a 11:; system if one excludes the two proton-bearing pyrrole nitrogens. Conversely, all atoms could be considered to be involved in a 11;s conjugation pathway. In summary, there is not sufficient evidence to distinguish whether the two n subsystems are conjugated together or not; the perceived conjugation extent will depend on the nature of the problem under discussion. As shown in Table 1, introduction of a C2,, distortion to the structure of P1 introduces considerable bond-order splittings. This results in the loss of the delocalization of the Ca-C, bonds and breaks the interpyrrole conjugation pathway. Such a pattern is not consistent with the known chemistry of P1 and provides additional evidence to suggest that the D 2 h structure is in fact the correct one. As the balance of CT and n forces, which controls this d i s t o r t i ~ n ,appears ~ ~ ? ~ ~somewhat delicate, it may be substitutionally inducible, thus providing an alternate mechanism for modulation of the electrical properties of oligoporphyrins.
3. Geometry and Bond Orders of 1,4,5,8-Tetrazaanthracene(TA) In Table 3 we list the optimized geometry of TA, which is of high symmetry, D2h. While its structure has not yet been
Lii et al.
11882 J. Phys. Chem., Vol. 98, No. 46, I994
TABLE 3: Experimental and Calculated PM3 Bond Lengths, in A, and n-Bond Orders bg of 1,4,5,8-Tetraazaanthracene(TA), Pyrrole, [30] and Pvrazine 1311 ~
rJ l
bond
obsd
TA C1-C3 c3-c5 C3-N7 N7-Cll Cll-C13
PYrrOl
calcd
b , calcd
1.399 1.424 1.410 1.312 1.445
0.40 0.30 0.16 0.74 0.16
0.55
C,-N C,-C+3 CPYCP
1.370 1.382 1.417
1.397 1.390 1.421
0.29 0.35
C-N
1.339 1.403
1.353 1.400
0.45 0.43
pyrazine
c-c
determined experimentally, the bonds of primary concern are Nl-CZ and C2-C3 (see Figure 2), and these can be considered as analogous to similar bonds in pyrazine; hence calculated and experimental results for this molecule are also included in Table 3. Indeed, PM3 provides an adequate description of pyrazine and is thus expected to also provide a reasonable description for TA. A pictorial view of the calculated PM3 conjugation pathway in TA is shown in Figure 4. The outer C-N bonds N1-C2 have a n-bond order of 0.74 and are quite localized, while the outer C-C bonds C2-C3 have a n-bond order of 0.16 and are highly localized. While all 14 atoms could be considered as forming a 11:; conjugation pathway, an almost perfectly conjugated six-membered ring exists in the center of this molecule. 4. PM3 Geometry and Conjugation of Oligoporphyrins
The PM3 geometries of different isomers of the oligoporphyrins shown in Figure 2 are described in detail as supplementary material and sketched in Figure 3. All of these structures are constrained to be planar, and some have additional symmetry constraints; in Figure 3, the molecular point group and the energy relative to the lowest-energy isomer found are indicated for each structure. There, a circle is drawn representing the porphyrin ring, which is overlaid by four shaded rectangles, each representing a Cp-Cp bond; parallel lines coming away from a box indicate the presence of a TA bridge unit attached to that pyrrole ring, and the location of the two inner-ring hydrogen atoms is indicated explicitly. The rectangle shading indicates the bond order of the Cp-Cfi bond. Molecules with symmetry-related trans hydrogens, like free base porphin (PI) itself, at the PM3 level of theory, are predicted to undergo a symmetry-breaking distortion which is most likely artifactual but could possibly be real. From Figure 3, we see that this effect appears additively in oligoporphyrins and is independent of TA substitution: a total of nine porphyrin rings in six different molecules are shown in this figure in both low and high symmetry and are seen to have a symmetrization energy cost of 6.6-8.8 kcallmol per porphyrin, averaging 7.2 kcal/mol. For these molecules, externally applied symmetry constraints appear to adequately correct the possible deficiencies in the PM3 Hamiltonian. Unfortunately, this same approach cannot be applied to molecules such as the bent isomers of PITA2, as symmetry is forcibly lowered by the porphyrin substitution. Hence the relative stability of the bent and linear isomers of this molecule may only be determined through comparison of the energies of the low-symmetry structures; similarly, it is only meaningful to compare the low-symmetry structures of cis- and trans-hydrogen isomers of a molecule.
The relative energetics of the placement of the intemal hydrogen atoms depends on whether or not (1) they are located cis or trans with respect to each other and (2) TA bridges are attached simultaneously to both proton-bearing pyrrole rings. Figure 3 shows that structures with cis hydrogens lie ca. 7 kcall mol higher in energy than corresponding trans structures if at most one hydrogen in the cis isomer is on a bridged pyrrole ring and 20 kcal/mol higher otherwise. A structure with trans hydrogens on two simultaneously bridged proton-bearing pyrrole rings, e.g., see PITA2 and PlTA3, lies 13 kcallmol higher than the alternate trans form. This has the consequence that, for long linear oligoporphyrins like P J T A ~shown in Figure 1, the terminal porphyrins would be expected to have equal mixtures of structures all with trans hydrogens but some with the hydrogens lying parallel to the chain length and with others lying perpendicular to it; all other porphyrins would be expected to have only trans hydrogens located perpendicular to the chain. While the preference of trans to cis isomers is known to be the case for P I and is expected to be a general property, the relative instability of trans isomers in which the proton-bearing pyrrole groups are both bridged can be understood in terms of the bond-order perturbations induced by the TA bridges. These changes are indicated qualitatively in Figure 3 by using four different shading patters to represent the Cp-Cp bond orders b,, namely: single bonds (0.13 bij < 0.18), aromatic bonds (0.43 < bij < OSI), weak double bonds (0.69 < bv < 0.72), and strong double bonds (0.78 < bi, < 0.85). Always, Cp-Cp bonds with TA bridges attached are single bonds. In terms of classical n-electron theory, resonance stabilization is reduced in any structure in which single Cp-Cp bonds are simultaneously enforced on opposite proton-bearing pyrrole rings, accounting for the relative instability of these isomers. Another example of this effect occurs for trans-tetrahydroporphine (bacteriochlorin); PM3 calculations place the structure with trans hydrogens perpendicular to the line joining the substituted Cp-Cp bonds 13 kcaVmol lower in energy than the alternate parallel isomer; see the supplementary material. The Cp-Cp bonds are the most sensitive to chemical effects and need to be treated explicitly in any model of the oligoporphyrins. As seen previously, all such bonds on bridged pyrroles are single bonds. If two nonbridged pyrroles are hydrogen bearing, then the Cfi-Cp bonds are either weak double bonds (high symmetry) or one strong double bond and one aromatic bond (low symmetry). Cp-Cp bonds on pyrroles which are neither bridged nor hydrogen bearing are typically strong double bonds but in exceptional cases are weak double bonds. The conjugation pathway through the oligoporphyrins as depicted by PM3 shows not a large fully-delocalized aromatic network which could possibly give rise to metallic-type conduction but rather depicts a series of weakly-interacting chromophore-based conjugation loops. As seen earlier for PI and TA themselves, no one single description of the delocalization is universally applicable. A characteristic description for PzTA1 is shown in Figure 4 and depicts weakly interacting porphyrin 11;; and TA 11:; systems. The weak interaction is useful in that it allows for the possibility of sensitive tuning of the coupling through both chemical and physical means and, e.g., the possibility of semiconduction. It might be naively supposed that this weak interaction is disadvantageous, as communication rates will be significantly reduced from their optimum values, such as those that would occur in a metallic coupling regime. In practical terms, this disadvantage is more than offset by the very large length spanned by each monomer unit of the oligoporphyrins of ca. 15.7 A, rendering these materials considerably more conducting than other potential
J. Phys. Chem., Vol. 98, No. 46, 1994 11883
Rigid Fused Oligoporphyrins
I
.
Figure 5. Description of the method for estimating the structure of an arbitrary oligoporphyrin P,TA, from the PITA, structures. Here, sections enclosed in boxes from PlTAz and PlTAl are combined to produce a structure for P3TA2.
molecular wires such as polyene^;^^,^^ we will explore this quantitatively in future publications. 5. Estimating the Structure of a n Arbitrary Oligoporphyrin
The MP3 structures for the molecules P,,TA, are sensitive to the local environment around each pyrrole ring (proton bearing or proton free, bridged or not bridged) and also to the arrangement of bridges around a particular porphyrin. This applies both to the structure of the porphyrin units and the TA bridge units. Simple schemes such as the use of standard C-C bond lengths to determine oligoporphyrin structure fail as they do not include these effects. We find no correlation between the structure of two porphyrins in an oligoporphyrin, and no correlation between TA units not connected to the same porphyrin. This suggests that a simple and sufficiently accurate empirical scheme can be devised for the construction of the geometry and estimating the relative energy of an arbitrary oligoporphyrin from the already-obtained structures of the molecules PITA,. How this works is illustrated in Figure 5 by the construction of a possible geometry of P3TA2 from the known geometries of PlTAz and P1TA1. In this example, the TA bridges are divided in half and the portion not attached to the porphyrin is discarded. The dashed boxes indicate the parts of the geometry of the fragments that are used; these are then combined together, averaging the coordinates of the C and H atoms at the center of TA. Many possible isomers can be generated in this fashion by combining different isomers of the fragments, possibly also in ways which produce different spatial symmetries for the synthesized molecules. Relative energies for these isomers can be estimated by adding the relative energies of the component fragments. This process is quite accurate; as a test, we have synthesized the structures of all of the PzTAl and P3TA2 isomers shown in Figure 3 and compared the results to the optimized structures obtained directly by using PM3; for all bonds considered, the RMS and maximum error is just 0.0006 and 0.0021 A, respectively. Also, the maximum error in the relative energy obtained by adding the fragment relative energies is just 0.1 kcaymol.
6. Substitution Effects As is mentioned above, it is unlikely that the particular compounds considered herein will actually be synthesized due to stability and solubility limitations. Commonly synthesized derivatives of these types of molecules include meso-tetraphenyl derivatives, and here we briefly consider possible effects of this substitution on the geometric properties of the oligoporphyrins considered earlier. We obtained PM3 structures of (i) PI, (ii) its meso-tetraphenyl derivative q i & , (iii) a linear oligoporphyrin similar to PITA2 but, for simplicity, with TA replaced by pyrazine Pl(pyrazine)2, and (iv) its meso-tetraphenyl derivative 44-Pl(pyrazine)z. The RMS bond length variation due to the
meso-phenyl substitution of PI and Pl(pyrazine)z are 0.004 and 0.005 A, respectively, with maximum changes of 0.008 and 0.010 A, respectively, for the C,-C, bonds. Other bonds, including the fused bonds, show no significant effects, and hence we conclude that results of studies on unsubstituted compounds should be readily applicable to meso-tetraphenyl-substituted molecules. These results are independent of the angle used between the planes of the phenyl and porphyrin rings. In crystal, solution, and gas phases (see ref 44),this angle is known to be the angle which brings van der Waals contact between rings, ca. 60°, but the barrier to rotation past 90" is known to be rather Both AM1 and PM3 predict very shallow rotational potentials in the gas phase, but they predict minima at 60" (02) and 90" (&), respectively. It is also common to replace the two inner hydrogen atoms with a metal atom such as Fe, Mg, Zn, or many others; this removes the proton-bearing/proton-free distinction from the pyrrole groups, resulting in the formation of molecules with D4h symmetry. As this substitution shifts and can invert the relative energy levels of the porphyrin highest and secondhighest occupied molecular orbitals, its effects on interporphyrin communication can be profound; we shall explore this in detail in future publications. The zinc derivative, Zn-PI, is believed to be similar to P1 itself, however, and this is verified by PM3 calculations on zinc-substituted PI, P1TA2, and P2TA1. Its primary effect is to average the related D2h bonds in free base porphin, producing D4h symmetry: the RMs difference between the D4h-symmetrized PI bond lengths and that of the zinc derivative is just 0.004 A. Directly comparing the bond lengths in high-symmetry isomers of PI, P1TA2, and P2TAl with those of their zinc derivatives gives RMS changes of 0.009, 0.010, and 0.006 A, respectively. Another interesting modification to the oligoporphyrins is the saturation of unbridged Cp-Cp bonds. For a nonterminal porphyrin in a linear chain, modeled say by P1TA2, this results in the inversion of the relative energies of the two trans structures with the one with the proton-bearing pyrroles bridged being 2.0 kcaymol more stable than the one with the protonfree pyrroles bridged. The result is that the degree of delocalization through the bridging pyrroles is significantly enhanced; see Figure 4. Altematively, the coupling through a TA bridge can be dramatically reduced by asymmetric protonation of the TA nitrogen atoms. The optimized PM3 structures of all substituted porphyrins considered are provided in the supplementary material. 7. Concluding Remarks A simple qualitative guide to the electronic properties of the proposed 1,4,5,8-tetraazaantene-bridgedoligoporphyrin molecular wires is given by the n-bond orders of these molecules, and more detailed properties are obtainable from the molecular energy levels. These connections we shall explore in detail in future publications. Here, we have seen that the molecular geometries are quite sensitive to the local environments of the porphyrin pyrrole rings, Le., the presence of an inner hydrogen atom or the presence of a TA bridge, and to the overall topology of the TA bridges around a single porphyrin. These geometry changes affect the bond orders and thence all other properties; so it is essential that any theoretical study of these systems be performed at acceptably accurate molecular geometries. As the molecules themselves can be rather large, geometry optimizations, even using semiempirical methods, quickly become not feasible; here, we devised a scheme for the rapid and accurate determination of the geometry of an arbitrary oligoporphyrin. Our results are for the simplest possible oligoporphyrins, containing no meso or substituents, no metal centers, and no reduced Cp-Cp bonds. While these molecules are unlikely to
11884 J. Phys. Chem., Vol. 98, No. 46, 1994 be produced in the laboratory, common substituents such as meso-tetraphenyl groups and zinc centers are known not to significantly perturb the structure of porphyrins, and this is verified by our calculations. Hence, results from our simple systems can be directly applied to these laboratory molecules. Also, preliminary results for highly perturbing modifications such as Cp-Cp hydrogenation qualitatively reflect known experimental trends, indicating that the semiempirical methods used herein should be capable of adequately describing such effects. A large number of isomers are postulated for each oligoporphyrin. Unfortunately, as PM3 predicts what is most likely an unphysical symmetry lowering of free base porphin and its derivatives, many of these isomers may be artifactual. Notwithstanding this, a significant number of isomers are possible, associated with the location of inner hydrogen atoms and possible substitution-induced asymmetries. The hydrogen-atom energetics for free base porphin calculated by using PM3 are qualitatively similar to that obtained37from AM 1; barrier heights are considerably reduced but remain much too high. Always, inner hydrogen atoms prefer to be related trans, i.e., on opposite pyrrole groups. In oligoporphyrins, the terminal porphyrins units with only one connected TA bridge (e.g., in PITA,) show no other preferential arrangement of the inner hydrogens with respect to the location of the bridge; inner hydrogens on central sections of a linear oligoporphin (eg., in P4TA3 shown in Figure 1) have a strong preference for alignment perpendicular to the chain. The origin of this effect is easily understood in terms of the number of available resonance structures, given the constraint that the presence of a TA bridge forces the fused Cp-Cp bond to be a single bond. The overall picture of the conjugation and communication between porphyrin rings in an oligoporphyrin that emerges is one of weak interunit coupling that is readily modulatable and tuneable. Compared to other possible molecular wires, these have the striking advantage of spanning large distances with just a few functional units, e.g., the 56 A spanned by P4TA3; see Figure 1. Hence, a little coupling goes a long way, and these molecules are expected to possess many practical advantages over alternative systems.
Acknowledgments. We are indebted to the Cooperative Research Centre for Molecular Engineering and Biosensor Technology (Sydney) for funding of this project; M.J.C. and J.R.R. gratefully acknowledge support from the Australian Research Council. Supplementary Material Available: Tables containing the PM3 optimized geometries and, where available, vibration frequencies for all of the isomers in Figure 3, the TS and SS structures, and the zinc, tetrahydro, and tetraphenyl derivatives considered herein; in all, there is a total of 5 1 molecules (18 pages). Ordering information is given on any current masthead Page. References and Notes (1) Crossley, M. J.; Burn, P. L. J . Chem. SOC.,Chem. Commun. 1987, I, 39.
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