Theoretical determination of the molecular and solid-state electronic structures of phthalocyanine and largely extended phthalocyanine macrocycles Enrique Orti,* Raul Crespo, M. Carmen Piqueras and Francisco Tomas Department de Quimica Fisica, Universitat de Valgncia, Doctor Moliner 50, E-46100 Burjassot (Valt?ncia), Spain The molecular and solid-state electronic structures of metal-free phthalocyanine and a series of linearly benzoannulated phthalocyanines have been investigated using the valence effective Hamiltonian (VEH) quantum-chemical method. Geometry optimizations show that, from the molecular structure standpoint, phthalocyanine-based macrocycles are the result of joining four polyacenic units to the CsNs central ring. The electronic structure calculated for the parent phthalocyanine is compared with that of porphyrin, and the consequences of benzoannulation and meso-tetraaza substitution on the optical properties of phthalocyanines are discussed.The VEH results obtained for extended phthalocyanines are in agreement with available photoemission, cyclic voltammetry and optical absorption data and help to rationalize the evolution of the electronic properties. The first ionization energy is predicted to decrease with linear benzoannulation and asymptotically converges to an extrapolated value of -5.7 eV. Strikingly, a non-convergent behaviour is obtained for the HOMO-LUMO energy gap and very low excitation energies are predicted for extended phthalocyanines. Band-structure calculations have been performed for one-dimensional stacks of the molecules investigated.The variation of the bandwidth with the staggering angle and the intermolecular separation provides a coherent picture of the electrical conductivities observed experimentally in crystals and polymers. Very small bandgaps lower than 0.5 eV are predicted for extended phthalocyanines. Since their accidental synthesis in 1907,l phthalocyanines (Pcs) have become one of the most intensely studied macrocycles owing to the unique properties they exhibit.2 Pcs are among the most stable organic materials and show remarkable optical properties. The conjugated macrocycle, which contains 42 rc electrons, leads to very intense absorption bands in the far red end of the visible spectrum (ca.670nm, Q band) and in the near-ultraviolet (ca. 340nm, B or Soret band). The intense colour and high thermal and chemical stability have for decades determined the use of phthalocyanines as dyes and pigments. Phthalocyanines are also of great interest owing to their electrical proper tie^.^ They were recognized as good photoconductors as early as 194S4 and are at present used in electrophotographic systems,’ photovoltaic cells for energy conversion,6 etc. More recently, phthalocyanines have been reported to form highly conducting materials. Cocrystallization of Pcs with oxidising agents like iodine yields ‘molecular metals’ with conductivities of the order of 10-lOOOScm-l at room tem- perat~re.~The packing of the phthalocyanine molecules in columnar stacks leads to an effective overlap between the rc molecular orbitals on adjacent macrocycles, which provides the electronic pathway for the delocalization of the charge carriers generated upon oxidation.The presence of metal atoms is therefore not a requirement to achieve high conduc- tivities in phthalocyanines and a value of 700 S cm-l has been reported for partially oxidized crystals of metal-free phthalocy- anine (H,Pc) at room temperature.’“ Higher room-temperature conductivities of around lo4 S cm-l have been measured recently for high-purity oxidized phthalocyanines H,PcI and NiPcLsb The presence of the central metal atom is, however, a requirement for the formation of cofacially joined metalloph- thalocyanine polymers [MPcL], where the metallomacro- cycles are linked together by bisaxially metal-bonded bridging ligands, L.9 Depending on L, these polymers exhibit compara- tively high semiconducting properties (oRT=0.05-0.3 S cm-‘)lo without external oxidative doping.These electrical properties make phthalocyanines prime candidates for use in electronics and molecular electronics. Indeed, they have already been employed in highly sensitive gas sensors,” rectifiers (molecular diodes)’, and tran~istors.’~ The potential applicability of phthalocyanines is being investigated in many other fields such us optical data storage,14 non-linear optics,” electrochromic devices,16 liquid crystals” and Langmuir-Blodgett (LB) films.” One of most recent applications is their potential use as photosensitizers in photo- dynamic therapy.” Phthalocyanines are more effective than porphyrins as photosensitizers because of the high absorption coefficient of the Q band, often exceeding lo5 1 mol-’ ern-'.The phthalocyanine ring offers sixteen potential sites of substitution through which the modulation of the electronic properties (optical absorptions, ionization and redox poten- tials, etc.) can be effected, enabling the possibility of obtaining phthalocyanine-based materials with optical or electrical properties adjusted to the desired application. In this context, extended phthalocyanines are of great relevance and, in particu- lar, 2,3-naphthalocyanines (2,3-Ncs) are the object of numerous investigations.Compared to phthalocyanines, the Q absorption band in 2,3-naphthalocyanines is shifted to the near-IR and appears at about 800 nm.20 This absorption makes 2,3-Ncs excellent can- didates for high-density optical recording (ODR) media since a long-wavelength absorption is required in the writing and reading processes using semiconductor lasers.21 2,3-Ncs are also very promising as sensitizers for photomedicine since bodily tissues allow deeper light penetration with increasing wavelength in the range 600-1200 nm.” They have also been used in the synthesis of cofacially linked polymers, showing higher conductivities than the analogous phthalocyanine-based materials.23 Non-linear optical properties have been measured for a variety of 2,3-N~s.,~ In a previous ~aper,~’ we studied the electronic structure of 2,3-naphthalocyanine and 1,2-naphthalocyanine as models of linearly and angularly annulated phthalocyanines.The results showed that the linear extension of the conjugated structure affects the electronic properties of the macrocycle more drasti- cally, suggesting that materials with improved electrical and optical properties might be obtained from linearly annulated phthal~cyanines.~~~~~Our goal in this work is to investigate the electronic properties of largely extended linearly annulated phthalocyanines at both the molecular and the solid-state levels. The geometric and electronic structures of metal-free J. Muter. Chern., 1996,6(11), 1751-1761 1751 2,3-naphthalocyanine (2,3-H2Nc), 2,3-anthracyanine (2,3-H2Ac) and 2,3-tetracenocyanine (2,3-H2Tc) are thus calculated using quantum-chemical methods.The molecular structures of 2,3-H,Nc, 2,3-H2Ac and 2,3-H2Tc are depicted in Fig. 1 together with that of H,Pc and that of the angularly annulated 9,lO-phenanthrenocyanine(H,Phc). The electronic structure of H,Pc is first analysed and compared with those calculated for the closely related metal-free porphyrin ( H2P) and tetra- benzoporphyrin (H,Tbp). Our aim is to provide a deep under- standing of the unique electronic properties of the phthalocyanine macrocycle that serves as a reference in the study of extended phthalocyanines. Electronic band-structure calculations are performed for one-dimensional molecular stacks of H,Pc, 2,3-H2Nc, 2,3-H2Ac, 2,3-H2Tc and H2Phc.Our aim is to discuss the electrical properties of phthalocyanine-based crystals and polymers. The first anthracyanines were obtained in 1971 as octapheny- lated derivative^.'^" The synthesis of different octa-tert-b~tylated,~~and unsubstituted28 2,3-Acs was also reported. Despite these early syntheses, little experimental work has been carried out on these enlarged macrocycles. More recently, metal-free tetra(tert-butyl)-2,3-anthracyanineand the corre-sponding cobalt complex have been obtained by Kobayashi et Two different Fe" complexes have been obtained by ~1.~~~1~~ Hanack et aL3' To our knowledge, only the synthesis of a vanadium complex of 2,3-tetracenocyanine has been reported in the literature.28 The photophysics and photochemistry of 2,3-Acs is at present being investigated in an attempt to obtain a new generation of photosensitizers for photodynamic the rap^.^ Computational details The molecular geometries of the metal-free macrocycles shown in Fig.1 were optimized using the MNDO-PM3 (modified neglect of diatomic overlap, parametric method number 3) 't+ X ' \ H2Phc 2,3-H2Ac g & \/ Fig. 1 Molecular structures of metal-free phthalocyanine ( H2Pc), 2,3-naphthalocyanine (2,3-H2Nc), 2,3-anthracyanine (2,3-H2Ac), 9,lO-phenanthrenocyanine (H2Phc) and 2,3-tetracenocyanine (2,3-H2Tc) 1752 J. Muter. Chem., 1996, 6(11), 1751-1761 semi-empirical method,32 as implemented in the MOPAC-6.0 system of programs,33 and assuming D,, symmetry constraints. The PM3 method has recently been applied to the study of largely extended porphyrins and olig~porphyrins.~~ Both the molecular electronic structure and the electronic 108.9 band structure of one-dimensional stacks of the macrocycles were investigated using the valence effective Hamiltonian 118.0 (VEH) pseudopotential method.The VEH approach was 121.3 originally developed to deal with and was later extended to treat stereoregular polymers,36 and has been used widely in the context of conjugated molecules and poly- mer~.~~,~'It constitutes an especially useful tool for dealing with large molecular or crystalline systems, since it is param- \ Nnl I .N 1.344 m 1 .;91 eterized to yield one-electron energies of ab initio double-l: 1.471 (DZ) quality without performing any self-consistent-field (SCF) process or calculating any two-electron integral.Its suitability for describing the electronic structure of phthalocy- 1.392 anine-type macrocycles is supported by previous ~ork.~~,~~-~~ In particular, an excellent correlation is found between the molecular and crystalline electronic structures calculated for H,Pc and experimental photoemission (UPS or XPS) All the calculations presented here were performed using the atomic potentials previously optimized for carbon, nitrogen and hydrogen.46 Compared to standard ab initio Hartree-Fock (HF) calcu- lations, the VEH method provides good estimates for the energies of the lowest-energy electronic transitions.This feature is due to the fact that the VEH parameterization is obtained only using the energies and functions of the occupied MOs and is therefore not contaminated by any information from the too diffuse virtual MOs that HF calculations pro-vide.38b,47,48Unoccupied MOs are thus expected to be as reliable as occupied MOs when calculated with the VEH method. In the case of phthalocyanine, the VEH method systematically underestimates the energy of the first optical transition associated with the HOMO-LUMO energy gap (E,) by 0.62 eV. This shortcoming comes from the parametriz- ation used for the nitrogen atom based on pyrrole and dimethylamine molecules.46 As was done previo~sly,~~*~~~~~ the 120.5 119.2 120.4 118.2 132.6 1.471 VEH E, values for all the phthalocyanines studied in this work are consistently increased by 0.62 eV.Results and Discussion Optimized molecular structures To our knowledge, experimental data on the molecular struc- ture of metal-free phthalocyanine-based macrocycles are only available for H,Pc. As early as 1935,49 Robertson performed an X-ray diffraction study of the lattice parameters of the p-polymorphic form of H,Pc and a year later reported a detailed structure of the carbon-nitrogen skeleton of the molecule.50 More recently, Hoskins et aL5' carried out a neutron diffraction study on the same p-polymorphic form and Yase et aL5, reported the X-ray structure of the a-polymorphic form. All these works agree in attributing a highly delocalized planar geometry to the carbon-nitrogen backbone.Fig. 2(a) summar- izes the PM3-optimized bond lengths and bond angles calcu- lated for H,Pc. The D,, constraints provide a highly delocalized structure with almost equivalent lengths for the carbon-nitro- gen bonds forming the C8N8 central ring, in agreement with experiment. The higher stability of this structure us. frozen resonant structures of C,, symmetry with alternating single and double bonds has been shown recently for metal-free p~rphyrin.~~ The theoretical parameters calculated for H,Pc cannot be compared easily with available experimental because these data do not differentiate between the two kinds of isoindole moieties present in H,Pc owing to the difficulty in locating the inner hydrogen atoms.The PM3 oresults predict almost identical lengths of 1.344 and 1.349 A for adjacent Fig. 2 DZhPM3-optimbzed parameters for (a) H,Pc and (b) 2,3-H2Nc. Bond lengths are inA and bond angles in degrees. N, denotes a pyrrole nitrogen and N, and N, denote pyrrole aza and rneso-bridging aza nitrogens, respectively. C, -N, bonds. These lengths are longer than the X-rax value of 1.33 A reported for ~-H,Pc.~~ The C,-N, (1.411 A) and C,-N, (1.386 A) bond distances are also calculated to be longer thFn the experimental values, which are about 1.36-1.38 A.51,52 The angles defined by the bonds forming the C8N8 central ring are in general wider than the X-ray angles by 1-3".The largest deviation is found for the C,-N,-C, angles, for which the PM3 method obtains a value of 125.9' and the X-ray data provide a value of 122.5' for ~-H,Pc.~, The PM3 value is in accord with that reported for the closely related tetraazaporphyrin (H,Tap) from ab initio DZ calcu-lations ( 125.0').54 The N;-.N, and N;--N, distances definiqg the size of the central ring have values of 3.98 and 4.17 A, respectively. The C-C bonds forming the peripheral benzene rings in H,Pc have typical aromatic bond lengths, indicating that the aromaticity of these rings is pre:erved in H,Pc. As a consequence, the C, -C, bonds (ca. 1.42 A) fusing the benzene rings to the pyrrole moieties are $gnificantly longer than those calculated for H,Tap (ca.1.36 A). The C,-C, bonds have lengths of 1.46-1.47 A. Fig. 2( b) displays the geometric parameters optimized for 2,3-H2Nc. The central CsNs ring is almost identical to that of J. Muter. Chern., 1996,6(11), 1751-1761 1753 H,Pc, the major differences being 0.002 for the bond lengths and 0.4" for the bond angles. As for H,Pc, the peripheral naphthalene units fused to the central tetraazaporphyrin ring preserve their structural aromaticity. Fig. 3 compares the geometry calculated for a naphthopyrrole unit in 2,3-H2Nc with the PM3-optimized geometries of isoindole, pyrrole and naphthalene molecules. There are marked differences between the geometry of the pyrrole units within naphthalocyanine and those in isoindole and pyrrole molecules.For pyrrole, the C,:C, bonds show a high degree of double-bond character (1.390 A), which is maintained in the isoindole molecule (1.405 A). This molecule must in fact be viewed as resulting from the union of a cis-buta-1,3-diene fragment on the top of the pyrrole ring. The situation is different in 2,3-H2Nc since the structure of pyrrole is not preserved. oThe C,-C, bonds mostly have single-bond character (1.463 A) and the naphtha- lene moieties have a geometry almost identical to that of naphthalene [cf. Fig. 3(a) and (d)]. Thus, 2,3-H,Nc can be visualized as the result of joining four naphthalene units to the central C8Ns macrocycle. The PM3-optimized geometries obtained for the more extended 2,3-H2Ac and 2,3-H2Tc are not displayed because they show the same geometric trends discussed above for H,Pc and 2,3-H2Nc; i.e., the C8N8 central ring is nearly identical to that of H,Pc and the polyacenic units preserve their structural identity showing geometries very close to those of anthracene (2,3-H2Ac) and tetracene (2,3-H2Tc).The size of the C8N8 central ring is predicted to increase slightly but continuously with linear extension. The Np...Np and N;..N, distances lengthen by 0.030 and 0.016 A, respectively, in passing from H~Pcto 2,3-H,Tc. Molecular electronic structures Table 1 summarizes the VEH molecular orbital (MO) distri- butions obtained for H,Pc, 2,3-H2Nc, 2,3-H,Ac and 2,3-H,Tc. It collects all the occupied orbitals with energies above -10.0eV and the lowest five unoccupied MOs.All these orbitals are of n-nature, the first occupied o-orbitals lying below -10.2 eV. The main characteristics of the electronic structure of phthalocyanine are first discussed by comparing them to those calculated for porphyrin (H2P) and tetrabenzo- porphyrin (H,Tbp). The effects of the n-system extension of the macrocycle on the electronic structure are then analysed. Metal-free phthalocyanine. The highest occupied molecular orbital (HOMO) of H,Pc corresponds to the 4a, level. This orbital is calculated to have an energy of -6.42 eV, in perfect agreement with the first ionization energy (6.41 eV) obtained from gas-phase UPS data.57 It is separated by an energy gap of ca. 2.5 eV from the next occupied 7b,, orbital heading a group of very close-lying MOs.The appearance of this gap is also in accord with experimental photoemission data since energy differences of 2.3-2.7 eV are found between the first 1.416 1.415 1.369 1.425 (1.417) (Jl.yJ2, (1.369) 1.463 1.405 (1.421) N 1.397 I 1 (1.370)I H (c) (d) Fig. 3 Comparison of PM3-optimized bond lengths (in A)of (a) naph- thopyrrole units in 2,3-H2Nc; (b) isoindole molecule; (c) pyrrole molecule (experimental microwave data from ref. 55 are given in parentheses); (d) naphthalene molecule (X-ray crystallographic data from ref. 56 are given in parentheses) 1754 J. Mater. Chern., 1996, 6(11), 1751-1761 Table 1 VEH one-electron energy levels (sign-reversed energies in eV) obtained for phthalocyanine (H,Pc), 2,3-naphthalocyanine (2,3-H2Nc), 2,3-anthracyanine (2,3-H2Ac) and 2,3-tetracenocyanine (2,3-H2Tc)" H,Pc 2,3-H,Nc 2,3-H,Ac 2,3-H,Tc 3.09 9b,, 4.02 llb3, 4.47 13b3, 4.63 3.34 llbl, 4.05 13bl, 4.66 15bl, 5.04 4.01 lob,, 4.27 12bl, 4.80 14b,, 5.14 5.16 8b2, 5.00 lob,, 5.03 12b3, 5.20 5.23 8b3, 5.02 lob,, 5.04 12b,, 5.22 6.42 6a, 6.05 8a, 5.88 10a, 5.79 9.01 5a, 8.56 7a, 7.90 9a, 7.48 9.39 7b3, 8.65 9b,, 7.98 llb3, 7.54 9.42 7b,, 8.66 9b,, 7.99 llb,, 7.55 9.43 4a, 8.96 6a, 8.23 8a, 7.73 9.43 9b1, 9.01 llb,, 9.00 7a, 8.96 9.64 9.71 9.72 10.04 8bl, 7b1, 6b2, 6b3, 9.21 9.26 9.26 9.25 lob,, 8b2, 9b1, 8b3, 9.13 9.16 9.16 9.16 lob3, lob,, 13bl, 6a, 9.00 9.00 9.01 9.08 5% 9.63 12bl, 9.10 7b3, 7b2, 4% 9.67 9.68 9.88 9b,, 9b,, llblu 9.11 9.12 9.21 "The occupied orbitals above -10.0eV and the lowest five unoccupied orbitals are included.Orbitals are labelled according to the D,, point group starting from the first occupied valence orbital. All orbitals are of n-nature. Fig. 4 Atomic orbital composition of the highest two occupied molecular orbitals of phthalocyanine (H,Pc) and porphyrin (H,P). The HOMOs of isoindole and pyrrole molecules are also shown for the sake of comparison. The sizes of the circles are proportional to the magnitude of the LCAO coefficients. Contributions smaller than 0.10 are not displayed. The VEH energies (inev) of the orbitals are given in parentheses.two ionization energie~.'~.~~-f- The high energy of the HOMO and its energy separation from the remaining occupied orbitals deserve special attention because they are the main reasons for the unique electronic properties that differentiate phthalocy- anines from other tetrapyrrolic systems like porphyrins. As illustrated in Fig.4, the HOMO of H,Pc spreads over the carbon backbone with nodes on N, and N, atoms and negligible contributions from the meso nitrogens N,. The HOMO of porphyrin shows the same atomic orbital (AO) composition and is calculated at -7.40 eV using a PM3-optimized geometry. It is therefore found to be 1.0eV lower in energy than the HOMO of H2Pc, in agreement with the higher first ionization energy reported for H,P (6.9-7.2 eV).59 The HOMOs of H2P (2a,) and H,Pc (4a,) actually originate 7 A detailed comparison of the valence electronic structure calculated for H,Pc with experimental photoemission data is given in ref.39 and 41. The slight differences between the one-electron energies reported in those works and those presented here are due to the previous use of an old version of the VEH parameterization for carbon and hydrogen atoms (see ref. 36b) and of an averaged crystallographic geometry for H,Pc. in the HOMOs of pyrrole (la,) and isoindole (2a,), respect- ively. These orbitals are calculated at -8.24 and -7.06 eV, in very good agreement with the first ionization energies measured in the gas phase for pyrrole (8.22 eV)60 and N-methylisoindole (7.12 eV).61 The destabilization of the HOMO in passing from pyrrole to H,P or from isoindole to H,Pc is due to the changes undergone by the bond lengths of the pyrrole and isoindole moieties, which tend to weaken the bonding interactions and to reinforce the antibonding interactions in H,P and H2Pc.For instance, the C,-C, bonds lengthen from 1.390 to 1.449 A in going from pyrrole to H2P, thus reducing the bonding interattions, while the C,-C, bonds shorten from 1.421 to 1.371 A, thus enhancing the antibonding interactions. Similar changes are found for these bonds in passing from isoindole to H,Pc [cf Fig. 2(a) and 3(b)]. The destabilization of the HOMO of H,Pc relative to the HOMO of H,P is similar to that obtained for the HOMO of isoindole with respect to the HOMO of pyrrole, and results from the antibonding inter- action of the cis-butadiene fragments with the HOMO of the pyrrole moieties.The HOMO -1 shows the same atomic orbital (AO) com- position for H,Pc and H,P and is mostly localized on nitrogens and on the meso bridging atoms. For H2P, it appears at -7.68 eV, very close in energy to the HOMO, while for H,Pc, it is calculated at -9.01 eV, i.e. 2.6 eV below the HOMO. The stabilization of the HOMO-1 of H,Pc results from the substitution of the methine linking units (CH,) of H,P by aza bridges (N,) in H,Pc, and is due to the higher nuclear charge of nitrogen atoms. Two main electronic effects are therefore derived from the structural differences between H2P and H,Pc.The destabiliz- ation of the HOMO of H,P in passing to H,Pc due to benzoannulation, and the removal of the HOMO-HOMO -1 near-degeneracy present in H2P due to meso-tetraaza substi- tution. The relationship existing between the molecular and the electronic structures is confirmed by examination of the electronic structure of tetrabenzoporphyrin. H,Tbp shows a molecular structure intermediate between those of H,Pc and H2P, since it has isoindole moieties like H,Pc but is linked by methine units as in H2P. The 4a, HOMO of H,Tbp is thus calculated at an energy of -6.50 eV, almost identical to the energy of the HOMO of H,Pc (-6.42 eV), while the 7bl, HOMO -1 is located at -7.74 eV as in H2P (-7.68 eV).The differences in the energies calculated for the HOMO and HOMO-1 of H,P, H,Tbp and H,Pc explain the different optical properties observed for these compounds as discussed below. These differences have recently been analysed on the basis of ab initio calculation^,^^ and have been used to rational- ize the different behaviour of porphyrin-based conductors compared to Pc-based ones.62 The lowest two unoccupied molecular orbitals (LUMO and LUMO + 1)of H,Pc correspond to a pair of almost degenerate 6b3, (-5.23 eV)-6b2, (-5.16 eV) n*-orbitals that are respect- ively located along the x and y axes (see Fig. 5). The quasi- Fig. 5 Atomic orbital composition of the lowest two unoccupied molecular orbitals of phthalocyanine. The sizes of the circles are proportional to the magnitude of the LCAO coefficients.Contributions smaller than 0.10 are not displayed. degeneracy of these two orbitals is due to the almost identical geometry predicted for the isoindole moieties. Their relative energy ordering is in fact very sensitive to the geometry used. Previous calculations on H,Pc using an averaged crystallo- graphic geometry placed the 6b2, orbital below the 6b3, orbital.25 The LUMO and LUMO+l of H,Tbp (-4.71 and -4.67 eV) and H2P (-5.04 and -4.91 eV) show the same topology. The vapour absorption spectra reported by Edwards and Go~terman~~for H,Pc show two sharp peaks in the visible region at 1.81 eV (Qx, 686.0 nm) and 1.99 eV (Qy, 622.5 nm), that constitute the so-called Q band, and a broad band centred at 3.65 eV, which extends from 3.3 to 4.1 eV and is called the B or Soret band.The double-peak Q band results from the HOMO+LUMO and HOMO+LUMO + 1 electronic trans- itions, since no other low-energy excitation is expected because the HOMO of H,Pc is well above the remaining occupied MOs and the LUMO and LUMO + 1 are ca. 2 eV below the 7b2,-7b3, n*-orbitals. The broad B band is usually assigned to the HOMO -1+LUMO,LUMO + 1 excitations, but other electronic transitions coming from the close-lying lower energy occupied orbitals to the LUMO and LUMO+ 1 (e.g. 6b,,, 5bl,, 3a,, etc.+6b3,, 6b2,) or from the HOMO to higher energy virtual orbitals (e.g. 4a, +7b,,, 7b3,) can contribute to this band, as was suggested by Stillman and Ny~kong~~ and has recently been shown by Kobayashi et ~1.~~‘and Zerner et al.65b for MPcs.The situation in H,P is completely different since the HOMO and HOMO -1 are nearly degenerate and lie ca. 2.5 eV above the remaining occupied orbitals. The electronic excitations from these two orbitals to the LUMO and LUMO + 1 therefore account for both the Q and the B bands, to which they contribute almost equally as recent ab initio calculations have demonstrated.66 This is the basis of the ‘four orbital model’ developed by Gouterman and co-worker~~~,~*to explain the spectra of porphyrins. The model is, however, not fully transferable to phthalocyanines owing to the participation of other MOs other than the HOMO and HOMO -1 and the LUMO and LUMO + 1 in the electronic transitions giving rise to the B band.The H2Tbp molecule is an intermediate case because the HOMO -1 is well isolated from both the HOMO and the low-lying occupied orbitals and the B band results from the HOMO-l+LUMO, LUMO + 1 transitions. This explains the sharpness of the B band for H,Tbp, which is well resolved in B, and By components.68 Extended phthalocyanines. Table 1 indicates that, as found for H,Pc, the HOMOs of the extended phthalocyanines 2,3- H,Nc, 2,3-H,Ac and 2,3-H,Tc correspond to levels of a, symmetry. The A0 compositions of these orbitals are identical to that shown in Fig.4 for the 4a, HOMO of H,Pc. The energy of the HOMO increases by 0.37 eV in passing from H,Pc to 2,3-H2Nc.This increase agrees with the shift of 0.41 eV to low binding energies observed when comparing the position of the first photoemission band in the UPS spectra of vapour- deposited thin films of ZnPc (6.29 eV) and 2,3-ZnNc (5.88 eV).69 The calculated HOMO destabilization further justifies the lower oxidation potentials measured for 2,3-naph- thalocyanine compounds. The naphthalocyanine macrocycle is easier to oxidize than the phthalocyanine macrocycle by ca. 0.4 V, e.g. 2,3-SiNc(OR),, +0.58 V; SiPc(OR),, + 1.00 V; 2,3- CoNc, +0.77 V; CoPc, + 1.15 V (potentials US. SCE).70,71 Owing to the low oxidation potentials of the 2,3-Nc macro- cycle, the 1,4-diisocyanobenzene bridged polymer [2,3-FeNc(dib)]. is doped by oxygen in the air and presents higher powder conductivities than those measured for the ‘undoped’ [FePc(dib)].p~lymer.~~?~~ The HOMO undergoes an additional destabilization of 0.17 eV when passing from 2,3-H2Nc to 2,3-H2Ac in agreement with the cyclic voltammetry data reported by Hanack et aL3’ J. Muter. Chem., 1996, 6(11), 1751-1761 1755 for a bis( pyridine) complex of (But),-2,3-FeAc. The oxidation of the macrocycle in this compound appears as a shoulder near the solvent limit at about +0.75 V and is compared with that measured for 2,3-FeNc at about +0.9 V (potentials us. SCE). A small destabilization of 0.09 eV is finally obtained in going from 2,3-H2Ac to 2,3-H2Tc. Fig. 6(a) summarizes the evolution of the energies of the HOMO and the LUMO as a function of the number of benzenes annulated following the axis of each pyrrole unit.The tetraazaporphyrin ring is taken as a reference. H,Pc, 2,3- H,Nc, 2,3-H2Ac and 2,3-H2Tc therefore correspond to annu- lation of one, two, three and four benzene rings per pyrrole unit, respectively. The energy of the HOMO increases along this series and shows an asymptotic behaviour converging to an extrapolated value of -5.69 eV. This value was obtained by fitting the energies calculated for the HOMO to a poly- nomial in inverse powers of N + 1 [y=a +b/(N+1)+ . . . +e/(N + 1)4], N being the number of benzene rings linearly fused to the tetraazaporphyrin ring per pyrrole unit. HOMO destabilizations smaller than 0.05 eV are therefore expected for extended macrocycles beyond 2,3-H2Tc. The rapid convergence achieved for a small number of benzene rings results from the fact that the contributions of the outermost rings to the HOMO decrease as the number of these rings increases.As discussed above for H2P and H,Pc and shown in Fig. 4, the destabilization of the HOMO with linear benzoannulation is due to the antibonding interactions with the fused fragments. The HOMO remains, however, mainly localized on the central tetraazaporphyrin ring and these interactions decrease in inten- sity with the number of benzene rings fused. The evolution of the energy of the lowest-lying two unoccu- pied orbitals with the extension of the macrocycle is not as regular as for the HOMO. The energy of the LUMO increases with linear benzoannulation, changing from -5.84 eV for I I I I I I 1 0 1 2 3 4 5 2.2 2 2 1.8 1 03 1.6 5 $1.4 U 1.2 l! I I I I I 0 1 2 3 4 5 N Fig.6 Variations of (a) the energy (E) of the HOMO and the LUMO and (b) the HOMO-LUMO energy gap (AEHOM~LUMO)for linearly extended phthalocyanines as a function of the number of benzene rings fused per pyrrole unit (N). The tetraazaporphyrin ring is taken as a reference (N=O). H,Pc, 2,3-H2Nc, 2,3-H2Ac and 2,3-H2Tc correspond to N= 1, 2, 3 and 4, respectively. The energies of the LUMO are shifted up by 0.62 eV as explained in the text. H,Tap to -5.23 eV for H,Pc and to -5.02 eV for 2,3-H2Nc. This trend, however, changes in passing to more extended systems like 2,3-H2Ac and 2,3-H2Tc, for which the LUMOs appear at -5.04 and -5.22 eV, respectively.The LUMO and LUMO + 1 of 2,3-H2Ac and 2,3-H2Tc exhibit in principle the same topologies as those shown in Fig. 5 for H,Pc, but with important contributions from the anthracene and tetracene units, respectively. The participation of the peripheral poly- acenic units is augmented along the series 2,3-H2Nc, 2,3-H2Ac, 2,3-H2Tc because the LUMOs of these units decrease in energy as the number of benzene rings increases: naphthalene, -3.91 eV; anthracene, -4.58 eV; tetracene, -4.99 eV. The interaction of the LUMO of the polyacenic units with the C,N, central ring along the x (b3,) or y (b,,) axes determines the stabilization of the lowest unoccupied orbitals in 2,3-H2Ac and 2,3-H,Tc and, as a consequence, the inversion in the evolution of the LUMO energy [see Fig.6(a)]. The energy of the LUMO is therefore not converged and lower energies are to be expected for more extended systems. The variations calculated for the energies of the HOMO and the LUMO jointly determine a continuous decrease of the HOMO-LUMO energy gap along the series H,Tap (2.08 eV), H,Pc ( 1.81eV), 2,3-H2Nc ( 1.65 eV), 2,3-H2Ac (1.46 eV), 2,3-H2Tc (1.19 eV). (As discussed in the Computational details section, these energies are obtained after adding up 0.62eV to compare with optical absorption data.) The narrowing of the HOMO-LUMO gap agrees with the bathochromic shift observed experimentally for the first absorption Q band along this series.Kobayashi20b has studied the UV-VIS-NIR absorption spectra of tetra-tert-butylated H,Tap, H,Pc, 2,3-H2Nc and 2,3-H2Ac in pyridine solution. The lowest optical transition appears at 619 nm (2.00 eV), 698 nm (1.78 eV), 784 nm (1.58 eV) and 858 nm (1.45 eV), respectively. Similar values were obtained by Hanack et ~1.~' for bidentate complexes of FePc (658 nm, 1.88 eV), 2,3-FeNc (751 nm, 1.65 eV) and 2,3-FeAc (829 nm, 1.50 eV). The Q band of vanadyl-2,3-tetracenocyanine, the only tetracenocyanine reported as yet, appears at 1055 nm (1.17 eV).,* The VEH results are in good agreement with all these experimental data. The energy of the Q band therefore seems to be far from being converged since a large bathochromic shift of ca.0.30eV is predicted theoretically and is observed experimentally in pass- ing from anthracyanines to tetracenocyanines. Fig. 6(b) represents the evolution of the HOMO-LUMO energy gap with the number of benzenes fused, N. The fitted curve shows a change in concavity with an inflexion point for N =2, indicating that the difference between the HOMO-LU MO gap calculated for two consecutive linearly annulated macrocycles decreases in going from H,Tap (N=0) to 2,3-H2Nc (N=2) but increases in going from 2,3-H2Nc to 2,3-H2Tc (N=4). This behaviour explains the non-asymptotic evolution of the energy of the Q band and suggests that greatly extended phthalocyanines could exhibit strong absorption bands in the near-IR with wavelengths significantly longer than 1000 nm.This possibility is especially attractive for the obtention of new photosensitizers and for the development of new materials for optoelectronics. We now turn to a discussion of the electronic structure associated with the occupied electronic levels lying between -7 and -10 eV (see Table 1). The 7bl, HOMO -1 of H,Pc (-9.01 eV) is not affected by the extension of the macrocycle because it is localized on the nitrogen atoms (see Fig. 4). Molecular orbitals with this A0 composition are found at exactly the same energy for 2,3-H2Nc (9b1,), 2,3-H2Ac (llblu) and 2,3-H2Tc ( 13bl,). All the remaining occupied orbitals above -10 eV are dominated by contributions from the poly- acenic units. For H,Pc, the four nearly degenerate MOs lying at -9.4 eV are located on the benzene moieties and their A0 composition corresponds to that of the le,, orbital of benzene with no contribution on the para carbons depicted in Fig.7(a). 1756 J. Muter. Chem., 1996, 6(11), 1751-1761 Fig. 7 Atomic orbital compositions and energies of the highest occupied molecular orbitals of (a) benzene, (b) naphthalene, (c) anthracene and (d) tetracene. Only orbitals above -10.0 eV are shown. The sizes of the circles are proportional to the magnitude of the LCAO coefficients. The following group of four orbitals between -9.6 and -10.0eV originates in the other le,, orbital of benzene. Similarly to H,Pc, two groups of four MOs appear for 2,3- H,Nc above -10eV. The A0 composition of the MOs forming these two groups indicates that they correspond to the la, HOMO and 2b1, HOMO-1, respectively, of the naphthalene molecule shown in Fig.7(b). The two groups of orbitals are in fact calculated to be centred at energies of about -8.6 and -9.2 eV, very similar to those found for the la, (-8.5 eV) and 2b,, (-9.3 eV) orbitals of naphthalene. For 2,3- H,Ac and 2,3-H2Tc, three groups of four MOs appear above -10 eV with topologies and energies identical to those shown in Fig. 7(c),(d) for the highest three occupied orbitals of anthra- cene and tetracene, respectively. In summary, each MO of the polyacenic units generates a group of four MOs in the macrocy- cle constituting a pair of b,,-b 3g. orbitals and two a, or b,, orbitals (see Table 1).The electronic structure of the macrocycle is thus dominated by the electronic levels of the peripheral polyacenic units and only the HOMO and the bl, orbital at -9.0 eV remain as electronic features intrinsically correspond- ing to the tetraazaporphyrin macrocycle. This has been shown for 2,3-naphthalocyanine, for which the photoelectron spec- unoccupied polyacenic orbitals that have appeared for extended Pcs. For 2,3-H,Ac, low-energy transitions can occur, for instance, between the 8a, HOMO and the llb3,,llb2, unoccupied levels or between the 7a,,6aU occupied orbitals and the 10b,,,10b3, LUMOs. One-dimensional electronic band structures The crystal structures of H,Pc and MPcs are well known since large monocrystals can be easily grown by sublimation at 400-500 "C, allowing for very precise X-ray diffraction mea~urements.~~~'~~~~The crystal growth of various MPcs has been studied recently in solid films prepared by vacuum deposition73 and molecular beam epita~y~~techniques.Phthalocyanines crystallize in columnar stacks where the planar macrocyclic molecules lie parallel to one another. Most of them are obtained in the so-called a-or in the thermo- dynamically more stable P-polymorphic form, where the Pc molecules adopt an 'eclipsed, slipped' stacking mode, as depicted in Fig. 8(a). The stacking axis forms an angle $ with the normal to the molecular plane, which has values of about 25" in the a-polymorph7' and of about 45" in the p-p~lymorph.~~-~~,~~ The 'face-to-face, staggered' molecular stacking displayed in Fig.8(b), where the stacking axis is perpendicular to the molecular plane and adjacent macrocycles in the stack are rotated alternatively by an angle 8, is obtained for doped Pcs like H,PcI (8= 40.0°)8" or NiPcI (8= 39.5")77 and also for one- dimensional polymeric Pcs like [ SiPcO], (8= 39").78 The dis; tance between adjacent moleFules in the stack is 3.23-3.25 A for doped Pcs~~,~~,~~ Phthalocyanineand 3.33 A for [ S~PCO],.~~ molecules adopt the 'face-to-face, eclipsed' orientation shoyn in Fig. 8(c) when the intrFstack interplanar spacing is > 3.50 A, as in [GePcO], (3.53 A)78 or in fluorinated polymers like [AlPcF], (3.66 A),80a [GaPcF], (3.87 and [ FePcF], (3.86 A).81 Kobayashi and U~eda~~ obtained thin [GePcO], films for w$ch the interplanar spacing was established to be only 3.40 A and adjacent rings in the stack were therefore observed to be staggered by an angle of 37".The crystal growth and molecular stacking of 2,3-metallo- naphthalocyanines (2,3-MNcs) have been investigated recently trum exhibits a one-to-one correspondence with the photoemis- sion bands observed for na~hthalene.~'" The appearance of polyacene-like occupied MOs at increas- ing energies above -9.0 eV and unoccupied MOs close to the b2g-b3g LUMOs explains the evolution of the optical properties $::/;IE -7 in the region of the B band. For H,Pc, the B band is centred 0,at 340 nm63 and has been mainly assigned to electronic exci- M-3--.A -8tations from the 7bl, HOMO-1 to the LUMO and LUMO+l.Since the energy of the 7bl, orbital remains constant upon benzoannulation, similar excitation energies should be expected for extended Pcs. This is exactly what is observed for naphthalocyanines and anthracyanines, for which the B band appears centred at about 340-360 nm.20b,29730 New absorption features are, however, detected on the low-energy side of the B band for these compounds. For instance, 2,3- anthracyanines show two weak absorption bands at about 440 and 570nm.20b,29,30 These new bands are due to electronic transitions involving the high-lying occupied and low-lying I I 0 da da da k k k Fig. 8 (a)-(c) Molecular stackings adopted by phthalocyanine-type macrocycles in crystals and thin solid films: (a) 'eclipsed, slipped'; (b) 'face-to-face, staggered'; (c) 'face-to-face, eclipsed'.(d)-( f ) VEH band structures calculated for 2,3-H2Nc along the one-dimensional stacks depicted on the top in (a)-(c). VB and CB denote valence and conduction bands, respectively. Unoccupied bands are shifted up by 0.62 eV to correct for the low excitation energies provided by the VEH method, J. Muter. Chern., 1996, 6(11), 1751-1761 1757 for various MNcs in epitaxial thin films vacuum deposited on alkali-metal halide substrates by means of X-ray and electron diffraction, IR spectroscopy and transmission electron microscopy.82 Divalent 2,3-H2Nc and 2,3-ZnNc are found to present a 'face-to-face, eclipsed' molecula! stacking with interplanar distances of only 3.29 and 3.31 A, respectively.82c As discussed above, this molecular stacking has not been reported for MPc crystals and is only observed f9r [MPcL] polymers when the inter-ring distance is > 3.50 A.Trivalent AlNcCl and GaNcF and tetravalent VONc are all found to present an 'eclipsed, slipped' stacking mode.82" To the best of our knowledge, no structural determination has been reported for more extended phthalocyanines. The molecular packing in columnar stacks determines a direct n-n interaction between adjacent molecules in the stack, but very weak interactions between molecules in adjacent stacks. One-dimensional VEH calculations have therefore been performed along the direction which gives rise to a significant n interaction, i.e.the stacking direction. Calculations have been carried out for the three molecular stackings depicted in Fig. 8(a)-(c). For the 'eclipsed, slipped' stacking, the crystalline data reported by Hoskins et aL5l for the more stable p-polymorphic form of H2Pc (intermolecular distance along the stacking axis, d = 4.73 A; angle of tilting, I,!I= 45.7") are adopted in the calculations. For the 'face-to-face, staggered' and 'face- to-face, edipsed' stackings, the data reported for doped H,PcI (d= 3.25 +,8 = 40.0")8" and for thin films of undoped 2,3-H2Nc (d= 3.29 A, 8= 0°)82care used, respectively. The VEH electronic band structures calculated for 2,3-H2Nc are drawn schematically in Fig.8(d)-(f ) below the respective molecular stackings. Similar band structures are obtained for H,Pc and 2,3-H2Ac. For 2,3-H2Tc, only the band structure corresponding to the 'face-to-face, eclipsed' stacking was calcu- lated due to the large size of the molecular system. Table 2 summarizes the VEH values computed for the valence band- width (W),ionization energy (&) and bandgap (EJ. The results of band-structure calculations on the angularly benzoannulated H,Phc are included for the sake of comparison. As illustrated in Fig. 8(d)-(f), the band structures show the same general aspect irrespective of the molecular stacking. The valence band (VB) lies alone well above the remaining occupied bands. It originates in the overlap of the a,(n) HOMOs of the macrocyclic monomers along the stack.The conduction band (CB) is formed by two nearly degenerate bands running parallel and resulting from the overlap of the b2g-b3g LUMOs. The electronic properties collected in Table 2 are, however, strongly affected by the stacking mode, which governs the overlap between adjacent molecules in the stack. The width of the VB increases in passing from the 'eclipsed, slipped' mode (0.34-0.36 eV) to the 'face-to-face, staggered' (0.82-1.00 eV) and 'face-to-face, eclipsed' (1.16-1.20 eV) modes owing to the Table 2 VEH-calculated width of the highest occupied electronic band (W),ionization energy (Ei) and bandgap energy (E,) of H,Pc, 2,3- H,Nc, 2,3-H2Ac, 2,3-H2Tc and H2Phc in various one-dimensional molecular stacks" 'eclipsed, slipped' 'face-to-face, 'face-to-face, staggered' eclipsed' W E, Egb W Ei E,b W Ei E,b H,Pc 0.34 6.16 1.76 0.92 5.95 1.64 1.20 5.81 1.74 2,3-H,Nc 0.36 5.87 1.51 0.86 5.61 1.43 1.18 5.45 1.58 2,3-H,Ac 0.35 5.70 1.21 0.82 5.45 1.11 1.17 5.28 1.39 2,3-H2Tc 1.16 5.20 1.13 H2Phc 0.35 6.57 1.74 1.00 6.32 1.58 1.19 6.24 1.72 "All values are ineV.bThe numbers quoted correspond to the minimum value of the direct energy gap. They are obtained after a shift of 0.62 eV to higher energies of the unoccupied bands to correct for the low excitation energies provided by the VEH method. 1758 J. Muter. Chern., 1996, 6(11), 1751-1761 more effective overlap achieved in these two stacking modes. The expansion of the macrocycle affects only slightly the width of the valence band because the outer benzene rings contribute to the HOMO to a lesser degree as the system is extended. Similar W values are thus obtained for all the macrocycles included in Table 2.The band structure of 'face-to-face' H,Pc stacks was calcu- lated for differept values of the staggering angle 8 (inter-ring distance=3.25 A), in order to study how the width of the valence band varies with rotation of neighbouring rings. Fig. 9 shows the variation calculated for W between 8=0 and 45". A symmetric behaviour is to be expected between 8=45 and 90" owing to the almost identical geometries of the isoindole moieties in H,Pc. The bandwidth presents a maximum value of 1.32 eV for the fully eclipsed rotamer (8=Oo) and a second maximum of 0.99 eV for the fully staggered rotamer (8=45").Between the two maxima the valence band becomes completely flat for a staggering angle of about 20" (W=0.03 eV). Similar behaviours were obtained by Whangbo and Stewarts3 using the extended-Huckel method and by Pietro et who calculated the transfer integral between adjacent rings for a phthalocyanine dimer using the Wolfsberg-Helmholtz approach. The variation of the bandwidth with 8 can be understood by reference to Fig. 10, where the interacting patterns at k=O between the HOMOs of two adjacent molecules are sketched for the 8=0 and 45" rotamers using only the C8N8 central ring. For the eclipsed rotamer, the interaction between neigh- bouring a,(n) orbitals is antibonding, while for the staggered rotamer it is less effective and bonding. Thus, in going from 8=0 to 45", the bonding interactions decrease and the snti- bonding interactions increase in such a way that they cancel each other at intermediate angles.The resulting non-bonding 1.4 1.2 1 0.8>z30.6 0.4 0.2 01 " I 0 15 30 45 eldegrees Fig.9 Variation of the valence bandwidth (w)with the staggering angle I3 between neighboucing rings in 'face-to-face' stackings of H,Pc (inter-ring distance = 3.25 A) Fig. 10 Interacting patterns at k=O between the a,(n) HOMOs of neighbouring H,Pc molecules arranged in 'face-to-face' stacks with staggering angles of (a) 8=Oo and (b) I3=45". H,Pc macrocycles are modelled by the C8N8 central ring.interaction explains the vanishing bandwidth obtained at about 20”. Phthalocyanines change from an ‘eclipsed, slipped’ stack- ing in the undoped state to a ‘face-to-face, staggered (8=40”)’ stacking when cocrystallized with oxidizing agents like iod- ine.8n,77,79This structural change is accompanied by a broaden- ing of the partially emptied valence band which facilitates the delocalization of the electrons, i.e. the charge carriers, giving rise to high metallic conductivities ( 101-104 S cm-’).8 As Pietro et al. discussed,84 if the doped material stacked with a staggering angle of ca. 20”, conductivity would only occur through an electron-hopping mechanism and the material would exhibit intrinsically activated conductivity instead of intrinsically metallic.Canadell and Alvarez also noted the relevance of the broadening of the VB for doped Pcs.~’ The MO interacting patterns depicted in Fig. 10 also explain the change in the sign of the slope of the VB in passing from the staggered to the eclipsed ‘face-to-face’ stacking [see Fig. 8(e) and (f)]. For the latter, the interaction is antibonding at k=O (in-phase translation) and bonding at k =n/a (out-of-phase translation). The VB therefore decreases in energy towards k= n/a and the highest occupied level corresponds to k=O. The opposite occurs for the staggered conformation, for which the interaction is bonding at k =0 and antibonding at k =n/a and the VB increases in energy towards k=n/a.This is also the case for the ‘eclipsed, slipped’ stacking mode [Fig. 8(d)]. The variation of the width of the valence band with the intermolecular distance was calculated for both the eclipsed (8=0”)and staggered (0=45”) ‘face-to-face’ stacking modes of H,Pc. As expected, the bandwidth decreases with increasing inter-ring distances owing to the weaker interactions that occur between adjacent macrocycles in the stack. For the eclipsed stacking, W is calculated to have values of 1.20,0.68, 0.52, 0.39 and 0.29 eV fy-intermolecular distances of 3.29, 3.50, 3.60, 3.70 and 3.80 A, respectively. Smaller values of 0.92, 0.81, 0.62, 0.47 and 0.36 eV are found fpr intermolecular distances of 3.25, 3.30, 3.40, 3.50 and 3.60A, respectively, for the staggered conformation.These bandwidths are an aid to understanding the room-temperature conductivities (uRT) measured for polycrystalline samples of doped phthalocyanine-based mate- rials. For example, the conductivity decreases along the series NiPcI (cRT >[(S~PCO)I~.~~],,=7.7 S ~m-~)~~~(0.67)86> [(G~PCO)~~.,~],,(0.11).86 All these materials present a ‘face- to-face, staggered’ stacking with 8=39:40” and intermol- (see Table 2). The decrease in the Ei is due to the larger values of the valence bandwidth. Lower ionization energies are obtained for linearly extended 2,3-H2Nc, 2,3-H2Ac and 2,3- H,Tc because of the continuously increasing energies of the HOMOS along this series. Minimum Ei values of only 5.45, 5.28 and 5.20 eV are thus calculated for the ‘face-to-face, eclipsed’ stackings of 2,3-H2Nc, 2,3-H2Ac and 2,3-H2Tc, respectively. The angularly annulated H,Phc system has Ei values ca.0.4eV higher than those in H,Pc, in accord with the lower energy of the HOMO of H,Phc. The values quoted in Table 2 for the energy gap separating the valence and conduction bands correspond to the minimum values of the direct energy gap found at k =n/afor the ‘eclipsed, slipped’ and ‘face-to-face, staggered’ stacking modes and at k =0 for the ‘face-to-face, eclipsed’ stacking mode. The E, calculated for the ‘face-to-face, staggered’ stacking mode is smaller than that calculated for the ‘face-to-face, eclipsed’ stacking mode because the CB is significantly narrower (e.g.0.48eV for 2,3-H2Nc) than the VB (0.86eV) for the former, while both bands have similar widths (1.04 and 1.18 eV, respectively) for the latter. The energy gap decreases for linearly extended systems and remains constant with respect to H,Pc for angularly extended systems such as H,Phc. Finally, it is important to note that the energy gap separating the top of the valence band from the bottom of the conduction band does not correspond to the direct energy gap at k=O or k =n/a, but to the indirect gap separating these two points of the Brillouin zone [see Fig. 8(d)-(f)]. An indirect E, of only 0.54 eV is calculated for the ‘face-to-face, eclipsed’ stacking observed experimentally for vacuum-deposited thin films of ~,~-H,Nc.~,‘The indirect E, decreases to 0.35 eV for 2,3-H,Ac and almost vanishes (0.09 eV) for 2,3-H2Tc.Since the intrinsic conducting properties of the material are largely determined by the energy gap separating the conduction and valence bands, high intrinsic conductivities are to be expected for stacks of linearly extended phthalocyanines. Summary and Conclusion The geometric and electronic structures of metal-free phthalo- cyanine and a series of linearly benzoannulated phthalocyan- ines have been investigated using the semi-empirical PM3 method and the non-empirical valence effective Hamiltonian ecular distances of 3.244, 3.30 and 3.48 A, re~pectively.~~“*~~ (VEH) pseudopotential technique. Geometry optimizations The increase of the intermolecular distance is accompanied by a narrowing of the partially emptied VB from ca.0.92 eV to ca. 0.47eV, thus explaining the decrease in the observed conductivities. Relatively high conductivities are also measured for doped polymeric Pcs such as [(A~PCF)(IF~)~.~-~.~], (OR= = 6 x lo-, S ~m-’),~~ (4.2 x[(G~PcF)(BF~),.~~]~ and [(F~PCF)I~.~],(5 x 10-3),81 yhich show longer inter-ring dis- tances of 3.66, 3.73 and 3.86 A, respectively. These conductivit- ies are explained as resulting from the fact that the eclipsed ring stacking observed for the undoped polymers persists for the doped materials. Thus, the inter-ring overlap loss due to the increase of the inter-ring separation is made up in large part by the more efficient overlap in the eclipsed conformation.Bandwidths between ca. 0.500and 0.25 eV are found for inter- ring distances of 3.60-3.90A in an eclipsed stacking mode, which are in fact slightly smaller than those found for a staggered stacking mode with inter-ring distances of 3.40-3.50 A (0.62-0.47 eV). The change in the sign of the slope of the VB depending on the molecular stacking mode means that the ionization energy onset corresponding to the top of the VB is situated at the edge of the Brillouin zone (k=n/a) for the ‘eclipsed, slipped‘ and ‘face-to-face, staggered’ stacking modes and at the centre of the Brillouin zone (k=0) for the ‘face-to-face, eclipsed’ stacking mode. For H,Pc, the ionization energy onset is calculated to have values of 6.16, 5.95 and 5.81 eV, respectively show that the peripheral polyacenic units (benzene, naphtha- lene, anthracene, etc.) preserve their structural identity in the macrocycles. Phthalocyanine-based compounds are therefore predicted to be the result of joining four polyacenic units to the C8N8 central ring.Linear benzoannulation strongly affects the electronic properties of the macrocycle. On the one hand, it produces a continuous destabilization of the HOMO, thus leading to lower ionization energies and oxidation potentials. On the other hand, it reduces the HOMO-LUMO energy gap, thus shifting the intense Q absorption band to the near-IR region. It is to be stressed that, in contrast to the HOMO, which shows asymptotic behaviour rapidly converging to an extrapo- lated energy of -5.69 eV, the HOMO-LUMO gap exhibits non-convergent behaviour and very low excitation energies are predicted for greatly extended phthalocyanines. Linear benzoannulation thus allows the modulation of the electronic properties and, in particular, the optical properties of the phthalocyanine macrocycle by controlling the number of ben- zene rings fused to each pyrrole axis.The extension can in fact be effected in a symmetric way on the four pyrrole axes as performed in this work, or in an asymmetric way by only extending one or two pyrrole axes as Kobayashi et al.*’ reported recently. The combination of these two strategies makes very fine adjustments of the redox and optical properties of the system possible.J. Mater. Chern., 1996, 6(11), 1751-1761 1759 VEH electronic band-structure calculations have been per- formed for the three one-dimensional molecular stacks more commonly found in crystals and polymers of phthalocyanines: ‘eclipsed, slipped’, ‘face-to-face, staggered’ and ‘face-to-face, eclipsed’. The width of the valence band, i.e. the band which is partially emptied upon oxidation for doped compounds, is 12 13 K. Abe, H. Sato, T. Kimura, Y. Ohkatsu and T. Kusano, Makromol. Chem., 1989,190,2693; T. L. Anderson, G. C. Komplin and W. J. Pietro, J. Phys. Chem., 1993,97, 6577; W. J. Pietro, Adv. Muter., 1994,6,239. R. Madru, G. Guillaud, M. A1 Sadoun, M. Maitrot, C. Clarisse, M. Le Contellec, J.-J. AndrC and J. Simon, Chem. Phys. Lett., 1987, 142, 103; R.Madru, G. Guillaud, M. A1 Sadoun, M. Maitrot, J- not affected by the extension of the macrocycle but depends strongly on the molecular stacking mode. For ‘face-to-face’ stacks, the bandwidth is determined by the twist angle, 8, between adjacent macrocycles and by the intermolecular dis- tance. A coherent picture of the conductivities observed exper- 14 15 J. Andre, J. Simon and R. Even, Chem. Phys. Lett., 1988, 145, 343; C. Clarisse and M-T. Riou, J. Appl. Phys., 1991,69,3324. J. E. Kuder, J. Zmag. Sci., 1988,32, 51; R. Ao, S. Jahn, L. Kummerl, R. Weiner and D. Haarer, Jpn. J. Appl. Phys., 1992,31, 693; R. Ao, L. Kummerl and D. Haarer, Adv. Muter., 1995,7,495. J. Simon, P. Bassoul and S. Norvez, New J. Chem., 1989, 13, 13; imentally for doped phthalocyanines is obtained by analysing M.K. Casstevens, M. Samoc, J. Pfleger and P. N. Prasad, J. Chem. the evolution of the bandwidth with 8 and the inter-ring distance. The linear expansion of the macrocycle produces a decrease of the ionization potential and the bandgap, similar to that found for the molecular systems. 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