Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy

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1 Spectrochimica Acta Part A 72 (2009) Contents lists available at ScienceDirect Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: IR spectroscopy investigation using DFT analysis on the structure of P 1 phosphorus dendrimer built from octasubstituted metal-free phthalocyanine core V.L. Furer a,, I.I. Vandyukova b, A. Pla-Quintana c, J.P. Majoral c, A.M. Caminade c, V.I. Kovalenko b, a Kazan State Architect and Civil Engineering University, Zelenaya 1, Kazan , Russia b A.E. Arbuzov Institute of Organic and Physical Chemistry, Russian Academy of Science, Arbuzov Str. 8, Kazan, Russia c Laboratorie de Chimie de Coordination, CNRS, 205 route de Narbonne, Toulouse Cedex 4, France article info abstract Article history: Received 11 September 2008 Received in revised form 5 November 2008 Accepted 5 November 2008 Keywords: Phosphorus-containing dendrimers IR spectra Normal vibrations DFT The IR spectra of P 1 phosphorus dendrimer built from an octasubstituted metal-free phthalocyanine core have been recorded in the region cm 1. Besides the phthalocyanine core, P 1 possess also eight C 6 H 4 CH N N(CH 3 ) P(S) arms and terminal P Cl groups. The optimized molecular geometry, frequency and intensity of the IR bands have been calculated using density functional theory (DFT). The P 1 molecules exist in a stable conformation with planar C 6 H 4 CH N N(CH 3 ) fragments and phthalocyanine core. The calculated geometrical parameters and harmonic vibrational frequencies are predicted in a good agreement with the experimental data. The experimental IR spectrum of P 1 dendrimer was interpreted by means of potential energy distributions. Relying on DFT calculations a complete vibrational assignment is proposed. The difference IR spectra of molecules built from the thiophosphoryl, cyclotriphosphazene, and phthalocyanine cores with the same repeated units and terminal groups were studied in order to undermine the role of the core functionality on the dendrimer architecture Elsevier B.V. All rights reserved. 1. Introduction Dendrimers are highly branched monodisperse macromolecular compounds [1 3]. The three structural components of dendrimers, namely an interior core, repeating branching units, radially attached to the core, and functional terminal groups can be tuned at will [2]. The concept of site isolation of the active core, leading to enhanced photo-physical properties was developed [3]. To yield a better understanding of the effect imparted by each component to the whole structure and the influence of each part on the others, it is highly desirable to introduce the density functional theory (DFT) studies of dendrimers. The preparation, IR and Raman spectra of phosphorus dendrimers with thiophosphoryl core built up to 12th generation with terminal aldehyde and P Cl groups were described [4,5]. The properties of dendrimers are closely related to the nature of the core [1 3]. A core, offering more functional groups gives a higher number of peripheral units for an equal number of synthetic steps [1 3]. The phosphorus-containing dendrimers built from the trifunctional, hexafunctional, and octafunctional cores with identi- Corresponding author. Tel.: ; fax: Corresponding author. Tel.: ; fax: addresses: furer@ksaba.ru (V.L. Furer), koval@iopc.knc.ru (V.I. Kovalenko). cal repeating units and terminal groups were prepared [4]. Thus a fine control of the overall size, shape, and container properties of dendrimers can be achieved [4]. Dendrimers with phthalocyanine core gave an opportunity to study a large variety of photo- and physico-chemical properties [6,7]. The isolation of the phthalocyanine core in dendrimers prevents their stacking, increase solubility [6,7]. It is important for application of phthalocyanines in photodynamic therapy, because aggregation induces a significant decrease in the photosensitising efficiency [6,7]. In this paper we report the IR spectra study combined with DFT calculations of P 1 which is the first generation phosphorus dendrimer built from an octasubstituted metal-free phthalocyanine core with P Cl terminal groups [6]. This work is an extension of the spectroscopic and quantum chemical studies concerning the structure and reactivity of phosphorus dendrimers [5]. The optimized structure parameters of the P 1 molecule and its IR spectra were obtained using DFT techniques. The values of calculated geometric parameters were compared with precise molecular structure derived by the X-ray analysis [6]. Thus the main aim of this work was to obtain the characteristic spectral features of structural parts of dendrimer: a phthalocyanine core, repeating units and terminal P Cl groups based on DFT quantum chemical analysis. The difference IR spectra of molecules built from the trifunctional thiophosphoryl, hexafunctional cyclotriphosphazene, /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.saa

2 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) Fig. 1. Structure of P 1, G c1 and G 1 molecules.

3 638 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) The synthesis and main characteristics of the studied phosphorus dendrimer were described earlier [4,6]. The molecular structure of the P 1 is the following: the octafunctional phthalocyanine core (P c ), the bifunctional repeating unit O C 6 H 4 CH N N(CH 3 ) P(S) and the chlorine atoms as the terminal groups (Fig. 1). The analogous molecules built from the trifunctional thiophosphoryl core S P( O ) 3 (G 1 ), the hexafunctional cyclotriphosphazene (NP) 3 core (G c1 ) and the same repeating units and terminal groups were studied in order to undermine the role of the core functionality on the dendrimer architecture (Fig. 1). IR spectra in the region cm 1 have been recorded with a Vector 22 Bruker FTIR spectrometer. The IR spectra of the solid samples were registered in KBr pellets. The spectral resolution was set at 4 cm 1. Sixty-four scans were added for each spectrum. 3. Computational method Fig. 2. The free base and dianionic forms of P 1. and octafunctional phthalocyanine cores with the same repeating units and terminal groups were studied in order to undermine the role of the core functionality on the dendrimer architecture. Analysis of IR spectra of dendrimers combined with DFT calculations is important for investigation of supramolecular properties of phosphorus-containing dendrimers as containers for different guest molecules. The calculation of electronic density spatial distribution reveals the existence of regions where appropriate environments would attract either ion or a metal atom. The interpretation of IR spectra of non-crystalline dendrimers is important for characterization their structure. The results that emerge from such an analysis contribute to the understanding of the structure, dynamics and properties of dendrimers. 2. Experimental Table 1 Experimental and calculated bond distances (Å) and bond angles ( )ofp 1. Calculations of IR spectra of dendrimer P 1 were carried out using the gradient-correlated density functional theory with Perdew Burke Ernzerhof exchange-correlation functional (DFT/PBE) [8]. This functional is very satisfactory from the theoretical point of view because it does not contain any fitting parameters [9]. The binding energies, geometries and dynamical properties of different molecules calculated with PBE functional show the best agreement with experiment [10,11]. Calculations were performed using three exponential basis with two polarising functions (TZ2P) [12]. This basis set was chosen in order to obtain the most advantageous relation of accuracy and computation time [12]. The program PRIRODA was used to perform DFT calculations [12]. All stationary points were characterised as minima by analysis of Hessian matrices. The software package SHRINK was used for transformation of quantum mechanical Cartesian force constants to the matrix in redundant internal coordinates and calculation of potential energy distribution [13]. No scaling procedure of frequencies or force constants was applied. Recently, we checked the selected functional and basis set by calculation of geometry and IR spectra of dendrimers [14] Experimental [16,17] Calculated Experimental [16,17] Calculated Bond distances C(1) C(2) C(2) C(4) C(30) O(1) C(9) N(4) C(33) O(1) C(4) N(1) C(33) C(34) C(2) C(6) C(38) C(39) C(39) N(9) N(9) N(10) P(1) N(10) P(1) S(1) C(40) N(10) P(1) Cl(1) C(39) N(9) Angles C(1) C(3) C(5) N(1) C(4) N(2) C(1) C(3) O(3) C(4) N(1) C(9) C(3) O(3) C(49) C(4) N(2) C(8) C(33) C(34) C(35) C(2) C(4) N(2) C(38) C(39) N(9) C(39) N(9) N(10) N(9) N(10) C(40) N(9) N(10) P(1) N(10) P(1) S(1) N(10) P(1) Cl(1) N(10) P(1) Cl(2) S(1) P(1) Cl(1) S(1) P(1) Cl(2) Dihedral angles C(28) C(30) O(1) C(33) C(30) O(1) C(33) C(34) C(30) C(32) O(2) C(39) C(32) O(2) C(39) C(41) C(1) C(2) C(6) C(7) C(36) C(37) C(38) C(39) C(1) C(2) C(6) C(8) C(2) C(6) C(8) N(2) C(2) C(6) C(8) N(3) C(4) N(2) C(8) N(3) C(4) N(2) C(8) C(6) N(2) C(4) N(1) C(9) C(4) N(1) C(9) N(4) C(38) C(39) N(9) N(10) C(39) N(9) N(10) C(40) C(39) N(9) N(10) P(1) N(9) N(10) P(1) S(1) N(9) N(10) P(1) Cl(1) N(9) N(10) P(1) Cl(2)

4 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) Fig. 3. Optimized geometry and atom numbering for the free base form of P 1. The minima of the potential surface were found by relaxing the geometric parameters with standard optimization methods. IR spectra were generated from a list of frequencies and intensities using Gaussian band shape and half-width of 10 cm 1 for each of N vibration modes calculated. The intensity of each band is A k in km/mol. I(v) = N { A k exp (v v } 0) k of phthalocyanine [17]. It was shown that most of phthalocyanine derivatives have planar conformation [17]. The calculated bond distances and bond angles correspond well to the experimental values (Table 1). An assignment of bands was fulfilled on the basis of calculated potential energy distribution (PED). 4. Results and discussion The X-ray diffraction experimental data of P 1 are absent. But we can use the geometric parameters of G 1 dendrimer and phthalocyanine [15,16]. The X-ray data for the G 1 dendrimer built from a trifunctional core show that molecule as a whole looks like a threeblade propeller when examined in the direction of P S group of the core and each O C 6 H 4 CH N N(CH 3 ) arm is planar [16]. To have a deeper insight on the acido/basicity properties of the phthalocyanine ring the liability of core hydrogens was studied. The four pyrrole nitrogen atoms can theoretically undergo protonation/deprotonation reactions (Fig. 2) which modify the symmetry of the phthalocyanine ring and affect particularly UV vis spectra [6]. The results of full geometry optimisation of the free base and dianionic forms of P 1 molecule are presented (Table 1). Although the comparison between gas phase and condensed phase structures is not direct, we can observe a reasonable agreement between theoretical calculations of the free base form of P 1 and experimental X-ray diffraction data [15,16] (Table 1). Full optimization yielded the conformer of P 1 with planar phthalocyanine ring (Fig. 3). The calculated dihedral angles of phthalocyanine ring are less than 4. Our data correspond to recent ab initio calculations Fig. 4. Theoretical of the free base (1) and dianionic forms (2) and experimental (3) IR spectrum of P 1.

5 640 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) From DFT calculations it follows that each O C 6 H 4 CH N N (CH 3 ) arm is planar. Thus, the molecular conformation is defined by the dihedral angles C(28) C(30) O(1) C(33) and C(30) C(32) O(2) C(41) which determine the orientation of the arms (Fig. 3). As it follows from the X-ray data the experimental dihedral angles C(28) C(30) O(1) C(33) and C(30) C(32) O(2) C(41) are equal to 64.2 and Full optimization of free base form yielded the conformer with dihedral angles and The experimental dihedral angles C(30) O(1) C(33) C(36) and C(32) O(2) C(41) C(42) are equal to and and correspond to calculated for the free base form values and Thus as it follows from the theoretical data of P 1 O C 6 H 4 CH N N(CH 3 ) P(S) arms are not coplanar with phthalocyanine core. The calculated bond distances and angles of the dianionic and free base forms of P 1 show little difference and correspond well to the experimental values. The conformations of O C 6 H 4 CH N N(CH 3 ) P(S) arms are slightly different for theoretical structures of the dianionic and free base forms of P 1. The calculated value of dihedral angle N(2) C(4) N(1) C(9) for free base form better corresponds to the experimental data thus this form is observed at room temperature. The repeating units of P 1 dendrimer are oriented out of the phthalocyanine core plane due to steric reasons. This imposes an isolation of the phthalocyanine core and the dendrite shell mimics a highly polar solvent. Our results are consistent with experimental data that the first generation of dendrimer is much more soluble than the zero generation. This means that the known tendency of phthalocyanines to stack, which causes their insolubility, is largely diminished, even for the first generation. The dendrimer shape can be characterized by ratios I 1 /I 3 and I 2 /I 3 of principal moments of gyration tensor. The difference of these ratios from 1 characterizes the deviation of dendrimer shape from the sphere. For the studied dendrimers the calculated values of ratios I 1 /I 3 and I 2 /I 3 of principal moments of gyration tensor are and (G 1 ), and (G c1 ), and (P 1 ). Thus all the studied phosphorus-containing dendrimers of the first generations have highly asymmetric shape and possess open structures. In order to evaluate the interactions between dendrimers and various active substances, such as drugs, pesticides, and perfumes, we calculated electronic density spatial distribution for the core and terminal groups. From our calculations it follows that the studied phosphorus-containing dendrimers incorporate C N polar bonds in the phthalocyanine core with Hirshfeld charges (in a.u.) on atoms [18]: N(1) 0.14, N(2) 0.03, N(4) 0.16 and C(4) The oxygen atoms of the repeated unit also have negative charges The S and P atoms of the S PCl 2 terminal group have values of charges 0.19 and +0.30, respectively. Thus the molecules of phosphoruscontaining dendrimers have a hydrophobic interior. Dipole moments may be used for characterization of dendrimer structure [16]. Recently it was shown that the experimental dipole moments of dendrimers built from thiophosphoryl core and P Cl terminal groups increase from 8.43 D (G 1 )to258d(g 10 ), the highest dipole moment values reported up to now for dendrite structures Table 2 Experimental and corresponded calculated frequencies (cm 1 ) and intensity I (km/mol) of bands in the IR spectra of P 1 in the region cm 1. Experiment Calculation Assignment a Free base form Dianionic form PED I I (CC ar), 11 (CCH), 9 (CN) (CCH), 30 (CC ar), 9 (CC) (CC ar), 17 (CO), 8 (CN) (CC ar), 21 (CC pyr), 8 (CN) (CC ar), 32 (CCH) (CC ar), 22 (CN), 10 (CC pyr) (CN), 6 (CCC), 5 (CCH) (CN), 12 (CC pyr), 8 (NCN) (CO), 20 (CC ar), 19 (CCH) (CC ar), 19 (CC pir ), 18 (CO) (CO), 16 (CCH), 7 (CCH) (CN), 14 (CO), 15 (CC ar) (CN), 12 (CC pir ), 6 (CNC) (CC pyr), 16 (CCH), 15 (CN) (CO), 15 (CCH), 14 (CC ar) (NCH), 7 (HCH) (CN), 16 (CO), 10 (CC pyr) (CN), 16 (CO), 13 (CC pyr) (PO) (NN), 20 (PN), 14 (CNH) (CH), 18 (CC ar), 5 (CNN) (CC ar), 18 (CH), 9 (CCH) (CH), 5 (CC) (CH), 6 (CC ar), 6 (CO) (CNC), 16 (CN), 14 (NCN) (OCC), 14 (CO), 14 (CC pyr) (CH), 33 (CC) (CN), 27 (CC), 12 (CH) (OCC), 26 (CCC), 10 (CCN) (CCC), 12 (OCC), 4 (CCH) (CN), 24 (CC), 11 (CCC) (CCC), 10 (COC) (PCl), 5 (NPCl), 4 (SPCl) (PCl), 6 (NPCl), 4 (SPCl) (CC), 13 (OCC), 7 (CH) (CC), 27 (CN), 7 (PN) a, stretch;, in-plane-bend;, out-of-plane bend;, torsion.

6 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) Fig. 5. The difference IR spectra P 1 G 1 (3) and IR spectra of G 1 (1) and P 1 (2). Fig. 6. The difference IR spectra P 1 G c1 (3) and IR spectra of G c1 (1) and P 1 (2). [16]. The calculated in gas phase dipole moment 5.8 D for the free base form of P 1 increases to 9.0 D for the dianionic form. Thus the P 1 dendrimer has the significant dipole moment. An increase of the local polarity induced by the arylhydrazone branches lead to the progressive protection of the phthalocyanine core for higher generations of dendrimer [6,7]. The band at 3250 cm 1 in the IR spectra, corresponding to the stretching of pyrrole NH bonds, is observed. Thus P 1 dendrimer at room temperature exists in the free base form. We calculated the IR spectra of P 1 containing the free base and dianionic forms of phthalocyanine core (Fig. 4, Table 2). The theoretical spectra of the free base and dianionic forms of P 1 are similar to each other (Fig. 4). The phthalocyanine core reveals itself by bands at 877, 1015, 1086, 1274 and 1440 cm 1 in the IR spectra of P 1. The repeating units show bands at 1601, 1503 cm 1 of (CC) ar stretch and 954 cm 1 assigned to P O stretch. The terminal groups are characterized by the well-defined bands at 495 and 527 cm 1 in the experimental IR spectra of P 1 assigned to the P Cl stretching vibrations. It is interesting to compare the IR spectra of P 1, G c1 and G 1 dendrimers built from phthalocyanine, cyclotriphosphazene and thiophosphoryl cores. The characteristic features of the studied IR spectra of P 1, G c1 and G 1 dendrimers are their similarity to each other (Figs. 5 and 6). The frequencies of most bands in the IR spectra of P 1, G c1 and G 1 dendrimers are just the same only changes of intensity of some bands occur. In order to clear up these changes the difference IR spectra of dendrimers were studied (Figs. 5 and 6). A dendrimer molecule consists of three types of units: initiator-core (C), repeating unit (R) and terminal group (T). A fine control of dendrimer structure enables one to assign bands in the IR spectra to the specific molecular fragments. A clear example of the above opportunity is given when in the difference spectra of dendrimer built from phthalocyanine and thiophosphoryl cores P 1 G 1 compensation is made by band of terminal group. The result of subtraction will be the difference spectra in which by one side of zero line will be situated the bands of phthalocyanine core (C 8 ), and on the other side the bands of the thiophosphoryl core (C 3 ). Such spectral additivity appears from the equations: C 8 = 1, R 1 = 8, T 1 = 16 (P 1 ). C 3 = 1, R 1 = 3, T 1 = 6(G 1 ). Then the subtraction G 1 from P 1 looks like: C 8 + 8R + 16T 8/3(C 3 + 3R + 6T) = C 8 8/3C 3. Thus, in difference spectra on side of P 1 the bands of the phthalocyanine core (C 8 ) and on the side of G 1 the bands of the thiophosphoryl core (C 3 ) with intensity, multiplied by factor 8/3 must be observed. Another example of the above opportunity is given when in the difference spectra of dendrimer built from phthalocyanine and cyclotriphosphazene cores P 1 G c1 compensation is made by band of terminal group. The subtraction G c1 from P 1 looks like: C 8 + 8R + 16T 4/3(C 6 + 6R + 12T) = C 8 4/3C 6. Thus, in difference spectra on side of P 1 the bands of the phthalocyanine core (C 8 ) and on the side of G c1 the bands of the cyclotriphosphazene core (C 6 ) with intensity, multiplied by factor 4/3 must be observed. In practice experimental IR spectra may not obey such simple and ideal arithmetic. Any differences in spectra must be connected with the changes of the environment of these fragments, variation of the conformational and crystalline state, modification of the intra- and intermolecular interactions and so on. The analysis of the difference IR spectra P 1 G 1, P 1 G c1 enables one to distinguish the bands of the phthalocyanine, thiophosphoryl and cyclotriphosphazene cores (Figs. 4 and 5). For example, in the difference IR spectra P 1 G 1 bands near 495, 527, 692, 748, 1218 and 1504 cm 1 show characteristic EPR-like character. The bands on side P 1 of the zero line in the difference IR spectra P 1 G 1 at 711, 748, 877, 1015, 1086, 1274 and 1440 cm 1 are connected with vibrations of the phthalocyanine core. The bands on side G 1 of the zero line in the difference IR spectra P 1 G 1 at 693, 782, 925 cm 1 are assigned to vibrations of the thiophosphoryl core. The bands on

7 642 V.L. Furer et al. / Spectrochimica Acta Part A 72 (2009) side G c1 of the zero line in the difference IR spectra P 1 G c1 at 691, 776, 878, 891, 1121, 1156, 1176 cm 1 are assigned to vibrations of the cyclotriphosphazene core. One may take into consideration, that in the real difference spectra the intensity of the bands of the core will be very small, and the significant part of the bands of repeating units and terminal groups is subtracted from each other. Thus it follows that the fine effects, connected with the distinction of the structure of P 1, G 1 and G c1 molecules (small shifts of bands, which are not displayed in ordinary spectra), will be clearly seen in the difference spectra. For example, the frequency of P O stretch band at 954 cm 1 in the experimental IR spectra of P 1 is computed at 935 cm 1 for free base form. In the IR spectra of G 1 dendrimer, with thiophosphoryl core, this band is shifted to 925 cm 1. Such shift is clearly observed in the difference IR spectra. The characteristic feature of IR and Raman spectra of the generations G 1 G 10 is their similarity to each other [5]. The band half-width and intensity show very little changes for the first four generations and then achieve saturation. The saturation of the band intensity is observed because the ratio of the repeating units and end groups tends to one when the generation numbers increase and reflects strong homogeneity of the dendrimer macromolecules. Thus some structural features of the first generation dendrimer built from phthalocyanine core obtained in this study are contained for the higher generations of dendrimers and define their properties. 5. Summary Experimental and computational studies of spectroscopic properties of dendritic phthalocyanines provide interesting insights into the structure of the phthalocyanine core and dendritic branches. The agreement between the experimental and calculated IR spectra, in terms of both frequencies and intensities is very satisfactory. The theoretical values of ratios of principal moments of gyration tensor reveal that all studied phosphorus-containing dendrimers of the first generations have highly asymmetric shape and possess open structures. The free base form of the first-generation dendrimer with a metal-free octasubstituted phthalocyanine is observed at room temperature in the FTIR experiment in accordance with DFT study. Acknowledgements Authors are grateful to Department of Chemistry and Materials Science of Russian Academy of Science for financial support (Program 7). We are also grateful to supercomputer center of collective use of Kazan Scientific Center RAS for access to computer resources. References [1] G.R. Newkome, C.N. Moorefield, F. Vogtle, Dendrimers and Dendrons: Concepts, Syntheses, Applications, VCH, Weinheim, [2] J.M.J. Frechet, D.A. Tomalia, Dendrimers and Other Dendritic Polymers, Wiley, New York, [3] S. Hecht, J.M.J. Frechet, J. Angew. Chem., Int. Ed. 40 (2001) 74. [4] J.P. Majoral, A.M. Caminade, V. Maraval, Chem. Commun. (2002) [5] V.I. Kovalenko, V.L. Furer, A.E. Vandyukov, R.R. Shagidullin, J.P. Majoral, A.M. Caminade, J. Mol. Struct. 604 (2002) 45. [6] J. Leclaire, R. Gagiral, S. Fery-Forgues, Y. Coppel, B. Donnadieu, A.M. Caminade, J.P. Majoral, J. Am. Chem. Soc. 127 (2005) [7] J. Leclaire, R. Gagiral, A. Pla-Quintana, A.M. Caminade, J.P. Majoral, Eur. J. Inorg. Chem. Soc (2007) [8] C. Lin, K. Wu, R. Sa, C. Mang, P. Liu, B. Zhuang, Chem. Phys. Lett. 363 (2002) 343. [9] J.P. Perdew, K. Burke, M. Erznzerhof, Phys. Rev. Lett. 77 (1996) [10] M. Erznzerhof, G.E. Scuseria, J. Chem. Phys. 110 (1999) [11] C. Adamo, V. Barone, J. Chem. Phys. 110 (1999) [12] D.N. Laikov, Yu.A. Ustynyuk, Russ. Chem. Bull., Int. Ed. 54 (2005) 821. [13] V.A. Sipachev, J. Mol. Struct. (Theochem.) 121 (1985) 143. [14] V.L. Furer, A.E. Vandyukov, J.P. Majoral, A.M. Caminade, V.I. Kovalenko, J. Mol. Struct. 785 (2006) 153. [15] S. Matsumoto, K. Matsuhama, J. Mizuguchi, Acta Cryst. C 55 (1999) 131. [16] M.L. Lartigue, B. Donnadieu, C. Galliot, A.M. Caminade, J.P. Majoral, Macromolecules 30 (1997) [17] A.B.J. Parusel, S. Grimme, J. Porphyrins Phthalocyanines 5 (2001) 1. [18] F.L. Hirshfeld, Theor. Chim. Acc. 44 (1977) 129.