Electronic structure and photophysics of the aza-analogues of hydroporphyrins

Chemical Physics 298 (2004) 1–16 www.elsevier.com/locate/chemphys

Electronic structure and photophysics of the aza-analogues of hydroporphyrins V.A. Kuzmitsky a

c

a,*

, E.A. Makarova b, P.P. Pershukevich a, I.K. Shushkevich a, K.N. Solovyov a,*, V.B. Tusov c

Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, Laboratory of Luminescence, F. Skaryna Ave., 70, 220072 Minsk, Belarus b Organic Intermediates and Dyes Institute, B. Sadovaya Str., 1/4, 103787 Moscow, Russia Biophysics Department, Faculty of Biology, M.V. Lomonosov State University, Vorobyovy Gory, 119992 Moscow, Russia Received 12 March 2003; accepted 29 October 2003

Abstract The spectra of fluorescence and fluorescence excitation of tetraazachlorin and tetraazabacteriochlorin substituted at the reduced pyrrole rings have been investigated at 290 and 77 K; the fluorescence quantum yield and life time have been measured at 290 K; the fluorescence polarization spectra have been obtained at 77 K. Quantum-chemical calculations have been performed for a series of porphin derivatives: porphin–chlorin–bacteriochlorin–tetraazaporphin (porphyrazine)–tetraazachlorin– tetraazabacteriochlorin by the CNDO/S method with the use of molecular geometry acquired by the AM1 and PM3 optimization. The visible and UV absorption spectra and the fluorescence polarization spectra are adequately described by the CNDO/S calculation results, as well as the spectral changes in the series porphyrazine–tetraazachlorin–tetraazabacteriochlorin and from bacteriochlorin to tetraazabacteriochlorin. Strong quenching of fluorescence on the pyrrole rings reduction in the porphyrazine macrocycle has been found. It is shown that this quenching cannot be wholly explained by the increase in the rate constant of the S1 , S0 internal conversion which may be due to the lowering of the S1 level. Supposedly, the increase in the rate constant of the S1 , T1 intersystem crossing is due to participation of intermediate triplet levels in this process. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Tetraazachlorin; Tetraazabacteriochlorin; UV–Vis absorption spectrum; Fluorescence polarization spectrum; Quantum-chemical calculation

1. Introduction The researchersÕ interest in the electronic structure and spectroscopic properties of hydroporphyrins is caused, to a considerable extent, by the presence of a hydrogenated pyrrole ring in the molecule of chlorophyll a, the universal photosynthetic pigment, and of two such rings in the molecule of bacteriochlorophyll which is responsible for the photosynthesis of purple bacteria. The specific feature of the porphyrin macrocycle is that the hydrogenation (more generally, reduction) of ‘‘semi-isolated’’ double bonds in one or two pyrrole rings does not result * Corresponding authors. Tel.: +375-17-2841725; fax: +375-172840030. E-mail addresses: [email protected] (V.A. Kuzmitsky), [email protected] (K.N. Solovyov).

0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.10.039

in the interruption of the main cyclic conjugation chain. At the same time, the reduction of pyrrole rings exerts considerable influence on the electronic absorption spectra. In particular, this is the cause of the green color of chlorophyll and of all vegetation on the Earth. The accumulated information on the properties of the excited electronic states and photophysics of the hydroporphyrin molecules has been treated in monographic literature [1–4] (theoretical work [5], which is partially of a review character, should also be mentioned). However, in the interpretation of the electronic spectra of hydroporphyrins there are unclear questions, as noted in [4]. Aza-substitution of the methine bridges is another known structural modification of the porphyrin macrocycle strongly affecting the electronic spectra of

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porphyrins [1,2,4]. Study of this structural factor is of considerable interest for establishing the physico-chemical kinship of porphyrins, as biologically important compounds, with synthetic dyestuffs, phthalocyanines, which find various practical applications in science and technology. Of essential importance, from the point of view of the influence of molecular structure of porphyrinic compounds on their physico-chemical properties, is the combination of tetraaza-substitution with the pyrrole rings reduction. The synthesis of this kind of compound was performed in [6,7]. In [6] unsubstituted tetraaza-dihydroporphin, or tetraazachlorin (H2 TAC) was obtained; its structure was proven, and, in particular, it was shown that the substance synthesized earlier, to which the

structure of tetraaza-tetrahydroporphin had been assigned [8], is in fact a dihydro-derivative, viz., H2 TAC. Unsubstituted tetraaza-tetrahydroporphin with opposite disposition of reduced pyrrole rings, or tetraazabacteriochlorin (H2 TABC), was not isolated due to instability [6]. Later, however, in [7] a number of quite stable derivatives of H2 TAC and H2 TABC was synthesized which contain attached to reduced pyrrole rings fragments preventing their dehydrogenation, specifically, those with di(tert-butylbenzo)barrelene fragments – H2 TACt and H2 TABCtt (Fig. 1). Molecules of H2 TAC and H2 TABC and their analogues of the type of H2 TACt or H2 TABCtt deserve detailed investigation by spectroscopic methods, in particular, from the standpoint of development of the-

Fig. 1. Structural formulae of porphin (H2 P); chlorin (H2 C); bacteriochlorin (H2 BC); tetraazaporphin (H2 TAP); tetraazachlorin (H2 TAC); tetraazabacteriochlorin (H2 TABC); 2,3-[9,10-dihydro-2,6-di(tert-butyl)anthracene-9,10-diyl]tetraazachlorin (H2 TACt ); 2,3:12,13-bis[9,10-dihydro-2,6di(tert-butyl)anthracene-9,10-diyl]tetraazabacteriochlorin (H2 TABCtt ). R0 ¼ –C(CH3 )3 .

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oretical models of the electronic structure and excited electronic states of tetrapyrrole macrocycle. It should be noted that aza-substitution is isoelectronic, the number of electrons in the p-system also remaining unchanged. In this work we report on the results of the experimental study of spectral-luminescent properties of H2 TACt and H2 TABCtt and those of quantum-chemical calculations for H2 TAC, H2 TABC, and for a number of related compounds: porphin (H2 P), chlorin (H2 C), bacteriochlorin (H2 BC), and porphyrazine, or tetraazaporphin (H2 TAP), whose structure is shown in Fig. 1. The data of experimental investigations have been presented in short communications [9,10]. It is necessary to note that, in parallel with this study, a research was carried out with the use of tetraaza-hydroporphyrins synthesized in the same institution (Organic Dyes and Intermediates Institute) in which, apart from spectral-luminescent measurements and quantum-chemical calculations, the methods of magnetic circular dichroism, time-resolved ESR, and cyclic voltammetry were also used [11].

2. Experimental The synthesis of the compounds investigated is described in [7]. Chromatographic purification was carried out on silica gel. By chromatography two fractions of H2 TABCtt have been revealed. With the help of the NMR method it has been established that one fraction corresponds to the trans-configuration, i.e., the dibenzobarrele fragments are disposed on different sides of the plane of macrocycle (‘‘chair’’), while the other corresponds to the cis-configuration (‘‘bath’’). Fluorescence spectra and fluorescence excitation spectra were recorded with an SDL-2 spectrofluorimeter consisting of an MDR-12 wide-aperture excitation monochromator and an MDR-23 detection monochromator. Fluorescence was excited by a DKsSh-120 xenon lamp and detected at a right angle to the direction of excitation. The light signal was detected with an FEU-62 cooled photomultiplier (in the 700–1100 nm spectral range) operating in the photon counting mode. The fluorescence excitation spectra were corrected for the spectral distribution of the excitation source at the monochromator exit slit by means of two independent methods: (i) using optically dense dye solutions as photon counters with the optical density D > 2 per 1 cm over the entire spectral range and (ii) using diluted dye solutions with D < 0:1 per 1 cm, whose absorption spectra and fluorescence excitation spectra were assumed to be coincident. A broad spectral correction range between 250 and 900 nm was provided by a set of dyes absorbing in the spectral range from UV to IR. The spectral sensitivity of the monochromator–photomultiplier detection system was corrected with the use of a TRSh 2850 standard tungsten lamp. The spectral

3

slit width of the excitation monochromator was 67.2 nm over the entire spectral range studied, and that of the detection monochromator was 2.6 nm in the 400– 800 nm spectral range and 5.2 nm in the 800–1100 nm range. Absorption spectra were recorded with a Cary 500 Scan UV–Vis–NIR spectrophotometer at room temperature. The fluorescence quantum yield, uF , was determined at room temperature for toluene solutions by a relative method using cresyl violet (oxazine 9) in ethanol as a standard having uF ¼ 0:61 (as measured by us relative to 3,6-diamino-N-methylphthalimide in ethanol for which uF ¼ 0:46 [12]). The measurements of fluorescence duration, sF , were carried out, also at room temperature in toluene, with the picosecond pulse fluorometer described in [13] (using a new Hamamatsu based detection system) at excitation by the third harmonic of neodymium laser (kexc ¼ 355:2 nm), i.e., near the maxima of intense absorption bands of the compounds investigated. For excitation, light pulses of duration Dtpulse
5 ps were used. Each experimental fluorescence kinetic curve was a result of 40– 50 accumulations. Mathematical treatment of the time evolution of fluorescence decay was performed by the convolution of a model curve, of the form IðtÞ ¼ P Ið0Þ Ai expðt=si ), with the instrument characteristic function of the detection system. Here, si and Ai are the duration and relative intensity of the ith component of the fluorescence decay kinetics, Ið0Þ is the fluorescence intensity at zero time. Rigid-glass forming mixture of solvents ET: ethyl ether–toluene (2:1 v/v) was used in low-temperature spectral and polarization measurements.

3. Details of calculation Geometrical structure of the molecules under consideration has been acquired on the basis of calculations by the methods AM1 [14] and PM3 [15] with the use of soft ware package [16]. In so doing, the restrictions corresponding to D2h symmetry were imposed on the geometry of the H2 P, H2 TAP, H2 BC, and H2 TABC molecules, while the C2v restrictions were imposed in the cases of H2 C and H2 TAC. The initial geometry of the pyrrole and pyrrolenine rings was taken from the X-ray data for H2 P [17,18], and the geometry of hydrogenated pyrrolenine rings – from X-ray data for phyllochlorin methyl ester [19] averaged in accordance with the used C2v symmetry restrictions. The calculations of the excited states were carried out by the CNDO/S method [20,21] using the modified (many times) program of one of the authors (V.A.K.) [22]. The number of singly excited electron configurations taken into account in the calculations was 400 (20 occupied MOs  20 vacant MOs).

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4. Results 4.1. Experiment The absorption spectra of the investigated compounds in toluene are shown in Fig. 2. They differ only slightly from the spectra of n-hexane solutions [7], i.e., the effect of solvent is insignificant. Comparison of the position of the main absorption bands for H2 TAC [6] and H2 TACt [7] shows that the influence of the dibenzobarrelene fragment on the disposition of the electronic levels of the macrocycle is weak: values of kmax 676, 518 and 344 nm for H2 TACt in benzene correspond to values 678, 520 and 345 nm for H2 TAC (in chlorobenzene). Such similarity is natural, since this fragment does not come into conjugation with the p-electron system. At the same time, this fact is very important because it allows, when investigating the effect of pyrrole rings reduction on spectral characteristics, to use parameters of substituted compounds in the absence of data for compounds with unsubstituted reduced pyrrole rings. For instance, one may state that the absorption spectrum of H2 TABCtt reflects that of H2 TABC with sufficient accuracy. Allowing for this circumstance, the data of Fig. 2, together with the absorption spectrum of H2 TAP (in benzene [23] or chloroform [7]) represent the series

Fig. 2. Absorption spectra of H2 TACt (dashed line) and H2 TABCtt (solid line) in toluene at 290 K (normalized at the Qx band maxima).

H2 TAP–H2 TAC–H2 TABC. In this series reduction of pyrrole rings leads to considerable bathochromic shifts of the longest-wavelength absorption band. Values of kmax of this band are 617 nm for H2 TAP, 678 nm for H2 TAC, and 792 nm for H2 TABCtt . The corresponding frequency shifts relative to H2 TAP are )1450 and )3600 cm1 . We studied the two mentioned above isomers of H2 TABCtt differing in the disposition of the dibenzobarrelene fragments relative to the macrocycle plane, on one side (cis-H2 TABCtt ) and on both sides (trans-H2 TABCtt ). In spectral properties they differ insignificantly (minor discrepancies are observed only in the 350–400 nm region), but difference in other properties is appreciable. For example, the ET solution of the cis-isomer forms stable rigid glasses on freezing, whereas glasses formed by the solution of the trans-isomer are unstable, prone to cracking. In the following the information refers to both isomers, if not stated otherwise. The fluorescence and fluorescence excitation spectra of H2 TACt , cis-H2 TABCtt , and trans-H2 TABCtt at room and liquid nitrogen temperatures have been acquired; the quantum yield, duration, and low-temperature polarization spectra of fluorescence have been measured. The fluorescence spectra at 290 and 77 K are given in Fig. 3. It is seen that the lowering of temperature results in essential band-harrowing and appearance of vibrational structure. The fluorescence excitation spectra (measured at monitoring in the range of 0–0 band of the fluorescence spectrum) at 290 K agree well with the absorption spectra which is evidence of the purity of preparations. At 77 K (Fig. 4) the narrowing of the absorption bands and minor hypsochromic shifts are observed. Thus, for H2 TACt at 77 K, kmax ¼ 675, 517, 344 nm; the corresponding shifts relative to the room temperature absorption spectrum in the same solvent (ET) are: )3, )2, and )6 nm, respectively. It is seen from Fig. 3(b) that in the fluorescence spectrum of H2 TABCtt at 77 K (curve 2) vibrations of frequencies about 600 and 1500 cm1 distinctly manifest themselves, the 600 cm1 modes being the most active, unlike the majority of the H2 P derivatives (see, e.g. [24]). Analogous vibrational structure is observed in the corresponding area of the fluorescence excitation spectrum measured at 77 K (Fig. 4(b), curve 1), i.e., the fluorescence spectrum and the absorption spectrum in the 700–800 nm range are approximately mirror symmetrical. At room temperature mirror symmetry of the spectra is violated. Whereas in the absorption spectrum [7] and in the fluorescence excitation spectrum measured by us at 290 K the vibrational structure is pronounced and corresponds to the data of the lowtemperature excitation spectrum, in the room temperature fluorescence spectrum the vibrational structure is feebly marked due to diffuseness of the bands (Fig. 3(b),

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Fig. 3. Fluorescence spectra of H2 TACt (a) and H2 TABCtt (b) at 290 (1) and 77 K (2) in ethyl ether–toluene (2:1 v/v) solvent.

Fig. 4. Low-temperature (77 K) fluorescence excitation spectra (1) and fluorescence polarization spectra (2) of H2 TACt (a) and H2 TABCtt (b) (monitoring at 680 (a) and 802 nm (b)) in ethyl ether–toluene (2:1 v/v) solvent.

curve 1). At the same time, the position of inflexions in the contour of the spectrum agrees with the position of the maxima in the low-temperature spectrum. Analogous behavior is observed for H2 TACt as well (see Fig. 3(a)), but the shift of the room temperature spectrum to the red in the latter case is larger. Note that the vibrational structure of the electronic spectra of H2 TAC has been investigated in [25] by the method of quasi-line spectra at 77 K in combination with normal coordinate analysis. In Fig. 4 the measured low-temperature fluorescence polarization spectra (i.e., the dependencies of the degree of polarization, PF , on the excitation wavelength kexc ) are also displayed. The juxtaposition of the polarization spectra with the excitation spectra at 77 K and the absorption spectra at 290 K leads to some conclusions concerning the nature of the absorption bands. First of all, in view of low values of PF the assignment of the relatively intense absorption bands at ca. 520 nm for H2 TACt and ca. 460 nm for H2 TABCtt to the second electronic transition G ! Qy [6,7] polarized along the Y axis (see Fig. 1) finds corroboration (G denotes the ground electronic state).

As should be noted, in our notation it is assumed that the longest-wavelength absorption band corresponds to the G ! Qx transition polarized along the X axis (see [4]). Many authors denote the lowest singlet excited state and, correspondingly, the longest-wavelength 0–0 absorption band of chlorins and chlorophylls by Qy (see [2]). The disagreement with our symbols is due to different choice of the X and Y coordinate axes (for more details, see Section 5). For the intense absorption band about 345 nm of H2 TACt which may be conventionally called an analogue of the Soret band of porphyrins and which is shifted bathochromically relative to H2 TAP by ca. 12 nm ()1000 cm1 ), the polarization data show that transitions polarized along the Y axis are dominant on its long-wavelength side (PF < 0) while the X-polarized transitions predominate on the short-wavelength side (PF > 0). Contrary to this, considerable negative polarization of fluorescence (PF
20%), i.e., predominant Y-polarization, is observed throughout the similar band of H2 TABCtt at 353 nm. The maximum of the polarization spectrum at ca. 430 nm, possibly, indicates that the

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weak absorption band at 413 nm belongs to an X-polarized electronic (or vibrationally induced vibronic) transition. The data on photophysical parameters show, that the reduction of pyrrole rings exerts quenching effect on the fluorescence of the porphyrazine macrocycle. The fluorescence quantum yield decreases by a factor of 3, the uF value for unsubstituted H2 TAC being approximately the same as for H2 TACt . The latter means that the introduction of the dibenzobarrelene fragment in the H2 TAC molecule weakly affects not only the electronic spectra, as stated above, but also channels of deactivation of electronic excitation. However, in the case of H2 TABC derivatives such a conclusion is valid to a lesser degree, as indicated by the difference found in the photophysics of the trans- and cis-isomers (see below). Our results on uF are only in qualitative agreement with the data of [11]. Our values of uF for H2 TAP and H2 TACt are 0.19 and 0.06, respectively (in toluene) whereas the corresponding values of [11] are 0.29 and 0.044 (in chloroform). This difference, probably, may be explained by the fact that the excitation and monitoring wavelengths used in [11] in measurements are located at the ‘‘tails’’ of the spectral bands. It is to be noted that the value of the fluorescence lifetime sF for H2 TACt obtained with the use of the picosecond fluorometer is somewhat higher, than that published in [9] (1.64 ns by the main, fast, component of the two-component kinetics, vs. 1.3 ns), and the former is undoubtedly more accurate (in measurements of sF [9] technical troubles took place). The reduction of the second pyrrole ring results in even more profound effect of fluorescence quenching, the quenching being stronger for the cis-isomer. For trans-H2 TABCtt uF
0:007, and for cis-H2 TABCtt uF
0:004. Fig. 5 shows the results of measurements of the fluorescence decay kinetics of the H2 TABCtt isomers. For the trans-isomer the decay law is well described by one exponent of sF ¼ 160 ps, and for the cis-isomer twoexponential kinetics has been obtained with the main component of sF ¼ 75 ps and a weak component of sF ¼ 440 ps. The cause of appearance of the relatively slow component is not clear. However, taking into account good agreement of the absorption spectra of the two isomers, emission monitoring in the red near-IR region in the kinetics measurements, as well as the smallness of the value of 440 ps, as compared to typical values of sF  2–10 ns for the H2 P derivatives, one may believe that this component does not belong to impurity, but rather is due to the presence of a form of the same substance having greater value of uF , possibly, because of the solvation effect. Qualitatively the change in sF when passing from the trans-isomer to the main form of the cis-isomer is in agreement with the change in uF , and allowing for difficulties of the quantum yield measure-

Fig. 5. Fluorescence decay kinetics of the H2 TABCtt isomers at 290 K: trans- (a) and cis- (b). Dotted lines are measured kinetic curves, solid lines are the results of fitting.

ments for weak luminescences, this agreement may be considered satisfactory. If, however, we take into account the presence of the slow, i.e., less-quenched, component of the fluorescence decay and assume that it corresponds to a substance with the same spectral characteristics, as the main component, the agreement between uF and sF becomes quantitative. Estimation by the fluorescence decay parameters si and Ai gives a correction (reducing) factor 1.3, i.e., the value of 75 ps is to be correlated with uF
0:003 which agrees well with the data for the transisomer (sF ¼ 160 ps, uF ¼ 0:007). 4.2. Quantum-chemical calculations Some of the molecules under consideration were a subject of numerous quantum-chemical calculations of different levels of approximation. To the greatest extent the attention was drawn by the molecule of H2 P, as the parent compound of the class of porphyrins, which became a certain test for the evaluation of applicability of the quantum chemistry methods being developed. In the framework of the aims of this work we may refer to a number of monographic and journal publications

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16

[2,4,26–38] in which one can find comprehensive bibliography on the quantum-chemical calculations of the electronic and geometrical structure, spectroscopic and other physico-chemical properties of H2 P. Other molecules of the investigated series were considered less intensively. Thus, the excited states of H2 TAP were calculated in the p-approximation by the PPP method (see [2,4,27,28]), in the all-valence-electron approximation by the CNDO/S method [39], by the ab initio methods [38,40]. Analogously, the excited states of H2 C were calculated in the p-electron approximation by the PPP method (see [2,4,5,27,28]), in the all valence electron approximation by the CNDO/S method [30,41], and also by the ab initio methods [38,42]. The excited states of H2 BC were calculated in the p-electron approximation by the PPP method (see [2,4,5,27,28]), in the valence approximation by the CNDO/S method [30] and by the ab initio method [38]. The H2 TABC molecule also was considered recently at the ab initio level [38]. In Fig. 6 the results of the CNDO/S calculation of the energies of one-electron states (MOs) of the molecules under consideration with the geometry, obtained by the AM1 method, are presented (the results based on the PM3 geometry are similar). In Table 1 numerical data are given on the energies of the two occupied MOs and two vacant MOs which are relevant for the description of the excited Q and B states (see Section 5). A characteristic feature of the system of the one-electron states of the molecule considered is the presence of nonbonding states (n-states) occupied by the non-shared electron pairs of the central nitrogen atoms of the pyrrolenine rings or of those of the bridge nitrogen atoms. Data on n-MOs are listed in Table 2. The calculation results for the excited many-electron states are presented in Table 3.

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Comparison of the calculation results for H2 TAC and H2 TABC (Table 3) with the experimental absorption spectra and fluorescence polarization spectra shows that the calculations adequately describe the experimental results although there are some minor quantitative discrepancies. Begin with the case of H2 TAC. In the visible region the calculation predicts two electronic transitions G ! Qx and G ! Qy . The configuration composition of the excited electronic states Qx and Qy is determined mainly by the u1 u1 and u1 u2 p-electron excitations. We use the designation of MOs by the Greek letter u with a positive subscript for vacant MOs, in the order of increasing energy, and with a negative subscript for filled MOs, in the order of decreasing energy. The calculated Qy –Qx interval amounts to 5700 cm1 while the experimental one is ca. 4500 cm1 . The position of the Qx level is predicted sufficiently well, within the limits of accuracy of quantum-chemical calculation: 13,100 vs. 14,750 cm1 in the experiment. It should be borne in mind that the allowance for the influence of solvent due to dispersion interactions would make the correspondence worse approximately by 500 cm1 . This estimate can be made from the data on Zn tetrabenzoporphin having, as well as H2 TAC, an intense Qð0; 0Þ band in absorption. Its position in pyridine is 15,950 cm1 [26,43] and in the fine-structure fluorescence excitation spectrum in a supersonic jet the line of the 0–0 transition is disposed at 16,580 cm1 [44]. The bathochromic shift in going from the gas phase to solution is thus obtained as 630 cm1 (without taking into account a small Stokes shift for the solution at room temperature). However, for the H2 C molecules, according to data of jet-cooled molecules spectroscopy [45] and quasi-line spectra (see, e.g. [1]), analogous shift in the

Fig. 6. Molecular orbital energy levels of the frontier orbitals of H2 P, H2 TAP, H2 C, H2 TAC, H2 BC, and H2 TABC.

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Table 1 The energy characteristics (eV) of the two occupied and two unoccupied MOs relevant for the description of the Q and B states of the molecules of porphin, chlorin, bacteriochlorin, and their tetraaza-analogues Molecule H2 P u1 , b2g

H2 TAP )2.84

u2 , b2g

da dh da þ dh daþh

)3.08 )0.24

u2 , a2

H2 TAC )2.22

u2 , a2

H2 BC )2.43

u2 , b2g

0.62

H2 TABC )1.85

u2 , b2g

u2 , b3g

)2.72

u1 , b3g

)3.48 )0.76

u1 , b1

)2.54

u1 , b1

)3.05

0.75 0.96 u1 , b3g

)0.58 )0.33 0.12 u1 , au

)7.18

0.40 u1 , au

da dh da þ dh daþh

)7.06 0.12

0.32 u1 , a2

)7.04

0.62 u1 , a2

)6.89

)2.86

u1 , b3g

)0.14

0.18

Deunocc

u1 , au

)6.47

1.63 u1 , au

)7.87

u2 , b1u

)9.20 )1.33

u2 , b1

)8.07

u3 , b1

)9.58

0.20 )1.13 )1.71 0.69

2.14

1.03

)6.42

0.71 0.26 0.29

u2 , b1u

)3.51 )0.90 )0.79

1.01

0.14

da dh da þ dh daþh

)1.88

0.99 0.38 0.41

da dh da þ dh daþh

Deocc

H2 C

2.69

0.83 0.76 u2 , b1u

)7.91 )0.04

1.44

u2 , b1u

)9.21 )1.37 )1.34 2.79

Note. da , dh , daþh are, respectively, the MO level shifts resulting from aza-substitution, pyrrole rings reduction, and their joint effect. Deocc and Deunocc are the splittings of the relevant occupied and unoccupied MOs.

case of n-octane matrix proves to be only 167 cm1 . It should be noted also that the calculation overestimates the intensity of the G ! Qy transition which is calculated the same as for the G ! Qx transition, whereas in the experimental spectrum its peak intensity is less by a factor of 1.9. At the same time the calculation correctly predicts equal intensity of the G ! Qx transitions for the H2 TAP and H2 TAC molecules, which has been noted for the experimental spectra in [6,7]. In the near UV region the calculation for H2 TAC correctly predicts the sequence of the intense G ! By , G ! Bx transitions, which is in accordance with the behavior of the polarization spectrum. We note, first, that the configuration composition of the By and Bx excited states is determined chiefly by the u3 u1 and u3 u2 excitations of p-electrons, the u3 MO being related to the u2 MO of the molecules of H2 P, H2 TAP, and H2 C (Fig. 6). It is on this basis that we designate the indicated states of H2 TAC by the symbols Bx and By . (See Section 5 for more details of the symbolism of the p-electron states.) Second, between the Qy and By levels a number of levels is disposed that correspond to states of different orbital nature, specifically Ny and Nx (Table 3). The G ! Nx and G ! Ny transitions are less intense than the G ! Bx , G ! By transitions. To them may belong the long-wavelength tail of the UV absorption

band, which above we have called an analogue of the Soret band. It follows from the aforesaid that this analogue is a sufficiently close one. In the case of H2 TABC the agreement between calculation and experiment is still better. For the longwavelength transitions the calculation predicts the increase in the Qy –Qx interval up to 7700 cm1 , and in experiment it is obtained even larger, 9000 cm1 . The calculated intensity of the G ! Qy transition is less than for G ! Qx by a factor of 3.7, in agreement with the experiment where this factor is 3.1. Also corresponds to the experimental data the theoretical position of the Qx level, 11,200 cm1 , while in the absorption spectrum it is 12,600 cm1 . We note nevertheless, that the predicted increase in intensity of the longest-wavelength transition for H2 TABC relative to H2 TAC is not observed experimentally. For the two most intense transitions in the UV region which we, as before, denote G ! By and G ! Bx calculation gives the Bx –By interval 8100 cm1 , the By level being the lowest (Table 3). This agrees well with the experimental polarization spectrum where high (in absolute value) negative polarization corresponds to the whole ‘‘Soret band’’. For H2 TABCtt in the region above 33,000 cm1 (300 nm) in n-hexane a rather intense structured absorption band has been recorded [7] that must correspond to the G ! Bx transition and, possibly,

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16 Table 2 The energies of the n orbitals and the degree of localization, L, on the central pyrrolenine (c) and bridge (b) nitrogen atoms for the molecules of porphin, chlorin, bacteriochlorin, and their tetraaza-analogues Molecule

ui


i (eV)

L (%)

H2 P

u8 , ag u10 , b2u

)11.16 )11.21

55 (c) 50 (c)

H2 C

u6 , a1 u9 , a1

)11.01 )11.48

52 (c) 50 (c)

H2 BC

u7 , ag u8 , b2u

)11.42 )11.43

51 (c) 44 (c)

H2 TAP

u8 , b2u u9 , ag u11 , b1g u12 , b3u u15 , b2u u17 , ag

)11.35 )11.40 )11.88 )12.20 )12.96 )13.44

51 59 66 62 49 66

(c) (c) (b) (b) (b) (b)

H2 TAC

u5 , a1 u8 , a1 u9 , b2 u11 , b2 u13 , a1 u16 , a1 u17 , a1

)10.90 )11.52 )11.71 )12.02 )12.81 )13.25 )13.40

55 46 63 62 35 56 30

(c) (c) (b) (b) (b) (b) (b)

H2 TABC

u7 , b2u u8 , b1g u9 , ag u10 , b3u u12 , b2u u14 , ag

)11.41 )11.54 )11.58 )11.92 )12.67 )13.04

41 68 56 65 17 65

(c) + 26 (b) (b) (c) (b) (c) + 41 (b) (b)

9

The calculation results on transition energy [38] (see Table 4) qualitatively agree with ours, but the Qy –Qx interval (13,800 cm1 ) is much larger than obtained by us, and it is considerably greater than the experimental value; contrary to this, the Bx –By interval is lesser than our value. The predicted location of the Qx level is almost the same as in our work – 10,900 cm1 , but the By level is obtained closer to the experimental position. At the same time, judging from the experimental polarization spectrum, the value of the Bx –By interval in [38] is grossly underestimated. One may constate that our calculation better corresponds to experiment. In [11] the quantum-chemical calculations by the ZINDO/S method were performed for H2 TAP, H2 TAC, H2 TABC, and tetraaza-iso-bacteriochlorin. The published data on the singlet excited states of the Q and B types are included in Table 4. Comparison of our calculation results with those of [11] for H2 TAC and H2 TABC shows that, as a whole the data of both computations are at the same level of accuracy. However, we note that (i) the correspondence of calculated energies of the Qx and Qy states with experiment is slightly better in [11]; (ii) the intensities of the G ! Qx and G ! Qy transitions are predicted better in our work for H2 TABC, but worse for H2 TAC; (iii) the parameters of Bx and By states are predicted significantly better in our work which may be associated with larger number of electronic configurations accounted for by us.

5. Discussion 5.1. Electronic structure and spectra as follows from the calculation data, to other less intense transitions. With decreasing kexc from 330 to 300 nm in the measured polarization spectrum a rise in the PF value is observed. Taking into account the potentialities of the used semi-empirical methods of optimization of the geometry of molecules and calculation of their excited states, the achieved agreement of the calculation results on the energy of singlet excited states with the experimental spectral data should be considered good (Table 4). It should be noted that the energy of the Q levels in the CNDO/S calculations is obtained systematically underestimated while the energy of the B levels is overestimated. Better agreement for the B levels, as expected, can be obtained by inclusion of doubly excited electronic configurations. Such result was acquired for H2 P (with INDO/S Hamiltonian); however, the energy of Q levels was found to be underestimated still more than when allowing for singly excited configurations only [32]. It has been mentioned above that the H2 TABC molecule was calculated in [38], where the Møller–Plesset perturbation theory for excited states was used based on the self-consistent field (SCF) ab initio calculations.

Characteristic feature of the electronic spectra of H2 P and its close analogues – porphyrins – are the low intensity of the two longest-wavelength electronic transitions polarized mutually perpendicularly, and the high intensity of the so called Soret band on the border between the visible and UV region [1–5]. The spectrum is simplified on the insertion of a metal atom into the center of the molecule of H2 P or its analogue – two longest-wavelength electronic transitions merge into one, and the Soret band narrows. Such behavior is caused mainly by the symmetry rise from D2h (H2 P) to D4h for metalloporphin (MP). It is to be added, that in the case of metalloporphins with weakly complexing metal atoms (e.g., Mg) the intensity of the longest wavelength absorption band remains very low [1,2,4]. For the theoretical explanation of spectroscopic properties of porphyrins Platt [46] and Gouterman [47] proposed the four-orbital model. One of its suppositions consists in the quasi-degeneracy of the two highest occupied MOs (HOMOs) of the a1u and a2u symmetry for MPs and closely related molecular systems of the D4h symmetry. The two lowest unoccupied MOs (LUMOs)

10

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16

Table 3 The energies, E (103 cm1 ), and oscillator strengths, f, of electronic transitions and main contributions to the configurational composition of the excited states for the molecules of porphin, chlorin, bacteriochlorin, and their tetraaza-analogues State

E

f

Configurational composition

H2 P 11 B3u (Qx ) 11 B2u (Qy ) 21 B3u (Bx ) 21 B2u (By ) 11 B1g 21 Ag 31 B3u (Nx ) 21 B1g 11 B3g ðnp ) 11 B1u (np ) 31 Ag 31 B2u (Ny ) 31 B1g 21 B2g (np ) 41 Ag 11 Au (np ) 41 B1g 41 B2u (Ly ) 41 B3u (Lx )

13.7 16.4 26.6 28.3 28.7 28.9 32.5 33.4 34.0 34.4 34.8 35.8 37.5 37.9 38.3 38.3 39.0 39.3 40.5

0.04 0.16 1.46 2.22 0 0 1.41 0 0 0.004 0 0.39 0 0 0 0 0 0.06 0.01

0:75u1 u2  0:64u2 u1 0:84u1 u1 þ 0:52u2 u2 0:57u1 u2 þ 0:63u2 u1  0:47u4 u1 0:51u1 u1  0:84u2 u2 0:91u3 u1 0:91u1 u3 0:41u2 u1 þ 0:82u4 u1 0:79u1 u4 0:79u8 u2 þ 0:38u10 u4 0:41u8 u4 þ 0:77u10 u2 0:95u3 u2 0:94u4 u2 0:53u1 u4 þ 0:78u2 u3 0:93u8 u1 0:48u2 u4 þ 0:64u5 u1 0:93u10 u1 0:72u5 u2 þ 0:62u6 u1 0:95u1 u5 0:86u1 u6

H2 C 11 B2 (Qx ) 21 A1 (Qy ) 31 A1 (By ) 21 B2 (Bx ) 11 B1 (np ) 41 A1 (Ny ) 51 A1 31 B2 (Nx ) 41 B2 21 B1 (np ) 61 A1 (Ly ) 51 B2 (Lx ) 31 B1 71 A1 61 B2

14.3 20.4 27.6 28.2 31.5 32.0 32.5 32.7 33.5 38.2 38.2 39.1 39.8 40.9 41.1

0.18 0.25 1.30 1.34 0.002 0.32 0.03 0.55 0.14 0.000 0.005 0.01 0.02 0.000 0.01

0.85u1 u1  0:48u2 u2 0.91u1 u2 þ 0:38u2 u1 0.32u1 u2  0:86u2 u1 0.48u1 u1 þ 0:82u2 u2 0.79u6 u1 þ 0:35u6 u4 0.54u1 u3 þ 0:73u3 u1 0.75u1 u3  0:62u3 u1 0.69u1 u4  0:56u3 u2 0.64u1 u4 þ 0:71u3 u2 0.67u9 u1  0:50u9 u4 0.56u1 u6 þ 0:56u2 u4 0:60u1 u5 þ 0:49u4 u1 0.53u1 u5  0:71u4 u1 0.55u1 u6  0:59u2 u4 0.41u1 u5 þ 0:79u2 u3

11.7 17.6 28.4 28.5 29.9 31.3 33.7 34.1 34.7 35.9 37.1 39.6 40.1 41.3 41.4

0.38 0.02 1.92 0 0 2.39 0 0.001 0 0.07 0 0.02 0 0 0.04

0.89u1 u1  0:42u2 u2 0.80u1 u2 þ 0:60u2 u1 0.59u1 u2  0:79u2 u1 0.96u1 u3 0.91u1 u4 0.42u1 u1 þ 0:89u2 u2 0.78u7 u1 þ 0:38u8 u3 0.41u7 u3 þ 0:75u8 u1 0.91u3 u1 0.97u1 u5 0.45u2 u3  0:72u4 u1 0.95u1 u6 0.57u1 u7 þ 0:58u2 u3 0.61u2 u4 þ 0:68u6 u1 0.97u5 u1

50.1

0.45

0.70u5 u2 þ 0:52u9 u1

H2 BC 11 B3u (Qx ) 11 B2u (Qy ) 21 B2u (By ) 11 B1g 21 Ag 21 B3u (Bx ) 11 B3g (np ) 11 B1u (np ) 21 B1g 31 B3u (Lx ) 31 Ag 31 B2u (Ly ) 41 Ag 31 B1g 41 B2u (Ny ) ... 61 B3u (Nx )

State

E

f

Configurational composition

H2 TAP 11 B3u (Qx ) 11 B2u (Qy ) 21 Ag 21 B3u (Bx ) 11 B1g 21 B2u (By ) 31 Ag 11 B1u (np ) 11 B2g (np ) 21 B1g 11 Au (np ) 11 B3g (np ) 31 B2u (Ny ) 21 B3g (np ) 21 B1u (np ) 31 B3u (Nx ) 41 B2u (Ly ) 21 B2g (np ) 21 Au (np ) 31 B1g 51 B2u 51 B3u (Lx )

12.8 15.7 24.3 26.7 27.4 29.1 31.2 31.2 31.6 32.0 33.2 33.4 34.3 34.3 35.0 35.2 35.8 36.2 36.9 37.4 38.5 38.8

0.51 0.50 0 0.34 0 0.92 0 0.01 0 0 0 0 1.19 0 0.000 2.20 0.03 0 0 0 0.001 0.02

0:90u1 u1  0:39u2 u2 0:93u1 u2 þ 0:35u2 u1 0:98u1 u3 0:66u2 u2  0:35u3 u3 þ 0:60u4 u2 0:88u3 u2 0:86u2 u1 þ 0:37u4 u1 0:99u3 u1 0:70u8 u1 þ 0:40u11 u3 0:38u9 u2  0:70u11 u1 0:95u1 u4 0:67u8 u2 þ 0:49u12 u1 0:31u8 u4 þ 0:84u9 u1 0:91u4 u1 0:58u11 u2 þ 0:48u12 u3 0:49u8 u1 þ 0:37u12 u5 0:60u2 u2 þ 0:67u4 u2 0:97u1 u5 0:80u11 u2 0:58u8 u2  0:64u15 u2 0.89u5 u1 0.95u7 u1 0.94u1 u6

H2 TAC 11 B2 (Qx ) 21 A1 (Qy ) 31 A1 (Ny ) 41 A1 21 B2 (Nx ) 11 B2 (np ) 31 B2 11 A2 (np ) 21 B1 (np ) 51 A1 (By ) 51 B2 (Bx ) 51 A1 (Ly ) 31 B1 (np ) 61 B2 (Lx ) 21 A2 ðnp )

13.1 18.8 27.7 28.8 29.1 29.2 30.8 31.1 33.4 33.9 35.6 37.1 37.1 37.7 39.1

0.53 0.53 0.10 0.01 0.03 0.003 0.11 0 0.002 1.12 1.58 0.07 0.000 0.05 0

0.94u1 u1 0.96u1 u2 0.52u1 u3  0:81u2 u1 0.82u1 u3 þ 0:51u2 u1 0.91u2 u2 0:83u5 u1 0.96u1 u4 0.71u9 u1 0.39u8 u1 þ 0:43u9 u2 0.93u3 u1 0:81u3 u2 0:93u1 u6 0.58u8 u1 þ 0:47u8 u4 0:92u1 u5 0.74u8 u2 þ 0:48u8 u3

11.2 18.5 26.7 27.7 30.1 32.2 32.2 33.7 34.3 35.1 35.3 35.6 36.3 37.2 37.6 38.1 38.2

0.82 0.21 0 0 1.45 0 0.004 0 0.12 0.000 0 0.002 0.005 0.01 0 0 2.19

0.94u1 u1  0:29u2 u2 0.91u1 u2 þ 0:39u2 u1 0.98u1 u3 0.97u1 u4 0.39u1 u2  0:91u2 u1 0.88u8 u1 0.85u7 u1 0.85u9 u1 0.98u1 u5 0:85u10 u1 0.93u3 u1 0.99u1 u6 0.37u8 u3  0:56u12 u1 0.98u5 u1 0.37u8 u3  0:56u12 u1 0.88u4 u1 0.30u1 u1 þ 0:90u2 u2

51.9

0.52

0.62u5 u2 þ 0:70u11 u1

H2 TABC 11 B3u (Qx ) 11 B2u (Qy ) 21 Ag 11 B1g 21 B2u (By ) 11 B2g (np ) 11 B1u (np ) 11 B3g (np ) 21 B3u (Lx ) 21 B1u (np ) 21 B1g 31 B2u (Ly ) 31 B1u (np ) 31 B2u (Ny ) 21 B3g (np ) 31 Ag 41 B3u (Bx ) ... 61 B3u (Nx )

Note. The Nx and Ny states of H2 P are mainly determined by the electronic configurations u4 (b1u )u1 (b2g ) and u4 (b1u )u2 (b3g ), respectively, and the Lx and Ly states – by u1 (au )u6 (b3g ) and u1 (au )u5 (b2g ). For the other molecules studied these symbols are used allowing for the genealogical relation between the indicated MOs and between the corresponding configurations.

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16

11

Table 4 Comparison between the experimental and calculated data for molecules of H2 TAC and H2 TABC Molecule

H2 TAC

H2 TABC

State

Experiment, this work and [7]

CNDO/S calculation, this work

Ab initio calculation [38]

ZINDO/S calculation [11]

E (103 cm1 )

emax a

E (103 cm1 )

f

E (103 cm1 )

f

E (103 cm1 )

f

Qx Qy DEQy Qx By Bx DEBx By

14.8 19.3 4.5 28.6 30.3 1.7

6.2 3.3

13.1 18.8 5.7 33.9 35.6 1.7

0.53 0.53

– –

– –

0.73 0.45

1.12 1.58

– – –

– –

14.1 19.6 5.5 34.6 39.0 4.4

Qx Qy DEQy Qx By Bx DEBx By

12.6 21.6 9.0 28.4 33.3 4.9

6.0 1.9

11.2 18.5 7.3 30.1 38.2 8.1

0.82 0.21

10.9 24.7 13.8 28.8 31.3 2.5

0.23 0.04

12.9 20.6 7.7 32.7 41.8 9.1

1.02 0.23

4.6b

4.1b 3c

1.45 2.19

1.27 1.29

1.79 2.48

1.91 2.64

a

emax is the molar extinction coefficient at the maximum of the absorption band in 104 l/mol cm. The Soret band is broadened. c Estimated for the longest-wavelength component of the complicated band. b

of the eg symmetry for molecules belonging to the D4h group are doubly degenerate, and, in the case of quasidegenerate HOMOs, for the electronic configurations a1u eg and a2u eg arise excited states which are similar to the states of the model of free electrons on a circle (the D1h symmetry). In the latter case two doubly degenerate states appear: the lower, ‘‘forbidden’’, and the upper, ‘‘allowed’’ (for dipole transitions from the ground state). Due to the difference of the real symmetry D4h from D1h the strict prohibition of the longest-wavelength transition becomes a quasi-prohibition. The lowest excited state acquired the designation Q, and the upper, B. For the D2h symmetry they split into Qx ; Qy and Bx ; By . It is accepted to retain the symbols Q and B in cases of lifted quasi-prohibition of the long-wavelength transitions and weakened Soret band. Starting with the calculations in the p-electron approximation by the PPP method [27], all calculations based on the SCF method gave, for MP and H2 P, a general result: the levels of the p-MOs a1u ; a2u ; eg and those of the corresponding MOs for the D2h symmetry: au , b1u , and b2g , b3g are separated from the others by large intervals, whereas the interval between the a1u and a2u levels is rather small. Moreover, the most perfect ab initio calculations (see, e.g. [34,36,37] and references therein) give the configuration composition of the Qx , Qy states, which is close to that of the four-orbital model. The case is somewhat more complicated for the Bx , By states for which the contribution of high-energy electronic states is considerable. Above the B levels the levels of states generated by transitions other than the transitions of the form of u1 ; u2 ! u1 ; u2 are disposed. A tradition was settled to denote them by letters N, L, M, etc. Apart from the odd states Eu (B2u , B3u for D2h ), from the B levels region

and higher the calculations predict the presence of even levels (‘‘forbidden’’ p, p states), as well as of n; p levels – see, for instance, the data of our calculations in Table 3. Note, specifically, that for H2 P the Nx and Ny states are determined by the electronic configurations u4 ðb1u Þu1 ðb2g Þ and u4 ðb1u Þu2 ðb3g Þ, respectively, while the Lx and Ly states – by u1 ðau Þu6 ðb3g Þ and u1 ðau Þu5 ðb2g Þ. For many MOs, in the same way as for the four of u1 ; u2 and u1 ; u2 , in passing from H2 P to other considered compounds the similarity in the electron density distribution takes place. Correspondingly, their excited states are related to the N and L states of H2 P, and these states are denoted by the same symbols. It is necessary also to make a comment concerning the choice of coordinate axes. In the molecules of H2 P and its close analogues of the D2h symmetry the longestwavelength transition is polarized along the NH–HN axis [1,2,4]. The calculations show that the same is true for all molecules considered in this work. Therefore we take the NH–HN axis as the X axis for all cases. Many authors, beginning with [26], for hydroporphyrins choose as the X axis the perpendicular direction (this is the C2 symmetry axis for H2 C); then the lowest excited state turns out to be Qy . It is seen from Fig. 6 that for H2 P the MO levels correspond to the four-orbital model: the au ðu1 ) and b1u ðu2 ) HOMOs and the b2g ðu1 Þ and b3g ðu2 Þ LUMOs are separated from other MOs by intervals of ca. 2 eV. However, the energy interval au –b1u seems to be overestimated since the calculated oscillator strengths of the G ! Qx and G ! Qy transitions (Table 3) exceed the experimental ones by an order of magnitude (according to a qualitative estimate). It is the important feature of the four-orbital model that the Q band intensity depends on the a1u –a2u interval (au –b1u for the D2h symmetry)

12

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16

[26,47]. The reason is that the Q band intensity is determined by partial cancellation of the transition moments of two one-electron transitions whose contributions are given by this energy interval. In the simplest case when the transition moments are equal in absolute value the Q band is zero if the a1u –a2u interval is zero. The corresponding explicit expression for the four-orbital model based on SCF MOs was obtained in [48]. The accuracy of the calculation of the energy of the Q and B states corresponds to the potentialities of the method. The energy values for the Qx ; Qy states are somewhat underestimated, and for the Bx ; By states – somewhat overestimated. The obtained Qy –Qx interval (2700 cm1 ) is in agreement with the experimental data: 3000 cm1 for solutions at room temperature according to the data of [23,49]: 2970 cm1 in frozen alcoholic glass at 93 K [49], ca. 3600 cm1 in the gas phase [45,50]. The Bx –By interval is overestimated. Admittedly, the Soret band of H2 P is not yet interpreted fully. However, the available limited data on the fluorescence polarization of H2 P [51] and the fluorescence polarization spectra of its derivatives enable one to state that the By – Bx interval for H2 P and its close analogues is not large (on the order of 100 cm1 ). This question is discussed in [52], where the polarization spectrum of a specially selected porphyrin was investigated which made it possible to eliminate one of the unclear aspects. The work [52] was performed in view of the appeared theoretical work [36] where the Soret band of H2 P was correlated with only one electronic transition G ! Bx while the electronic transition G ! By (the energy of the By level was obtained higher than Bx by 1600 cm1 ) was correlated with the band which is traditionally interpreted as the result of the G ! Nx and G ! Ny transitions. The experimental data of [52] in total with the literature data adduced therein allowed its authors to reject the interpretation proposed in [36]. It should be mentioned that our calculation results conform well to the earlier works [29,31], which rested upon the experimental geometry of H2 P. As is seen from Fig. 6, on the considered structural changes the quasi-degeneracy of the HOMOs and LUMOs is lifted, especially, on tetraaza-substitution. The additivity of the effect of aza-substitution and pyrrole rings reduction sometimes does not take place, as shown by the data of Table 1. From Fig. 6 it is seen also that the isolation of the four ‘‘optical’’ orbitals is broken; particularly, this concerns the HOMOs of H2 TAP and H2 TAC. In the latter case the inversion of two occupied b1u MOs is noted. The isolation mentioned is recovered in H2 TABC, that is, probably, what causes the good agreement between the calculated and experimental spectra for this molecule. Besides p-electrons, the electrons of unshared pairs (n-electrons) may participate in the electronic transitions

in the near UV spectral region. In the porphyrin macrocycle proper (metal-free) there are two such pairs – on the central tertiary nitrogen atoms, and on aza-substitution the n-electrons of the bridge nitrogen atoms (also tertiary) are added to them. The results of calculation of n-orbitals are presented in Table 2. Of the data of Table 2 we note the following: (1) The energy levels of the bridge electrons lie lower than for the central ones. (2) Pyrrole rings reduction affects the energy of n-electrons relatively weakly. (3) Aza-substitution influences the energy of central n-electrons still less. (4) n-MOs, being symmetrical relative to reflexion in the molecular plane, due to interaction with other r-MOs of appropriate symmetry, are delocalized to a considerable degree. The calculation of the energy of singlet p; p -states of the H2 TAP molecule reproduces, as a whole, the data of early work [39] with the participation of authors (V.A.K., K.N.S.); for H2 TAP the accuracy of correspondence to experiment is roughly the same as in the case of H2 P. Thus, e.g., the Qy –Qx interval is obtained equal to 2900 vs. 2100 cm1 in experiment. It is necessary to note that the calculated here energies of the 1 ðn; p ) states, as compared to [39], are lowered very significantly: by ca. 2000 cm1 for n-MOs with the participation of central nelectrons and by ca. 7000 cm1 – for the bridge ones. Undoubtedly, this is due to the allowance for greater number of electronic configurations in this work. It is necessary to emphasize that in both calculations the energies of 1 ðn; p ) states belonging to the central nitrogen atoms are obtained considerably lower than for the bridge n-electrons. Note also that in going from H2 P to H2 TAP the energies of the lower 1 ðn; p ) states decrease by 2500 cm1 and get into the region of the Bx and By states. It is possible, however, that the lowest levels of the 1 ðn; p ) type in reality are disposed still lower. In [39] for the zinc complex of tetraazaporphin (ZnTAP) it was shown that in the 390 nm range there is an appreciable out-of-plane component of absorption which is natural to ascribe to n ! p transitions, there being no central nelectrons in the ZnTAP molecule, i.e., the n ! p transitions are associated with the excitation of the nitrogen bridge n-electrons. If this interpretation is correct, the lowest 1 ðn; p ) level belonging to nitrogen bridges is in fact disposed at ca. 26,000 cm1 . The worst result in the investigated series of molecules has been obtained for H2 C. The calculation gives shifts of the Qx and Qy levels, relative to H2 P, upwards by 600 and 4000 cm1 , respectively, and, most unsuccessfully, greater intensity of the G ! Qy transition than for the G ! Qx transition – all in contrast with experiment. In the experimental absorption spectra, in passing from H2 P to H2 C, the longest-wavelength Qx ð0; 0Þ band is shifted bathochromically by 21.5 nm ()550 cm1 ), and its intensity sharply increases [1,53]. The quasi-forbidden G ! Qy transition is weakened so, that its revealing

V.A. Kuzmitsky et al. / Chemical Physics 298 (2004) 1–16

required a special investigation [54], which showed that the Qy –Qx interval of H2 C in the n-octane matrix is 3664 cm1 . This agrees with the data for octaethylchlorin, whose Qy ð0; 0Þ band is sufficiently intense, and the Qy –Qx interval is 3670 cm1 [55,56]. The reason of this discrepancy seems to consist in the systematic overestimation of the energy interval between the levels of the ‘‘a1u ’’ and ‘‘a2u ’’ HOMOs; in the case of H2 C these are the a2 and b1 orbitals (Fig. 6). In the fourorbital model for H2 C the intensity rise of the Qx band, quasi-forbidden G ! Qy transition and splitting of the Soret band are obtained if one assumes equal the distance between the levels u1 ; u2 and that between the levels u1 ; u2 [26]. It is seen from Fig. 6 that for H2 C the interval between the two HOMOs is considerably greater than between the two LUMOs. This seems to be associated with considerable ‘‘splitting’’ of the pair u1 ; u2 already for H2 P. For tetraaza-substituted compounds the distance between the two HOMOs is large, and such minor discordance does not exert essential influence on the predicted absorption spectra. From the data of Table 3 it follows that the electronic absorption spectrum of H2 BC is predicted in the calculation rather well: an intense longest-wavelength Qx band, a weak Qy band, two intense B bands. Besides, the calculated Qy –Qx interval is 5900 cm1 , the interval Bx –By is 2900 cm1 , and the sequence of lower excited states of odd symmetry: Qx ; Qy ; By ; Bx corresponds to experiment. In experiment the Qy –Qx interval amounts to 6650 cm1 [57,58] and the Bx –By interval, 1950 cm1 [58]. As is usual in the semi-empirical calculations of porphyrins, the energy of the Qx level is somewhat lowered: 11,700 cm1 vs. 13,800 cm1 [57,58]. For the closely related octaethyl-derivative of H2 BC the Qy –Qx interval is equal to 6600 cm1 , and the Bx –By interval, to 2200 cm1 [56]. We return now to the main subjects of our inquiry: H2 TAC and H2 TABC in theoretical consideration, H2 TACt and H2 TABCtt in experimental study. In Sections 4 and 4.2 we have described in detail the calculation data for H2 TAC and H2 TABC. The calculations reproduce well the disposition of the Qx and Qy levels, distance between them, intensities of the visible bands, position of the Bx and By levels, and correct succession of the four levels which is reflected in the experimental polarization spectrum. Here we intend to correlate the data for these molecules with those for other molecules of the series investigated. It follows from the comparison of the calculation results for H2 BC with those for H2 TABC that the tetraaza-substitution gives the lowering of the Qx level by 500 cm1 and the elevation of the Qy level by 900 cm1 . In the experimental absorption spectra the Qx ð0; 0Þ and Qy ð0; 0Þ bands of H2 BC are disposed at 722.5 and 488 nm [57], and those of H2 TABCtt – at 792 and 462 nm [7] (closely related solvents were used, n-octane and n-hex-

13

ane, respectively). Thus, on aza-substitution the shift of Qx ð0; 0Þ band amounts to )1200 cm1 , and for the Qy band it is +1150 cm1 . As noted above, the calculation somewhat underestimates, the value of DEQy Qx for H2 TABC. Nevertheless, the agreement between experiment and theory for the spectral shifts of the visible bands may be regarded sufficiently good. The data of Table 3 and Fig. 6 reveal interesting regularities in the behavior of the excited states of the B and N types. For the H2 P molecule the Nx and Ny states are determined by the promotion of an electron from the u4 ðb1u Þ MO to the u1 ðb2g Þ or u2 ðb3g Þ MOs, respectively. (The relation of the u4 MO of H2 P with the MOs of other molecules is marked by dashed–dotted lines in Fig. 6.) It is seen from Table 3 that for all six calculated structures there exists a kinship of the electronic configurations describing the Nx and Ny states (taking into account the correlation of MOs). In going from H2 P to H2 BC, i.e., on the reduction of two opposite pyrrole rings, the calculated intervals Nx –Bx and Ny –By drastically increase and the configuration composition of the Bx and By states becomes close to that for the four-orbital model at lifted degeneracy of the u2 ,u1 and u1 ,u2 MOs and isolation of the four of these MOs from the others. In the case of H2 TAP the B and N states are heavily mixed. The reduction of one pyrrole ring in the porphyrazine macrocycle (passage from H2 TAP to H2 TAC) strongly lowers the Nx and Ny levels, and they go away from ‘‘resonance’’ with the Bx and By levels; the configuration composition of the Bx and By states is again close to that of the four-orbital model. The reduction of two pyrrole rings in the presence of tetraaza-substitution (passage from H2 TAP to H2 TABC) gives lesser up-shifts of the Nx and Ny than in the case of H2 BC, as well as increases the Bx –By interval; as a result, the level of the By state proves to be partially isolated and it is mainly described by the configuration superposition 0.39u1 u2  0:91u2 u1 (Table 3), i.e., the contribution of the four-orbital model configurations is predominant. The next level is Ny , which does not contradict to the experimental polarization spectrum. Summarizing, one may state that the results of performed quantum-chemical calculations adequately describe the changes in the electronic absorption spectra in the series H2 TAP–H2 TACt –H2 TABCtt (the effect of pyrrole rings reduction) and also in passing from H2 BC to H2 TABCtt (the effect of tetraaza-substitution). 5.2. Photophysical properties We turn now to consideration of photophysical parameters of fluorescence, as dependent on the pyrrole rings reduction and aza-substitution. The main result of the present work in this respect is the dramatic quenching of fluorescence on the reduction of pyrrole

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rings in the H2 TAP molecule, or, otherwise, on the tetraaza-substitution in the H2 C and H2 BC molecules. The available material, unfortunately, does not allow unambiguous explanation of this quenching. However, we believe, based on indirect data, that the quenching under consideration is due to rise in the probability of intersystem crossing S1 , T1 . Thus, one may state that the alternative version involving the rise in the S1 , S0 internal conversion probability is unsuitable for the explanation of the quenching by a factor of 10 in going from H2 TACt to H2 TABCtt . For the estimation of such effect we made use of the results of [59], where it was shown that, when the energy of the S1 level is lowered below ca. 14,000 cm1 , the S1 , S0 internal conversion begins to make a considerable contribution to the deactivation process in chlorophyll-like molecules which leads to deviations from the Ermolaev–Sveshnikova rule uF þ uT ¼ 1 [60], whose validity in the case of chlorophyll and porphyrins is established reliably (see, e.g., review [4] and also paper [61] and references therein). In particular, this rule is obeyed for phthalocyanines [62,63] molecules of which have four nitrogen bridges as have porphyrazines studied here. In [59] it was shown that the observed rise in the probability kS1 ;S0 as well as the behavior of other nonradiative transitions, corresponds to the energy gap law [64–67]: kijnr ¼ Aij exp½aij ðEi  Ej Þ, where kijnr is the probability (rate constant) of the non-radiative transition from the electronic level i to the electronic level j, Ei and Ej are the energies of the levels, Aij and aij are constants. For the S1 , S0 transition, as well as for T1 , S0 , the value aij ¼ 1:35  103 cm was obtained [59]. Taking as the basis the values of uS1 ;S0 and kSnr1 ;S0 for bacteriopheophytin a, for our subject of inquiry, H2 TABCtt , we obtain that in passing from bacteriopheophytin a to H2 TABCtt (lowering of the S1 level by ca. 650 cm1 ) the value of the S1 , S0 non-radiative transition probability should increase approximately by 2.5 times – to be more specific, from the value of ca. 1.3  108 s1 to ca. 3.5  108 s1 which in any way cannot be responsible for the values of sF on the order of 100 ps. Analogous evidence is found in the data on photophysics of AlCl complexes of phthalocyanine and naphthalocyanine [68] which have uF values of 0.64 and 0.18, respectively; the corresponding sF values are 5.3 and 2.7 ns. The energies of the S1 levels of these molecules are comparable with those of the H2 TACt and H2 TABCtt molecules (the Q bands are at 683 and 784 nm, respectively, vs. the Qx bands of hydroporphyrazines at 676 and 792 nm), but the effect of fluorescence quenching due to the lowering of the S1 level is much weaker than in passing from H2 TACt to H2 TABCtt . Therefore, we prefer a different explanation. First of all, we note that already in the case of H2 TAP a certain quenching of fluorescence is observed in comparison

with MgTAP as noted in the early work [69]. Passing to H2 TAC leads to a decrease in uF by a factor of 3 at practically constant kF , while the reduction of the second pyrrole ring results in still stronger quenching. We suppose that these facts may be explained by the participation in deactivation processes of transitions from the S1 level onto an upper triplet level T3 (or T4 ), which proves to be close to the S1 level in the case of H2 TABCtt . It should be noted that in going from H2 P to H2 C the intersystem crossing probability also increases (from 7.2  107 to 9.7  107 s1 ), the role of internal conversion being negligible [62], but the fluorescence quantum yield rises, due to a sharp increase in the S1 ! S0 radiative transition probability. The given explanation is hypothetical since the energy of the T1 state and, hence, of the upper triplet states is unknown. In experiments we could not detect the phosphorescence of the compounds studied. As regards the CNDO/S quantum-chemical calculations of the triplet states, which could have helped in the interpretation of the experimental data on fluorescence quenching, they give unfortunately drastically underestimated values of the energy of the T1 state already for H2 P [31,70] and H2 TAP [39]. Therefore, the calculation results for triplet states were not used in discussion. Indirect evidence in favor of our interpretation may be found in the data on time-resolved ESR [11]. Indeed, if the quenching of the H2 TABCtt fluorescence (the total rate constant of non-radiative deactivation is >1010 s1 ) were caused by the S1 , S0 internal conversion, the population of the T1 state would be very low and the ESR would not be observed. To photophysical aspects one may attribute also the violation of mirror symmetry of the absorption and fluorescence spectra of the H2 TACt and H2 TABCtt at room temperature noted in 4.1. Since at 77 K the spectra are mirror-symmetrical, this violation (fluorescence spectrum broadening) must be caused by the rearrangement of the ‘‘molecule – solvate shell’’ system after the photo-excitation and the appearance of ‘‘dynamical’’ inhomogeneous broadening. It may be noted here that the temperature dependence of uF of H2 TABCtt is insignificant.

6. Conclusion In the present work the absorption spectra of dihydro- and tetrahydro-derivatives of porphyrazine (H2 TAP), the aza-analogues of chlorophyll and bacteriochlorophyll, are interpreted in detail on the basis of experimental studies of spectral-luminescent properties and the theoretical calculations of excited electronic states by the CNDO/S method. It is shown that the effect of reduction of the pyrrole rings in the porphyrazine macrocycle on the electronic spectra is adequately de-

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scribed by quantum chemical calculations using this method. The comparison between the electronic spectra in the series H2 P–H2 C–H2 BC and H2 TAP–H2 TAC(H2 TACt )–H2 TABCtt reveals two essential distinctions in the visible spectrum for these series: in the porphyrazine series (i) the influence of the pyrrole rings reduction on the frequencies of electronic transitions is stronger – bathochromic shifts of the longest-wavelength band Qx ð0; 0Þ as well as the Qy –Qx intervals are larger than those in the porphin series (the Qy ð0; 0Þ band being shifted hypsochromically); (ii) the intensity of the Qx ð0; 0Þ band is only weakly sensitive to the reduction of the pyrrole rings. The quantum-chemical calculation predicts for H2 TABC a considerably greater interval Bx –By (large up-shift of the Bx level) than for H2 BC which is in good agreement with the fluorescence polarization spectrum. Strong quenching of fluorescence on the pyrrole rings reduction in the porphyrazine macrocycle has been established. The increase in the total probability of nonradiative deactivation of the S1 level in the H2 TAP– H2 TACt –H2 TABCtt series is considerably larger than in the H2 P–H2 C–H2 BC series. It is shown that this cannot be wholly explained by the increase in the probability of the S1 , S0 internal conversion. Supposedly, the increase in the probability of the S1 , T1 intersystem crossing is due to participation of intermediate triplet levels in this process.

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