Separation of variables in 0(3)-invariant wave equations for quadrupole coordinates

Linear, 0(3) invariant equations for a multicomponent wave function, which depends on quadrupole coordinates, are examined. Vibrational, rotational, and spin parts in the Hamiltonian are separated, on which basis angular and internal variables are separated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–83, July, 1982.I thank S. A. Vladimirov for formulating the problem and for useful discussions.     

Formation of antiferromagnetically coupled C(60)(*)(-) and diamagnetic (C(70)(-))(2) dimers in ionic complexes of fullerenes with (MDABCO(+))(2).M(II)TPP (M = Zn, Co, Mn, and Fe) assemblies

A series of ionic multicomponent complexes comprising C60 and C70 anions and coordinating assemblies of methyldiazabicyclooctane cations with metal tetraphenylporphyrins, (MDABCO+)2.MIITPP.(C60(70)-)2.Sol. (C60, M = Zn (1); C60, M = Co (2); C60, M = Mn (3); C60, M = Fe (4); C70, M = Mn (5); and C70, M = Fe (6)) has been obtained. IR- and UV-vis-NIR spectra of 1-6 justified the formation of C60*- in 1-4 and single-bonded (C70-)2 dimers in 5 and 6. Co and Mn atoms are six-coordinated in the (MDABCO+)2.MIITPP units with relatively long M-N bonds of 2.475(2), 2.553(2), and 2.511(3) A for 2, 3, and 5, respectively. Isostructural complexes 2 and 3 contain C60*- zigzag chains separated by the (MDABCO+)2.MIITPP units, whereas in 5 the layers formed by the (C70-)2 dimers alternate with those composed of the (MDABCO+)2.MnIITPP units and noncoordinating MDABCO+ cations. Negative Weiss constants of -13 (1), -2 (3), and -2 (4) K indicate the antiferromagnetic interaction of spins, which decreases the magnetic moment of the complexes below 70-120 K. The EPR signals of 1 and 4 attributed to C60*- are split into two components at the same temperatures, which broaden and shift to higher and lower magnetic fields with the temperature decrease. Complexes 2 and 3 show single EPR signals with g-factors equal to 2.1082 and approximately 2.4 at 293 K, respectively. These values are mean between those characteristic of MIITPP and C60*-, and, consequently, the signals appear due to exchange coupling between these paramagnetic species. The antiferromagnetic ordering of C60*- spins below 70-100 K shifts g-factor values closer to those characteristic of individual MIITPP (g = 2.1907 (2) and approximately 4.9 (3) at 4 K). In contrast to 1-4, complex 5 shows paramagnetic behavior with Weiss constant close to 0.     

Structure and properties of ionic fullerene complex Co(+)(dppe)2·(C60˙-)·(C6H4Cl2)2: distortion of the ordered fullerene cage of C60˙- radical anions

New ionic complex {Co(+)(dppe)(2)}·(C(60)˙(-))·(C(6)H(4)Cl(2))(2) (1) was obtained by the reduction of a Co(dppe)Br(2) and C(60) mixture by TDAE in o-dichlorobenzene followed by precipitation of crystals by hexane. Optical and EPR spectra of 1 indicated the formation of C(60)˙(-) radical anions and diamagnetic Co(+)(dppe)(2) cations. The structure of 1 solved at 100(2) K involves chains of C(60)˙(-) arranged along the lattice a-axis with a center-to-center distance of 10.271 ?. The chains are separated by bulky Co(+)(dppe)(2) cations and solvent molecules. All components of 1 are well ordered allowing the distortion of the C(60)˙(-) radical anion to be analyzed. An elongation of the C(60)˙(-) sphere by 0.0254(2) was found. It is essentially smaller than those in the salts (Cp*(2)Ni(+))·(C(60)˙(-))·CS(2) and (PPN(+))(2)·(C(60)(2-)) with greater distortion of the fullerene cage. The calculation of the electronic structure of fullerene by the extended Hückel method showed slight splitting of the C(60) LUMO, due to the distortion, by three levels. Two levels are located 180 and 710 cm(-1) higher than the ground level. The averaged 6-6 and 5-6 bonds in C(60)˙(-) with lengths of 1.397(2) and 1.449(2) ? are close to those determined for the C(60)(2-) dianions in (PPN(+))(2)·(C(60)(2-)), but are slightly longer and shorter, respectively, than the length of these bonds in neutral C(60).     

New complexes of fullerences C60 and C70 with CoII and MnII tetraphenylporphyrinates and their ESR study

Complexes of fullerenes C₆₀ and C₇₀ with cobalt(II) and manganese(II) tetraphenylporphyrinates of compositions Mn(TPP)·(C₆₀)₂(CS₂)_1.5 (1), Mn(TPP)·C₇₀(CS₂) _x , wherex<=1.25 (2), Co(TPP)·C₆₀(CS₂)_0.5 (3), and Co(TPP)·C₇₀(CS₂) _x , wherex<0.25 (4), were synthesized and studied by ESR spectroscopy. At 77 K, complexes1 and2 have singlet ESR spectra characteristic of the low-spin (S=1/2) state of Mn^II, withg=2.002 and linewidths of 250 G and 300 G, respectively, and differing significantly from that of the initial Mn^II(TPP) (g ₁=5.9 andg=2.0,S=5/2). The spectra of complexes1 and2 exposed to oxygen exhibit hyperfine structure due to interaction with⁵⁵Mn and¹⁴N nuclei. The ESR spectra of complexes3 and4 are asymmetric (<g>=2.4, ΔH _pp=(500–600) G), which is due to the overlap of parallel and perpendicular spectral components. The absence of ESR signals from C₆₀ ^.− and C₇₀ ^.− radical anions makes it possible to conclude that the formation of complexes1–4 is not accompanied by electron transfer from Co(TPP) and Mn(TPP) to fullerences C₆₀ and C₇₀. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 722–725, April, 1999.     

Magnetic properties of fullerene salts containing d- and f-metal cations (Co2+, Ni2+, Fe2+, Mn2+, Eu2+, Cd2+). Specific features of the interaction between C60·? and the metal cations

The interaction between the radical anions C₆₀ ^·− and divalent d- and f-metal (Co, Fe, Ni, Mn, Eu, Cd) cations in DMF and acetonitrile-benzonitrile (AN-BN) mixture was studied. Black solid polycrystalline salts (C₆₀ ^·−)₂{(M²⁺)(DMF) _x } (x = 2.4–4, 1–6) containing the radical anions C₆₀ ^·− and metal(ii) cations solvated by DMF were prepared for the first time and their optical and magnetic properties were studied. The salts containing Co²⁺, Fe²⁺, and Ni²⁺ are characterized by antiferromagnetic interactions between the radical anions C₆₀ ^·−, which result in unusually large broadening of the EPR signal of C₆₀ ^·− upon lowering the temperature (from 5.55–12.6 mT at room temperature to 35–40 mT at 6 K for Co²⁺ and Ni²⁺). The salts containing Mn²⁺ and Eu²⁺ form diamagnetic dimers (C₆₀ ⁻)₂, which causes a jumpwise decrease in the magnetic moment of the complexes and disappearance of the EPR signal of C₆₀ ^·− in the temperature range 210–130 K. A feature of salt 6 is magnetic isolation of the radical anions C₆₀ ^·− due to the presence of diamagnetic cation Cd²⁺. The salts prepared are unstable in air and decompose in o-dichlorobenzene or AN. Reactions of C₆₀ ^·− with metal(ii) cations in AN-BN mixture result in decomposition products of the salts that contain neutral fullerene dimers and metals solvated by BN. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1909–1919, September, 2008.     

Solid-State Properties of Hexaazatriphenylenehexacarbonitrile HAT(CN)6.− Radical Anions in Crystalline Salts Containing Cryptand(M+) and Crystal Violet Cations

Crystalline {Cryptand[2.2.2](Na⁺)}{HAT(CN)₆^.−}⋅0.5C₆H₄Cl₂ ( 1 ), {Cryptand[2.2.2](K⁺)}{HAT(CN)₆^.−} ( 2 ), (CV⁺){HAT(CN)₆^.−} ( 3 ), and (CV⁺){HAT(CN)₆^.−}⋅2C₆H₄Cl₂ ( 4 ) salts (where CV⁺ is the crystal violet cation) containing hexaazatriphenylenehexacarbonitrile radical anions have been obtained. The solid-state molecular structure as well as the optical and magnetic properties of HAT(CN)₆^.− are studied. The formation of HAT(CN)₆^.− in 1 – 4 leads to the appearance of new bands in the visible range, at 694 and 740 nm. The HAT(CN)₆^.− radical anions have spin state S=1/2 and are packed in one-dimensional stacks containing the {HAT(CN)₆^.−}₂ dimers alternated with weaker interacting pairs of HAT(CN)₆^.− in 1 and nearly isolated {HAT(CN)₆^.−}₂ dimers in 2 . The {HAT(CN)₆^.−}₂ dimers are diamagnetic in 1 but they effectively mediate one-dimensional antiferromagnetic coupling of spins within the stacks with moderate exchange interaction of J/k_B = −80 K. The behaviour of salt 2 is described by a singlet–triplet model for the {HAT(CN)₆^.−}₂ dimers with an energy gap of 434(±7) K. Magnetic behaviour of both salts agree well with the data of extended Hückel calculations. Salts 3 and 4 contain isolated stacks of alternated HAT(CN)₆^.− and CV⁺ ions, and in this case, nearly paramagnetic behaviour is observed with Weiss temperatures of −1 and −7 K, respectively. Narrow Lorentzian EPR signals with g = 2.0033–2.0039 were found for the HAT(CN)₆^.− radical anions in 1 and 4 but in solution g-factor shifts to 1.9964. The electronic structure of HAT(CN)₆^.− is analysed based on X-ray diffraction data for 2 , showing a Jahn–Teller distortion of the radical anion that reduces the symmetry from D_3h to C_s and splits the initially degenerated LUMOs.     

Erratum to:Influence of Chlorides of Mono- and Divalent Metals on the Oligomeric Composition of Lysozyme Crystallization Solutions and Further Crystal Growth

Crystallography Reports - An Erratum to this paper has been published: https://doi.org/10.1134/S1063774521340046     

Steric conditions for donor–acceptor interactions in C60 complexes with planar organic donors

Charge transfer complexes of fullerene C₆₀ with planar donors of tetrathiafulvalene, dithiadiazafulvalene and pyranylidene family were investigated by IR- and UV-VIS-NIR spectroscopy. The analysis of IR and X-ray data shows that the charge transfer complexes of fullerene with the planar donors are involved in polarization interactions of van der Waals type. Charge transfer is very weak in these compounds and is hindered by unfavourable steric factors. As a result, the CT rate does not correlate with the ionization potential of the donor; the charge transfer absorption bands are very weak too.