Structure and electronic properties of hollow‐caged C60 fullerene‐derived (MN4)nC6(10 − n) (M = Zn,Mg, Fe,n = 1−6) complexes

Unique hollow‐caged (MN₄)_nC_{6(10 ? n)} (M = Zn, Mg, Fe, n = 1?6) complexes designed by introduction of n porphyrinoid fragments in C₆₀ fullerene structure were proposed and the atomic and electronic structures were calculated using LC‐DFT MPWB95 and M06 potentials and 6‐311G(d)/6‐31G(d) basis sets. The complexes were optimized using various symmetric configurations from the highest O_h to the lowest C₁ point groups in different spin states from S = 0 (singlet) to S = 7 (quindectet) for M = Fe to define energetically preferable atomic and electronic structures. Several metastable complexes were determined and the key role of the metal ions in stabilization of the atomic structure of the complexes was revealed. For Fe₆N₂₄C₂₄, the minimum energy was reported for C_2h, D_2h, and D_4h symmetry of pentet state S = 2, so the complex can be regarded as unique molecular magnet. It was found that the metal partial density of states determine the nature of HOMO and LUMO levels making the clusters promising catalysts. © 2014 Wiley Periodicals, Inc.     

Algorithm for variational calculations of molecular symmetry in solving anharmonic vibrational problems

A universal program for variational calculations of molecular symmetry in solving anharmonic vibrational problems, realized by the author, is described. The program uses the group-theoretical method. Symmetrized basis wave functions are constructed with the aid of the generalized KJebsch-Gordan series suggested by the author. The method of constructing symmetrized basis wave functions and the program for adequate calculations of molecular symmetry were verified for many molecules of different symmetry groups: O_h, O, T_d, T_h, T, D_∞h, C_t8v, D_nd, D_nh, D_n, C_nv, C_nh, S_2n, C_n, C_i, C_s, and C₁ where 2 ≤n ≤6. It was confirmed that the program provides correct results and high-speed operation. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1146–1153, November–December, 1997.     

Conformational study of C24 cyclic polyyne clusters

Polyynes were first synthesized before the year 1900, and isolated and characterized after 2000. Cyclic polyynes are of particular interest since possess a high order of symmetry. Furthermore, some studies reported special mechanical properties of the condensed polyyne bulks. The optimal size of polyynes to form rings has been previously investigated and was found to be 24 with a stable cluster of crossing four C₂₄ cyclic polyynes. We investigated in this study the conformation of clusters of polyynes (nC₂₄) by the pattern previously identified to stabilize the cluster. Clusters of 4C₂₄, 10C₂₄, 22C₂₄, 46C₂₄, and 94C₂₄ were designed and subjected to energy minimization. The main finding is the preservation of the symmetry for the nC₂₄ cluster with the increase of its size. The study revealed that 4C₂₄, 10C₂₄, and 22C₂₄ preserve a high symmetry and the calculations suggest an excellent increasing of the cluster stability with the increase of the number of polyyne rings. A 22C₂₄ derived cluster namely 28C₂₄ was found as the one likely to limit the growth of the polyyne clusters.     

Algebraic expressions of irreducible bases for molecules C20H20, C80, and C240

Using the symmetrized boson representation technique, concise algebraic expressions of the irreducible bases symmetry adapted to the group chain I_h⊃C₅ for the fullerene molecules C₂₀H₂₀, C₈₀, and C₂₄₀ are derived for the most general cases and those for any specific case can be derived from them easily without a projection procedure. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 283–297, 1999     

Facile Synthesis of (S,S)‐1,2‐Diacylamides and (S,S)‐1,2‐Diamines with C 2‐Symmetry

A series of chiral vicinal tertiary diacylamides with C ₂‐symmetry was synthesized from (S)‐α‐phenylethylamine, different aromatic aldehydes, and oxalyl chloride. The diacylamides obtained were then reduced to afford chiral vicinal diamines with C ₂‐symmetry. We propose that the diacylamides existed in four stable conformational isomers in solution because of the dihedral angle between acylamide bonds.     

Time-reversal symmetry in molecular rovibronic states and in second-order processes

A unified treatment of time-reversal symmetry is given for molecular systems. The treatment allows for interconversion of electronic, rotational, and vibrational angular momenta on equal footing because of a coherent phase choice. It also allows for correlation from a continuous group (of spherical or cylindrical symmetry) to lower point groups (such as C₃, C₄, C₆, S₄, S_g, T, etc.). General, many-electron molecular states that form time-reversal degenerate components are constructed. Attention is called to the Kramers' doublets as the special odd-electron case of such double degeneracy. Specific examples of a spiropentane and a 5-azoniaspiro(4.4) nonane with S₄ symmetry and possible time-reversal degeneracy are given. The optical rotation due to a time-odd polarizability tensor in one of the two time-degenerate components is shown to be of an opposite sign to that in the other component. The above result is from a second-order matrix element (over the polarizability tensor) and is proved to be independent of even- or odd-number of electron spins. It is shown to hold also for Kramers' doubly degenerate components. This result is contrasted with that of a first-order Jahn-Teller effect which depends on the number of electron spins.     

Continuous Symmetry Measures. VI. The Relations Between Polyhedral Point-Group/Subgroup Symmetries

We extend our analysis of the symmetry content of the classical polyhedra [1] to the analysis of the degree of polyhedral subgroup symmetries. The quantitative levels of the hierarchical polyhedral symmetries series of O_h, D_4h and D_2h of hexacoordinated structures, as well as the relations between them, serve as an example. A distinction is made between two types of measures: quantitative evaluation of the degree of symmetry, and quantitative evaluation of the degree of content of a reference shape.     

The dimer,trimer and 1,2,4‐tri­thiol­ane of adamantane­thione

The mol­ecules of di­spiro­[1,3‐dithietane‐2,2′:4,2′′‐diadamantane], C₂₀H₂₈S₂, have crystallographic C_i symmetry, as well as local D_2h symmetry, and a planar 1,3‐dithietane ring. The mol­ecules of tri­spiro­[1,3,5‐tri­thia­ne‐2,2′:4,2′′:6,2′′′‐triadamantane], C₃₀H₄₂S₃, have approximate C₂ symmetry and the 1,3,5‐tri­thia­ne ring has a twist–boat conformation. The C—S—C bond angles within the ring are about 8° larger than observed in most related 1,3,5‐tri­thia­ne structures. In di­spiro­[1,2,4‐tri­thiol­ane‐3,2′:5,2′′‐diadamantane], C₂₀H₂₈S₃, the mol­ecules have local C₂ symmetry and the 1,2,4‐tri­thiol­ane ring has a half‐chair conformation.     

Construction of linearly independent relativistic symmetry orbitals for finite double-point groups including time reversal symmetry

A formalism is developed for the construction of relativistic symmetry-adapted molecular basis functions under consideration of time reversal invariance. The theory is applicable to the finite double point groups C_n, C_nh, S_n, C_nv, D_n, D_nd, D_nh, T, T_h, T_d, O, and O_h. It is based on the LCAO method. A projection operator technique is employed to construct molecular symmetry orbitals from atomic orbitals. The search for linearly independent basis function is simplified by means of group theoretical considerations.     

Topological structures of tetrahedral (Td and T) fullerenes with hexagonal and triangular faces and their vibration and NMR spectra

On analyzing the topological structures of the three types of tetrahedral fullerenes (which consist only of triangles and hexagons), (1) C _n (T _d ,n=12h ²; h=1,2,…), (2) C _n (T _d ,n=4h ²;h=1,2,…), and (3) C _n (T,n=4(h ²+hk+k ²);h>k,h,k=1,2,…), we have obtained theoretically the Infrared and Raman active modes by means of the derived formulas for the decomposition of their nuclear motions into irreducible representations, and the ¹³C NMR spectra with natural abundance for ¹³C by using the distribution functions for all of the tetrahedral (T _d and T) fullerenes, respectively. Received: 25 May 1998 / Accepted: 30 July 1998 / Published online: 23 November 1998     

Molecular dynamics in the nematic,SA and SC phases of 8S5 and 9S5 as studied by dielectric methods

Abstract

Two experimental techniques—time domain spectroscopy (TDS) and a steady state frequency method—have been used to study dielectric spectra for the isotropic, nematic, S_A, S_C and S_Y phases of two thioesters (4-n-pentylphenyl-4′-n-octyloxy-and 4′-n-nonyloxythiobenzoates (C _n H_2n+1 O?C₆ H₄?COS?C₆H₄?C₅H₁₁, where n = 8 and n = 9) known as 8S5 and 9S5, in the frequency range from 10 Hz to 10 GHz. In the case of 8S5 a deuteriated sample (8S5-d ₂₈) has been used to study relaxation processes in the nematic and smectic phases.     

Optical Rotation of Time-Reversal Degenerate States

It is shown that time-reversal (doubly-) degenerate, many-electron states in molecules of point-group symmetry C₃, C₄, C₆, S₄, and S₆ and T etc., can have non-vanishing matrix elements over a time-odd (electric dipole-electric dipole) polarizability operator contributing to optical rotation. In agreement with well-known results for Kramers' doublets, the optical rotations of the two separated and oriented states of this doublet have opposite signs in this polarizability mechanism, and they have the same sign in the time-even pseudoscalar mechanism which is the usual natural optical rotation of chiral molecules. These results are proven, in an alternative formulation using time-reversal in a second-order process, to hold regardless of even or odd numbers of spins—in contrast to the first-order processes such as the Jahn-Teller effect. The universality of time-reversal in spin, orbital and rotational angular momentum, in point and continuous groups, is show in a unified treatment with consistent phases. It was shown also how time-reversal symmetry can resolve the ambiguities in lower point-groups and determine relationships for which the point-group symmetry is powerless.     

Earth Alkaline Tetrathiosquarates. II. – Syntheses and Crystal Structures of SrC4S4·4 H2O and Ba4K2(C4S4)5·16 H2O

Concentrated aqueous solutions of strontium chloride and barium chloride, respectively, allow on addition of the potassium salt of tetrathiosquarate, K₂C₄S₄·H₂O, the isolation of the earth alkaline salts SrC₄S₄·4 H₂O ( 1 ) and Ba₄K₂(C₄S₄)₅·16 H₂O ( 2 ), both as dark red crystals. The crystal structure determinations ( 1 : orthorhombic, Pnma, a = 8.149(1), b = 12.907(2), c = 10.790(2) Å, Z = 4; 2 : orthorhombic, Pbca, a = 15.875(3), b = 21.325(5), c = 16.119(1) Å, Z = 4) show the presence of C₄S₄²⁻ ions with only slightly distorted D_4h symmetry having average C–C and C–S bond lengths of 1.41Å and 1.681Å for 1 and 1.450Å and 1.657Å for 2 . The structure of 1 contains concatenated edge‐sharing Sr(H₂O)₆S₂ polyhedra. The Sr²⁺ ions are in eight‐fold coordination with Sr–O distances of 2.50–2.72Å and Sr–S distances of 3.21Å, (C₄S₄)²⁻ acts as a chelating ligand towards Sr²⁺. The structure is closely related to the previously reported Ca²⁺ containing analogue, which is of lower symmetry belonging to the monoclinic crystal system. A supergroup‐subgroup relation between the space groups of both structures is present. The structure of 2 is made up of Ba²⁺ and K⁺ ions in eight and nine‐fold coordination by H₂O molecules and (C₄S₄)²⁻ ions which act as chelating ligands towards one cation and bridging between two cations. The coordination polyhedra of the cations are connected by common edges and corners in two dimensions to layers which are connected by tetrathiosquarate ions to a three‐dimensional network. The infrared and Raman spectra show bands typical for the molecular building units of the two compounds.     

Synthesis of Nordstrandite and Nordstrandite-Derived Layered Double Hydroxides of Li and Al: A Comparative Study with the Bayerite Counterpart

The layered double hydroxides (LDHs) of Li and Al can be synthesized from the four polymorphs of Al(OH)₃, namely gibbsite, bayerite, nordstrandite, and doyleite. The crystal structure of this class of compounds depends on the type of the precursor used due to their topotactic reaction mechanism. While the LDHs derived from gibbsite and bayerite yield different crystal structures, the incorporation of Li into nordstrandite was expected to yield new LDH structures different from those derived from gibbsite and bayerite. The structure of nordstrandite derived LDHs were however identical to that derived from the bayerite counterpart. The absence of symmetry in the interlayer of nordstrandite (C₁) makes it unsuitable to accommodate the intercalating anions with different molecular symmetries. To make the interlayer gallery suitable for the anions, the metal hydroxide layers of the nordstrandite translate, transforming nordstrandite to bayerite. The bayerite with site symmetries O_h and C₂ stabilizes the anions in the interlayer by hydrogen bonding. The transformation of nordstrandite to bayerite, when soaked in lithium salt solution is, therefore, a manifestation of the intercalating anions.     

Synthesis,Separation, and Characterization of Optically Pure C76 Mono-Adducts

Nucleophilic Bingel cyclopropanation of D₂-C₇₆ with bis[(S)-1-phenylbutyl] 2-bromomalonate in toluene in the presence of base yielded three constitutionally isomeric pairs of diastereoisomeric mono-adducts together with one other constitutional isomer. All seven mono-adducts were isolated in optically pure form by prep. HPLC on a (S,S)-Whelk-O1 chiral stationary phase. They represent the first optically pure adducts of an inherently chiral fullerene. Characterization by UV/VIS, CD, ¹³C- and ¹H-NMR spectroscopy allowed identification of pairs of stereoisomers and symmetry assignments: the two pairs of diastereoisomers which were isolated as the major product possess C₁ symmetry, whereas the third pair of diastereoisomers, which is a minor product, is C₂-symmetrical. The circular dichroism spectra of the optically active C₇₆-adducts showed very pronounced Cotton effects resulting from strong chiroptical contributions of the chiral fullerene chromophore with the maximum observed Δε values being twice as high than those previously measured for optically active adducts of achiral fullerenes with a chiral addition pattern. Whereas the regioselectivity of mono-additions to C₇₀ correlates with the degree of local bond curvature and the regioselectivity of multiple Bingel cyclopropanations of C₆₀ with electronic parameters such as coefficients of the lowest unoccupied molecular orbital (LUMO), no such simple predictive correlations exist for the nucleophilic addition to C₇₆. Despite full spectral characterization, an unambiguous structural assignment of the isolated compounds was not possible, except for the two C₂-symmetrical isomers. Based on considerations of local bond curvature and the previous experiences with the chemistry of C₇₀, the structures of the C₂-symmetrical stereoisomers were assigned as (S,S,^fC)- 3 and (S,S,^fA)- 3 , resulting from addition to the polar α-type C(1)? C(6) bond.     

Synthesis,crystal structures and characterizations of two homochiral coordination polymers based on a chiral reduced Schiff base ligand

Two homochiral coordination polymers based on a chiral reduced Schiff base ligand, namely poly[(μ₅‐4‐{[(NR,1S)‐(1‐carboxylato‐2‐phenylethyl)amino]methyl}benzoato)zinc(II)], [Zn(C₁₇H₁₅NO₄)]_n, (1), and poly[(μ₅‐4‐{[(NR,1S)‐(1‐carboxylato‐2‐phenylethyl)amino]methyl}benzoato)cobalt(II)], [Co(C₁₇H₁₅NO₄)]_n, (2), have been obtained by hydrothermal methods and studied by single‐crystal X‐ray diffraction, elemental analyses, powder X‐ray diffraction, thermogravimetric analysis, IR spectroscopy and fluorescence spectroscopy. Compounds (1) and (2) are isostructural and crystallize in the P2₁2₁2₁ space group. Both display a three‐dimensional network structure with a one‐dimensional channel, with the benzyl group of the ligand directed towards the channel. An investigation of photoluminescence properties shows that compound (1) displays a strong emission in the purple region.     

Algebraic solutions for point groups: Cubic groups G in the group chain G⊃T⊃D2⊃C2

Concise algebraic expressions of the symmetry‐adapted functions (SAFs) for both single‐valued and double‐valued representations are derived for the group chain O⊃T⊃D₂⊃C₂ and O⊃D₄⊃D₂⊃C₂, which are functions of only the quantum numbers of the respective group chain without involving any irreducible matrix elements. It is shown that the SAFs of the cubic groups G=O,T_d,T_h,O_h can be expressed in a simple way in terms of the SAFs of the group T. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 585–599, 2000     

A new P,S‐coordinating ferrocenyl ligand: synthesis of a precursor and its coordination compounds with PdII and PtII

In our ongoing development of ferrocene ligands, 1‐dimethylamino‐2‐(diphenylphosphinothioyl)ferrocene is being used as a convenient building block to obtain racemic or enantiomerically pure ligands. Using this building block in large excess allowed the formation of several by‐products, two of which have already been reported; the structure of a third by‐product, namely 1‐(diphenylphosphinothioyl)‐2‐{[(diphenylphosphinothioyl)sulfanyl]methyl}ferrocene, [Fe(C₅H₅)(C₃₀H₂₅P₂S₃)], is presented here. The crystal structure is built up from a ferrocene unit, with one of the cyclopentadienyl (Cp) rings substituted in the 1‐ and 2‐positions by a protected diphenylphosphinothioyl group and a [(diphenylphosphinothioyl)sulfanyl]methyl fragment, –CH₂SP(=S)Ph₂. There are C—H...S interactions which result in the formation of chains parallel to the c axis. After desulfurization, the crude material was then reacted with Pd and Pt (M) precursors [MCl₂(CH₃CN)₂] to yield two isostructural dinuclear complexes arranged around twofold axes, namely (R,R/S,S)‐bis{μ‐[2‐(diphenylphosphanyl)ferrocen‐1‐yl]methanethiolato‐κ³P,S:S}bis[chloridopalladium(II)] pentane disolvate, [Pd₂{Fe(C₅H₅)(C₁₈H₁₅PS)}₂Cl₂]·2C₅H₁₂, and the platinum(II) analogue, (R,R/S,S)‐bis{μ‐[2‐(diphenylphosphanyl)ferrocen‐1‐yl]methanethiolato‐κ³P,S:S}bis[chloridoplatinum(II)] toluene monosolvate, [Pt₂{Fe(C₅H₅)(C₁₈H₁₅PS)}₂Cl₂]·C₇H₈, in which the two metal atoms present a slightly distorted square‐planar geometry formed by two bridging S atoms and P and Cl atoms. The P,S‐chelating ligand results from the rupture of one of the P—S bonds in the starting ligand. These dinuclear complexes display a butterfly geometry. Surprisingly, only the (R,R/S,S) diastereoisomer has been isolated.     

Tribenzotriquinacene Receptors for C60 Fullerene Rotors: Towards C3 Symmetrical Chiral Stators for Unidirectionally Operating Nanoratchets

The synthesis of a stereochemically pure concave tribenzotriquinacene receptor ( 7 ) for C₆₀ fullerene, possessing C₃ point group symmetry, by threefold condensation of C₂‐symmetric 1,2‐diketone synthons ( 5 ) and a hexaaminotribenzotriquinacene core ( 6 ) is described. The chiral diketone was synthesized in a five‐step reaction sequence starting from C_2h‐symmetric 2,6‐di‐tert‐butylanthracene. The highly diastereo‐discriminating Diels–Alder reaction of 2,6‐di‐tert‐butylanthracene with fumaric acid di(?)menthyl ester, catalyzed by aluminium chloride, is the relevant stereochemistry introducing step. The structure of the fullerene receptor was verified by ¹H and ¹³C NMR spectroscopy, mass spectrometry and single crystal X‐ray diffraction. VCD and ECD spectra were recorded, which were corroborated by ab initio DFT calculations, establishing the chiral nature of 7 with about 99.7 % ee, based on the ee (99.9 %) of the chiral synthon ( 1 ). The absolute configuration of 7 could thus be established as all‐S [(2S,7S,16S,21S,30S,35S)‐( 7 )]. Spectroscopic titration experiments reveal that the host forms 1:1 complexes with either pure fullerene (C₆₀) or fullerene derivatives, such as rotor 1′‐(4‐nitrophenyl)‐3′‐(4‐N,N‐dimethylaminophenyl)‐pyrazolino[4′,5′:1,2][60]fullerene ( R ). The complex stability constants of the complexes dissolved in CHCl₃/CS₂ (1:1 vol. %) are K([ C₆₀ ? 7 ])=319(±156) M ^?1 and K([ R ? 7 ])=110(±50) M ^?1. With molecular dynamics simulations using a first‐principles parameterized force field the asymmetry of the rotational potential for [ R ? 7 ] was shown, demonstrating the potential suitability of receptor 7 to act as a stator in a unidirectionally operating nanoratchet.     

Structure of Pyridazine in the S1 State: Experiment and Theory

The molecular structure of pyridazine in the first electronically excited state (S₁) is deduced from the combined use of resonance‐enhanced two‐photon ionization and mass‐analyzed threshold ionization spectroscopic methods. The equation‐of‐motion coupled‐cluster single and double (EOM–CCSD) calculation gives the distorted planar geometry for the most stable structure of the S₁ pyridazine. The symmetry constraint of C_2v is relaxed to that of C_s, and consequently many in‐plane vibrational modes are found to be optically active in both S₁–S₀ and D₀–S₁ excitation spectra, being appropriately assigned from the comparison of their frequencies with ab initio values. This indicates that the S₁–S₀ excitation is partially localized, and provides an alternative explanation for the long‐standing spectroscopic puzzle in S₁ pyridazine.