Fuzzy symmetries of two classes of linear polyacene molecules

The fuzzy symmetries of two kinds of linear polyacene molecules are probed into in the paper. In these molecules, any one of the benzene rings abreast connects at most other two rings in two ways: either its two opposite C–C bonds combine with two other rings, respectively, or its two meta-position C–C bonds connect two rings in cis- and trans-form, respectively. The former is called p-polyacenes (or straight polyacenes), and the latter is m-polyacenes (or kinked ones). It can be thought as the planar molecule with approximate one-dimensional space periodic transformation (parallel translation) symmetry, namely, group G₁²{{\rm G}_{1}^{2}} symmetry, when the number of its benzene ring is very large; on the other hand, it can be considered as the fuzzy group G₁²{{\rm G}_{1}^{2}} symmetry, if the benzene ring number is not large enough. The p-polyacene and m-polyacene with 20 benzene rings are analyzed as typical examples, and the energies of the π-molecular orbital (MO) and the fuzzy symmetry characters related to the space symmetry transformations are carefully examined. Moreover, the π-MOs of the p-polyacenes and m-polyacenes with different numbers of benzene ring are investigated to obtain the related rules.     

Fourier-transform infrared spectroscopic studies of dithia tetraphenylporphine

We present here infrared absorption spectra of dithia tetraphenylporphine and its cation in the 450–1600 and 2900–3400 cm⁻¹ regions. Most of the allowed IR bands are observed in pairs due to overallD _2h point group symmetry of the molecule. The observed bands have been assigned to the porphyrin skeleton and phenyl ring modes. Some weak bands, which are forbidden underD _2h , also appear in the spectra due to the distortion of the molecule from planarity-caused by the out-of-plane positioned N and S atoms. Increased intensity of some phenyl ring bands compared to free-base tetraphenylporphine is explained on the basis of rotation of phenyl rings towards the mean molecular plane. Contrary to the point group symmetry of cation of dithia tetraphenylporphine, certain bands are observed to be degenerate due to identical bonding arrangements in pyrrole rings of the cation     

Synthesis and study of the properties of K2Y1 ? x ? yEuxTby(MoO4)(PO4) and K2Y1 ? x ? yEuxTby(MoO4)(PO4)1?δ(VO4)δ solid solutions

Al synthesized samples are isostructural and crystallize in the orthorhombic symmetry system, space group Ibca. Particles of the final product of ∼200 nm in size have been obtained. The introduction of the vanadate anion into the matrix composition leads to the lowering of the symmetry of the Eu³⁺ environment and to the rise of the defect luminescence at 450–550 nm because of the unit cell distortion. The luminescence of defects in terbium-europium-containing samples is determined by the sample surface area, which decreases on annealing. The τ, W ₀ and γ parameters of the luminescence kinetics of the samples have been determined.     

Gas-phase structures of 1-adamantylphosphines,PH<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(1-Ad)<Subscript>3−<Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–3)

The gas-phase structure of 1-adamantylphosphine has been determined by electron diffraction, supplemented with data from ab initio and DFT calculations. The adamantyl fragment was modeled with local C _3v symmetry and the phosphino group was found to be in a position almost bisecting a mirror plane of the adamantyl group, giving the molecule overall approximate C _s symmetry. There is a small displacement of the C–P bond from the local threefold axis of the adamantyl group. Geometry optimizations were also performed for bis-(1-adamantyl)phosphine (C ₁ point-group symmetry) and tris-(1-adamantyl)phosphine (C ₃ symmetry), demonstrating extremely crowded environments around the phosphorus atoms leading to adamantyl groups that were much less symmetric. The adamantyl groups were also found to twist by a significant amount to minimize the strain.     

Simultaneous electron diffraction and mass spectrometric studies of molecular structure of manganese trifluoride

It is shown that two geometrical models of the MnF₃ molecule equally fit experimental electron diffraction data: a pyramidal model of C_3v symmetry and a planar model with nonequivalent F-F distances of C_2v symmetry. Ivanovo Chemical Technological Institute. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 4. pp. 61–67, July–August, 1994. Translated by L. Smolina     

Jahn–Teller Distortion Versus Spin–Orbit Splitting: Symmetry of Small Heavy-Metal Atom Clusters

Metal clusters often show slight deviations from high molecular point group symmetry. The reason for this is a Jahn–Teller distortion because of partial occupation of orbitals that are degenerate in the highly symmetric case. For heavy elements spin–orbit coupling, which usually is not regarded in quantum chemical treatments of clusters, becomes non-negligible. This leads to splitting of degenerate orbitals, so that the reason for distortion is no longer given. In a rigorous study of neutral, cationic and anionic 4–6 atomic clusters of W, Re, Tl and Pb it is demonstrated that in some cases regarding spin–orbit coupling indeed yields a highly symmetric global minimum structure, whereas neglecting this effect leads to distorted structures of lower symmetry.     

Structures and aromaticity of the planar Al<Subscript>2</Subscript>P<Subscript>2</Subscript><Superscript><Emphasis Type="Italic">n</Emphasis>−</Superscript> (<Emphasis Type="Italic">n</Emphasis>=1–4) clusters

Clusters Al₂P₂ ⁿ⁻ (n = 1–4) were theoretically investigated using density functional theory (DFT) methods at the B3LYP/6-311+G* and B3PW91/6-311+G* levels of theory. The calculated results showed that the planar structure (D _2h symmetry) of Al₂P₂ ⁿ⁻ (n = 1–4) species was the global minimum. And the negative nucleus-independent chemical shift (NICS) value of Al₂P₂ ⁿ⁻ (n = 1–4) species indicated the existence of a ring current in the planar structure (D _2h symmetry). A detailed molecular orbital (MO) analysis revealed that the planar structures (D _2h symmetry) had π aromaticity, which further exhibited the strongly aromatic character for Al₂P₂ ⁿ⁻ (n = 1–4) species.     

Evaluating molecular asymmetry

A method for calculating the asymmetry parameters of molecules based on Avnir’s CSM approach combined with the “dissymmetry function” method is suggested. The performance of the approach is demonstrated on various geometrical models — high-symmetry antiprisms of S₁₀ and D₅ symmetry groups, helices, and molecular objects. It is shown that the MCSM method unambiguously determines the symmetry element or estimates the degree of asymmetry for molecules from different structural classes. A. V. Bogatskii Physiocochemical Institute, Ukrainian Academy of Sciences. Odessa State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 547–552, May–June, 1998.     

A quantum-chemical and gas phase electron diffraction study of the structure of formylphosphine and acetyldimethylphosphine

The equilibrium geometry and energy and structural changes accompanying inversion motion in the phosphorus fragment and acyl group internal rotation in the H₂PCHO and Me₂PCMeO molecules were calculated by the MP2(full) method using basis sets from 6–31G(d, p) to 6–311G(3df, 2p). The structure of Me₂PCMeO was determined by electron diffraction using the dynamic model of acyl group internal rotation based on the quantum-chemical potential function of torsional motion. Acylphosphines have amide-type equilibrium conformations with acyl groups rotated through ∼100° from their orientation in the C=O/PX₂ anti- form, where X = H, Me (C ₁ symmetry). Considerable pyramidality of the phosphorus fragment distinguishes the equilibrium structures of acylphosphines from amides with a planar molecular frame (C _s symmetry). The r _h1 geometric parameters of the Me₂PCMeO molecule determined by electron diffraction closely agree with quantum-chemical estimates for the equilibrium configuration.     

Spinor optimization for a relativistic spin-dependent CASSCF program

Detailed formulae for the implementation of the multi-configuration SCF spinor optimization in a basis of Kramers pair 2-spinors – i.e. exploiting time-reversal symmetry – are presented. Full expressions for the spinor gradient and spinor Hessian elements are given in abstract form as well as within the usual CASSCF subspace division. As far as possible, the resulting terms are grouped to relativistic inactive and active Fock matrices, which have been introduced previously. Approximations for the Hessian are introduced so as to initialize it in an inverse Hessian update algorithm for a diagonal first approximation within the standard quasi-Newton-Raphson procedure. The effects of double group symmetry arising from spin dependence on Fock matrices and therefore gradient and Hessian are discussed and a group scheme for the implementation is proposed. Received: 14 January 1997 / Accepted: 3 February 1997     

Local dipole interactions induce helicity of (<Emphasis Type="Italic">S</Emphasis>)-2-butyl-<Emphasis Type="Italic">N</Emphasis>-(1,8-naphthaloyl)-2-aminobenzoate molecules containing 1,8-naphthalimide rings utilized as a column building blocks: X-ray and quantum mechanical studies

In the crystal of triclinic symmetry the title compound contains four independent molecules, which differ in the conformation of the aliphatic carbon chain (T, G ⁺and G ⁻) and in the helicity (M or P) of the N-(1,8-naphthaloyl)-2-aminobenzoate (NAB) unit. Quantum chemical MP2 calculations showed that isolated molecules favor helicity of NAB bichromophores most likely due to attractive interactions between local dipoles formed along carbonyl bonds, such that the helical arrangement of O=C–C–C–N–C=O fragments is stabilized by intramolecular interactions between terminal anti-parallel local carbonyl dipoles. In the crystal structure, columnar stacking of the anti-parallel 1,8-naphalimide rings is observed. In a column the neighboring NAB units display opposite helicity.     

Structures of Rydberg transitions in the absorption spectra of methyl-substituted derivatives of bis(η6-benzene)chromium

The effect of methylation of ligands in bis(η⁶-benzene)chromium (1) on the structure of Rydberg transitions in absorption spectra has been studied. A detailed analysis and interpretation of all Rydberg elements of the vapor-phase spectra of bis(η⁶-benzene)chromium (2), bis(η⁶-o-xylene)chromium (3), bis(η⁶-m-xylene)chromium (4), and bis(η⁶-mesitylene)chromium (5) was carried out. The vapor-phase electronic absorption spectrum of bis(η⁶-p-xylene)chromium (6) was measured, and the assignment of the Rydberg bands was made for the first time. The first ionization potentials of complexes 2–5 were refined. The energy of detachment of the 3d_z ² electron and the parameters of the Rydberg excitations for molecule 6 were determined. The vibronic components of the 3d_z ²→R4p _x,y transition in the spectra of complexes 2 and 6 were assigned. The differences in the Rydberg structure of the spectra of compounds 2–6 were analyzed in terms of the selection rules for optical transitions in the corresponding symmetry groups. The vapor-phase spectra correspond to conformers with the symmetry groupsC _2v andC ₂ for complexes 2–4, with the symmetry groupsD _3h andD ₃ for compound 5, and with the symmetry groupD _2d for complex 6. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 897–903, May, 1998.     

Full Non-rigid Group of Sponge and Pina

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing a subgroup of order 324 without inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C ₂ and C _i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively. The character tables of these groups are also computed.     

Composition and structure refinement of superconducting crystals Y1? x Tb x Ba2Cu3O6+δ ( x = 0.10; δ = 0.75)

Crystals of Y_0.90Tb_0.10Ba₂Cu₃O_6.75 have been prepared by spontaneous crystallization from slowly cooled non-stoichiometric melt of the system Y-Tb-Ba-Cu-O. Average size of platelet crystals having mirror surface is 2×2, the largest — 8×9 mm with thickness 0.1–0.2 mm. The crystals have been characterized by powder X-ray diffraction and electron microprobe analysis. Tetragonal symmetry of the crystals has been determined by X-ray diffraction. Magnetic susceptibility measurements have revealed that the crystals manifest transition to superconducting state without additional annealing (T _c = 60 K). Structures and compositions — Y/Tb ratio (σ = 0.01) and oxygen content (σ = 0.04) — have been refined for two single crystals. Possibility of rhombic distortion of the tetragonal symmetry is discussed. __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 6, pp. 1101–1107, November–December, 2008. Original Russian Text Copyright ? 2008 by L. P. Kozeeva, N. V. Podberezskaya, N. V. Kuratieva, M. Yu. Kamaneva, and A. G. Blinov     

Crycom program for approximate symmetry recognition in crystal structures

The CRYCOM program was previously proposed for recognition of similarity between crystal structures. It compares unit cell parameters and atomic coordinates, taking into consideration all factors leading to various structure representations (the choice of basic lattice vectors, the origin of coordinates, segregation domain, and atomic displacements). The program can also be utilized for seeking approximate symmetry by comparing an original structure representation with its equivalent representations. Operation of the program is illustrated by an example of distorted hexagonal symmetry recognition in the monoclinic structure of strontium aluminate. L. Ya. Karpov Physicochemical Research Institute. Translated fromZhurnal Struktumoi Khimii, Vol. 35, No. 5, pp. 149–152, September–October, 1994. Translated by O. Kharlamova     

Interaction of nitrogen dioxide with sublimed films ofmeso-tetraphenylporphyrinatozinc

The interaction of NO₂ with sublimed films ofmeso-tetraphenylporphyrinatozinc was studied by IR and UV-VIS spectroscopy. The π-radical cation (ZnTPP)^•+NO₂ ⁻ containing an unpaired electron on HOMO of the A_2u symmetry is formed at the first stage of the reaction. The second NO₂ molecule attacks themeso-carbon atom to form zinc isoporphyrin with the covalently bound nitro group. The IR data indicate that the NO₂ ⁻ anion is axially coordinated to the central metal atom, and the NO₂ group is covalently bonded through the N atom. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 665–668, April, 1998.     

Spectrum of states in icosahedral structures of the electronic configuration gn (N = 1–7). 1. Invariant expansion for integrals and energies

The energy spectrum of the states that appear in structures of icosahedral (I,I_h symmetry with open electronic shells g^N (dim g = 4; N = 1–7) is reported. The energies are obtained in terms of integral invariants (reduced matrix elements of electron-electron interaction) H^k (g, g). The latter are analogs of the Slater-Condon parameters F^k(l,l) for atoms with the l^N electronic configuration. A similar representation is proposed for the integrals mm’≨’) of electron-electron interaction on the 4-fold degenerate g orbitals in the “standard” representation. The relation between the terms of the g^N(I,I_h) configuration and the parent states of the orthogonal group O⁺(4) is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 1, pp. 3–13, January–February, 1997.     

Determination of molecular constants of scandium triiodide monomer and dimer from electron diffraction data

The molecular intensity function of a ScI₃+SC₂I₆ mixture is solved using gas-phase electron diffractometry and taking into account the theoretical values of l(Sc-I). The symmetry of geometrical configuration, the internuclear distances, and vibration frequencies of the scandium triiodide monomer and dimer are determined. Translated fromZhurnal Struktumoi Khimii, Vol. 38, No. 3, pp. 489–494, May–June, 1997.     

Free electron model in cluster structure theory. Electronic structures of [Mo6S8(CN)6]6?, [Mo6Se8(CN)6]6?, [Re6S8(CN)6]4?, and Rh6(CO)16 clusters

The results of quantum chemical calculations of the electronic structure and geometry of octahedral clusters [Mo₆S₈(CN)₆]⁶⁻, [Mo₆Se₈(CN)₆]⁶⁻, [Re₆S₈(CN)₆]⁴⁻, and Rh₆(CO)₁₆ by the ab initio SCF (RHF) and DFT (B3LYP) methods with various basis sets are presented. The electronic states of the clusters under study in ideal spherically symmetric potential were classified in the orbital quantum number l (1s, 1p, 1d, 1f, 1g, 1h, 1i), l = 0–6. In real crystal field with O_h symmetry these states are split. The calculated new electronic states were matched to the irreducible representations of the point symmetry group O_h. The polarizabilities of the compounds considered are 55–65 ų. A new model for the electronic structure of octahedral clusters containing M₆ groups was proposed. The model is based on the idea of free electrons moving in spherically symmetric potential field. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2617–2624, December, 2005.     

Molecular and crystal structure of methyl-4-anti-hydroxyimino-1-dioxolano-13-isopropyl-10a,7-dimethylpentacyclo×[10b.8.5.04b,10b.06a,10a.01a,4a]icos-14-ene-7-carboxylate

Synthesis is performed and the molecular structure is analyzed of methyl-4-anti-hydroxyimino-1-dioxolano-13-isopropyl-10a,7-dimethylpentacyclo[10b.8.5.0^4b,10b.0^6a,10a.0^1a,4a]icos-14-ene-7-carboxylate IIa. Compound IIa C₂₇H₄₀O₄ crystallizes in monoclinic symmetry with cell parameters: a = 13.785(13) ?, b = 7.302(7) ?, c = 13.817(13) ?, β = 94.799(19)°, space group P2(1), Z = 2, d = 1.164 g/cm³. Original Russian Text Copyright ? 2009 by I. E. Smirnova, E. V. Tret’yakova, O. B. Kazakova, and Z. A. Starikova __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 2, pp. 393–395, March–April, 2009.