Open-shell calculation on molecules with icosahedral symmetry

The ground and excited states of footballene C₆₀ and dodecahedral C₂₀ carbon species and their ions are calculated in the-electron approximation by means of Roothaan's open-shell method adjusted for systems of icosahedral symmetry. Ionization potentials and electron affinities are presented. The lowest singlet and triplet transitions of all possible symmetry types of the I_h-group are obtained for these molecules by a Cl method including all singly excited configurations.     

Spin relaxation in cubic liquid crystals. The role of symmetry

Abstract

Cubic liquid-crystalline phases are usually regarded as isotropic systems. This view is justified for physical properties that transform as second rank tensors. However, the time correlation functions describing spin relaxation in cubic phases include components that transform as fourth rank tensors, which distinguish between cubic and spherical symmetry. In this work we explore the consequences of this fact for spin relaxation behaviour in cubic phases using group theoretical methods. We identify the two irreducible crystal frame time correlation functions of a cubic phase, derive the orientation dependence of the laboratory frame time correlation functions for single crystal samples, and discuss the relation of the cubic (fourth rank) order parameter to the microstructure of the phase. Finally, as an illustration of the general results, we derive the time correlation functions for a specific model of a micellar cubic phase.     

Spin relaxation in cubic liquid crystals. The role of symmetry

Cubic liquid-crystalline phases are usually regarded as isotropic systems. This view is justified for physical properties that transform as second rank tensors. However, the time correlation functions describing spin relaxation in cubic phases include components that transform as fourth rank tensors, which distinguish between cubic and spherical symmetry. In this work we explore the consequences of this fact for spin relaxation behaviour in cubic phases using group theoretical methods. We identify the two irreducible crystal frame time correlation functions of a cubic phase, derive the orientation dependence of the laboratory frame time correlation functions for single crystal samples, and discuss the relation of the cubic (fourth rank) order parameter to the microstructure of the phase. Finally, as an illustration of the general results, we derive the time correlation functions for a specific model of a micellar cubic phase.     

Linear dichroism of molecules with cubic symmetry

Linear dichroism (LD) of chromophores which belong to the cubic point group of symmetry has been observed. The molecules CrO²⁻₄, Fe(CN)³⁻₆ and Mo(CO)₆ were dissolved in several lyotropic liquid crystals. These systems can be macroscopically aligned which is a prerequisite in LD spectroscopy. The observed LD is ascribed to distortions of the cubic symmetry caused by the uniaxial constraints in the liquid crystals. Contributions to the LD due to the inherent optical birefringence of the systems were taken into account. Furthermore, NMR of CrO²⁻₄ and ESR of Mn²⁺ in various lyotropic liquid crystals strongly support that the symmetry is distorted.     

Description of metallic and covalent clusters with icosahedral symmetry: the polytope model

Compact and tetravalent clusters with icosahedral local or global symmetries are generated by mapping from ideal structures in curved space onto a tangent euclidean 3D space. The observed elastic energy of the clusters can thus be interpreted as an intrinsic curvature associated to a frustrated local order. It is then proposed a kind of classification of the very rich family of possible clusters using a limited set of parameters.     

Compositions of nanoparticles of cubic symmetry

The formulas for calculation of the number of particles in structures of cubic symmetry O _h are reported. The numbers of atoms in the shells of cubic symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of the shells of cubic symmetry is presented, and eight classes of shells are revealed. A key role in this classification is played by basic shells; in the case of close-packed spheres, these basic shells are repeated every six layers. The sum of all coordination numbers of all atoms of subshells is 24. The possibility of the existence of new fullerenes and nanoparticles of elemental boron and its oxides is considered.     

Single-crystal mesostructured semiconductors with cubic Ia3d symmetry and ion-exchange properties

If the full scientific and technological potential of mesostructured materials is to be achieved, systems with continuous domains in the form of single crystals or films must be prepared. Here we report a reliable and facile system for making large single-crystal particles of chalcogenido mesostructured materials with a highly organized cubic structure, accessible pore structure, and semiconducting properties. Building blocks with square planar bonding topology, Pt(2+) and [Sn(2)Se(6)](4)(-), in combination with long-chain pyridinium surfactants (C(n)PyBr, n = 18, 20) favor faceted single-crystal particles with the highest possible space group symmetry Ia3d. This is an important step toward developing large single-domain crystalline mesostructured semiconductors and usable natural self-assembled antidot array systems. The tendency toward cubic symmetry is so strong that the materials assemble readily under experimental conditions that can tolerate considerable variation and form micrometer-sized rhombic dodecahedral cubosome particles. The c-C(n)PyPtSnSe materials are the first to exhibit reversible ion-exchange properties. The surfactant molecules can be ion-exchanged reversibly and without loss of the cubic structure and particle morphology. The cubosomes possess a three-dimensional open Pt-Sn-Se framework with a low-energy band gap of approximately 1.7 eV.     

A method for modeling icosahedral virions: Rotational symmetry boundary conditions

We present two techniques for implementing a new method of simulating an entire virion. Earlier computer simulations of a capsid protein revealed large edge effects due to the use of free standing boundaries. Because of the size of a given protomer, conventional three-dimensional periodic boundary conditions would be extremely wasteful. This would require an extremely large number of solvent molecules, and therefore would be computationally feasible for only a fragment of the entire virion. The new method employs non-space-filling computational cells in molecular modeling and molecular dynamics with the boundary conditions based on the icosahedral group. The method is general and could be used for any molecular system with a point group symmetry. With this method, the dynamical and spatial intra and interprotomer correlations can be studied at atomic levels. The technique is applicable to any virion with icosahedral symmetry. A sample calculation involving a geometry optimization of the human rhinovirus coat proteins is given to demonstrate the technique.     

Nanoscale cF96 cubic versus icosahedral phase in devitrified Hf-based metallic glasses

The devitrification behaviour of the rapidly solidified quaternary hafnium-based alloys of Hf₆₅NM_17.5TM₁₀Al_7.5 composition (NM- noble metal, TM- 3d transition metal) was studied using differential scanning calorimetry. The purpose of the study was to evaluate the influence of composition on the devitrification products at the primary stage. The structure was analysed by using X-ray diffraction and transmission electron microscopy. The formation of the nanoparticles of the Hf-based quasicrystalline icosahedral or cubic cF96 Fd₃⁻m Ti₂Ni-type phase about 10 nm in size was observed at the primary devitrification stage in different metallic glasses with close compositions. The icosahedral phase consists of 137-atom Bergmann rhombic triacontahedra. The alloys in systems in which the stable Hf-based cF96 phase exists do not show the formation of the icosahedral phase from the amorphous matrix. The cF96 phase and the icosahedral phase formed by primary devitrification from the amorphous phase may inherit the local order of the icosahedral clusters in the amorphous matrix.     

Non-tortuous ionic transport in robust micellar liquid crystalline phases with cubic symmetry

A micellar cubic LC phase consisting of a hydrophilic matrix exhibited enhanced ionic transport and mechanical properties without macroscopic orientation, which are attributed to the non-tortuous ionic transport and highly symmetric cubic lattice, respectively.     

Facile preparation of macroscopic soft colloidal crystals with fiber symmetry

A facile, efficient way to fabricate macroscopic soft colloidal crystals with fiber symmetry by drying a latex dispersion in a tube is presented. A transparent, stable colloidal crystal was obtained from a 25 wt % latex dispersion by complete water evaporation for 4 days. The centimeter-long sample was investigated by means of synchrotron small-angle X-ray diffraction (SAXD). Analysis of a large number of distinct Bragg peaks reveals that uniaxially oriented colloidal crystals with face-centered cubic lattice structure were formed. The measurement of evaporation rates under different conditions indicates that the water evaporates primarily through the optically clear regions (i.e., via the solid material) even when the region is more than 2 mm thick.     

Density of non-Bloch electron states in perfect cubic crystals

This paper gives an abbreviated method for the calculation of the density of states of a crystal on the basis of that band theory in which the crystal electron states are represented by the standinglike wave functions classified according to the point-group symmetry species. The crystal is a large but finite sphere filled regularly with atoms, and the wave functions are quantized at the boundary of the sphere. The Bloch theorem is not satisfied in this theory since the wave functions are not basis functions of the irreducible representations of the translation subgroup. On the other hand, a theorem is established that the density of states can be made up of contributions given by all irreducible representations of the crystal point group, any contribution being proportional to the square of the dimension of the irreducible representation. In distinction to a former approach, the band structure is calculated solely from the energy eigenvalues obtained with the aid of the diagonalization process of the Wannier–Slater differential operator. A simple cubic lattice with an s atomic orbital on each lattice site is taken as an example, and the results are compared with Bloch's theory.     

A group theoretical study of f n systems in an environment of approximately icosahedral symmetry

Group theoretical methods are developed to determine in a generalised format for an f ⁿ ion in a crystal field environment of icosahedral symmetry, the effect on the energy level scheme when a crystal field distortion is considered parallel to any direction. As an illustration, the effect on the g-tensor components are examined as a function of the magnitude and the direction of the crystal field distortion. All appropriate reduced matrix elements in group theoretical terminology are evaluated for the f ⁿ -ion ground states. Specific results are given for the f ³-ion case and compared with electron paramagnetic resonance, optical, and magnetic susceptibility data.     

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non‐Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z‐component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half‐filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non‐Abelian point group. The C₆₀ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Formation and properties of reverse micellar cubic liquid crystals and derived emulsions

The structure of the reverse micellar cubic (I2) liquid crystal and the adjacent micellar phase in amphiphilic block copolymer/water/oil systems has been studied by small-angle X-ray scattering (SAXS), rheometry, and differential scanning calorimetry (DSC). Upon addition of water to the copolymer/oil mixture, spherical micelles are formed and grow in size until a disorder-order transition takes place, which is related to a sudden increase in the viscosity and shear modulus. The transition is driven by the packing of the spherical micelles into a Fd3m cubic lattice. The single-phase I2 liquid crystals show gel-like behavior and elastic moduli higher than 104 Pa, as determined by oscillatory measurements. Further addition of water induces phase separation, and it is found that reverse water-in-oil emulsions with high internal phase ratio and stabilized by I2 liquid crystals can be prepared in the two-phase region. Contrary to liquid-liquid emulsions, both the elastic modulus and the viscosity decrease with the fraction of dispersed water, due to a decrease in the crystalline fraction in the sample, although the reverse emulsions remain gel-like even at high volume fractions of the dispersed phase. A temperature induced order-disorder transition can be detected by calorimetry and rheometry. Upon heating the I2 liquid crystals, two thermal events associated with small enthalpy values were detected: one endothermic, related to the "melting" of the liquid crystal, and the other exothermic, attributed to phase separation. The melting of the liquid crystal is associated with a sudden drop in viscosity and shear moduli. Results are relevant for understanding the formation of cubic-phase-based reverse emulsions and for their application as templates for the synthesis of structured materials.     

Synthesis of ordered mesoporous carbon monoliths with bicontinuous cubic pore structure of Ia3d symmetry

Large-diameter-sized mesoporous carbon monoliths with bicontinuous cubic structure of Ia3d symmetry have been synthesized by using mesoporous silica monoliths as hard templates; such carbon monoliths show potential application of advanced electrodes and electrochemical double layer capacitors.