Symmetry and the polar state of condensed molecular matter

Polar molecular crystals seem to contradict a quantum mechanical statement, according to which no stationary state of a system features a permanent electrical polarization. By stationary we understand here an ensemble for which thermal averaging applies. In the language of statistical mechanics we have thus to ask for the thermal expectation value of the polarization in molecular crystals. Nucleation aggregates and growing crystal surfaces can provide a single degree of freedom for polar molecules required to average the polarization. By means of group theoretical reasoning and Monte Carlo simulations we show that such systems thermalize into a bi-polar state featuring zero bulk polarity. A two domain, i.e. bipolar state is obtained because boundaries are setting up opposing effective electrical fields. Described phenomena can be understood as a process of partial ergodicity-restoring. Experimentally, a bi-polar state of molecular crystals was demonstrated using phase sensitive second harmonic generation and scanning pyroelectric microscopy

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Paleoecology, Diagenesis and Biological Affinity of Tetradiids in the Upper Ordovician (Sandbian) Black River Group of the Kingston Area, Ontario, Canada

Tetradiids are a group of colonial, tubular fossils that occur globally in Middle to Upper Ordovician strata. Tetradiids were first described as a type of tabulate coral; however, based on their four-fold symmetry, division, and presence of a central-sparry canal, they were recently reinterpreted as a florideophyte rhodophyte algae, a reinterpretation that is tested in this thesis. This study focused on understanding the affinity and taphonomy of this order of fossil. Research was conducted by stratigraphic and petrographic analyses of the Black River Group in the Kingston, Ontario region. Tetradiid occurrences were divided into fragment or colonial, with three morphologies of tetradiids described (Tetradium, Phytopsis and Paratetradium). Morphology is specific to depositional environment, with compact Tetradium consistently within ooid grainstones and open branching Phytopsis and chained Paratetradium consistently within mudstones. Two types of patch reefs were recognized: a Paratetradium bioherm, and a Paratetradium, Phytopsis, stromatolite bioherm. The presence of bioherms implies that tetradiids were capable of hypercalcifying. Preservation styles of tetradiids were investigated, and were compared to brachiopods, echinoderms, mollusks, and ooids. Tetradiids were preferentially preserved as molds and demonstrated complete dissolution of skeletal material. Rare specimens, however, demonstrated preserved horizontal partitions, central plates, and a double wall. Skeletal molds were filled with either calcite spar, mud or encrusted by a cryptomicrobial colony. Both calcitic and aragonitic ooids were discovered. The co-occurrence of aragonitic ooids, aragonitic crytodontids, and the evolution of aragonitic, hypercalcifying tetradiids is interpreted as representing the geochemical favoring of aragonite and HMC in a time of global calcite seas. The geochemical favoring of aragonite is interpreted to be independent to global Mg: Ca ratios, but was the result of increased saturation levels and temperature driven by high atmospheric pCO2. Based on the presence of epitheca, tabulae, septa, and the commonality of growth forms, tetradiids are interpreted as an order of Cnidaria. The evolution of an aragonitic skeleton in tetradiids is interpreted to be the result of de novo acquisition of a skeleton from an unmineralized clade.

High pressure studies on group VI metal hexacarbonyl molecular solids

Group VI metal hexacarbonyls, M(CO)6 (M = Cr, Mo and W), are of extreme importance as catalysts in industry and also of fundamental interest due to the established charge transfer mechanism between the carbon monoxide and the metal. They condense to molecular solids at ambient conditions retaining the octahedral (Oh) symmetry of gas phase and have been extensively investigated by previous workers to understand their fundamental chemical bonding and possible industrial applications. However little is known about their behavior at high pressures which is the focus of this dissertation. Metal hexacarbonyls were subjected to high pressures in Diamond-Anvil cells to understand the pressure effect on chemical bonding using Raman scattering in situ. The high-pressure results on each of the three metal hexacarbonyls are presented and are followed by a critical analysis of the entire family. The Raman study was conducted at pressures up to 45 GPa and X-ray up to 58 GPa. This is followed by a discussion on infra red spectra in conjunction with Raman and X-ray analysis to provide a rationale for polymerization. Finally the probable synthesis of extremely reactive species under high-pressures and as identified via Raman is discussed. The high-pressure Raman scattering, up to 30 GPa, demonstrated the absence of Π-backbonding. The disappearance of parental Raman spectra for (M = Cr, Mo and W) at 29.6, 23.3 and 22.2 GPa respectively was attributed to the total collapse of the Oh symmetry. This collapse under high-pressure lead to metal-mediated polymeric phase characterized by Raman active δ(OCO) feature, originating from intermolecular vibrational coupling in the parent sample. Further increase in pressures up to 45 GPa, did not affect this feature. The pressure quenched Raman spectra, revealed various chemical groups non-characteristic of the parent sample and adsorption of CO in addition to the characteristic δ(OCO) feature. The thus recorded Raman, complemented with the far and mid-infrared pressure quenched spectra, reveal the formation of novel metal-mediated polymers. The X-ray diffraction on W(CO)6 up to 58 GPa revealed the generation of amorphous polymeric pattern which was retained back to ambient conditions.

Paleoecology, Diagenesis and Biological Affinity of Tetradiids in the Upper Ordovician (Sandbian) Black River Group of the Kingston Area, Ontario, Canada

Tetradiids are a group of colonial, tubular fossils that occur globally in Middle to Upper Ordovician strata. Tetradiids were first described as a type of tabulate coral; however, based on their four-fold symmetry, division, and presence of a central-sparry canal, they were recently reinterpreted as a florideophyte rhodophyte algae, a reinterpretation that is tested in this thesis. This study focused on understanding the affinity and taphonomy of this order of fossil. Research was conducted by stratigraphic and petrographic analyses of the Black River Group in the Kingston, Ontario region. Tetradiid occurrences were divided into fragment or colonial, with three morphologies of tetradiids described (Tetradium, Phytopsis and Paratetradium). Morphology is specific to depositional environment, with compact Tetradium consistently within ooid grainstones and open branching Phytopsis and chained Paratetradium consistently within mudstones. Two types of patch reefs were recognized: a Paratetradium bioherm, and a Paratetradium, Phytopsis, stromatolite bioherm. The presence of bioherms implies that tetradiids were capable of hypercalcifying. Preservation styles of tetradiids were investigated, and were compared to brachiopods, echinoderms, mollusks, and ooids. Tetradiids were preferentially preserved as molds and demonstrated complete dissolution of skeletal material. Rare specimens, however, demonstrated preserved horizontal partitions, central plates, and a double wall. Skeletal molds were filled with either calcite spar, mud or encrusted by a cryptomicrobial colony. Both calcitic and aragonitic ooids were discovered. The co-occurrence of aragonitic ooids, aragonitic crytodontids, and the evolution of aragonitic, hypercalcifying tetradiids is interpreted as representing the geochemical favoring of aragonite and HMC in a time of global calcite seas. The geochemical favoring of aragonite is interpreted to be independent to global Mg: Ca ratios, but was the result of increased saturation levels and temperature driven by high atmospheric pCO2. Based on the presence of epitheca, tabulae, septa, and the commonality of growth forms, tetradiids are interpreted as an order of Cnidaria. The evolution of an aragonitic skeleton in tetradiids is interpreted to be the result of de novo acquisition of a skeleton from an unmineralized clade.

Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.

Electronic and vibrational spectra of gaspeite

Visible, near-infrared, IR and Raman spectra of magnesian gaspeite are presented. Nickel ion is the main source of the electronic bands as it is the principal component in the mineral where as the bands in IR and Raman spectra are due to the vibrational processes in the carbonate ion as an entity. The combination of electronic absorption and vibrational spectra (including near-infrared, FTIR and Raman) of magnesian gaspeite are explained in terms of the cation co-ordination and the behaviour of CO32– anion in the Ni–Mg carbonate. The electronic absorption spectrum consists of three broad and intense bands at 8130, 13160 and 22730 cm–1 due to spin-allowed transitions and two weak bands at 20410 and 30300 cm–1 are assigned to spin-forbidden transitions of Ni2+ in an octahedral symmetry. The crystal field parameters evaluated from the observed bands are Dq = 810; B = 800 and C = 3200 cm–1. The two bands in the near-infrared spectrum at 4330 and 5130 cm–1 are overtone and combination of CO32– vibrational modes. For the carbonate group, infrared bands are observed at 1020 cm–1(1 ), 870 cm–1 (2), 1418 cm–1 (3) and 750 cm–1 (4), of which3, the asymmetric stretching mode is most intense. Three well resolved Raman bands at 1571, 1088 and 331 cm–1 are assigned to 3, 1 and MO stretching vibrations.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].