The Nature of the Chemical Process. 1. Symmetry Evolution - Revised Information Theory, Similarity Principle and Ugly Symmetry

Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L (L=lnw, w is the number of microstates, or the sum of entropy and information, L=S+I) of the universe is a constant (the first law of information theory). The entropy S of the universe tends toward a maximum (the second law law of information theory). For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law law of information theory). Based on the Gibbs inequality and the second law of the revised information theory we have proved the similarity principle (a continuous higher similarity-higher entropy relation after the rejection of the Gibbs paradox) and proved the Curie-Rosen symmetry principle (a higher symmetry-higher stability relation) as a special case of the similarity principle. Some examples in chemical physics have been given. Spontaneous processes of all kinds of molecular interaction, phase separation and phase transition, including symmetry breaking and the densest molecular packing and crystallization, are all driven by information minimization or symmetry maximization. The evolution of the universe in general and evolution of life in particular can be quantitatively considered as a series of symmetry breaking processes. The two empirical rules - similarity rule and complementarity rule - have been given a theoretical foundation. All kinds of periodicity in space and time are symmetries and contribute to the stability. Symmetry is beautiful because it renders stability. However, symmetry is in principle ugly because it is associated with information loss.Comment: 29 pages, 14 figure

Symmetry Breaking Constraints: Recent Results

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetryComment: To appear in Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12

Charge Nematicity and Electronic Raman Scattering in Iron-based Superconductors

We review the recent developments in electronic Raman scattering measurements of charge nematic fluctuations in iron-based superconductors. A simple theoretical framework of a $d$-wave Pomeranchuk transition is proposed in order to capture the salient features of the spectra. We discuss the available Raman data in the normal state of 122 iron-based systems, particularly Co doped BaFe$_2$As$_2$, and we show that the low energy quasi-elastic peak, the extracted nematic susceptibility and the scattering rates are consistent with an electronic driven structural phase transition. In the superconducting state with a full gap the quasi-elastic peak transforms into a finite frequency nematic resonance, evidences for which are particularly strong in the electron doped systems. A crucial feature of the analysis is the fact that the electronic Raman signal is unaffected by the acoustic phonons. This makes Raman spectroscopy a unique probe of electronic nematicity.Comment: Invited review to a special issue in Iron-based superconductor

Jahn-Teller orbital glass state in the expanded fcc Cs3C60 fulleride

The most expanded fcc-structured alkali fulleride, Cs3C60, is a Mott insulator at ambient pressure because of the weak overlap between the frontier t1u molecular orbitals of the C603− anions. It has a severely disordered antiferromagnetic ground state that becomes a superconductor with a high critical temperature, Tc of 35 K upon compression. The effect of the localised t1u3 electronic configuration on the properties of the material is not well-understood. Here we study the relationship between the intrinsic crystallographic C603− orientational disorder and the molecular Jahn–Teller (JT) effect dynamics in the Mott insulating state. The high-resolution 13C magic-angle-spinning (MAS) NMR spectrum at room temperature comprises three peaks in the intensity ratio 1:2:2 consistent with the presence of three crystallographically-inequivalent carbon sites in the fcc unit cell and revealing that the JT-effect dynamics are fast on the NMR time-scale of 10−5 s despite the presence of the frozen-in C603− merohedral disorder disclosed by the 133Cs MAS NMR fine splitting of the tetrahedral and octahedral 133Cs resonances. Cooling to sub-liquid-nitrogen temperatures leads to severe broadening of both the 13C and 133Cs MAS NMR multiplets, which provides the signature of an increased number of inequivalent 13C and 133Cs sites. This is attributed to the freezing out of the C603− JT dynamics and the development of a t1u electronic orbital glass state guided by the merohedral disorder of the fcc structure. The observation of the dynamic and static JT effect in the Mott insulating state of the metrically cubic but merohedrally disordered Cs3C60 fulleride in different temperature ranges reveals the intimate relation between charge localization, magnetic ground state, lifting of electronic degeneracy, and orientational disorder in these strongly-correlated systems

Spontaneous Octahedral Tilting in the Cubic Inorganic Caesium Halide Perovskites CsSnX3_3 and CsPbX3_3 (X = F, Cl, Br, I)

The local crystal structures of many perovskite-structured materials deviate from the average space group symmetry. We demonstrate, from lattice-dynamics calculations based on quantum chemical force constants, that all the caesium-lead and caesium-tin halide perovskites exhibit vibrational instabilities associated with octahedral titling in their high-temperature cubic phase. Anharmonic double-well potentials are found for zone-boundary phonon modes in all compounds with barriers ranging from 108 to 512 meV. The well depth is correlated with the tolerance factor and the chemistry of the composition, but is not proportional to the imaginary harmonic phonon frequency. We provide quantitative insights into the thermodynamic driving forces and distinguish between dynamic and static disorder based on the potential-energy landscape. A positive band gap deformation (spectral blueshift) accompanies the structural distortion, with implications for understanding the performance of these materials in applications areas including solar cells and light-emitting diodes