The calculation of frequency-dependent hyperpolarizabilities including electron correlation effects

The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation.     

Algebraic properties of the 1 + 1-dimensional Heisenberg spin field model

The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system is generated.     

Mössbauer spectroscopic study of Prussian Blue from different provenances

Ferric ferrocyanides synthesized from different sources of ferric cations and ferrocyanide anions and those derived from ferrous ferricyanide, ferrous ferrocyanide and ferric ferricyanide have been studied using Mössbauer and XRD techniques. Structural information of the effect of the provenance on the properties of the final compound is obtained. Significant correlations between isomer shift and quadrupole splitting of inner and outer iron cations have been observed.     

Formation of β-distonic oxonium ions: Study of ROCH2CH2OR′ radical cations

Radical cations derived from the ethers ROCH₂CH₂OR′ (R, R′ = H, CH₃, C₂₅) were studied, since β-distonic oxonium ions are often prepared from ionized ethers of glycol. The first step in the fragmentation is a 1,5-transfer of an α-hydrogen to oxygen of a terminal alkoxy group leading to a δ-distonic oxonium ion. This step is thermo-neutral and reversible in the ROCH₂CH₂OH radical cations and exothermic and irreversible in the dialkyl ether radical cations. Depending on R and R,′ these δ-distonic oxonium ions fragment by three reactions: the loss of an alcohol or a water molecule, the formation of a β-distonic oxonium ion ˙CH₂CH₂O(H)⁺R and a 1,4-H migration between carbon atoms. Competition between these processes is discussed.     

Periodic solution finder for an impact oscillator with a drift

In this paper, an efficient semi-analytical method is developed to compute periodic solutions for a new model of an impact oscillator with a drift, which explains the progression mechanism in vibro-impact systems and can be used to optimize their performance. The method constructs a periodic response assuming that each period is comprised of a sequence of distinct phases for which analytical solutions are known. For example, a period may consist of the following sequential phases: (I) contact with progression, (II) contact without progression, (III) no contact and (IV) contact without progression. Using this information, a system of four piecewise linear first order differential equations is transformed to a system of non-linear algebraic equations. The method allows one to accurately predict a range of control parameters for which the best progression rates are obtained.     

An observation of electron phase transition in SmB6 at low temperatures

In order to reveal the nature of the ground state of archetypal intermediate-valence compound SmB₆, a comprehensive study of its transport and magnetic properties was carried out on high-quality single crystals at temperatures of 1.8-300 K in magnetic fields up to 7 T. A drastic enhancement of negative magnetoresistance was observed below 14 K, with the maximum absolute value of Δρ/ρB²∼2.2×10⁻³ T⁻² at T≈5.2 K. This effect seems to be attributable to anomalous magnetic scattering of many-body (exciton-polaronic) complexes induced by fast valence fluctuations on Sm sites. The observed anomalies of magnetotransport, thermoelectric and magnetic characteristics are discussed in terms of electron phase transition to the coherent state of interacting many-body complexes occurring at T^*∼5 K.     

Underbody and ground effects on rotating disc flow: a global scale inviscid study

The flow induced by a finite disc rotating near horizontal ground is considered, including the effects of an underbody. This paper concentrates on determining the shape of the free layer beyond the rim of the disc which is horizontal in the absence of the underbody and ground but forced to deform to ensure that conditions across the layer are satisfied when the underbody or ground is added. The far-field behaviour, the inviscid flow produced by a nominally infinite disc near the ground and the global solution for small ground clearances are considered analytically, and the full problem is posed as an integral problem. This is then solved numerically and analytically. Results are presented for various heights of the disc above the ground and for discs with an axisymmetric underbody present. A universal form is found for the farfield shape (which is controlled by entrainment into the free layer) but both the underbody and the ground effects are found to increase very significantly for reduced clearances.     

Chemical Reactivity of Tetrasulfur Tetranitride: Synthesis,Physical Properties,and Structural Characterization of the Amorphous Phase Cu7S4N4

Tetrasulfur tetranitride, S₄N₄, reacts with elemental Cu within inert solvents to a black‐blue material of approximate composition Cu₇S₄N₄ which is totally amorphous to X‐rays and which cannot be made crystalline by either thermal treatment or electron radiation. Cu₇S₄N₄ explodes if heated above 234 °C or when subjected to mechanical shock to eventually yield copper(I) sulfide; this together with the characteristic infrared spectrum of Cu₇S₄N₄ indicates the presence of molecular S₄N₄ units inside the amorphous phase. The metastable nature of Cu₇S₄N₄ is also mirrored by electron microscopy which furthermore allows the structural characterization of its degradation products. Based on experimental EXAFS data offering characteristic Cu—N and Cu—S distances, a theoretical crystalline approximant of Cu₇S₄N₄ was suggested and structurally optimized by density‐functional total‐energy calculations including periodic boundary conditions. This model incorporates a central S₄N₄ unit bonded to three shells of Cu atoms of different functionalities; in addition, a partial rupture of the S₄N₄ unit is likely to allow for a lowering of the total energy of the metastable phase. The latter observation supports the impossibility to make Cu₇S₄N₄ crystallize using ₄N₄ crystallize using whatever kind of measures.