Doubling Constants Research Articles

Copper(II) succinate complexes with 1,2-di-4-pyridylethane and 1,3-di-4-pyridylpropane

The compounds poly[di-mu(4)-succinato-mu(2)-1,2-di-4-pyridylethane-dicopper(II)], [Cu(2)(C(4)H(4)O(4))(2)(C(12)H(12)N(2))](n), (I), and poly[di-mu(4)-succinato-mu(2)-1,3-di-4-pyridylpropane-dicopper(II)], [Cu(2)(C(4)H(4)O(4))(2)(C(13)H(14)N(2))](n), (II), exhibit polymeric structures with the dicopper units doubly bridged by bis-bidentate succinate groups and crosslinked by the separator bis(pyridyl) molecules. In (I), the molecule exhibits a centre of inversion located midway between the core Cu-dimer atoms and another that relates half of the bis(pyridyl)ethane ligand to the other half. Compound (II) has a similar molecular packing but with a doubled lattice constant and noncentrosymmetric core units. An antiferromagnetic interaction due to the dinuclear copper units was deduced from magnetic subsceptibility measurements, and spin triplet signals were detected in the electron paramagnetic resonance spectra for both compounds.

Electronic Spectrum of AuF: Hyperfine Structure of the [17.7]1 State

The [17.7]1-X(1)Sigma(+) (0,0) band of AuF at 566 nm has been studied by laser excitation spectroscopy. The molecule was prepared in a dc electric discharge by flowing a dilute mixture of SF(6) in argon through a hollow gold cathode. The rotational structure of the band has been analyzed for the first time, yielding accurate values for the rotational and Omega-type doubling constants of the upper state. Hyperfine splittings arising from both the (197)Au and (19)F nuclei have been resolved by recording the spectrum at sub-Doppler resolution using the technique of intermodulated fluorescence spectroscopy. The hyperfine structure is dominated by the (197)Au magnetic dipole interaction in the [17.7]1 state, with the (197)Au magnetic hyperfine constant determined to be h(1) = -543(4) MHz. It is demonstrated that the negative value of this constant implies that the [17.7]1 state has significant (3)Delta(1) character and that spin-orbit mixing with a (1)Pi(1) state may be providing the transition intensity to the ground electronic state.

Freiman–Ruzsa-type theory for small doubling constant

AbstractIn this paper, we study the linear structure of sets A ⊂ $\mathbb{F}_2^n$ with doubling constant σ(A) < 2, where σ(A):=|A+A|/|A|. In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with |V| ≤ |A|. Finally, we classify all binary sets with small doubling constant.

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Laboratory experiments on the gastric evacuation of juvenile herring ( Clupea harengus L.)

Laboratory experiments were conducted on groups of 9.9 to 13 cm (mean) total length (L T) juvenile herring ( Clupea harengus L.) to describe the temperature dependency of the gastric evacuation. Experiments were conducted at 13 and 16 °C. The parameters of the general gastric evacuation model were B = 0.953 and R = 0.082 at 13 °C and B = 1.323 and R = 0.843 at 16 °C indicating an exponential evacuation. The evacuation constants of the exponential gastric evacuation model were R = 0.098 at 13 and R = 0.202 at 16 °C resulting in a temperature dependency parameter (A) of 0.241. The internal dynamics of the stomach and its storage capacity were studied by the use of stained copepods. Investigations on the functional response of herring to different food densities were described by the Michaelis-Menten equation. Our experimental design allowed us to test the hypothesis of Richter et al. [Richter, H., Lückstädt, C., Schlechtriem, C., Focken, U., Becker, K., 2002. Do the fish stomach content models currently used for daily ration estimation really work? Evidence of violation of a basic assumption concerning stomach evacuation rates. Arch. Fish. Mar. Res. 49 (3), 171–188] that fish have two evacuation modes, one evacuation constant while only evacuating food and a significant higher constant while feeding, which would question the basic assumption of most consumption models, that only use one evacuation constant for consumption estimates. The experiments of Richter et al. [Richter, H., Lückstädt, C., Schlechtriem, C., Focken, U., Becker, K., 2002. Do the fish stomach content models currently used for daily ration estimation really work? Evidence of violation of a basic assumption concerning stomach evacuation rates. Arch. Fish. Mar. Res. 49 (3), 171–188] suggested that a doubled constant would give the best match of observed feeding and estimates of consumption models. Through the results of simulations of two experiments in which we combined observed snatching rates, estimated evacuation constants and particle weights of consumed copepods, we cannot support this hypothesis. A doubled evacuation constant did not improve our simulations, on the contrary the simulations with a doubled constant gave a worse fit with our observed values. Knowledge on the gastric evacuation is a prerequisite for the evaluation of a potential top-down impact of this zooplanktivorous species on the plankton community.

Coupled cluster calculations for (potential) interstellar anions: The C2nH− series (n = 2–6)

The coupled cluster variant CCSD(T) in conjunction with a large basis set has been used to calculate spectroscopic properties for anions of type C2nH− (n=2–6), three of which were recently observed in the interstellar medium by means of radio astronomy. Accurate equilibrium structures and electric dipole moments are predicted for all five species. A variety of spectroscopic constants (vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants and centrifugal distortion constants) are reported for various isotopomers of C4H− and C6H−. The harmonic bending vibrations of chains up to C10H− and HC9N are analyzed by means of “mass plots” which draw the wavenumbers of interest as a function of the “hydrogen” mass, which is regarded as a continuous variable.

A note on l-type doubling constants in linear triatomic molecules ClHCl −: A molecular anion with an unusual q

In this note it will be recalled that the sign of the quantity which is called l-type doubling constant in linear triatomic molecules is determined by two factors which are independent. The first factor depends on the construction of the wavefunction describing the rovibrational motion of the linear molecule. The second one is a result of the interplay between the molecular potential energy function and the atomic masses. The latter effect makes in almost all linear triatomic molecules the same contribution to the sign. In this paper an exception to this rule will be presented: ClHCl − shows an unusual l-type coupling constant.

The pure rotational spectrum of CrCN (X 6 Σ +): an unexpected geometry and unusual spin interactions

The pure rotational spectrum of CrCN (X 6Σ+) has been recorded in the frequency range 250–520 GHz using direct-absorption techniques. This is the first spectroscopic investigation of the CrCN radical. This species was synthesized by reacting Cr vapour with (CN)2. Spectra were obtained for the main isotopic species, the 53Cr and 13C isotopologues, and the heavy atom stretch and several quanta of the bending vibration. The molecule was found to have a linear cyanide geometry and a 6Σ+ ground state. Rotational, fine structure, and l-type doubling constants have been determined. The spin–spin parametre λ was found to be small–a likely result of competing second-order spin–orbit contributions from excited 4Σ−, 4Π, and 6Π states. However, λ increased significantly in the bending mode, which may be caused by a reduction of the 6Σ+−4Π interaction strength due to spin–orbit vibronic coupling. In contrast, the value of γ, arising from interactions with a nearby 6Πstate, was independent of v 2. The CrCN bond lengths were determined to be r Cr–C = 2.019 Å and r C–N = 1.148 Å. Delocalization of the 3dπ electrons into the CN 2π* orbital, which is polarized towards the carbon atom, may account for the CrCN structure.

On sum-product representations in $\Bbb Z_q$

The purpose of this paper is to investigate efficient representations of the residue classes modulo q , by performing sum and product set operations starting from a given subset A of \mathbb Z_q . We consider the case of very small sets A and composite q for which not much seemed known (nontrivial results were recently obtained when q is prime or when \log |A| \sim \log q ). Roughly speaking we show that all residue classes are obtained from a k -fold sum of an r -fold product set of A , where r\ll \log q and \log k \ll \log q , provided the residue sets \pi_{q'} (A) are large for all large divisors q' of q . Even in the special case of prime modulus q , some results are new, when considering large but bounded sets A . It follows for instance from our estimates that one can obtain r as small as r\sim\log q/\log|A| with similar restriction on k , something not covered by earlier work of Konyagin and Shparlinski. On the technical side, essential use is made of Freiman's structural theorem on sets with small doubling constant. Taking for A=H a possibly very small multiplicative subgroup, bounds on exponential sums and lower bounds on \min_{a \in \mathbb Z_q^*} \max_{x \in H} \Vert ax/q\Vert are obtained. This is an extension to the results obtained by Konyagin, Shparlinski and Robinson on the distribution of solutions of x^m = a (mod q) to composite modulus q .

Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type

If a metric subspace Mo of an arbitrary metric space M carries a doubling measure µ, then there is a simultaneous linear extension of all Lipschitz functions on Mo ranged in a Banach space to those on M. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of µ.

Terahertz Vibration−Rotation-Tunneling Spectroscopy of the Ammonia Dimer: Characterization of an out of Plane Vibration

The terahertz vibration-rotation-tunneling (VRT) spectrum of the ammonia dimer (NH(3))(2) has been measured between ca. 78.5 and 91.9 cm(-1). The dipole-allowed transitions are separated into three groups that correspond to the 3-fold internal rotation of the NH(3) subunits. Transitions have been assigned for VRT states of the A-A (ortho-ortho) combinations of NH(3) monomer states. The spectrum is further complicated by strong Coriolis interactions. K = 0 <-- 0, K = 1 <-- 0, K = 0 <-- 1, and K = 1 <-- 1 progressions have been assigned. The band origins, rotational constants, asymmetry doubling, centrifugal distortion, and Coriolis coupling constant have been determined from the fit to an effective Hamiltonian. These VRT transitions are tentatively assigned to an out of plane vibration with a K = 0 state at 89.141305(47) cm(-1), and a K = 1 state at 86.77785(9) cm(-1).

Rotational spectra of the carbon-chain radicals HC5O, HC6O, and HC7O

Three new free carbon-chain radicals, HC5O, HC6O, and HC7O, and their deuterated isotopic species have been observed by Fourier transform microwave spectroscopy of a supersonic molecular beam. In contrast to the shorter HCnO radicals, these all have linear heavy-atom backbones and 2Pi electronic ground states. Like the isovalent HCnS radicals, the ground states of the HCnO radicals alternate with odd and even numbers of carbon atoms: those of HC5O and HC7O are 2Pi1/2 and that of HC6O is 2Pi3/2. From frequency measurements between 6 and 26 GHz, the rotational constant B, the centrifugal distortion constant D, and the lambda-type doubling and magnetic hyperfine constants have been determined to high precision for each chain. Predicted properties from coupled-cluster calculations are also reported for chains up to HC9O. The production of HCnO radicals for n even was highly favored when O2 was used as the source of oxygen, but those with n odd were best produced with CO.

Structure and spectroscopic properties of (AA′)(BB′)O3mixed-perovskite crystals

Five different mixed-perovskite (AA′)(BB′)O3single crystals were grown, where A = La, Nd; A′ = Sr; B = Al, Ga; and B′ = Ta, Nb. The as-grown crystals were yellowish/brownish. After annealing in air, the coloration was more intense. Annealing in a reducing atmosphere decreased coloration. The crystals were investigated by transmission spectroscopy, electron spectroscopy for chemical analysis (ESCA), and single-crystal x-ray diffraction. Additional broad absorption bands in the transmission spectra were observed for the as-grown samples. They are in line with the changes of the shape of O(1s) ESCA peaks. Redundant interstitial oxygen ions were recognized as the reason for the crystal coloration. All structures were solved and refined in different space groups of the regular system. Some of the unit cells have a doubled lattice constant: (i) lanthanum strontium gallium niobate,Pm3m,3.9323(5) Å, at 100 K, 3.9270(5) Å; (ii) neodymium strontium aluminum tantalate,Pm3m,3.8353(4) Å; (iii) lanthanum strontium aluminum tantalate,Pn3m,7.720(1) Å, annealed in reducing atmosphere, 7.708(1) Å; (iv) neodymium strontium aluminum niobate,Fm3m,7.744(4) Å.

Linear Carbon Chains of Type SiCnO (n = 3−8): Results of Coupled Cluster Calculations

On the basis of (R)CCSD(T) calculations with the cc-pVQZ basis set, accurate equilibrium bond lengths (ca. 0.0005 A accuracy) are established for linear carbon chains of type SiCnO with n = 3-8. SiC and CO equilibrium bond lengths are in the range 1.683-1.735 and 1.165-1.167 A, respectively. A narrow range (1.272-1.287 A) is obtained for all 25 carbon-carbon equilibrium distances. The equilibrium dipole moments (mu(e)) exhibit large correlation effects. The mu(e) values for the closed-shell species with even integer n are larger than those for the triplet ground states of SiCnO chains with odd n values. Various spectroscopic constants such as harmonic vibrational wavenumbers, vibration-rotation coupling, and l-type doubling constants are calculated. The ground-state rotational constants of SiC3O, SiC4O, and SiC5O are predicted with ca. 0.1% accuracy to be 1386.5, 867.0, and 564.4 MHz.

Measured descent: a new embedding method for finite metrics

We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the two primary methods of constructing Frechet embeddings for finite metrics, due to Bourgain (1985) and Rao (1999). We prove that any n-point metric space (X, d) embeds in Hilbert space with distortion $$O{\left( {{\sqrt {\alpha _{X} \cdot \log n} }} \right)},$$ where α X is a geometric estimate on the decomposability of X. As an immediate corollary, we obtain an $$O{\left( {{\sqrt {(\log \lambda _{X} )\log n} }} \right)}$$ distortion embedding, where λ X is the doubling constant of X. Since λ X ≤ n, this result recovers Bourgain’s theorem, but when the metric X is, in a sense, “low-dimensional,” improved bounds are achieved. Our embeddings are volume-respecting for subsets of arbitrary size. One consequence is the existence of (k, O(log n)) volume-respecting embeddings for all 1 ≤ k ≤ n, which is the best possible, and answers positively a question posed by U. Feige. Our techniques are also used to answer positively a question of Y. Rabinovich, showing that any weighted n-point planar graph embeds in $${\ell }^{{O(\log n)}}_{\infty } $$ with O(1) distortion. The O(log n) bound on the dimension is optimal, and improves upon the previously known bound of O((log n)2).

SiCCO and CCCO: accurate equilibrium structures and spectroscopic constants

Cubic force fields have been calculated for SiCCO and CCCO by means of the coupled cluster variant CCSD(T) and Dunning's cc-pVQZ basis set. There from, a variety of spectroscopic constants (harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants and equilibrium quartic centrifugal distortion constants) has been computed. Accurate equilibrium structures are established for both molecules and precise predictions are made for the ground-state rotational constants of less abundant isotopomers of SiCCO.

Vibrationally excited states of HC 5N: millimeter-wave spectroscopy and coupled cluster calculations

The rotational spectrum of HC 5N has been investigated in the millimeter-wave region, from 60 to 290 GHz, for 15 vibrationally excited states which lie approximately between 500 and 860 cm −1, namely ( v 6 v 7 v 8 v 9 v 10 v 11) = (000005), (000006), (000007), (000008), (000020), (000030), (001000), (010000), (100000), (000021), (000101), (001001), (010001), (000110), and (001010). Gas-phase copyrolysis of pyridine and phosphorus trichloride or, alternatively, a dc discharge in a gaseous mixture of vinyl cyanide and acetylene were used to produce the semi-stable HC 5N molecule. A large number of vibrational and rovibrational interactions has been taken into account to fit properly the measured transition frequencies of the states investigated. The most important perturbations are caused by the high-order Coriolis resonances observed between the ( v 8, v 10) and ( v 8 − 1, v 10 + 2) states, and between the ( v 7, v 10, v 11) and ( v 7 − 1, v 10 + 3, v 11 − 1) states, and by the cubic anharmonic interactions which mix the ( v 6, v 8, v 11) states with the ( v 6 − 1, v 8 + 1, v 11 + 1) states, and the ( v 6, v 10) states with the ( v 6 − 1, v 10 + 2) states. The analysis of the spectra was facilitated by CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. Excellent agreement between experiment and theory was generally observed, even when the experimental data were strongly perturbed by resonance effects.

High-resolution laser spectroscopy of the [formula omitted] transition of MgCCH

The 0 0 0 and 3 0 1 bands of the A ˜ 2 Π – X ˜ 2 Σ + electronic transition of the MgCCH radical have been recorded at low and high resolution using laser-induced fluorescence. The molecules were created in a laser ablation/molecular beam source through reaction of magnesium atoms ablated from a solid rod with methane gas entrained in helium. The rotationally resolved high-resolution data were fit to a 2Π ( a)– 2Σ + ( b) Hamiltonian, with standard deviations of 0.0025 cm −1 ( 0 0 0 ) and 0.0028 cm −1 ( 3 0 1 ) . The Λ-type doubling constants p and q in the à 2Π state are unexpectedly positive, indicating that interaction between à 2Π and the next highest 2Σ + state is not the dominant cause of the doubling, as was assumed in the structurally similar molecules CaCCH, CaOH, and SrOH in which p and q are larger and negative.

Transmission electron microscopy and electron diffraction study of the short-range ordering structure of α-LiFeO2

The basic structure of alpha-LiFeO2, lithium iron oxide, is a cubic NaCl-type structure with a lattice constant of 0.42 nm; some short-range ordering characterized by octahedral clusters exists. The local structure of the short-range ordering was investigated by transmission electron microscopy and electron diffraction. A new short-range ordering structure was found in local areas. The local structure has a cubic lattice with a doubled lattice constant. The occupation factors of cations on Wyckoff sites 4(a) and 4(b) are different from those on 24(d) sites, but the stoichiometric composition in cubic clusters is the same as the macroscopic composition. The number of pairs in which iron cations exist in nearest-neighbor sites and next nearest-neighbor sites is reduced in the structure. This means that a magnetic interaction between the iron cations is reduced by cation ordering even without spin ordering at room temperature.

Bending vibration of platinum monocarbonyl PtCO: observation of the millimeter- and submillimeter-wave spectra in the ν 2 excited vibrational state

The millimeter- and submillimeter-wave spectra of PtCO in the ground and ν 2 excited vibrational states were observed by employing a source-modulated microwave spectrometer. The PtCO molecule was generated in a free space cell by the sputtering reaction from a platinum sheet lining the inner surface of a stainless steel cathode using a dc glow plasma of CO and Ar. From the molecular constants determined for the ν 2 excited state, especially the l-type doubling constant, its harmonic wavenumber was determined to be ≈420 cm −1, which resolved the reported discrepancy between the previous matrix-infrared and theoretical estimates.