Stability and phase transition of localized modes in Bose–Einstein condensates with both two- and three-body interactions

We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localized states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions.     

Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking

The lowest-energy state of a macroscopic system in which symmetry is spontaneously broken, is a very stable wavepacket centered around a spontaneously chosen, classical direction in symmetry space. However, for a Heisenberg ferromagnet the quantum groundstate is exactly the classical groundstate, there are no quantum fluctuations. This coincides with seven exceptional properties of the ferromagnet, including spontaneous time-reversal symmetry breaking, a reduced number of Nambu–Goldstone modes and the absence of a thin spectrum (Anderson tower of states). Recent discoveries of other non-relativistic systems with fewer Nambu–Goldstone modes suggest these specialties apply there as well. I establish precise criteria for the absence of quantum fluctuations and all the other features. In particular, it is not sufficient that the order parameter operator commutes with the Hamiltonian. It leads to a measurably larger coherence time of superpositions in small but macroscopic systems.     

2,3‐Di(2‐pyridyl)‐5‐phenylpyrazine: A NN‐CNN‐Type Bridging Ligand for Dinuclear Transition‐Metal Complexes

A new bridging ligand, 2,3‐di(2‐pyridyl)‐5‐phenylpyrazine (dpppzH), has been synthesized. This ligand was designed so that it could bind two metals through a NN‐CNN‐type coordination mode. The reaction of dpppzH with cis‐[(bpy)₂RuCl₂] (bpy=2,2′‐bipyridine) affords monoruthenium complex [(bpy)₂Ru(dpppzH)]²⁺ ( 12+ ) in 64 % yield, in which dpppzH behaves as a NN bidentate ligand. The asymmetric biruthenium complex [(bpy)₂Ru(dpppz)Ru(Mebip)]³⁺ ( 23+ ) was prepared from complex 12+ and [(Mebip)RuCl₃] (Mebip=bis(N‐methylbenzimidazolyl)pyridine), in which one hydrogen atom on the phenyl ring of dpppzH is lost and the bridging ligand binds to the second ruthenium atom in a CNN tridentate fashion. In addition, the RuPt heterobimetallic complex [(bpy)₂Ru(dpppz)Pt(C?CPh)]²⁺ ( 42+ ) has been prepared from complex 12+ , in which the bridging ligand binds to the platinum atom through a CNN binding mode. The electronic properties of these complexes have been probed by using electrochemical and spectroscopic techniques and studied by theoretical calculations. Complex 12+ is emissive at room temperature, with an emission λ_max=695 nm. No emission was detected for complex 23+ at room temperature in MeCN, whereas complex 42+ displayed an emission at about 750 nm. The emission properties of these complexes are compared to those of previously reported Ru and RuPt bimetallic complexes with a related ligand, 2,3‐di(2‐pyridyl)‐5,6‐diphenylpyrazine.     

Theoretical analysis of correlation between ionization threshold fluence in IR‐MALDI and IR absorption spectrum of matrix molecules

To investigate the correlation between the wavelength dependence of ionization threshold fluence of target molecule in matrix‐assisted laser desorption/ionization by infrared (IR) laser and the IR absorption spectrum of matrix molecule, we have analyzed the IR absorption spectra of four matrix molecules using density functional theory and correlated ab initio molecular orbital method. The calculated IR absorption spectra of the isolated molecules showed more qualitative correlation with the wavelength dependence of ionization threshold fluence than those of the solid state structures. We can consider that a portion of matrix molecules lost the ordered crystal structure and that the transition to the diluted or isolated state occurred at the early process of IR laser irradiation. © 2012 Wiley Periodicals, Inc.     

PICVib: An accurate,fast, and simple procedure to investigate selected vibrational modes at high theoretical levels

A new approach Procedure for Investigating Categories of Vibrations (PICVib) for estimating vibrational frequencies of selected modes using only the structure and energy calculations at a more demanding computational level is presented and explored. The PICVib has an excellent performance at only a small fraction of the computational demand required for a complete analytical calculation. The errors are smaller than ca. 0.5% when DFT functionals are combined with high level ab initio methods. The approach is general because it can use any quantum chemical program and electronic structure method. It is very robust because it was validated for a wide range of frequency values (ca. 20–4800 cm^–1) and systems: XH₃ (D_3h) with X = B, Al, Ga, N, P, As, O, S, and Se, YH₄ (D_4h) with Y = C, Si, and Ge, conformers of RDX, S_N2 and E2 reactions, [W(dppe)₂(NNC₅H₁₀)] complex, carbon nanotubes, and hydrogen‐bonded complexes including guanine‐cytosine pair. © 2012 Wiley Periodicals, Inc.     

Harnessing the Flexibility of Peptidic Scaffolds to Control their Copper(II)‐Coordination Properties: A Potentiometric and Spectroscopic Study

Designing small peptides that are capable of binding Cu²⁺ ions mainly through the side‐chain functionalities is a hard task because the amide nitrogen atoms strongly compete for Cu²⁺ ion coordination. However, the design of such peptides is important for obtaining biomimetic small systems of metalloenyzmes as well as for the development of artificial systems. With this in mind, a cyclic decapeptide, C‐Asp, which contained three His residues and one Asp residue, and its linear derivative, O‐Asp, were synthesized. The C‐Asp peptide has two Pro? Gly β‐turn‐inducer units and, as a result of cyclization, and as shown by CD spectroscopy, its backbone is constrained into a more defined conformation than O‐Asp, which is linear and contains a single Pro? Gly unit. A detailed potentiometric, mass spectrometric, and spectroscopic study (UV/Vis, CD, and EPR spectroscopy) showed that at a 1:1 Cu²⁺/peptide ratio, both peptides formed a major [CuHL]²⁺ species in the pH range 5.0–7.5 (C‐Asp) and 5.5–7.0 (O‐Asp). The corrected stability constants of the protonated species (log K*_CuH(O?Asp)=9.28 and log K*_CuH(C?Asp)=10.79) indicate that the cyclic peptide binds Cu²⁺ ions with higher affinity. In addition, the calculated value of K_eff shows that this higher affinity for Cu²⁺ ions prevails at all pH values, not only for a 1:1 ratio but even for a 2:1 ratio. The spectroscopic data of both [CuHL]²⁺ species are consistent with the exclusive coordination of Cu²⁺ ions by the side‐chain functionalities of the three His residues and the Asp residue in a square‐planar or square‐pyramidal geometry. Nonetheless, although these data show that, upon metal coordination, both peptides adopt a similar fold, the larger conformational constraints that are present in the cyclic scaffold results in different behaviour for both [CuHL]²⁺ species. CD and NMR analysis revealed the formation of a more rigid structure and a slower Cu²⁺‐exchange rate for [CuH(C‐Asp)]²⁺ compared to [CuH(O‐Asp]²⁺. This detailed comparative study shows that cyclization has a remarkable effect on the Cu²⁺‐coordination properties of the C‐Asp peptide, which binds Cu²⁺ ions with higher affinity at all pH values, stabilizes the [CuHL]²⁺ species in a wider pH range, and has a slower Cu²⁺‐exchange rate compared to O‐Asp.     

Systematic Investigation of Silver–Carbon Bonding in Coordination Frameworks with Aryl Ligands That Contain Ethynyl and Ethenyl Substituents

Single‐crystal X‐ray diffraction of a series of ten crystalline silver(I)–trifluoroacetate complexes that contained designed ligands, each of which was composed of an aromatic system that was functionalized with terminal and internal ethynyl groups and a vinyl substituent, provided detailed information on the influence of ligand disposition and orientation, coordination preferences, and the co‐existence of different types of silver(I)–carbon bonding interactions (silver–ethynide, silver–ethynyl, silver–ethenyl, and silver–aromatic) on the construction of coordination networks that were consolidated by argentophilic and weak inter/intramolecular interactions. The complex Ag L10? 6 AgCF₃CO₂ ? H₂O ? MeOH ( HL10 =1‐{[4‐(prop‐2‐ynyloxy)‐3‐vinylphenyl]ethynyl}naphthalene) is the first reported example that exhibits all four kinds of silver(I)–carbon bonding interactions in the solid state.     

Thermodynamic and Structural Trends in Hexavalent Actinyl Cations: Complexation of Dipicolinic Acid with NpO22+ and PuO22+ in Comparison with UO22+

The complexation of NpO₂²⁺ and PuO₂²⁺ with dipicolinic acid (DPA) has been investigated in 0.1 M NaClO₄ by spectrophotometry, microcalorimetry, and single crystal diffractometry. Formation of 1:1 and 1:2 (metal/ligand molar ratio) complexes of DPA with NpO₂²⁺ and PuO₂²⁺ were identified and the thermodynamic parameters were determined and compared with those of UO₂²⁺. All three hexavalent actinyl cations form strong 1:1 DPA complexes with slightly decreasing but comparable stability constants from UO₂²⁺ to PuO₂²⁺, whereas the stability constants of the 1:2 complexes (log β₂) decrease substantially along the series (16.3 for UO₂L₂^2?, 15.17 for NpO₂L₂^2?, and 14.17 for PuO₂L₂^2? at 25 °C). The enthalpies of complexation for the 1:2 complexes become less exothermic from UO₂L₂^2? (?28.9 kJ mol^?1), through NpO₂L₂^2? (?27.2 kJ mol^?1), and to PuO₂L₂^2? (?22.7 kJ mol^?1). The trends in the thermodynamic parameters are discussed in terms of the effective charge of the cations and the steric constraints in the structures of the complexes. In addition, the features of the absorption spectra, including the wavelength and intensity of the absorption bands, are related to the perturbation of the ligand field and the symmetry of the actinyl complexes.     

Parametric inference for multiple repairable systems under dependent competing risks

The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd.