Improved third-order Møller-Plesset perturbation theory

Based on a partitioning of the total correlation energy into contributions from parallel‐ and antiparallel‐spin pairs of electrons, a modified third‐order Møller–Plesset (MP) perturbation theory is developed. The method, termed SCS–MP3 (SCS for spin‐component‐scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third‐order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C₂₀ isomers, transition states) demonstrate that the SCS–MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529–1537, 2003     

Single-crystal 2H NMR of deuterated 1,10-decanedicarboxylic acid included in hydrogenated urea channels

The intergrowth of 1,10-decanedicarboxylic acid and urea give infinite hydrogen-bonded chains of the guest included in the hexagonal urea host. A deuterium high-resolution solid-state NMR study of the selectively deuterated intergrowth compound 1,10-decanedicarboxylic acid/hydrogenated urea at variable temperature in the range 90 < or = T < or = 300 K was performed on a single crystal. The analysis of the second moment as a function of temperature is shown to be compatible with the known phase transition occurring near T(c) = 203 K. Moreover, the spectra indicate that the orientational disorder is strong, and is compared to an axial uniform disorder. For this purpose, the general equation for the second moment of a system with uniform two-dimensional axial orientational disorder is given, and a method to take into account the non-uniform excitation of the pulse sequence is proposed.     

Ternary and tetrahedral symmetry in hybrid fluorides, fluoride carbonates and carbonates

Tren amine cations and carbonate anions adopt a ternary symmetry while tetra amine cations are tetrahedral. The symmetry of these constitutive ions influences strongly the nature of the solids which crystallise from solutions. Large fluorinated aluminate polyanions with tetrahedral symmetry appear in the presence of tren amine, while infinite chains of AlF₆ octahedra are observed with tetra amine and that noncentrosymmetric structures are frequently encountered in rare earth fluoride carbonates.     

Spectroscopic study of solid-state photoreaction in organic crystal: Photopolymerization of dimethyl ester of α,α′-dicyano-p-phenylenediacrylic acid and diethyl ester of p-phenylenediacrylic acid

Raman spectroscopy has been used to study solid-state photopolymerization reactions in dimethyl ester of α,α′-dicyano-p-phenylenediacrylic acid (p-CPAMe) and diethyl ester of p-phenylenediacrylic acid (p-PDAEt). The reactants and products were characterized by infrared and Raman spectroscopy. Excitation and emission spectra suggest that in p-CPAMe exciton–phonon coupling is strong, but in the other monomer it is very weak. Raman phonon spectroscopic study reveal that in both the samples the reaction mechanism is homogeneous in the initial stages. However, in the later stages the reaction becomes heterogeneous in p-PDAEt. In p-CPAMe the lattice becomes disordered with the progress of polymerization and finally becomes amorphous whereas in p-PDAEt the lattice remains highly ordered. © 1992 John Wiley & Sons, Inc.     

A note on “Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part”, by Hei Li-jun,Nonlinear Anal. Real World Appl. 5, 2004

In this short paper I report on a paper published in Nonlinear Analysis: Real World Applications in 2004. There is a major mistake early in that paper which makes most of its claims false. The class of reaction–diffusion systems considered in the paper has been the object of a renewed investigation in the past few years, by myself and others, and recent discoveries provide explicit counter-examples.     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Optimal life strategies in organisms exposed to recurrent critical events

The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion.     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.