Ab initio study of the structure,cooperativity, and vibrational properties in the mixed hydrogen‐bonded trimers of hydrogen isocyanide and water

The five trimers of H₂O···HNC···H₂O, H₂O···H₂O···HNC, HNC···H₂O···H₂O, H₂O···HNC···HNC, and HNC···HNC···H₂O have been studied with quantum chemical calculations. Their structures, harmonic vibrational frequencies and interaction energies have been calculated at the B3LYP and MP2 levels with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets. The cooperative effect on these properties has also been studied quantitatively. For HNC:(H₂O)₂ systems, the cyclic H₂O···H₂O···HNC trimer is most stable with an interaction energy of ?16.01 kcal/mol and a large cooperative energy of ?3.25 kcal/mol at the MP2/aug‐cc‐pVTZ level. For H₂O:(HNC)₂ systems, the interaction energy and cooperative energy in the H₂O···HNC···HNC trimer are larger than those in the HNC···HNC···H₂O trimer. The NH stretch frequency has a blue shift for the terminal HNC molecule in the HNC···H₂O···H₂O and HNC···HNC···H₂O trimers and a red shift in other cases. A many‐body analysis has also been performed to understand the interaction energies in these hydrogen‐bonded clusters. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Dynamics and effective actions of BCS superconductors

We derive the effective dynamical theory for BCS superconductors, based on the effective action formalism. Both the metallic regime and the superconducting regime are studied in the clean and dirty limit. The full electrodynamics of the problem is formulated in a manifestly gauge-invariant and transparent way. Furthermore, we consider the effect of particle-hole asymmetry in the band structure, and discuss its consequences for vortex dynamics and the topological term in the effective action. The effective action is the starting point for treating (quantum-) dynamical problems involving BCS superconductors. Received 23 November 1998     

Self-consistent electronic structure of quantum wells by invariant embedding method

A new approach based on the invariant embedding method for the self-consistent calculation of electronic structure of quantum wells is presented and is applied to both neutral quantum well and parabolic quantum well. Numerical results obtained for these structures agree very well with those of previous theoretical and experiment studies. The present approach is expected to lead to a more efficient and stable scheme for the calculation of electronic band structure of quantum structures. Realistic boundary conditions are naturally taken into account in the present calculation which provides a convenient way for studying boundary effects. Received 21 September     

Geometrical properties of nodal surfaces of many‐electron wave functions

Hypothesis of the exclusion of equipotential surfaces for many‐electron wave functions (MWF) has been enunciated. This hypothesis clarifies the physical meaning of the Pauli exclusion principle and opens the way for future progress of new quantum‐chemical methods for the construction of approximate MWFs differing from the traditional Hartree–Fock approximation. The equipotential surface exclusion principle has been tested on traditional representative “test systems” of quantum mechanics: the helium atom, the lithium atom, and the hydrogen molecule. Judging by the results of these tests, the use of the suggested approach can lead to a considerable increase in the efficiency of high‐accuracy quantum‐chemical calculations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

带非奇扰动项的(2, p)-Laplace方程无穷多解的存在性

本文研究带非奇扰动项的(2,p)-Laplace方程{-△u-△pu=a(x)|u|q-2u+f(x,u),u=0, x∈Ω,x∈(e)Ω,其中Ω (∈) RN是有界光滑区域,1＜q＜2＜p＜N,a∈C((Ω))可变号,f关于u不必是奇函数.利用变分方法,本文获得该方程无穷多解的存在性.     

Infinitely many weak solutions for p(x)-Laplacian-like problems with Neumann condition

The paper studies the existence of infinitely many solutions for a Neumann problem involving the p(x)-Laplacian-like depending on two parameters. Our approach is based on variational methods.     

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

We study radial solutions of the semilinear elliptic equation

$\mathrm{\Delta }u+f(u)=0$

under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., $\mathrm{\Delta }u+u^p=0$ and $\mathrm{\Delta }u+e^u=0$.