超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。     

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by L?wdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.     

Solid-state optical properties of a chiral supramolecular fluorophore consisting of chiral (1R,2R)-1,2-diphenylethylenediamine and fluorescent carboxylic acid derivatives

By using (1R,2R)-1,2-diphenylethylenediamine as a chiral molecule and 2-anthracenecarboxylic acid as a fluorescent molecule, we created a chiral supramolecular organic fluorophore having circularly polarized luminescence properties in the solid-state.     

PREPARATION AND CHARACTERIZATION OF SHISH-KEBAB TYPE LIQUID CRYSTALLINE POLY（p-PHENYLENEVINYLENE）

Novel shish-kebab type liquid crystalline poly（p-phenylenevinylene） derivatives were synthesized by Stille coupling reaction from 2,5-bis[（4-n-alkoxyl）benzoyloxy]1,4-dibromobenzene （monomer l） and 1,2-bis（tributylstannyl） ethylene （monomer 2）. The polymers with alkoxy groups are soluble in common organic solvents and exhibit blue fluorescence. Both the cast film and the annealed film have large red-shifts in fluorescence spectra and show yellow fluorescence. The polymers with CN and NO2 groups show poor solubility and green fluorescence. All the polymers possess liquid crystalline smectic phases. The melting point （Tm） of the polymers decreases when the length of the alkoxy tails of the mesogenic units increases. The polymers are easily aligned under a magnetic field of 10 Tesla. It is found that the conjugated backbone and LC side chain are aligned perpendicular and parallel to the magnetic field, respectively. The polymers show optical dichroism in fluorescence spectra, suggesting that they are available for advance materials with linear optical polarization.     

Scaling in second-order electron correlation calculations using systematic sequences of even-tempered basis sets

Improved results can often be obtained from second-order Rayleigh-Schrödinger perturbation calculations of electron correlation energies using large basis sets by introducing a scaling factor in the zero-order Hamiltonian. The scaling parameter may be determined from full third-order calculations using a smaller basis set. This scaling procedure can be applied in a systematic fashion by employing a sequence of even-tempered basis sets. Calculations illustrating this approach for the beryllium atom and the neon atom are presented. The scaling procedure is also employed in conjunction with a universal systematic sequence of basis functions. Calculations illustrating this Correlation energy — Mang-body perturbation theory.Work supported in part by S.R.C. Research Grant GR/B/4738.6.S.R.C. Advanced Fellow.     

PEO-LiClO_4-ZSM5 composite polymer electrolyte (IV): Polarized optical microscopy study

All solid-state lithium polymer batteries may be one of the best choices for the future electrochemical power source, characterized by high energy densities, good cyclability, reliability and safety[1,2]. Owing to its potential capability to replace the t…     

Electron-density-dependent fused-sphere surfaces derived from pseudopotential calculations

Fused-sphere surfaces can be used to mimic a molecular boundary associated with a constant value of the electron density. The simplest of such fused-sphere models are constructed by using the atomic radii for the spherical isodensity surfaces of individual atoms. In this work, we discuss the extension of this model to molecules containing atoms beyond the second row. In these many- electron systems, the computation of electron densities is usually simplified by adopting a pseudopotential (or effective-core potential) approach. Here, we discuss the performance of large- and small-core pseudo-potential calculations as a tool to derive atomic radii. Our results provide an optimum set of variable radii that can be used to build fused-sphere surfaces. This continuum of surfaces provides a simple approximation to the low-electron-density regions around molecules with heavy atoms.     

Accurate Gaussian basis sets for the H2O molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H₂O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H₂O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.