Some thoughts about the stability and reliability of commonly used exchange–correlation functionals – coverage of dynamic and nondynamic correlation effects

 The self-interaction error (SIE) of commonly used density functional theory (DFT) exchange functionals mimics long-range (nondynamic) pair correlation effects in an unspecified way. Slater exchange suffers from a larger SIE and, therefore, covers more nondynamic correlation effects than Becke exchange, which is the reason why exchange–correlation (XC) functionals based on Slater exchange lead to stabler restricted DFT solutions than those based on Becke exchange. However, the stability of an XC functional does not guarantee higher accuracy. On the contrary, if system-specific nondynamic correlation effects have to be introduced via the form of the wave function, these will be suppressed by nondynamic correlation effects already covered by the exchange functional. Hybrid functionals suffer less from the SIE and, therefore, cover a smaller number of nondynamic electron correlation effects. Accordingly, they are better suited when nondynamic electron correlation has to be introduced by the form of the wave function. It is shown that, for example, broken-symmetry unrestricted DFT calculations are more accurate when carried out with B3LYP than BLYP contrary to claims made in the literature. Received: 8 November 2001 / Accepted: 30 January 2002 / Published online: 8 April 2002     

DYNAMIC MONTE CARLO STUDY ON THE CORRELATION BETWEEN SHAPE AND SIZE OF LINEAR POLYMER CHAINS

The correlation between shape and size of linear chains on the simple cubic lattice is investigated using a dynamicMonte Carlo technique. A positive correlation between the asphericity parameter A and the square of the end-to-end distanceR~2, as well as that between A and the square of the radius of gyration S~2, is found for both RW and SAW chains, indicatingthat a chain conformation of small size is usually more spherical than one of large size. The result can explain why the shapeof the SAW chain deviate much more from a sphere than that of the RW chain, and can also explain the similar dependenceof size and shape on chain stiffness and on the distance of the first bead of a chain from an infinitely large flat surface.     

Binary interaction parameter kij for calculating the second cross-virial coefficients of mixtures

The binary interaction parameters, k_ij, of 119 mixtures were determined by fitting the second cross-virial coefficients of mixtures with correlations for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120; L. Meng, Y.Y. Duan, Fluid Phase Equilib., 258 (2007) 29–33] and classical mixing rules. The mixtures included nonpolar/polar (associated), polar/polar, quantum/nonpolar (quantum) binaries. Very simple correlations for k_ij of H₂O/n-alkane, CO/nonpolar and quantum/nonpolar (quantum) binaries were successfully developed. The results show that the present correlations can accurately predict the second cross-virial coefficients.     

Correlation lengths for oriented percolation

Oriented percolation has two correlation lengths, one in the space and one in the time direction. In this paper we define these quantities for the two-dimensional model in terms of the exponential decay of suitably chosen quantities, and study the relationship between the various definitions. The definitions are used in a companion paper to prove inequalities between critical exponents.     

土壤－水稻系统中砷污染表征与相关性校验

研究了青紫泥田、黄筋泥田和红砂田中水溶性砷、酸溶性砷和总砷与水稻生物产量和砷积累的关系，探讨了它们之间的相关性，为表征和校验土壤水稻系统中砷污染提供依据。     

强偶合体系异核二维相关NMR谱解析

本文对异核二维相关NMR谱中强偶合的影响进行了分析,给出量子力学的定量描述。用所建立的计算机NMR谱解析系统模拟了AB(X)自旋体系以及蔗糖的异核二维相关谱。     

Hartree-fock calculations for excited rydberg states

A method is introduced which allows to compute self-consistent restricted Hartree-Fock wave functions for excited Rydberg configurations. The concepts of reorganization and electron correlation of Rydberg states are discussed. As an illustration Hartree-Fock calculations for the (ls)(nl) Rydberg series of He are presented.     

Bond centred functions in relativistic and non-relativistic calculations for diatomics

In this paper, we discuss the performance of molecular basis sets consisting of atomic centred (AC) functions augmented with bond centred (BC) functions in relativistic and non-relativistic calculations carried out at the Hartree–Fock and several correlated levels of approximation. While usually non-correlated calculations employing BC functions can be performed at a lower computational cost as compared with those making use of energy optimized AC basis sets, the correlated calculations are always more accurate and less expensive with the latter. It is demonstrated that both correlated or non-correlated calculations always benefit from the addition of a few BC functions with a moderate increase of computational effort. The performance of basis sets containing even-tempered BC functions is also studied and their usage is advocated in case of relativistic calculations.     

A method for molecular correlation energy calculations. Application to the determination of dissociation energies of diatomic and polyatomic molecules

A simple and economical method for molecular correlation energy calculations is developed. In this method, the internal part of the correlation energy is calculated by means of a CI in a minimal basis set and the non-internal part (semi-internal and all-external) is evaluated using an original atoms-in-molecule method. It is successfully applied to the determination of dissociation energies of some diatomic (H₂, NH, C₂, CN, N₂, CO, NO, O₂, F₂) and polyatomic (H₂O, N₂O, CO₂, N₃H, CH₂N₂, CH₂CO, C₂N₂) molecules. The results are compared to those obtained using very elaborate variational methods.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Global weathering of aromatic engineering thermoplastics

The rates of gloss loss and color shift for 24 aromatic engineering thermoplastics at nine exposure sites world-wide have been compared relative to a commercial Miami exposure site. The scatter among individual samples was large, but on average, light dose alone was enough to account for almost all of the rate differences among the various sites for these materials. Temperature, humidity, rainfall, and acid rain seemed to play minor roles for most samples. Samples containing no particulate pigment had more erratic gloss loss and showed some dependency on the amount of rainfall. The overall “cleanliness” of the samples seemed to be an important factor in gloss retention, and washing protocols during the exposure period and before readings were important variables in cases of slow erosion and/or no particulate pigment. Microbial growth (fungus) was observed on Miami samples after 12–18 months of exposure, but none was seen at any other site.

Relative to Miami defined as 1.0, the average rates of color shift and gloss loss were approximately 0.67 in the northern U.S., 0.8 in the central U.S., and 1.15 in the U.S. desert southwest. Southern Europe was nearly as harsh as Miami, while Northern Europe was comparable to the northern U.S. Northern Europe was found to be somewhat harsher than expected while the northern U.S. was slightly less harsh than expected based on light dose or temperature-weighted light dose. These conclusions apply only to aromatic engineering plastics and should not be assumed to hold for other kinds of materials, such as polyolefins or coatings, without experimental verification.