Simple evaluation of Franck–Condon factors and non‐Condon effects in the Morse potential

The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002     

QSPR Modeling of the Reactivity Parameters of Monomers in Radical Copolymerizations

For a series of monomers, QSPR test analysis is performed by optimizing the correlation weights of the local invariants of molecular graphs representing monomer structures in order to construct models of the reactivity parameters of monomers Q and e. This approach may be used as a tool in reactivity predictions for monomers for which no experimental data on Q and e are available.Original Russian Text Copyright © 2004 by A. A. Toropov, V. O. Kudyshkin, N. L. Voropaeva, I. N. Ruban, and S. Sh. Rashidova__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 994–998, November–December, 2004.     

原子结构参数的改进Xa法计算

六十年代后期,在Hartree－Fock-Slater法的基础上,提出了Xα法［1］．用于原子结构计算的Xα法与HF（Hartree－Fock）法的主要区别在于：用简单的统计平均交换势替代了HF法中计算最为困难的电子交换势,从而在保持较高理论严谨性和计算精确度的同时,大大减少了计算工作量,近年来获得了广泛的应用．我们尝试用经过适当修改的Xα方法,计算原子参数,解决分子结构中的某些问题．用原子参数解决分子问题,历来是化学和物理工作者常用的方法．本工作的意图是引入一个比HF法简单的容易在微机上实现的某种表现原子参数的计算方法,提供…     

Elucidating dominant factors of PO43-, Cd2+ and nitrobenzene removal by biochar: A comparative investigation based on distinguishable biochars

Four distinct biochars were employed to remove three typical pollutants, meanwhile, path analysis, a multi-statistical regression method, was performed to elucidate the dominant factors of biochar adsorption. This work can provide a new insight to prepare a targeted biochar as adsorbents.     

Fraktionierte Kristallisation von Ammonium- und Magnesiumdoppelnitraten der Ceriterden; Bestimmung der Trennfaktoren und Vergleich der Trennwirkung

Summary The Separation Factors for Pr/La, Nd/Pr, and Sm/Nd, characterizing the crystallization of ammonium and magnesium double nitrates under practical conditions, were determined analytically and are discussed. They confirm that La and Pr can be separated better by fractional crystallization of ammonium double nitrates, whereas in the presence of Sm the magnesium double nitrates are preferable.

     

Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Franck-Condon matrix elements for bound-continuum vibrational transitions calculated by numerical integration and basis set expansion techniques

Franck-Condon factor distributions for bound-to-continuum transitions of one-dimensional vibrational states are calculated by a) using numerical integration, b) employing a finite number of square integrable harmonic oscillator functions. The methods are generally applicable to any kind of bound or repulsive potential involved. Results are presented and compared to model potential calculations previously reported by Krüger [1].     

DETERMINATION OF DEGREE OF CRYSTALLINITY OF NYLON 1212 BY WIDE-ANGLE X-RAY DIFFRACTION

Based on the X-ray scattering intensity theory and using the approximate expression for the atomic scattering factor, the correction factors for three crystalline peaks and an amorphous peak of Nylon 1212 were calculated and the formula of degree of crystallinity of Nylon 1212 was derived by a graphic multipeak resolution method. The degree of crystallinity calculated from the WAXD method is compatible with those obtained by density and calorimetry methods.     

CS2+离子 C2Σg+←B2Σu+跃迁的Franck-Condon因子计算以及与光解离谱的比较

将线性三原子分子离子CS2+的对称伸缩振动简化为SC和S之间的简谐振动, 用谐振子的势能曲线和波函数对CS2+分子离子 C2Σg+和 B2Σu+电子态(对称伸缩)振动能级间跃迁的Franck-Condon因子进行了计算, 得到的结果与 C2Σg+←B2Σu+跃迁的光解离谱实验强度进行了比较, 对前人给出的分子数据(转动常数、分子平衡核间距)进行了验证和分析, 讨论了经由 C2Σg+←B2Σu+电子态振动能级间跃迁的光解离机理.