On the application of the geometric approximation to the calculation of ring-current properties

Burrows' formula giving an upper bound for the error in the geometric approximation is applied to the calculation of the ring-current contribution to the diamagnetic anisotropies of conjugated molecules. It is also emphasized that this approximation is easily applied in practice.     

A purely geometric derivation of the scaled particle theory formula for the work of cavity creation in a liquid

A very simple statistical geometric approach is devised that allows the derivation of a formula for the work to create a spherical cavity in a liquid consisting of spherical molecules in the small cavity size limit. This formula exactly corresponds to the general expression for the work of cavity creation provided by scaled particle theory. The origin of the success of the present statistical geometric approach needs further insight.     

Geometric approximation to nuclear spin–spin coupling constants in the water molecule

The geometric aproximation is used within the framework of triple perturbation theory to evaluate the contributions to nuclear spin–spin coupling constants in the water molecule provided by the Fermi contact, the spin–orbit, and the spin–dipolar interactions. The results, obtained with SCF wave functions expanded over Gaussian basis sets of increasing quality, are compared with corresponding coupled Hartree–Fock estimates. The limits of the geometric approximation to coupling constants are discussed.     

Generalization of the bandshape expansion formula for the circular dichroism of chromophore aggregates

A generalized expression of the bandshape expansion formula for the circular dichroism of chromophore aggregates is derived using an extended Green's function method. Basic properties of the generalized bandshape expansion formula are studied in comparison with the perturbation expansion equation given by the usual decorrelation approximation.     

Cyclic-N3. II. Significant geometric phase effects in the vibrational spectra

An accurate theoretical prediction of the vibrational spectra for a pure nitrogen ring (cyclic-N(3)) molecule is obtained up to the energy of the (2)A(2)/(2)B(1) conical intersection. A coupled-channel approach using the hyperspherical coordinates and the recently published ab initio potential energy surface [D. Babikov, P. Zhang, and K. Morokuma, J. Chem. Phys. 121, 6743 (2004)] is employed. Two independent sets of calculations are reported: In the first set, the standard Born-Oppenheimer approximation is used and the geometric phase effects are totally neglected. In the second set, the generalized Born-Oppenhimer approximation is used and the geometric phase effects due to the D(3h) conical intersection are accurately treated. All vibrational states are analyzed and assigned in terms of the normal vibration mode quantum numbers. The magnitude of the geometric phase effect is determined for each state. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-N(3): it is approximately 100 cm(-1) for the low-lying vibrational states and exceeds 600 cm(-1) for several upper states. On average, this is almost two orders of magnitude larger than in the previously reported studies. This unique example suggests a favorable path to experimental validation.     

Toward making the mean spherical approximation of primitive model electrolytes analytic: an analytic approximation of the MSA screening parameter

The mean spherical approximation (MSA) for the primitive model of electrolytes provides reasonable estimates of thermodynamic quantities such as the excess chemical potential and screening length. It is especially widely used because of its explicit formulas so that numerically solving equations is minimized. As originally formulated, the MSA screening parameter Γ (akin to the reciprocal of the Debye screening length) does not have an explicit analytic formula; an equation for Γ must be solved numerically. Here, an analytic approximation for Γ is presented whose relative error is generally ?10(-5). If more accuracy is desired, one step of an iterative procedure (which also produces an explicit formula for Γ) is shown to give relative errors within machine precision in many cases. Even when ion diameter ratios are ～10 and ion valences are ～10, the relative error for the analytic approximation is still ?10(-3) and for the single iterative substitution it is ?10(-9).     

中药色谱指纹图谱相似度计算中保留时间校正方法的研究

从保留时间校正方法对线性推移、非线性推移和时间延迟的校正效果方面探讨了保留时间校正方法的适用范围。认为一点法校正仅能校正线性推移;两点法可以校正时间延迟和线性推移,并能部分校正非线性推移。多点法使用分段线性逼近的方法对非线性推移有良好的校正效果。     

Hysteresis effects in the plasma-electrode boundary sheath for frequencies of the order of the ion plasma frequency

The well-known boundary sheath theory applicable to low frequencies is extended for frequencies of the order of the ion plasma frequency. Phase shifts in the linear and nonlinear oscillations exist at different points of the sheath. A hysteresis effect is observed for the current-voltage characteristics and for the dependence of the sheath capacity on the voltage. An analytical approximation of the hysteresis curve is given. A comparison with experiments confirms the applicability of the theory. A simple analytical approximation formula for the sheath thickness as a function of the applied voltage is given.     

On the method of quasi-steady-state approximation

Sufficient conditions for the validity of the quasi-steady-state approximation widely used in chemical kinetics are considered by means of the qualitative geometric theory of differential equations with small parameters.     

Electric dipole polarizability of the hydrogen molecule by many-body perturbation theory

Many-body perturbation theory is used to calculate the static electric dipole polarizability of the hydrogen molecule with a basis set of gaussian orbitals. Corrections complete through second order in electron correlation are calculated, and partial summation of certain classes of diagrams are extensively explored. The results are discussed in connection with the geometric approximation incorporating higher-order corrections.     

化学反应中的几何相效应

锥形交叉可以通过几何相效应影响核动力学.在过去的一些年里关于锥形交叉的理论有大量的发展和进步,本文综述了分子反应动力学领域针对几何相效应研究的一些理论成果.介绍了分子反应动力学中与几何相效应直接相关的一些最新成果,同时也对这些重要结果进行了解释.我们相信几何相效应将会在非绝热化学中发挥最重要的作用.     

Theoretical consideration of the role of the Franck—Condon factor in chemical reactions

A new cross section formula for stripping type chemical reactions is developed by making use of the Born approximation. The result indicates that Franck—Condon factors play an important role for the above type of chemical reaction.     

Semiquantal analysis of hydrogen bond

The semiquantal time-dependent Hartree (SQTDH) theory is applied to the coupled Morse and modified Lippincott-Schroeder (LS) model potentials of hydrogen bond. The structural correlation between the heavy atoms distance and the proton position, the geometric isotope effect, the energy of hydrogen bond formation, and the proton vibrational frequency shift are examined in a broad range of structural parameters. In particular, the geometric isotope effect is found to depend notably on the choice of the potential model, for which the LS potential gives the isotope shift of the heavy atoms distance in the range of 0.02-0.04 A, in quantitative agreement with the experimental findings from assortment of hydrogen bonding crystals. The fourth-order expansion approximation to the semiquantal extended potential was confirmed to be highly accurate in reproducing the full SQTDH results. The approximation is computationally efficient and flexible enough to be applied to general models of hydrogen bond.     

Magnetic field effects in chemical reactions in viscous liquids: the cidep amplitude

An expression for the chemically induced dynamic electron polarization (CIDEP) in geminate radical pair recombinations is obtained within the recently proposed correct sudden approximation. This expression is valid for both low and high viscosities and reduces the problem to simple matrix operations. In the (ST_o) approximation a simple analytical formula for the CIDEP is deduced which accurately reproduces the results of numerical calculations.     

Linear extrapolation in iterative methods

The application of extrapolation methods in an iterative process of general type is investigated. It is shown that extrapolation methods are obtained by two successive approximations from the formula defining an iterative process. The first approximation gives the general formula for extrapolation methods, while particular examples are obtained from this formula by introducing different approximations for the operator defining the iterative process.Alexander von Humboldt fellow.     

非线性色谱保留时间与进样量关系的实验分析

随着制备色谱的发展,对非线性色谱的研究日益深入,非线性色谱中保留时间与进样量的关系是非线性色谱研究中的重要课题.非线性色谱理论研究从40年代开始,主要工作是数学模型的求解与分析.结合理论的实验研究工作较少,关于非线性色谱中进样量与保留时间关系的研究更是这样.对于柱效为无限的理想情形,Aris 与Amundson 曾从理论上作过详细分析,在理想条件下,色谱方程为     

Closed-form expressions of quantum electron transfer rate based on the stationary-phase approximation

Closed-form rate expressions are derived on the basis of the stationary-phase approximation for the Fermi golden rule expression of the quantum electron-transfer (ET) rate. First, on the basis of approximate solutions of the stationary-phase points near DeltaG = 0, -lambda, and lambda, where DeltaG is the reaction free energy and lambda is the reorganization energy, three closed-form rate expressions are derived, which are respectively valid near each value of DeltaG. Numerical tests for a model Ohmic spectral density with an exponential cutoff demonstrate good performance of the derived expressions in the respective regions of their validity. In particular, the expression near DeltaG = -lambda, which differs from the semiclassical approximation only by a prefactor quadratic in DeltaG, works substantially better than the latter. Then, a unified formula is suggested, which interpolates the three approximate expressions and serves as a good approximation in all three regions. We have also demonstrated that the interpolation formula can serve as a good quantitative means for understanding the temperature dependence of the quantum ET rate.     

粒子隧道几率的一种新形式

基于二阶线型微分方程的多个任意阶转向点，建立了粒子进入或跳出势垒或势井时状态波函数的连结公式，导出了粒子穿过势垒的隧道几率公式，并利用严格的数学方法讨论了粒子进入势井时的量子化条件。该公式可合理地还原到一阶转向点情况，并与早期利用一阶转向点近似所推导出的公式相一致。     

On the extraction of optical sums from experimental generalized oscillator strengths and the experimental determination of the x-ray incoherent scattering factory by electron scattering

The connection between an experimentally measured Bethe surface and certain optical sum rules is discussed. The simplest procedure for constructing optical sums involves summing (integrating) the generalized oscillator strength over energy loss at a fixed scattering angle. This involves an approximation and an error formula is developed to estimate the magnitude of the correction involved. The approximation is shown to be extremely accurate in the limit of high incident energy and large momentum transfer. The sum S(?1,K) which is simply related to the X-ray incoherent scattering factor is found to have a small first order correction in the case of electron scattering from He with 25 keV electrons even at angles as small as 1°.     

Communication: limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.